TSTP Solution File: SWW669_2 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWW669_2 : TPTP v8.1.0. Released v6.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 29 20:59:36 EDT 2022
% Result : Theorem 0.78s 0.74s
% Output : Proof 1.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SWW669_2 : TPTP v8.1.0. Released v6.1.0.
% 0.03/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.35 % Computer : n017.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sun Sep 4 20:10:25 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.14/0.36 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.36 Usage: tptp [options] [-file:]file
% 0.14/0.36 -h, -? prints this message.
% 0.14/0.36 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.36 -m, -model generate model.
% 0.14/0.36 -p, -proof generate proof.
% 0.14/0.36 -c, -core generate unsat core of named formulas.
% 0.14/0.36 -st, -statistics display statistics.
% 0.14/0.36 -t:timeout set timeout (in second).
% 0.14/0.36 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.36 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.36 -<param>:<value> configuration parameter and value.
% 0.14/0.36 -o:<output-file> file to place output in.
% 0.78/0.74 % SZS status Theorem
% 0.78/0.74 % SZS output start Proof
% 0.78/0.74 tff(tb2t_type, type, (
% 0.78/0.74 tb2t: uni > $int)).
% 0.78/0.74 tff(get_type, type, (
% 0.78/0.74 get: ( ty * ty * uni * uni ) > uni)).
% 0.78/0.74 tff(t2tb_type, type, (
% 0.78/0.74 t2tb: $int > uni)).
% 0.78/0.74 tff(tptp_fun_Pos_4_type, type, (
% 0.78/0.74 tptp_fun_Pos_4: $int)).
% 0.78/0.74 tff(t2tb2_type, type, (
% 0.78/0.74 t2tb2: map_int_int > uni)).
% 0.78/0.74 tff(tptp_fun_B1_15_type, type, (
% 0.78/0.74 tptp_fun_B1_15: map_int_int)).
% 0.78/0.74 tff(int_type, type, (
% 0.78/0.74 int: ty)).
% 0.78/0.74 tff(tptp_fun_B_16_type, type, (
% 0.78/0.74 tptp_fun_B_16: $int)).
% 0.78/0.74 tff(tptp_fun_N_5_type, type, (
% 0.78/0.74 tptp_fun_N_5: $int)).
% 0.78/0.74 tff(eq_board1_type, type, (
% 0.78/0.74 eq_board1: ( array_int * array_int * $int ) > $o)).
% 0.78/0.74 tff(tb2t1_type, type, (
% 0.78/0.74 tb2t1: uni > array_int)).
% 0.78/0.74 tff(mk_array1_type, type, (
% 0.78/0.74 mk_array1: ( ty * $int * uni ) > uni)).
% 0.78/0.74 tff(tptp_fun_Board4_14_type, type, (
% 0.78/0.74 tptp_fun_Board4_14: map_int_int)).
% 0.78/0.74 tff(tptp_fun_Board_7_type, type, (
% 0.78/0.74 tptp_fun_Board_7: $int)).
% 0.78/0.74 tff(tptp_fun_I_11_type, type, (
% 0.78/0.74 tptp_fun_I_11: $int)).
% 0.78/0.74 tff(is_board1_type, type, (
% 0.78/0.74 is_board1: ( array_int * $int ) > $o)).
% 0.78/0.74 tff(solution1_type, type, (
% 0.78/0.74 solution1: ( array_int * $int ) > $o)).
% 0.78/0.74 tff(tptp_fun_Board1_6_type, type, (
% 0.78/0.74 tptp_fun_Board1_6: map_int_int)).
% 0.78/0.74 tff(tptp_fun_Board3_12_type, type, (
% 0.78/0.74 tptp_fun_Board3_12: map_int_int)).
% 0.78/0.74 tff(true1_type, type, (
% 0.78/0.74 true1: bool1)).
% 0.78/0.74 tff(tptp_fun_Result_13_type, type, (
% 0.78/0.74 tptp_fun_Result_13: bool1)).
% 0.78/0.74 tff(tptp_fun_B1_18_type, type, (
% 0.78/0.74 tptp_fun_B1_18: map_int_int)).
% 0.78/0.74 tff(tptp_fun_B_19_type, type, (
% 0.78/0.74 tptp_fun_B_19: $int)).
% 0.78/0.74 tff(is_consistent1_type, type, (
% 0.78/0.74 is_consistent1: ( array_int * $int ) > $o)).
% 0.78/0.74 tff(tptp_fun_B_21_type, type, (
% 0.78/0.74 tptp_fun_B_21: $int)).
% 0.78/0.74 tff(tptp_fun_B1_20_type, type, (
% 0.78/0.74 tptp_fun_B1_20: map_int_int)).
% 0.78/0.74 tff(tptp_fun_Board2_10_type, type, (
% 0.78/0.74 tptp_fun_Board2_10: map_int_int)).
% 0.78/0.74 tff(tptp_fun_Board4_17_type, type, (
% 0.78/0.74 tptp_fun_Board4_17: map_int_int)).
% 0.78/0.74 tff(tb2t2_type, type, (
% 0.78/0.74 tb2t2: uni > map_int_int)).
% 0.78/0.74 tff(set_type, type, (
% 0.78/0.74 set: ( ty * ty * uni * uni * uni ) > uni)).
% 0.78/0.74 tff(tptp_fun_B_9_type, type, (
% 0.78/0.74 tptp_fun_B_9: $int)).
% 0.78/0.74 tff(tptp_fun_B1_8_type, type, (
% 0.78/0.74 tptp_fun_B1_8: map_int_int)).
% 0.78/0.74 tff(tptp_fun_Q_2_type, type, (
% 0.78/0.74 tptp_fun_Q_2: ( $int * array_int ) > $int)).
% 0.78/0.74 tff(get2_type, type, (
% 0.78/0.74 get2: ( ty * uni * $int ) > uni)).
% 0.78/0.74 tff(t2tb1_type, type, (
% 0.78/0.74 t2tb1: array_int > uni)).
% 0.78/0.74 tff(length1_type, type, (
% 0.78/0.74 length1: ( ty * uni ) > $int)).
% 0.78/0.74 tff(tptp_fun_Q_3_type, type, (
% 0.78/0.74 tptp_fun_Q_3: ( $int * array_int ) > $int)).
% 0.78/0.74 tff(elts_type, type, (
% 0.78/0.74 elts: ( ty * uni ) > uni)).
% 0.78/0.74 tff(sort1_type, type, (
% 0.78/0.74 sort1: ( ty * uni ) > $o)).
% 0.78/0.74 tff(map_type, type, (
% 0.78/0.74 map: ( ty * ty ) > ty)).
% 0.78/0.74 tff(tptp_fun_Q_0_type, type, (
% 0.78/0.74 tptp_fun_Q_0: ( $int * array_int * array_int ) > $int)).
% 0.78/0.74 tff(1,plain,
% 0.78/0.74 ((($greatereq(Board!7, 0) & ($sum(N!5, $product(-1, Board!7)) = 0) & $greatereq(Pos!4, 0) & $lesseq($sum(Pos!4, $product(-1, N!5)), 0) & solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) & ((~((~($sum(Pos!4, $product(-1, N!5)) = 0)) | solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), N!5))) | ((~($sum(Pos!4, $product(-1, N!5)) = 0)) & (((~$greatereq(N!5, 1)) & ((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!9, t2tb2(B1!8))), N!5)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, B!9, t2tb2(B1!8))), Pos!4)) | (~is_board1(tb2t1(mk_array1(int, B!9, t2tb2(B1!8))), N!5)) | (~($sum(N!5, $product(-1, B!9)) = 0)))))) | ($greatereq(N!5, 1) & ((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | ($greatereq(I!11, 0) & $greatereq($sum(N!5, $product(-1, I!11)), 1) & eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4) & ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos!4)) | (~($greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), 0) & (~$greatereq($sum(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), $product(-1, I!11)), 0))))) & ((~$greatereq(Board!7, 0)) | (~$greatereq(Pos!4, 0)) | $greatereq($sum(Pos!4, $product(-1, Board!7)), 0) | ($greatereq(Board!7, 0) & (Board3!12 = tb2t2(set(int, int, t2tb2(Board2!10), t2tb(Pos!4), t2tb(I!11)))) & ((~$greatereq(Pos!4, 0)) | $greatereq($sum(Pos!4, $product(-1, Board!7)), 0) | (((Result!13 = true1) <=> is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) & (((Result!13 = true1) & ((~$lesseq($sum(Pos!4, $product(-1, N!5)), 0)) | (~($sum(N!5, $product(-1, Board!7)) = 0)) | (~$greatereq(Pos!4, -1)) | (~$lesseq($sum(Pos!4, $product(-1, N!5)), -1)) | (~solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~((~($greatereq(Board!7, 0) & solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!17))), N!5))) | solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!17))), N!5))) | ($greatereq(Board!7, 0) & eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4)) & ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B, t2tb2(B1))), $sum(1, Pos!4)))) & ((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~($greatereq(tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))), 0) & (~$lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))))), -1)))) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), Pos!4)) | (~($sum(N!5, $product(-1, B!16)) = 0)))))))) | ((~(Result!13 = true1)) & ((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~($greatereq(tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))), 0) & (~$lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))))), -1)))) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Pos!4)) | (~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~($sum(N!5, $product(-1, B!19)) = 0)))))))))))) | (eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4) & ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~($greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), 0) & (~$lesseq($sum(N!5, $product(-1, tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))))), 0)))) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos!4))) & ((~$greatereq(Board!7, 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), Pos!4)) | (~($sum(N!5, $product(-1, B!21)) = 0)))))))))))) <=> ($greatereq(Board!7, 0) & ($sum(N!5, $product(-1, Board!7)) = 0) & $greatereq(Pos!4, 0) & $lesseq($sum(Pos!4, $product(-1, N!5)), 0) & solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4) & ((~((~($sum(Pos!4, $product(-1, N!5)) = 0)) | solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), N!5))) | ((~($sum(Pos!4, $product(-1, N!5)) = 0)) & (((~$greatereq(N!5, 1)) & ((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!9, t2tb2(B1!8))), N!5)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, B!9, t2tb2(B1!8))), Pos!4)) | (~is_board1(tb2t1(mk_array1(int, B!9, t2tb2(B1!8))), N!5)) | (~($sum(N!5, $product(-1, B!9)) = 0)))))) | ($greatereq(N!5, 1) & ((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | ($greatereq(I!11, 0) & $greatereq($sum(N!5, $product(-1, I!11)), 1) & eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4) & ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos!4)) | (~($greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), 0) & (~$greatereq($sum(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), $product(-1, I!11)), 0))))) & ((~$greatereq(Board!7, 0)) | (~$greatereq(Pos!4, 0)) | $greatereq($sum(Pos!4, $product(-1, Board!7)), 0) | ($greatereq(Board!7, 0) & (Board3!12 = tb2t2(set(int, int, t2tb2(Board2!10), t2tb(Pos!4), t2tb(I!11)))) & ((~$greatereq(Pos!4, 0)) | $greatereq($sum(Pos!4, $product(-1, Board!7)), 0) | (((Result!13 = true1) <=> is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) & (((Result!13 = true1) & ((~$lesseq($sum(Pos!4, $product(-1, N!5)), 0)) | (~($sum(N!5, $product(-1, Board!7)) = 0)) | (~$greatereq(Pos!4, -1)) | (~$lesseq($sum(Pos!4, $product(-1, N!5)), -1)) | (~solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~((~($greatereq(Board!7, 0) & solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!17))), N!5))) | solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!17))), N!5))) | ($greatereq(Board!7, 0) & eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4)) & ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B, t2tb2(B1))), $sum(1, Pos!4)))) & ((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~($greatereq(tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))), 0) & (~$lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))))), -1)))) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), Pos!4)) | (~($sum(N!5, $product(-1, B!16)) = 0)))))))) | ((~(Result!13 = true1)) & ((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~($greatereq(tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))), 0) & (~$lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))))), -1)))) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Pos!4)) | (~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~($sum(N!5, $product(-1, B!19)) = 0)))))))))))) | (eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4) & ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~($greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), 0) & (~$lesseq($sum(N!5, $product(-1, tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))))), 0)))) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos!4))) & ((~$greatereq(Board!7, 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), Pos!4)) | (~($sum(N!5, $product(-1, B!21)) = 0))))))))))))),
% 0.78/0.75 inference(rewrite,[status(thm)],[])).
% 0.78/0.75 tff(2,plain,
% 0.78/0.75 (((~((~($sum(N!5, $product(-1, Pos!4)) = 0)) | solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), N!5))) | ((~($sum(N!5, $product(-1, Pos!4)) = 0)) & (((~$greatereq(N!5, 1)) & ((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!9, t2tb2(B1!8))), N!5)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, B!9, t2tb2(B1!8))), Pos!4)) | (~is_board1(tb2t1(mk_array1(int, B!9, t2tb2(B1!8))), N!5)) | (~($sum(B!9, $product(-1, N!5)) = 0)))))) | ((~(~$greatereq(N!5, 1))) & ((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (((~(~($greatereq(I!11, 0) & $lesseq($sum(I!11, $product(-1, N!5)), -1)))) & (eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4) & ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), 0) & (~$lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))))), 0)))) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos!4)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)))) & ((~$greatereq(Board!7, 0)) | (~$greatereq(Pos!4, 0)) | (~(~$greatereq($sum(Pos!4, $product(-1, Board!7)), 0))) | ((~(~($greatereq(Board!7, 0) & (Board3!12 = tb2t2(set(int, int, t2tb2(Board2!10), t2tb(Pos!4), t2tb(I!11))))))) & ((~$greatereq(Pos!4, 0)) | (~(~$greatereq($sum(Pos!4, $product(-1, Board!7)), 0))) | ((~((~(Result!13 = true1)) <=> is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4))) & (((~(~(Result!13 = true1))) & ((~$lesseq($sum(Pos!4, $product(-1, N!5)), 0)) | (~($sum(N!5, $product(-1, Board!7)) = 0)) | (~$greatereq(Pos!4, -1)) | (~$lesseq($sum(Pos!4, $product(-1, N!5)), -1)) | (~solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (($greatereq(Board!7, 0) & eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4)) & ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B, t2tb2(B1))), $sum(1, Pos!4))) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)))) & ((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~($greatereq(tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))), 0) & (~$lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))))), -1)))) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), Pos!4)) | (~($sum(B!16, $product(-1, N!5)) = 0)))))) | (~((~($greatereq(Board!7, 0) & solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!17))), N!5))) | solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!17))), N!5))))) | ((~(Result!13 = true1)) & ((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~($greatereq(tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))), 0) & (~$lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))))), -1)))) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Pos!4)) | (~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~($sum(B!19, $product(-1, N!5)) = 0)))))))))))) | ((eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4) & ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), 0) & (~$lesseq($sum(N!5, $product(-1, tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))))), 0)))) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos!4)) | (~($sum(B, $product(-1, N!5)) = 0)))) & ((~$greatereq(Board!7, 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), Pos!4)) | (~($sum(B!21, $product(-1, N!5)) = 0)))))))))))) <=> ((~((~($sum(Pos!4, $product(-1, N!5)) = 0)) | solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), N!5))) | ((~($sum(Pos!4, $product(-1, N!5)) = 0)) & (((~$greatereq(N!5, 1)) & ((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!9, t2tb2(B1!8))), N!5)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, B!9, t2tb2(B1!8))), Pos!4)) | (~is_board1(tb2t1(mk_array1(int, B!9, t2tb2(B1!8))), N!5)) | (~($sum(N!5, $product(-1, B!9)) = 0)))))) | ($greatereq(N!5, 1) & ((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | ($greatereq(I!11, 0) & $greatereq($sum(N!5, $product(-1, I!11)), 1) & eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4) & ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos!4)) | (~($greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), 0) & (~$greatereq($sum(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), $product(-1, I!11)), 0))))) & ((~$greatereq(Board!7, 0)) | (~$greatereq(Pos!4, 0)) | $greatereq($sum(Pos!4, $product(-1, Board!7)), 0) | ($greatereq(Board!7, 0) & (Board3!12 = tb2t2(set(int, int, t2tb2(Board2!10), t2tb(Pos!4), t2tb(I!11)))) & ((~$greatereq(Pos!4, 0)) | $greatereq($sum(Pos!4, $product(-1, Board!7)), 0) | (((Result!13 = true1) <=> is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) & (((Result!13 = true1) & ((~$lesseq($sum(Pos!4, $product(-1, N!5)), 0)) | (~($sum(N!5, $product(-1, Board!7)) = 0)) | (~$greatereq(Pos!4, -1)) | (~$lesseq($sum(Pos!4, $product(-1, N!5)), -1)) | (~solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~((~($greatereq(Board!7, 0) & solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!17))), N!5))) | solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!17))), N!5))) | ($greatereq(Board!7, 0) & eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4)) & ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B, t2tb2(B1))), $sum(1, Pos!4)))) & ((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~($greatereq(tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))), 0) & (~$lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))))), -1)))) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), Pos!4)) | (~($sum(N!5, $product(-1, B!16)) = 0)))))))) | ((~(Result!13 = true1)) & ((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~($greatereq(tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))), 0) & (~$lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))))), -1)))) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Pos!4)) | (~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~($sum(N!5, $product(-1, B!19)) = 0)))))))))))) | (eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4) & ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~($greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), 0) & (~$lesseq($sum(N!5, $product(-1, tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))))), 0)))) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos!4))) & ((~$greatereq(Board!7, 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), Pos!4)) | (~($sum(N!5, $product(-1, B!21)) = 0)))))))))))),
% 0.78/0.76 inference(rewrite,[status(thm)],[])).
% 0.78/0.76 tff(3,plain,
% 0.78/0.76 ((~(~($greatereq(Board!7, 0) & ($sum(N!5, $product(-1, Board!7)) = 0) & $greatereq(Pos!4, 0) & $lesseq($sum(Pos!4, $product(-1, N!5)), 0) & solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)))) <=> ($greatereq(Board!7, 0) & ($sum(N!5, $product(-1, Board!7)) = 0) & $greatereq(Pos!4, 0) & $lesseq($sum(Pos!4, $product(-1, N!5)), 0) & solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4))),
% 0.78/0.76 inference(rewrite,[status(thm)],[])).
% 0.78/0.76 tff(4,plain,
% 0.78/0.76 ((~($greatereq(Board!7, 0) & ($sum(N!5, $product(-1, Board!7)) = 0) & $greatereq(Pos!4, 0) & $greatereq($sum(N!5, $product(-1, Pos!4)), 0) & solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4))) <=> (~($greatereq(Board!7, 0) & ($sum(N!5, $product(-1, Board!7)) = 0) & $greatereq(Pos!4, 0) & $lesseq($sum(Pos!4, $product(-1, N!5)), 0) & solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)))),
% 0.78/0.76 inference(rewrite,[status(thm)],[])).
% 0.78/0.76 tff(5,plain,
% 0.78/0.76 ((~(~($greatereq(Board!7, 0) & ($sum(N!5, $product(-1, Board!7)) = 0) & $greatereq(Pos!4, 0) & $greatereq($sum(N!5, $product(-1, Pos!4)), 0) & solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)))) <=> (~(~($greatereq(Board!7, 0) & ($sum(N!5, $product(-1, Board!7)) = 0) & $greatereq(Pos!4, 0) & $lesseq($sum(Pos!4, $product(-1, N!5)), 0) & solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4))))),
% 0.78/0.76 inference(monotonicity,[status(thm)],[4])).
% 0.78/0.76 tff(6,plain,
% 0.78/0.76 ((~(~($greatereq(Board!7, 0) & ($sum(N!5, $product(-1, Board!7)) = 0) & $greatereq(Pos!4, 0) & $greatereq($sum(N!5, $product(-1, Pos!4)), 0) & solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)))) <=> ($greatereq(Board!7, 0) & ($sum(N!5, $product(-1, Board!7)) = 0) & $greatereq(Pos!4, 0) & $lesseq($sum(Pos!4, $product(-1, N!5)), 0) & solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4))),
% 0.78/0.76 inference(transitivity,[status(thm)],[5, 3])).
% 0.78/0.76 tff(7,plain,
% 0.78/0.76 (((~(~($greatereq(Board!7, 0) & ($sum(N!5, $product(-1, Board!7)) = 0) & $greatereq(Pos!4, 0) & $greatereq($sum(N!5, $product(-1, Pos!4)), 0) & solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)))) & ((~((~($sum(N!5, $product(-1, Pos!4)) = 0)) | solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), N!5))) | ((~($sum(N!5, $product(-1, Pos!4)) = 0)) & (((~$greatereq(N!5, 1)) & ((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!9, t2tb2(B1!8))), N!5)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, B!9, t2tb2(B1!8))), Pos!4)) | (~is_board1(tb2t1(mk_array1(int, B!9, t2tb2(B1!8))), N!5)) | (~($sum(B!9, $product(-1, N!5)) = 0)))))) | ((~(~$greatereq(N!5, 1))) & ((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (((~(~($greatereq(I!11, 0) & $lesseq($sum(I!11, $product(-1, N!5)), -1)))) & (eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4) & ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), 0) & (~$lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))))), 0)))) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos!4)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)))) & ((~$greatereq(Board!7, 0)) | (~$greatereq(Pos!4, 0)) | (~(~$greatereq($sum(Pos!4, $product(-1, Board!7)), 0))) | ((~(~($greatereq(Board!7, 0) & (Board3!12 = tb2t2(set(int, int, t2tb2(Board2!10), t2tb(Pos!4), t2tb(I!11))))))) & ((~$greatereq(Pos!4, 0)) | (~(~$greatereq($sum(Pos!4, $product(-1, Board!7)), 0))) | ((~((~(Result!13 = true1)) <=> is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4))) & (((~(~(Result!13 = true1))) & ((~$lesseq($sum(Pos!4, $product(-1, N!5)), 0)) | (~($sum(N!5, $product(-1, Board!7)) = 0)) | (~$greatereq(Pos!4, -1)) | (~$lesseq($sum(Pos!4, $product(-1, N!5)), -1)) | (~solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (($greatereq(Board!7, 0) & eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4)) & ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B, t2tb2(B1))), $sum(1, Pos!4))) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)))) & ((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~($greatereq(tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))), 0) & (~$lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))))), -1)))) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), Pos!4)) | (~($sum(B!16, $product(-1, N!5)) = 0)))))) | (~((~($greatereq(Board!7, 0) & solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!17))), N!5))) | solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!17))), N!5))))) | ((~(Result!13 = true1)) & ((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~($greatereq(tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))), 0) & (~$lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))))), -1)))) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Pos!4)) | (~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~($sum(B!19, $product(-1, N!5)) = 0)))))))))))) | ((eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4) & ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), 0) & (~$lesseq($sum(N!5, $product(-1, tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))))), 0)))) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos!4)) | (~($sum(B, $product(-1, N!5)) = 0)))) & ((~$greatereq(Board!7, 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), Pos!4)) | (~($sum(B!21, $product(-1, N!5)) = 0))))))))))))) <=> (($greatereq(Board!7, 0) & ($sum(N!5, $product(-1, Board!7)) = 0) & $greatereq(Pos!4, 0) & $lesseq($sum(Pos!4, $product(-1, N!5)), 0) & solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) & ((~((~($sum(Pos!4, $product(-1, N!5)) = 0)) | solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), N!5))) | ((~($sum(Pos!4, $product(-1, N!5)) = 0)) & (((~$greatereq(N!5, 1)) & ((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!9, t2tb2(B1!8))), N!5)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, B!9, t2tb2(B1!8))), Pos!4)) | (~is_board1(tb2t1(mk_array1(int, B!9, t2tb2(B1!8))), N!5)) | (~($sum(N!5, $product(-1, B!9)) = 0)))))) | ($greatereq(N!5, 1) & ((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | ($greatereq(I!11, 0) & $greatereq($sum(N!5, $product(-1, I!11)), 1) & eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4) & ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos!4)) | (~($greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), 0) & (~$greatereq($sum(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), $product(-1, I!11)), 0))))) & ((~$greatereq(Board!7, 0)) | (~$greatereq(Pos!4, 0)) | $greatereq($sum(Pos!4, $product(-1, Board!7)), 0) | ($greatereq(Board!7, 0) & (Board3!12 = tb2t2(set(int, int, t2tb2(Board2!10), t2tb(Pos!4), t2tb(I!11)))) & ((~$greatereq(Pos!4, 0)) | $greatereq($sum(Pos!4, $product(-1, Board!7)), 0) | (((Result!13 = true1) <=> is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) & (((Result!13 = true1) & ((~$lesseq($sum(Pos!4, $product(-1, N!5)), 0)) | (~($sum(N!5, $product(-1, Board!7)) = 0)) | (~$greatereq(Pos!4, -1)) | (~$lesseq($sum(Pos!4, $product(-1, N!5)), -1)) | (~solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~((~($greatereq(Board!7, 0) & solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!17))), N!5))) | solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!17))), N!5))) | ($greatereq(Board!7, 0) & eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4)) & ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B, t2tb2(B1))), $sum(1, Pos!4)))) & ((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~($greatereq(tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))), 0) & (~$lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))))), -1)))) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), Pos!4)) | (~($sum(N!5, $product(-1, B!16)) = 0)))))))) | ((~(Result!13 = true1)) & ((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~($greatereq(tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))), 0) & (~$lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))))), -1)))) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Pos!4)) | (~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~($sum(N!5, $product(-1, B!19)) = 0)))))))))))) | (eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4) & ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~($greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), 0) & (~$lesseq($sum(N!5, $product(-1, tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))))), 0)))) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos!4))) & ((~$greatereq(Board!7, 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), Pos!4)) | (~($sum(N!5, $product(-1, B!21)) = 0))))))))))))),
% 0.81/0.76 inference(monotonicity,[status(thm)],[6, 2])).
% 0.81/0.76 tff(8,plain,
% 0.81/0.76 (((~(~($greatereq(Board!7, 0) & ($sum(N!5, $product(-1, Board!7)) = 0) & $greatereq(Pos!4, 0) & $greatereq($sum(N!5, $product(-1, Pos!4)), 0) & solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)))) & ((~((~($sum(N!5, $product(-1, Pos!4)) = 0)) | solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), N!5))) | ((~($sum(N!5, $product(-1, Pos!4)) = 0)) & (((~$greatereq(N!5, 1)) & ((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!9, t2tb2(B1!8))), N!5)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, B!9, t2tb2(B1!8))), Pos!4)) | (~is_board1(tb2t1(mk_array1(int, B!9, t2tb2(B1!8))), N!5)) | (~($sum(B!9, $product(-1, N!5)) = 0)))))) | ((~(~$greatereq(N!5, 1))) & ((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (((~(~($greatereq(I!11, 0) & $lesseq($sum(I!11, $product(-1, N!5)), -1)))) & (eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4) & ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), 0) & (~$lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))))), 0)))) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos!4)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)))) & ((~$greatereq(Board!7, 0)) | (~$greatereq(Pos!4, 0)) | (~(~$greatereq($sum(Pos!4, $product(-1, Board!7)), 0))) | ((~(~($greatereq(Board!7, 0) & (Board3!12 = tb2t2(set(int, int, t2tb2(Board2!10), t2tb(Pos!4), t2tb(I!11))))))) & ((~$greatereq(Pos!4, 0)) | (~(~$greatereq($sum(Pos!4, $product(-1, Board!7)), 0))) | ((~((~(Result!13 = true1)) <=> is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4))) & (((~(~(Result!13 = true1))) & ((~$lesseq($sum(Pos!4, $product(-1, N!5)), 0)) | (~($sum(N!5, $product(-1, Board!7)) = 0)) | (~$greatereq(Pos!4, -1)) | (~$lesseq($sum(Pos!4, $product(-1, N!5)), -1)) | (~solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (($greatereq(Board!7, 0) & eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4)) & ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B, t2tb2(B1))), $sum(1, Pos!4))) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)))) & ((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~($greatereq(tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))), 0) & (~$lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))))), -1)))) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), Pos!4)) | (~($sum(B!16, $product(-1, N!5)) = 0)))))) | (~((~($greatereq(Board!7, 0) & solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!17))), N!5))) | solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!17))), N!5))))) | ((~(Result!13 = true1)) & ((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~($greatereq(tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))), 0) & (~$lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))))), -1)))) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Pos!4)) | (~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~($sum(B!19, $product(-1, N!5)) = 0)))))))))))) | ((eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4) & ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), 0) & (~$lesseq($sum(N!5, $product(-1, tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))))), 0)))) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos!4)) | (~($sum(B, $product(-1, N!5)) = 0)))) & ((~$greatereq(Board!7, 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), Pos!4)) | (~($sum(B!21, $product(-1, N!5)) = 0))))))))))))) <=> ($greatereq(Board!7, 0) & ($sum(N!5, $product(-1, Board!7)) = 0) & $greatereq(Pos!4, 0) & $lesseq($sum(Pos!4, $product(-1, N!5)), 0) & solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4) & ((~((~($sum(Pos!4, $product(-1, N!5)) = 0)) | solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), N!5))) | ((~($sum(Pos!4, $product(-1, N!5)) = 0)) & (((~$greatereq(N!5, 1)) & ((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!9, t2tb2(B1!8))), N!5)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, B!9, t2tb2(B1!8))), Pos!4)) | (~is_board1(tb2t1(mk_array1(int, B!9, t2tb2(B1!8))), N!5)) | (~($sum(N!5, $product(-1, B!9)) = 0)))))) | ($greatereq(N!5, 1) & ((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | ($greatereq(I!11, 0) & $greatereq($sum(N!5, $product(-1, I!11)), 1) & eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4) & ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos!4)) | (~($greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), 0) & (~$greatereq($sum(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), $product(-1, I!11)), 0))))) & ((~$greatereq(Board!7, 0)) | (~$greatereq(Pos!4, 0)) | $greatereq($sum(Pos!4, $product(-1, Board!7)), 0) | ($greatereq(Board!7, 0) & (Board3!12 = tb2t2(set(int, int, t2tb2(Board2!10), t2tb(Pos!4), t2tb(I!11)))) & ((~$greatereq(Pos!4, 0)) | $greatereq($sum(Pos!4, $product(-1, Board!7)), 0) | (((Result!13 = true1) <=> is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) & (((Result!13 = true1) & ((~$lesseq($sum(Pos!4, $product(-1, N!5)), 0)) | (~($sum(N!5, $product(-1, Board!7)) = 0)) | (~$greatereq(Pos!4, -1)) | (~$lesseq($sum(Pos!4, $product(-1, N!5)), -1)) | (~solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~((~($greatereq(Board!7, 0) & solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!17))), N!5))) | solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!17))), N!5))) | ($greatereq(Board!7, 0) & eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4)) & ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B, t2tb2(B1))), $sum(1, Pos!4)))) & ((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~($greatereq(tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))), 0) & (~$lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))))), -1)))) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), Pos!4)) | (~($sum(N!5, $product(-1, B!16)) = 0)))))))) | ((~(Result!13 = true1)) & ((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~($greatereq(tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))), 0) & (~$lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))))), -1)))) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Pos!4)) | (~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~($sum(N!5, $product(-1, B!19)) = 0)))))))))))) | (eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4) & ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~($greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), 0) & (~$lesseq($sum(N!5, $product(-1, tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))))), 0)))) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos!4))) & ((~$greatereq(Board!7, 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), Pos!4)) | (~($sum(N!5, $product(-1, B!21)) = 0))))))))))))),
% 0.81/0.77 inference(transitivity,[status(thm)],[7, 1])).
% 0.81/0.77 tff(9,plain,
% 0.81/0.77 ((~![Board: $int, Board1: map_int_int, N: $int, Pos: $int] : ((~($greatereq(Board, 0) & ($sum(N, $product(-1, Board)) = 0) & $greatereq(Pos, 0) & $greatereq($sum(N, $product(-1, Pos)), 0) & solution1(tb2t1(mk_array1(int, Board, t2tb2(Board1))), Pos))) | (((~($sum(N, $product(-1, Pos)) = 0)) | solution1(tb2t1(mk_array1(int, Board, t2tb2(Board1))), N)) & (($sum(N, $product(-1, Pos)) = 0) | (($greatereq(N, 1) | (eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board1))), tb2t1(mk_array1(int, Board, t2tb2(Board1))), Pos) & ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board1))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~($sum(B, $product(-1, N)) = 0))))) & ((~$greatereq(N, 1)) | (eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board1))), tb2t1(mk_array1(int, Board, t2tb2(Board1))), Pos) & ![Board2: map_int_int] : (![I: $int] : ((~($greatereq(I, 0) & $lesseq($sum(I, $product(-1, N)), -1))) | (~(eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board2))), tb2t1(mk_array1(int, Board, t2tb2(Board1))), Pos) & ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~($greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos))), 0) & (~$lesseq($sum(I, $product(-1, tb2t(get(int, int, t2tb2(B1), t2tb(Pos))))), 0)))) | (~eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board2))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~($sum(B, $product(-1, N)) = 0))))) | ($greatereq(Board, 0) & $greatereq(Pos, 0) & (~$greatereq($sum(Pos, $product(-1, Board)), 0)) & ![Board3: map_int_int] : ((~($greatereq(Board, 0) & (Board3 = tb2t2(set(int, int, t2tb2(Board2), t2tb(Pos), t2tb(I)))))) | ($greatereq(Pos, 0) & (~$greatereq($sum(Pos, $product(-1, Board)), 0)) & ![Result: bool1] : (((~(Result = true1)) <=> is_consistent1(tb2t1(mk_array1(int, Board, t2tb2(Board3))), Pos)) | (((~(Result = true1)) | ($lesseq($sum(Pos, $product(-1, N)), 0) & ($sum(N, $product(-1, Board)) = 0) & $greatereq(Pos, -1) & $lesseq($sum(Pos, $product(-1, N)), -1) & solution1(tb2t1(mk_array1(int, Board, t2tb2(Board3))), $sum(1, Pos)) & ![Board4: map_int_int] : ((~($greatereq(Board, 0) & eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board4))), tb2t1(mk_array1(int, Board, t2tb2(Board3))), $sum(1, Pos)) & ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board4))), tb2t1(mk_array1(int, B, t2tb2(B1))), $sum(1, Pos))) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~($sum(B, $product(-1, N)) = 0))))) | (eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board4))), tb2t1(mk_array1(int, Board, t2tb2(Board1))), Pos) & ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~($greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos))), 0) & (~$lesseq($sum(I, $product(-1, tb2t(get(int, int, t2tb2(B1), t2tb(Pos))))), -1)))) | (~eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board4))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos)) | (~($sum(B, $product(-1, N)) = 0))))) & ![Board4: map_int_int] : ((~($greatereq(Board, 0) & solution1(tb2t1(mk_array1(int, Board, t2tb2(Board4))), N))) | solution1(tb2t1(mk_array1(int, Board, t2tb2(Board4))), N)))) & ((Result = true1) | (eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board3))), tb2t1(mk_array1(int, Board, t2tb2(Board1))), Pos) & ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~($greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos))), 0) & (~$lesseq($sum(I, $product(-1, tb2t(get(int, int, t2tb2(B1), t2tb(Pos))))), -1)))) | (~eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board3))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~($sum(B, $product(-1, N)) = 0))))))))))) & ((~(eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board2))), tb2t1(mk_array1(int, Board, t2tb2(Board1))), Pos) & ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~($greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos))), 0) & (~$lesseq($sum(N, $product(-1, tb2t(get(int, int, t2tb2(B1), t2tb(Pos))))), 0)))) | (~eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board2))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos)) | (~($sum(B, $product(-1, N)) = 0))))) | ($greatereq(Board, 0) & eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board2))), tb2t1(mk_array1(int, Board, t2tb2(Board1))), Pos) & ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board2))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos)) | (~($sum(B, $product(-1, N)) = 0))))))))))))) <=> (~![Board: $int, Board1: map_int_int, N: $int, Pos: $int] : ((~($greatereq(Board, 0) & ($sum(N, $product(-1, Board)) = 0) & $greatereq(Pos, 0) & $greatereq($sum(N, $product(-1, Pos)), 0) & solution1(tb2t1(mk_array1(int, Board, t2tb2(Board1))), Pos))) | (((~($sum(N, $product(-1, Pos)) = 0)) | solution1(tb2t1(mk_array1(int, Board, t2tb2(Board1))), N)) & (($sum(N, $product(-1, Pos)) = 0) | (($greatereq(N, 1) | (eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board1))), tb2t1(mk_array1(int, Board, t2tb2(Board1))), Pos) & ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board1))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~($sum(B, $product(-1, N)) = 0))))) & ((~$greatereq(N, 1)) | (eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board1))), tb2t1(mk_array1(int, Board, t2tb2(Board1))), Pos) & ![Board2: map_int_int] : (![I: $int] : ((~($greatereq(I, 0) & $lesseq($sum(I, $product(-1, N)), -1))) | (~(eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board2))), tb2t1(mk_array1(int, Board, t2tb2(Board1))), Pos) & ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~($greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos))), 0) & (~$lesseq($sum(I, $product(-1, tb2t(get(int, int, t2tb2(B1), t2tb(Pos))))), 0)))) | (~eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board2))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~($sum(B, $product(-1, N)) = 0))))) | ($greatereq(Board, 0) & $greatereq(Pos, 0) & (~$greatereq($sum(Pos, $product(-1, Board)), 0)) & ![Board3: map_int_int] : ((~($greatereq(Board, 0) & (Board3 = tb2t2(set(int, int, t2tb2(Board2), t2tb(Pos), t2tb(I)))))) | ($greatereq(Pos, 0) & (~$greatereq($sum(Pos, $product(-1, Board)), 0)) & ![Result: bool1] : (((~(Result = true1)) <=> is_consistent1(tb2t1(mk_array1(int, Board, t2tb2(Board3))), Pos)) | (((~(Result = true1)) | ($lesseq($sum(Pos, $product(-1, N)), 0) & ($sum(N, $product(-1, Board)) = 0) & $greatereq(Pos, -1) & $lesseq($sum(Pos, $product(-1, N)), -1) & solution1(tb2t1(mk_array1(int, Board, t2tb2(Board3))), $sum(1, Pos)) & ![Board4: map_int_int] : ((~($greatereq(Board, 0) & eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board4))), tb2t1(mk_array1(int, Board, t2tb2(Board3))), $sum(1, Pos)) & ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board4))), tb2t1(mk_array1(int, B, t2tb2(B1))), $sum(1, Pos))) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~($sum(B, $product(-1, N)) = 0))))) | (eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board4))), tb2t1(mk_array1(int, Board, t2tb2(Board1))), Pos) & ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~($greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos))), 0) & (~$lesseq($sum(I, $product(-1, tb2t(get(int, int, t2tb2(B1), t2tb(Pos))))), -1)))) | (~eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board4))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos)) | (~($sum(B, $product(-1, N)) = 0))))) & ![Board4: map_int_int] : ((~($greatereq(Board, 0) & solution1(tb2t1(mk_array1(int, Board, t2tb2(Board4))), N))) | solution1(tb2t1(mk_array1(int, Board, t2tb2(Board4))), N)))) & ((Result = true1) | (eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board3))), tb2t1(mk_array1(int, Board, t2tb2(Board1))), Pos) & ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~($greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos))), 0) & (~$lesseq($sum(I, $product(-1, tb2t(get(int, int, t2tb2(B1), t2tb(Pos))))), -1)))) | (~eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board3))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~($sum(B, $product(-1, N)) = 0))))))))))) & ((~(eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board2))), tb2t1(mk_array1(int, Board, t2tb2(Board1))), Pos) & ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~($greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos))), 0) & (~$lesseq($sum(N, $product(-1, tb2t(get(int, int, t2tb2(B1), t2tb(Pos))))), 0)))) | (~eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board2))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos)) | (~($sum(B, $product(-1, N)) = 0))))) | ($greatereq(Board, 0) & eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board2))), tb2t1(mk_array1(int, Board, t2tb2(Board1))), Pos) & ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board2))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos)) | (~($sum(B, $product(-1, N)) = 0)))))))))))))),
% 0.81/0.77 inference(rewrite,[status(thm)],[])).
% 0.81/0.77 tff(10,plain,
% 0.81/0.77 ((~![Board: $int, Board1: map_int_int, N: $int, Pos: $int] : ((~($greatereq(Board, 0) & ($sum(Board, $product(-1, N)) = 0) & $greatereq(Pos, 0) & $lesseq($sum(Pos, $product(-1, N)), 0) & solution1(tb2t1(mk_array1(int, Board, t2tb2(Board1))), Pos))) | (((~($sum(Pos, $product(-1, N)) = 0)) | solution1(tb2t1(mk_array1(int, Board, t2tb2(Board1))), N)) & (($sum(Pos, $product(-1, N)) = 0) | (($greatereq(N, 1) | (eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board1))), tb2t1(mk_array1(int, Board, t2tb2(Board1))), Pos) & ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board1))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~($sum(B, $product(-1, N)) = 0))))) & ((~$greatereq(N, 1)) | (eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board1))), tb2t1(mk_array1(int, Board, t2tb2(Board1))), Pos) & ![Board2: map_int_int] : (![I: $int] : ((~($greatereq(I, 0) & $lesseq($sum(I, $product(-1, N)), -1))) | (~(eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board2))), tb2t1(mk_array1(int, Board, t2tb2(Board1))), Pos) & ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~($greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos))), 0) & (~$lesseq($sum(I, $product(-1, tb2t(get(int, int, t2tb2(B1), t2tb(Pos))))), 0)))) | (~eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board2))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~($sum(B, $product(-1, N)) = 0))))) | ($greatereq(Board, 0) & $greatereq(Pos, 0) & (~$lesseq($sum(Board, $product(-1, Pos)), 0)) & ![Board3: map_int_int] : ((~($greatereq(Board, 0) & (Board3 = tb2t2(set(int, int, t2tb2(Board2), t2tb(Pos), t2tb(I)))))) | ($greatereq(Pos, 0) & (~$lesseq($sum(Board, $product(-1, Pos)), 0)) & ![Result: bool1] : (((~(Result = true1)) <=> is_consistent1(tb2t1(mk_array1(int, Board, t2tb2(Board3))), Pos)) | (((~(Result = true1)) | ($greatereq($sum(N, $product(-1, Pos)), 0) & ($sum(Board, $product(-1, N)) = 0) & $greatereq(Pos, -1) & $lesseq($sum(Pos, $product(-1, N)), -1) & solution1(tb2t1(mk_array1(int, Board, t2tb2(Board3))), $sum(1, Pos)) & ![Board4: map_int_int] : ((~($greatereq(Board, 0) & eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board4))), tb2t1(mk_array1(int, Board, t2tb2(Board3))), $sum(1, Pos)) & ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board4))), tb2t1(mk_array1(int, B, t2tb2(B1))), $sum(1, Pos))) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~($sum(B, $product(-1, N)) = 0))))) | (eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board4))), tb2t1(mk_array1(int, Board, t2tb2(Board1))), Pos) & ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~($greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos))), 0) & (~$lesseq($sum(I, $product(-1, tb2t(get(int, int, t2tb2(B1), t2tb(Pos))))), -1)))) | (~eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board4))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos)) | (~($sum(B, $product(-1, N)) = 0))))) & ![Board4: map_int_int] : ((~($greatereq(Board, 0) & solution1(tb2t1(mk_array1(int, Board, t2tb2(Board4))), N))) | solution1(tb2t1(mk_array1(int, Board, t2tb2(Board4))), N)))) & ((Result = true1) | (eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board3))), tb2t1(mk_array1(int, Board, t2tb2(Board1))), Pos) & ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~($greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos))), 0) & (~$lesseq($sum(I, $product(-1, tb2t(get(int, int, t2tb2(B1), t2tb(Pos))))), -1)))) | (~eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board3))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~($sum(B, $product(-1, N)) = 0))))))))))) & ((~(eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board2))), tb2t1(mk_array1(int, Board, t2tb2(Board1))), Pos) & ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~($greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos))), 0) & (~$lesseq($sum(N, $product(-1, tb2t(get(int, int, t2tb2(B1), t2tb(Pos))))), 0)))) | (~eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board2))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos)) | (~($sum(B, $product(-1, N)) = 0))))) | ($greatereq(Board, 0) & eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board2))), tb2t1(mk_array1(int, Board, t2tb2(Board1))), Pos) & ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board2))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos)) | (~($sum(B, $product(-1, N)) = 0))))))))))))) <=> (~![Board: $int, Board1: map_int_int, N: $int, Pos: $int] : ((~($greatereq(Board, 0) & ($sum(N, $product(-1, Board)) = 0) & $greatereq(Pos, 0) & $greatereq($sum(N, $product(-1, Pos)), 0) & solution1(tb2t1(mk_array1(int, Board, t2tb2(Board1))), Pos))) | (((~($sum(N, $product(-1, Pos)) = 0)) | solution1(tb2t1(mk_array1(int, Board, t2tb2(Board1))), N)) & (($sum(N, $product(-1, Pos)) = 0) | (($greatereq(N, 1) | (eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board1))), tb2t1(mk_array1(int, Board, t2tb2(Board1))), Pos) & ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board1))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~($sum(B, $product(-1, N)) = 0))))) & ((~$greatereq(N, 1)) | (eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board1))), tb2t1(mk_array1(int, Board, t2tb2(Board1))), Pos) & ![Board2: map_int_int] : (![I: $int] : ((~($greatereq(I, 0) & $lesseq($sum(I, $product(-1, N)), -1))) | (~(eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board2))), tb2t1(mk_array1(int, Board, t2tb2(Board1))), Pos) & ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~($greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos))), 0) & (~$lesseq($sum(I, $product(-1, tb2t(get(int, int, t2tb2(B1), t2tb(Pos))))), 0)))) | (~eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board2))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~($sum(B, $product(-1, N)) = 0))))) | ($greatereq(Board, 0) & $greatereq(Pos, 0) & (~$greatereq($sum(Pos, $product(-1, Board)), 0)) & ![Board3: map_int_int] : ((~($greatereq(Board, 0) & (Board3 = tb2t2(set(int, int, t2tb2(Board2), t2tb(Pos), t2tb(I)))))) | ($greatereq(Pos, 0) & (~$greatereq($sum(Pos, $product(-1, Board)), 0)) & ![Result: bool1] : (((~(Result = true1)) <=> is_consistent1(tb2t1(mk_array1(int, Board, t2tb2(Board3))), Pos)) | (((~(Result = true1)) | ($lesseq($sum(Pos, $product(-1, N)), 0) & ($sum(N, $product(-1, Board)) = 0) & $greatereq(Pos, -1) & $lesseq($sum(Pos, $product(-1, N)), -1) & solution1(tb2t1(mk_array1(int, Board, t2tb2(Board3))), $sum(1, Pos)) & ![Board4: map_int_int] : ((~($greatereq(Board, 0) & eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board4))), tb2t1(mk_array1(int, Board, t2tb2(Board3))), $sum(1, Pos)) & ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board4))), tb2t1(mk_array1(int, B, t2tb2(B1))), $sum(1, Pos))) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~($sum(B, $product(-1, N)) = 0))))) | (eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board4))), tb2t1(mk_array1(int, Board, t2tb2(Board1))), Pos) & ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~($greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos))), 0) & (~$lesseq($sum(I, $product(-1, tb2t(get(int, int, t2tb2(B1), t2tb(Pos))))), -1)))) | (~eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board4))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos)) | (~($sum(B, $product(-1, N)) = 0))))) & ![Board4: map_int_int] : ((~($greatereq(Board, 0) & solution1(tb2t1(mk_array1(int, Board, t2tb2(Board4))), N))) | solution1(tb2t1(mk_array1(int, Board, t2tb2(Board4))), N)))) & ((Result = true1) | (eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board3))), tb2t1(mk_array1(int, Board, t2tb2(Board1))), Pos) & ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~($greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos))), 0) & (~$lesseq($sum(I, $product(-1, tb2t(get(int, int, t2tb2(B1), t2tb(Pos))))), -1)))) | (~eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board3))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~($sum(B, $product(-1, N)) = 0))))))))))) & ((~(eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board2))), tb2t1(mk_array1(int, Board, t2tb2(Board1))), Pos) & ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~($greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos))), 0) & (~$lesseq($sum(N, $product(-1, tb2t(get(int, int, t2tb2(B1), t2tb(Pos))))), 0)))) | (~eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board2))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos)) | (~($sum(B, $product(-1, N)) = 0))))) | ($greatereq(Board, 0) & eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board2))), tb2t1(mk_array1(int, Board, t2tb2(Board1))), Pos) & ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board2))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos)) | (~($sum(B, $product(-1, N)) = 0)))))))))))))),
% 0.81/0.77 inference(rewrite,[status(thm)],[])).
% 0.81/0.77 tff(11,plain,
% 0.81/0.77 ((~![Board: $int, Board1: map_int_int, N: $int, Pos: $int] : ((~($lesseq(0, Board) & (Board = N) & $lesseq(0, Pos) & $lesseq(Pos, N) & solution1(tb2t1(mk_array1(int, Board, t2tb2(Board1))), Pos))) | (((~(Pos = N)) | solution1(tb2t1(mk_array1(int, Board, t2tb2(Board1))), N)) & ((Pos = N) | (($lesseq(1, N) | (eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board1))), tb2t1(mk_array1(int, Board, t2tb2(Board1))), Pos) & ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board1))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~(B = N))))) & ((~$lesseq(1, N)) | (eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board1))), tb2t1(mk_array1(int, Board, t2tb2(Board1))), Pos) & ![Board2: map_int_int] : (![I: $int] : ((~(eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board2))), tb2t1(mk_array1(int, Board, t2tb2(Board1))), Pos) & ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board2))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~(B = N)) | (~($lesseq(0, tb2t(get(int, int, t2tb2(B1), t2tb(Pos)))) & (~$lesseq(I, tb2t(get(int, int, t2tb2(B1), t2tb(Pos)))))))))) | (~($lesseq(0, I) & $lesseq(I, $sum(-1, N)))) | ($lesseq(0, Board) & $lesseq(0, Pos) & (~$lesseq(Board, Pos)) & ![Board3: map_int_int] : ((~($lesseq(0, Board) & (Board3 = tb2t2(set(int, int, t2tb2(Board2), t2tb(Pos), t2tb(I)))))) | ($lesseq(0, Pos) & (~$lesseq(Board, Pos)) & ![Result: bool1] : (((~(Result = true1)) <=> is_consistent1(tb2t1(mk_array1(int, Board, t2tb2(Board3))), Pos)) | (((~(Result = true1)) | ($lesseq(0, $sum(N, $product(-1, Pos))) & (Board = N) & $lesseq(-1, Pos) & $lesseq(Pos, $sum(-1, N)) & solution1(tb2t1(mk_array1(int, Board, t2tb2(Board3))), $sum(1, Pos)) & ![Board4: map_int_int] : ((~($lesseq(0, Board) & eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board4))), tb2t1(mk_array1(int, Board, t2tb2(Board3))), $sum(1, Pos)) & ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board4))), tb2t1(mk_array1(int, B, t2tb2(B1))), $sum(1, Pos))) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~(B = N))))) | (eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board4))), tb2t1(mk_array1(int, Board, t2tb2(Board1))), Pos) & ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~(B = N)) | (~eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board4))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos)) | (~($lesseq(0, tb2t(get(int, int, t2tb2(B1), t2tb(Pos)))) & (~$lesseq(I, $sum(-1, tb2t(get(int, int, t2tb2(B1), t2tb(Pos))))))))))) & ![Board4: map_int_int] : ((~($lesseq(0, Board) & solution1(tb2t1(mk_array1(int, Board, t2tb2(Board4))), N))) | solution1(tb2t1(mk_array1(int, Board, t2tb2(Board4))), N)))) & ((Result = true1) | (eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board3))), tb2t1(mk_array1(int, Board, t2tb2(Board1))), Pos) & ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board3))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~(B = N)) | (~($lesseq(0, tb2t(get(int, int, t2tb2(B1), t2tb(Pos)))) & (~$lesseq(I, $sum(-1, tb2t(get(int, int, t2tb2(B1), t2tb(Pos))))))))))))))))) & ((~(eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board2))), tb2t1(mk_array1(int, Board, t2tb2(Board1))), Pos) & ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board2))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos)) | (~(B = N)) | (~($lesseq(0, tb2t(get(int, int, t2tb2(B1), t2tb(Pos)))) & (~$lesseq(N, tb2t(get(int, int, t2tb2(B1), t2tb(Pos)))))))))) | ($lesseq(0, Board) & eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board2))), tb2t1(mk_array1(int, Board, t2tb2(Board1))), Pos) & ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board2))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos)) | (~(B = N))))))))))))) <=> (~![Board: $int, Board1: map_int_int, N: $int, Pos: $int] : ((~($greatereq(Board, 0) & ($sum(Board, $product(-1, N)) = 0) & $greatereq(Pos, 0) & $lesseq($sum(Pos, $product(-1, N)), 0) & solution1(tb2t1(mk_array1(int, Board, t2tb2(Board1))), Pos))) | (((~($sum(Pos, $product(-1, N)) = 0)) | solution1(tb2t1(mk_array1(int, Board, t2tb2(Board1))), N)) & (($sum(Pos, $product(-1, N)) = 0) | (($greatereq(N, 1) | (eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board1))), tb2t1(mk_array1(int, Board, t2tb2(Board1))), Pos) & ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board1))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~($sum(B, $product(-1, N)) = 0))))) & ((~$greatereq(N, 1)) | (eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board1))), tb2t1(mk_array1(int, Board, t2tb2(Board1))), Pos) & ![Board2: map_int_int] : (![I: $int] : ((~($greatereq(I, 0) & $lesseq($sum(I, $product(-1, N)), -1))) | (~(eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board2))), tb2t1(mk_array1(int, Board, t2tb2(Board1))), Pos) & ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~($greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos))), 0) & (~$lesseq($sum(I, $product(-1, tb2t(get(int, int, t2tb2(B1), t2tb(Pos))))), 0)))) | (~eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board2))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~($sum(B, $product(-1, N)) = 0))))) | ($greatereq(Board, 0) & $greatereq(Pos, 0) & (~$lesseq($sum(Board, $product(-1, Pos)), 0)) & ![Board3: map_int_int] : ((~($greatereq(Board, 0) & (Board3 = tb2t2(set(int, int, t2tb2(Board2), t2tb(Pos), t2tb(I)))))) | ($greatereq(Pos, 0) & (~$lesseq($sum(Board, $product(-1, Pos)), 0)) & ![Result: bool1] : (((~(Result = true1)) <=> is_consistent1(tb2t1(mk_array1(int, Board, t2tb2(Board3))), Pos)) | (((~(Result = true1)) | ($greatereq($sum(N, $product(-1, Pos)), 0) & ($sum(Board, $product(-1, N)) = 0) & $greatereq(Pos, -1) & $lesseq($sum(Pos, $product(-1, N)), -1) & solution1(tb2t1(mk_array1(int, Board, t2tb2(Board3))), $sum(1, Pos)) & ![Board4: map_int_int] : ((~($greatereq(Board, 0) & eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board4))), tb2t1(mk_array1(int, Board, t2tb2(Board3))), $sum(1, Pos)) & ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board4))), tb2t1(mk_array1(int, B, t2tb2(B1))), $sum(1, Pos))) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~($sum(B, $product(-1, N)) = 0))))) | (eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board4))), tb2t1(mk_array1(int, Board, t2tb2(Board1))), Pos) & ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~($greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos))), 0) & (~$lesseq($sum(I, $product(-1, tb2t(get(int, int, t2tb2(B1), t2tb(Pos))))), -1)))) | (~eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board4))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos)) | (~($sum(B, $product(-1, N)) = 0))))) & ![Board4: map_int_int] : ((~($greatereq(Board, 0) & solution1(tb2t1(mk_array1(int, Board, t2tb2(Board4))), N))) | solution1(tb2t1(mk_array1(int, Board, t2tb2(Board4))), N)))) & ((Result = true1) | (eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board3))), tb2t1(mk_array1(int, Board, t2tb2(Board1))), Pos) & ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~($greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos))), 0) & (~$lesseq($sum(I, $product(-1, tb2t(get(int, int, t2tb2(B1), t2tb(Pos))))), -1)))) | (~eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board3))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~($sum(B, $product(-1, N)) = 0))))))))))) & ((~(eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board2))), tb2t1(mk_array1(int, Board, t2tb2(Board1))), Pos) & ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~($greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos))), 0) & (~$lesseq($sum(N, $product(-1, tb2t(get(int, int, t2tb2(B1), t2tb(Pos))))), 0)))) | (~eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board2))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos)) | (~($sum(B, $product(-1, N)) = 0))))) | ($greatereq(Board, 0) & eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board2))), tb2t1(mk_array1(int, Board, t2tb2(Board1))), Pos) & ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board2))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos)) | (~($sum(B, $product(-1, N)) = 0)))))))))))))),
% 0.81/0.78 inference(rewrite,[status(thm)],[])).
% 0.81/0.78 tff(12,plain,
% 0.81/0.78 ((~![Board: $int, Board1: map_int_int, N: $int, Pos: $int] : ((~($lesseq(0, Board) & (Board = N) & $lesseq(0, Pos) & $lesseq(Pos, N) & solution1(tb2t1(mk_array1(int, Board, t2tb2(Board1))), Pos))) | (((~(Pos = N)) | solution1(tb2t1(mk_array1(int, Board, t2tb2(Board1))), N)) & ((Pos = N) | (($lesseq(1, N) | (eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board1))), tb2t1(mk_array1(int, Board, t2tb2(Board1))), Pos) & ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board1))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~(B = N))))) & ((~$lesseq(1, N)) | (eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board1))), tb2t1(mk_array1(int, Board, t2tb2(Board1))), Pos) & ![Board2: map_int_int] : (![I: $int] : ((~(eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board2))), tb2t1(mk_array1(int, Board, t2tb2(Board1))), Pos) & ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board2))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~(B = N)) | (~($lesseq(0, tb2t(get(int, int, t2tb2(B1), t2tb(Pos)))) & (~$lesseq(I, tb2t(get(int, int, t2tb2(B1), t2tb(Pos)))))))))) | (~($lesseq(0, I) & $lesseq(I, $sum(-1, N)))) | ($lesseq(0, Board) & $lesseq(0, Pos) & (~$lesseq(Board, Pos)) & ![Board3: map_int_int] : ((~($lesseq(0, Board) & (Board3 = tb2t2(set(int, int, t2tb2(Board2), t2tb(Pos), t2tb(I)))))) | ($lesseq(0, Pos) & (~$lesseq(Board, Pos)) & ![Result: bool1] : (((~(Result = true1)) <=> is_consistent1(tb2t1(mk_array1(int, Board, t2tb2(Board3))), Pos)) | (((~(Result = true1)) | ($lesseq(0, $sum(N, $product(-1, Pos))) & (Board = N) & $lesseq(-1, Pos) & $lesseq(Pos, $sum(-1, N)) & solution1(tb2t1(mk_array1(int, Board, t2tb2(Board3))), $sum(1, Pos)) & ![Board4: map_int_int] : ((~($lesseq(0, Board) & eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board4))), tb2t1(mk_array1(int, Board, t2tb2(Board3))), $sum(1, Pos)) & ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board4))), tb2t1(mk_array1(int, B, t2tb2(B1))), $sum(1, Pos))) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~(B = N))))) | (eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board4))), tb2t1(mk_array1(int, Board, t2tb2(Board1))), Pos) & ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~(B = N)) | (~eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board4))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos)) | (~($lesseq(0, tb2t(get(int, int, t2tb2(B1), t2tb(Pos)))) & (~$lesseq(I, $sum(-1, tb2t(get(int, int, t2tb2(B1), t2tb(Pos))))))))))) & ![Board4: map_int_int] : ((~($lesseq(0, Board) & solution1(tb2t1(mk_array1(int, Board, t2tb2(Board4))), N))) | solution1(tb2t1(mk_array1(int, Board, t2tb2(Board4))), N)))) & ((Result = true1) | (eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board3))), tb2t1(mk_array1(int, Board, t2tb2(Board1))), Pos) & ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board3))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~(B = N)) | (~($lesseq(0, tb2t(get(int, int, t2tb2(B1), t2tb(Pos)))) & (~$lesseq(I, $sum(-1, tb2t(get(int, int, t2tb2(B1), t2tb(Pos))))))))))))))))) & ((~(eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board2))), tb2t1(mk_array1(int, Board, t2tb2(Board1))), Pos) & ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board2))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos)) | (~(B = N)) | (~($lesseq(0, tb2t(get(int, int, t2tb2(B1), t2tb(Pos)))) & (~$lesseq(N, tb2t(get(int, int, t2tb2(B1), t2tb(Pos)))))))))) | ($lesseq(0, Board) & eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board2))), tb2t1(mk_array1(int, Board, t2tb2(Board1))), Pos) & ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board2))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos)) | (~(B = N))))))))))))) <=> (~![Board: $int, Board1: map_int_int, N: $int, Pos: $int] : ((~($lesseq(0, Board) & (Board = N) & $lesseq(0, Pos) & $lesseq(Pos, N) & solution1(tb2t1(mk_array1(int, Board, t2tb2(Board1))), Pos))) | (((~(Pos = N)) | solution1(tb2t1(mk_array1(int, Board, t2tb2(Board1))), N)) & ((Pos = N) | (($lesseq(1, N) | (eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board1))), tb2t1(mk_array1(int, Board, t2tb2(Board1))), Pos) & ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board1))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~(B = N))))) & ((~$lesseq(1, N)) | (eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board1))), tb2t1(mk_array1(int, Board, t2tb2(Board1))), Pos) & ![Board2: map_int_int] : (![I: $int] : ((~(eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board2))), tb2t1(mk_array1(int, Board, t2tb2(Board1))), Pos) & ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board2))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~(B = N)) | (~($lesseq(0, tb2t(get(int, int, t2tb2(B1), t2tb(Pos)))) & (~$lesseq(I, tb2t(get(int, int, t2tb2(B1), t2tb(Pos)))))))))) | (~($lesseq(0, I) & $lesseq(I, $sum(-1, N)))) | ($lesseq(0, Board) & $lesseq(0, Pos) & (~$lesseq(Board, Pos)) & ![Board3: map_int_int] : ((~($lesseq(0, Board) & (Board3 = tb2t2(set(int, int, t2tb2(Board2), t2tb(Pos), t2tb(I)))))) | ($lesseq(0, Pos) & (~$lesseq(Board, Pos)) & ![Result: bool1] : (((~(Result = true1)) <=> is_consistent1(tb2t1(mk_array1(int, Board, t2tb2(Board3))), Pos)) | (((~(Result = true1)) | ($lesseq(0, $sum(N, $product(-1, Pos))) & (Board = N) & $lesseq(-1, Pos) & $lesseq(Pos, $sum(-1, N)) & solution1(tb2t1(mk_array1(int, Board, t2tb2(Board3))), $sum(1, Pos)) & ![Board4: map_int_int] : ((~($lesseq(0, Board) & eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board4))), tb2t1(mk_array1(int, Board, t2tb2(Board3))), $sum(1, Pos)) & ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board4))), tb2t1(mk_array1(int, B, t2tb2(B1))), $sum(1, Pos))) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~(B = N))))) | (eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board4))), tb2t1(mk_array1(int, Board, t2tb2(Board1))), Pos) & ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~(B = N)) | (~eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board4))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos)) | (~($lesseq(0, tb2t(get(int, int, t2tb2(B1), t2tb(Pos)))) & (~$lesseq(I, $sum(-1, tb2t(get(int, int, t2tb2(B1), t2tb(Pos))))))))))) & ![Board4: map_int_int] : ((~($lesseq(0, Board) & solution1(tb2t1(mk_array1(int, Board, t2tb2(Board4))), N))) | solution1(tb2t1(mk_array1(int, Board, t2tb2(Board4))), N)))) & ((Result = true1) | (eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board3))), tb2t1(mk_array1(int, Board, t2tb2(Board1))), Pos) & ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board3))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~(B = N)) | (~($lesseq(0, tb2t(get(int, int, t2tb2(B1), t2tb(Pos)))) & (~$lesseq(I, $sum(-1, tb2t(get(int, int, t2tb2(B1), t2tb(Pos))))))))))))))))) & ((~(eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board2))), tb2t1(mk_array1(int, Board, t2tb2(Board1))), Pos) & ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board2))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos)) | (~(B = N)) | (~($lesseq(0, tb2t(get(int, int, t2tb2(B1), t2tb(Pos)))) & (~$lesseq(N, tb2t(get(int, int, t2tb2(B1), t2tb(Pos)))))))))) | ($lesseq(0, Board) & eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board2))), tb2t1(mk_array1(int, Board, t2tb2(Board1))), Pos) & ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board2))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos)) | (~(B = N)))))))))))))),
% 0.81/0.78 inference(rewrite,[status(thm)],[])).
% 0.81/0.78 tff(13,plain,
% 0.81/0.78 ((~![Board: $int, Board1: map_int_int, N: $int, Pos: $int] : ((((($lesseq(0, Board) & (Board = N)) & $lesseq(0, Pos)) & $lesseq(Pos, N)) & solution1(tb2t1(mk_array1(int, Board, t2tb2(Board1))), Pos)) => (((Pos = N) => solution1(tb2t1(mk_array1(int, Board, t2tb2(Board1))), N)) & ((~(Pos = N)) => (($less($difference(N, 1), 0) => (eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board1))), tb2t1(mk_array1(int, Board, t2tb2(Board1))), Pos) & ![B: $int, B1: map_int_int] : ((B = N) => (is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N) => (eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board1))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos) => (~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N))))))) & ($lesseq(0, $difference(N, 1)) => ((eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board1))), tb2t1(mk_array1(int, Board, t2tb2(Board1))), Pos) & ![B: $int, B1: map_int_int] : ((B = N) => (is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N) => (eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board1))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos) => (($lesseq(0, tb2t(get(int, int, t2tb2(B1), t2tb(Pos)))) & $less(tb2t(get(int, int, t2tb2(B1), t2tb(Pos))), 0)) => (~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N))))))) & ![Board2: map_int_int] : (![I: $int] : (($lesseq(0, I) & $lesseq(I, $difference(N, 1))) => ((eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board2))), tb2t1(mk_array1(int, Board, t2tb2(Board1))), Pos) & ![B: $int, B1: map_int_int] : ((B = N) => (is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N) => (eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board2))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos) => (($lesseq(0, tb2t(get(int, int, t2tb2(B1), t2tb(Pos)))) & $less(tb2t(get(int, int, t2tb2(B1), t2tb(Pos))), I)) => (~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N))))))) => ((($lesseq(0, Board) & $lesseq(0, Pos)) & $less(Pos, Board)) & ![Board3: map_int_int] : (($lesseq(0, Board) & (Board3 = tb2t2(set(int, int, t2tb2(Board2), t2tb(Pos), t2tb(I))))) => (($lesseq(0, Pos) & $less(Pos, Board)) & ![Result: bool1] : (((Result = true1) <=> is_consistent1(tb2t1(mk_array1(int, Board, t2tb2(Board3))), Pos)) => (((Result = true1) => ((((((($lesseq(0, $difference(N, Pos)) & $less($difference(N, $sum(Pos, 1)), $difference(N, Pos))) & (Board = N)) & $lesseq(0, $sum(Pos, 1))) & $lesseq($sum(Pos, 1), N)) & solution1(tb2t1(mk_array1(int, Board, t2tb2(Board3))), $sum(Pos, 1))) & ![Board4: map_int_int] : ((($lesseq(0, Board) & eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board4))), tb2t1(mk_array1(int, Board, t2tb2(Board3))), $sum(Pos, 1))) & ![B: $int, B1: map_int_int] : ((B = N) => (is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N) => (eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board4))), tb2t1(mk_array1(int, B, t2tb2(B1))), $sum(Pos, 1)) => (~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)))))) => (eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board4))), tb2t1(mk_array1(int, Board, t2tb2(Board1))), Pos) & ![B: $int, B1: map_int_int] : ((B = N) => (is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N) => (eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board4))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos) => (($lesseq(0, tb2t(get(int, int, t2tb2(B1), t2tb(Pos)))) & $less(tb2t(get(int, int, t2tb2(B1), t2tb(Pos))), $sum(I, 1))) => (~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N))))))))) & ![Board4: map_int_int] : (($lesseq(0, Board) & solution1(tb2t1(mk_array1(int, Board, t2tb2(Board4))), N)) => solution1(tb2t1(mk_array1(int, Board, t2tb2(Board4))), N)))) & ((~(Result = true1)) => (eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board3))), tb2t1(mk_array1(int, Board, t2tb2(Board1))), Pos) & ![B: $int, B1: map_int_int] : ((B = N) => (is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N) => (eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board3))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos) => (($lesseq(0, tb2t(get(int, int, t2tb2(B1), t2tb(Pos)))) & $less(tb2t(get(int, int, t2tb2(B1), t2tb(Pos))), $sum(I, 1))) => (~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N))))))))))))))) & ((eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board2))), tb2t1(mk_array1(int, Board, t2tb2(Board1))), Pos) & ![B: $int, B1: map_int_int] : ((B = N) => (is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N) => (eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board2))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos) => (($lesseq(0, tb2t(get(int, int, t2tb2(B1), t2tb(Pos)))) & $less(tb2t(get(int, int, t2tb2(B1), t2tb(Pos))), $sum($difference(N, 1), 1))) => (~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N))))))) => (($lesseq(0, Board) & eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board2))), tb2t1(mk_array1(int, Board, t2tb2(Board1))), Pos)) & ![B: $int, B1: map_int_int] : ((B = N) => (is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N) => (eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board2))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos) => (~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N))))))))))))))) <=> (~![Board: $int, Board1: map_int_int, N: $int, Pos: $int] : ((~($lesseq(0, Board) & (Board = N) & $lesseq(0, Pos) & $lesseq(Pos, N) & solution1(tb2t1(mk_array1(int, Board, t2tb2(Board1))), Pos))) | (((~(Pos = N)) | solution1(tb2t1(mk_array1(int, Board, t2tb2(Board1))), N)) & ((Pos = N) | (($lesseq(1, N) | (eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board1))), tb2t1(mk_array1(int, Board, t2tb2(Board1))), Pos) & ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board1))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~(B = N))))) & ((~$lesseq(1, N)) | (eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board1))), tb2t1(mk_array1(int, Board, t2tb2(Board1))), Pos) & ![Board2: map_int_int] : (![I: $int] : ((~(eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board2))), tb2t1(mk_array1(int, Board, t2tb2(Board1))), Pos) & ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board2))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~(B = N)) | (~($lesseq(0, tb2t(get(int, int, t2tb2(B1), t2tb(Pos)))) & (~$lesseq(I, tb2t(get(int, int, t2tb2(B1), t2tb(Pos)))))))))) | (~($lesseq(0, I) & $lesseq(I, $sum(-1, N)))) | ($lesseq(0, Board) & $lesseq(0, Pos) & (~$lesseq(Board, Pos)) & ![Board3: map_int_int] : ((~($lesseq(0, Board) & (Board3 = tb2t2(set(int, int, t2tb2(Board2), t2tb(Pos), t2tb(I)))))) | ($lesseq(0, Pos) & (~$lesseq(Board, Pos)) & ![Result: bool1] : (((~(Result = true1)) <=> is_consistent1(tb2t1(mk_array1(int, Board, t2tb2(Board3))), Pos)) | (((~(Result = true1)) | ($lesseq(0, $sum(N, $product(-1, Pos))) & (Board = N) & $lesseq(-1, Pos) & $lesseq(Pos, $sum(-1, N)) & solution1(tb2t1(mk_array1(int, Board, t2tb2(Board3))), $sum(1, Pos)) & ![Board4: map_int_int] : ((~($lesseq(0, Board) & eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board4))), tb2t1(mk_array1(int, Board, t2tb2(Board3))), $sum(1, Pos)) & ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board4))), tb2t1(mk_array1(int, B, t2tb2(B1))), $sum(1, Pos))) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~(B = N))))) | (eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board4))), tb2t1(mk_array1(int, Board, t2tb2(Board1))), Pos) & ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~(B = N)) | (~eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board4))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos)) | (~($lesseq(0, tb2t(get(int, int, t2tb2(B1), t2tb(Pos)))) & (~$lesseq(I, $sum(-1, tb2t(get(int, int, t2tb2(B1), t2tb(Pos))))))))))) & ![Board4: map_int_int] : ((~($lesseq(0, Board) & solution1(tb2t1(mk_array1(int, Board, t2tb2(Board4))), N))) | solution1(tb2t1(mk_array1(int, Board, t2tb2(Board4))), N)))) & ((Result = true1) | (eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board3))), tb2t1(mk_array1(int, Board, t2tb2(Board1))), Pos) & ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board3))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~(B = N)) | (~($lesseq(0, tb2t(get(int, int, t2tb2(B1), t2tb(Pos)))) & (~$lesseq(I, $sum(-1, tb2t(get(int, int, t2tb2(B1), t2tb(Pos))))))))))))))))) & ((~(eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board2))), tb2t1(mk_array1(int, Board, t2tb2(Board1))), Pos) & ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board2))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos)) | (~(B = N)) | (~($lesseq(0, tb2t(get(int, int, t2tb2(B1), t2tb(Pos)))) & (~$lesseq(N, tb2t(get(int, int, t2tb2(B1), t2tb(Pos)))))))))) | ($lesseq(0, Board) & eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board2))), tb2t1(mk_array1(int, Board, t2tb2(Board1))), Pos) & ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board2))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos)) | (~(B = N)))))))))))))),
% 0.81/0.78 inference(rewrite,[status(thm)],[])).
% 0.81/0.78 tff(14,axiom,(~![Board: $int, Board1: map_int_int, N: $int, Pos: $int] : ((((($lesseq(0, Board) & (Board = N)) & $lesseq(0, Pos)) & $lesseq(Pos, N)) & solution1(tb2t1(mk_array1(int, Board, t2tb2(Board1))), Pos)) => (((Pos = N) => solution1(tb2t1(mk_array1(int, Board, t2tb2(Board1))), N)) & ((~(Pos = N)) => (($less($difference(N, 1), 0) => (eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board1))), tb2t1(mk_array1(int, Board, t2tb2(Board1))), Pos) & ![B: $int, B1: map_int_int] : ((B = N) => (is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N) => (eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board1))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos) => (~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N))))))) & ($lesseq(0, $difference(N, 1)) => ((eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board1))), tb2t1(mk_array1(int, Board, t2tb2(Board1))), Pos) & ![B: $int, B1: map_int_int] : ((B = N) => (is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N) => (eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board1))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos) => (($lesseq(0, tb2t(get(int, int, t2tb2(B1), t2tb(Pos)))) & $less(tb2t(get(int, int, t2tb2(B1), t2tb(Pos))), 0)) => (~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N))))))) & ![Board2: map_int_int] : (![I: $int] : (($lesseq(0, I) & $lesseq(I, $difference(N, 1))) => ((eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board2))), tb2t1(mk_array1(int, Board, t2tb2(Board1))), Pos) & ![B: $int, B1: map_int_int] : ((B = N) => (is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N) => (eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board2))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos) => (($lesseq(0, tb2t(get(int, int, t2tb2(B1), t2tb(Pos)))) & $less(tb2t(get(int, int, t2tb2(B1), t2tb(Pos))), I)) => (~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N))))))) => ((($lesseq(0, Board) & $lesseq(0, Pos)) & $less(Pos, Board)) & ![Board3: map_int_int] : (($lesseq(0, Board) & (Board3 = tb2t2(set(int, int, t2tb2(Board2), t2tb(Pos), t2tb(I))))) => (($lesseq(0, Pos) & $less(Pos, Board)) & ![Result: bool1] : (((Result = true1) <=> is_consistent1(tb2t1(mk_array1(int, Board, t2tb2(Board3))), Pos)) => (((Result = true1) => ((((((($lesseq(0, $difference(N, Pos)) & $less($difference(N, $sum(Pos, 1)), $difference(N, Pos))) & (Board = N)) & $lesseq(0, $sum(Pos, 1))) & $lesseq($sum(Pos, 1), N)) & solution1(tb2t1(mk_array1(int, Board, t2tb2(Board3))), $sum(Pos, 1))) & ![Board4: map_int_int] : ((($lesseq(0, Board) & eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board4))), tb2t1(mk_array1(int, Board, t2tb2(Board3))), $sum(Pos, 1))) & ![B: $int, B1: map_int_int] : ((B = N) => (is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N) => (eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board4))), tb2t1(mk_array1(int, B, t2tb2(B1))), $sum(Pos, 1)) => (~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)))))) => (eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board4))), tb2t1(mk_array1(int, Board, t2tb2(Board1))), Pos) & ![B: $int, B1: map_int_int] : ((B = N) => (is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N) => (eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board4))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos) => (($lesseq(0, tb2t(get(int, int, t2tb2(B1), t2tb(Pos)))) & $less(tb2t(get(int, int, t2tb2(B1), t2tb(Pos))), $sum(I, 1))) => (~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N))))))))) & ![Board4: map_int_int] : (($lesseq(0, Board) & solution1(tb2t1(mk_array1(int, Board, t2tb2(Board4))), N)) => solution1(tb2t1(mk_array1(int, Board, t2tb2(Board4))), N)))) & ((~(Result = true1)) => (eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board3))), tb2t1(mk_array1(int, Board, t2tb2(Board1))), Pos) & ![B: $int, B1: map_int_int] : ((B = N) => (is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N) => (eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board3))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos) => (($lesseq(0, tb2t(get(int, int, t2tb2(B1), t2tb(Pos)))) & $less(tb2t(get(int, int, t2tb2(B1), t2tb(Pos))), $sum(I, 1))) => (~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N))))))))))))))) & ((eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board2))), tb2t1(mk_array1(int, Board, t2tb2(Board1))), Pos) & ![B: $int, B1: map_int_int] : ((B = N) => (is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N) => (eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board2))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos) => (($lesseq(0, tb2t(get(int, int, t2tb2(B1), t2tb(Pos)))) & $less(tb2t(get(int, int, t2tb2(B1), t2tb(Pos))), $sum($difference(N, 1), 1))) => (~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N))))))) => (($lesseq(0, Board) & eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board2))), tb2t1(mk_array1(int, Board, t2tb2(Board1))), Pos)) & ![B: $int, B1: map_int_int] : ((B = N) => (is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N) => (eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board2))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos) => (~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N))))))))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','wP_parameter_bt_queens')).
% 0.81/0.79 tff(15,plain,
% 0.81/0.79 (~![Board: $int, Board1: map_int_int, N: $int, Pos: $int] : ((~($lesseq(0, Board) & (Board = N) & $lesseq(0, Pos) & $lesseq(Pos, N) & solution1(tb2t1(mk_array1(int, Board, t2tb2(Board1))), Pos))) | (((~(Pos = N)) | solution1(tb2t1(mk_array1(int, Board, t2tb2(Board1))), N)) & ((Pos = N) | (($lesseq(1, N) | (eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board1))), tb2t1(mk_array1(int, Board, t2tb2(Board1))), Pos) & ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board1))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~(B = N))))) & ((~$lesseq(1, N)) | (eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board1))), tb2t1(mk_array1(int, Board, t2tb2(Board1))), Pos) & ![Board2: map_int_int] : (![I: $int] : ((~(eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board2))), tb2t1(mk_array1(int, Board, t2tb2(Board1))), Pos) & ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board2))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~(B = N)) | (~($lesseq(0, tb2t(get(int, int, t2tb2(B1), t2tb(Pos)))) & (~$lesseq(I, tb2t(get(int, int, t2tb2(B1), t2tb(Pos)))))))))) | (~($lesseq(0, I) & $lesseq(I, $sum(-1, N)))) | ($lesseq(0, Board) & $lesseq(0, Pos) & (~$lesseq(Board, Pos)) & ![Board3: map_int_int] : ((~($lesseq(0, Board) & (Board3 = tb2t2(set(int, int, t2tb2(Board2), t2tb(Pos), t2tb(I)))))) | ($lesseq(0, Pos) & (~$lesseq(Board, Pos)) & ![Result: bool1] : (((~(Result = true1)) <=> is_consistent1(tb2t1(mk_array1(int, Board, t2tb2(Board3))), Pos)) | (((~(Result = true1)) | ($lesseq(0, $sum(N, $product(-1, Pos))) & (Board = N) & $lesseq(-1, Pos) & $lesseq(Pos, $sum(-1, N)) & solution1(tb2t1(mk_array1(int, Board, t2tb2(Board3))), $sum(1, Pos)) & ![Board4: map_int_int] : ((~($lesseq(0, Board) & eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board4))), tb2t1(mk_array1(int, Board, t2tb2(Board3))), $sum(1, Pos)) & ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board4))), tb2t1(mk_array1(int, B, t2tb2(B1))), $sum(1, Pos))) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~(B = N))))) | (eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board4))), tb2t1(mk_array1(int, Board, t2tb2(Board1))), Pos) & ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~(B = N)) | (~eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board4))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos)) | (~($lesseq(0, tb2t(get(int, int, t2tb2(B1), t2tb(Pos)))) & (~$lesseq(I, $sum(-1, tb2t(get(int, int, t2tb2(B1), t2tb(Pos))))))))))) & ![Board4: map_int_int] : ((~($lesseq(0, Board) & solution1(tb2t1(mk_array1(int, Board, t2tb2(Board4))), N))) | solution1(tb2t1(mk_array1(int, Board, t2tb2(Board4))), N)))) & ((Result = true1) | (eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board3))), tb2t1(mk_array1(int, Board, t2tb2(Board1))), Pos) & ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board3))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~(B = N)) | (~($lesseq(0, tb2t(get(int, int, t2tb2(B1), t2tb(Pos)))) & (~$lesseq(I, $sum(-1, tb2t(get(int, int, t2tb2(B1), t2tb(Pos))))))))))))))))) & ((~(eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board2))), tb2t1(mk_array1(int, Board, t2tb2(Board1))), Pos) & ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board2))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos)) | (~(B = N)) | (~($lesseq(0, tb2t(get(int, int, t2tb2(B1), t2tb(Pos)))) & (~$lesseq(N, tb2t(get(int, int, t2tb2(B1), t2tb(Pos)))))))))) | ($lesseq(0, Board) & eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board2))), tb2t1(mk_array1(int, Board, t2tb2(Board1))), Pos) & ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board2))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos)) | (~(B = N))))))))))))),
% 0.81/0.79 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.81/0.79 tff(16,plain,
% 0.81/0.79 (~![Board: $int, Board1: map_int_int, N: $int, Pos: $int] : ((~($lesseq(0, Board) & (Board = N) & $lesseq(0, Pos) & $lesseq(Pos, N) & solution1(tb2t1(mk_array1(int, Board, t2tb2(Board1))), Pos))) | (((~(Pos = N)) | solution1(tb2t1(mk_array1(int, Board, t2tb2(Board1))), N)) & ((Pos = N) | (($lesseq(1, N) | (eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board1))), tb2t1(mk_array1(int, Board, t2tb2(Board1))), Pos) & ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board1))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~(B = N))))) & ((~$lesseq(1, N)) | (eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board1))), tb2t1(mk_array1(int, Board, t2tb2(Board1))), Pos) & ![Board2: map_int_int] : (![I: $int] : ((~(eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board2))), tb2t1(mk_array1(int, Board, t2tb2(Board1))), Pos) & ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board2))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~(B = N)) | (~($lesseq(0, tb2t(get(int, int, t2tb2(B1), t2tb(Pos)))) & (~$lesseq(I, tb2t(get(int, int, t2tb2(B1), t2tb(Pos)))))))))) | (~($lesseq(0, I) & $lesseq(I, $sum(-1, N)))) | ($lesseq(0, Board) & $lesseq(0, Pos) & (~$lesseq(Board, Pos)) & ![Board3: map_int_int] : ((~($lesseq(0, Board) & (Board3 = tb2t2(set(int, int, t2tb2(Board2), t2tb(Pos), t2tb(I)))))) | ($lesseq(0, Pos) & (~$lesseq(Board, Pos)) & ![Result: bool1] : (((~(Result = true1)) <=> is_consistent1(tb2t1(mk_array1(int, Board, t2tb2(Board3))), Pos)) | (((~(Result = true1)) | ($lesseq(0, $sum(N, $product(-1, Pos))) & (Board = N) & $lesseq(-1, Pos) & $lesseq(Pos, $sum(-1, N)) & solution1(tb2t1(mk_array1(int, Board, t2tb2(Board3))), $sum(1, Pos)) & ![Board4: map_int_int] : ((~($lesseq(0, Board) & eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board4))), tb2t1(mk_array1(int, Board, t2tb2(Board3))), $sum(1, Pos)) & ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board4))), tb2t1(mk_array1(int, B, t2tb2(B1))), $sum(1, Pos))) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~(B = N))))) | (eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board4))), tb2t1(mk_array1(int, Board, t2tb2(Board1))), Pos) & ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~(B = N)) | (~eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board4))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos)) | (~($lesseq(0, tb2t(get(int, int, t2tb2(B1), t2tb(Pos)))) & (~$lesseq(I, $sum(-1, tb2t(get(int, int, t2tb2(B1), t2tb(Pos))))))))))) & ![Board4: map_int_int] : ((~($lesseq(0, Board) & solution1(tb2t1(mk_array1(int, Board, t2tb2(Board4))), N))) | solution1(tb2t1(mk_array1(int, Board, t2tb2(Board4))), N)))) & ((Result = true1) | (eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board3))), tb2t1(mk_array1(int, Board, t2tb2(Board1))), Pos) & ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board3))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~(B = N)) | (~($lesseq(0, tb2t(get(int, int, t2tb2(B1), t2tb(Pos)))) & (~$lesseq(I, $sum(-1, tb2t(get(int, int, t2tb2(B1), t2tb(Pos))))))))))))))))) & ((~(eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board2))), tb2t1(mk_array1(int, Board, t2tb2(Board1))), Pos) & ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board2))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos)) | (~(B = N)) | (~($lesseq(0, tb2t(get(int, int, t2tb2(B1), t2tb(Pos)))) & (~$lesseq(N, tb2t(get(int, int, t2tb2(B1), t2tb(Pos)))))))))) | ($lesseq(0, Board) & eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board2))), tb2t1(mk_array1(int, Board, t2tb2(Board1))), Pos) & ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board2))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos)) | (~(B = N))))))))))))),
% 0.81/0.79 inference(modus_ponens,[status(thm)],[15, 12])).
% 0.81/0.79 tff(17,plain,
% 0.81/0.79 (~![Board: $int, Board1: map_int_int, N: $int, Pos: $int] : ((~($lesseq(0, Board) & (Board = N) & $lesseq(0, Pos) & $lesseq(Pos, N) & solution1(tb2t1(mk_array1(int, Board, t2tb2(Board1))), Pos))) | (((~(Pos = N)) | solution1(tb2t1(mk_array1(int, Board, t2tb2(Board1))), N)) & ((Pos = N) | (($lesseq(1, N) | (eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board1))), tb2t1(mk_array1(int, Board, t2tb2(Board1))), Pos) & ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board1))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~(B = N))))) & ((~$lesseq(1, N)) | (eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board1))), tb2t1(mk_array1(int, Board, t2tb2(Board1))), Pos) & ![Board2: map_int_int] : (![I: $int] : ((~(eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board2))), tb2t1(mk_array1(int, Board, t2tb2(Board1))), Pos) & ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board2))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~(B = N)) | (~($lesseq(0, tb2t(get(int, int, t2tb2(B1), t2tb(Pos)))) & (~$lesseq(I, tb2t(get(int, int, t2tb2(B1), t2tb(Pos)))))))))) | (~($lesseq(0, I) & $lesseq(I, $sum(-1, N)))) | ($lesseq(0, Board) & $lesseq(0, Pos) & (~$lesseq(Board, Pos)) & ![Board3: map_int_int] : ((~($lesseq(0, Board) & (Board3 = tb2t2(set(int, int, t2tb2(Board2), t2tb(Pos), t2tb(I)))))) | ($lesseq(0, Pos) & (~$lesseq(Board, Pos)) & ![Result: bool1] : (((~(Result = true1)) <=> is_consistent1(tb2t1(mk_array1(int, Board, t2tb2(Board3))), Pos)) | (((~(Result = true1)) | ($lesseq(0, $sum(N, $product(-1, Pos))) & (Board = N) & $lesseq(-1, Pos) & $lesseq(Pos, $sum(-1, N)) & solution1(tb2t1(mk_array1(int, Board, t2tb2(Board3))), $sum(1, Pos)) & ![Board4: map_int_int] : ((~($lesseq(0, Board) & eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board4))), tb2t1(mk_array1(int, Board, t2tb2(Board3))), $sum(1, Pos)) & ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board4))), tb2t1(mk_array1(int, B, t2tb2(B1))), $sum(1, Pos))) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~(B = N))))) | (eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board4))), tb2t1(mk_array1(int, Board, t2tb2(Board1))), Pos) & ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~(B = N)) | (~eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board4))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos)) | (~($lesseq(0, tb2t(get(int, int, t2tb2(B1), t2tb(Pos)))) & (~$lesseq(I, $sum(-1, tb2t(get(int, int, t2tb2(B1), t2tb(Pos))))))))))) & ![Board4: map_int_int] : ((~($lesseq(0, Board) & solution1(tb2t1(mk_array1(int, Board, t2tb2(Board4))), N))) | solution1(tb2t1(mk_array1(int, Board, t2tb2(Board4))), N)))) & ((Result = true1) | (eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board3))), tb2t1(mk_array1(int, Board, t2tb2(Board1))), Pos) & ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board3))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~(B = N)) | (~($lesseq(0, tb2t(get(int, int, t2tb2(B1), t2tb(Pos)))) & (~$lesseq(I, $sum(-1, tb2t(get(int, int, t2tb2(B1), t2tb(Pos))))))))))))))))) & ((~(eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board2))), tb2t1(mk_array1(int, Board, t2tb2(Board1))), Pos) & ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board2))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos)) | (~(B = N)) | (~($lesseq(0, tb2t(get(int, int, t2tb2(B1), t2tb(Pos)))) & (~$lesseq(N, tb2t(get(int, int, t2tb2(B1), t2tb(Pos)))))))))) | ($lesseq(0, Board) & eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board2))), tb2t1(mk_array1(int, Board, t2tb2(Board1))), Pos) & ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board2))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos)) | (~(B = N))))))))))))),
% 0.81/0.79 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.81/0.79 tff(18,plain,
% 0.81/0.79 (~![Board: $int, Board1: map_int_int, N: $int, Pos: $int] : ((~($lesseq(0, Board) & (Board = N) & $lesseq(0, Pos) & $lesseq(Pos, N) & solution1(tb2t1(mk_array1(int, Board, t2tb2(Board1))), Pos))) | (((~(Pos = N)) | solution1(tb2t1(mk_array1(int, Board, t2tb2(Board1))), N)) & ((Pos = N) | (($lesseq(1, N) | (eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board1))), tb2t1(mk_array1(int, Board, t2tb2(Board1))), Pos) & ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board1))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~(B = N))))) & ((~$lesseq(1, N)) | (eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board1))), tb2t1(mk_array1(int, Board, t2tb2(Board1))), Pos) & ![Board2: map_int_int] : (![I: $int] : ((~(eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board2))), tb2t1(mk_array1(int, Board, t2tb2(Board1))), Pos) & ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board2))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~(B = N)) | (~($lesseq(0, tb2t(get(int, int, t2tb2(B1), t2tb(Pos)))) & (~$lesseq(I, tb2t(get(int, int, t2tb2(B1), t2tb(Pos)))))))))) | (~($lesseq(0, I) & $lesseq(I, $sum(-1, N)))) | ($lesseq(0, Board) & $lesseq(0, Pos) & (~$lesseq(Board, Pos)) & ![Board3: map_int_int] : ((~($lesseq(0, Board) & (Board3 = tb2t2(set(int, int, t2tb2(Board2), t2tb(Pos), t2tb(I)))))) | ($lesseq(0, Pos) & (~$lesseq(Board, Pos)) & ![Result: bool1] : (((~(Result = true1)) <=> is_consistent1(tb2t1(mk_array1(int, Board, t2tb2(Board3))), Pos)) | (((~(Result = true1)) | ($lesseq(0, $sum(N, $product(-1, Pos))) & (Board = N) & $lesseq(-1, Pos) & $lesseq(Pos, $sum(-1, N)) & solution1(tb2t1(mk_array1(int, Board, t2tb2(Board3))), $sum(1, Pos)) & ![Board4: map_int_int] : ((~($lesseq(0, Board) & eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board4))), tb2t1(mk_array1(int, Board, t2tb2(Board3))), $sum(1, Pos)) & ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board4))), tb2t1(mk_array1(int, B, t2tb2(B1))), $sum(1, Pos))) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~(B = N))))) | (eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board4))), tb2t1(mk_array1(int, Board, t2tb2(Board1))), Pos) & ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~(B = N)) | (~eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board4))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos)) | (~($lesseq(0, tb2t(get(int, int, t2tb2(B1), t2tb(Pos)))) & (~$lesseq(I, $sum(-1, tb2t(get(int, int, t2tb2(B1), t2tb(Pos))))))))))) & ![Board4: map_int_int] : ((~($lesseq(0, Board) & solution1(tb2t1(mk_array1(int, Board, t2tb2(Board4))), N))) | solution1(tb2t1(mk_array1(int, Board, t2tb2(Board4))), N)))) & ((Result = true1) | (eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board3))), tb2t1(mk_array1(int, Board, t2tb2(Board1))), Pos) & ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board3))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~(B = N)) | (~($lesseq(0, tb2t(get(int, int, t2tb2(B1), t2tb(Pos)))) & (~$lesseq(I, $sum(-1, tb2t(get(int, int, t2tb2(B1), t2tb(Pos))))))))))))))))) & ((~(eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board2))), tb2t1(mk_array1(int, Board, t2tb2(Board1))), Pos) & ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board2))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos)) | (~(B = N)) | (~($lesseq(0, tb2t(get(int, int, t2tb2(B1), t2tb(Pos)))) & (~$lesseq(N, tb2t(get(int, int, t2tb2(B1), t2tb(Pos)))))))))) | ($lesseq(0, Board) & eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board2))), tb2t1(mk_array1(int, Board, t2tb2(Board1))), Pos) & ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board2))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos)) | (~(B = N))))))))))))),
% 0.81/0.79 inference(modus_ponens,[status(thm)],[17, 12])).
% 0.81/0.79 tff(19,plain,
% 0.81/0.79 (~![Board: $int, Board1: map_int_int, N: $int, Pos: $int] : ((~($greatereq(Board, 0) & ($sum(Board, $product(-1, N)) = 0) & $greatereq(Pos, 0) & $lesseq($sum(Pos, $product(-1, N)), 0) & solution1(tb2t1(mk_array1(int, Board, t2tb2(Board1))), Pos))) | (((~($sum(Pos, $product(-1, N)) = 0)) | solution1(tb2t1(mk_array1(int, Board, t2tb2(Board1))), N)) & (($sum(Pos, $product(-1, N)) = 0) | (($greatereq(N, 1) | (eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board1))), tb2t1(mk_array1(int, Board, t2tb2(Board1))), Pos) & ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board1))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~($sum(B, $product(-1, N)) = 0))))) & ((~$greatereq(N, 1)) | (eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board1))), tb2t1(mk_array1(int, Board, t2tb2(Board1))), Pos) & ![Board2: map_int_int] : (![I: $int] : ((~($greatereq(I, 0) & $lesseq($sum(I, $product(-1, N)), -1))) | (~(eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board2))), tb2t1(mk_array1(int, Board, t2tb2(Board1))), Pos) & ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~($greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos))), 0) & (~$lesseq($sum(I, $product(-1, tb2t(get(int, int, t2tb2(B1), t2tb(Pos))))), 0)))) | (~eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board2))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~($sum(B, $product(-1, N)) = 0))))) | ($greatereq(Board, 0) & $greatereq(Pos, 0) & (~$lesseq($sum(Board, $product(-1, Pos)), 0)) & ![Board3: map_int_int] : ((~($greatereq(Board, 0) & (Board3 = tb2t2(set(int, int, t2tb2(Board2), t2tb(Pos), t2tb(I)))))) | ($greatereq(Pos, 0) & (~$lesseq($sum(Board, $product(-1, Pos)), 0)) & ![Result: bool1] : (((~(Result = true1)) <=> is_consistent1(tb2t1(mk_array1(int, Board, t2tb2(Board3))), Pos)) | (((~(Result = true1)) | ($greatereq($sum(N, $product(-1, Pos)), 0) & ($sum(Board, $product(-1, N)) = 0) & $greatereq(Pos, -1) & $lesseq($sum(Pos, $product(-1, N)), -1) & solution1(tb2t1(mk_array1(int, Board, t2tb2(Board3))), $sum(1, Pos)) & ![Board4: map_int_int] : ((~($greatereq(Board, 0) & eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board4))), tb2t1(mk_array1(int, Board, t2tb2(Board3))), $sum(1, Pos)) & ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board4))), tb2t1(mk_array1(int, B, t2tb2(B1))), $sum(1, Pos))) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~($sum(B, $product(-1, N)) = 0))))) | (eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board4))), tb2t1(mk_array1(int, Board, t2tb2(Board1))), Pos) & ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~($greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos))), 0) & (~$lesseq($sum(I, $product(-1, tb2t(get(int, int, t2tb2(B1), t2tb(Pos))))), -1)))) | (~eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board4))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos)) | (~($sum(B, $product(-1, N)) = 0))))) & ![Board4: map_int_int] : ((~($greatereq(Board, 0) & solution1(tb2t1(mk_array1(int, Board, t2tb2(Board4))), N))) | solution1(tb2t1(mk_array1(int, Board, t2tb2(Board4))), N)))) & ((Result = true1) | (eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board3))), tb2t1(mk_array1(int, Board, t2tb2(Board1))), Pos) & ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~($greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos))), 0) & (~$lesseq($sum(I, $product(-1, tb2t(get(int, int, t2tb2(B1), t2tb(Pos))))), -1)))) | (~eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board3))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~($sum(B, $product(-1, N)) = 0))))))))))) & ((~(eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board2))), tb2t1(mk_array1(int, Board, t2tb2(Board1))), Pos) & ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~($greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos))), 0) & (~$lesseq($sum(N, $product(-1, tb2t(get(int, int, t2tb2(B1), t2tb(Pos))))), 0)))) | (~eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board2))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos)) | (~($sum(B, $product(-1, N)) = 0))))) | ($greatereq(Board, 0) & eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board2))), tb2t1(mk_array1(int, Board, t2tb2(Board1))), Pos) & ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board2))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos)) | (~($sum(B, $product(-1, N)) = 0))))))))))))),
% 0.81/0.79 inference(modus_ponens,[status(thm)],[18, 11])).
% 0.81/0.79 tff(20,plain,
% 0.81/0.79 (~![Board: $int, Board1: map_int_int, N: $int, Pos: $int] : ((~($greatereq(Board, 0) & ($sum(N, $product(-1, Board)) = 0) & $greatereq(Pos, 0) & $greatereq($sum(N, $product(-1, Pos)), 0) & solution1(tb2t1(mk_array1(int, Board, t2tb2(Board1))), Pos))) | (((~($sum(N, $product(-1, Pos)) = 0)) | solution1(tb2t1(mk_array1(int, Board, t2tb2(Board1))), N)) & (($sum(N, $product(-1, Pos)) = 0) | (($greatereq(N, 1) | (eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board1))), tb2t1(mk_array1(int, Board, t2tb2(Board1))), Pos) & ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board1))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~($sum(B, $product(-1, N)) = 0))))) & ((~$greatereq(N, 1)) | (eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board1))), tb2t1(mk_array1(int, Board, t2tb2(Board1))), Pos) & ![Board2: map_int_int] : (![I: $int] : ((~($greatereq(I, 0) & $lesseq($sum(I, $product(-1, N)), -1))) | (~(eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board2))), tb2t1(mk_array1(int, Board, t2tb2(Board1))), Pos) & ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~($greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos))), 0) & (~$lesseq($sum(I, $product(-1, tb2t(get(int, int, t2tb2(B1), t2tb(Pos))))), 0)))) | (~eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board2))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~($sum(B, $product(-1, N)) = 0))))) | ($greatereq(Board, 0) & $greatereq(Pos, 0) & (~$greatereq($sum(Pos, $product(-1, Board)), 0)) & ![Board3: map_int_int] : ((~($greatereq(Board, 0) & (Board3 = tb2t2(set(int, int, t2tb2(Board2), t2tb(Pos), t2tb(I)))))) | ($greatereq(Pos, 0) & (~$greatereq($sum(Pos, $product(-1, Board)), 0)) & ![Result: bool1] : (((~(Result = true1)) <=> is_consistent1(tb2t1(mk_array1(int, Board, t2tb2(Board3))), Pos)) | (((~(Result = true1)) | ($lesseq($sum(Pos, $product(-1, N)), 0) & ($sum(N, $product(-1, Board)) = 0) & $greatereq(Pos, -1) & $lesseq($sum(Pos, $product(-1, N)), -1) & solution1(tb2t1(mk_array1(int, Board, t2tb2(Board3))), $sum(1, Pos)) & ![Board4: map_int_int] : ((~($greatereq(Board, 0) & eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board4))), tb2t1(mk_array1(int, Board, t2tb2(Board3))), $sum(1, Pos)) & ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board4))), tb2t1(mk_array1(int, B, t2tb2(B1))), $sum(1, Pos))) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~($sum(B, $product(-1, N)) = 0))))) | (eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board4))), tb2t1(mk_array1(int, Board, t2tb2(Board1))), Pos) & ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~($greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos))), 0) & (~$lesseq($sum(I, $product(-1, tb2t(get(int, int, t2tb2(B1), t2tb(Pos))))), -1)))) | (~eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board4))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos)) | (~($sum(B, $product(-1, N)) = 0))))) & ![Board4: map_int_int] : ((~($greatereq(Board, 0) & solution1(tb2t1(mk_array1(int, Board, t2tb2(Board4))), N))) | solution1(tb2t1(mk_array1(int, Board, t2tb2(Board4))), N)))) & ((Result = true1) | (eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board3))), tb2t1(mk_array1(int, Board, t2tb2(Board1))), Pos) & ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~($greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos))), 0) & (~$lesseq($sum(I, $product(-1, tb2t(get(int, int, t2tb2(B1), t2tb(Pos))))), -1)))) | (~eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board3))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~($sum(B, $product(-1, N)) = 0))))))))))) & ((~(eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board2))), tb2t1(mk_array1(int, Board, t2tb2(Board1))), Pos) & ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~($greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos))), 0) & (~$lesseq($sum(N, $product(-1, tb2t(get(int, int, t2tb2(B1), t2tb(Pos))))), 0)))) | (~eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board2))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos)) | (~($sum(B, $product(-1, N)) = 0))))) | ($greatereq(Board, 0) & eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board2))), tb2t1(mk_array1(int, Board, t2tb2(Board1))), Pos) & ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board2))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos)) | (~($sum(B, $product(-1, N)) = 0))))))))))))),
% 0.81/0.79 inference(modus_ponens,[status(thm)],[19, 10])).
% 0.81/0.79 tff(21,plain,
% 0.81/0.79 (~![Board: $int, Board1: map_int_int, N: $int, Pos: $int] : ((~($greatereq(Board, 0) & ($sum(N, $product(-1, Board)) = 0) & $greatereq(Pos, 0) & $greatereq($sum(N, $product(-1, Pos)), 0) & solution1(tb2t1(mk_array1(int, Board, t2tb2(Board1))), Pos))) | (((~($sum(N, $product(-1, Pos)) = 0)) | solution1(tb2t1(mk_array1(int, Board, t2tb2(Board1))), N)) & (($sum(N, $product(-1, Pos)) = 0) | (($greatereq(N, 1) | (eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board1))), tb2t1(mk_array1(int, Board, t2tb2(Board1))), Pos) & ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board1))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~($sum(B, $product(-1, N)) = 0))))) & ((~$greatereq(N, 1)) | (eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board1))), tb2t1(mk_array1(int, Board, t2tb2(Board1))), Pos) & ![Board2: map_int_int] : (![I: $int] : ((~($greatereq(I, 0) & $lesseq($sum(I, $product(-1, N)), -1))) | (~(eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board2))), tb2t1(mk_array1(int, Board, t2tb2(Board1))), Pos) & ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~($greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos))), 0) & (~$lesseq($sum(I, $product(-1, tb2t(get(int, int, t2tb2(B1), t2tb(Pos))))), 0)))) | (~eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board2))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~($sum(B, $product(-1, N)) = 0))))) | ($greatereq(Board, 0) & $greatereq(Pos, 0) & (~$greatereq($sum(Pos, $product(-1, Board)), 0)) & ![Board3: map_int_int] : ((~($greatereq(Board, 0) & (Board3 = tb2t2(set(int, int, t2tb2(Board2), t2tb(Pos), t2tb(I)))))) | ($greatereq(Pos, 0) & (~$greatereq($sum(Pos, $product(-1, Board)), 0)) & ![Result: bool1] : (((~(Result = true1)) <=> is_consistent1(tb2t1(mk_array1(int, Board, t2tb2(Board3))), Pos)) | (((~(Result = true1)) | ($lesseq($sum(Pos, $product(-1, N)), 0) & ($sum(N, $product(-1, Board)) = 0) & $greatereq(Pos, -1) & $lesseq($sum(Pos, $product(-1, N)), -1) & solution1(tb2t1(mk_array1(int, Board, t2tb2(Board3))), $sum(1, Pos)) & ![Board4: map_int_int] : ((~($greatereq(Board, 0) & eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board4))), tb2t1(mk_array1(int, Board, t2tb2(Board3))), $sum(1, Pos)) & ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board4))), tb2t1(mk_array1(int, B, t2tb2(B1))), $sum(1, Pos))) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~($sum(B, $product(-1, N)) = 0))))) | (eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board4))), tb2t1(mk_array1(int, Board, t2tb2(Board1))), Pos) & ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~($greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos))), 0) & (~$lesseq($sum(I, $product(-1, tb2t(get(int, int, t2tb2(B1), t2tb(Pos))))), -1)))) | (~eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board4))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos)) | (~($sum(B, $product(-1, N)) = 0))))) & ![Board4: map_int_int] : ((~($greatereq(Board, 0) & solution1(tb2t1(mk_array1(int, Board, t2tb2(Board4))), N))) | solution1(tb2t1(mk_array1(int, Board, t2tb2(Board4))), N)))) & ((Result = true1) | (eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board3))), tb2t1(mk_array1(int, Board, t2tb2(Board1))), Pos) & ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~($greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos))), 0) & (~$lesseq($sum(I, $product(-1, tb2t(get(int, int, t2tb2(B1), t2tb(Pos))))), -1)))) | (~eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board3))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~($sum(B, $product(-1, N)) = 0))))))))))) & ((~(eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board2))), tb2t1(mk_array1(int, Board, t2tb2(Board1))), Pos) & ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~($greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos))), 0) & (~$lesseq($sum(N, $product(-1, tb2t(get(int, int, t2tb2(B1), t2tb(Pos))))), 0)))) | (~eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board2))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos)) | (~($sum(B, $product(-1, N)) = 0))))) | ($greatereq(Board, 0) & eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board2))), tb2t1(mk_array1(int, Board, t2tb2(Board1))), Pos) & ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board2))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos)) | (~($sum(B, $product(-1, N)) = 0))))))))))))),
% 0.81/0.80 inference(modus_ponens,[status(thm)],[20, 9])).
% 0.81/0.80 tff(22,plain,
% 0.81/0.80 (~![Board: $int, Board1: map_int_int, N: $int, Pos: $int] : ((~($greatereq(Board, 0) & ($sum(N, $product(-1, Board)) = 0) & $greatereq(Pos, 0) & $greatereq($sum(N, $product(-1, Pos)), 0) & solution1(tb2t1(mk_array1(int, Board, t2tb2(Board1))), Pos))) | (((~($sum(N, $product(-1, Pos)) = 0)) | solution1(tb2t1(mk_array1(int, Board, t2tb2(Board1))), N)) & (($sum(N, $product(-1, Pos)) = 0) | (($greatereq(N, 1) | (eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board1))), tb2t1(mk_array1(int, Board, t2tb2(Board1))), Pos) & ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board1))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~($sum(B, $product(-1, N)) = 0))))) & ((~$greatereq(N, 1)) | (eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board1))), tb2t1(mk_array1(int, Board, t2tb2(Board1))), Pos) & ![Board2: map_int_int] : (![I: $int] : ((~($greatereq(I, 0) & $lesseq($sum(I, $product(-1, N)), -1))) | (~(eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board2))), tb2t1(mk_array1(int, Board, t2tb2(Board1))), Pos) & ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~($greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos))), 0) & (~$lesseq($sum(I, $product(-1, tb2t(get(int, int, t2tb2(B1), t2tb(Pos))))), 0)))) | (~eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board2))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~($sum(B, $product(-1, N)) = 0))))) | ($greatereq(Board, 0) & $greatereq(Pos, 0) & (~$greatereq($sum(Pos, $product(-1, Board)), 0)) & ![Board3: map_int_int] : ((~($greatereq(Board, 0) & (Board3 = tb2t2(set(int, int, t2tb2(Board2), t2tb(Pos), t2tb(I)))))) | ($greatereq(Pos, 0) & (~$greatereq($sum(Pos, $product(-1, Board)), 0)) & ![Result: bool1] : (((~(Result = true1)) <=> is_consistent1(tb2t1(mk_array1(int, Board, t2tb2(Board3))), Pos)) | (((~(Result = true1)) | ($lesseq($sum(Pos, $product(-1, N)), 0) & ($sum(N, $product(-1, Board)) = 0) & $greatereq(Pos, -1) & $lesseq($sum(Pos, $product(-1, N)), -1) & solution1(tb2t1(mk_array1(int, Board, t2tb2(Board3))), $sum(1, Pos)) & ![Board4: map_int_int] : ((~($greatereq(Board, 0) & eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board4))), tb2t1(mk_array1(int, Board, t2tb2(Board3))), $sum(1, Pos)) & ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board4))), tb2t1(mk_array1(int, B, t2tb2(B1))), $sum(1, Pos))) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~($sum(B, $product(-1, N)) = 0))))) | (eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board4))), tb2t1(mk_array1(int, Board, t2tb2(Board1))), Pos) & ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~($greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos))), 0) & (~$lesseq($sum(I, $product(-1, tb2t(get(int, int, t2tb2(B1), t2tb(Pos))))), -1)))) | (~eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board4))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos)) | (~($sum(B, $product(-1, N)) = 0))))) & ![Board4: map_int_int] : ((~($greatereq(Board, 0) & solution1(tb2t1(mk_array1(int, Board, t2tb2(Board4))), N))) | solution1(tb2t1(mk_array1(int, Board, t2tb2(Board4))), N)))) & ((Result = true1) | (eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board3))), tb2t1(mk_array1(int, Board, t2tb2(Board1))), Pos) & ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~($greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos))), 0) & (~$lesseq($sum(I, $product(-1, tb2t(get(int, int, t2tb2(B1), t2tb(Pos))))), -1)))) | (~eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board3))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~($sum(B, $product(-1, N)) = 0))))))))))) & ((~(eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board2))), tb2t1(mk_array1(int, Board, t2tb2(Board1))), Pos) & ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~($greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos))), 0) & (~$lesseq($sum(N, $product(-1, tb2t(get(int, int, t2tb2(B1), t2tb(Pos))))), 0)))) | (~eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board2))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos)) | (~($sum(B, $product(-1, N)) = 0))))) | ($greatereq(Board, 0) & eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board2))), tb2t1(mk_array1(int, Board, t2tb2(Board1))), Pos) & ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N)) | (~eq_board1(tb2t1(mk_array1(int, Board, t2tb2(Board2))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos)) | (~($sum(B, $product(-1, N)) = 0))))))))))))),
% 0.81/0.80 inference(modus_ponens,[status(thm)],[21, 9])).
% 0.81/0.80 tff(23,plain,
% 0.81/0.80 ($greatereq(Board!7, 0) & ($sum(N!5, $product(-1, Board!7)) = 0) & $greatereq(Pos!4, 0) & $lesseq($sum(Pos!4, $product(-1, N!5)), 0) & solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4) & ((~((~($sum(Pos!4, $product(-1, N!5)) = 0)) | solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), N!5))) | ((~($sum(Pos!4, $product(-1, N!5)) = 0)) & (((~$greatereq(N!5, 1)) & ((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!9, t2tb2(B1!8))), N!5)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, B!9, t2tb2(B1!8))), Pos!4)) | (~is_board1(tb2t1(mk_array1(int, B!9, t2tb2(B1!8))), N!5)) | (~($sum(N!5, $product(-1, B!9)) = 0)))))) | ($greatereq(N!5, 1) & ((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | ($greatereq(I!11, 0) & $greatereq($sum(N!5, $product(-1, I!11)), 1) & eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4) & ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos!4)) | (~($greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), 0) & (~$greatereq($sum(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), $product(-1, I!11)), 0))))) & ((~$greatereq(Board!7, 0)) | (~$greatereq(Pos!4, 0)) | $greatereq($sum(Pos!4, $product(-1, Board!7)), 0) | ($greatereq(Board!7, 0) & (Board3!12 = tb2t2(set(int, int, t2tb2(Board2!10), t2tb(Pos!4), t2tb(I!11)))) & ((~$greatereq(Pos!4, 0)) | $greatereq($sum(Pos!4, $product(-1, Board!7)), 0) | (((Result!13 = true1) <=> is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) & (((Result!13 = true1) & ((~$lesseq($sum(Pos!4, $product(-1, N!5)), 0)) | (~($sum(N!5, $product(-1, Board!7)) = 0)) | (~$greatereq(Pos!4, -1)) | (~$lesseq($sum(Pos!4, $product(-1, N!5)), -1)) | (~solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~((~($greatereq(Board!7, 0) & solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!17))), N!5))) | solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!17))), N!5))) | ($greatereq(Board!7, 0) & eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4)) & ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B, t2tb2(B1))), $sum(1, Pos!4)))) & ((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~($greatereq(tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))), 0) & (~$lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))))), -1)))) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), Pos!4)) | (~($sum(N!5, $product(-1, B!16)) = 0)))))))) | ((~(Result!13 = true1)) & ((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~($greatereq(tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))), 0) & (~$lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))))), -1)))) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Pos!4)) | (~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~($sum(N!5, $product(-1, B!19)) = 0)))))))))))) | (eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4) & ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~($greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), 0) & (~$lesseq($sum(N!5, $product(-1, tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))))), 0)))) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos!4))) & ((~$greatereq(Board!7, 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), Pos!4)) | (~($sum(N!5, $product(-1, B!21)) = 0)))))))))))),
% 0.81/0.80 inference(modus_ponens,[status(thm)],[22, 8])).
% 0.81/0.80 tff(24,plain,
% 0.81/0.80 ($lesseq($sum(Pos!4, $product(-1, N!5)), 0)),
% 0.81/0.80 inference(and_elim,[status(thm)],[23])).
% 0.81/0.80 tff(25,assumption,($greatereq($sum(Pos!4, $product(-1, N!5)), 0)), introduced(assumption)).
% 0.81/0.80 tff(26,plain,
% 0.81/0.80 (Pos!4 = N!5),
% 0.81/0.80 inference(theory_lemma,[status(thm)],[25, 24])).
% 0.81/0.80 tff(27,plain,
% 0.81/0.80 (solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4) <=> solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), N!5)),
% 0.81/0.80 inference(monotonicity,[status(thm)],[26])).
% 0.81/0.80 tff(28,plain,
% 0.81/0.80 (solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), N!5) <=> solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)),
% 0.81/0.80 inference(symmetry,[status(thm)],[27])).
% 0.81/0.80 tff(29,plain,
% 0.81/0.80 ((~solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), N!5)) <=> (~solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4))),
% 0.81/0.80 inference(monotonicity,[status(thm)],[28])).
% 0.81/0.80 tff(30,plain,
% 0.81/0.80 (($sum(Pos!4, $product(-1, N!5)) = 0) | (~$lesseq($sum(Pos!4, $product(-1, N!5)), 0)) | (~$greatereq($sum(Pos!4, $product(-1, N!5)), 0))),
% 0.81/0.80 inference(theory_lemma,[status(thm)],[])).
% 0.81/0.80 tff(31,plain,
% 0.81/0.80 (($sum(Pos!4, $product(-1, N!5)) = 0) | (~$greatereq($sum(Pos!4, $product(-1, N!5)), 0))),
% 0.81/0.80 inference(unit_resolution,[status(thm)],[30, 24])).
% 0.81/0.80 tff(32,plain,
% 0.81/0.80 ($sum(Pos!4, $product(-1, N!5)) = 0),
% 0.81/0.80 inference(unit_resolution,[status(thm)],[31, 25])).
% 0.81/0.80 tff(33,plain,
% 0.81/0.80 ((($sum(Pos!4, $product(-1, N!5)) = 0) | (~((~($greatereq(N!5, 1) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!9, t2tb2(B1!8))), N!5)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, B!9, t2tb2(B1!8))), Pos!4)) | (~is_board1(tb2t1(mk_array1(int, B!9, t2tb2(B1!8))), N!5)) | (~($sum(N!5, $product(-1, B!9)) = 0)))))))) | (~((~$greatereq(N!5, 1)) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~$greatereq(I!11, 0)) | (~$greatereq($sum(N!5, $product(-1, I!11)), 1)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos!4)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), 0)) | $greatereq($sum(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), $product(-1, I!11)), 0))) | (~($greatereq($sum(Pos!4, $product(-1, Board!7)), 0) | (~$greatereq(Board!7, 0)) | (~$greatereq(Pos!4, 0)) | (~((~$greatereq(Board!7, 0)) | (~(Board3!12 = tb2t2(set(int, int, t2tb2(Board2!10), t2tb(Pos!4), t2tb(I!11))))) | (~($greatereq($sum(Pos!4, $product(-1, Board!7)), 0) | (~$greatereq(Pos!4, 0)) | (~(((~(Result!13 = true1)) <=> is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | (~((~((Result!13 = true1) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Pos!4)) | (~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~($sum(N!5, $product(-1, B!19)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))), 0)))))))) | (~((~(Result!13 = true1)) | (~((~$lesseq($sum(Pos!4, $product(-1, N!5)), 0)) | (~($sum(N!5, $product(-1, Board!7)) = 0)) | (~$greatereq(Pos!4, -1)) | (~$lesseq($sum(Pos!4, $product(-1, N!5)), -1)) | (~solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~((~$greatereq(Board!7, 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B, t2tb2(B1))), $sum(1, Pos!4))))) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), Pos!4)) | (~($sum(N!5, $product(-1, B!16)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))), 0)))))))))))))))))))))))) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~$greatereq(Board!7, 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), Pos!4)) | (~($sum(N!5, $product(-1, B!21)) = 0)))))) | (~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | $lesseq($sum(N!5, $product(-1, tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))))), 0) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos!4)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), 0))))))))))))) | (~($sum(Pos!4, $product(-1, N!5)) = 0))),
% 0.81/0.80 inference(tautology,[status(thm)],[])).
% 0.81/0.80 tff(34,plain,
% 0.81/0.80 (($sum(Pos!4, $product(-1, N!5)) = 0) | (~((~($greatereq(N!5, 1) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!9, t2tb2(B1!8))), N!5)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, B!9, t2tb2(B1!8))), Pos!4)) | (~is_board1(tb2t1(mk_array1(int, B!9, t2tb2(B1!8))), N!5)) | (~($sum(N!5, $product(-1, B!9)) = 0)))))))) | (~((~$greatereq(N!5, 1)) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~$greatereq(I!11, 0)) | (~$greatereq($sum(N!5, $product(-1, I!11)), 1)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos!4)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), 0)) | $greatereq($sum(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), $product(-1, I!11)), 0))) | (~($greatereq($sum(Pos!4, $product(-1, Board!7)), 0) | (~$greatereq(Board!7, 0)) | (~$greatereq(Pos!4, 0)) | (~((~$greatereq(Board!7, 0)) | (~(Board3!12 = tb2t2(set(int, int, t2tb2(Board2!10), t2tb(Pos!4), t2tb(I!11))))) | (~($greatereq($sum(Pos!4, $product(-1, Board!7)), 0) | (~$greatereq(Pos!4, 0)) | (~(((~(Result!13 = true1)) <=> is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | (~((~((Result!13 = true1) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Pos!4)) | (~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~($sum(N!5, $product(-1, B!19)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))), 0)))))))) | (~((~(Result!13 = true1)) | (~((~$lesseq($sum(Pos!4, $product(-1, N!5)), 0)) | (~($sum(N!5, $product(-1, Board!7)) = 0)) | (~$greatereq(Pos!4, -1)) | (~$lesseq($sum(Pos!4, $product(-1, N!5)), -1)) | (~solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~((~$greatereq(Board!7, 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B, t2tb2(B1))), $sum(1, Pos!4))))) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), Pos!4)) | (~($sum(N!5, $product(-1, B!16)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))), 0)))))))))))))))))))))))) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~$greatereq(Board!7, 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), Pos!4)) | (~($sum(N!5, $product(-1, B!21)) = 0)))))) | (~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | $lesseq($sum(N!5, $product(-1, tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))))), 0) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos!4)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), 0))))))))))))),
% 0.81/0.81 inference(unit_resolution,[status(thm)],[33, 32])).
% 0.81/0.81 tff(35,plain,
% 0.81/0.81 (((~((~($sum(Pos!4, $product(-1, N!5)) = 0)) | solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), N!5))) | (~(($sum(Pos!4, $product(-1, N!5)) = 0) | (~((~($greatereq(N!5, 1) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!9, t2tb2(B1!8))), N!5)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, B!9, t2tb2(B1!8))), Pos!4)) | (~is_board1(tb2t1(mk_array1(int, B!9, t2tb2(B1!8))), N!5)) | (~($sum(N!5, $product(-1, B!9)) = 0)))))))) | (~((~$greatereq(N!5, 1)) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~$greatereq(I!11, 0)) | (~$greatereq($sum(N!5, $product(-1, I!11)), 1)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos!4)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), 0)) | $greatereq($sum(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), $product(-1, I!11)), 0))) | (~($greatereq($sum(Pos!4, $product(-1, Board!7)), 0) | (~$greatereq(Board!7, 0)) | (~$greatereq(Pos!4, 0)) | (~((~$greatereq(Board!7, 0)) | (~(Board3!12 = tb2t2(set(int, int, t2tb2(Board2!10), t2tb(Pos!4), t2tb(I!11))))) | (~($greatereq($sum(Pos!4, $product(-1, Board!7)), 0) | (~$greatereq(Pos!4, 0)) | (~(((~(Result!13 = true1)) <=> is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | (~((~((~(Result!13 = true1)) | (~((~$lesseq($sum(Pos!4, $product(-1, N!5)), 0)) | (~($sum(N!5, $product(-1, Board!7)) = 0)) | (~$greatereq(Pos!4, -1)) | (~$lesseq($sum(Pos!4, $product(-1, N!5)), -1)) | (~solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~((~$greatereq(Board!7, 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B, t2tb2(B1))), $sum(1, Pos!4))))) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), Pos!4)) | (~($sum(N!5, $product(-1, B!16)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))), 0)))))))))))) | (~((Result!13 = true1) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Pos!4)) | (~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~($sum(N!5, $product(-1, B!19)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))), 0)))))))))))))))))))) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | $lesseq($sum(N!5, $product(-1, tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))))), 0) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos!4)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), 0)))) | (~((~$greatereq(Board!7, 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), Pos!4)) | (~($sum(N!5, $product(-1, B!21)) = 0))))))))))))))))) <=> ((~((~($sum(Pos!4, $product(-1, N!5)) = 0)) | solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), N!5))) | (~(($sum(Pos!4, $product(-1, N!5)) = 0) | (~((~($greatereq(N!5, 1) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!9, t2tb2(B1!8))), N!5)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, B!9, t2tb2(B1!8))), Pos!4)) | (~is_board1(tb2t1(mk_array1(int, B!9, t2tb2(B1!8))), N!5)) | (~($sum(N!5, $product(-1, B!9)) = 0)))))))) | (~((~$greatereq(N!5, 1)) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~$greatereq(I!11, 0)) | (~$greatereq($sum(N!5, $product(-1, I!11)), 1)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos!4)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), 0)) | $greatereq($sum(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), $product(-1, I!11)), 0))) | (~($greatereq($sum(Pos!4, $product(-1, Board!7)), 0) | (~$greatereq(Board!7, 0)) | (~$greatereq(Pos!4, 0)) | (~((~$greatereq(Board!7, 0)) | (~(Board3!12 = tb2t2(set(int, int, t2tb2(Board2!10), t2tb(Pos!4), t2tb(I!11))))) | (~($greatereq($sum(Pos!4, $product(-1, Board!7)), 0) | (~$greatereq(Pos!4, 0)) | (~(((~(Result!13 = true1)) <=> is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | (~((~((Result!13 = true1) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Pos!4)) | (~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~($sum(N!5, $product(-1, B!19)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))), 0)))))))) | (~((~(Result!13 = true1)) | (~((~$lesseq($sum(Pos!4, $product(-1, N!5)), 0)) | (~($sum(N!5, $product(-1, Board!7)) = 0)) | (~$greatereq(Pos!4, -1)) | (~$lesseq($sum(Pos!4, $product(-1, N!5)), -1)) | (~solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~((~$greatereq(Board!7, 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B, t2tb2(B1))), $sum(1, Pos!4))))) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), Pos!4)) | (~($sum(N!5, $product(-1, B!16)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))), 0)))))))))))))))))))))))) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~$greatereq(Board!7, 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), Pos!4)) | (~($sum(N!5, $product(-1, B!21)) = 0)))))) | (~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | $lesseq($sum(N!5, $product(-1, tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))))), 0) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos!4)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), 0)))))))))))))))),
% 0.81/0.81 inference(rewrite,[status(thm)],[])).
% 0.81/0.81 tff(36,plain,
% 0.81/0.81 (((~((~($sum(Pos!4, $product(-1, N!5)) = 0)) | solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), N!5))) | (~(($sum(Pos!4, $product(-1, N!5)) = 0) | (~((~($greatereq(N!5, 1) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!9, t2tb2(B1!8))), N!5)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, B!9, t2tb2(B1!8))), Pos!4)) | (~is_board1(tb2t1(mk_array1(int, B!9, t2tb2(B1!8))), N!5)) | (~($sum(N!5, $product(-1, B!9)) = 0)))))))) | (~((~$greatereq(N!5, 1)) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~$greatereq(I!11, 0)) | (~$greatereq($sum(N!5, $product(-1, I!11)), 1)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos!4)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), 0)) | $greatereq($sum(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), $product(-1, I!11)), 0))) | (~($greatereq($sum(Pos!4, $product(-1, Board!7)), 0) | (~$greatereq(Board!7, 0)) | (~$greatereq(Pos!4, 0)) | (~((~$greatereq(Board!7, 0)) | (~(Board3!12 = tb2t2(set(int, int, t2tb2(Board2!10), t2tb(Pos!4), t2tb(I!11))))) | (~($greatereq($sum(Pos!4, $product(-1, Board!7)), 0) | (~$greatereq(Pos!4, 0)) | (~(((~(Result!13 = true1)) <=> is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | (~((~((~(Result!13 = true1)) | (~((~$lesseq($sum(Pos!4, $product(-1, N!5)), 0)) | (~($sum(N!5, $product(-1, Board!7)) = 0)) | (~$greatereq(Pos!4, -1)) | (~$lesseq($sum(Pos!4, $product(-1, N!5)), -1)) | (~solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~((~$greatereq(Board!7, 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B, t2tb2(B1))), $sum(1, Pos!4))))) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), Pos!4)) | (~($sum(N!5, $product(-1, B!16)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))), 0)))))))))))) | (~((Result!13 = true1) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Pos!4)) | (~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~($sum(N!5, $product(-1, B!19)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))), 0)))))))))))))))))))) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | $lesseq($sum(N!5, $product(-1, tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))))), 0) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos!4)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), 0)))) | (~((~$greatereq(Board!7, 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), Pos!4)) | (~($sum(N!5, $product(-1, B!21)) = 0))))))))))))))))) <=> ((~((~($sum(Pos!4, $product(-1, N!5)) = 0)) | solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), N!5))) | (~(($sum(Pos!4, $product(-1, N!5)) = 0) | (~((~($greatereq(N!5, 1) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!9, t2tb2(B1!8))), N!5)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, B!9, t2tb2(B1!8))), Pos!4)) | (~is_board1(tb2t1(mk_array1(int, B!9, t2tb2(B1!8))), N!5)) | (~($sum(N!5, $product(-1, B!9)) = 0)))))))) | (~((~$greatereq(N!5, 1)) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~$greatereq(I!11, 0)) | (~$greatereq($sum(N!5, $product(-1, I!11)), 1)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos!4)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), 0)) | $greatereq($sum(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), $product(-1, I!11)), 0))) | (~($greatereq($sum(Pos!4, $product(-1, Board!7)), 0) | (~$greatereq(Board!7, 0)) | (~$greatereq(Pos!4, 0)) | (~((~$greatereq(Board!7, 0)) | (~(Board3!12 = tb2t2(set(int, int, t2tb2(Board2!10), t2tb(Pos!4), t2tb(I!11))))) | (~($greatereq($sum(Pos!4, $product(-1, Board!7)), 0) | (~$greatereq(Pos!4, 0)) | (~(((~(Result!13 = true1)) <=> is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | (~((~((~(Result!13 = true1)) | (~((~$lesseq($sum(Pos!4, $product(-1, N!5)), 0)) | (~($sum(N!5, $product(-1, Board!7)) = 0)) | (~$greatereq(Pos!4, -1)) | (~$lesseq($sum(Pos!4, $product(-1, N!5)), -1)) | (~solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~((~$greatereq(Board!7, 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B, t2tb2(B1))), $sum(1, Pos!4))))) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), Pos!4)) | (~($sum(N!5, $product(-1, B!16)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))), 0)))))))))))) | (~((Result!13 = true1) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Pos!4)) | (~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~($sum(N!5, $product(-1, B!19)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))), 0)))))))))))))))))))) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | $lesseq($sum(N!5, $product(-1, tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))))), 0) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos!4)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), 0)))) | (~((~$greatereq(Board!7, 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), Pos!4)) | (~($sum(N!5, $product(-1, B!21)) = 0)))))))))))))))))),
% 0.81/0.82 inference(rewrite,[status(thm)],[])).
% 0.81/0.82 tff(37,plain,
% 0.81/0.82 (((~((~($sum(Pos!4, $product(-1, N!5)) = 0)) | solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), N!5))) | ((~($sum(Pos!4, $product(-1, N!5)) = 0)) & (((~$greatereq(N!5, 1)) & ((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!9, t2tb2(B1!8))), N!5)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, B!9, t2tb2(B1!8))), Pos!4)) | (~is_board1(tb2t1(mk_array1(int, B!9, t2tb2(B1!8))), N!5)) | (~($sum(N!5, $product(-1, B!9)) = 0)))))) | ($greatereq(N!5, 1) & ((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | ($greatereq(I!11, 0) & $greatereq($sum(N!5, $product(-1, I!11)), 1) & eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4) & ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos!4)) | (~($greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), 0) & (~$greatereq($sum(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), $product(-1, I!11)), 0))))) & ((~$greatereq(Board!7, 0)) | (~$greatereq(Pos!4, 0)) | $greatereq($sum(Pos!4, $product(-1, Board!7)), 0) | ($greatereq(Board!7, 0) & (Board3!12 = tb2t2(set(int, int, t2tb2(Board2!10), t2tb(Pos!4), t2tb(I!11)))) & ((~$greatereq(Pos!4, 0)) | $greatereq($sum(Pos!4, $product(-1, Board!7)), 0) | (((Result!13 = true1) <=> is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) & (((Result!13 = true1) & ((~$lesseq($sum(Pos!4, $product(-1, N!5)), 0)) | (~($sum(N!5, $product(-1, Board!7)) = 0)) | (~$greatereq(Pos!4, -1)) | (~$lesseq($sum(Pos!4, $product(-1, N!5)), -1)) | (~solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~((~($greatereq(Board!7, 0) & solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!17))), N!5))) | solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!17))), N!5))) | ($greatereq(Board!7, 0) & eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4)) & ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B, t2tb2(B1))), $sum(1, Pos!4)))) & ((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~($greatereq(tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))), 0) & (~$lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))))), -1)))) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), Pos!4)) | (~($sum(N!5, $product(-1, B!16)) = 0)))))))) | ((~(Result!13 = true1)) & ((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~($greatereq(tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))), 0) & (~$lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))))), -1)))) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Pos!4)) | (~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~($sum(N!5, $product(-1, B!19)) = 0)))))))))))) | (eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4) & ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~($greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), 0) & (~$lesseq($sum(N!5, $product(-1, tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))))), 0)))) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos!4))) & ((~$greatereq(Board!7, 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), Pos!4)) | (~($sum(N!5, $product(-1, B!21)) = 0))))))))))) <=> ((~((~($sum(Pos!4, $product(-1, N!5)) = 0)) | solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), N!5))) | (~(($sum(Pos!4, $product(-1, N!5)) = 0) | (~((~($greatereq(N!5, 1) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!9, t2tb2(B1!8))), N!5)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, B!9, t2tb2(B1!8))), Pos!4)) | (~is_board1(tb2t1(mk_array1(int, B!9, t2tb2(B1!8))), N!5)) | (~($sum(N!5, $product(-1, B!9)) = 0)))))))) | (~((~$greatereq(N!5, 1)) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~$greatereq(I!11, 0)) | (~$greatereq($sum(N!5, $product(-1, I!11)), 1)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos!4)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), 0)) | $greatereq($sum(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), $product(-1, I!11)), 0))) | (~($greatereq($sum(Pos!4, $product(-1, Board!7)), 0) | (~$greatereq(Board!7, 0)) | (~$greatereq(Pos!4, 0)) | (~((~$greatereq(Board!7, 0)) | (~(Board3!12 = tb2t2(set(int, int, t2tb2(Board2!10), t2tb(Pos!4), t2tb(I!11))))) | (~($greatereq($sum(Pos!4, $product(-1, Board!7)), 0) | (~$greatereq(Pos!4, 0)) | (~(((~(Result!13 = true1)) <=> is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | (~((~((~(Result!13 = true1)) | (~((~$lesseq($sum(Pos!4, $product(-1, N!5)), 0)) | (~($sum(N!5, $product(-1, Board!7)) = 0)) | (~$greatereq(Pos!4, -1)) | (~$lesseq($sum(Pos!4, $product(-1, N!5)), -1)) | (~solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~((~$greatereq(Board!7, 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B, t2tb2(B1))), $sum(1, Pos!4))))) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), Pos!4)) | (~($sum(N!5, $product(-1, B!16)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))), 0)))))))))))) | (~((Result!13 = true1) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Pos!4)) | (~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~($sum(N!5, $product(-1, B!19)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))), 0)))))))))))))))))))) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | $lesseq($sum(N!5, $product(-1, tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))))), 0) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos!4)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), 0)))) | (~((~$greatereq(Board!7, 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), Pos!4)) | (~($sum(N!5, $product(-1, B!21)) = 0)))))))))))))))))),
% 0.81/0.82 inference(rewrite,[status(thm)],[])).
% 0.81/0.82 tff(38,plain,
% 0.81/0.82 ((~((~($sum(Pos!4, $product(-1, N!5)) = 0)) | solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), N!5))) | ((~($sum(Pos!4, $product(-1, N!5)) = 0)) & (((~$greatereq(N!5, 1)) & ((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!9, t2tb2(B1!8))), N!5)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, B!9, t2tb2(B1!8))), Pos!4)) | (~is_board1(tb2t1(mk_array1(int, B!9, t2tb2(B1!8))), N!5)) | (~($sum(N!5, $product(-1, B!9)) = 0)))))) | ($greatereq(N!5, 1) & ((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | ($greatereq(I!11, 0) & $greatereq($sum(N!5, $product(-1, I!11)), 1) & eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4) & ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos!4)) | (~($greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), 0) & (~$greatereq($sum(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), $product(-1, I!11)), 0))))) & ((~$greatereq(Board!7, 0)) | (~$greatereq(Pos!4, 0)) | $greatereq($sum(Pos!4, $product(-1, Board!7)), 0) | ($greatereq(Board!7, 0) & (Board3!12 = tb2t2(set(int, int, t2tb2(Board2!10), t2tb(Pos!4), t2tb(I!11)))) & ((~$greatereq(Pos!4, 0)) | $greatereq($sum(Pos!4, $product(-1, Board!7)), 0) | (((Result!13 = true1) <=> is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) & (((Result!13 = true1) & ((~$lesseq($sum(Pos!4, $product(-1, N!5)), 0)) | (~($sum(N!5, $product(-1, Board!7)) = 0)) | (~$greatereq(Pos!4, -1)) | (~$lesseq($sum(Pos!4, $product(-1, N!5)), -1)) | (~solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~((~($greatereq(Board!7, 0) & solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!17))), N!5))) | solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!17))), N!5))) | ($greatereq(Board!7, 0) & eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4)) & ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B, t2tb2(B1))), $sum(1, Pos!4)))) & ((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~($greatereq(tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))), 0) & (~$lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))))), -1)))) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), Pos!4)) | (~($sum(N!5, $product(-1, B!16)) = 0)))))))) | ((~(Result!13 = true1)) & ((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~($greatereq(tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))), 0) & (~$lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))))), -1)))) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Pos!4)) | (~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~($sum(N!5, $product(-1, B!19)) = 0)))))))))))) | (eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4) & ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~($greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), 0) & (~$lesseq($sum(N!5, $product(-1, tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))))), 0)))) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos!4))) & ((~$greatereq(Board!7, 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), Pos!4)) | (~($sum(N!5, $product(-1, B!21)) = 0))))))))))),
% 0.87/0.82 inference(and_elim,[status(thm)],[23])).
% 0.87/0.82 tff(39,plain,
% 0.87/0.82 ((~((~($sum(Pos!4, $product(-1, N!5)) = 0)) | solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), N!5))) | (~(($sum(Pos!4, $product(-1, N!5)) = 0) | (~((~($greatereq(N!5, 1) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!9, t2tb2(B1!8))), N!5)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, B!9, t2tb2(B1!8))), Pos!4)) | (~is_board1(tb2t1(mk_array1(int, B!9, t2tb2(B1!8))), N!5)) | (~($sum(N!5, $product(-1, B!9)) = 0)))))))) | (~((~$greatereq(N!5, 1)) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~$greatereq(I!11, 0)) | (~$greatereq($sum(N!5, $product(-1, I!11)), 1)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos!4)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), 0)) | $greatereq($sum(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), $product(-1, I!11)), 0))) | (~($greatereq($sum(Pos!4, $product(-1, Board!7)), 0) | (~$greatereq(Board!7, 0)) | (~$greatereq(Pos!4, 0)) | (~((~$greatereq(Board!7, 0)) | (~(Board3!12 = tb2t2(set(int, int, t2tb2(Board2!10), t2tb(Pos!4), t2tb(I!11))))) | (~($greatereq($sum(Pos!4, $product(-1, Board!7)), 0) | (~$greatereq(Pos!4, 0)) | (~(((~(Result!13 = true1)) <=> is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | (~((~((~(Result!13 = true1)) | (~((~$lesseq($sum(Pos!4, $product(-1, N!5)), 0)) | (~($sum(N!5, $product(-1, Board!7)) = 0)) | (~$greatereq(Pos!4, -1)) | (~$lesseq($sum(Pos!4, $product(-1, N!5)), -1)) | (~solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~((~$greatereq(Board!7, 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B, t2tb2(B1))), $sum(1, Pos!4))))) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), Pos!4)) | (~($sum(N!5, $product(-1, B!16)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))), 0)))))))))))) | (~((Result!13 = true1) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Pos!4)) | (~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~($sum(N!5, $product(-1, B!19)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))), 0)))))))))))))))))))) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | $lesseq($sum(N!5, $product(-1, tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))))), 0) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos!4)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), 0)))) | (~((~$greatereq(Board!7, 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), Pos!4)) | (~($sum(N!5, $product(-1, B!21)) = 0))))))))))))))))),
% 0.87/0.82 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.87/0.82 tff(40,plain,
% 0.87/0.82 ((~((~($sum(Pos!4, $product(-1, N!5)) = 0)) | solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), N!5))) | (~(($sum(Pos!4, $product(-1, N!5)) = 0) | (~((~($greatereq(N!5, 1) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!9, t2tb2(B1!8))), N!5)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, B!9, t2tb2(B1!8))), Pos!4)) | (~is_board1(tb2t1(mk_array1(int, B!9, t2tb2(B1!8))), N!5)) | (~($sum(N!5, $product(-1, B!9)) = 0)))))))) | (~((~$greatereq(N!5, 1)) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~$greatereq(I!11, 0)) | (~$greatereq($sum(N!5, $product(-1, I!11)), 1)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos!4)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), 0)) | $greatereq($sum(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), $product(-1, I!11)), 0))) | (~($greatereq($sum(Pos!4, $product(-1, Board!7)), 0) | (~$greatereq(Board!7, 0)) | (~$greatereq(Pos!4, 0)) | (~((~$greatereq(Board!7, 0)) | (~(Board3!12 = tb2t2(set(int, int, t2tb2(Board2!10), t2tb(Pos!4), t2tb(I!11))))) | (~($greatereq($sum(Pos!4, $product(-1, Board!7)), 0) | (~$greatereq(Pos!4, 0)) | (~(((~(Result!13 = true1)) <=> is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | (~((~((~(Result!13 = true1)) | (~((~$lesseq($sum(Pos!4, $product(-1, N!5)), 0)) | (~($sum(N!5, $product(-1, Board!7)) = 0)) | (~$greatereq(Pos!4, -1)) | (~$lesseq($sum(Pos!4, $product(-1, N!5)), -1)) | (~solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~((~$greatereq(Board!7, 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B, t2tb2(B1))), $sum(1, Pos!4))))) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), Pos!4)) | (~($sum(N!5, $product(-1, B!16)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))), 0)))))))))))) | (~((Result!13 = true1) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Pos!4)) | (~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~($sum(N!5, $product(-1, B!19)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))), 0)))))))))))))))))))) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | $lesseq($sum(N!5, $product(-1, tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))))), 0) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos!4)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), 0)))) | (~((~$greatereq(Board!7, 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), Pos!4)) | (~($sum(N!5, $product(-1, B!21)) = 0))))))))))))))))),
% 0.87/0.83 inference(modus_ponens,[status(thm)],[39, 36])).
% 0.87/0.83 tff(41,plain,
% 0.87/0.83 ((~((~($sum(Pos!4, $product(-1, N!5)) = 0)) | solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), N!5))) | (~(($sum(Pos!4, $product(-1, N!5)) = 0) | (~((~($greatereq(N!5, 1) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!9, t2tb2(B1!8))), N!5)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, B!9, t2tb2(B1!8))), Pos!4)) | (~is_board1(tb2t1(mk_array1(int, B!9, t2tb2(B1!8))), N!5)) | (~($sum(N!5, $product(-1, B!9)) = 0)))))))) | (~((~$greatereq(N!5, 1)) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~$greatereq(I!11, 0)) | (~$greatereq($sum(N!5, $product(-1, I!11)), 1)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos!4)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), 0)) | $greatereq($sum(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), $product(-1, I!11)), 0))) | (~($greatereq($sum(Pos!4, $product(-1, Board!7)), 0) | (~$greatereq(Board!7, 0)) | (~$greatereq(Pos!4, 0)) | (~((~$greatereq(Board!7, 0)) | (~(Board3!12 = tb2t2(set(int, int, t2tb2(Board2!10), t2tb(Pos!4), t2tb(I!11))))) | (~($greatereq($sum(Pos!4, $product(-1, Board!7)), 0) | (~$greatereq(Pos!4, 0)) | (~(((~(Result!13 = true1)) <=> is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | (~((~((Result!13 = true1) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Pos!4)) | (~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~($sum(N!5, $product(-1, B!19)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))), 0)))))))) | (~((~(Result!13 = true1)) | (~((~$lesseq($sum(Pos!4, $product(-1, N!5)), 0)) | (~($sum(N!5, $product(-1, Board!7)) = 0)) | (~$greatereq(Pos!4, -1)) | (~$lesseq($sum(Pos!4, $product(-1, N!5)), -1)) | (~solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~((~$greatereq(Board!7, 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B, t2tb2(B1))), $sum(1, Pos!4))))) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), Pos!4)) | (~($sum(N!5, $product(-1, B!16)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))), 0)))))))))))))))))))))))) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~$greatereq(Board!7, 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), Pos!4)) | (~($sum(N!5, $product(-1, B!21)) = 0)))))) | (~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | $lesseq($sum(N!5, $product(-1, tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))))), 0) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos!4)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), 0))))))))))))))),
% 0.87/0.83 inference(modus_ponens,[status(thm)],[40, 35])).
% 0.87/0.83 tff(42,plain,
% 0.87/0.83 (~((~($sum(Pos!4, $product(-1, N!5)) = 0)) | solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), N!5))),
% 0.87/0.83 inference(unit_resolution,[status(thm)],[41, 34])).
% 0.87/0.83 tff(43,plain,
% 0.87/0.83 (((~($sum(Pos!4, $product(-1, N!5)) = 0)) | solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), N!5)) | (~solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), N!5))),
% 0.87/0.83 inference(tautology,[status(thm)],[])).
% 0.87/0.83 tff(44,plain,
% 0.87/0.83 (~solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), N!5)),
% 0.87/0.83 inference(unit_resolution,[status(thm)],[43, 42])).
% 0.87/0.83 tff(45,plain,
% 0.87/0.83 (~solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)),
% 0.87/0.83 inference(modus_ponens,[status(thm)],[44, 29])).
% 0.87/0.83 tff(46,plain,
% 0.87/0.83 (solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)),
% 0.87/0.83 inference(and_elim,[status(thm)],[23])).
% 0.87/0.83 tff(47,plain,
% 0.87/0.83 ($false),
% 0.87/0.83 inference(unit_resolution,[status(thm)],[46, 45])).
% 0.87/0.83 tff(48,plain,(~$greatereq($sum(Pos!4, $product(-1, N!5)), 0)), inference(lemma,lemma(discharge,[]))).
% 0.87/0.83 tff(49,plain,
% 0.87/0.83 (^[Board: array_int, Pos: $int] : refl((~((~((~is_board1(Board, Pos)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(Board), Q)), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(Board), Q)), $product(-1, length1(int, t2tb1(Board)))), 0)))))) | (~(is_board1(Board, Pos) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_2(Pos, Board))), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(Board), tptp_fun_Q_2(Pos, Board))), 0)) | $lesseq($sum(length1(int, t2tb1(Board)), $product(-1, tb2t(get2(int, t2tb1(Board), tptp_fun_Q_2(Pos, Board))))), 0))) | (~$greatereq(tptp_fun_Q_2(Pos, Board), 0)))))))) <=> (~((~((~is_board1(Board, Pos)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(Board), Q)), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(Board), Q)), $product(-1, length1(int, t2tb1(Board)))), 0)))))) | (~(is_board1(Board, Pos) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_2(Pos, Board))), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(Board), tptp_fun_Q_2(Pos, Board))), 0)) | $lesseq($sum(length1(int, t2tb1(Board)), $product(-1, tb2t(get2(int, t2tb1(Board), tptp_fun_Q_2(Pos, Board))))), 0))) | (~$greatereq(tptp_fun_Q_2(Pos, Board), 0)))))))))),
% 0.87/0.83 inference(bind,[status(th)],[])).
% 0.87/0.83 tff(50,plain,
% 0.87/0.83 (![Board: array_int, Pos: $int] : (~((~((~is_board1(Board, Pos)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(Board), Q)), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(Board), Q)), $product(-1, length1(int, t2tb1(Board)))), 0)))))) | (~(is_board1(Board, Pos) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_2(Pos, Board))), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(Board), tptp_fun_Q_2(Pos, Board))), 0)) | $lesseq($sum(length1(int, t2tb1(Board)), $product(-1, tb2t(get2(int, t2tb1(Board), tptp_fun_Q_2(Pos, Board))))), 0))) | (~$greatereq(tptp_fun_Q_2(Pos, Board), 0)))))))) <=> ![Board: array_int, Pos: $int] : (~((~((~is_board1(Board, Pos)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(Board), Q)), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(Board), Q)), $product(-1, length1(int, t2tb1(Board)))), 0)))))) | (~(is_board1(Board, Pos) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_2(Pos, Board))), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(Board), tptp_fun_Q_2(Pos, Board))), 0)) | $lesseq($sum(length1(int, t2tb1(Board)), $product(-1, tb2t(get2(int, t2tb1(Board), tptp_fun_Q_2(Pos, Board))))), 0))) | (~$greatereq(tptp_fun_Q_2(Pos, Board), 0))))))))),
% 0.87/0.83 inference(quant_intro,[status(thm)],[49])).
% 0.87/0.83 tff(51,plain,
% 0.87/0.83 (^[Board: array_int, Pos: $int] : rewrite((~((~((~is_board1(Board, Pos)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(Board), Q)), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(Board), Q)), $product(-1, length1(int, t2tb1(Board)))), 0)))))) | (~(is_board1(Board, Pos) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_2(Pos, Board))), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(Board), tptp_fun_Q_2(Pos, Board))), 0)) | $lesseq($sum(length1(int, t2tb1(Board)), $product(-1, tb2t(get2(int, t2tb1(Board), tptp_fun_Q_2(Pos, Board))))), 0))) | (~$greatereq(tptp_fun_Q_2(Pos, Board), 0)))))))) <=> (~((~((~is_board1(Board, Pos)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(Board), Q)), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(Board), Q)), $product(-1, length1(int, t2tb1(Board)))), 0)))))) | (~(is_board1(Board, Pos) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_2(Pos, Board))), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(Board), tptp_fun_Q_2(Pos, Board))), 0)) | $lesseq($sum(length1(int, t2tb1(Board)), $product(-1, tb2t(get2(int, t2tb1(Board), tptp_fun_Q_2(Pos, Board))))), 0))) | (~$greatereq(tptp_fun_Q_2(Pos, Board), 0)))))))))),
% 0.87/0.83 inference(bind,[status(th)],[])).
% 0.87/0.83 tff(52,plain,
% 0.87/0.83 (![Board: array_int, Pos: $int] : (~((~((~is_board1(Board, Pos)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(Board), Q)), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(Board), Q)), $product(-1, length1(int, t2tb1(Board)))), 0)))))) | (~(is_board1(Board, Pos) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_2(Pos, Board))), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(Board), tptp_fun_Q_2(Pos, Board))), 0)) | $lesseq($sum(length1(int, t2tb1(Board)), $product(-1, tb2t(get2(int, t2tb1(Board), tptp_fun_Q_2(Pos, Board))))), 0))) | (~$greatereq(tptp_fun_Q_2(Pos, Board), 0)))))))) <=> ![Board: array_int, Pos: $int] : (~((~((~is_board1(Board, Pos)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(Board), Q)), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(Board), Q)), $product(-1, length1(int, t2tb1(Board)))), 0)))))) | (~(is_board1(Board, Pos) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_2(Pos, Board))), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(Board), tptp_fun_Q_2(Pos, Board))), 0)) | $lesseq($sum(length1(int, t2tb1(Board)), $product(-1, tb2t(get2(int, t2tb1(Board), tptp_fun_Q_2(Pos, Board))))), 0))) | (~$greatereq(tptp_fun_Q_2(Pos, Board), 0))))))))),
% 0.87/0.83 inference(quant_intro,[status(thm)],[51])).
% 0.87/0.83 tff(53,plain,
% 0.87/0.83 (![Board: array_int, Pos: $int] : (~((~((~is_board1(Board, Pos)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(Board), Q)), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(Board), Q)), $product(-1, length1(int, t2tb1(Board)))), 0)))))) | (~(is_board1(Board, Pos) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_2(Pos, Board))), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(Board), tptp_fun_Q_2(Pos, Board))), 0)) | $lesseq($sum(length1(int, t2tb1(Board)), $product(-1, tb2t(get2(int, t2tb1(Board), tptp_fun_Q_2(Pos, Board))))), 0))) | (~$greatereq(tptp_fun_Q_2(Pos, Board), 0)))))))) <=> ![Board: array_int, Pos: $int] : (~((~((~is_board1(Board, Pos)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(Board), Q)), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(Board), Q)), $product(-1, length1(int, t2tb1(Board)))), 0)))))) | (~(is_board1(Board, Pos) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_2(Pos, Board))), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(Board), tptp_fun_Q_2(Pos, Board))), 0)) | $lesseq($sum(length1(int, t2tb1(Board)), $product(-1, tb2t(get2(int, t2tb1(Board), tptp_fun_Q_2(Pos, Board))))), 0))) | (~$greatereq(tptp_fun_Q_2(Pos, Board), 0))))))))),
% 0.87/0.83 inference(transitivity,[status(thm)],[52, 50])).
% 0.87/0.83 tff(54,plain,
% 0.87/0.83 (^[Board: array_int, Pos: $int] : trans(monotonicity(rewrite(((~is_board1(Board, Pos)) | ![Q: $int] : ((~($greatereq(Q, 0) & (~$lesseq($sum(Pos, $product(-1, Q)), 0)))) | ($greatereq(tb2t(get2(int, t2tb1(Board), Q)), 0) & (~$greatereq($sum(tb2t(get2(int, t2tb1(Board), Q)), $product(-1, length1(int, t2tb1(Board)))), 0))))) <=> ((~is_board1(Board, Pos)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(Board), Q)), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(Board), Q)), $product(-1, length1(int, t2tb1(Board)))), 0)))))), trans(monotonicity(rewrite((~((~($greatereq(tptp_fun_Q_2(Pos, Board), 0) & (~$lesseq($sum(Pos, $product(-1, tptp_fun_Q_2(Pos, Board))), 0)))) | ($greatereq(tb2t(get2(int, t2tb1(Board), tptp_fun_Q_2(Pos, Board))), 0) & (~$lesseq($sum(length1(int, t2tb1(Board)), $product(-1, tb2t(get2(int, t2tb1(Board), tptp_fun_Q_2(Pos, Board))))), 0))))) <=> (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_2(Pos, Board))), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(Board), tptp_fun_Q_2(Pos, Board))), 0)) | $lesseq($sum(length1(int, t2tb1(Board)), $product(-1, tb2t(get2(int, t2tb1(Board), tptp_fun_Q_2(Pos, Board))))), 0))) | (~$greatereq(tptp_fun_Q_2(Pos, Board), 0))))), ((is_board1(Board, Pos) | (~((~($greatereq(tptp_fun_Q_2(Pos, Board), 0) & (~$lesseq($sum(Pos, $product(-1, tptp_fun_Q_2(Pos, Board))), 0)))) | ($greatereq(tb2t(get2(int, t2tb1(Board), tptp_fun_Q_2(Pos, Board))), 0) & (~$lesseq($sum(length1(int, t2tb1(Board)), $product(-1, tb2t(get2(int, t2tb1(Board), tptp_fun_Q_2(Pos, Board))))), 0)))))) <=> (is_board1(Board, Pos) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_2(Pos, Board))), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(Board), tptp_fun_Q_2(Pos, Board))), 0)) | $lesseq($sum(length1(int, t2tb1(Board)), $product(-1, tb2t(get2(int, t2tb1(Board), tptp_fun_Q_2(Pos, Board))))), 0))) | (~$greatereq(tptp_fun_Q_2(Pos, Board), 0))))))), rewrite((is_board1(Board, Pos) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_2(Pos, Board))), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(Board), tptp_fun_Q_2(Pos, Board))), 0)) | $lesseq($sum(length1(int, t2tb1(Board)), $product(-1, tb2t(get2(int, t2tb1(Board), tptp_fun_Q_2(Pos, Board))))), 0))) | (~$greatereq(tptp_fun_Q_2(Pos, Board), 0))))) <=> (is_board1(Board, Pos) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_2(Pos, Board))), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(Board), tptp_fun_Q_2(Pos, Board))), 0)) | $lesseq($sum(length1(int, t2tb1(Board)), $product(-1, tb2t(get2(int, t2tb1(Board), tptp_fun_Q_2(Pos, Board))))), 0))) | (~$greatereq(tptp_fun_Q_2(Pos, Board), 0)))))), ((is_board1(Board, Pos) | (~((~($greatereq(tptp_fun_Q_2(Pos, Board), 0) & (~$lesseq($sum(Pos, $product(-1, tptp_fun_Q_2(Pos, Board))), 0)))) | ($greatereq(tb2t(get2(int, t2tb1(Board), tptp_fun_Q_2(Pos, Board))), 0) & (~$lesseq($sum(length1(int, t2tb1(Board)), $product(-1, tb2t(get2(int, t2tb1(Board), tptp_fun_Q_2(Pos, Board))))), 0)))))) <=> (is_board1(Board, Pos) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_2(Pos, Board))), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(Board), tptp_fun_Q_2(Pos, Board))), 0)) | $lesseq($sum(length1(int, t2tb1(Board)), $product(-1, tb2t(get2(int, t2tb1(Board), tptp_fun_Q_2(Pos, Board))))), 0))) | (~$greatereq(tptp_fun_Q_2(Pos, Board), 0))))))), ((((~is_board1(Board, Pos)) | ![Q: $int] : ((~($greatereq(Q, 0) & (~$lesseq($sum(Pos, $product(-1, Q)), 0)))) | ($greatereq(tb2t(get2(int, t2tb1(Board), Q)), 0) & (~$greatereq($sum(tb2t(get2(int, t2tb1(Board), Q)), $product(-1, length1(int, t2tb1(Board)))), 0))))) & (is_board1(Board, Pos) | (~((~($greatereq(tptp_fun_Q_2(Pos, Board), 0) & (~$lesseq($sum(Pos, $product(-1, tptp_fun_Q_2(Pos, Board))), 0)))) | ($greatereq(tb2t(get2(int, t2tb1(Board), tptp_fun_Q_2(Pos, Board))), 0) & (~$lesseq($sum(length1(int, t2tb1(Board)), $product(-1, tb2t(get2(int, t2tb1(Board), tptp_fun_Q_2(Pos, Board))))), 0))))))) <=> (((~is_board1(Board, Pos)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(Board), Q)), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(Board), Q)), $product(-1, length1(int, t2tb1(Board)))), 0))))) & (is_board1(Board, Pos) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_2(Pos, Board))), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(Board), tptp_fun_Q_2(Pos, Board))), 0)) | $lesseq($sum(length1(int, t2tb1(Board)), $product(-1, tb2t(get2(int, t2tb1(Board), tptp_fun_Q_2(Pos, Board))))), 0))) | (~$greatereq(tptp_fun_Q_2(Pos, Board), 0)))))))), rewrite((((~is_board1(Board, Pos)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(Board), Q)), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(Board), Q)), $product(-1, length1(int, t2tb1(Board)))), 0))))) & (is_board1(Board, Pos) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_2(Pos, Board))), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(Board), tptp_fun_Q_2(Pos, Board))), 0)) | $lesseq($sum(length1(int, t2tb1(Board)), $product(-1, tb2t(get2(int, t2tb1(Board), tptp_fun_Q_2(Pos, Board))))), 0))) | (~$greatereq(tptp_fun_Q_2(Pos, Board), 0)))))) <=> (~((~((~is_board1(Board, Pos)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(Board), Q)), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(Board), Q)), $product(-1, length1(int, t2tb1(Board)))), 0)))))) | (~(is_board1(Board, Pos) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_2(Pos, Board))), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(Board), tptp_fun_Q_2(Pos, Board))), 0)) | $lesseq($sum(length1(int, t2tb1(Board)), $product(-1, tb2t(get2(int, t2tb1(Board), tptp_fun_Q_2(Pos, Board))))), 0))) | (~$greatereq(tptp_fun_Q_2(Pos, Board), 0))))))))), ((((~is_board1(Board, Pos)) | ![Q: $int] : ((~($greatereq(Q, 0) & (~$lesseq($sum(Pos, $product(-1, Q)), 0)))) | ($greatereq(tb2t(get2(int, t2tb1(Board), Q)), 0) & (~$greatereq($sum(tb2t(get2(int, t2tb1(Board), Q)), $product(-1, length1(int, t2tb1(Board)))), 0))))) & (is_board1(Board, Pos) | (~((~($greatereq(tptp_fun_Q_2(Pos, Board), 0) & (~$lesseq($sum(Pos, $product(-1, tptp_fun_Q_2(Pos, Board))), 0)))) | ($greatereq(tb2t(get2(int, t2tb1(Board), tptp_fun_Q_2(Pos, Board))), 0) & (~$lesseq($sum(length1(int, t2tb1(Board)), $product(-1, tb2t(get2(int, t2tb1(Board), tptp_fun_Q_2(Pos, Board))))), 0))))))) <=> (~((~((~is_board1(Board, Pos)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(Board), Q)), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(Board), Q)), $product(-1, length1(int, t2tb1(Board)))), 0)))))) | (~(is_board1(Board, Pos) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_2(Pos, Board))), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(Board), tptp_fun_Q_2(Pos, Board))), 0)) | $lesseq($sum(length1(int, t2tb1(Board)), $product(-1, tb2t(get2(int, t2tb1(Board), tptp_fun_Q_2(Pos, Board))))), 0))) | (~$greatereq(tptp_fun_Q_2(Pos, Board), 0))))))))))),
% 0.87/0.83 inference(bind,[status(th)],[])).
% 0.87/0.83 tff(55,plain,
% 0.87/0.83 (![Board: array_int, Pos: $int] : (((~is_board1(Board, Pos)) | ![Q: $int] : ((~($greatereq(Q, 0) & (~$lesseq($sum(Pos, $product(-1, Q)), 0)))) | ($greatereq(tb2t(get2(int, t2tb1(Board), Q)), 0) & (~$greatereq($sum(tb2t(get2(int, t2tb1(Board), Q)), $product(-1, length1(int, t2tb1(Board)))), 0))))) & (is_board1(Board, Pos) | (~((~($greatereq(tptp_fun_Q_2(Pos, Board), 0) & (~$lesseq($sum(Pos, $product(-1, tptp_fun_Q_2(Pos, Board))), 0)))) | ($greatereq(tb2t(get2(int, t2tb1(Board), tptp_fun_Q_2(Pos, Board))), 0) & (~$lesseq($sum(length1(int, t2tb1(Board)), $product(-1, tb2t(get2(int, t2tb1(Board), tptp_fun_Q_2(Pos, Board))))), 0))))))) <=> ![Board: array_int, Pos: $int] : (~((~((~is_board1(Board, Pos)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(Board), Q)), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(Board), Q)), $product(-1, length1(int, t2tb1(Board)))), 0)))))) | (~(is_board1(Board, Pos) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_2(Pos, Board))), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(Board), tptp_fun_Q_2(Pos, Board))), 0)) | $lesseq($sum(length1(int, t2tb1(Board)), $product(-1, tb2t(get2(int, t2tb1(Board), tptp_fun_Q_2(Pos, Board))))), 0))) | (~$greatereq(tptp_fun_Q_2(Pos, Board), 0))))))))),
% 0.87/0.83 inference(quant_intro,[status(thm)],[54])).
% 0.87/0.83 tff(56,plain,
% 0.87/0.83 (^[Board: array_int, Pos: $int] : rewrite((((~is_board1(Board, Pos)) | ![Q: $int] : ((~($greatereq(Q, 0) & (~$lesseq($sum(Pos, $product(-1, Q)), 0)))) | ($greatereq(tb2t(get2(int, t2tb1(Board), Q)), 0) & (~$greatereq($sum(tb2t(get2(int, t2tb1(Board), Q)), $product(-1, length1(int, t2tb1(Board)))), 0))))) & (is_board1(Board, Pos) | (~((~($greatereq(tptp_fun_Q_2(Pos, Board), 0) & (~$lesseq($sum(Pos, $product(-1, tptp_fun_Q_2(Pos, Board))), 0)))) | ($greatereq(tb2t(get2(int, t2tb1(Board), tptp_fun_Q_2(Pos, Board))), 0) & (~$greatereq($sum(tb2t(get2(int, t2tb1(Board), tptp_fun_Q_2(Pos, Board))), $product(-1, length1(int, t2tb1(Board)))), 0))))))) <=> (((~is_board1(Board, Pos)) | ![Q: $int] : ((~($greatereq(Q, 0) & (~$lesseq($sum(Pos, $product(-1, Q)), 0)))) | ($greatereq(tb2t(get2(int, t2tb1(Board), Q)), 0) & (~$greatereq($sum(tb2t(get2(int, t2tb1(Board), Q)), $product(-1, length1(int, t2tb1(Board)))), 0))))) & (is_board1(Board, Pos) | (~((~($greatereq(tptp_fun_Q_2(Pos, Board), 0) & (~$lesseq($sum(Pos, $product(-1, tptp_fun_Q_2(Pos, Board))), 0)))) | ($greatereq(tb2t(get2(int, t2tb1(Board), tptp_fun_Q_2(Pos, Board))), 0) & (~$lesseq($sum(length1(int, t2tb1(Board)), $product(-1, tb2t(get2(int, t2tb1(Board), tptp_fun_Q_2(Pos, Board))))), 0))))))))),
% 0.87/0.83 inference(bind,[status(th)],[])).
% 0.87/0.83 tff(57,plain,
% 0.87/0.83 (![Board: array_int, Pos: $int] : (((~is_board1(Board, Pos)) | ![Q: $int] : ((~($greatereq(Q, 0) & (~$lesseq($sum(Pos, $product(-1, Q)), 0)))) | ($greatereq(tb2t(get2(int, t2tb1(Board), Q)), 0) & (~$greatereq($sum(tb2t(get2(int, t2tb1(Board), Q)), $product(-1, length1(int, t2tb1(Board)))), 0))))) & (is_board1(Board, Pos) | (~((~($greatereq(tptp_fun_Q_2(Pos, Board), 0) & (~$lesseq($sum(Pos, $product(-1, tptp_fun_Q_2(Pos, Board))), 0)))) | ($greatereq(tb2t(get2(int, t2tb1(Board), tptp_fun_Q_2(Pos, Board))), 0) & (~$greatereq($sum(tb2t(get2(int, t2tb1(Board), tptp_fun_Q_2(Pos, Board))), $product(-1, length1(int, t2tb1(Board)))), 0))))))) <=> ![Board: array_int, Pos: $int] : (((~is_board1(Board, Pos)) | ![Q: $int] : ((~($greatereq(Q, 0) & (~$lesseq($sum(Pos, $product(-1, Q)), 0)))) | ($greatereq(tb2t(get2(int, t2tb1(Board), Q)), 0) & (~$greatereq($sum(tb2t(get2(int, t2tb1(Board), Q)), $product(-1, length1(int, t2tb1(Board)))), 0))))) & (is_board1(Board, Pos) | (~((~($greatereq(tptp_fun_Q_2(Pos, Board), 0) & (~$lesseq($sum(Pos, $product(-1, tptp_fun_Q_2(Pos, Board))), 0)))) | ($greatereq(tb2t(get2(int, t2tb1(Board), tptp_fun_Q_2(Pos, Board))), 0) & (~$lesseq($sum(length1(int, t2tb1(Board)), $product(-1, tb2t(get2(int, t2tb1(Board), tptp_fun_Q_2(Pos, Board))))), 0)))))))),
% 0.87/0.83 inference(quant_intro,[status(thm)],[56])).
% 0.87/0.83 tff(58,plain,
% 0.87/0.83 (^[Board: array_int, Pos: $int] : rewrite((is_board1(Board, Pos) <=> ![Q: $int] : ((~($greatereq(Q, 0) & (~$lesseq($sum(Pos, $product(-1, Q)), 0)))) | ($greatereq(tb2t(get2(int, t2tb1(Board), Q)), 0) & (~$lesseq($sum(length1(int, t2tb1(Board)), $product(-1, tb2t(get2(int, t2tb1(Board), Q)))), 0))))) <=> (is_board1(Board, Pos) <=> ![Q: $int] : ((~($greatereq(Q, 0) & (~$lesseq($sum(Pos, $product(-1, Q)), 0)))) | ($greatereq(tb2t(get2(int, t2tb1(Board), Q)), 0) & (~$greatereq($sum(tb2t(get2(int, t2tb1(Board), Q)), $product(-1, length1(int, t2tb1(Board)))), 0))))))),
% 0.87/0.83 inference(bind,[status(th)],[])).
% 0.87/0.83 tff(59,plain,
% 0.87/0.83 (![Board: array_int, Pos: $int] : (is_board1(Board, Pos) <=> ![Q: $int] : ((~($greatereq(Q, 0) & (~$lesseq($sum(Pos, $product(-1, Q)), 0)))) | ($greatereq(tb2t(get2(int, t2tb1(Board), Q)), 0) & (~$lesseq($sum(length1(int, t2tb1(Board)), $product(-1, tb2t(get2(int, t2tb1(Board), Q)))), 0))))) <=> ![Board: array_int, Pos: $int] : (is_board1(Board, Pos) <=> ![Q: $int] : ((~($greatereq(Q, 0) & (~$lesseq($sum(Pos, $product(-1, Q)), 0)))) | ($greatereq(tb2t(get2(int, t2tb1(Board), Q)), 0) & (~$greatereq($sum(tb2t(get2(int, t2tb1(Board), Q)), $product(-1, length1(int, t2tb1(Board)))), 0)))))),
% 0.87/0.83 inference(quant_intro,[status(thm)],[58])).
% 0.87/0.83 tff(60,plain,
% 0.87/0.83 (^[Board: array_int, Pos: $int] : rewrite((is_board1(Board, Pos) <=> ![Q: $int] : ((~($lesseq(0, Q) & (~$lesseq(Pos, Q)))) | ($lesseq(0, tb2t(get2(int, t2tb1(Board), Q))) & (~$lesseq(length1(int, t2tb1(Board)), tb2t(get2(int, t2tb1(Board), Q))))))) <=> (is_board1(Board, Pos) <=> ![Q: $int] : ((~($greatereq(Q, 0) & (~$lesseq($sum(Pos, $product(-1, Q)), 0)))) | ($greatereq(tb2t(get2(int, t2tb1(Board), Q)), 0) & (~$lesseq($sum(length1(int, t2tb1(Board)), $product(-1, tb2t(get2(int, t2tb1(Board), Q)))), 0))))))),
% 0.87/0.83 inference(bind,[status(th)],[])).
% 0.87/0.83 tff(61,plain,
% 0.87/0.83 (![Board: array_int, Pos: $int] : (is_board1(Board, Pos) <=> ![Q: $int] : ((~($lesseq(0, Q) & (~$lesseq(Pos, Q)))) | ($lesseq(0, tb2t(get2(int, t2tb1(Board), Q))) & (~$lesseq(length1(int, t2tb1(Board)), tb2t(get2(int, t2tb1(Board), Q))))))) <=> ![Board: array_int, Pos: $int] : (is_board1(Board, Pos) <=> ![Q: $int] : ((~($greatereq(Q, 0) & (~$lesseq($sum(Pos, $product(-1, Q)), 0)))) | ($greatereq(tb2t(get2(int, t2tb1(Board), Q)), 0) & (~$lesseq($sum(length1(int, t2tb1(Board)), $product(-1, tb2t(get2(int, t2tb1(Board), Q)))), 0)))))),
% 0.87/0.83 inference(quant_intro,[status(thm)],[60])).
% 0.87/0.83 tff(62,plain,
% 0.87/0.83 (![Board: array_int, Pos: $int] : (is_board1(Board, Pos) <=> ![Q: $int] : ((~($lesseq(0, Q) & (~$lesseq(Pos, Q)))) | ($lesseq(0, tb2t(get2(int, t2tb1(Board), Q))) & (~$lesseq(length1(int, t2tb1(Board)), tb2t(get2(int, t2tb1(Board), Q))))))) <=> ![Board: array_int, Pos: $int] : (is_board1(Board, Pos) <=> ![Q: $int] : ((~($lesseq(0, Q) & (~$lesseq(Pos, Q)))) | ($lesseq(0, tb2t(get2(int, t2tb1(Board), Q))) & (~$lesseq(length1(int, t2tb1(Board)), tb2t(get2(int, t2tb1(Board), Q)))))))),
% 0.87/0.83 inference(rewrite,[status(thm)],[])).
% 0.87/0.83 tff(63,plain,
% 0.87/0.83 (^[Board: array_int, Pos: $int] : rewrite((is_board1(Board, Pos) <=> ![Q: $int] : (($lesseq(0, Q) & $less(Q, Pos)) => ($lesseq(0, tb2t(get2(int, t2tb1(Board), Q))) & $less(tb2t(get2(int, t2tb1(Board), Q)), length1(int, t2tb1(Board)))))) <=> (is_board1(Board, Pos) <=> ![Q: $int] : ((~($lesseq(0, Q) & (~$lesseq(Pos, Q)))) | ($lesseq(0, tb2t(get2(int, t2tb1(Board), Q))) & (~$lesseq(length1(int, t2tb1(Board)), tb2t(get2(int, t2tb1(Board), Q))))))))),
% 0.87/0.83 inference(bind,[status(th)],[])).
% 0.87/0.83 tff(64,plain,
% 0.87/0.83 (![Board: array_int, Pos: $int] : (is_board1(Board, Pos) <=> ![Q: $int] : (($lesseq(0, Q) & $less(Q, Pos)) => ($lesseq(0, tb2t(get2(int, t2tb1(Board), Q))) & $less(tb2t(get2(int, t2tb1(Board), Q)), length1(int, t2tb1(Board)))))) <=> ![Board: array_int, Pos: $int] : (is_board1(Board, Pos) <=> ![Q: $int] : ((~($lesseq(0, Q) & (~$lesseq(Pos, Q)))) | ($lesseq(0, tb2t(get2(int, t2tb1(Board), Q))) & (~$lesseq(length1(int, t2tb1(Board)), tb2t(get2(int, t2tb1(Board), Q)))))))),
% 0.87/0.83 inference(quant_intro,[status(thm)],[63])).
% 0.87/0.83 tff(65,axiom,(![Board: array_int, Pos: $int] : (is_board1(Board, Pos) <=> ![Q: $int] : (($lesseq(0, Q) & $less(Q, Pos)) => ($lesseq(0, tb2t(get2(int, t2tb1(Board), Q))) & $less(tb2t(get2(int, t2tb1(Board), Q)), length1(int, t2tb1(Board))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','is_board_def')).
% 0.87/0.83 tff(66,plain,
% 0.87/0.83 (![Board: array_int, Pos: $int] : (is_board1(Board, Pos) <=> ![Q: $int] : ((~($lesseq(0, Q) & (~$lesseq(Pos, Q)))) | ($lesseq(0, tb2t(get2(int, t2tb1(Board), Q))) & (~$lesseq(length1(int, t2tb1(Board)), tb2t(get2(int, t2tb1(Board), Q)))))))),
% 0.87/0.83 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.87/0.83 tff(67,plain,
% 0.87/0.83 (![Board: array_int, Pos: $int] : (is_board1(Board, Pos) <=> ![Q: $int] : ((~($lesseq(0, Q) & (~$lesseq(Pos, Q)))) | ($lesseq(0, tb2t(get2(int, t2tb1(Board), Q))) & (~$lesseq(length1(int, t2tb1(Board)), tb2t(get2(int, t2tb1(Board), Q)))))))),
% 0.87/0.83 inference(modus_ponens,[status(thm)],[66, 62])).
% 0.87/0.83 tff(68,plain,
% 0.87/0.83 (![Board: array_int, Pos: $int] : (is_board1(Board, Pos) <=> ![Q: $int] : ((~($greatereq(Q, 0) & (~$lesseq($sum(Pos, $product(-1, Q)), 0)))) | ($greatereq(tb2t(get2(int, t2tb1(Board), Q)), 0) & (~$lesseq($sum(length1(int, t2tb1(Board)), $product(-1, tb2t(get2(int, t2tb1(Board), Q)))), 0)))))),
% 0.87/0.83 inference(modus_ponens,[status(thm)],[67, 61])).
% 0.87/0.83 tff(69,plain,
% 0.87/0.83 (![Board: array_int, Pos: $int] : (is_board1(Board, Pos) <=> ![Q: $int] : ((~($greatereq(Q, 0) & (~$lesseq($sum(Pos, $product(-1, Q)), 0)))) | ($greatereq(tb2t(get2(int, t2tb1(Board), Q)), 0) & (~$greatereq($sum(tb2t(get2(int, t2tb1(Board), Q)), $product(-1, length1(int, t2tb1(Board)))), 0)))))),
% 0.87/0.83 inference(modus_ponens,[status(thm)],[68, 59])).
% 0.87/0.83 tff(70,plain,(
% 0.87/0.83 ![Board: array_int, Pos: $int] : (((~is_board1(Board, Pos)) | ![Q: $int] : ((~($greatereq(Q, 0) & (~$lesseq($sum(Pos, $product(-1, Q)), 0)))) | ($greatereq(tb2t(get2(int, t2tb1(Board), Q)), 0) & (~$greatereq($sum(tb2t(get2(int, t2tb1(Board), Q)), $product(-1, length1(int, t2tb1(Board)))), 0))))) & (is_board1(Board, Pos) | (~((~($greatereq(tptp_fun_Q_2(Pos, Board), 0) & (~$lesseq($sum(Pos, $product(-1, tptp_fun_Q_2(Pos, Board))), 0)))) | ($greatereq(tb2t(get2(int, t2tb1(Board), tptp_fun_Q_2(Pos, Board))), 0) & (~$greatereq($sum(tb2t(get2(int, t2tb1(Board), tptp_fun_Q_2(Pos, Board))), $product(-1, length1(int, t2tb1(Board)))), 0)))))))),
% 0.87/0.83 inference(skolemize,[status(sab)],[69])).
% 0.87/0.83 tff(71,plain,
% 0.87/0.83 (![Board: array_int, Pos: $int] : (((~is_board1(Board, Pos)) | ![Q: $int] : ((~($greatereq(Q, 0) & (~$lesseq($sum(Pos, $product(-1, Q)), 0)))) | ($greatereq(tb2t(get2(int, t2tb1(Board), Q)), 0) & (~$greatereq($sum(tb2t(get2(int, t2tb1(Board), Q)), $product(-1, length1(int, t2tb1(Board)))), 0))))) & (is_board1(Board, Pos) | (~((~($greatereq(tptp_fun_Q_2(Pos, Board), 0) & (~$lesseq($sum(Pos, $product(-1, tptp_fun_Q_2(Pos, Board))), 0)))) | ($greatereq(tb2t(get2(int, t2tb1(Board), tptp_fun_Q_2(Pos, Board))), 0) & (~$lesseq($sum(length1(int, t2tb1(Board)), $product(-1, tb2t(get2(int, t2tb1(Board), tptp_fun_Q_2(Pos, Board))))), 0)))))))),
% 0.87/0.83 inference(modus_ponens,[status(thm)],[70, 57])).
% 0.87/0.83 tff(72,plain,
% 0.87/0.83 (![Board: array_int, Pos: $int] : (~((~((~is_board1(Board, Pos)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(Board), Q)), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(Board), Q)), $product(-1, length1(int, t2tb1(Board)))), 0)))))) | (~(is_board1(Board, Pos) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_2(Pos, Board))), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(Board), tptp_fun_Q_2(Pos, Board))), 0)) | $lesseq($sum(length1(int, t2tb1(Board)), $product(-1, tb2t(get2(int, t2tb1(Board), tptp_fun_Q_2(Pos, Board))))), 0))) | (~$greatereq(tptp_fun_Q_2(Pos, Board), 0))))))))),
% 0.87/0.83 inference(modus_ponens,[status(thm)],[71, 55])).
% 0.87/0.83 tff(73,plain,
% 0.87/0.83 (![Board: array_int, Pos: $int] : (~((~((~is_board1(Board, Pos)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(Board), Q)), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(Board), Q)), $product(-1, length1(int, t2tb1(Board)))), 0)))))) | (~(is_board1(Board, Pos) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_2(Pos, Board))), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(Board), tptp_fun_Q_2(Pos, Board))), 0)) | $lesseq($sum(length1(int, t2tb1(Board)), $product(-1, tb2t(get2(int, t2tb1(Board), tptp_fun_Q_2(Pos, Board))))), 0))) | (~$greatereq(tptp_fun_Q_2(Pos, Board), 0))))))))),
% 0.87/0.83 inference(modus_ponens,[status(thm)],[72, 53])).
% 0.87/0.83 tff(74,plain,
% 0.87/0.83 (((~![Board: array_int, Pos: $int] : (~((~((~is_board1(Board, Pos)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(Board), Q)), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(Board), Q)), $product(-1, length1(int, t2tb1(Board)))), 0)))))) | (~(is_board1(Board, Pos) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_2(Pos, Board))), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(Board), tptp_fun_Q_2(Pos, Board))), 0)) | $lesseq($sum(length1(int, t2tb1(Board)), $product(-1, tb2t(get2(int, t2tb1(Board), tptp_fun_Q_2(Pos, Board))))), 0))) | (~$greatereq(tptp_fun_Q_2(Pos, Board), 0))))))))) | (~((~((~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), $sum(1, Pos!4))) | ![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 1) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), Q)), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), Q)), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))))), 0)))))) | (~(is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), $sum(1, Pos!4)) | (~((~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), 0)) | $lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))))), 0))) | (~$greatereq(tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), 0)) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), -1)))))))) <=> ((~![Board: array_int, Pos: $int] : (~((~((~is_board1(Board, Pos)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(Board), Q)), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(Board), Q)), $product(-1, length1(int, t2tb1(Board)))), 0)))))) | (~(is_board1(Board, Pos) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_2(Pos, Board))), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(Board), tptp_fun_Q_2(Pos, Board))), 0)) | $lesseq($sum(length1(int, t2tb1(Board)), $product(-1, tb2t(get2(int, t2tb1(Board), tptp_fun_Q_2(Pos, Board))))), 0))) | (~$greatereq(tptp_fun_Q_2(Pos, Board), 0))))))))) | (~((~((~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), $sum(1, Pos!4))) | ![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 1) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), Q)), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), Q)), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))))), 0)))))) | (~(is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), $sum(1, Pos!4)) | (~((~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), 0)) | $lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))))), 0))) | (~$greatereq(tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), 0)) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), -1))))))))),
% 0.87/0.83 inference(rewrite,[status(thm)],[])).
% 0.87/0.83 tff(75,plain,
% 0.87/0.83 ((~((~((~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), $sum(1, Pos!4))) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum($sum(1, Pos!4), $product(-1, Q)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), Q)), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), Q)), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))))), 0)))))) | (~(is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), $sum(1, Pos!4)) | (~($lesseq($sum($sum(1, Pos!4), $product(-1, tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), 0)) | $lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))))), 0))) | (~$greatereq(tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), 0)))))))) <=> (~((~((~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), $sum(1, Pos!4))) | ![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 1) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), Q)), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), Q)), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))))), 0)))))) | (~(is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), $sum(1, Pos!4)) | (~((~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), 0)) | $lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))))), 0))) | (~$greatereq(tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), 0)) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), -1)))))))),
% 0.87/0.83 inference(rewrite,[status(thm)],[])).
% 0.87/0.83 tff(76,plain,
% 0.87/0.83 (((~![Board: array_int, Pos: $int] : (~((~((~is_board1(Board, Pos)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(Board), Q)), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(Board), Q)), $product(-1, length1(int, t2tb1(Board)))), 0)))))) | (~(is_board1(Board, Pos) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_2(Pos, Board))), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(Board), tptp_fun_Q_2(Pos, Board))), 0)) | $lesseq($sum(length1(int, t2tb1(Board)), $product(-1, tb2t(get2(int, t2tb1(Board), tptp_fun_Q_2(Pos, Board))))), 0))) | (~$greatereq(tptp_fun_Q_2(Pos, Board), 0))))))))) | (~((~((~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), $sum(1, Pos!4))) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum($sum(1, Pos!4), $product(-1, Q)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), Q)), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), Q)), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))))), 0)))))) | (~(is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), $sum(1, Pos!4)) | (~($lesseq($sum($sum(1, Pos!4), $product(-1, tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), 0)) | $lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))))), 0))) | (~$greatereq(tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), 0))))))))) <=> ((~![Board: array_int, Pos: $int] : (~((~((~is_board1(Board, Pos)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(Board), Q)), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(Board), Q)), $product(-1, length1(int, t2tb1(Board)))), 0)))))) | (~(is_board1(Board, Pos) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_2(Pos, Board))), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(Board), tptp_fun_Q_2(Pos, Board))), 0)) | $lesseq($sum(length1(int, t2tb1(Board)), $product(-1, tb2t(get2(int, t2tb1(Board), tptp_fun_Q_2(Pos, Board))))), 0))) | (~$greatereq(tptp_fun_Q_2(Pos, Board), 0))))))))) | (~((~((~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), $sum(1, Pos!4))) | ![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 1) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), Q)), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), Q)), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))))), 0)))))) | (~(is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), $sum(1, Pos!4)) | (~((~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), 0)) | $lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))))), 0))) | (~$greatereq(tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), 0)) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), -1))))))))),
% 0.87/0.84 inference(monotonicity,[status(thm)],[75])).
% 0.87/0.84 tff(77,plain,
% 0.87/0.84 (((~![Board: array_int, Pos: $int] : (~((~((~is_board1(Board, Pos)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(Board), Q)), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(Board), Q)), $product(-1, length1(int, t2tb1(Board)))), 0)))))) | (~(is_board1(Board, Pos) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_2(Pos, Board))), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(Board), tptp_fun_Q_2(Pos, Board))), 0)) | $lesseq($sum(length1(int, t2tb1(Board)), $product(-1, tb2t(get2(int, t2tb1(Board), tptp_fun_Q_2(Pos, Board))))), 0))) | (~$greatereq(tptp_fun_Q_2(Pos, Board), 0))))))))) | (~((~((~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), $sum(1, Pos!4))) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum($sum(1, Pos!4), $product(-1, Q)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), Q)), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), Q)), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))))), 0)))))) | (~(is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), $sum(1, Pos!4)) | (~($lesseq($sum($sum(1, Pos!4), $product(-1, tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), 0)) | $lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))))), 0))) | (~$greatereq(tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), 0))))))))) <=> ((~![Board: array_int, Pos: $int] : (~((~((~is_board1(Board, Pos)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(Board), Q)), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(Board), Q)), $product(-1, length1(int, t2tb1(Board)))), 0)))))) | (~(is_board1(Board, Pos) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_2(Pos, Board))), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(Board), tptp_fun_Q_2(Pos, Board))), 0)) | $lesseq($sum(length1(int, t2tb1(Board)), $product(-1, tb2t(get2(int, t2tb1(Board), tptp_fun_Q_2(Pos, Board))))), 0))) | (~$greatereq(tptp_fun_Q_2(Pos, Board), 0))))))))) | (~((~((~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), $sum(1, Pos!4))) | ![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 1) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), Q)), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), Q)), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))))), 0)))))) | (~(is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), $sum(1, Pos!4)) | (~((~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), 0)) | $lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))))), 0))) | (~$greatereq(tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), 0)) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), -1))))))))),
% 0.87/0.84 inference(transitivity,[status(thm)],[76, 74])).
% 0.87/0.84 tff(78,plain,
% 0.87/0.84 ((~![Board: array_int, Pos: $int] : (~((~((~is_board1(Board, Pos)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(Board), Q)), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(Board), Q)), $product(-1, length1(int, t2tb1(Board)))), 0)))))) | (~(is_board1(Board, Pos) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_2(Pos, Board))), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(Board), tptp_fun_Q_2(Pos, Board))), 0)) | $lesseq($sum(length1(int, t2tb1(Board)), $product(-1, tb2t(get2(int, t2tb1(Board), tptp_fun_Q_2(Pos, Board))))), 0))) | (~$greatereq(tptp_fun_Q_2(Pos, Board), 0))))))))) | (~((~((~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), $sum(1, Pos!4))) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum($sum(1, Pos!4), $product(-1, Q)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), Q)), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), Q)), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))))), 0)))))) | (~(is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), $sum(1, Pos!4)) | (~($lesseq($sum($sum(1, Pos!4), $product(-1, tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), 0)) | $lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))))), 0))) | (~$greatereq(tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), 0))))))))),
% 0.87/0.84 inference(quant_inst,[status(thm)],[])).
% 0.87/0.84 tff(79,plain,
% 0.87/0.84 ((~![Board: array_int, Pos: $int] : (~((~((~is_board1(Board, Pos)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(Board), Q)), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(Board), Q)), $product(-1, length1(int, t2tb1(Board)))), 0)))))) | (~(is_board1(Board, Pos) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_2(Pos, Board))), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(Board), tptp_fun_Q_2(Pos, Board))), 0)) | $lesseq($sum(length1(int, t2tb1(Board)), $product(-1, tb2t(get2(int, t2tb1(Board), tptp_fun_Q_2(Pos, Board))))), 0))) | (~$greatereq(tptp_fun_Q_2(Pos, Board), 0))))))))) | (~((~((~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), $sum(1, Pos!4))) | ![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 1) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), Q)), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), Q)), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))))), 0)))))) | (~(is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), $sum(1, Pos!4)) | (~((~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), 0)) | $lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))))), 0))) | (~$greatereq(tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), 0)) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), -1)))))))),
% 0.87/0.84 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.87/0.84 tff(80,plain,
% 0.87/0.84 (~((~((~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), $sum(1, Pos!4))) | ![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 1) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), Q)), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), Q)), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))))), 0)))))) | (~(is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), $sum(1, Pos!4)) | (~((~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), 0)) | $lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))))), 0))) | (~$greatereq(tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), 0)) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), -1))))))),
% 0.87/0.84 inference(unit_resolution,[status(thm)],[79, 73])).
% 0.87/0.84 tff(81,plain,
% 0.87/0.84 (((~((~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), $sum(1, Pos!4))) | ![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 1) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), Q)), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), Q)), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))))), 0)))))) | (~(is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), $sum(1, Pos!4)) | (~((~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), 0)) | $lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))))), 0))) | (~$greatereq(tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), 0)) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), -1)))))) | (is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), $sum(1, Pos!4)) | (~((~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), 0)) | $lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))))), 0))) | (~$greatereq(tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), 0)) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), -1))))),
% 0.87/0.84 inference(tautology,[status(thm)],[])).
% 0.87/0.84 tff(82,plain,
% 0.87/0.84 (is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), $sum(1, Pos!4)) | (~((~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), 0)) | $lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))))), 0))) | (~$greatereq(tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), 0)) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), -1)))),
% 0.87/0.84 inference(unit_resolution,[status(thm)],[81, 80])).
% 0.87/0.84 tff(83,plain,
% 0.87/0.84 (^[Board: array_int, Pos: $int] : rewrite((~((~((~solution1(Board, Pos)) | (~((~is_board1(Board, Pos)) | (~![Q: $int] : (is_consistent1(Board, Q) | (~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0))))))) | (~(solution1(Board, Pos) | (~is_board1(Board, Pos)) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_3(Pos, Board))), 0) | is_consistent1(Board, tptp_fun_Q_3(Pos, Board)) | (~$greatereq(tptp_fun_Q_3(Pos, Board), 0)))))))) <=> (~((~(solution1(Board, Pos) | (~is_board1(Board, Pos)) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_3(Pos, Board))), 0) | is_consistent1(Board, tptp_fun_Q_3(Pos, Board)) | (~$greatereq(tptp_fun_Q_3(Pos, Board), 0)))))) | (~((~solution1(Board, Pos)) | (~((~is_board1(Board, Pos)) | (~![Q: $int] : (is_consistent1(Board, Q) | (~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0))))))))))),
% 0.87/0.84 inference(bind,[status(th)],[])).
% 0.87/0.84 tff(84,plain,
% 0.87/0.84 (![Board: array_int, Pos: $int] : (~((~((~solution1(Board, Pos)) | (~((~is_board1(Board, Pos)) | (~![Q: $int] : (is_consistent1(Board, Q) | (~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0))))))) | (~(solution1(Board, Pos) | (~is_board1(Board, Pos)) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_3(Pos, Board))), 0) | is_consistent1(Board, tptp_fun_Q_3(Pos, Board)) | (~$greatereq(tptp_fun_Q_3(Pos, Board), 0)))))))) <=> ![Board: array_int, Pos: $int] : (~((~(solution1(Board, Pos) | (~is_board1(Board, Pos)) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_3(Pos, Board))), 0) | is_consistent1(Board, tptp_fun_Q_3(Pos, Board)) | (~$greatereq(tptp_fun_Q_3(Pos, Board), 0)))))) | (~((~solution1(Board, Pos)) | (~((~is_board1(Board, Pos)) | (~![Q: $int] : (is_consistent1(Board, Q) | (~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0)))))))))),
% 0.87/0.84 inference(quant_intro,[status(thm)],[83])).
% 0.87/0.84 tff(85,plain,
% 0.87/0.84 (^[Board: array_int, Pos: $int] : refl((~((~((~solution1(Board, Pos)) | (~((~is_board1(Board, Pos)) | (~![Q: $int] : (is_consistent1(Board, Q) | (~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0))))))) | (~(solution1(Board, Pos) | (~is_board1(Board, Pos)) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_3(Pos, Board))), 0) | is_consistent1(Board, tptp_fun_Q_3(Pos, Board)) | (~$greatereq(tptp_fun_Q_3(Pos, Board), 0)))))))) <=> (~((~((~solution1(Board, Pos)) | (~((~is_board1(Board, Pos)) | (~![Q: $int] : (is_consistent1(Board, Q) | (~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0))))))) | (~(solution1(Board, Pos) | (~is_board1(Board, Pos)) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_3(Pos, Board))), 0) | is_consistent1(Board, tptp_fun_Q_3(Pos, Board)) | (~$greatereq(tptp_fun_Q_3(Pos, Board), 0)))))))))),
% 0.87/0.84 inference(bind,[status(th)],[])).
% 0.87/0.84 tff(86,plain,
% 0.87/0.84 (![Board: array_int, Pos: $int] : (~((~((~solution1(Board, Pos)) | (~((~is_board1(Board, Pos)) | (~![Q: $int] : (is_consistent1(Board, Q) | (~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0))))))) | (~(solution1(Board, Pos) | (~is_board1(Board, Pos)) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_3(Pos, Board))), 0) | is_consistent1(Board, tptp_fun_Q_3(Pos, Board)) | (~$greatereq(tptp_fun_Q_3(Pos, Board), 0)))))))) <=> ![Board: array_int, Pos: $int] : (~((~((~solution1(Board, Pos)) | (~((~is_board1(Board, Pos)) | (~![Q: $int] : (is_consistent1(Board, Q) | (~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0))))))) | (~(solution1(Board, Pos) | (~is_board1(Board, Pos)) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_3(Pos, Board))), 0) | is_consistent1(Board, tptp_fun_Q_3(Pos, Board)) | (~$greatereq(tptp_fun_Q_3(Pos, Board), 0))))))))),
% 0.87/0.84 inference(quant_intro,[status(thm)],[85])).
% 0.87/0.84 tff(87,plain,
% 0.87/0.84 (^[Board: array_int, Pos: $int] : rewrite((~((~((~solution1(Board, Pos)) | (~((~is_board1(Board, Pos)) | (~![Q: $int] : (is_consistent1(Board, Q) | (~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0))))))) | (~(solution1(Board, Pos) | (~is_board1(Board, Pos)) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_3(Pos, Board))), 0) | is_consistent1(Board, tptp_fun_Q_3(Pos, Board)) | (~$greatereq(tptp_fun_Q_3(Pos, Board), 0)))))))) <=> (~((~((~solution1(Board, Pos)) | (~((~is_board1(Board, Pos)) | (~![Q: $int] : (is_consistent1(Board, Q) | (~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0))))))) | (~(solution1(Board, Pos) | (~is_board1(Board, Pos)) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_3(Pos, Board))), 0) | is_consistent1(Board, tptp_fun_Q_3(Pos, Board)) | (~$greatereq(tptp_fun_Q_3(Pos, Board), 0)))))))))),
% 0.87/0.84 inference(bind,[status(th)],[])).
% 0.87/0.84 tff(88,plain,
% 0.87/0.84 (![Board: array_int, Pos: $int] : (~((~((~solution1(Board, Pos)) | (~((~is_board1(Board, Pos)) | (~![Q: $int] : (is_consistent1(Board, Q) | (~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0))))))) | (~(solution1(Board, Pos) | (~is_board1(Board, Pos)) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_3(Pos, Board))), 0) | is_consistent1(Board, tptp_fun_Q_3(Pos, Board)) | (~$greatereq(tptp_fun_Q_3(Pos, Board), 0)))))))) <=> ![Board: array_int, Pos: $int] : (~((~((~solution1(Board, Pos)) | (~((~is_board1(Board, Pos)) | (~![Q: $int] : (is_consistent1(Board, Q) | (~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0))))))) | (~(solution1(Board, Pos) | (~is_board1(Board, Pos)) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_3(Pos, Board))), 0) | is_consistent1(Board, tptp_fun_Q_3(Pos, Board)) | (~$greatereq(tptp_fun_Q_3(Pos, Board), 0))))))))),
% 0.87/0.84 inference(quant_intro,[status(thm)],[87])).
% 0.87/0.84 tff(89,plain,
% 0.87/0.84 (![Board: array_int, Pos: $int] : (~((~((~solution1(Board, Pos)) | (~((~is_board1(Board, Pos)) | (~![Q: $int] : (is_consistent1(Board, Q) | (~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0))))))) | (~(solution1(Board, Pos) | (~is_board1(Board, Pos)) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_3(Pos, Board))), 0) | is_consistent1(Board, tptp_fun_Q_3(Pos, Board)) | (~$greatereq(tptp_fun_Q_3(Pos, Board), 0)))))))) <=> ![Board: array_int, Pos: $int] : (~((~((~solution1(Board, Pos)) | (~((~is_board1(Board, Pos)) | (~![Q: $int] : (is_consistent1(Board, Q) | (~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0))))))) | (~(solution1(Board, Pos) | (~is_board1(Board, Pos)) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_3(Pos, Board))), 0) | is_consistent1(Board, tptp_fun_Q_3(Pos, Board)) | (~$greatereq(tptp_fun_Q_3(Pos, Board), 0))))))))),
% 0.87/0.84 inference(transitivity,[status(thm)],[88, 86])).
% 0.87/0.84 tff(90,plain,
% 0.87/0.84 (^[Board: array_int, Pos: $int] : trans(monotonicity(rewrite(((~solution1(Board, Pos)) | (is_board1(Board, Pos) & ![Q: $int] : ((~($greatereq(Q, 0) & (~$lesseq($sum(Pos, $product(-1, Q)), 0)))) | is_consistent1(Board, Q)))) <=> ((~solution1(Board, Pos)) | (~((~is_board1(Board, Pos)) | (~![Q: $int] : (is_consistent1(Board, Q) | (~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0))))))), trans(monotonicity(rewrite((~((~($greatereq(tptp_fun_Q_3(Pos, Board), 0) & (~$lesseq($sum(Pos, $product(-1, tptp_fun_Q_3(Pos, Board))), 0)))) | is_consistent1(Board, tptp_fun_Q_3(Pos, Board)))) <=> (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_3(Pos, Board))), 0) | is_consistent1(Board, tptp_fun_Q_3(Pos, Board)) | (~$greatereq(tptp_fun_Q_3(Pos, Board), 0))))), ((solution1(Board, Pos) | (~is_board1(Board, Pos)) | (~((~($greatereq(tptp_fun_Q_3(Pos, Board), 0) & (~$lesseq($sum(Pos, $product(-1, tptp_fun_Q_3(Pos, Board))), 0)))) | is_consistent1(Board, tptp_fun_Q_3(Pos, Board))))) <=> (solution1(Board, Pos) | (~is_board1(Board, Pos)) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_3(Pos, Board))), 0) | is_consistent1(Board, tptp_fun_Q_3(Pos, Board)) | (~$greatereq(tptp_fun_Q_3(Pos, Board), 0))))))), rewrite((solution1(Board, Pos) | (~is_board1(Board, Pos)) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_3(Pos, Board))), 0) | is_consistent1(Board, tptp_fun_Q_3(Pos, Board)) | (~$greatereq(tptp_fun_Q_3(Pos, Board), 0))))) <=> (solution1(Board, Pos) | (~is_board1(Board, Pos)) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_3(Pos, Board))), 0) | is_consistent1(Board, tptp_fun_Q_3(Pos, Board)) | (~$greatereq(tptp_fun_Q_3(Pos, Board), 0)))))), ((solution1(Board, Pos) | (~is_board1(Board, Pos)) | (~((~($greatereq(tptp_fun_Q_3(Pos, Board), 0) & (~$lesseq($sum(Pos, $product(-1, tptp_fun_Q_3(Pos, Board))), 0)))) | is_consistent1(Board, tptp_fun_Q_3(Pos, Board))))) <=> (solution1(Board, Pos) | (~is_board1(Board, Pos)) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_3(Pos, Board))), 0) | is_consistent1(Board, tptp_fun_Q_3(Pos, Board)) | (~$greatereq(tptp_fun_Q_3(Pos, Board), 0))))))), ((((~solution1(Board, Pos)) | (is_board1(Board, Pos) & ![Q: $int] : ((~($greatereq(Q, 0) & (~$lesseq($sum(Pos, $product(-1, Q)), 0)))) | is_consistent1(Board, Q)))) & (solution1(Board, Pos) | (~is_board1(Board, Pos)) | (~((~($greatereq(tptp_fun_Q_3(Pos, Board), 0) & (~$lesseq($sum(Pos, $product(-1, tptp_fun_Q_3(Pos, Board))), 0)))) | is_consistent1(Board, tptp_fun_Q_3(Pos, Board)))))) <=> (((~solution1(Board, Pos)) | (~((~is_board1(Board, Pos)) | (~![Q: $int] : (is_consistent1(Board, Q) | (~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0)))))) & (solution1(Board, Pos) | (~is_board1(Board, Pos)) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_3(Pos, Board))), 0) | is_consistent1(Board, tptp_fun_Q_3(Pos, Board)) | (~$greatereq(tptp_fun_Q_3(Pos, Board), 0)))))))), rewrite((((~solution1(Board, Pos)) | (~((~is_board1(Board, Pos)) | (~![Q: $int] : (is_consistent1(Board, Q) | (~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0)))))) & (solution1(Board, Pos) | (~is_board1(Board, Pos)) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_3(Pos, Board))), 0) | is_consistent1(Board, tptp_fun_Q_3(Pos, Board)) | (~$greatereq(tptp_fun_Q_3(Pos, Board), 0)))))) <=> (~((~((~solution1(Board, Pos)) | (~((~is_board1(Board, Pos)) | (~![Q: $int] : (is_consistent1(Board, Q) | (~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0))))))) | (~(solution1(Board, Pos) | (~is_board1(Board, Pos)) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_3(Pos, Board))), 0) | is_consistent1(Board, tptp_fun_Q_3(Pos, Board)) | (~$greatereq(tptp_fun_Q_3(Pos, Board), 0))))))))), ((((~solution1(Board, Pos)) | (is_board1(Board, Pos) & ![Q: $int] : ((~($greatereq(Q, 0) & (~$lesseq($sum(Pos, $product(-1, Q)), 0)))) | is_consistent1(Board, Q)))) & (solution1(Board, Pos) | (~is_board1(Board, Pos)) | (~((~($greatereq(tptp_fun_Q_3(Pos, Board), 0) & (~$lesseq($sum(Pos, $product(-1, tptp_fun_Q_3(Pos, Board))), 0)))) | is_consistent1(Board, tptp_fun_Q_3(Pos, Board)))))) <=> (~((~((~solution1(Board, Pos)) | (~((~is_board1(Board, Pos)) | (~![Q: $int] : (is_consistent1(Board, Q) | (~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0))))))) | (~(solution1(Board, Pos) | (~is_board1(Board, Pos)) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_3(Pos, Board))), 0) | is_consistent1(Board, tptp_fun_Q_3(Pos, Board)) | (~$greatereq(tptp_fun_Q_3(Pos, Board), 0))))))))))),
% 0.87/0.84 inference(bind,[status(th)],[])).
% 0.87/0.84 tff(91,plain,
% 0.87/0.84 (![Board: array_int, Pos: $int] : (((~solution1(Board, Pos)) | (is_board1(Board, Pos) & ![Q: $int] : ((~($greatereq(Q, 0) & (~$lesseq($sum(Pos, $product(-1, Q)), 0)))) | is_consistent1(Board, Q)))) & (solution1(Board, Pos) | (~is_board1(Board, Pos)) | (~((~($greatereq(tptp_fun_Q_3(Pos, Board), 0) & (~$lesseq($sum(Pos, $product(-1, tptp_fun_Q_3(Pos, Board))), 0)))) | is_consistent1(Board, tptp_fun_Q_3(Pos, Board)))))) <=> ![Board: array_int, Pos: $int] : (~((~((~solution1(Board, Pos)) | (~((~is_board1(Board, Pos)) | (~![Q: $int] : (is_consistent1(Board, Q) | (~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0))))))) | (~(solution1(Board, Pos) | (~is_board1(Board, Pos)) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_3(Pos, Board))), 0) | is_consistent1(Board, tptp_fun_Q_3(Pos, Board)) | (~$greatereq(tptp_fun_Q_3(Pos, Board), 0))))))))),
% 0.87/0.84 inference(quant_intro,[status(thm)],[90])).
% 0.87/0.84 tff(92,plain,
% 0.87/0.84 (^[Board: array_int, Pos: $int] : rewrite((((~solution1(Board, Pos)) | (is_board1(Board, Pos) & ![Q: $int] : ((~($greatereq(Q, 0) & (~$lesseq($sum(Pos, $product(-1, Q)), 0)))) | is_consistent1(Board, Q)))) & (solution1(Board, Pos) | ((~is_board1(Board, Pos)) | (~((~($greatereq(tptp_fun_Q_3(Pos, Board), 0) & (~$lesseq($sum(Pos, $product(-1, tptp_fun_Q_3(Pos, Board))), 0)))) | is_consistent1(Board, tptp_fun_Q_3(Pos, Board))))))) <=> (((~solution1(Board, Pos)) | (is_board1(Board, Pos) & ![Q: $int] : ((~($greatereq(Q, 0) & (~$lesseq($sum(Pos, $product(-1, Q)), 0)))) | is_consistent1(Board, Q)))) & (solution1(Board, Pos) | (~is_board1(Board, Pos)) | (~((~($greatereq(tptp_fun_Q_3(Pos, Board), 0) & (~$lesseq($sum(Pos, $product(-1, tptp_fun_Q_3(Pos, Board))), 0)))) | is_consistent1(Board, tptp_fun_Q_3(Pos, Board)))))))),
% 0.87/0.84 inference(bind,[status(th)],[])).
% 0.87/0.84 tff(93,plain,
% 0.87/0.84 (![Board: array_int, Pos: $int] : (((~solution1(Board, Pos)) | (is_board1(Board, Pos) & ![Q: $int] : ((~($greatereq(Q, 0) & (~$lesseq($sum(Pos, $product(-1, Q)), 0)))) | is_consistent1(Board, Q)))) & (solution1(Board, Pos) | ((~is_board1(Board, Pos)) | (~((~($greatereq(tptp_fun_Q_3(Pos, Board), 0) & (~$lesseq($sum(Pos, $product(-1, tptp_fun_Q_3(Pos, Board))), 0)))) | is_consistent1(Board, tptp_fun_Q_3(Pos, Board))))))) <=> ![Board: array_int, Pos: $int] : (((~solution1(Board, Pos)) | (is_board1(Board, Pos) & ![Q: $int] : ((~($greatereq(Q, 0) & (~$lesseq($sum(Pos, $product(-1, Q)), 0)))) | is_consistent1(Board, Q)))) & (solution1(Board, Pos) | (~is_board1(Board, Pos)) | (~((~($greatereq(tptp_fun_Q_3(Pos, Board), 0) & (~$lesseq($sum(Pos, $product(-1, tptp_fun_Q_3(Pos, Board))), 0)))) | is_consistent1(Board, tptp_fun_Q_3(Pos, Board))))))),
% 0.87/0.84 inference(quant_intro,[status(thm)],[92])).
% 0.87/0.84 tff(94,plain,
% 0.87/0.84 (^[Board: array_int, Pos: $int] : rewrite((solution1(Board, Pos) <=> (is_board1(Board, Pos) & ![Q: $int] : ((~($lesseq(0, Q) & (~$lesseq(Pos, Q)))) | is_consistent1(Board, Q)))) <=> (solution1(Board, Pos) <=> (is_board1(Board, Pos) & ![Q: $int] : ((~($greatereq(Q, 0) & (~$lesseq($sum(Pos, $product(-1, Q)), 0)))) | is_consistent1(Board, Q)))))),
% 0.87/0.84 inference(bind,[status(th)],[])).
% 0.87/0.84 tff(95,plain,
% 0.87/0.84 (![Board: array_int, Pos: $int] : (solution1(Board, Pos) <=> (is_board1(Board, Pos) & ![Q: $int] : ((~($lesseq(0, Q) & (~$lesseq(Pos, Q)))) | is_consistent1(Board, Q)))) <=> ![Board: array_int, Pos: $int] : (solution1(Board, Pos) <=> (is_board1(Board, Pos) & ![Q: $int] : ((~($greatereq(Q, 0) & (~$lesseq($sum(Pos, $product(-1, Q)), 0)))) | is_consistent1(Board, Q))))),
% 0.87/0.84 inference(quant_intro,[status(thm)],[94])).
% 0.87/0.84 tff(96,plain,
% 0.87/0.84 (![Board: array_int, Pos: $int] : (solution1(Board, Pos) <=> (is_board1(Board, Pos) & ![Q: $int] : ((~($lesseq(0, Q) & (~$lesseq(Pos, Q)))) | is_consistent1(Board, Q)))) <=> ![Board: array_int, Pos: $int] : (solution1(Board, Pos) <=> (is_board1(Board, Pos) & ![Q: $int] : ((~($lesseq(0, Q) & (~$lesseq(Pos, Q)))) | is_consistent1(Board, Q))))),
% 0.87/0.84 inference(rewrite,[status(thm)],[])).
% 0.87/0.84 tff(97,plain,
% 0.87/0.84 (^[Board: array_int, Pos: $int] : rewrite((solution1(Board, Pos) <=> (is_board1(Board, Pos) & ![Q: $int] : (($lesseq(0, Q) & $less(Q, Pos)) => is_consistent1(Board, Q)))) <=> (solution1(Board, Pos) <=> (is_board1(Board, Pos) & ![Q: $int] : ((~($lesseq(0, Q) & (~$lesseq(Pos, Q)))) | is_consistent1(Board, Q)))))),
% 0.87/0.84 inference(bind,[status(th)],[])).
% 0.87/0.84 tff(98,plain,
% 0.87/0.84 (![Board: array_int, Pos: $int] : (solution1(Board, Pos) <=> (is_board1(Board, Pos) & ![Q: $int] : (($lesseq(0, Q) & $less(Q, Pos)) => is_consistent1(Board, Q)))) <=> ![Board: array_int, Pos: $int] : (solution1(Board, Pos) <=> (is_board1(Board, Pos) & ![Q: $int] : ((~($lesseq(0, Q) & (~$lesseq(Pos, Q)))) | is_consistent1(Board, Q))))),
% 0.87/0.84 inference(quant_intro,[status(thm)],[97])).
% 0.87/0.84 tff(99,axiom,(![Board: array_int, Pos: $int] : (solution1(Board, Pos) <=> (is_board1(Board, Pos) & ![Q: $int] : (($lesseq(0, Q) & $less(Q, Pos)) => is_consistent1(Board, Q))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','solution_def')).
% 0.87/0.84 tff(100,plain,
% 0.87/0.84 (![Board: array_int, Pos: $int] : (solution1(Board, Pos) <=> (is_board1(Board, Pos) & ![Q: $int] : ((~($lesseq(0, Q) & (~$lesseq(Pos, Q)))) | is_consistent1(Board, Q))))),
% 0.87/0.84 inference(modus_ponens,[status(thm)],[99, 98])).
% 0.87/0.84 tff(101,plain,
% 0.87/0.84 (![Board: array_int, Pos: $int] : (solution1(Board, Pos) <=> (is_board1(Board, Pos) & ![Q: $int] : ((~($lesseq(0, Q) & (~$lesseq(Pos, Q)))) | is_consistent1(Board, Q))))),
% 0.87/0.84 inference(modus_ponens,[status(thm)],[100, 96])).
% 0.87/0.84 tff(102,plain,
% 0.87/0.84 (![Board: array_int, Pos: $int] : (solution1(Board, Pos) <=> (is_board1(Board, Pos) & ![Q: $int] : ((~($greatereq(Q, 0) & (~$lesseq($sum(Pos, $product(-1, Q)), 0)))) | is_consistent1(Board, Q))))),
% 0.87/0.84 inference(modus_ponens,[status(thm)],[101, 95])).
% 0.87/0.84 tff(103,plain,(
% 0.87/0.84 ![Board: array_int, Pos: $int] : (((~solution1(Board, Pos)) | (is_board1(Board, Pos) & ![Q: $int] : ((~($greatereq(Q, 0) & (~$lesseq($sum(Pos, $product(-1, Q)), 0)))) | is_consistent1(Board, Q)))) & (solution1(Board, Pos) | ((~is_board1(Board, Pos)) | (~((~($greatereq(tptp_fun_Q_3(Pos, Board), 0) & (~$lesseq($sum(Pos, $product(-1, tptp_fun_Q_3(Pos, Board))), 0)))) | is_consistent1(Board, tptp_fun_Q_3(Pos, Board)))))))),
% 0.87/0.84 inference(skolemize,[status(sab)],[102])).
% 0.87/0.84 tff(104,plain,
% 0.87/0.84 (![Board: array_int, Pos: $int] : (((~solution1(Board, Pos)) | (is_board1(Board, Pos) & ![Q: $int] : ((~($greatereq(Q, 0) & (~$lesseq($sum(Pos, $product(-1, Q)), 0)))) | is_consistent1(Board, Q)))) & (solution1(Board, Pos) | (~is_board1(Board, Pos)) | (~((~($greatereq(tptp_fun_Q_3(Pos, Board), 0) & (~$lesseq($sum(Pos, $product(-1, tptp_fun_Q_3(Pos, Board))), 0)))) | is_consistent1(Board, tptp_fun_Q_3(Pos, Board))))))),
% 0.87/0.84 inference(modus_ponens,[status(thm)],[103, 93])).
% 0.87/0.84 tff(105,plain,
% 0.87/0.84 (![Board: array_int, Pos: $int] : (~((~((~solution1(Board, Pos)) | (~((~is_board1(Board, Pos)) | (~![Q: $int] : (is_consistent1(Board, Q) | (~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0))))))) | (~(solution1(Board, Pos) | (~is_board1(Board, Pos)) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_3(Pos, Board))), 0) | is_consistent1(Board, tptp_fun_Q_3(Pos, Board)) | (~$greatereq(tptp_fun_Q_3(Pos, Board), 0))))))))),
% 0.87/0.84 inference(modus_ponens,[status(thm)],[104, 91])).
% 0.87/0.84 tff(106,plain,
% 0.87/0.84 (![Board: array_int, Pos: $int] : (~((~((~solution1(Board, Pos)) | (~((~is_board1(Board, Pos)) | (~![Q: $int] : (is_consistent1(Board, Q) | (~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0))))))) | (~(solution1(Board, Pos) | (~is_board1(Board, Pos)) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_3(Pos, Board))), 0) | is_consistent1(Board, tptp_fun_Q_3(Pos, Board)) | (~$greatereq(tptp_fun_Q_3(Pos, Board), 0))))))))),
% 0.87/0.84 inference(modus_ponens,[status(thm)],[105, 89])).
% 0.87/0.84 tff(107,plain,
% 0.87/0.84 (![Board: array_int, Pos: $int] : (~((~(solution1(Board, Pos) | (~is_board1(Board, Pos)) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_3(Pos, Board))), 0) | is_consistent1(Board, tptp_fun_Q_3(Pos, Board)) | (~$greatereq(tptp_fun_Q_3(Pos, Board), 0)))))) | (~((~solution1(Board, Pos)) | (~((~is_board1(Board, Pos)) | (~![Q: $int] : (is_consistent1(Board, Q) | (~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0)))))))))),
% 0.87/0.84 inference(modus_ponens,[status(thm)],[106, 84])).
% 0.87/0.84 tff(108,plain,
% 0.87/0.84 (((~![Board: array_int, Pos: $int] : (~((~(solution1(Board, Pos) | (~is_board1(Board, Pos)) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_3(Pos, Board))), 0) | is_consistent1(Board, tptp_fun_Q_3(Pos, Board)) | (~$greatereq(tptp_fun_Q_3(Pos, Board), 0)))))) | (~((~solution1(Board, Pos)) | (~((~is_board1(Board, Pos)) | (~![Q: $int] : (is_consistent1(Board, Q) | (~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0)))))))))) | (~((~(solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), $sum(1, Pos!4)) | (~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), $sum(1, Pos!4))) | (~(is_consistent1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))) | (~$greatereq(tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), 0)) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), -1))))) | (~((~solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), $sum(1, Pos!4))) | (~((~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), $sum(1, Pos!4))) | (~![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 1) | is_consistent1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Q)))))))))) <=> ((~![Board: array_int, Pos: $int] : (~((~(solution1(Board, Pos) | (~is_board1(Board, Pos)) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_3(Pos, Board))), 0) | is_consistent1(Board, tptp_fun_Q_3(Pos, Board)) | (~$greatereq(tptp_fun_Q_3(Pos, Board), 0)))))) | (~((~solution1(Board, Pos)) | (~((~is_board1(Board, Pos)) | (~![Q: $int] : (is_consistent1(Board, Q) | (~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0)))))))))) | (~((~(solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), $sum(1, Pos!4)) | (~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), $sum(1, Pos!4))) | (~(is_consistent1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))) | (~$greatereq(tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), 0)) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), -1))))) | (~((~solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), $sum(1, Pos!4))) | (~((~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), $sum(1, Pos!4))) | (~![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 1) | is_consistent1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Q))))))))))),
% 0.87/0.84 inference(rewrite,[status(thm)],[])).
% 0.87/0.84 tff(109,plain,
% 0.87/0.84 ((~((~(solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), $sum(1, Pos!4)) | (~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), $sum(1, Pos!4))) | (~($lesseq($sum($sum(1, Pos!4), $product(-1, tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), 0) | is_consistent1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))) | (~$greatereq(tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), 0)))))) | (~((~solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), $sum(1, Pos!4))) | (~((~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), $sum(1, Pos!4))) | (~![Q: $int] : (is_consistent1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Q) | (~$greatereq(Q, 0)) | $lesseq($sum($sum(1, Pos!4), $product(-1, Q)), 0))))))))) <=> (~((~(solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), $sum(1, Pos!4)) | (~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), $sum(1, Pos!4))) | (~(is_consistent1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))) | (~$greatereq(tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), 0)) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), -1))))) | (~((~solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), $sum(1, Pos!4))) | (~((~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), $sum(1, Pos!4))) | (~![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 1) | is_consistent1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Q)))))))))),
% 0.87/0.84 inference(rewrite,[status(thm)],[])).
% 0.87/0.84 tff(110,plain,
% 0.87/0.84 (((~![Board: array_int, Pos: $int] : (~((~(solution1(Board, Pos) | (~is_board1(Board, Pos)) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_3(Pos, Board))), 0) | is_consistent1(Board, tptp_fun_Q_3(Pos, Board)) | (~$greatereq(tptp_fun_Q_3(Pos, Board), 0)))))) | (~((~solution1(Board, Pos)) | (~((~is_board1(Board, Pos)) | (~![Q: $int] : (is_consistent1(Board, Q) | (~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0)))))))))) | (~((~(solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), $sum(1, Pos!4)) | (~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), $sum(1, Pos!4))) | (~($lesseq($sum($sum(1, Pos!4), $product(-1, tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), 0) | is_consistent1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))) | (~$greatereq(tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), 0)))))) | (~((~solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), $sum(1, Pos!4))) | (~((~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), $sum(1, Pos!4))) | (~![Q: $int] : (is_consistent1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Q) | (~$greatereq(Q, 0)) | $lesseq($sum($sum(1, Pos!4), $product(-1, Q)), 0)))))))))) <=> ((~![Board: array_int, Pos: $int] : (~((~(solution1(Board, Pos) | (~is_board1(Board, Pos)) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_3(Pos, Board))), 0) | is_consistent1(Board, tptp_fun_Q_3(Pos, Board)) | (~$greatereq(tptp_fun_Q_3(Pos, Board), 0)))))) | (~((~solution1(Board, Pos)) | (~((~is_board1(Board, Pos)) | (~![Q: $int] : (is_consistent1(Board, Q) | (~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0)))))))))) | (~((~(solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), $sum(1, Pos!4)) | (~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), $sum(1, Pos!4))) | (~(is_consistent1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))) | (~$greatereq(tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), 0)) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), -1))))) | (~((~solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), $sum(1, Pos!4))) | (~((~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), $sum(1, Pos!4))) | (~![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 1) | is_consistent1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Q))))))))))),
% 0.87/0.84 inference(monotonicity,[status(thm)],[109])).
% 0.87/0.84 tff(111,plain,
% 0.87/0.84 (((~![Board: array_int, Pos: $int] : (~((~(solution1(Board, Pos) | (~is_board1(Board, Pos)) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_3(Pos, Board))), 0) | is_consistent1(Board, tptp_fun_Q_3(Pos, Board)) | (~$greatereq(tptp_fun_Q_3(Pos, Board), 0)))))) | (~((~solution1(Board, Pos)) | (~((~is_board1(Board, Pos)) | (~![Q: $int] : (is_consistent1(Board, Q) | (~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0)))))))))) | (~((~(solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), $sum(1, Pos!4)) | (~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), $sum(1, Pos!4))) | (~($lesseq($sum($sum(1, Pos!4), $product(-1, tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), 0) | is_consistent1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))) | (~$greatereq(tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), 0)))))) | (~((~solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), $sum(1, Pos!4))) | (~((~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), $sum(1, Pos!4))) | (~![Q: $int] : (is_consistent1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Q) | (~$greatereq(Q, 0)) | $lesseq($sum($sum(1, Pos!4), $product(-1, Q)), 0)))))))))) <=> ((~![Board: array_int, Pos: $int] : (~((~(solution1(Board, Pos) | (~is_board1(Board, Pos)) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_3(Pos, Board))), 0) | is_consistent1(Board, tptp_fun_Q_3(Pos, Board)) | (~$greatereq(tptp_fun_Q_3(Pos, Board), 0)))))) | (~((~solution1(Board, Pos)) | (~((~is_board1(Board, Pos)) | (~![Q: $int] : (is_consistent1(Board, Q) | (~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0)))))))))) | (~((~(solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), $sum(1, Pos!4)) | (~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), $sum(1, Pos!4))) | (~(is_consistent1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))) | (~$greatereq(tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), 0)) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), -1))))) | (~((~solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), $sum(1, Pos!4))) | (~((~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), $sum(1, Pos!4))) | (~![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 1) | is_consistent1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Q))))))))))),
% 0.87/0.84 inference(transitivity,[status(thm)],[110, 108])).
% 0.87/0.84 tff(112,plain,
% 0.87/0.84 ((~![Board: array_int, Pos: $int] : (~((~(solution1(Board, Pos) | (~is_board1(Board, Pos)) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_3(Pos, Board))), 0) | is_consistent1(Board, tptp_fun_Q_3(Pos, Board)) | (~$greatereq(tptp_fun_Q_3(Pos, Board), 0)))))) | (~((~solution1(Board, Pos)) | (~((~is_board1(Board, Pos)) | (~![Q: $int] : (is_consistent1(Board, Q) | (~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0)))))))))) | (~((~(solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), $sum(1, Pos!4)) | (~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), $sum(1, Pos!4))) | (~($lesseq($sum($sum(1, Pos!4), $product(-1, tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), 0) | is_consistent1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))) | (~$greatereq(tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), 0)))))) | (~((~solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), $sum(1, Pos!4))) | (~((~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), $sum(1, Pos!4))) | (~![Q: $int] : (is_consistent1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Q) | (~$greatereq(Q, 0)) | $lesseq($sum($sum(1, Pos!4), $product(-1, Q)), 0)))))))))),
% 0.87/0.84 inference(quant_inst,[status(thm)],[])).
% 0.87/0.84 tff(113,plain,
% 0.87/0.84 ((~![Board: array_int, Pos: $int] : (~((~(solution1(Board, Pos) | (~is_board1(Board, Pos)) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_3(Pos, Board))), 0) | is_consistent1(Board, tptp_fun_Q_3(Pos, Board)) | (~$greatereq(tptp_fun_Q_3(Pos, Board), 0)))))) | (~((~solution1(Board, Pos)) | (~((~is_board1(Board, Pos)) | (~![Q: $int] : (is_consistent1(Board, Q) | (~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0)))))))))) | (~((~(solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), $sum(1, Pos!4)) | (~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), $sum(1, Pos!4))) | (~(is_consistent1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))) | (~$greatereq(tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), 0)) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), -1))))) | (~((~solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), $sum(1, Pos!4))) | (~((~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), $sum(1, Pos!4))) | (~![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 1) | is_consistent1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Q)))))))))),
% 0.87/0.85 inference(modus_ponens,[status(thm)],[112, 111])).
% 0.87/0.85 tff(114,plain,
% 0.87/0.85 (~((~(solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), $sum(1, Pos!4)) | (~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), $sum(1, Pos!4))) | (~(is_consistent1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))) | (~$greatereq(tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), 0)) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), -1))))) | (~((~solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), $sum(1, Pos!4))) | (~((~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), $sum(1, Pos!4))) | (~![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 1) | is_consistent1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Q))))))))),
% 0.87/0.85 inference(unit_resolution,[status(thm)],[113, 107])).
% 0.87/0.85 tff(115,plain,
% 0.87/0.85 (((~(solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), $sum(1, Pos!4)) | (~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), $sum(1, Pos!4))) | (~(is_consistent1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))) | (~$greatereq(tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), 0)) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), -1))))) | (~((~solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), $sum(1, Pos!4))) | (~((~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), $sum(1, Pos!4))) | (~![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 1) | is_consistent1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Q)))))))) | (solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), $sum(1, Pos!4)) | (~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), $sum(1, Pos!4))) | (~(is_consistent1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))) | (~$greatereq(tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), 0)) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), -1))))),
% 0.87/0.85 inference(tautology,[status(thm)],[])).
% 0.87/0.85 tff(116,plain,
% 0.87/0.85 (solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), $sum(1, Pos!4)) | (~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), $sum(1, Pos!4))) | (~(is_consistent1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))) | (~$greatereq(tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), 0)) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), -1)))),
% 0.87/0.85 inference(unit_resolution,[status(thm)],[115, 114])).
% 0.87/0.85 tff(117,assumption,(~is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)), introduced(assumption)).
% 0.87/0.85 tff(118,plain,
% 0.87/0.85 ($sum(N!5, $product(-1, Board!7)) = 0),
% 0.87/0.85 inference(and_elim,[status(thm)],[23])).
% 0.87/0.85 tff(119,plain,
% 0.87/0.85 ((~($sum(N!5, $product(-1, Board!7)) = 0)) | $lesseq($sum(N!5, $product(-1, Board!7)), 0)),
% 0.87/0.85 inference(theory_lemma,[status(thm)],[])).
% 0.87/0.85 tff(120,plain,
% 0.87/0.85 ($lesseq($sum(N!5, $product(-1, Board!7)), 0)),
% 0.87/0.85 inference(unit_resolution,[status(thm)],[119, 118])).
% 0.87/0.85 tff(121,plain,
% 0.87/0.85 ((~$greatereq($sum(Pos!4, $product(-1, Board!7)), 0)) | (~$lesseq($sum(N!5, $product(-1, Board!7)), 0)) | $greatereq($sum(Pos!4, $product(-1, N!5)), 0)),
% 0.87/0.85 inference(theory_lemma,[status(thm)],[])).
% 0.87/0.85 tff(122,plain,
% 0.87/0.85 ((~$greatereq($sum(Pos!4, $product(-1, Board!7)), 0)) | $greatereq($sum(Pos!4, $product(-1, N!5)), 0)),
% 0.87/0.85 inference(unit_resolution,[status(thm)],[121, 120])).
% 0.87/0.85 tff(123,plain,
% 0.87/0.85 (~$greatereq($sum(Pos!4, $product(-1, Board!7)), 0)),
% 0.87/0.85 inference(unit_resolution,[status(thm)],[122, 48])).
% 0.87/0.85 tff(124,assumption,(~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~$greatereq(Board!7, 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), Pos!4)) | (~($sum(N!5, $product(-1, B!21)) = 0)))))) | (~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | $lesseq($sum(N!5, $product(-1, tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))))), 0) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos!4)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), 0)))))), introduced(assumption)).
% 0.87/0.85 tff(125,plain,
% 0.87/0.85 (((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~$greatereq(Board!7, 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), Pos!4)) | (~($sum(N!5, $product(-1, B!21)) = 0)))))) | (~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | $lesseq($sum(N!5, $product(-1, tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))))), 0) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos!4)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), 0))))) | ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | $lesseq($sum(N!5, $product(-1, tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))))), 0) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos!4)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), 0)))),
% 0.87/0.85 inference(tautology,[status(thm)],[])).
% 0.87/0.85 tff(126,plain,
% 0.87/0.85 (![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | $lesseq($sum(N!5, $product(-1, tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))))), 0) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos!4)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), 0)))),
% 0.87/0.85 inference(unit_resolution,[status(thm)],[125, 124])).
% 0.87/0.85 tff(127,plain,
% 0.87/0.85 (((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~$greatereq(Board!7, 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), Pos!4)) | (~($sum(N!5, $product(-1, B!21)) = 0)))))) | (~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | $lesseq($sum(N!5, $product(-1, tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))))), 0) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos!4)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), 0))))) | ((~$greatereq(Board!7, 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), Pos!4)) | (~($sum(N!5, $product(-1, B!21)) = 0)))))),
% 0.87/0.85 inference(tautology,[status(thm)],[])).
% 0.87/0.85 tff(128,plain,
% 0.87/0.85 ((~$greatereq(Board!7, 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), Pos!4)) | (~($sum(N!5, $product(-1, B!21)) = 0))))),
% 0.87/0.85 inference(unit_resolution,[status(thm)],[127, 124])).
% 0.87/0.85 tff(129,plain,
% 0.87/0.85 (((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~$greatereq(Board!7, 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), Pos!4)) | (~($sum(N!5, $product(-1, B!21)) = 0)))))) | (~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | $lesseq($sum(N!5, $product(-1, tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))))), 0) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos!4)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), 0))))) | eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)),
% 0.87/0.85 inference(tautology,[status(thm)],[])).
% 0.87/0.85 tff(130,plain,
% 0.87/0.85 (eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)),
% 0.87/0.85 inference(unit_resolution,[status(thm)],[129, 124])).
% 0.87/0.85 tff(131,plain,
% 0.87/0.85 ($greatereq(Board!7, 0)),
% 0.87/0.85 inference(and_elim,[status(thm)],[23])).
% 0.87/0.85 tff(132,plain,
% 0.87/0.85 ((~((~$greatereq(Board!7, 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), Pos!4)) | (~($sum(N!5, $product(-1, B!21)) = 0)))))) | (~$greatereq(Board!7, 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), Pos!4)) | (~($sum(N!5, $product(-1, B!21)) = 0))))),
% 0.87/0.85 inference(tautology,[status(thm)],[])).
% 0.87/0.85 tff(133,plain,
% 0.87/0.85 ((~((~$greatereq(Board!7, 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), Pos!4)) | (~($sum(N!5, $product(-1, B!21)) = 0)))))) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), Pos!4)) | (~($sum(N!5, $product(-1, B!21)) = 0))))),
% 0.87/0.85 inference(unit_resolution,[status(thm)],[132, 131])).
% 0.87/0.85 tff(134,plain,
% 0.87/0.85 (~((~solution1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), Pos!4)) | (~($sum(N!5, $product(-1, B!21)) = 0)))),
% 0.87/0.85 inference(unit_resolution,[status(thm)],[133, 130, 128])).
% 0.87/0.85 tff(135,plain,
% 0.87/0.85 (((~solution1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), Pos!4)) | (~($sum(N!5, $product(-1, B!21)) = 0))) | ($sum(N!5, $product(-1, B!21)) = 0)),
% 0.87/0.85 inference(tautology,[status(thm)],[])).
% 0.87/0.85 tff(136,plain,
% 0.87/0.85 ($sum(N!5, $product(-1, B!21)) = 0),
% 0.87/0.85 inference(unit_resolution,[status(thm)],[135, 134])).
% 0.87/0.85 tff(137,plain,
% 0.87/0.85 (((~solution1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), Pos!4)) | (~($sum(N!5, $product(-1, B!21)) = 0))) | eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), Pos!4)),
% 0.87/0.85 inference(tautology,[status(thm)],[])).
% 0.87/0.85 tff(138,plain,
% 0.87/0.85 (eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), Pos!4)),
% 0.87/0.85 inference(unit_resolution,[status(thm)],[137, 134])).
% 0.87/0.85 tff(139,plain,
% 0.87/0.85 (((~solution1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), Pos!4)) | (~($sum(N!5, $product(-1, B!21)) = 0))) | is_board1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)),
% 0.87/0.85 inference(tautology,[status(thm)],[])).
% 0.87/0.85 tff(140,plain,
% 0.87/0.85 (is_board1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)),
% 0.87/0.85 inference(unit_resolution,[status(thm)],[139, 134])).
% 0.87/0.85 tff(141,plain,
% 0.87/0.85 (((~solution1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), Pos!4)) | (~($sum(N!5, $product(-1, B!21)) = 0))) | solution1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)),
% 0.87/0.85 inference(tautology,[status(thm)],[])).
% 0.87/0.85 tff(142,plain,
% 0.87/0.85 (solution1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)),
% 0.87/0.85 inference(unit_resolution,[status(thm)],[141, 134])).
% 0.87/0.85 tff(143,assumption,(~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))), Pos!4)), 0)) | $lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))), Pos!4)))), 0))), introduced(assumption)).
% 0.87/0.85 tff(144,plain,
% 0.87/0.85 (((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))), Pos!4)), 0)) | $lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))), Pos!4)))), 0)) | (~$lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))), Pos!4)))), 0))),
% 0.87/0.85 inference(tautology,[status(thm)],[])).
% 0.87/0.85 tff(145,plain,
% 0.87/0.85 (~$lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))), Pos!4)))), 0)),
% 0.87/0.85 inference(unit_resolution,[status(thm)],[144, 143])).
% 0.87/0.85 tff(146,plain,
% 0.87/0.85 (((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))), Pos!4)), 0)) | $lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))), Pos!4)))), 0)) | $greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))), Pos!4)), 0)),
% 0.87/0.85 inference(tautology,[status(thm)],[])).
% 0.87/0.85 tff(147,plain,
% 0.87/0.85 ($greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))), Pos!4)), 0)),
% 0.87/0.85 inference(unit_resolution,[status(thm)],[146, 143])).
% 0.87/0.85 tff(148,assumption,($greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))), Pos!4)), 0)), introduced(assumption)).
% 0.87/0.85 tff(149,plain,
% 0.87/0.85 (![J: uni] : (t2tb1(tb2t1(J)) = J) <=> ![J: uni] : (t2tb1(tb2t1(J)) = J)),
% 0.87/0.85 inference(rewrite,[status(thm)],[])).
% 0.87/0.85 tff(150,plain,
% 0.87/0.85 (![J: uni] : (t2tb1(tb2t1(J)) = J) <=> ![J: uni] : (t2tb1(tb2t1(J)) = J)),
% 0.87/0.85 inference(rewrite,[status(thm)],[])).
% 0.87/0.85 tff(151,axiom,(![J: uni] : (t2tb1(tb2t1(J)) = J)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bridgeR1')).
% 0.87/0.85 tff(152,plain,
% 0.87/0.85 (![J: uni] : (t2tb1(tb2t1(J)) = J)),
% 0.87/0.85 inference(modus_ponens,[status(thm)],[151, 150])).
% 0.87/0.85 tff(153,plain,(
% 0.87/0.85 ![J: uni] : (t2tb1(tb2t1(J)) = J)),
% 0.87/0.85 inference(skolemize,[status(sab)],[152])).
% 0.87/0.85 tff(154,plain,
% 0.87/0.85 (![J: uni] : (t2tb1(tb2t1(J)) = J)),
% 0.87/0.85 inference(modus_ponens,[status(thm)],[153, 149])).
% 0.87/0.85 tff(155,plain,
% 0.87/0.85 ((~![J: uni] : (t2tb1(tb2t1(J)) = J)) | (t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))) = mk_array1(int, B!21, t2tb2(B1!20)))),
% 0.87/0.85 inference(quant_inst,[status(thm)],[])).
% 0.87/0.85 tff(156,plain,
% 0.87/0.85 (t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))) = mk_array1(int, B!21, t2tb2(B1!20))),
% 0.87/0.85 inference(unit_resolution,[status(thm)],[155, 154])).
% 0.87/0.85 tff(157,plain,
% 0.87/0.85 (mk_array1(int, B!21, t2tb2(B1!20)) = t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))))),
% 0.87/0.85 inference(symmetry,[status(thm)],[156])).
% 0.87/0.85 tff(158,plain,
% 0.87/0.85 (get2(int, mk_array1(int, B!21, t2tb2(B1!20)), Pos!4) = get2(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))), Pos!4)),
% 0.87/0.85 inference(monotonicity,[status(thm)],[157])).
% 0.87/0.85 tff(159,plain,
% 0.87/0.85 (^[A: ty, A1: uni, I: $int] : refl((get2(A, A1, I) = get(A, int, elts(A, A1), t2tb(I))) <=> (get2(A, A1, I) = get(A, int, elts(A, A1), t2tb(I))))),
% 0.87/0.85 inference(bind,[status(th)],[])).
% 0.87/0.85 tff(160,plain,
% 0.87/0.85 (![A: ty, A1: uni, I: $int] : (get2(A, A1, I) = get(A, int, elts(A, A1), t2tb(I))) <=> ![A: ty, A1: uni, I: $int] : (get2(A, A1, I) = get(A, int, elts(A, A1), t2tb(I)))),
% 0.87/0.85 inference(quant_intro,[status(thm)],[159])).
% 0.87/0.85 tff(161,plain,
% 0.87/0.85 (![A: ty, A1: uni, I: $int] : (get2(A, A1, I) = get(A, int, elts(A, A1), t2tb(I))) <=> ![A: ty, A1: uni, I: $int] : (get2(A, A1, I) = get(A, int, elts(A, A1), t2tb(I)))),
% 0.87/0.85 inference(rewrite,[status(thm)],[])).
% 0.87/0.85 tff(162,axiom,(![A: ty, A1: uni, I: $int] : (get2(A, A1, I) = get(A, int, elts(A, A1), t2tb(I)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','get_def')).
% 0.87/0.85 tff(163,plain,
% 0.87/0.85 (![A: ty, A1: uni, I: $int] : (get2(A, A1, I) = get(A, int, elts(A, A1), t2tb(I)))),
% 0.87/0.85 inference(modus_ponens,[status(thm)],[162, 161])).
% 0.87/0.85 tff(164,plain,(
% 0.87/0.85 ![A: ty, A1: uni, I: $int] : (get2(A, A1, I) = get(A, int, elts(A, A1), t2tb(I)))),
% 0.87/0.85 inference(skolemize,[status(sab)],[163])).
% 0.87/0.85 tff(165,plain,
% 0.87/0.85 (![A: ty, A1: uni, I: $int] : (get2(A, A1, I) = get(A, int, elts(A, A1), t2tb(I)))),
% 0.87/0.85 inference(modus_ponens,[status(thm)],[164, 160])).
% 0.87/0.85 tff(166,plain,
% 0.87/0.85 ((~![A: ty, A1: uni, I: $int] : (get2(A, A1, I) = get(A, int, elts(A, A1), t2tb(I)))) | (get2(int, mk_array1(int, B!21, t2tb2(B1!20)), Pos!4) = get(int, int, elts(int, mk_array1(int, B!21, t2tb2(B1!20))), t2tb(Pos!4)))),
% 0.87/0.85 inference(quant_inst,[status(thm)],[])).
% 0.87/0.85 tff(167,plain,
% 0.87/0.85 (get2(int, mk_array1(int, B!21, t2tb2(B1!20)), Pos!4) = get(int, int, elts(int, mk_array1(int, B!21, t2tb2(B1!20))), t2tb(Pos!4))),
% 0.87/0.85 inference(unit_resolution,[status(thm)],[166, 165])).
% 0.87/0.85 tff(168,plain,
% 0.87/0.85 (get(int, int, elts(int, mk_array1(int, B!21, t2tb2(B1!20))), t2tb(Pos!4)) = get2(int, mk_array1(int, B!21, t2tb2(B1!20)), Pos!4)),
% 0.87/0.85 inference(symmetry,[status(thm)],[167])).
% 0.87/0.85 tff(169,plain,
% 0.87/0.85 (^[X: map_int_int] : refl(sort1(map(int, int), t2tb2(X)) <=> sort1(map(int, int), t2tb2(X)))),
% 0.87/0.85 inference(bind,[status(th)],[])).
% 0.87/0.85 tff(170,plain,
% 0.87/0.85 (![X: map_int_int] : sort1(map(int, int), t2tb2(X)) <=> ![X: map_int_int] : sort1(map(int, int), t2tb2(X))),
% 0.87/0.85 inference(quant_intro,[status(thm)],[169])).
% 0.87/0.85 tff(171,plain,
% 0.87/0.85 (![X: map_int_int] : sort1(map(int, int), t2tb2(X)) <=> ![X: map_int_int] : sort1(map(int, int), t2tb2(X))),
% 0.87/0.85 inference(rewrite,[status(thm)],[])).
% 0.87/0.85 tff(172,axiom,(![X: map_int_int] : sort1(map(int, int), t2tb2(X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t2tb_sort2')).
% 0.87/0.85 tff(173,plain,
% 0.87/0.85 (![X: map_int_int] : sort1(map(int, int), t2tb2(X))),
% 0.87/0.85 inference(modus_ponens,[status(thm)],[172, 171])).
% 0.87/0.85 tff(174,plain,(
% 0.87/0.85 ![X: map_int_int] : sort1(map(int, int), t2tb2(X))),
% 0.87/0.85 inference(skolemize,[status(sab)],[173])).
% 0.87/0.85 tff(175,plain,
% 0.87/0.85 (![X: map_int_int] : sort1(map(int, int), t2tb2(X))),
% 0.87/0.85 inference(modus_ponens,[status(thm)],[174, 170])).
% 0.87/0.85 tff(176,plain,
% 0.87/0.85 ((~![X: map_int_int] : sort1(map(int, int), t2tb2(X))) | sort1(map(int, int), t2tb2(B1!20))),
% 0.87/0.85 inference(quant_inst,[status(thm)],[])).
% 0.87/0.85 tff(177,plain,
% 0.87/0.85 (sort1(map(int, int), t2tb2(B1!20))),
% 0.87/0.85 inference(unit_resolution,[status(thm)],[176, 175])).
% 0.87/0.85 tff(178,plain,
% 0.87/0.85 (^[A: ty, U: $int, U1: uni] : refl(((~sort1(map(int, A), U1)) | (elts(A, mk_array1(A, U, U1)) = U1)) <=> ((~sort1(map(int, A), U1)) | (elts(A, mk_array1(A, U, U1)) = U1)))),
% 0.87/0.85 inference(bind,[status(th)],[])).
% 0.87/0.85 tff(179,plain,
% 0.87/0.85 (![A: ty, U: $int, U1: uni] : ((~sort1(map(int, A), U1)) | (elts(A, mk_array1(A, U, U1)) = U1)) <=> ![A: ty, U: $int, U1: uni] : ((~sort1(map(int, A), U1)) | (elts(A, mk_array1(A, U, U1)) = U1))),
% 0.87/0.85 inference(quant_intro,[status(thm)],[178])).
% 0.87/0.85 tff(180,plain,
% 0.87/0.85 (![A: ty, U: $int, U1: uni] : ((~sort1(map(int, A), U1)) | (elts(A, mk_array1(A, U, U1)) = U1)) <=> ![A: ty, U: $int, U1: uni] : ((~sort1(map(int, A), U1)) | (elts(A, mk_array1(A, U, U1)) = U1))),
% 0.87/0.85 inference(rewrite,[status(thm)],[])).
% 0.87/0.85 tff(181,plain,
% 0.87/0.85 (^[A: ty, U: $int, U1: uni] : rewrite((sort1(map(int, A), U1) => (elts(A, mk_array1(A, U, U1)) = U1)) <=> ((~sort1(map(int, A), U1)) | (elts(A, mk_array1(A, U, U1)) = U1)))),
% 0.87/0.85 inference(bind,[status(th)],[])).
% 0.87/0.85 tff(182,plain,
% 0.87/0.85 (![A: ty, U: $int, U1: uni] : (sort1(map(int, A), U1) => (elts(A, mk_array1(A, U, U1)) = U1)) <=> ![A: ty, U: $int, U1: uni] : ((~sort1(map(int, A), U1)) | (elts(A, mk_array1(A, U, U1)) = U1))),
% 0.87/0.85 inference(quant_intro,[status(thm)],[181])).
% 0.87/0.85 tff(183,axiom,(![A: ty, U: $int, U1: uni] : (sort1(map(int, A), U1) => (elts(A, mk_array1(A, U, U1)) = U1))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','elts_def1')).
% 0.87/0.85 tff(184,plain,
% 0.87/0.85 (![A: ty, U: $int, U1: uni] : ((~sort1(map(int, A), U1)) | (elts(A, mk_array1(A, U, U1)) = U1))),
% 0.87/0.85 inference(modus_ponens,[status(thm)],[183, 182])).
% 0.87/0.85 tff(185,plain,
% 0.87/0.85 (![A: ty, U: $int, U1: uni] : ((~sort1(map(int, A), U1)) | (elts(A, mk_array1(A, U, U1)) = U1))),
% 0.87/0.85 inference(modus_ponens,[status(thm)],[184, 180])).
% 0.87/0.85 tff(186,plain,(
% 0.87/0.85 ![A: ty, U: $int, U1: uni] : ((~sort1(map(int, A), U1)) | (elts(A, mk_array1(A, U, U1)) = U1))),
% 0.87/0.85 inference(skolemize,[status(sab)],[185])).
% 0.87/0.85 tff(187,plain,
% 0.87/0.85 (![A: ty, U: $int, U1: uni] : ((~sort1(map(int, A), U1)) | (elts(A, mk_array1(A, U, U1)) = U1))),
% 0.87/0.85 inference(modus_ponens,[status(thm)],[186, 179])).
% 0.87/0.85 tff(188,plain,
% 0.87/0.85 (((~![A: ty, U: $int, U1: uni] : ((~sort1(map(int, A), U1)) | (elts(A, mk_array1(A, U, U1)) = U1))) | ((~sort1(map(int, int), t2tb2(B1!20))) | (elts(int, mk_array1(int, B!21, t2tb2(B1!20))) = t2tb2(B1!20)))) <=> ((~![A: ty, U: $int, U1: uni] : ((~sort1(map(int, A), U1)) | (elts(A, mk_array1(A, U, U1)) = U1))) | (~sort1(map(int, int), t2tb2(B1!20))) | (elts(int, mk_array1(int, B!21, t2tb2(B1!20))) = t2tb2(B1!20)))),
% 0.87/0.85 inference(rewrite,[status(thm)],[])).
% 0.87/0.85 tff(189,plain,
% 0.87/0.85 ((~![A: ty, U: $int, U1: uni] : ((~sort1(map(int, A), U1)) | (elts(A, mk_array1(A, U, U1)) = U1))) | ((~sort1(map(int, int), t2tb2(B1!20))) | (elts(int, mk_array1(int, B!21, t2tb2(B1!20))) = t2tb2(B1!20)))),
% 0.87/0.85 inference(quant_inst,[status(thm)],[])).
% 0.87/0.85 tff(190,plain,
% 0.87/0.85 ((~![A: ty, U: $int, U1: uni] : ((~sort1(map(int, A), U1)) | (elts(A, mk_array1(A, U, U1)) = U1))) | (~sort1(map(int, int), t2tb2(B1!20))) | (elts(int, mk_array1(int, B!21, t2tb2(B1!20))) = t2tb2(B1!20))),
% 0.87/0.86 inference(modus_ponens,[status(thm)],[189, 188])).
% 0.87/0.86 tff(191,plain,
% 0.87/0.86 ((~sort1(map(int, int), t2tb2(B1!20))) | (elts(int, mk_array1(int, B!21, t2tb2(B1!20))) = t2tb2(B1!20))),
% 0.87/0.86 inference(unit_resolution,[status(thm)],[190, 187])).
% 0.87/0.86 tff(192,plain,
% 0.87/0.86 (elts(int, mk_array1(int, B!21, t2tb2(B1!20))) = t2tb2(B1!20)),
% 0.87/0.86 inference(unit_resolution,[status(thm)],[191, 177])).
% 0.87/0.86 tff(193,plain,
% 0.87/0.86 (t2tb2(B1!20) = elts(int, mk_array1(int, B!21, t2tb2(B1!20)))),
% 0.87/0.86 inference(symmetry,[status(thm)],[192])).
% 0.87/0.86 tff(194,plain,
% 0.87/0.86 (get(int, int, t2tb2(B1!20), t2tb(Pos!4)) = get(int, int, elts(int, mk_array1(int, B!21, t2tb2(B1!20))), t2tb(Pos!4))),
% 0.87/0.86 inference(monotonicity,[status(thm)],[193])).
% 0.87/0.86 tff(195,plain,
% 0.87/0.86 (get(int, int, t2tb2(B1!20), t2tb(Pos!4)) = get2(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))), Pos!4)),
% 0.87/0.86 inference(transitivity,[status(thm)],[194, 168, 158])).
% 0.87/0.86 tff(196,plain,
% 0.87/0.86 (tb2t(get(int, int, t2tb2(B1!20), t2tb(Pos!4))) = tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))), Pos!4))),
% 0.87/0.86 inference(monotonicity,[status(thm)],[195])).
% 0.87/0.86 tff(197,plain,
% 0.87/0.86 (tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))), Pos!4)) = tb2t(get(int, int, t2tb2(B1!20), t2tb(Pos!4)))),
% 0.87/0.86 inference(symmetry,[status(thm)],[196])).
% 0.87/0.86 tff(198,plain,
% 0.87/0.86 ((~(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))), Pos!4)) = tb2t(get(int, int, t2tb2(B1!20), t2tb(Pos!4))))) | $lesseq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))), Pos!4)), $product(-1, tb2t(get(int, int, t2tb2(B1!20), t2tb(Pos!4))))), 0)),
% 0.87/0.86 inference(theory_lemma,[status(thm)],[])).
% 0.87/0.86 tff(199,plain,
% 0.87/0.86 ($lesseq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))), Pos!4)), $product(-1, tb2t(get(int, int, t2tb2(B1!20), t2tb(Pos!4))))), 0)),
% 0.87/0.86 inference(unit_resolution,[status(thm)],[198, 197])).
% 0.87/0.86 tff(200,assumption,(~$greatereq(tb2t(get(int, int, t2tb2(B1!20), t2tb(Pos!4))), 0)), introduced(assumption)).
% 0.87/0.86 tff(201,plain,
% 0.87/0.86 ($false),
% 0.87/0.86 inference(theory_lemma,[status(thm)],[200, 199, 148])).
% 0.87/0.86 tff(202,plain,($greatereq(tb2t(get(int, int, t2tb2(B1!20), t2tb(Pos!4))), 0) | (~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))), Pos!4)), 0))), inference(lemma,lemma(discharge,[]))).
% 0.87/0.86 tff(203,plain,
% 0.87/0.86 ($greatereq(tb2t(get(int, int, t2tb2(B1!20), t2tb(Pos!4))), 0)),
% 0.87/0.86 inference(unit_resolution,[status(thm)],[202, 147])).
% 0.87/0.86 tff(204,assumption,(![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | $lesseq($sum(N!5, $product(-1, tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))))), 0) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos!4)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), 0)))), introduced(assumption)).
% 0.87/0.86 tff(205,assumption,($sum(N!5, $product(-1, B!21)) = 0), introduced(assumption)).
% 0.87/0.86 tff(206,assumption,(eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), Pos!4)), introduced(assumption)).
% 0.87/0.86 tff(207,assumption,(is_board1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)), introduced(assumption)).
% 0.87/0.86 tff(208,assumption,(solution1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)), introduced(assumption)).
% 0.87/0.86 tff(209,plain,
% 0.87/0.86 (((~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | $lesseq($sum(N!5, $product(-1, tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))))), 0) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos!4)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), 0)))) | ((~solution1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), Pos!4)) | (~($sum(N!5, $product(-1, B!21)) = 0)) | $lesseq($sum(N!5, $product(-1, tb2t(get(int, int, t2tb2(B1!20), t2tb(Pos!4))))), 0) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!20), t2tb(Pos!4))), 0)))) <=> ((~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | $lesseq($sum(N!5, $product(-1, tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))))), 0) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos!4)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), 0)))) | (~solution1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), Pos!4)) | (~($sum(N!5, $product(-1, B!21)) = 0)) | $lesseq($sum(N!5, $product(-1, tb2t(get(int, int, t2tb2(B1!20), t2tb(Pos!4))))), 0) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!20), t2tb(Pos!4))), 0)))),
% 0.87/0.86 inference(rewrite,[status(thm)],[])).
% 0.87/0.86 tff(210,plain,
% 0.87/0.86 (((~solution1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | (~($sum(N!5, $product(-1, B!21)) = 0)) | $lesseq($sum(N!5, $product(-1, tb2t(get(int, int, t2tb2(B1!20), t2tb(Pos!4))))), 0) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), Pos!4)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!20), t2tb(Pos!4))), 0))) <=> ((~solution1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), Pos!4)) | (~($sum(N!5, $product(-1, B!21)) = 0)) | $lesseq($sum(N!5, $product(-1, tb2t(get(int, int, t2tb2(B1!20), t2tb(Pos!4))))), 0) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!20), t2tb(Pos!4))), 0)))),
% 0.87/0.86 inference(rewrite,[status(thm)],[])).
% 0.87/0.86 tff(211,plain,
% 0.87/0.86 ((~($sum(B!21, $product(-1, N!5)) = 0)) <=> (~($sum(N!5, $product(-1, B!21)) = 0))),
% 0.87/0.86 inference(rewrite,[status(thm)],[])).
% 0.87/0.86 tff(212,plain,
% 0.87/0.86 (((~solution1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | (~($sum(B!21, $product(-1, N!5)) = 0)) | $lesseq($sum(N!5, $product(-1, tb2t(get(int, int, t2tb2(B1!20), t2tb(Pos!4))))), 0) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), Pos!4)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!20), t2tb(Pos!4))), 0))) <=> ((~solution1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | (~($sum(N!5, $product(-1, B!21)) = 0)) | $lesseq($sum(N!5, $product(-1, tb2t(get(int, int, t2tb2(B1!20), t2tb(Pos!4))))), 0) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), Pos!4)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!20), t2tb(Pos!4))), 0)))),
% 0.87/0.86 inference(monotonicity,[status(thm)],[211])).
% 0.87/0.86 tff(213,plain,
% 0.87/0.86 (((~solution1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | (~($sum(B!21, $product(-1, N!5)) = 0)) | $lesseq($sum(N!5, $product(-1, tb2t(get(int, int, t2tb2(B1!20), t2tb(Pos!4))))), 0) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), Pos!4)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!20), t2tb(Pos!4))), 0))) <=> ((~solution1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), Pos!4)) | (~($sum(N!5, $product(-1, B!21)) = 0)) | $lesseq($sum(N!5, $product(-1, tb2t(get(int, int, t2tb2(B1!20), t2tb(Pos!4))))), 0) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!20), t2tb(Pos!4))), 0)))),
% 0.87/0.86 inference(transitivity,[status(thm)],[212, 210])).
% 0.87/0.86 tff(214,plain,
% 0.87/0.86 (((~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | $lesseq($sum(N!5, $product(-1, tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))))), 0) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos!4)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), 0)))) | ((~solution1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | (~($sum(B!21, $product(-1, N!5)) = 0)) | $lesseq($sum(N!5, $product(-1, tb2t(get(int, int, t2tb2(B1!20), t2tb(Pos!4))))), 0) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), Pos!4)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!20), t2tb(Pos!4))), 0)))) <=> ((~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | $lesseq($sum(N!5, $product(-1, tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))))), 0) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos!4)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), 0)))) | ((~solution1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), Pos!4)) | (~($sum(N!5, $product(-1, B!21)) = 0)) | $lesseq($sum(N!5, $product(-1, tb2t(get(int, int, t2tb2(B1!20), t2tb(Pos!4))))), 0) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!20), t2tb(Pos!4))), 0))))),
% 0.87/0.86 inference(monotonicity,[status(thm)],[213])).
% 0.87/0.86 tff(215,plain,
% 0.87/0.86 (((~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | $lesseq($sum(N!5, $product(-1, tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))))), 0) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos!4)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), 0)))) | ((~solution1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | (~($sum(B!21, $product(-1, N!5)) = 0)) | $lesseq($sum(N!5, $product(-1, tb2t(get(int, int, t2tb2(B1!20), t2tb(Pos!4))))), 0) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), Pos!4)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!20), t2tb(Pos!4))), 0)))) <=> ((~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | $lesseq($sum(N!5, $product(-1, tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))))), 0) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos!4)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), 0)))) | (~solution1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), Pos!4)) | (~($sum(N!5, $product(-1, B!21)) = 0)) | $lesseq($sum(N!5, $product(-1, tb2t(get(int, int, t2tb2(B1!20), t2tb(Pos!4))))), 0) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!20), t2tb(Pos!4))), 0)))),
% 0.87/0.86 inference(transitivity,[status(thm)],[214, 209])).
% 0.87/0.86 tff(216,plain,
% 0.87/0.86 ((~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | $lesseq($sum(N!5, $product(-1, tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))))), 0) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos!4)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), 0)))) | ((~solution1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | (~($sum(B!21, $product(-1, N!5)) = 0)) | $lesseq($sum(N!5, $product(-1, tb2t(get(int, int, t2tb2(B1!20), t2tb(Pos!4))))), 0) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), Pos!4)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!20), t2tb(Pos!4))), 0)))),
% 0.91/0.86 inference(quant_inst,[status(thm)],[])).
% 0.91/0.86 tff(217,plain,
% 0.91/0.86 ((~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | $lesseq($sum(N!5, $product(-1, tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))))), 0) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos!4)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), 0)))) | (~solution1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), Pos!4)) | (~($sum(N!5, $product(-1, B!21)) = 0)) | $lesseq($sum(N!5, $product(-1, tb2t(get(int, int, t2tb2(B1!20), t2tb(Pos!4))))), 0) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!20), t2tb(Pos!4))), 0))),
% 0.91/0.86 inference(modus_ponens,[status(thm)],[216, 215])).
% 0.91/0.86 tff(218,plain,
% 0.91/0.86 ($lesseq($sum(N!5, $product(-1, tb2t(get(int, int, t2tb2(B1!20), t2tb(Pos!4))))), 0) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!20), t2tb(Pos!4))), 0))),
% 0.91/0.86 inference(unit_resolution,[status(thm)],[217, 208, 207, 206, 205, 204])).
% 0.91/0.86 tff(219,plain,
% 0.91/0.86 ($lesseq($sum(N!5, $product(-1, tb2t(get(int, int, t2tb2(B1!20), t2tb(Pos!4))))), 0)),
% 0.91/0.86 inference(unit_resolution,[status(thm)],[218, 203])).
% 0.91/0.86 tff(220,plain,
% 0.91/0.86 ((~($sum(N!5, $product(-1, B!21)) = 0)) | $greatereq($sum(N!5, $product(-1, B!21)), 0)),
% 0.91/0.86 inference(theory_lemma,[status(thm)],[])).
% 0.91/0.86 tff(221,plain,
% 0.91/0.86 ($greatereq($sum(N!5, $product(-1, B!21)), 0)),
% 0.91/0.86 inference(unit_resolution,[status(thm)],[220, 205])).
% 0.91/0.86 tff(222,plain,
% 0.91/0.86 (^[A: ty, U: $int, U1: uni] : refl(($sum(U, $product(-1, length1(A, mk_array1(A, U, U1)))) = 0) <=> ($sum(U, $product(-1, length1(A, mk_array1(A, U, U1)))) = 0))),
% 0.91/0.86 inference(bind,[status(th)],[])).
% 0.91/0.86 tff(223,plain,
% 0.91/0.86 (![A: ty, U: $int, U1: uni] : ($sum(U, $product(-1, length1(A, mk_array1(A, U, U1)))) = 0) <=> ![A: ty, U: $int, U1: uni] : ($sum(U, $product(-1, length1(A, mk_array1(A, U, U1)))) = 0)),
% 0.91/0.86 inference(quant_intro,[status(thm)],[222])).
% 0.91/0.86 tff(224,plain,
% 0.91/0.86 (^[A: ty, U: $int, U1: uni] : trans(monotonicity(rewrite($sum(length1(A, mk_array1(A, U, U1)), $product(-1, U)) = $sum($product(-1, U), length1(A, mk_array1(A, U, U1)))), (($sum(length1(A, mk_array1(A, U, U1)), $product(-1, U)) = 0) <=> ($sum($product(-1, U), length1(A, mk_array1(A, U, U1))) = 0))), rewrite(($sum($product(-1, U), length1(A, mk_array1(A, U, U1))) = 0) <=> ($sum(U, $product(-1, length1(A, mk_array1(A, U, U1)))) = 0)), (($sum(length1(A, mk_array1(A, U, U1)), $product(-1, U)) = 0) <=> ($sum(U, $product(-1, length1(A, mk_array1(A, U, U1)))) = 0)))),
% 0.91/0.86 inference(bind,[status(th)],[])).
% 0.91/0.86 tff(225,plain,
% 0.91/0.86 (![A: ty, U: $int, U1: uni] : ($sum(length1(A, mk_array1(A, U, U1)), $product(-1, U)) = 0) <=> ![A: ty, U: $int, U1: uni] : ($sum(U, $product(-1, length1(A, mk_array1(A, U, U1)))) = 0)),
% 0.91/0.86 inference(quant_intro,[status(thm)],[224])).
% 0.91/0.86 tff(226,plain,
% 0.91/0.86 (^[A: ty, U: $int, U1: uni] : rewrite((length1(A, mk_array1(A, U, U1)) = U) <=> ($sum(length1(A, mk_array1(A, U, U1)), $product(-1, U)) = 0))),
% 0.91/0.86 inference(bind,[status(th)],[])).
% 0.91/0.86 tff(227,plain,
% 0.91/0.86 (![A: ty, U: $int, U1: uni] : (length1(A, mk_array1(A, U, U1)) = U) <=> ![A: ty, U: $int, U1: uni] : ($sum(length1(A, mk_array1(A, U, U1)), $product(-1, U)) = 0)),
% 0.91/0.86 inference(quant_intro,[status(thm)],[226])).
% 0.91/0.86 tff(228,plain,
% 0.91/0.86 (![A: ty, U: $int, U1: uni] : (length1(A, mk_array1(A, U, U1)) = U) <=> ![A: ty, U: $int, U1: uni] : (length1(A, mk_array1(A, U, U1)) = U)),
% 0.91/0.86 inference(rewrite,[status(thm)],[])).
% 0.91/0.86 tff(229,axiom,(![A: ty, U: $int, U1: uni] : (length1(A, mk_array1(A, U, U1)) = U)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','length_def1')).
% 0.91/0.86 tff(230,plain,
% 0.91/0.86 (![A: ty, U: $int, U1: uni] : (length1(A, mk_array1(A, U, U1)) = U)),
% 0.91/0.86 inference(modus_ponens,[status(thm)],[229, 228])).
% 0.91/0.86 tff(231,plain,
% 0.91/0.86 (![A: ty, U: $int, U1: uni] : ($sum(length1(A, mk_array1(A, U, U1)), $product(-1, U)) = 0)),
% 0.91/0.86 inference(modus_ponens,[status(thm)],[230, 227])).
% 0.91/0.86 tff(232,plain,
% 0.91/0.86 (![A: ty, U: $int, U1: uni] : ($sum(U, $product(-1, length1(A, mk_array1(A, U, U1)))) = 0)),
% 0.91/0.86 inference(modus_ponens,[status(thm)],[231, 225])).
% 0.91/0.86 tff(233,plain,(
% 0.91/0.86 ![A: ty, U: $int, U1: uni] : ($sum(U, $product(-1, length1(A, mk_array1(A, U, U1)))) = 0)),
% 0.91/0.86 inference(skolemize,[status(sab)],[232])).
% 0.91/0.86 tff(234,plain,
% 0.91/0.86 (![A: ty, U: $int, U1: uni] : ($sum(U, $product(-1, length1(A, mk_array1(A, U, U1)))) = 0)),
% 0.91/0.86 inference(modus_ponens,[status(thm)],[233, 223])).
% 0.91/0.86 tff(235,plain,
% 0.91/0.86 ((~![A: ty, U: $int, U1: uni] : ($sum(U, $product(-1, length1(A, mk_array1(A, U, U1)))) = 0)) | ($sum(B!21, $product(-1, length1(int, mk_array1(int, B!21, t2tb2(B1!20))))) = 0)),
% 0.91/0.86 inference(quant_inst,[status(thm)],[])).
% 0.91/0.86 tff(236,plain,
% 0.91/0.86 ($sum(B!21, $product(-1, length1(int, mk_array1(int, B!21, t2tb2(B1!20))))) = 0),
% 0.91/0.86 inference(unit_resolution,[status(thm)],[235, 234])).
% 0.91/0.86 tff(237,plain,
% 0.91/0.86 ((~($sum(B!21, $product(-1, length1(int, mk_array1(int, B!21, t2tb2(B1!20))))) = 0)) | $greatereq($sum(B!21, $product(-1, length1(int, mk_array1(int, B!21, t2tb2(B1!20))))), 0)),
% 0.91/0.86 inference(theory_lemma,[status(thm)],[])).
% 0.91/0.86 tff(238,plain,
% 0.91/0.86 ($greatereq($sum(B!21, $product(-1, length1(int, mk_array1(int, B!21, t2tb2(B1!20))))), 0)),
% 0.91/0.86 inference(unit_resolution,[status(thm)],[237, 236])).
% 0.91/0.86 tff(239,plain,
% 0.91/0.86 (length1(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))))) = length1(int, mk_array1(int, B!21, t2tb2(B1!20)))),
% 0.91/0.86 inference(monotonicity,[status(thm)],[156])).
% 0.91/0.86 tff(240,plain,
% 0.91/0.86 ((~(length1(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))))) = length1(int, mk_array1(int, B!21, t2tb2(B1!20))))) | $lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))))), $product(-1, length1(int, mk_array1(int, B!21, t2tb2(B1!20))))), 0)),
% 0.91/0.86 inference(theory_lemma,[status(thm)],[])).
% 0.91/0.86 tff(241,plain,
% 0.91/0.86 ($lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))))), $product(-1, length1(int, mk_array1(int, B!21, t2tb2(B1!20))))), 0)),
% 0.91/0.86 inference(unit_resolution,[status(thm)],[240, 239])).
% 0.91/0.86 tff(242,plain,
% 0.91/0.86 ((~(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))), Pos!4)) = tb2t(get(int, int, t2tb2(B1!20), t2tb(Pos!4))))) | $greatereq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))), Pos!4)), $product(-1, tb2t(get(int, int, t2tb2(B1!20), t2tb(Pos!4))))), 0)),
% 0.91/0.86 inference(theory_lemma,[status(thm)],[])).
% 0.91/0.86 tff(243,plain,
% 0.91/0.86 ($greatereq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))), Pos!4)), $product(-1, tb2t(get(int, int, t2tb2(B1!20), t2tb(Pos!4))))), 0)),
% 0.91/0.86 inference(unit_resolution,[status(thm)],[242, 197])).
% 0.91/0.86 tff(244,plain,
% 0.91/0.86 ($false),
% 0.91/0.86 inference(theory_lemma,[status(thm)],[243, 241, 238, 221, 219, 145])).
% 0.91/0.86 tff(245,plain,(((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))), Pos!4)), 0)) | $lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))), Pos!4)))), 0)) | (~solution1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), Pos!4)) | (~($sum(N!5, $product(-1, B!21)) = 0)) | (~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | $lesseq($sum(N!5, $product(-1, tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))))), 0) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos!4)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), 0))))), inference(lemma,lemma(discharge,[]))).
% 0.91/0.86 tff(246,plain,
% 0.91/0.86 ((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))), Pos!4)), 0)) | $lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))), Pos!4)))), 0)),
% 0.91/0.86 inference(unit_resolution,[status(thm)],[245, 142, 140, 138, 136, 126])).
% 0.91/0.86 tff(247,plain,
% 0.91/0.86 (((~![Board: array_int, Pos: $int] : (~((~((~is_board1(Board, Pos)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(Board), Q)), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(Board), Q)), $product(-1, length1(int, t2tb1(Board)))), 0)))))) | (~(is_board1(Board, Pos) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_2(Pos, Board))), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(Board), tptp_fun_Q_2(Pos, Board))), 0)) | $lesseq($sum(length1(int, t2tb1(Board)), $product(-1, tb2t(get2(int, t2tb1(Board), tptp_fun_Q_2(Pos, Board))))), 0))) | (~$greatereq(tptp_fun_Q_2(Pos, Board), 0))))))))) | (~((~((~is_board1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, N!5)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))), Q)), 0)) | $lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))), Q)))), 0)))))) | (~(is_board1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5) | (~($lesseq($sum(N!5, $product(-1, tptp_fun_Q_2(N!5, tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))))), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))), tptp_fun_Q_2(N!5, tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))))), 0)) | $lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))), tptp_fun_Q_2(N!5, tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))))))), 0))) | (~$greatereq(tptp_fun_Q_2(N!5, tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))), 0))))))))) <=> ((~![Board: array_int, Pos: $int] : (~((~((~is_board1(Board, Pos)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(Board), Q)), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(Board), Q)), $product(-1, length1(int, t2tb1(Board)))), 0)))))) | (~(is_board1(Board, Pos) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_2(Pos, Board))), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(Board), tptp_fun_Q_2(Pos, Board))), 0)) | $lesseq($sum(length1(int, t2tb1(Board)), $product(-1, tb2t(get2(int, t2tb1(Board), tptp_fun_Q_2(Pos, Board))))), 0))) | (~$greatereq(tptp_fun_Q_2(Pos, Board), 0))))))))) | (~((~((~is_board1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, N!5)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))), Q)), 0)) | $lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))), Q)))), 0)))))) | (~(is_board1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5) | (~($lesseq($sum(N!5, $product(-1, tptp_fun_Q_2(N!5, tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))))), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))), tptp_fun_Q_2(N!5, tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))))), 0)) | $lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))), tptp_fun_Q_2(N!5, tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))))))), 0))) | (~$greatereq(tptp_fun_Q_2(N!5, tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))), 0)))))))))),
% 0.91/0.86 inference(rewrite,[status(thm)],[])).
% 0.91/0.86 tff(248,plain,
% 0.91/0.86 ((~((~((~is_board1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(N!5, $product(-1, Q)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))), Q)), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))), Q)), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))))))), 0)))))) | (~(is_board1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5) | (~($lesseq($sum(N!5, $product(-1, tptp_fun_Q_2(N!5, tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))))), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))), tptp_fun_Q_2(N!5, tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))))), 0)) | $lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))), tptp_fun_Q_2(N!5, tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))))))), 0))) | (~$greatereq(tptp_fun_Q_2(N!5, tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))), 0)))))))) <=> (~((~((~is_board1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, N!5)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))), Q)), 0)) | $lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))), Q)))), 0)))))) | (~(is_board1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5) | (~($lesseq($sum(N!5, $product(-1, tptp_fun_Q_2(N!5, tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))))), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))), tptp_fun_Q_2(N!5, tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))))), 0)) | $lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))), tptp_fun_Q_2(N!5, tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))))))), 0))) | (~$greatereq(tptp_fun_Q_2(N!5, tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))), 0))))))))),
% 0.91/0.86 inference(rewrite,[status(thm)],[])).
% 0.91/0.86 tff(249,plain,
% 0.91/0.86 (((~![Board: array_int, Pos: $int] : (~((~((~is_board1(Board, Pos)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(Board), Q)), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(Board), Q)), $product(-1, length1(int, t2tb1(Board)))), 0)))))) | (~(is_board1(Board, Pos) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_2(Pos, Board))), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(Board), tptp_fun_Q_2(Pos, Board))), 0)) | $lesseq($sum(length1(int, t2tb1(Board)), $product(-1, tb2t(get2(int, t2tb1(Board), tptp_fun_Q_2(Pos, Board))))), 0))) | (~$greatereq(tptp_fun_Q_2(Pos, Board), 0))))))))) | (~((~((~is_board1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(N!5, $product(-1, Q)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))), Q)), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))), Q)), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))))))), 0)))))) | (~(is_board1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5) | (~($lesseq($sum(N!5, $product(-1, tptp_fun_Q_2(N!5, tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))))), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))), tptp_fun_Q_2(N!5, tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))))), 0)) | $lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))), tptp_fun_Q_2(N!5, tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))))))), 0))) | (~$greatereq(tptp_fun_Q_2(N!5, tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))), 0))))))))) <=> ((~![Board: array_int, Pos: $int] : (~((~((~is_board1(Board, Pos)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(Board), Q)), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(Board), Q)), $product(-1, length1(int, t2tb1(Board)))), 0)))))) | (~(is_board1(Board, Pos) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_2(Pos, Board))), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(Board), tptp_fun_Q_2(Pos, Board))), 0)) | $lesseq($sum(length1(int, t2tb1(Board)), $product(-1, tb2t(get2(int, t2tb1(Board), tptp_fun_Q_2(Pos, Board))))), 0))) | (~$greatereq(tptp_fun_Q_2(Pos, Board), 0))))))))) | (~((~((~is_board1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, N!5)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))), Q)), 0)) | $lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))), Q)))), 0)))))) | (~(is_board1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5) | (~($lesseq($sum(N!5, $product(-1, tptp_fun_Q_2(N!5, tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))))), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))), tptp_fun_Q_2(N!5, tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))))), 0)) | $lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))), tptp_fun_Q_2(N!5, tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))))))), 0))) | (~$greatereq(tptp_fun_Q_2(N!5, tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))), 0)))))))))),
% 0.91/0.87 inference(monotonicity,[status(thm)],[248])).
% 0.91/0.87 tff(250,plain,
% 0.91/0.87 (((~![Board: array_int, Pos: $int] : (~((~((~is_board1(Board, Pos)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(Board), Q)), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(Board), Q)), $product(-1, length1(int, t2tb1(Board)))), 0)))))) | (~(is_board1(Board, Pos) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_2(Pos, Board))), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(Board), tptp_fun_Q_2(Pos, Board))), 0)) | $lesseq($sum(length1(int, t2tb1(Board)), $product(-1, tb2t(get2(int, t2tb1(Board), tptp_fun_Q_2(Pos, Board))))), 0))) | (~$greatereq(tptp_fun_Q_2(Pos, Board), 0))))))))) | (~((~((~is_board1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(N!5, $product(-1, Q)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))), Q)), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))), Q)), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))))))), 0)))))) | (~(is_board1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5) | (~($lesseq($sum(N!5, $product(-1, tptp_fun_Q_2(N!5, tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))))), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))), tptp_fun_Q_2(N!5, tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))))), 0)) | $lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))), tptp_fun_Q_2(N!5, tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))))))), 0))) | (~$greatereq(tptp_fun_Q_2(N!5, tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))), 0))))))))) <=> ((~![Board: array_int, Pos: $int] : (~((~((~is_board1(Board, Pos)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(Board), Q)), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(Board), Q)), $product(-1, length1(int, t2tb1(Board)))), 0)))))) | (~(is_board1(Board, Pos) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_2(Pos, Board))), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(Board), tptp_fun_Q_2(Pos, Board))), 0)) | $lesseq($sum(length1(int, t2tb1(Board)), $product(-1, tb2t(get2(int, t2tb1(Board), tptp_fun_Q_2(Pos, Board))))), 0))) | (~$greatereq(tptp_fun_Q_2(Pos, Board), 0))))))))) | (~((~((~is_board1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, N!5)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))), Q)), 0)) | $lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))), Q)))), 0)))))) | (~(is_board1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5) | (~($lesseq($sum(N!5, $product(-1, tptp_fun_Q_2(N!5, tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))))), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))), tptp_fun_Q_2(N!5, tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))))), 0)) | $lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))), tptp_fun_Q_2(N!5, tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))))))), 0))) | (~$greatereq(tptp_fun_Q_2(N!5, tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))), 0)))))))))),
% 0.91/0.87 inference(transitivity,[status(thm)],[249, 247])).
% 0.91/0.87 tff(251,plain,
% 0.91/0.87 ((~![Board: array_int, Pos: $int] : (~((~((~is_board1(Board, Pos)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(Board), Q)), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(Board), Q)), $product(-1, length1(int, t2tb1(Board)))), 0)))))) | (~(is_board1(Board, Pos) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_2(Pos, Board))), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(Board), tptp_fun_Q_2(Pos, Board))), 0)) | $lesseq($sum(length1(int, t2tb1(Board)), $product(-1, tb2t(get2(int, t2tb1(Board), tptp_fun_Q_2(Pos, Board))))), 0))) | (~$greatereq(tptp_fun_Q_2(Pos, Board), 0))))))))) | (~((~((~is_board1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(N!5, $product(-1, Q)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))), Q)), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))), Q)), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))))))), 0)))))) | (~(is_board1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5) | (~($lesseq($sum(N!5, $product(-1, tptp_fun_Q_2(N!5, tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))))), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))), tptp_fun_Q_2(N!5, tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))))), 0)) | $lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))), tptp_fun_Q_2(N!5, tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))))))), 0))) | (~$greatereq(tptp_fun_Q_2(N!5, tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))), 0))))))))),
% 0.91/0.87 inference(quant_inst,[status(thm)],[])).
% 0.91/0.87 tff(252,plain,
% 0.91/0.87 ((~![Board: array_int, Pos: $int] : (~((~((~is_board1(Board, Pos)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(Board), Q)), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(Board), Q)), $product(-1, length1(int, t2tb1(Board)))), 0)))))) | (~(is_board1(Board, Pos) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_2(Pos, Board))), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(Board), tptp_fun_Q_2(Pos, Board))), 0)) | $lesseq($sum(length1(int, t2tb1(Board)), $product(-1, tb2t(get2(int, t2tb1(Board), tptp_fun_Q_2(Pos, Board))))), 0))) | (~$greatereq(tptp_fun_Q_2(Pos, Board), 0))))))))) | (~((~((~is_board1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, N!5)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))), Q)), 0)) | $lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))), Q)))), 0)))))) | (~(is_board1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5) | (~($lesseq($sum(N!5, $product(-1, tptp_fun_Q_2(N!5, tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))))), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))), tptp_fun_Q_2(N!5, tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))))), 0)) | $lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))), tptp_fun_Q_2(N!5, tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))))))), 0))) | (~$greatereq(tptp_fun_Q_2(N!5, tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))), 0))))))))),
% 0.91/0.87 inference(modus_ponens,[status(thm)],[251, 250])).
% 0.91/0.87 tff(253,plain,
% 0.91/0.87 (~((~((~is_board1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, N!5)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))), Q)), 0)) | $lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))), Q)))), 0)))))) | (~(is_board1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5) | (~($lesseq($sum(N!5, $product(-1, tptp_fun_Q_2(N!5, tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))))), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))), tptp_fun_Q_2(N!5, tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))))), 0)) | $lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))), tptp_fun_Q_2(N!5, tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))))))), 0))) | (~$greatereq(tptp_fun_Q_2(N!5, tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))), 0)))))))),
% 0.91/0.87 inference(unit_resolution,[status(thm)],[252, 73])).
% 0.91/0.87 tff(254,plain,
% 0.91/0.87 (((~((~is_board1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, N!5)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))), Q)), 0)) | $lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))), Q)))), 0)))))) | (~(is_board1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5) | (~($lesseq($sum(N!5, $product(-1, tptp_fun_Q_2(N!5, tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))))), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))), tptp_fun_Q_2(N!5, tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))))), 0)) | $lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))), tptp_fun_Q_2(N!5, tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))))))), 0))) | (~$greatereq(tptp_fun_Q_2(N!5, tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))), 0))))))) | ((~is_board1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, N!5)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))), Q)), 0)) | $lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))), Q)))), 0)))))),
% 0.91/0.87 inference(tautology,[status(thm)],[])).
% 0.91/0.87 tff(255,plain,
% 0.91/0.87 ((~is_board1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, N!5)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))), Q)), 0)) | $lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))), Q)))), 0))))),
% 0.91/0.87 inference(unit_resolution,[status(thm)],[254, 253])).
% 0.91/0.87 tff(256,plain,
% 0.91/0.87 ((~((~is_board1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, N!5)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))), Q)), 0)) | $lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))), Q)))), 0)))))) | (~is_board1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, N!5)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))), Q)), 0)) | $lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))), Q)))), 0))))),
% 0.91/0.87 inference(tautology,[status(thm)],[])).
% 0.91/0.87 tff(257,plain,
% 0.91/0.87 ((~((~is_board1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, N!5)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))), Q)), 0)) | $lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))), Q)))), 0)))))) | ![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, N!5)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))), Q)), 0)) | $lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))), Q)))), 0))))),
% 0.91/0.87 inference(unit_resolution,[status(thm)],[256, 140])).
% 0.91/0.87 tff(258,plain,
% 0.91/0.87 (![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, N!5)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))), Q)), 0)) | $lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))), Q)))), 0))))),
% 0.91/0.87 inference(unit_resolution,[status(thm)],[257, 255])).
% 0.91/0.87 tff(259,assumption,(~$greatereq($sum(Pos!4, $product(-1, N!5)), 0)), introduced(assumption)).
% 0.91/0.87 tff(260,plain,
% 0.91/0.87 ($greatereq(Pos!4, 0)),
% 0.91/0.87 inference(and_elim,[status(thm)],[23])).
% 0.91/0.87 tff(261,plain,
% 0.91/0.87 (((~![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, N!5)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))), Q)), 0)) | $lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))), Q)))), 0))))) | ((~$greatereq(Pos!4, 0)) | $greatereq($sum(Pos!4, $product(-1, N!5)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))), Pos!4)), 0)) | $lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))), Pos!4)))), 0))))) <=> ((~![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, N!5)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))), Q)), 0)) | $lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))), Q)))), 0))))) | (~$greatereq(Pos!4, 0)) | $greatereq($sum(Pos!4, $product(-1, N!5)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))), Pos!4)), 0)) | $lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))), Pos!4)))), 0))))),
% 0.91/0.87 inference(rewrite,[status(thm)],[])).
% 0.91/0.87 tff(262,plain,
% 0.91/0.87 ((~![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, N!5)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))), Q)), 0)) | $lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))), Q)))), 0))))) | ((~$greatereq(Pos!4, 0)) | $greatereq($sum(Pos!4, $product(-1, N!5)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))), Pos!4)), 0)) | $lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))), Pos!4)))), 0))))),
% 0.91/0.87 inference(quant_inst,[status(thm)],[])).
% 0.91/0.87 tff(263,plain,
% 0.91/0.87 ((~![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, N!5)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))), Q)), 0)) | $lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))), Q)))), 0))))) | (~$greatereq(Pos!4, 0)) | $greatereq($sum(Pos!4, $product(-1, N!5)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))), Pos!4)), 0)) | $lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20)))), Pos!4)))), 0)))),
% 0.91/0.87 inference(modus_ponens,[status(thm)],[262, 261])).
% 0.91/0.87 tff(264,plain,
% 0.91/0.87 ($false),
% 0.91/0.87 inference(unit_resolution,[status(thm)],[263, 260, 259, 258, 246])).
% 0.91/0.87 tff(265,plain,(((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~$greatereq(Board!7, 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), Pos!4)) | (~($sum(N!5, $product(-1, B!21)) = 0)))))) | (~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | $lesseq($sum(N!5, $product(-1, tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))))), 0) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos!4)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), 0))))) | $greatereq($sum(Pos!4, $product(-1, N!5)), 0)), inference(lemma,lemma(discharge,[]))).
% 0.91/0.87 tff(266,plain,
% 0.91/0.87 ((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~$greatereq(Board!7, 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), Pos!4)) | (~($sum(N!5, $product(-1, B!21)) = 0)))))) | (~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | $lesseq($sum(N!5, $product(-1, tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))))), 0) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos!4)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), 0))))),
% 0.91/0.87 inference(unit_resolution,[status(thm)],[265, 48])).
% 0.91/0.87 tff(267,assumption,((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~$greatereq(Board!7, 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), Pos!4)) | (~($sum(N!5, $product(-1, B!21)) = 0)))))) | (~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | $lesseq($sum(N!5, $product(-1, tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))))), 0) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos!4)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), 0))))), introduced(assumption)).
% 0.91/0.87 tff(268,assumption,((~$greatereq(Board!7, 0)) | (~(Board3!12 = tb2t2(set(int, int, t2tb2(Board2!10), t2tb(Pos!4), t2tb(I!11))))) | (~($greatereq($sum(Pos!4, $product(-1, Board!7)), 0) | (~$greatereq(Pos!4, 0)) | (~(((~(Result!13 = true1)) <=> is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | (~((~((Result!13 = true1) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Pos!4)) | (~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~($sum(N!5, $product(-1, B!19)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))), 0)))))))) | (~((~(Result!13 = true1)) | (~((~$lesseq($sum(Pos!4, $product(-1, N!5)), 0)) | (~($sum(N!5, $product(-1, Board!7)) = 0)) | (~$greatereq(Pos!4, -1)) | (~$lesseq($sum(Pos!4, $product(-1, N!5)), -1)) | (~solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~((~$greatereq(Board!7, 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B, t2tb2(B1))), $sum(1, Pos!4))))) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), Pos!4)) | (~($sum(N!5, $product(-1, B!16)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))), 0))))))))))))))))))), introduced(assumption)).
% 0.91/0.87 tff(269,plain,
% 0.91/0.87 (~$greatereq($sum(Pos!4, $product(-1, Board!7)), 0)),
% 0.91/0.87 inference(unit_resolution,[status(thm)],[122, 259])).
% 0.91/0.87 tff(270,plain,
% 0.91/0.87 ((~($greatereq($sum(Pos!4, $product(-1, Board!7)), 0) | (~$greatereq(Board!7, 0)) | (~$greatereq(Pos!4, 0)) | (~((~$greatereq(Board!7, 0)) | (~(Board3!12 = tb2t2(set(int, int, t2tb2(Board2!10), t2tb(Pos!4), t2tb(I!11))))) | (~($greatereq($sum(Pos!4, $product(-1, Board!7)), 0) | (~$greatereq(Pos!4, 0)) | (~(((~(Result!13 = true1)) <=> is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | (~((~((Result!13 = true1) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Pos!4)) | (~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~($sum(N!5, $product(-1, B!19)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))), 0)))))))) | (~((~(Result!13 = true1)) | (~((~$lesseq($sum(Pos!4, $product(-1, N!5)), 0)) | (~($sum(N!5, $product(-1, Board!7)) = 0)) | (~$greatereq(Pos!4, -1)) | (~$lesseq($sum(Pos!4, $product(-1, N!5)), -1)) | (~solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~((~$greatereq(Board!7, 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B, t2tb2(B1))), $sum(1, Pos!4))))) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), Pos!4)) | (~($sum(N!5, $product(-1, B!16)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))), 0)))))))))))))))))))))) | $greatereq($sum(Pos!4, $product(-1, Board!7)), 0) | (~$greatereq(Board!7, 0)) | (~$greatereq(Pos!4, 0)) | (~((~$greatereq(Board!7, 0)) | (~(Board3!12 = tb2t2(set(int, int, t2tb2(Board2!10), t2tb(Pos!4), t2tb(I!11))))) | (~($greatereq($sum(Pos!4, $product(-1, Board!7)), 0) | (~$greatereq(Pos!4, 0)) | (~(((~(Result!13 = true1)) <=> is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | (~((~((Result!13 = true1) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Pos!4)) | (~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~($sum(N!5, $product(-1, B!19)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))), 0)))))))) | (~((~(Result!13 = true1)) | (~((~$lesseq($sum(Pos!4, $product(-1, N!5)), 0)) | (~($sum(N!5, $product(-1, Board!7)) = 0)) | (~$greatereq(Pos!4, -1)) | (~$lesseq($sum(Pos!4, $product(-1, N!5)), -1)) | (~solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~((~$greatereq(Board!7, 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B, t2tb2(B1))), $sum(1, Pos!4))))) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), Pos!4)) | (~($sum(N!5, $product(-1, B!16)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))), 0))))))))))))))))))))),
% 0.91/0.88 inference(tautology,[status(thm)],[])).
% 0.91/0.88 tff(271,plain,
% 0.91/0.88 ((~($greatereq($sum(Pos!4, $product(-1, Board!7)), 0) | (~$greatereq(Board!7, 0)) | (~$greatereq(Pos!4, 0)) | (~((~$greatereq(Board!7, 0)) | (~(Board3!12 = tb2t2(set(int, int, t2tb2(Board2!10), t2tb(Pos!4), t2tb(I!11))))) | (~($greatereq($sum(Pos!4, $product(-1, Board!7)), 0) | (~$greatereq(Pos!4, 0)) | (~(((~(Result!13 = true1)) <=> is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | (~((~((Result!13 = true1) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Pos!4)) | (~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~($sum(N!5, $product(-1, B!19)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))), 0)))))))) | (~((~(Result!13 = true1)) | (~((~$lesseq($sum(Pos!4, $product(-1, N!5)), 0)) | (~($sum(N!5, $product(-1, Board!7)) = 0)) | (~$greatereq(Pos!4, -1)) | (~$lesseq($sum(Pos!4, $product(-1, N!5)), -1)) | (~solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~((~$greatereq(Board!7, 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B, t2tb2(B1))), $sum(1, Pos!4))))) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), Pos!4)) | (~($sum(N!5, $product(-1, B!16)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))), 0)))))))))))))))))))))) | $greatereq($sum(Pos!4, $product(-1, Board!7)), 0) | (~((~$greatereq(Board!7, 0)) | (~(Board3!12 = tb2t2(set(int, int, t2tb2(Board2!10), t2tb(Pos!4), t2tb(I!11))))) | (~($greatereq($sum(Pos!4, $product(-1, Board!7)), 0) | (~$greatereq(Pos!4, 0)) | (~(((~(Result!13 = true1)) <=> is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | (~((~((Result!13 = true1) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Pos!4)) | (~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~($sum(N!5, $product(-1, B!19)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))), 0)))))))) | (~((~(Result!13 = true1)) | (~((~$lesseq($sum(Pos!4, $product(-1, N!5)), 0)) | (~($sum(N!5, $product(-1, Board!7)) = 0)) | (~$greatereq(Pos!4, -1)) | (~$lesseq($sum(Pos!4, $product(-1, N!5)), -1)) | (~solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~((~$greatereq(Board!7, 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B, t2tb2(B1))), $sum(1, Pos!4))))) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), Pos!4)) | (~($sum(N!5, $product(-1, B!16)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))), 0))))))))))))))))))))),
% 0.91/0.88 inference(unit_resolution,[status(thm)],[270, 131, 260])).
% 0.91/0.88 tff(272,plain,
% 0.91/0.88 (~($greatereq($sum(Pos!4, $product(-1, Board!7)), 0) | (~$greatereq(Board!7, 0)) | (~$greatereq(Pos!4, 0)) | (~((~$greatereq(Board!7, 0)) | (~(Board3!12 = tb2t2(set(int, int, t2tb2(Board2!10), t2tb(Pos!4), t2tb(I!11))))) | (~($greatereq($sum(Pos!4, $product(-1, Board!7)), 0) | (~$greatereq(Pos!4, 0)) | (~(((~(Result!13 = true1)) <=> is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | (~((~((Result!13 = true1) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Pos!4)) | (~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~($sum(N!5, $product(-1, B!19)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))), 0)))))))) | (~((~(Result!13 = true1)) | (~((~$lesseq($sum(Pos!4, $product(-1, N!5)), 0)) | (~($sum(N!5, $product(-1, Board!7)) = 0)) | (~$greatereq(Pos!4, -1)) | (~$lesseq($sum(Pos!4, $product(-1, N!5)), -1)) | (~solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~((~$greatereq(Board!7, 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B, t2tb2(B1))), $sum(1, Pos!4))))) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), Pos!4)) | (~($sum(N!5, $product(-1, B!16)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))), 0)))))))))))))))))))))),
% 0.91/0.88 inference(unit_resolution,[status(thm)],[271, 269, 268])).
% 0.91/0.88 tff(273,plain,
% 0.91/0.88 (((~$greatereq(I!11, 0)) | (~$greatereq($sum(N!5, $product(-1, I!11)), 1)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos!4)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), 0)) | $greatereq($sum(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), $product(-1, I!11)), 0))) | (~($greatereq($sum(Pos!4, $product(-1, Board!7)), 0) | (~$greatereq(Board!7, 0)) | (~$greatereq(Pos!4, 0)) | (~((~$greatereq(Board!7, 0)) | (~(Board3!12 = tb2t2(set(int, int, t2tb2(Board2!10), t2tb(Pos!4), t2tb(I!11))))) | (~($greatereq($sum(Pos!4, $product(-1, Board!7)), 0) | (~$greatereq(Pos!4, 0)) | (~(((~(Result!13 = true1)) <=> is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | (~((~((Result!13 = true1) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Pos!4)) | (~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~($sum(N!5, $product(-1, B!19)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))), 0)))))))) | (~((~(Result!13 = true1)) | (~((~$lesseq($sum(Pos!4, $product(-1, N!5)), 0)) | (~($sum(N!5, $product(-1, Board!7)) = 0)) | (~$greatereq(Pos!4, -1)) | (~$lesseq($sum(Pos!4, $product(-1, N!5)), -1)) | (~solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~((~$greatereq(Board!7, 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B, t2tb2(B1))), $sum(1, Pos!4))))) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), Pos!4)) | (~($sum(N!5, $product(-1, B!16)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))), 0))))))))))))))))))))))) | ($greatereq($sum(Pos!4, $product(-1, Board!7)), 0) | (~$greatereq(Board!7, 0)) | (~$greatereq(Pos!4, 0)) | (~((~$greatereq(Board!7, 0)) | (~(Board3!12 = tb2t2(set(int, int, t2tb2(Board2!10), t2tb(Pos!4), t2tb(I!11))))) | (~($greatereq($sum(Pos!4, $product(-1, Board!7)), 0) | (~$greatereq(Pos!4, 0)) | (~(((~(Result!13 = true1)) <=> is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | (~((~((Result!13 = true1) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Pos!4)) | (~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~($sum(N!5, $product(-1, B!19)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))), 0)))))))) | (~((~(Result!13 = true1)) | (~((~$lesseq($sum(Pos!4, $product(-1, N!5)), 0)) | (~($sum(N!5, $product(-1, Board!7)) = 0)) | (~$greatereq(Pos!4, -1)) | (~$lesseq($sum(Pos!4, $product(-1, N!5)), -1)) | (~solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~((~$greatereq(Board!7, 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B, t2tb2(B1))), $sum(1, Pos!4))))) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), Pos!4)) | (~($sum(N!5, $product(-1, B!16)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))), 0)))))))))))))))))))))),
% 0.91/0.88 inference(tautology,[status(thm)],[])).
% 0.91/0.88 tff(274,plain,
% 0.91/0.88 ((~$greatereq(I!11, 0)) | (~$greatereq($sum(N!5, $product(-1, I!11)), 1)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos!4)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), 0)) | $greatereq($sum(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), $product(-1, I!11)), 0))) | (~($greatereq($sum(Pos!4, $product(-1, Board!7)), 0) | (~$greatereq(Board!7, 0)) | (~$greatereq(Pos!4, 0)) | (~((~$greatereq(Board!7, 0)) | (~(Board3!12 = tb2t2(set(int, int, t2tb2(Board2!10), t2tb(Pos!4), t2tb(I!11))))) | (~($greatereq($sum(Pos!4, $product(-1, Board!7)), 0) | (~$greatereq(Pos!4, 0)) | (~(((~(Result!13 = true1)) <=> is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | (~((~((Result!13 = true1) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Pos!4)) | (~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~($sum(N!5, $product(-1, B!19)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))), 0)))))))) | (~((~(Result!13 = true1)) | (~((~$lesseq($sum(Pos!4, $product(-1, N!5)), 0)) | (~($sum(N!5, $product(-1, Board!7)) = 0)) | (~$greatereq(Pos!4, -1)) | (~$lesseq($sum(Pos!4, $product(-1, N!5)), -1)) | (~solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~((~$greatereq(Board!7, 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B, t2tb2(B1))), $sum(1, Pos!4))))) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), Pos!4)) | (~($sum(N!5, $product(-1, B!16)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))), 0))))))))))))))))))))))),
% 0.91/0.88 inference(unit_resolution,[status(thm)],[273, 272])).
% 0.91/0.88 tff(275,assumption,(~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)), introduced(assumption)).
% 0.91/0.88 tff(276,plain,
% 0.91/0.88 (^[B1: array_int, B2: array_int, Pos: $int] : refl((~((~((~eq_board1(B1, B2, Pos)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0) | ($sum(tb2t(get2(int, t2tb1(B2), Q)), $product(-1, tb2t(get2(int, t2tb1(B1), Q)))) = 0)))) | (~(eq_board1(B1, B2, Pos) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_0(Pos, B2, B1))), 0) | ($sum(tb2t(get2(int, t2tb1(B2), tptp_fun_Q_0(Pos, B2, B1))), $product(-1, tb2t(get2(int, t2tb1(B1), tptp_fun_Q_0(Pos, B2, B1))))) = 0) | (~$greatereq(tptp_fun_Q_0(Pos, B2, B1), 0)))))))) <=> (~((~((~eq_board1(B1, B2, Pos)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0) | ($sum(tb2t(get2(int, t2tb1(B2), Q)), $product(-1, tb2t(get2(int, t2tb1(B1), Q)))) = 0)))) | (~(eq_board1(B1, B2, Pos) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_0(Pos, B2, B1))), 0) | ($sum(tb2t(get2(int, t2tb1(B2), tptp_fun_Q_0(Pos, B2, B1))), $product(-1, tb2t(get2(int, t2tb1(B1), tptp_fun_Q_0(Pos, B2, B1))))) = 0) | (~$greatereq(tptp_fun_Q_0(Pos, B2, B1), 0)))))))))),
% 0.91/0.88 inference(bind,[status(th)],[])).
% 0.91/0.88 tff(277,plain,
% 0.91/0.88 (![B1: array_int, B2: array_int, Pos: $int] : (~((~((~eq_board1(B1, B2, Pos)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0) | ($sum(tb2t(get2(int, t2tb1(B2), Q)), $product(-1, tb2t(get2(int, t2tb1(B1), Q)))) = 0)))) | (~(eq_board1(B1, B2, Pos) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_0(Pos, B2, B1))), 0) | ($sum(tb2t(get2(int, t2tb1(B2), tptp_fun_Q_0(Pos, B2, B1))), $product(-1, tb2t(get2(int, t2tb1(B1), tptp_fun_Q_0(Pos, B2, B1))))) = 0) | (~$greatereq(tptp_fun_Q_0(Pos, B2, B1), 0)))))))) <=> ![B1: array_int, B2: array_int, Pos: $int] : (~((~((~eq_board1(B1, B2, Pos)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0) | ($sum(tb2t(get2(int, t2tb1(B2), Q)), $product(-1, tb2t(get2(int, t2tb1(B1), Q)))) = 0)))) | (~(eq_board1(B1, B2, Pos) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_0(Pos, B2, B1))), 0) | ($sum(tb2t(get2(int, t2tb1(B2), tptp_fun_Q_0(Pos, B2, B1))), $product(-1, tb2t(get2(int, t2tb1(B1), tptp_fun_Q_0(Pos, B2, B1))))) = 0) | (~$greatereq(tptp_fun_Q_0(Pos, B2, B1), 0))))))))),
% 0.91/0.88 inference(quant_intro,[status(thm)],[276])).
% 0.91/0.88 tff(278,plain,
% 0.91/0.88 (^[B1: array_int, B2: array_int, Pos: $int] : rewrite((~((~((~eq_board1(B1, B2, Pos)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0) | ($sum(tb2t(get2(int, t2tb1(B2), Q)), $product(-1, tb2t(get2(int, t2tb1(B1), Q)))) = 0)))) | (~(eq_board1(B1, B2, Pos) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_0(Pos, B2, B1))), 0) | ($sum(tb2t(get2(int, t2tb1(B2), tptp_fun_Q_0(Pos, B2, B1))), $product(-1, tb2t(get2(int, t2tb1(B1), tptp_fun_Q_0(Pos, B2, B1))))) = 0) | (~$greatereq(tptp_fun_Q_0(Pos, B2, B1), 0)))))))) <=> (~((~((~eq_board1(B1, B2, Pos)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0) | ($sum(tb2t(get2(int, t2tb1(B2), Q)), $product(-1, tb2t(get2(int, t2tb1(B1), Q)))) = 0)))) | (~(eq_board1(B1, B2, Pos) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_0(Pos, B2, B1))), 0) | ($sum(tb2t(get2(int, t2tb1(B2), tptp_fun_Q_0(Pos, B2, B1))), $product(-1, tb2t(get2(int, t2tb1(B1), tptp_fun_Q_0(Pos, B2, B1))))) = 0) | (~$greatereq(tptp_fun_Q_0(Pos, B2, B1), 0)))))))))),
% 0.91/0.88 inference(bind,[status(th)],[])).
% 0.91/0.88 tff(279,plain,
% 0.91/0.88 (![B1: array_int, B2: array_int, Pos: $int] : (~((~((~eq_board1(B1, B2, Pos)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0) | ($sum(tb2t(get2(int, t2tb1(B2), Q)), $product(-1, tb2t(get2(int, t2tb1(B1), Q)))) = 0)))) | (~(eq_board1(B1, B2, Pos) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_0(Pos, B2, B1))), 0) | ($sum(tb2t(get2(int, t2tb1(B2), tptp_fun_Q_0(Pos, B2, B1))), $product(-1, tb2t(get2(int, t2tb1(B1), tptp_fun_Q_0(Pos, B2, B1))))) = 0) | (~$greatereq(tptp_fun_Q_0(Pos, B2, B1), 0)))))))) <=> ![B1: array_int, B2: array_int, Pos: $int] : (~((~((~eq_board1(B1, B2, Pos)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0) | ($sum(tb2t(get2(int, t2tb1(B2), Q)), $product(-1, tb2t(get2(int, t2tb1(B1), Q)))) = 0)))) | (~(eq_board1(B1, B2, Pos) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_0(Pos, B2, B1))), 0) | ($sum(tb2t(get2(int, t2tb1(B2), tptp_fun_Q_0(Pos, B2, B1))), $product(-1, tb2t(get2(int, t2tb1(B1), tptp_fun_Q_0(Pos, B2, B1))))) = 0) | (~$greatereq(tptp_fun_Q_0(Pos, B2, B1), 0))))))))),
% 0.91/0.88 inference(quant_intro,[status(thm)],[278])).
% 0.91/0.88 tff(280,plain,
% 0.91/0.88 (![B1: array_int, B2: array_int, Pos: $int] : (~((~((~eq_board1(B1, B2, Pos)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0) | ($sum(tb2t(get2(int, t2tb1(B2), Q)), $product(-1, tb2t(get2(int, t2tb1(B1), Q)))) = 0)))) | (~(eq_board1(B1, B2, Pos) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_0(Pos, B2, B1))), 0) | ($sum(tb2t(get2(int, t2tb1(B2), tptp_fun_Q_0(Pos, B2, B1))), $product(-1, tb2t(get2(int, t2tb1(B1), tptp_fun_Q_0(Pos, B2, B1))))) = 0) | (~$greatereq(tptp_fun_Q_0(Pos, B2, B1), 0)))))))) <=> ![B1: array_int, B2: array_int, Pos: $int] : (~((~((~eq_board1(B1, B2, Pos)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0) | ($sum(tb2t(get2(int, t2tb1(B2), Q)), $product(-1, tb2t(get2(int, t2tb1(B1), Q)))) = 0)))) | (~(eq_board1(B1, B2, Pos) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_0(Pos, B2, B1))), 0) | ($sum(tb2t(get2(int, t2tb1(B2), tptp_fun_Q_0(Pos, B2, B1))), $product(-1, tb2t(get2(int, t2tb1(B1), tptp_fun_Q_0(Pos, B2, B1))))) = 0) | (~$greatereq(tptp_fun_Q_0(Pos, B2, B1), 0))))))))),
% 0.91/0.88 inference(transitivity,[status(thm)],[279, 277])).
% 0.91/0.88 tff(281,plain,
% 0.91/0.88 (^[B1: array_int, B2: array_int, Pos: $int] : trans(monotonicity(rewrite(((~eq_board1(B1, B2, Pos)) | ![Q: $int] : ((~($greatereq(Q, 0) & (~$lesseq($sum(Pos, $product(-1, Q)), 0)))) | ($sum(tb2t(get2(int, t2tb1(B2), Q)), $product(-1, tb2t(get2(int, t2tb1(B1), Q)))) = 0))) <=> ((~eq_board1(B1, B2, Pos)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0) | ($sum(tb2t(get2(int, t2tb1(B2), Q)), $product(-1, tb2t(get2(int, t2tb1(B1), Q)))) = 0)))), trans(monotonicity(rewrite((~((~($greatereq(tptp_fun_Q_0(Pos, B2, B1), 0) & (~$lesseq($sum(Pos, $product(-1, tptp_fun_Q_0(Pos, B2, B1))), 0)))) | ($sum(tb2t(get2(int, t2tb1(B2), tptp_fun_Q_0(Pos, B2, B1))), $product(-1, tb2t(get2(int, t2tb1(B1), tptp_fun_Q_0(Pos, B2, B1))))) = 0))) <=> (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_0(Pos, B2, B1))), 0) | ($sum(tb2t(get2(int, t2tb1(B2), tptp_fun_Q_0(Pos, B2, B1))), $product(-1, tb2t(get2(int, t2tb1(B1), tptp_fun_Q_0(Pos, B2, B1))))) = 0) | (~$greatereq(tptp_fun_Q_0(Pos, B2, B1), 0))))), ((eq_board1(B1, B2, Pos) | (~((~($greatereq(tptp_fun_Q_0(Pos, B2, B1), 0) & (~$lesseq($sum(Pos, $product(-1, tptp_fun_Q_0(Pos, B2, B1))), 0)))) | ($sum(tb2t(get2(int, t2tb1(B2), tptp_fun_Q_0(Pos, B2, B1))), $product(-1, tb2t(get2(int, t2tb1(B1), tptp_fun_Q_0(Pos, B2, B1))))) = 0)))) <=> (eq_board1(B1, B2, Pos) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_0(Pos, B2, B1))), 0) | ($sum(tb2t(get2(int, t2tb1(B2), tptp_fun_Q_0(Pos, B2, B1))), $product(-1, tb2t(get2(int, t2tb1(B1), tptp_fun_Q_0(Pos, B2, B1))))) = 0) | (~$greatereq(tptp_fun_Q_0(Pos, B2, B1), 0))))))), rewrite((eq_board1(B1, B2, Pos) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_0(Pos, B2, B1))), 0) | ($sum(tb2t(get2(int, t2tb1(B2), tptp_fun_Q_0(Pos, B2, B1))), $product(-1, tb2t(get2(int, t2tb1(B1), tptp_fun_Q_0(Pos, B2, B1))))) = 0) | (~$greatereq(tptp_fun_Q_0(Pos, B2, B1), 0))))) <=> (eq_board1(B1, B2, Pos) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_0(Pos, B2, B1))), 0) | ($sum(tb2t(get2(int, t2tb1(B2), tptp_fun_Q_0(Pos, B2, B1))), $product(-1, tb2t(get2(int, t2tb1(B1), tptp_fun_Q_0(Pos, B2, B1))))) = 0) | (~$greatereq(tptp_fun_Q_0(Pos, B2, B1), 0)))))), ((eq_board1(B1, B2, Pos) | (~((~($greatereq(tptp_fun_Q_0(Pos, B2, B1), 0) & (~$lesseq($sum(Pos, $product(-1, tptp_fun_Q_0(Pos, B2, B1))), 0)))) | ($sum(tb2t(get2(int, t2tb1(B2), tptp_fun_Q_0(Pos, B2, B1))), $product(-1, tb2t(get2(int, t2tb1(B1), tptp_fun_Q_0(Pos, B2, B1))))) = 0)))) <=> (eq_board1(B1, B2, Pos) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_0(Pos, B2, B1))), 0) | ($sum(tb2t(get2(int, t2tb1(B2), tptp_fun_Q_0(Pos, B2, B1))), $product(-1, tb2t(get2(int, t2tb1(B1), tptp_fun_Q_0(Pos, B2, B1))))) = 0) | (~$greatereq(tptp_fun_Q_0(Pos, B2, B1), 0))))))), ((((~eq_board1(B1, B2, Pos)) | ![Q: $int] : ((~($greatereq(Q, 0) & (~$lesseq($sum(Pos, $product(-1, Q)), 0)))) | ($sum(tb2t(get2(int, t2tb1(B2), Q)), $product(-1, tb2t(get2(int, t2tb1(B1), Q)))) = 0))) & (eq_board1(B1, B2, Pos) | (~((~($greatereq(tptp_fun_Q_0(Pos, B2, B1), 0) & (~$lesseq($sum(Pos, $product(-1, tptp_fun_Q_0(Pos, B2, B1))), 0)))) | ($sum(tb2t(get2(int, t2tb1(B2), tptp_fun_Q_0(Pos, B2, B1))), $product(-1, tb2t(get2(int, t2tb1(B1), tptp_fun_Q_0(Pos, B2, B1))))) = 0))))) <=> (((~eq_board1(B1, B2, Pos)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0) | ($sum(tb2t(get2(int, t2tb1(B2), Q)), $product(-1, tb2t(get2(int, t2tb1(B1), Q)))) = 0))) & (eq_board1(B1, B2, Pos) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_0(Pos, B2, B1))), 0) | ($sum(tb2t(get2(int, t2tb1(B2), tptp_fun_Q_0(Pos, B2, B1))), $product(-1, tb2t(get2(int, t2tb1(B1), tptp_fun_Q_0(Pos, B2, B1))))) = 0) | (~$greatereq(tptp_fun_Q_0(Pos, B2, B1), 0)))))))), rewrite((((~eq_board1(B1, B2, Pos)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0) | ($sum(tb2t(get2(int, t2tb1(B2), Q)), $product(-1, tb2t(get2(int, t2tb1(B1), Q)))) = 0))) & (eq_board1(B1, B2, Pos) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_0(Pos, B2, B1))), 0) | ($sum(tb2t(get2(int, t2tb1(B2), tptp_fun_Q_0(Pos, B2, B1))), $product(-1, tb2t(get2(int, t2tb1(B1), tptp_fun_Q_0(Pos, B2, B1))))) = 0) | (~$greatereq(tptp_fun_Q_0(Pos, B2, B1), 0)))))) <=> (~((~((~eq_board1(B1, B2, Pos)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0) | ($sum(tb2t(get2(int, t2tb1(B2), Q)), $product(-1, tb2t(get2(int, t2tb1(B1), Q)))) = 0)))) | (~(eq_board1(B1, B2, Pos) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_0(Pos, B2, B1))), 0) | ($sum(tb2t(get2(int, t2tb1(B2), tptp_fun_Q_0(Pos, B2, B1))), $product(-1, tb2t(get2(int, t2tb1(B1), tptp_fun_Q_0(Pos, B2, B1))))) = 0) | (~$greatereq(tptp_fun_Q_0(Pos, B2, B1), 0))))))))), ((((~eq_board1(B1, B2, Pos)) | ![Q: $int] : ((~($greatereq(Q, 0) & (~$lesseq($sum(Pos, $product(-1, Q)), 0)))) | ($sum(tb2t(get2(int, t2tb1(B2), Q)), $product(-1, tb2t(get2(int, t2tb1(B1), Q)))) = 0))) & (eq_board1(B1, B2, Pos) | (~((~($greatereq(tptp_fun_Q_0(Pos, B2, B1), 0) & (~$lesseq($sum(Pos, $product(-1, tptp_fun_Q_0(Pos, B2, B1))), 0)))) | ($sum(tb2t(get2(int, t2tb1(B2), tptp_fun_Q_0(Pos, B2, B1))), $product(-1, tb2t(get2(int, t2tb1(B1), tptp_fun_Q_0(Pos, B2, B1))))) = 0))))) <=> (~((~((~eq_board1(B1, B2, Pos)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0) | ($sum(tb2t(get2(int, t2tb1(B2), Q)), $product(-1, tb2t(get2(int, t2tb1(B1), Q)))) = 0)))) | (~(eq_board1(B1, B2, Pos) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_0(Pos, B2, B1))), 0) | ($sum(tb2t(get2(int, t2tb1(B2), tptp_fun_Q_0(Pos, B2, B1))), $product(-1, tb2t(get2(int, t2tb1(B1), tptp_fun_Q_0(Pos, B2, B1))))) = 0) | (~$greatereq(tptp_fun_Q_0(Pos, B2, B1), 0))))))))))),
% 0.91/0.88 inference(bind,[status(th)],[])).
% 0.91/0.88 tff(282,plain,
% 0.91/0.88 (![B1: array_int, B2: array_int, Pos: $int] : (((~eq_board1(B1, B2, Pos)) | ![Q: $int] : ((~($greatereq(Q, 0) & (~$lesseq($sum(Pos, $product(-1, Q)), 0)))) | ($sum(tb2t(get2(int, t2tb1(B2), Q)), $product(-1, tb2t(get2(int, t2tb1(B1), Q)))) = 0))) & (eq_board1(B1, B2, Pos) | (~((~($greatereq(tptp_fun_Q_0(Pos, B2, B1), 0) & (~$lesseq($sum(Pos, $product(-1, tptp_fun_Q_0(Pos, B2, B1))), 0)))) | ($sum(tb2t(get2(int, t2tb1(B2), tptp_fun_Q_0(Pos, B2, B1))), $product(-1, tb2t(get2(int, t2tb1(B1), tptp_fun_Q_0(Pos, B2, B1))))) = 0))))) <=> ![B1: array_int, B2: array_int, Pos: $int] : (~((~((~eq_board1(B1, B2, Pos)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0) | ($sum(tb2t(get2(int, t2tb1(B2), Q)), $product(-1, tb2t(get2(int, t2tb1(B1), Q)))) = 0)))) | (~(eq_board1(B1, B2, Pos) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_0(Pos, B2, B1))), 0) | ($sum(tb2t(get2(int, t2tb1(B2), tptp_fun_Q_0(Pos, B2, B1))), $product(-1, tb2t(get2(int, t2tb1(B1), tptp_fun_Q_0(Pos, B2, B1))))) = 0) | (~$greatereq(tptp_fun_Q_0(Pos, B2, B1), 0))))))))),
% 0.91/0.88 inference(quant_intro,[status(thm)],[281])).
% 0.91/0.88 tff(283,plain,
% 0.91/0.88 (^[B1: array_int, B2: array_int, Pos: $int] : rewrite((eq_board1(B1, B2, Pos) <=> ![Q: $int] : ((~($greatereq(Q, 0) & (~$lesseq($sum(Pos, $product(-1, Q)), 0)))) | ($sum(tb2t(get2(int, t2tb1(B1), Q)), $product(-1, tb2t(get2(int, t2tb1(B2), Q)))) = 0))) <=> (eq_board1(B1, B2, Pos) <=> ![Q: $int] : ((~($greatereq(Q, 0) & (~$lesseq($sum(Pos, $product(-1, Q)), 0)))) | ($sum(tb2t(get2(int, t2tb1(B2), Q)), $product(-1, tb2t(get2(int, t2tb1(B1), Q)))) = 0))))),
% 0.91/0.88 inference(bind,[status(th)],[])).
% 0.91/0.88 tff(284,plain,
% 0.91/0.88 (![B1: array_int, B2: array_int, Pos: $int] : (eq_board1(B1, B2, Pos) <=> ![Q: $int] : ((~($greatereq(Q, 0) & (~$lesseq($sum(Pos, $product(-1, Q)), 0)))) | ($sum(tb2t(get2(int, t2tb1(B1), Q)), $product(-1, tb2t(get2(int, t2tb1(B2), Q)))) = 0))) <=> ![B1: array_int, B2: array_int, Pos: $int] : (eq_board1(B1, B2, Pos) <=> ![Q: $int] : ((~($greatereq(Q, 0) & (~$lesseq($sum(Pos, $product(-1, Q)), 0)))) | ($sum(tb2t(get2(int, t2tb1(B2), Q)), $product(-1, tb2t(get2(int, t2tb1(B1), Q)))) = 0)))),
% 0.91/0.88 inference(quant_intro,[status(thm)],[283])).
% 0.91/0.88 tff(285,plain,
% 0.91/0.88 (^[B1: array_int, B2: array_int, Pos: $int] : rewrite((eq_board1(B1, B2, Pos) <=> ![Q: $int] : ((~($lesseq(0, Q) & (~$lesseq(Pos, Q)))) | (tb2t(get2(int, t2tb1(B1), Q)) = tb2t(get2(int, t2tb1(B2), Q))))) <=> (eq_board1(B1, B2, Pos) <=> ![Q: $int] : ((~($greatereq(Q, 0) & (~$lesseq($sum(Pos, $product(-1, Q)), 0)))) | ($sum(tb2t(get2(int, t2tb1(B1), Q)), $product(-1, tb2t(get2(int, t2tb1(B2), Q)))) = 0))))),
% 0.91/0.88 inference(bind,[status(th)],[])).
% 0.91/0.88 tff(286,plain,
% 0.91/0.88 (![B1: array_int, B2: array_int, Pos: $int] : (eq_board1(B1, B2, Pos) <=> ![Q: $int] : ((~($lesseq(0, Q) & (~$lesseq(Pos, Q)))) | (tb2t(get2(int, t2tb1(B1), Q)) = tb2t(get2(int, t2tb1(B2), Q))))) <=> ![B1: array_int, B2: array_int, Pos: $int] : (eq_board1(B1, B2, Pos) <=> ![Q: $int] : ((~($greatereq(Q, 0) & (~$lesseq($sum(Pos, $product(-1, Q)), 0)))) | ($sum(tb2t(get2(int, t2tb1(B1), Q)), $product(-1, tb2t(get2(int, t2tb1(B2), Q)))) = 0)))),
% 0.91/0.88 inference(quant_intro,[status(thm)],[285])).
% 0.91/0.88 tff(287,plain,
% 0.91/0.88 (![B1: array_int, B2: array_int, Pos: $int] : (eq_board1(B1, B2, Pos) <=> ![Q: $int] : ((~($lesseq(0, Q) & (~$lesseq(Pos, Q)))) | (tb2t(get2(int, t2tb1(B1), Q)) = tb2t(get2(int, t2tb1(B2), Q))))) <=> ![B1: array_int, B2: array_int, Pos: $int] : (eq_board1(B1, B2, Pos) <=> ![Q: $int] : ((~($lesseq(0, Q) & (~$lesseq(Pos, Q)))) | (tb2t(get2(int, t2tb1(B1), Q)) = tb2t(get2(int, t2tb1(B2), Q)))))),
% 0.91/0.88 inference(rewrite,[status(thm)],[])).
% 0.91/0.88 tff(288,plain,
% 0.91/0.88 (^[B1: array_int, B2: array_int, Pos: $int] : rewrite((eq_board1(B1, B2, Pos) <=> ![Q: $int] : (($lesseq(0, Q) & $less(Q, Pos)) => (tb2t(get2(int, t2tb1(B1), Q)) = tb2t(get2(int, t2tb1(B2), Q))))) <=> (eq_board1(B1, B2, Pos) <=> ![Q: $int] : ((~($lesseq(0, Q) & (~$lesseq(Pos, Q)))) | (tb2t(get2(int, t2tb1(B1), Q)) = tb2t(get2(int, t2tb1(B2), Q))))))),
% 0.91/0.88 inference(bind,[status(th)],[])).
% 0.91/0.88 tff(289,plain,
% 0.91/0.88 (![B1: array_int, B2: array_int, Pos: $int] : (eq_board1(B1, B2, Pos) <=> ![Q: $int] : (($lesseq(0, Q) & $less(Q, Pos)) => (tb2t(get2(int, t2tb1(B1), Q)) = tb2t(get2(int, t2tb1(B2), Q))))) <=> ![B1: array_int, B2: array_int, Pos: $int] : (eq_board1(B1, B2, Pos) <=> ![Q: $int] : ((~($lesseq(0, Q) & (~$lesseq(Pos, Q)))) | (tb2t(get2(int, t2tb1(B1), Q)) = tb2t(get2(int, t2tb1(B2), Q)))))),
% 0.91/0.88 inference(quant_intro,[status(thm)],[288])).
% 0.91/0.88 tff(290,axiom,(![B1: array_int, B2: array_int, Pos: $int] : (eq_board1(B1, B2, Pos) <=> ![Q: $int] : (($lesseq(0, Q) & $less(Q, Pos)) => (tb2t(get2(int, t2tb1(B1), Q)) = tb2t(get2(int, t2tb1(B2), Q)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','eq_board_def')).
% 0.91/0.88 tff(291,plain,
% 0.91/0.88 (![B1: array_int, B2: array_int, Pos: $int] : (eq_board1(B1, B2, Pos) <=> ![Q: $int] : ((~($lesseq(0, Q) & (~$lesseq(Pos, Q)))) | (tb2t(get2(int, t2tb1(B1), Q)) = tb2t(get2(int, t2tb1(B2), Q)))))),
% 0.91/0.88 inference(modus_ponens,[status(thm)],[290, 289])).
% 0.91/0.88 tff(292,plain,
% 0.91/0.88 (![B1: array_int, B2: array_int, Pos: $int] : (eq_board1(B1, B2, Pos) <=> ![Q: $int] : ((~($lesseq(0, Q) & (~$lesseq(Pos, Q)))) | (tb2t(get2(int, t2tb1(B1), Q)) = tb2t(get2(int, t2tb1(B2), Q)))))),
% 0.91/0.88 inference(modus_ponens,[status(thm)],[291, 287])).
% 0.91/0.88 tff(293,plain,
% 0.91/0.88 (![B1: array_int, B2: array_int, Pos: $int] : (eq_board1(B1, B2, Pos) <=> ![Q: $int] : ((~($greatereq(Q, 0) & (~$lesseq($sum(Pos, $product(-1, Q)), 0)))) | ($sum(tb2t(get2(int, t2tb1(B1), Q)), $product(-1, tb2t(get2(int, t2tb1(B2), Q)))) = 0)))),
% 0.91/0.88 inference(modus_ponens,[status(thm)],[292, 286])).
% 0.91/0.88 tff(294,plain,
% 0.91/0.88 (![B1: array_int, B2: array_int, Pos: $int] : (eq_board1(B1, B2, Pos) <=> ![Q: $int] : ((~($greatereq(Q, 0) & (~$lesseq($sum(Pos, $product(-1, Q)), 0)))) | ($sum(tb2t(get2(int, t2tb1(B2), Q)), $product(-1, tb2t(get2(int, t2tb1(B1), Q)))) = 0)))),
% 0.91/0.88 inference(modus_ponens,[status(thm)],[293, 284])).
% 0.91/0.88 tff(295,plain,(
% 0.91/0.88 ![B1: array_int, B2: array_int, Pos: $int] : (((~eq_board1(B1, B2, Pos)) | ![Q: $int] : ((~($greatereq(Q, 0) & (~$lesseq($sum(Pos, $product(-1, Q)), 0)))) | ($sum(tb2t(get2(int, t2tb1(B2), Q)), $product(-1, tb2t(get2(int, t2tb1(B1), Q)))) = 0))) & (eq_board1(B1, B2, Pos) | (~((~($greatereq(tptp_fun_Q_0(Pos, B2, B1), 0) & (~$lesseq($sum(Pos, $product(-1, tptp_fun_Q_0(Pos, B2, B1))), 0)))) | ($sum(tb2t(get2(int, t2tb1(B2), tptp_fun_Q_0(Pos, B2, B1))), $product(-1, tb2t(get2(int, t2tb1(B1), tptp_fun_Q_0(Pos, B2, B1))))) = 0)))))),
% 0.91/0.88 inference(skolemize,[status(sab)],[294])).
% 0.91/0.88 tff(296,plain,
% 0.91/0.88 (![B1: array_int, B2: array_int, Pos: $int] : (~((~((~eq_board1(B1, B2, Pos)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0) | ($sum(tb2t(get2(int, t2tb1(B2), Q)), $product(-1, tb2t(get2(int, t2tb1(B1), Q)))) = 0)))) | (~(eq_board1(B1, B2, Pos) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_0(Pos, B2, B1))), 0) | ($sum(tb2t(get2(int, t2tb1(B2), tptp_fun_Q_0(Pos, B2, B1))), $product(-1, tb2t(get2(int, t2tb1(B1), tptp_fun_Q_0(Pos, B2, B1))))) = 0) | (~$greatereq(tptp_fun_Q_0(Pos, B2, B1), 0))))))))),
% 0.91/0.89 inference(modus_ponens,[status(thm)],[295, 282])).
% 0.91/0.89 tff(297,plain,
% 0.91/0.89 (![B1: array_int, B2: array_int, Pos: $int] : (~((~((~eq_board1(B1, B2, Pos)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0) | ($sum(tb2t(get2(int, t2tb1(B2), Q)), $product(-1, tb2t(get2(int, t2tb1(B1), Q)))) = 0)))) | (~(eq_board1(B1, B2, Pos) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_0(Pos, B2, B1))), 0) | ($sum(tb2t(get2(int, t2tb1(B2), tptp_fun_Q_0(Pos, B2, B1))), $product(-1, tb2t(get2(int, t2tb1(B1), tptp_fun_Q_0(Pos, B2, B1))))) = 0) | (~$greatereq(tptp_fun_Q_0(Pos, B2, B1), 0))))))))),
% 0.91/0.89 inference(modus_ponens,[status(thm)],[296, 280])).
% 0.91/0.89 tff(298,plain,
% 0.91/0.89 (((~![B1: array_int, B2: array_int, Pos: $int] : (~((~((~eq_board1(B1, B2, Pos)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0) | ($sum(tb2t(get2(int, t2tb1(B2), Q)), $product(-1, tb2t(get2(int, t2tb1(B1), Q)))) = 0)))) | (~(eq_board1(B1, B2, Pos) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_0(Pos, B2, B1))), 0) | ($sum(tb2t(get2(int, t2tb1(B2), tptp_fun_Q_0(Pos, B2, B1))), $product(-1, tb2t(get2(int, t2tb1(B1), tptp_fun_Q_0(Pos, B2, B1))))) = 0) | (~$greatereq(tptp_fun_Q_0(Pos, B2, B1), 0))))))))) | eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) <=> ((~![B1: array_int, B2: array_int, Pos: $int] : (~((~((~eq_board1(B1, B2, Pos)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0) | ($sum(tb2t(get2(int, t2tb1(B2), Q)), $product(-1, tb2t(get2(int, t2tb1(B1), Q)))) = 0)))) | (~(eq_board1(B1, B2, Pos) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_0(Pos, B2, B1))), 0) | ($sum(tb2t(get2(int, t2tb1(B2), tptp_fun_Q_0(Pos, B2, B1))), $product(-1, tb2t(get2(int, t2tb1(B1), tptp_fun_Q_0(Pos, B2, B1))))) = 0) | (~$greatereq(tptp_fun_Q_0(Pos, B2, B1), 0))))))))) | eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4))),
% 0.91/0.89 inference(rewrite,[status(thm)],[])).
% 0.91/0.89 tff(299,plain,
% 0.91/0.89 ((~(~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4))) <=> eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)),
% 0.91/0.89 inference(rewrite,[status(thm)],[])).
% 0.91/0.89 tff(300,plain,
% 0.91/0.89 (($false | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4))) <=> (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4))),
% 0.91/0.89 inference(rewrite,[status(thm)],[])).
% 0.91/0.89 tff(301,plain,
% 0.91/0.89 ((~(eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4) | (~($lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6)))))), 0) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6)))), tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6)))), tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6)))))))) = 0) | (~$greatereq(tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6)))), 0)))))) <=> (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4))),
% 0.91/0.89 inference(rewrite,[status(thm)],[])).
% 0.91/0.89 tff(302,plain,
% 0.91/0.89 ((~$true) <=> $false),
% 0.91/0.89 inference(rewrite,[status(thm)],[])).
% 0.91/0.89 tff(303,plain,
% 0.91/0.89 (((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | $true) <=> $true),
% 0.91/0.89 inference(rewrite,[status(thm)],[])).
% 0.91/0.89 tff(304,plain,
% 0.91/0.89 (![Q: $int] : $true <=> $true),
% 0.91/0.89 inference(elim_unused_vars,[status(thm)],[])).
% 0.91/0.89 tff(305,plain,
% 0.91/0.89 (![Q: $int] : $true <=> ![Q: $int] : $true),
% 0.91/0.89 inference(rewrite,[status(thm)],[])).
% 0.91/0.89 tff(306,plain,
% 0.91/0.89 (![Q: $int] : $true <=> $true),
% 0.91/0.89 inference(transitivity,[status(thm)],[305, 304])).
% 0.91/0.89 tff(307,plain,
% 0.91/0.89 (^[Q: $int] : trans(monotonicity(trans(monotonicity(rewrite($sum(Pos!4, $product(-1, Q)) = $sum($product(-1, Q), Pos!4)), ($lesseq($sum(Pos!4, $product(-1, Q)), 0) <=> $lesseq($sum($product(-1, Q), Pos!4), 0))), rewrite($lesseq($sum($product(-1, Q), Pos!4), 0) <=> $greatereq($sum(Q, $product(-1, Pos!4)), 0)), ($lesseq($sum(Pos!4, $product(-1, Q)), 0) <=> $greatereq($sum(Q, $product(-1, Pos!4)), 0))), trans(monotonicity(rewrite($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6)))), Q)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6)))), Q)))) = 0), (($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6)))), Q)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6)))), Q)))) = 0) <=> (0 = 0))), rewrite((0 = 0) <=> $true), (($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6)))), Q)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6)))), Q)))) = 0) <=> $true)), (((~$greatereq(Q, 0)) | $lesseq($sum(Pos!4, $product(-1, Q)), 0) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6)))), Q)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6)))), Q)))) = 0)) <=> ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 0) | $true))), rewrite(((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 0) | $true) <=> $true), (((~$greatereq(Q, 0)) | $lesseq($sum(Pos!4, $product(-1, Q)), 0) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6)))), Q)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6)))), Q)))) = 0)) <=> $true))),
% 0.91/0.89 inference(bind,[status(th)],[])).
% 0.91/0.89 tff(308,plain,
% 0.91/0.89 (![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos!4, $product(-1, Q)), 0) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6)))), Q)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6)))), Q)))) = 0)) <=> ![Q: $int] : $true),
% 0.91/0.89 inference(quant_intro,[status(thm)],[307])).
% 0.91/0.89 tff(309,plain,
% 0.91/0.89 (![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos!4, $product(-1, Q)), 0) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6)))), Q)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6)))), Q)))) = 0)) <=> $true),
% 0.91/0.89 inference(transitivity,[status(thm)],[308, 306])).
% 0.91/0.89 tff(310,plain,
% 0.91/0.89 (((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos!4, $product(-1, Q)), 0) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6)))), Q)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6)))), Q)))) = 0))) <=> ((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | $true)),
% 0.91/0.89 inference(monotonicity,[status(thm)],[309])).
% 0.91/0.89 tff(311,plain,
% 0.91/0.89 (((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos!4, $product(-1, Q)), 0) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6)))), Q)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6)))), Q)))) = 0))) <=> $true),
% 0.91/0.89 inference(transitivity,[status(thm)],[310, 303])).
% 0.91/0.89 tff(312,plain,
% 0.91/0.89 ((~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos!4, $product(-1, Q)), 0) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6)))), Q)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6)))), Q)))) = 0)))) <=> (~$true)),
% 0.91/0.89 inference(monotonicity,[status(thm)],[311])).
% 0.91/0.89 tff(313,plain,
% 0.91/0.89 ((~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos!4, $product(-1, Q)), 0) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6)))), Q)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6)))), Q)))) = 0)))) <=> $false),
% 0.91/0.89 inference(transitivity,[status(thm)],[312, 302])).
% 0.91/0.89 tff(314,plain,
% 0.91/0.89 (((~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos!4, $product(-1, Q)), 0) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6)))), Q)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6)))), Q)))) = 0)))) | (~(eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4) | (~($lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6)))))), 0) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6)))), tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6)))), tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6)))))))) = 0) | (~$greatereq(tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6)))), 0))))))) <=> ($false | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)))),
% 0.91/0.89 inference(monotonicity,[status(thm)],[313, 301])).
% 0.91/0.89 tff(315,plain,
% 0.91/0.89 (((~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos!4, $product(-1, Q)), 0) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6)))), Q)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6)))), Q)))) = 0)))) | (~(eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4) | (~($lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6)))))), 0) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6)))), tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6)))), tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6)))))))) = 0) | (~$greatereq(tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6)))), 0))))))) <=> (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4))),
% 0.91/0.89 inference(transitivity,[status(thm)],[314, 300])).
% 0.91/0.89 tff(316,plain,
% 0.91/0.89 ((~((~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos!4, $product(-1, Q)), 0) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6)))), Q)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6)))), Q)))) = 0)))) | (~(eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4) | (~($lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6)))))), 0) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6)))), tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6)))), tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6)))))))) = 0) | (~$greatereq(tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6)))), 0)))))))) <=> (~(~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)))),
% 0.91/0.89 inference(monotonicity,[status(thm)],[315])).
% 0.91/0.89 tff(317,plain,
% 0.91/0.89 ((~((~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos!4, $product(-1, Q)), 0) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6)))), Q)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6)))), Q)))) = 0)))) | (~(eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4) | (~($lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6)))))), 0) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6)))), tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6)))), tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6)))))))) = 0) | (~$greatereq(tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6)))), 0)))))))) <=> eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)),
% 0.91/0.89 inference(transitivity,[status(thm)],[316, 299])).
% 0.91/0.89 tff(318,plain,
% 0.91/0.89 (((~![B1: array_int, B2: array_int, Pos: $int] : (~((~((~eq_board1(B1, B2, Pos)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0) | ($sum(tb2t(get2(int, t2tb1(B2), Q)), $product(-1, tb2t(get2(int, t2tb1(B1), Q)))) = 0)))) | (~(eq_board1(B1, B2, Pos) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_0(Pos, B2, B1))), 0) | ($sum(tb2t(get2(int, t2tb1(B2), tptp_fun_Q_0(Pos, B2, B1))), $product(-1, tb2t(get2(int, t2tb1(B1), tptp_fun_Q_0(Pos, B2, B1))))) = 0) | (~$greatereq(tptp_fun_Q_0(Pos, B2, B1), 0))))))))) | (~((~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos!4, $product(-1, Q)), 0) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6)))), Q)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6)))), Q)))) = 0)))) | (~(eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4) | (~($lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6)))))), 0) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6)))), tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6)))), tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6)))))))) = 0) | (~$greatereq(tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6)))), 0))))))))) <=> ((~![B1: array_int, B2: array_int, Pos: $int] : (~((~((~eq_board1(B1, B2, Pos)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0) | ($sum(tb2t(get2(int, t2tb1(B2), Q)), $product(-1, tb2t(get2(int, t2tb1(B1), Q)))) = 0)))) | (~(eq_board1(B1, B2, Pos) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_0(Pos, B2, B1))), 0) | ($sum(tb2t(get2(int, t2tb1(B2), tptp_fun_Q_0(Pos, B2, B1))), $product(-1, tb2t(get2(int, t2tb1(B1), tptp_fun_Q_0(Pos, B2, B1))))) = 0) | (~$greatereq(tptp_fun_Q_0(Pos, B2, B1), 0))))))))) | eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4))),
% 0.91/0.89 inference(monotonicity,[status(thm)],[317])).
% 0.91/0.89 tff(319,plain,
% 0.91/0.89 (((~![B1: array_int, B2: array_int, Pos: $int] : (~((~((~eq_board1(B1, B2, Pos)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0) | ($sum(tb2t(get2(int, t2tb1(B2), Q)), $product(-1, tb2t(get2(int, t2tb1(B1), Q)))) = 0)))) | (~(eq_board1(B1, B2, Pos) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_0(Pos, B2, B1))), 0) | ($sum(tb2t(get2(int, t2tb1(B2), tptp_fun_Q_0(Pos, B2, B1))), $product(-1, tb2t(get2(int, t2tb1(B1), tptp_fun_Q_0(Pos, B2, B1))))) = 0) | (~$greatereq(tptp_fun_Q_0(Pos, B2, B1), 0))))))))) | (~((~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos!4, $product(-1, Q)), 0) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6)))), Q)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6)))), Q)))) = 0)))) | (~(eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4) | (~($lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6)))))), 0) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6)))), tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6)))), tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6)))))))) = 0) | (~$greatereq(tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6)))), 0))))))))) <=> ((~![B1: array_int, B2: array_int, Pos: $int] : (~((~((~eq_board1(B1, B2, Pos)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0) | ($sum(tb2t(get2(int, t2tb1(B2), Q)), $product(-1, tb2t(get2(int, t2tb1(B1), Q)))) = 0)))) | (~(eq_board1(B1, B2, Pos) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_0(Pos, B2, B1))), 0) | ($sum(tb2t(get2(int, t2tb1(B2), tptp_fun_Q_0(Pos, B2, B1))), $product(-1, tb2t(get2(int, t2tb1(B1), tptp_fun_Q_0(Pos, B2, B1))))) = 0) | (~$greatereq(tptp_fun_Q_0(Pos, B2, B1), 0))))))))) | eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4))),
% 0.91/0.89 inference(transitivity,[status(thm)],[318, 298])).
% 0.91/0.89 tff(320,plain,
% 0.91/0.89 ((~![B1: array_int, B2: array_int, Pos: $int] : (~((~((~eq_board1(B1, B2, Pos)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0) | ($sum(tb2t(get2(int, t2tb1(B2), Q)), $product(-1, tb2t(get2(int, t2tb1(B1), Q)))) = 0)))) | (~(eq_board1(B1, B2, Pos) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_0(Pos, B2, B1))), 0) | ($sum(tb2t(get2(int, t2tb1(B2), tptp_fun_Q_0(Pos, B2, B1))), $product(-1, tb2t(get2(int, t2tb1(B1), tptp_fun_Q_0(Pos, B2, B1))))) = 0) | (~$greatereq(tptp_fun_Q_0(Pos, B2, B1), 0))))))))) | (~((~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos!4, $product(-1, Q)), 0) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6)))), Q)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6)))), Q)))) = 0)))) | (~(eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4) | (~($lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6)))))), 0) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6)))), tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6)))), tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6)))))))) = 0) | (~$greatereq(tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6)))), 0))))))))),
% 0.91/0.89 inference(quant_inst,[status(thm)],[])).
% 0.91/0.89 tff(321,plain,
% 0.91/0.89 ((~![B1: array_int, B2: array_int, Pos: $int] : (~((~((~eq_board1(B1, B2, Pos)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0) | ($sum(tb2t(get2(int, t2tb1(B2), Q)), $product(-1, tb2t(get2(int, t2tb1(B1), Q)))) = 0)))) | (~(eq_board1(B1, B2, Pos) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_0(Pos, B2, B1))), 0) | ($sum(tb2t(get2(int, t2tb1(B2), tptp_fun_Q_0(Pos, B2, B1))), $product(-1, tb2t(get2(int, t2tb1(B1), tptp_fun_Q_0(Pos, B2, B1))))) = 0) | (~$greatereq(tptp_fun_Q_0(Pos, B2, B1), 0))))))))) | eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)),
% 0.91/0.89 inference(modus_ponens,[status(thm)],[320, 319])).
% 0.91/0.89 tff(322,plain,
% 0.91/0.89 ($false),
% 0.91/0.89 inference(unit_resolution,[status(thm)],[321, 297, 275])).
% 0.91/0.89 tff(323,plain,(eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)), inference(lemma,lemma(discharge,[]))).
% 0.91/0.89 tff(324,plain,
% 0.91/0.89 ((~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~$greatereq(I!11, 0)) | (~$greatereq($sum(N!5, $product(-1, I!11)), 1)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos!4)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), 0)) | $greatereq($sum(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), $product(-1, I!11)), 0))) | (~($greatereq($sum(Pos!4, $product(-1, Board!7)), 0) | (~$greatereq(Board!7, 0)) | (~$greatereq(Pos!4, 0)) | (~((~$greatereq(Board!7, 0)) | (~(Board3!12 = tb2t2(set(int, int, t2tb2(Board2!10), t2tb(Pos!4), t2tb(I!11))))) | (~($greatereq($sum(Pos!4, $product(-1, Board!7)), 0) | (~$greatereq(Pos!4, 0)) | (~(((~(Result!13 = true1)) <=> is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | (~((~((Result!13 = true1) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Pos!4)) | (~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~($sum(N!5, $product(-1, B!19)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))), 0)))))))) | (~((~(Result!13 = true1)) | (~((~$lesseq($sum(Pos!4, $product(-1, N!5)), 0)) | (~($sum(N!5, $product(-1, Board!7)) = 0)) | (~$greatereq(Pos!4, -1)) | (~$lesseq($sum(Pos!4, $product(-1, N!5)), -1)) | (~solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~((~$greatereq(Board!7, 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B, t2tb2(B1))), $sum(1, Pos!4))))) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), Pos!4)) | (~($sum(N!5, $product(-1, B!16)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))), 0)))))))))))))))))))))))) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~$greatereq(Board!7, 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), Pos!4)) | (~($sum(N!5, $product(-1, B!21)) = 0)))))) | (~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | $lesseq($sum(N!5, $product(-1, tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))))), 0) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos!4)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), 0)))))))) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~$greatereq(I!11, 0)) | (~$greatereq($sum(N!5, $product(-1, I!11)), 1)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos!4)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), 0)) | $greatereq($sum(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), $product(-1, I!11)), 0))) | (~($greatereq($sum(Pos!4, $product(-1, Board!7)), 0) | (~$greatereq(Board!7, 0)) | (~$greatereq(Pos!4, 0)) | (~((~$greatereq(Board!7, 0)) | (~(Board3!12 = tb2t2(set(int, int, t2tb2(Board2!10), t2tb(Pos!4), t2tb(I!11))))) | (~($greatereq($sum(Pos!4, $product(-1, Board!7)), 0) | (~$greatereq(Pos!4, 0)) | (~(((~(Result!13 = true1)) <=> is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | (~((~((Result!13 = true1) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Pos!4)) | (~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~($sum(N!5, $product(-1, B!19)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))), 0)))))))) | (~((~(Result!13 = true1)) | (~((~$lesseq($sum(Pos!4, $product(-1, N!5)), 0)) | (~($sum(N!5, $product(-1, Board!7)) = 0)) | (~$greatereq(Pos!4, -1)) | (~$lesseq($sum(Pos!4, $product(-1, N!5)), -1)) | (~solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~((~$greatereq(Board!7, 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B, t2tb2(B1))), $sum(1, Pos!4))))) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), Pos!4)) | (~($sum(N!5, $product(-1, B!16)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))), 0)))))))))))))))))))))))) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~$greatereq(Board!7, 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), Pos!4)) | (~($sum(N!5, $product(-1, B!21)) = 0)))))) | (~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | $lesseq($sum(N!5, $product(-1, tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))))), 0) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos!4)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), 0))))))),
% 0.91/0.90 inference(tautology,[status(thm)],[])).
% 0.91/0.90 tff(325,plain,
% 0.91/0.90 ((~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~$greatereq(I!11, 0)) | (~$greatereq($sum(N!5, $product(-1, I!11)), 1)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos!4)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), 0)) | $greatereq($sum(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), $product(-1, I!11)), 0))) | (~($greatereq($sum(Pos!4, $product(-1, Board!7)), 0) | (~$greatereq(Board!7, 0)) | (~$greatereq(Pos!4, 0)) | (~((~$greatereq(Board!7, 0)) | (~(Board3!12 = tb2t2(set(int, int, t2tb2(Board2!10), t2tb(Pos!4), t2tb(I!11))))) | (~($greatereq($sum(Pos!4, $product(-1, Board!7)), 0) | (~$greatereq(Pos!4, 0)) | (~(((~(Result!13 = true1)) <=> is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | (~((~((Result!13 = true1) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Pos!4)) | (~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~($sum(N!5, $product(-1, B!19)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))), 0)))))))) | (~((~(Result!13 = true1)) | (~((~$lesseq($sum(Pos!4, $product(-1, N!5)), 0)) | (~($sum(N!5, $product(-1, Board!7)) = 0)) | (~$greatereq(Pos!4, -1)) | (~$lesseq($sum(Pos!4, $product(-1, N!5)), -1)) | (~solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~((~$greatereq(Board!7, 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B, t2tb2(B1))), $sum(1, Pos!4))))) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), Pos!4)) | (~($sum(N!5, $product(-1, B!16)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))), 0)))))))))))))))))))))))) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~$greatereq(Board!7, 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), Pos!4)) | (~($sum(N!5, $product(-1, B!21)) = 0)))))) | (~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | $lesseq($sum(N!5, $product(-1, tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))))), 0) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos!4)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), 0)))))))) | (~((~$greatereq(I!11, 0)) | (~$greatereq($sum(N!5, $product(-1, I!11)), 1)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos!4)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), 0)) | $greatereq($sum(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), $product(-1, I!11)), 0))) | (~($greatereq($sum(Pos!4, $product(-1, Board!7)), 0) | (~$greatereq(Board!7, 0)) | (~$greatereq(Pos!4, 0)) | (~((~$greatereq(Board!7, 0)) | (~(Board3!12 = tb2t2(set(int, int, t2tb2(Board2!10), t2tb(Pos!4), t2tb(I!11))))) | (~($greatereq($sum(Pos!4, $product(-1, Board!7)), 0) | (~$greatereq(Pos!4, 0)) | (~(((~(Result!13 = true1)) <=> is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | (~((~((Result!13 = true1) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Pos!4)) | (~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~($sum(N!5, $product(-1, B!19)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))), 0)))))))) | (~((~(Result!13 = true1)) | (~((~$lesseq($sum(Pos!4, $product(-1, N!5)), 0)) | (~($sum(N!5, $product(-1, Board!7)) = 0)) | (~$greatereq(Pos!4, -1)) | (~$lesseq($sum(Pos!4, $product(-1, N!5)), -1)) | (~solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~((~$greatereq(Board!7, 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B, t2tb2(B1))), $sum(1, Pos!4))))) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), Pos!4)) | (~($sum(N!5, $product(-1, B!16)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))), 0)))))))))))))))))))))))) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~$greatereq(Board!7, 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), Pos!4)) | (~($sum(N!5, $product(-1, B!21)) = 0)))))) | (~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | $lesseq($sum(N!5, $product(-1, tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))))), 0) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos!4)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), 0))))))),
% 0.91/0.90 inference(unit_resolution,[status(thm)],[324, 323])).
% 0.91/0.90 tff(326,plain,
% 0.91/0.90 (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~$greatereq(I!11, 0)) | (~$greatereq($sum(N!5, $product(-1, I!11)), 1)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos!4)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), 0)) | $greatereq($sum(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), $product(-1, I!11)), 0))) | (~($greatereq($sum(Pos!4, $product(-1, Board!7)), 0) | (~$greatereq(Board!7, 0)) | (~$greatereq(Pos!4, 0)) | (~((~$greatereq(Board!7, 0)) | (~(Board3!12 = tb2t2(set(int, int, t2tb2(Board2!10), t2tb(Pos!4), t2tb(I!11))))) | (~($greatereq($sum(Pos!4, $product(-1, Board!7)), 0) | (~$greatereq(Pos!4, 0)) | (~(((~(Result!13 = true1)) <=> is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | (~((~((Result!13 = true1) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Pos!4)) | (~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~($sum(N!5, $product(-1, B!19)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))), 0)))))))) | (~((~(Result!13 = true1)) | (~((~$lesseq($sum(Pos!4, $product(-1, N!5)), 0)) | (~($sum(N!5, $product(-1, Board!7)) = 0)) | (~$greatereq(Pos!4, -1)) | (~$lesseq($sum(Pos!4, $product(-1, N!5)), -1)) | (~solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~((~$greatereq(Board!7, 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B, t2tb2(B1))), $sum(1, Pos!4))))) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), Pos!4)) | (~($sum(N!5, $product(-1, B!16)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))), 0)))))))))))))))))))))))) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~$greatereq(Board!7, 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), Pos!4)) | (~($sum(N!5, $product(-1, B!21)) = 0)))))) | (~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | $lesseq($sum(N!5, $product(-1, tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))))), 0) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos!4)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), 0)))))))),
% 0.91/0.90 inference(unit_resolution,[status(thm)],[325, 274, 267])).
% 0.91/0.90 tff(327,plain,
% 0.91/0.90 ($greatereq(N!5, 1) | (~$greatereq(Pos!4, 0)) | $greatereq($sum(Pos!4, $product(-1, N!5)), 0)),
% 0.91/0.90 inference(theory_lemma,[status(thm)],[])).
% 0.91/0.90 tff(328,plain,
% 0.91/0.90 ($greatereq(N!5, 1) | $greatereq($sum(Pos!4, $product(-1, N!5)), 0)),
% 0.91/0.90 inference(unit_resolution,[status(thm)],[327, 260])).
% 0.91/0.90 tff(329,plain,
% 0.91/0.90 ($greatereq(N!5, 1)),
% 0.91/0.90 inference(unit_resolution,[status(thm)],[328, 259])).
% 0.91/0.90 tff(330,plain,
% 0.91/0.90 (($greatereq(N!5, 1) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!9, t2tb2(B1!8))), N!5)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, B!9, t2tb2(B1!8))), Pos!4)) | (~is_board1(tb2t1(mk_array1(int, B!9, t2tb2(B1!8))), N!5)) | (~($sum(N!5, $product(-1, B!9)) = 0))))))) | (~$greatereq(N!5, 1))),
% 0.91/0.90 inference(tautology,[status(thm)],[])).
% 0.91/0.90 tff(331,plain,
% 0.91/0.90 ($greatereq(N!5, 1) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!9, t2tb2(B1!8))), N!5)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, B!9, t2tb2(B1!8))), Pos!4)) | (~is_board1(tb2t1(mk_array1(int, B!9, t2tb2(B1!8))), N!5)) | (~($sum(N!5, $product(-1, B!9)) = 0))))))),
% 0.91/0.90 inference(unit_resolution,[status(thm)],[330, 329])).
% 0.91/0.90 tff(332,plain,
% 0.91/0.90 ((~($sum(Pos!4, $product(-1, N!5)) = 0)) | $greatereq($sum(Pos!4, $product(-1, N!5)), 0)),
% 0.91/0.90 inference(theory_lemma,[status(thm)],[])).
% 0.91/0.90 tff(333,plain,
% 0.91/0.90 (~($sum(Pos!4, $product(-1, N!5)) = 0)),
% 0.91/0.90 inference(unit_resolution,[status(thm)],[332, 259])).
% 0.91/0.90 tff(334,plain,
% 0.91/0.90 (((~($sum(Pos!4, $product(-1, N!5)) = 0)) | solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), N!5)) | ($sum(Pos!4, $product(-1, N!5)) = 0)),
% 0.91/0.90 inference(tautology,[status(thm)],[])).
% 0.91/0.90 tff(335,plain,
% 0.91/0.90 ((~($sum(Pos!4, $product(-1, N!5)) = 0)) | solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), N!5)),
% 0.91/0.90 inference(unit_resolution,[status(thm)],[334, 333])).
% 0.91/0.90 tff(336,plain,
% 0.91/0.90 (~(($sum(Pos!4, $product(-1, N!5)) = 0) | (~((~($greatereq(N!5, 1) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!9, t2tb2(B1!8))), N!5)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, B!9, t2tb2(B1!8))), Pos!4)) | (~is_board1(tb2t1(mk_array1(int, B!9, t2tb2(B1!8))), N!5)) | (~($sum(N!5, $product(-1, B!9)) = 0)))))))) | (~((~$greatereq(N!5, 1)) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~$greatereq(I!11, 0)) | (~$greatereq($sum(N!5, $product(-1, I!11)), 1)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos!4)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), 0)) | $greatereq($sum(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), $product(-1, I!11)), 0))) | (~($greatereq($sum(Pos!4, $product(-1, Board!7)), 0) | (~$greatereq(Board!7, 0)) | (~$greatereq(Pos!4, 0)) | (~((~$greatereq(Board!7, 0)) | (~(Board3!12 = tb2t2(set(int, int, t2tb2(Board2!10), t2tb(Pos!4), t2tb(I!11))))) | (~($greatereq($sum(Pos!4, $product(-1, Board!7)), 0) | (~$greatereq(Pos!4, 0)) | (~(((~(Result!13 = true1)) <=> is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | (~((~((Result!13 = true1) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Pos!4)) | (~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~($sum(N!5, $product(-1, B!19)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))), 0)))))))) | (~((~(Result!13 = true1)) | (~((~$lesseq($sum(Pos!4, $product(-1, N!5)), 0)) | (~($sum(N!5, $product(-1, Board!7)) = 0)) | (~$greatereq(Pos!4, -1)) | (~$lesseq($sum(Pos!4, $product(-1, N!5)), -1)) | (~solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~((~$greatereq(Board!7, 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B, t2tb2(B1))), $sum(1, Pos!4))))) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), Pos!4)) | (~($sum(N!5, $product(-1, B!16)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))), 0)))))))))))))))))))))))) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~$greatereq(Board!7, 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), Pos!4)) | (~($sum(N!5, $product(-1, B!21)) = 0)))))) | (~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | $lesseq($sum(N!5, $product(-1, tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))))), 0) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos!4)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), 0)))))))))))))),
% 0.91/0.91 inference(unit_resolution,[status(thm)],[41, 335])).
% 0.91/0.91 tff(337,plain,
% 0.91/0.91 ((($sum(Pos!4, $product(-1, N!5)) = 0) | (~((~($greatereq(N!5, 1) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!9, t2tb2(B1!8))), N!5)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, B!9, t2tb2(B1!8))), Pos!4)) | (~is_board1(tb2t1(mk_array1(int, B!9, t2tb2(B1!8))), N!5)) | (~($sum(N!5, $product(-1, B!9)) = 0)))))))) | (~((~$greatereq(N!5, 1)) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~$greatereq(I!11, 0)) | (~$greatereq($sum(N!5, $product(-1, I!11)), 1)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos!4)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), 0)) | $greatereq($sum(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), $product(-1, I!11)), 0))) | (~($greatereq($sum(Pos!4, $product(-1, Board!7)), 0) | (~$greatereq(Board!7, 0)) | (~$greatereq(Pos!4, 0)) | (~((~$greatereq(Board!7, 0)) | (~(Board3!12 = tb2t2(set(int, int, t2tb2(Board2!10), t2tb(Pos!4), t2tb(I!11))))) | (~($greatereq($sum(Pos!4, $product(-1, Board!7)), 0) | (~$greatereq(Pos!4, 0)) | (~(((~(Result!13 = true1)) <=> is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | (~((~((Result!13 = true1) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Pos!4)) | (~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~($sum(N!5, $product(-1, B!19)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))), 0)))))))) | (~((~(Result!13 = true1)) | (~((~$lesseq($sum(Pos!4, $product(-1, N!5)), 0)) | (~($sum(N!5, $product(-1, Board!7)) = 0)) | (~$greatereq(Pos!4, -1)) | (~$lesseq($sum(Pos!4, $product(-1, N!5)), -1)) | (~solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~((~$greatereq(Board!7, 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B, t2tb2(B1))), $sum(1, Pos!4))))) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), Pos!4)) | (~($sum(N!5, $product(-1, B!16)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))), 0)))))))))))))))))))))))) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~$greatereq(Board!7, 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), Pos!4)) | (~($sum(N!5, $product(-1, B!21)) = 0)))))) | (~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | $lesseq($sum(N!5, $product(-1, tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))))), 0) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos!4)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), 0))))))))))))) | ((~($greatereq(N!5, 1) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!9, t2tb2(B1!8))), N!5)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, B!9, t2tb2(B1!8))), Pos!4)) | (~is_board1(tb2t1(mk_array1(int, B!9, t2tb2(B1!8))), N!5)) | (~($sum(N!5, $product(-1, B!9)) = 0)))))))) | (~((~$greatereq(N!5, 1)) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~$greatereq(I!11, 0)) | (~$greatereq($sum(N!5, $product(-1, I!11)), 1)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos!4)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), 0)) | $greatereq($sum(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), $product(-1, I!11)), 0))) | (~($greatereq($sum(Pos!4, $product(-1, Board!7)), 0) | (~$greatereq(Board!7, 0)) | (~$greatereq(Pos!4, 0)) | (~((~$greatereq(Board!7, 0)) | (~(Board3!12 = tb2t2(set(int, int, t2tb2(Board2!10), t2tb(Pos!4), t2tb(I!11))))) | (~($greatereq($sum(Pos!4, $product(-1, Board!7)), 0) | (~$greatereq(Pos!4, 0)) | (~(((~(Result!13 = true1)) <=> is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | (~((~((Result!13 = true1) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Pos!4)) | (~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~($sum(N!5, $product(-1, B!19)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))), 0)))))))) | (~((~(Result!13 = true1)) | (~((~$lesseq($sum(Pos!4, $product(-1, N!5)), 0)) | (~($sum(N!5, $product(-1, Board!7)) = 0)) | (~$greatereq(Pos!4, -1)) | (~$lesseq($sum(Pos!4, $product(-1, N!5)), -1)) | (~solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~((~$greatereq(Board!7, 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B, t2tb2(B1))), $sum(1, Pos!4))))) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), Pos!4)) | (~($sum(N!5, $product(-1, B!16)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))), 0)))))))))))))))))))))))) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~$greatereq(Board!7, 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), Pos!4)) | (~($sum(N!5, $product(-1, B!21)) = 0)))))) | (~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | $lesseq($sum(N!5, $product(-1, tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))))), 0) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos!4)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), 0)))))))))))),
% 0.91/0.91 inference(tautology,[status(thm)],[])).
% 0.91/0.91 tff(338,plain,
% 0.91/0.91 ((~($greatereq(N!5, 1) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!9, t2tb2(B1!8))), N!5)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, B!9, t2tb2(B1!8))), Pos!4)) | (~is_board1(tb2t1(mk_array1(int, B!9, t2tb2(B1!8))), N!5)) | (~($sum(N!5, $product(-1, B!9)) = 0)))))))) | (~((~$greatereq(N!5, 1)) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~$greatereq(I!11, 0)) | (~$greatereq($sum(N!5, $product(-1, I!11)), 1)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos!4)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), 0)) | $greatereq($sum(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), $product(-1, I!11)), 0))) | (~($greatereq($sum(Pos!4, $product(-1, Board!7)), 0) | (~$greatereq(Board!7, 0)) | (~$greatereq(Pos!4, 0)) | (~((~$greatereq(Board!7, 0)) | (~(Board3!12 = tb2t2(set(int, int, t2tb2(Board2!10), t2tb(Pos!4), t2tb(I!11))))) | (~($greatereq($sum(Pos!4, $product(-1, Board!7)), 0) | (~$greatereq(Pos!4, 0)) | (~(((~(Result!13 = true1)) <=> is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | (~((~((Result!13 = true1) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Pos!4)) | (~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~($sum(N!5, $product(-1, B!19)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))), 0)))))))) | (~((~(Result!13 = true1)) | (~((~$lesseq($sum(Pos!4, $product(-1, N!5)), 0)) | (~($sum(N!5, $product(-1, Board!7)) = 0)) | (~$greatereq(Pos!4, -1)) | (~$lesseq($sum(Pos!4, $product(-1, N!5)), -1)) | (~solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~((~$greatereq(Board!7, 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B, t2tb2(B1))), $sum(1, Pos!4))))) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), Pos!4)) | (~($sum(N!5, $product(-1, B!16)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))), 0)))))))))))))))))))))))) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~$greatereq(Board!7, 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), Pos!4)) | (~($sum(N!5, $product(-1, B!21)) = 0)))))) | (~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | $lesseq($sum(N!5, $product(-1, tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))))), 0) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos!4)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), 0))))))))))),
% 0.91/0.91 inference(unit_resolution,[status(thm)],[337, 336])).
% 0.91/0.91 tff(339,plain,
% 0.91/0.91 ((~((~($greatereq(N!5, 1) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!9, t2tb2(B1!8))), N!5)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, B!9, t2tb2(B1!8))), Pos!4)) | (~is_board1(tb2t1(mk_array1(int, B!9, t2tb2(B1!8))), N!5)) | (~($sum(N!5, $product(-1, B!9)) = 0)))))))) | (~((~$greatereq(N!5, 1)) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~$greatereq(I!11, 0)) | (~$greatereq($sum(N!5, $product(-1, I!11)), 1)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos!4)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), 0)) | $greatereq($sum(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), $product(-1, I!11)), 0))) | (~($greatereq($sum(Pos!4, $product(-1, Board!7)), 0) | (~$greatereq(Board!7, 0)) | (~$greatereq(Pos!4, 0)) | (~((~$greatereq(Board!7, 0)) | (~(Board3!12 = tb2t2(set(int, int, t2tb2(Board2!10), t2tb(Pos!4), t2tb(I!11))))) | (~($greatereq($sum(Pos!4, $product(-1, Board!7)), 0) | (~$greatereq(Pos!4, 0)) | (~(((~(Result!13 = true1)) <=> is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | (~((~((Result!13 = true1) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Pos!4)) | (~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~($sum(N!5, $product(-1, B!19)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))), 0)))))))) | (~((~(Result!13 = true1)) | (~((~$lesseq($sum(Pos!4, $product(-1, N!5)), 0)) | (~($sum(N!5, $product(-1, Board!7)) = 0)) | (~$greatereq(Pos!4, -1)) | (~$lesseq($sum(Pos!4, $product(-1, N!5)), -1)) | (~solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~((~$greatereq(Board!7, 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B, t2tb2(B1))), $sum(1, Pos!4))))) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), Pos!4)) | (~($sum(N!5, $product(-1, B!16)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))), 0)))))))))))))))))))))))) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~$greatereq(Board!7, 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), Pos!4)) | (~($sum(N!5, $product(-1, B!21)) = 0)))))) | (~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | $lesseq($sum(N!5, $product(-1, tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))))), 0) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos!4)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), 0)))))))))))) | (~($greatereq(N!5, 1) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!9, t2tb2(B1!8))), N!5)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, B!9, t2tb2(B1!8))), Pos!4)) | (~is_board1(tb2t1(mk_array1(int, B!9, t2tb2(B1!8))), N!5)) | (~($sum(N!5, $product(-1, B!9)) = 0)))))))) | (~((~$greatereq(N!5, 1)) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~$greatereq(I!11, 0)) | (~$greatereq($sum(N!5, $product(-1, I!11)), 1)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos!4)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), 0)) | $greatereq($sum(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), $product(-1, I!11)), 0))) | (~($greatereq($sum(Pos!4, $product(-1, Board!7)), 0) | (~$greatereq(Board!7, 0)) | (~$greatereq(Pos!4, 0)) | (~((~$greatereq(Board!7, 0)) | (~(Board3!12 = tb2t2(set(int, int, t2tb2(Board2!10), t2tb(Pos!4), t2tb(I!11))))) | (~($greatereq($sum(Pos!4, $product(-1, Board!7)), 0) | (~$greatereq(Pos!4, 0)) | (~(((~(Result!13 = true1)) <=> is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | (~((~((Result!13 = true1) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Pos!4)) | (~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~($sum(N!5, $product(-1, B!19)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))), 0)))))))) | (~((~(Result!13 = true1)) | (~((~$lesseq($sum(Pos!4, $product(-1, N!5)), 0)) | (~($sum(N!5, $product(-1, Board!7)) = 0)) | (~$greatereq(Pos!4, -1)) | (~$lesseq($sum(Pos!4, $product(-1, N!5)), -1)) | (~solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~((~$greatereq(Board!7, 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B, t2tb2(B1))), $sum(1, Pos!4))))) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), Pos!4)) | (~($sum(N!5, $product(-1, B!16)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))), 0)))))))))))))))))))))))) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~$greatereq(Board!7, 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), Pos!4)) | (~($sum(N!5, $product(-1, B!21)) = 0)))))) | (~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | $lesseq($sum(N!5, $product(-1, tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))))), 0) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos!4)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), 0))))))))))),
% 0.91/0.91 inference(tautology,[status(thm)],[])).
% 0.91/0.91 tff(340,plain,
% 0.91/0.91 (~((~$greatereq(N!5, 1)) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~$greatereq(I!11, 0)) | (~$greatereq($sum(N!5, $product(-1, I!11)), 1)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos!4)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), 0)) | $greatereq($sum(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), $product(-1, I!11)), 0))) | (~($greatereq($sum(Pos!4, $product(-1, Board!7)), 0) | (~$greatereq(Board!7, 0)) | (~$greatereq(Pos!4, 0)) | (~((~$greatereq(Board!7, 0)) | (~(Board3!12 = tb2t2(set(int, int, t2tb2(Board2!10), t2tb(Pos!4), t2tb(I!11))))) | (~($greatereq($sum(Pos!4, $product(-1, Board!7)), 0) | (~$greatereq(Pos!4, 0)) | (~(((~(Result!13 = true1)) <=> is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | (~((~((Result!13 = true1) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Pos!4)) | (~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~($sum(N!5, $product(-1, B!19)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))), 0)))))))) | (~((~(Result!13 = true1)) | (~((~$lesseq($sum(Pos!4, $product(-1, N!5)), 0)) | (~($sum(N!5, $product(-1, Board!7)) = 0)) | (~$greatereq(Pos!4, -1)) | (~$lesseq($sum(Pos!4, $product(-1, N!5)), -1)) | (~solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~((~$greatereq(Board!7, 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B, t2tb2(B1))), $sum(1, Pos!4))))) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), Pos!4)) | (~($sum(N!5, $product(-1, B!16)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))), 0)))))))))))))))))))))))) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~$greatereq(Board!7, 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), Pos!4)) | (~($sum(N!5, $product(-1, B!21)) = 0)))))) | (~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | $lesseq($sum(N!5, $product(-1, tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))))), 0) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos!4)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), 0)))))))))),
% 0.91/0.92 inference(unit_resolution,[status(thm)],[339, 338, 331])).
% 0.91/0.92 tff(341,plain,
% 0.91/0.92 (((~$greatereq(N!5, 1)) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~$greatereq(I!11, 0)) | (~$greatereq($sum(N!5, $product(-1, I!11)), 1)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos!4)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), 0)) | $greatereq($sum(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), $product(-1, I!11)), 0))) | (~($greatereq($sum(Pos!4, $product(-1, Board!7)), 0) | (~$greatereq(Board!7, 0)) | (~$greatereq(Pos!4, 0)) | (~((~$greatereq(Board!7, 0)) | (~(Board3!12 = tb2t2(set(int, int, t2tb2(Board2!10), t2tb(Pos!4), t2tb(I!11))))) | (~($greatereq($sum(Pos!4, $product(-1, Board!7)), 0) | (~$greatereq(Pos!4, 0)) | (~(((~(Result!13 = true1)) <=> is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | (~((~((Result!13 = true1) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Pos!4)) | (~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~($sum(N!5, $product(-1, B!19)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))), 0)))))))) | (~((~(Result!13 = true1)) | (~((~$lesseq($sum(Pos!4, $product(-1, N!5)), 0)) | (~($sum(N!5, $product(-1, Board!7)) = 0)) | (~$greatereq(Pos!4, -1)) | (~$lesseq($sum(Pos!4, $product(-1, N!5)), -1)) | (~solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~((~$greatereq(Board!7, 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B, t2tb2(B1))), $sum(1, Pos!4))))) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), Pos!4)) | (~($sum(N!5, $product(-1, B!16)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))), 0)))))))))))))))))))))))) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~$greatereq(Board!7, 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), Pos!4)) | (~($sum(N!5, $product(-1, B!21)) = 0)))))) | (~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | $lesseq($sum(N!5, $product(-1, tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))))), 0) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos!4)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), 0))))))))) | ((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~$greatereq(I!11, 0)) | (~$greatereq($sum(N!5, $product(-1, I!11)), 1)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos!4)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), 0)) | $greatereq($sum(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), $product(-1, I!11)), 0))) | (~($greatereq($sum(Pos!4, $product(-1, Board!7)), 0) | (~$greatereq(Board!7, 0)) | (~$greatereq(Pos!4, 0)) | (~((~$greatereq(Board!7, 0)) | (~(Board3!12 = tb2t2(set(int, int, t2tb2(Board2!10), t2tb(Pos!4), t2tb(I!11))))) | (~($greatereq($sum(Pos!4, $product(-1, Board!7)), 0) | (~$greatereq(Pos!4, 0)) | (~(((~(Result!13 = true1)) <=> is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | (~((~((Result!13 = true1) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Pos!4)) | (~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~($sum(N!5, $product(-1, B!19)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))), 0)))))))) | (~((~(Result!13 = true1)) | (~((~$lesseq($sum(Pos!4, $product(-1, N!5)), 0)) | (~($sum(N!5, $product(-1, Board!7)) = 0)) | (~$greatereq(Pos!4, -1)) | (~$lesseq($sum(Pos!4, $product(-1, N!5)), -1)) | (~solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~((~$greatereq(Board!7, 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B, t2tb2(B1))), $sum(1, Pos!4))))) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), Pos!4)) | (~($sum(N!5, $product(-1, B!16)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))), 0)))))))))))))))))))))))) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~$greatereq(Board!7, 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), Pos!4)) | (~($sum(N!5, $product(-1, B!21)) = 0)))))) | (~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | $lesseq($sum(N!5, $product(-1, tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))))), 0) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos!4)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), 0)))))))),
% 0.91/0.92 inference(tautology,[status(thm)],[])).
% 0.91/0.92 tff(342,plain,
% 0.91/0.92 ($false),
% 0.91/0.92 inference(unit_resolution,[status(thm)],[341, 340, 326])).
% 0.91/0.92 tff(343,plain,($greatereq($sum(Pos!4, $product(-1, N!5)), 0) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~$greatereq(Board!7, 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), Pos!4)) | (~($sum(N!5, $product(-1, B!21)) = 0)))))) | (~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | $lesseq($sum(N!5, $product(-1, tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))))), 0) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos!4)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), 0)))))) | (~((~$greatereq(Board!7, 0)) | (~(Board3!12 = tb2t2(set(int, int, t2tb2(Board2!10), t2tb(Pos!4), t2tb(I!11))))) | (~($greatereq($sum(Pos!4, $product(-1, Board!7)), 0) | (~$greatereq(Pos!4, 0)) | (~(((~(Result!13 = true1)) <=> is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | (~((~((Result!13 = true1) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Pos!4)) | (~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~($sum(N!5, $product(-1, B!19)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))), 0)))))))) | (~((~(Result!13 = true1)) | (~((~$lesseq($sum(Pos!4, $product(-1, N!5)), 0)) | (~($sum(N!5, $product(-1, Board!7)) = 0)) | (~$greatereq(Pos!4, -1)) | (~$lesseq($sum(Pos!4, $product(-1, N!5)), -1)) | (~solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~((~$greatereq(Board!7, 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B, t2tb2(B1))), $sum(1, Pos!4))))) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), Pos!4)) | (~($sum(N!5, $product(-1, B!16)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))), 0))))))))))))))))))))), inference(lemma,lemma(discharge,[]))).
% 0.91/0.92 tff(344,plain,
% 0.91/0.92 (~((~$greatereq(Board!7, 0)) | (~(Board3!12 = tb2t2(set(int, int, t2tb2(Board2!10), t2tb(Pos!4), t2tb(I!11))))) | (~($greatereq($sum(Pos!4, $product(-1, Board!7)), 0) | (~$greatereq(Pos!4, 0)) | (~(((~(Result!13 = true1)) <=> is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | (~((~((Result!13 = true1) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Pos!4)) | (~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~($sum(N!5, $product(-1, B!19)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))), 0)))))))) | (~((~(Result!13 = true1)) | (~((~$lesseq($sum(Pos!4, $product(-1, N!5)), 0)) | (~($sum(N!5, $product(-1, Board!7)) = 0)) | (~$greatereq(Pos!4, -1)) | (~$lesseq($sum(Pos!4, $product(-1, N!5)), -1)) | (~solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~((~$greatereq(Board!7, 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B, t2tb2(B1))), $sum(1, Pos!4))))) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), Pos!4)) | (~($sum(N!5, $product(-1, B!16)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))), 0)))))))))))))))))))),
% 0.91/0.92 inference(unit_resolution,[status(thm)],[343, 48, 266])).
% 0.91/0.92 tff(345,plain,
% 0.91/0.92 (((~$greatereq(Board!7, 0)) | (~(Board3!12 = tb2t2(set(int, int, t2tb2(Board2!10), t2tb(Pos!4), t2tb(I!11))))) | (~($greatereq($sum(Pos!4, $product(-1, Board!7)), 0) | (~$greatereq(Pos!4, 0)) | (~(((~(Result!13 = true1)) <=> is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | (~((~((Result!13 = true1) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Pos!4)) | (~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~($sum(N!5, $product(-1, B!19)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))), 0)))))))) | (~((~(Result!13 = true1)) | (~((~$lesseq($sum(Pos!4, $product(-1, N!5)), 0)) | (~($sum(N!5, $product(-1, Board!7)) = 0)) | (~$greatereq(Pos!4, -1)) | (~$lesseq($sum(Pos!4, $product(-1, N!5)), -1)) | (~solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~((~$greatereq(Board!7, 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B, t2tb2(B1))), $sum(1, Pos!4))))) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), Pos!4)) | (~($sum(N!5, $product(-1, B!16)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))), 0))))))))))))))))))) | ($greatereq($sum(Pos!4, $product(-1, Board!7)), 0) | (~$greatereq(Pos!4, 0)) | (~(((~(Result!13 = true1)) <=> is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | (~((~((Result!13 = true1) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Pos!4)) | (~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~($sum(N!5, $product(-1, B!19)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))), 0)))))))) | (~((~(Result!13 = true1)) | (~((~$lesseq($sum(Pos!4, $product(-1, N!5)), 0)) | (~($sum(N!5, $product(-1, Board!7)) = 0)) | (~$greatereq(Pos!4, -1)) | (~$lesseq($sum(Pos!4, $product(-1, N!5)), -1)) | (~solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~((~$greatereq(Board!7, 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B, t2tb2(B1))), $sum(1, Pos!4))))) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), Pos!4)) | (~($sum(N!5, $product(-1, B!16)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))), 0)))))))))))))))))),
% 0.91/0.92 inference(tautology,[status(thm)],[])).
% 0.91/0.92 tff(346,plain,
% 0.91/0.92 ($greatereq($sum(Pos!4, $product(-1, Board!7)), 0) | (~$greatereq(Pos!4, 0)) | (~(((~(Result!13 = true1)) <=> is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | (~((~((Result!13 = true1) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Pos!4)) | (~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~($sum(N!5, $product(-1, B!19)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))), 0)))))))) | (~((~(Result!13 = true1)) | (~((~$lesseq($sum(Pos!4, $product(-1, N!5)), 0)) | (~($sum(N!5, $product(-1, Board!7)) = 0)) | (~$greatereq(Pos!4, -1)) | (~$lesseq($sum(Pos!4, $product(-1, N!5)), -1)) | (~solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~((~$greatereq(Board!7, 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B, t2tb2(B1))), $sum(1, Pos!4))))) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), Pos!4)) | (~($sum(N!5, $product(-1, B!16)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))), 0))))))))))))))))),
% 0.91/0.92 inference(unit_resolution,[status(thm)],[345, 344])).
% 0.91/0.92 tff(347,plain,
% 0.91/0.92 ((~($greatereq($sum(Pos!4, $product(-1, Board!7)), 0) | (~$greatereq(Pos!4, 0)) | (~(((~(Result!13 = true1)) <=> is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | (~((~((Result!13 = true1) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Pos!4)) | (~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~($sum(N!5, $product(-1, B!19)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))), 0)))))))) | (~((~(Result!13 = true1)) | (~((~$lesseq($sum(Pos!4, $product(-1, N!5)), 0)) | (~($sum(N!5, $product(-1, Board!7)) = 0)) | (~$greatereq(Pos!4, -1)) | (~$lesseq($sum(Pos!4, $product(-1, N!5)), -1)) | (~solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~((~$greatereq(Board!7, 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B, t2tb2(B1))), $sum(1, Pos!4))))) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), Pos!4)) | (~($sum(N!5, $product(-1, B!16)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))), 0)))))))))))))))))) | $greatereq($sum(Pos!4, $product(-1, Board!7)), 0) | (~$greatereq(Pos!4, 0)) | (~(((~(Result!13 = true1)) <=> is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | (~((~((Result!13 = true1) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Pos!4)) | (~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~($sum(N!5, $product(-1, B!19)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))), 0)))))))) | (~((~(Result!13 = true1)) | (~((~$lesseq($sum(Pos!4, $product(-1, N!5)), 0)) | (~($sum(N!5, $product(-1, Board!7)) = 0)) | (~$greatereq(Pos!4, -1)) | (~$lesseq($sum(Pos!4, $product(-1, N!5)), -1)) | (~solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~((~$greatereq(Board!7, 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B, t2tb2(B1))), $sum(1, Pos!4))))) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), Pos!4)) | (~($sum(N!5, $product(-1, B!16)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))), 0))))))))))))))))),
% 0.91/0.93 inference(tautology,[status(thm)],[])).
% 0.91/0.93 tff(348,plain,
% 0.91/0.93 ((~($greatereq($sum(Pos!4, $product(-1, Board!7)), 0) | (~$greatereq(Pos!4, 0)) | (~(((~(Result!13 = true1)) <=> is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | (~((~((Result!13 = true1) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Pos!4)) | (~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~($sum(N!5, $product(-1, B!19)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))), 0)))))))) | (~((~(Result!13 = true1)) | (~((~$lesseq($sum(Pos!4, $product(-1, N!5)), 0)) | (~($sum(N!5, $product(-1, Board!7)) = 0)) | (~$greatereq(Pos!4, -1)) | (~$lesseq($sum(Pos!4, $product(-1, N!5)), -1)) | (~solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~((~$greatereq(Board!7, 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B, t2tb2(B1))), $sum(1, Pos!4))))) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), Pos!4)) | (~($sum(N!5, $product(-1, B!16)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))), 0)))))))))))))))))) | $greatereq($sum(Pos!4, $product(-1, Board!7)), 0) | (~(((~(Result!13 = true1)) <=> is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | (~((~((Result!13 = true1) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Pos!4)) | (~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~($sum(N!5, $product(-1, B!19)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))), 0)))))))) | (~((~(Result!13 = true1)) | (~((~$lesseq($sum(Pos!4, $product(-1, N!5)), 0)) | (~($sum(N!5, $product(-1, Board!7)) = 0)) | (~$greatereq(Pos!4, -1)) | (~$lesseq($sum(Pos!4, $product(-1, N!5)), -1)) | (~solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~((~$greatereq(Board!7, 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B, t2tb2(B1))), $sum(1, Pos!4))))) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), Pos!4)) | (~($sum(N!5, $product(-1, B!16)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))), 0))))))))))))))))),
% 0.91/0.93 inference(unit_resolution,[status(thm)],[347, 260])).
% 0.91/0.93 tff(349,plain,
% 0.91/0.93 (~(((~(Result!13 = true1)) <=> is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | (~((~((Result!13 = true1) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Pos!4)) | (~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~($sum(N!5, $product(-1, B!19)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))), 0)))))))) | (~((~(Result!13 = true1)) | (~((~$lesseq($sum(Pos!4, $product(-1, N!5)), 0)) | (~($sum(N!5, $product(-1, Board!7)) = 0)) | (~$greatereq(Pos!4, -1)) | (~$lesseq($sum(Pos!4, $product(-1, N!5)), -1)) | (~solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~((~$greatereq(Board!7, 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B, t2tb2(B1))), $sum(1, Pos!4))))) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), Pos!4)) | (~($sum(N!5, $product(-1, B!16)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))), 0)))))))))))))))),
% 0.91/0.93 inference(unit_resolution,[status(thm)],[348, 346, 123])).
% 0.91/0.93 tff(350,plain,
% 0.91/0.93 ((((~(Result!13 = true1)) <=> is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | (~((~((Result!13 = true1) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Pos!4)) | (~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~($sum(N!5, $product(-1, B!19)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))), 0)))))))) | (~((~(Result!13 = true1)) | (~((~$lesseq($sum(Pos!4, $product(-1, N!5)), 0)) | (~($sum(N!5, $product(-1, Board!7)) = 0)) | (~$greatereq(Pos!4, -1)) | (~$lesseq($sum(Pos!4, $product(-1, N!5)), -1)) | (~solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~((~$greatereq(Board!7, 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B, t2tb2(B1))), $sum(1, Pos!4))))) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), Pos!4)) | (~($sum(N!5, $product(-1, B!16)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))), 0))))))))))))))) | (~((~(Result!13 = true1)) <=> is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)))),
% 0.91/0.93 inference(tautology,[status(thm)],[])).
% 0.91/0.93 tff(351,plain,
% 0.91/0.93 (~((~(Result!13 = true1)) <=> is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4))),
% 0.91/0.93 inference(unit_resolution,[status(thm)],[350, 349])).
% 0.91/0.93 tff(352,plain,
% 0.91/0.93 (((~(Result!13 = true1)) <=> is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | (~(Result!13 = true1)) | is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)),
% 0.91/0.93 inference(tautology,[status(thm)],[])).
% 0.91/0.93 tff(353,plain,
% 0.91/0.93 ((~(Result!13 = true1)) | is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)),
% 0.91/0.93 inference(unit_resolution,[status(thm)],[352, 351])).
% 0.91/0.93 tff(354,plain,
% 0.91/0.93 (~(Result!13 = true1)),
% 0.91/0.93 inference(unit_resolution,[status(thm)],[353, 117])).
% 0.91/0.93 tff(355,plain,
% 0.91/0.93 (((~(Result!13 = true1)) | (~((~$lesseq($sum(Pos!4, $product(-1, N!5)), 0)) | (~($sum(N!5, $product(-1, Board!7)) = 0)) | (~$greatereq(Pos!4, -1)) | (~$lesseq($sum(Pos!4, $product(-1, N!5)), -1)) | (~solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~((~$greatereq(Board!7, 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B, t2tb2(B1))), $sum(1, Pos!4))))) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), Pos!4)) | (~($sum(N!5, $product(-1, B!16)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))), 0))))))))))) | (Result!13 = true1)),
% 0.91/0.93 inference(tautology,[status(thm)],[])).
% 0.91/0.93 tff(356,plain,
% 0.91/0.93 ((~(Result!13 = true1)) | (~((~$lesseq($sum(Pos!4, $product(-1, N!5)), 0)) | (~($sum(N!5, $product(-1, Board!7)) = 0)) | (~$greatereq(Pos!4, -1)) | (~$lesseq($sum(Pos!4, $product(-1, N!5)), -1)) | (~solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~((~$greatereq(Board!7, 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B, t2tb2(B1))), $sum(1, Pos!4))))) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), Pos!4)) | (~($sum(N!5, $product(-1, B!16)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))), 0))))))))))),
% 0.91/0.93 inference(unit_resolution,[status(thm)],[355, 354])).
% 0.91/0.93 tff(357,plain,
% 0.91/0.93 ((((~(Result!13 = true1)) <=> is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | (~((~((Result!13 = true1) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Pos!4)) | (~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~($sum(N!5, $product(-1, B!19)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))), 0)))))))) | (~((~(Result!13 = true1)) | (~((~$lesseq($sum(Pos!4, $product(-1, N!5)), 0)) | (~($sum(N!5, $product(-1, Board!7)) = 0)) | (~$greatereq(Pos!4, -1)) | (~$lesseq($sum(Pos!4, $product(-1, N!5)), -1)) | (~solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~((~$greatereq(Board!7, 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B, t2tb2(B1))), $sum(1, Pos!4))))) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), Pos!4)) | (~($sum(N!5, $product(-1, B!16)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))), 0))))))))))))))) | ((~((Result!13 = true1) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Pos!4)) | (~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~($sum(N!5, $product(-1, B!19)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))), 0)))))))) | (~((~(Result!13 = true1)) | (~((~$lesseq($sum(Pos!4, $product(-1, N!5)), 0)) | (~($sum(N!5, $product(-1, Board!7)) = 0)) | (~$greatereq(Pos!4, -1)) | (~$lesseq($sum(Pos!4, $product(-1, N!5)), -1)) | (~solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~((~$greatereq(Board!7, 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B, t2tb2(B1))), $sum(1, Pos!4))))) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), Pos!4)) | (~($sum(N!5, $product(-1, B!16)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))), 0)))))))))))))),
% 0.98/0.93 inference(tautology,[status(thm)],[])).
% 0.98/0.93 tff(358,plain,
% 0.98/0.93 ((~((Result!13 = true1) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Pos!4)) | (~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~($sum(N!5, $product(-1, B!19)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))), 0)))))))) | (~((~(Result!13 = true1)) | (~((~$lesseq($sum(Pos!4, $product(-1, N!5)), 0)) | (~($sum(N!5, $product(-1, Board!7)) = 0)) | (~$greatereq(Pos!4, -1)) | (~$lesseq($sum(Pos!4, $product(-1, N!5)), -1)) | (~solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~((~$greatereq(Board!7, 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B, t2tb2(B1))), $sum(1, Pos!4))))) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), Pos!4)) | (~($sum(N!5, $product(-1, B!16)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))), 0))))))))))))),
% 0.98/0.94 inference(unit_resolution,[status(thm)],[357, 349])).
% 0.98/0.94 tff(359,plain,
% 0.98/0.94 ((~((~((Result!13 = true1) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Pos!4)) | (~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~($sum(N!5, $product(-1, B!19)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))), 0)))))))) | (~((~(Result!13 = true1)) | (~((~$lesseq($sum(Pos!4, $product(-1, N!5)), 0)) | (~($sum(N!5, $product(-1, Board!7)) = 0)) | (~$greatereq(Pos!4, -1)) | (~$lesseq($sum(Pos!4, $product(-1, N!5)), -1)) | (~solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~((~$greatereq(Board!7, 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B, t2tb2(B1))), $sum(1, Pos!4))))) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), Pos!4)) | (~($sum(N!5, $product(-1, B!16)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))), 0)))))))))))))) | (~((Result!13 = true1) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Pos!4)) | (~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~($sum(N!5, $product(-1, B!19)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))), 0)))))))) | (~((~(Result!13 = true1)) | (~((~$lesseq($sum(Pos!4, $product(-1, N!5)), 0)) | (~($sum(N!5, $product(-1, Board!7)) = 0)) | (~$greatereq(Pos!4, -1)) | (~$lesseq($sum(Pos!4, $product(-1, N!5)), -1)) | (~solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~((~$greatereq(Board!7, 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B, t2tb2(B1))), $sum(1, Pos!4))))) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), Pos!4)) | (~($sum(N!5, $product(-1, B!16)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))), 0))))))))))))),
% 0.98/0.94 inference(tautology,[status(thm)],[])).
% 0.98/0.94 tff(360,plain,
% 0.98/0.94 ((~((Result!13 = true1) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Pos!4)) | (~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~($sum(N!5, $product(-1, B!19)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))), 0)))))))) | (~((~(Result!13 = true1)) | (~((~$lesseq($sum(Pos!4, $product(-1, N!5)), 0)) | (~($sum(N!5, $product(-1, Board!7)) = 0)) | (~$greatereq(Pos!4, -1)) | (~$lesseq($sum(Pos!4, $product(-1, N!5)), -1)) | (~solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~((~$greatereq(Board!7, 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B, t2tb2(B1))), $sum(1, Pos!4))))) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), Pos!4)) | (~($sum(N!5, $product(-1, B!16)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))), 0))))))))))))),
% 0.98/0.94 inference(unit_resolution,[status(thm)],[359, 358])).
% 0.98/0.94 tff(361,plain,
% 0.98/0.94 (~((Result!13 = true1) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Pos!4)) | (~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~($sum(N!5, $product(-1, B!19)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))), 0)))))))),
% 0.98/0.94 inference(unit_resolution,[status(thm)],[360, 356])).
% 0.98/0.94 tff(362,plain,
% 0.98/0.94 (((Result!13 = true1) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Pos!4)) | (~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~($sum(N!5, $product(-1, B!19)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))), 0))))))) | ((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Pos!4)) | (~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~($sum(N!5, $product(-1, B!19)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))), 0)))))),
% 0.98/0.94 inference(tautology,[status(thm)],[])).
% 0.98/0.94 tff(363,plain,
% 0.98/0.94 ((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Pos!4)) | (~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~($sum(N!5, $product(-1, B!19)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))), 0))))),
% 0.98/0.94 inference(unit_resolution,[status(thm)],[362, 361])).
% 0.98/0.94 tff(364,plain,
% 0.98/0.94 (((~$greatereq(Board!7, 0)) | (~(Board3!12 = tb2t2(set(int, int, t2tb2(Board2!10), t2tb(Pos!4), t2tb(I!11))))) | (~($greatereq($sum(Pos!4, $product(-1, Board!7)), 0) | (~$greatereq(Pos!4, 0)) | (~(((~(Result!13 = true1)) <=> is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | (~((~((Result!13 = true1) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Pos!4)) | (~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~($sum(N!5, $product(-1, B!19)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))), 0)))))))) | (~((~(Result!13 = true1)) | (~((~$lesseq($sum(Pos!4, $product(-1, N!5)), 0)) | (~($sum(N!5, $product(-1, Board!7)) = 0)) | (~$greatereq(Pos!4, -1)) | (~$lesseq($sum(Pos!4, $product(-1, N!5)), -1)) | (~solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~((~$greatereq(Board!7, 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B, t2tb2(B1))), $sum(1, Pos!4))))) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), Pos!4)) | (~($sum(N!5, $product(-1, B!16)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))), 0))))))))))))))))))) | (Board3!12 = tb2t2(set(int, int, t2tb2(Board2!10), t2tb(Pos!4), t2tb(I!11))))),
% 0.98/0.94 inference(tautology,[status(thm)],[])).
% 0.98/0.94 tff(365,plain,
% 0.98/0.94 (Board3!12 = tb2t2(set(int, int, t2tb2(Board2!10), t2tb(Pos!4), t2tb(I!11)))),
% 0.98/0.94 inference(unit_resolution,[status(thm)],[364, 344])).
% 0.98/0.94 tff(366,plain,
% 0.98/0.94 (t2tb2(Board3!12) = t2tb2(tb2t2(set(int, int, t2tb2(Board2!10), t2tb(Pos!4), t2tb(I!11))))),
% 0.98/0.94 inference(monotonicity,[status(thm)],[365])).
% 0.98/0.94 tff(367,plain,
% 0.98/0.94 (t2tb2(tb2t2(set(int, int, t2tb2(Board2!10), t2tb(Pos!4), t2tb(I!11)))) = t2tb2(Board3!12)),
% 0.98/0.94 inference(symmetry,[status(thm)],[366])).
% 0.98/0.94 tff(368,plain,
% 0.98/0.94 ((~($sum(N!5, $product(-1, Board!7)) = 0)) | $greatereq($sum(N!5, $product(-1, Board!7)), 0)),
% 0.98/0.94 inference(theory_lemma,[status(thm)],[])).
% 0.98/0.94 tff(369,plain,
% 0.98/0.94 ($greatereq($sum(N!5, $product(-1, Board!7)), 0)),
% 0.98/0.94 inference(unit_resolution,[status(thm)],[368, 118])).
% 0.98/0.94 tff(370,plain,
% 0.98/0.94 (N!5 = Board!7),
% 0.98/0.94 inference(theory_lemma,[status(thm)],[369, 120])).
% 0.98/0.94 tff(371,plain,
% 0.98/0.94 (mk_array1(int, N!5, t2tb2(tb2t2(set(int, int, t2tb2(Board2!10), t2tb(Pos!4), t2tb(I!11))))) = mk_array1(int, Board!7, t2tb2(Board3!12))),
% 0.98/0.94 inference(monotonicity,[status(thm)],[370, 367])).
% 0.98/0.94 tff(372,plain,
% 0.98/0.94 (tb2t1(mk_array1(int, N!5, t2tb2(tb2t2(set(int, int, t2tb2(Board2!10), t2tb(Pos!4), t2tb(I!11)))))) = tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))),
% 0.98/0.94 inference(monotonicity,[status(thm)],[371])).
% 0.98/0.94 tff(373,plain,
% 0.98/0.94 (tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))) = tb2t1(mk_array1(int, N!5, t2tb2(tb2t2(set(int, int, t2tb2(Board2!10), t2tb(Pos!4), t2tb(I!11))))))),
% 0.98/0.94 inference(symmetry,[status(thm)],[372])).
% 0.98/0.94 tff(374,plain,
% 0.98/0.94 (eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4) <=> eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, N!5, t2tb2(tb2t2(set(int, int, t2tb2(Board2!10), t2tb(Pos!4), t2tb(I!11)))))), Pos!4)),
% 0.98/0.94 inference(monotonicity,[status(thm)],[373])).
% 0.98/0.94 tff(375,plain,
% 0.98/0.94 (eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, N!5, t2tb2(tb2t2(set(int, int, t2tb2(Board2!10), t2tb(Pos!4), t2tb(I!11)))))), Pos!4) <=> eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)),
% 0.98/0.94 inference(symmetry,[status(thm)],[374])).
% 0.98/0.94 tff(376,plain,
% 0.98/0.94 (^[I: $int] : refl(($sum(I, $product(-1, tb2t(t2tb(I)))) = 0) <=> ($sum(I, $product(-1, tb2t(t2tb(I)))) = 0))),
% 0.98/0.94 inference(bind,[status(th)],[])).
% 0.98/0.94 tff(377,plain,
% 0.98/0.94 (![I: $int] : ($sum(I, $product(-1, tb2t(t2tb(I)))) = 0) <=> ![I: $int] : ($sum(I, $product(-1, tb2t(t2tb(I)))) = 0)),
% 0.98/0.94 inference(quant_intro,[status(thm)],[376])).
% 0.98/0.94 tff(378,plain,
% 0.98/0.94 (^[I: $int] : trans(monotonicity(rewrite($sum(tb2t(t2tb(I)), $product(-1, I)) = $sum($product(-1, I), tb2t(t2tb(I)))), (($sum(tb2t(t2tb(I)), $product(-1, I)) = 0) <=> ($sum($product(-1, I), tb2t(t2tb(I))) = 0))), rewrite(($sum($product(-1, I), tb2t(t2tb(I))) = 0) <=> ($sum(I, $product(-1, tb2t(t2tb(I)))) = 0)), (($sum(tb2t(t2tb(I)), $product(-1, I)) = 0) <=> ($sum(I, $product(-1, tb2t(t2tb(I)))) = 0)))),
% 0.98/0.94 inference(bind,[status(th)],[])).
% 0.98/0.94 tff(379,plain,
% 0.98/0.94 (![I: $int] : ($sum(tb2t(t2tb(I)), $product(-1, I)) = 0) <=> ![I: $int] : ($sum(I, $product(-1, tb2t(t2tb(I)))) = 0)),
% 0.98/0.94 inference(quant_intro,[status(thm)],[378])).
% 0.98/0.94 tff(380,plain,
% 0.98/0.94 (^[I: $int] : rewrite((tb2t(t2tb(I)) = I) <=> ($sum(tb2t(t2tb(I)), $product(-1, I)) = 0))),
% 0.98/0.94 inference(bind,[status(th)],[])).
% 0.98/0.94 tff(381,plain,
% 0.98/0.94 (![I: $int] : (tb2t(t2tb(I)) = I) <=> ![I: $int] : ($sum(tb2t(t2tb(I)), $product(-1, I)) = 0)),
% 0.98/0.94 inference(quant_intro,[status(thm)],[380])).
% 0.98/0.94 tff(382,plain,
% 0.98/0.94 (![I: $int] : (tb2t(t2tb(I)) = I) <=> ![I: $int] : (tb2t(t2tb(I)) = I)),
% 0.98/0.94 inference(rewrite,[status(thm)],[])).
% 0.98/0.94 tff(383,axiom,(![I: $int] : (tb2t(t2tb(I)) = I)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bridgeL')).
% 0.98/0.94 tff(384,plain,
% 0.98/0.94 (![I: $int] : (tb2t(t2tb(I)) = I)),
% 0.98/0.94 inference(modus_ponens,[status(thm)],[383, 382])).
% 0.98/0.94 tff(385,plain,
% 0.98/0.94 (![I: $int] : ($sum(tb2t(t2tb(I)), $product(-1, I)) = 0)),
% 0.98/0.94 inference(modus_ponens,[status(thm)],[384, 381])).
% 0.98/0.94 tff(386,plain,
% 0.98/0.94 (![I: $int] : ($sum(I, $product(-1, tb2t(t2tb(I)))) = 0)),
% 0.98/0.94 inference(modus_ponens,[status(thm)],[385, 379])).
% 0.98/0.94 tff(387,plain,(
% 0.98/0.94 ![I: $int] : ($sum(I, $product(-1, tb2t(t2tb(I)))) = 0)),
% 0.98/0.94 inference(skolemize,[status(sab)],[386])).
% 0.98/0.94 tff(388,plain,
% 0.98/0.94 (![I: $int] : ($sum(I, $product(-1, tb2t(t2tb(I)))) = 0)),
% 0.98/0.94 inference(modus_ponens,[status(thm)],[387, 377])).
% 0.98/0.94 tff(389,plain,
% 0.98/0.94 ((~![I: $int] : ($sum(I, $product(-1, tb2t(t2tb(I)))) = 0)) | ($sum(Pos!4, $product(-1, tb2t(t2tb(Pos!4)))) = 0)),
% 0.98/0.94 inference(quant_inst,[status(thm)],[])).
% 0.98/0.94 tff(390,plain,
% 0.98/0.94 ($sum(Pos!4, $product(-1, tb2t(t2tb(Pos!4)))) = 0),
% 0.98/0.94 inference(unit_resolution,[status(thm)],[389, 388])).
% 0.98/0.94 tff(391,plain,
% 0.98/0.94 ((~($sum(Pos!4, $product(-1, tb2t(t2tb(Pos!4)))) = 0)) | $lesseq($sum(Pos!4, $product(-1, tb2t(t2tb(Pos!4)))), 0)),
% 0.98/0.94 inference(theory_lemma,[status(thm)],[])).
% 0.98/0.94 tff(392,plain,
% 0.98/0.94 ($lesseq($sum(Pos!4, $product(-1, tb2t(t2tb(Pos!4)))), 0)),
% 0.98/0.94 inference(unit_resolution,[status(thm)],[391, 390])).
% 0.98/0.94 tff(393,plain,
% 0.98/0.94 ((~($sum(Pos!4, $product(-1, tb2t(t2tb(Pos!4)))) = 0)) | $greatereq($sum(Pos!4, $product(-1, tb2t(t2tb(Pos!4)))), 0)),
% 0.98/0.94 inference(theory_lemma,[status(thm)],[])).
% 0.98/0.94 tff(394,plain,
% 0.98/0.94 ($greatereq($sum(Pos!4, $product(-1, tb2t(t2tb(Pos!4)))), 0)),
% 0.98/0.94 inference(unit_resolution,[status(thm)],[393, 390])).
% 0.98/0.94 tff(395,plain,
% 0.98/0.94 (Pos!4 = tb2t(t2tb(Pos!4))),
% 0.98/0.94 inference(theory_lemma,[status(thm)],[394, 392])).
% 0.98/0.94 tff(396,plain,
% 0.98/0.94 (tb2t(t2tb(Pos!4)) = Pos!4),
% 0.98/0.94 inference(symmetry,[status(thm)],[395])).
% 0.98/0.94 tff(397,plain,
% 0.98/0.94 (eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t(t2tb(Pos!4))) <=> eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, N!5, t2tb2(tb2t2(set(int, int, t2tb2(Board2!10), t2tb(Pos!4), t2tb(I!11)))))), Pos!4)),
% 0.98/0.94 inference(monotonicity,[status(thm)],[373, 396])).
% 0.98/0.94 tff(398,assumption,(~($lesseq($sum(tb2t(t2tb(Pos!4)), $product(-1, tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))), 0) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))), tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))))) = 0) | (~$greatereq(tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))), 0)))), introduced(assumption)).
% 0.98/0.94 tff(399,plain,
% 0.98/0.94 (($lesseq($sum(tb2t(t2tb(Pos!4)), $product(-1, tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))), 0) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))), tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))))) = 0) | (~$greatereq(tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))), 0))) | (~($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))), tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))))) = 0))),
% 0.98/0.94 inference(tautology,[status(thm)],[])).
% 0.98/0.94 tff(400,plain,
% 0.98/0.94 (~($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))), tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))))) = 0)),
% 0.98/0.94 inference(unit_resolution,[status(thm)],[399, 398])).
% 0.98/0.94 tff(401,plain,
% 0.98/0.94 ((~![J: uni] : (t2tb1(tb2t1(J)) = J)) | (t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))) = mk_array1(int, Board!7, t2tb2(Board2!10)))),
% 0.98/0.94 inference(quant_inst,[status(thm)],[])).
% 0.98/0.94 tff(402,plain,
% 0.98/0.94 (t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))) = mk_array1(int, Board!7, t2tb2(Board2!10))),
% 0.98/0.94 inference(unit_resolution,[status(thm)],[401, 154])).
% 0.98/0.94 tff(403,plain,
% 0.98/0.94 (mk_array1(int, Board!7, t2tb2(Board2!10)) = t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))))),
% 0.98/0.94 inference(symmetry,[status(thm)],[402])).
% 0.98/0.94 tff(404,plain,
% 0.98/0.94 (get2(int, mk_array1(int, Board!7, t2tb2(Board2!10)), tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))))) = get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))), tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))),
% 0.98/0.94 inference(monotonicity,[status(thm)],[403])).
% 0.98/0.94 tff(405,plain,
% 0.98/0.94 ((~![A: ty, A1: uni, I: $int] : (get2(A, A1, I) = get(A, int, elts(A, A1), t2tb(I)))) | (get2(int, mk_array1(int, Board!7, t2tb2(Board2!10)), tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))))) = get(int, int, elts(int, mk_array1(int, Board!7, t2tb2(Board2!10))), t2tb(tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))))),
% 0.98/0.94 inference(quant_inst,[status(thm)],[])).
% 0.98/0.94 tff(406,plain,
% 0.98/0.94 (get2(int, mk_array1(int, Board!7, t2tb2(Board2!10)), tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))))) = get(int, int, elts(int, mk_array1(int, Board!7, t2tb2(Board2!10))), t2tb(tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))))))),
% 0.98/0.94 inference(unit_resolution,[status(thm)],[405, 165])).
% 0.98/0.94 tff(407,plain,
% 0.98/0.94 (get(int, int, elts(int, mk_array1(int, Board!7, t2tb2(Board2!10))), t2tb(tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))) = get2(int, mk_array1(int, Board!7, t2tb2(Board2!10)), tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))),
% 0.98/0.94 inference(symmetry,[status(thm)],[406])).
% 0.98/0.94 tff(408,plain,
% 0.98/0.94 (mk_array1(int, N!5, t2tb2(Board2!10)) = mk_array1(int, Board!7, t2tb2(Board2!10))),
% 0.98/0.94 inference(monotonicity,[status(thm)],[370])).
% 0.98/0.94 tff(409,plain,
% 0.98/0.94 (mk_array1(int, Board!7, t2tb2(Board2!10)) = mk_array1(int, N!5, t2tb2(Board2!10))),
% 0.98/0.94 inference(symmetry,[status(thm)],[408])).
% 0.98/0.94 tff(410,plain,
% 0.98/0.94 (elts(int, mk_array1(int, Board!7, t2tb2(Board2!10))) = elts(int, mk_array1(int, N!5, t2tb2(Board2!10)))),
% 0.98/0.94 inference(monotonicity,[status(thm)],[409])).
% 0.98/0.94 tff(411,plain,
% 0.98/0.94 (elts(int, mk_array1(int, N!5, t2tb2(Board2!10))) = elts(int, mk_array1(int, Board!7, t2tb2(Board2!10)))),
% 0.98/0.94 inference(symmetry,[status(thm)],[410])).
% 0.98/0.94 tff(412,plain,
% 0.98/0.94 ((~![X: map_int_int] : sort1(map(int, int), t2tb2(X))) | sort1(map(int, int), t2tb2(Board2!10))),
% 0.98/0.94 inference(quant_inst,[status(thm)],[])).
% 0.98/0.94 tff(413,plain,
% 0.98/0.94 (sort1(map(int, int), t2tb2(Board2!10))),
% 0.98/0.94 inference(unit_resolution,[status(thm)],[412, 175])).
% 0.98/0.94 tff(414,plain,
% 0.98/0.94 (((~![A: ty, U: $int, U1: uni] : ((~sort1(map(int, A), U1)) | (elts(A, mk_array1(A, U, U1)) = U1))) | ((~sort1(map(int, int), t2tb2(Board2!10))) | (elts(int, mk_array1(int, N!5, t2tb2(Board2!10))) = t2tb2(Board2!10)))) <=> ((~![A: ty, U: $int, U1: uni] : ((~sort1(map(int, A), U1)) | (elts(A, mk_array1(A, U, U1)) = U1))) | (~sort1(map(int, int), t2tb2(Board2!10))) | (elts(int, mk_array1(int, N!5, t2tb2(Board2!10))) = t2tb2(Board2!10)))),
% 0.98/0.94 inference(rewrite,[status(thm)],[])).
% 0.98/0.94 tff(415,plain,
% 0.98/0.94 ((~![A: ty, U: $int, U1: uni] : ((~sort1(map(int, A), U1)) | (elts(A, mk_array1(A, U, U1)) = U1))) | ((~sort1(map(int, int), t2tb2(Board2!10))) | (elts(int, mk_array1(int, N!5, t2tb2(Board2!10))) = t2tb2(Board2!10)))),
% 0.98/0.94 inference(quant_inst,[status(thm)],[])).
% 0.98/0.94 tff(416,plain,
% 0.98/0.94 ((~![A: ty, U: $int, U1: uni] : ((~sort1(map(int, A), U1)) | (elts(A, mk_array1(A, U, U1)) = U1))) | (~sort1(map(int, int), t2tb2(Board2!10))) | (elts(int, mk_array1(int, N!5, t2tb2(Board2!10))) = t2tb2(Board2!10))),
% 0.98/0.94 inference(modus_ponens,[status(thm)],[415, 414])).
% 0.98/0.94 tff(417,plain,
% 0.98/0.94 ((~sort1(map(int, int), t2tb2(Board2!10))) | (elts(int, mk_array1(int, N!5, t2tb2(Board2!10))) = t2tb2(Board2!10))),
% 0.98/0.94 inference(unit_resolution,[status(thm)],[416, 187])).
% 0.98/0.94 tff(418,plain,
% 0.98/0.94 (elts(int, mk_array1(int, N!5, t2tb2(Board2!10))) = t2tb2(Board2!10)),
% 0.98/0.94 inference(unit_resolution,[status(thm)],[417, 413])).
% 0.98/0.94 tff(419,plain,
% 0.98/0.94 (t2tb2(Board2!10) = elts(int, mk_array1(int, N!5, t2tb2(Board2!10)))),
% 0.98/0.94 inference(symmetry,[status(thm)],[418])).
% 0.98/0.94 tff(420,plain,
% 0.98/0.94 (t2tb2(Board2!10) = elts(int, mk_array1(int, Board!7, t2tb2(Board2!10)))),
% 0.98/0.94 inference(transitivity,[status(thm)],[419, 411])).
% 0.98/0.94 tff(421,plain,
% 0.98/0.94 (get(int, int, t2tb2(Board2!10), t2tb(tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))) = get(int, int, elts(int, mk_array1(int, Board!7, t2tb2(Board2!10))), t2tb(tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))))))),
% 0.98/0.94 inference(monotonicity,[status(thm)],[420])).
% 0.98/0.94 tff(422,plain,
% 0.98/0.94 (($lesseq($sum(tb2t(t2tb(Pos!4)), $product(-1, tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))), 0) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))), tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))))) = 0) | (~$greatereq(tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))), 0))) | (~$lesseq($sum(tb2t(t2tb(Pos!4)), $product(-1, tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))), 0))),
% 0.98/0.94 inference(tautology,[status(thm)],[])).
% 0.98/0.94 tff(423,plain,
% 0.98/0.94 (~$lesseq($sum(tb2t(t2tb(Pos!4)), $product(-1, tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))), 0)),
% 0.98/0.94 inference(unit_resolution,[status(thm)],[422, 398])).
% 0.98/0.94 tff(424,assumption,(~$lesseq($sum(tb2t(t2tb(Pos!4)), $product(-1, tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))), 0)), introduced(assumption)).
% 0.98/0.94 tff(425,assumption,($lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))), 0)), introduced(assumption)).
% 0.98/0.94 tff(426,plain,
% 0.98/0.94 ($false),
% 0.98/0.94 inference(theory_lemma,[status(thm)],[394, 425, 424])).
% 0.98/0.94 tff(427,plain,((~$lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))), 0)) | $lesseq($sum(tb2t(t2tb(Pos!4)), $product(-1, tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))), 0)), inference(lemma,lemma(discharge,[]))).
% 0.98/0.95 tff(428,plain,
% 0.98/0.95 (~$lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))), 0)),
% 0.98/0.95 inference(unit_resolution,[status(thm)],[427, 423])).
% 0.98/0.95 tff(429,plain,
% 0.98/0.95 ((~![I: $int] : ($sum(I, $product(-1, tb2t(t2tb(I)))) = 0)) | ($sum(tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))), $product(-1, tb2t(t2tb(tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))))) = 0)),
% 0.98/0.95 inference(quant_inst,[status(thm)],[])).
% 0.98/0.95 tff(430,plain,
% 0.98/0.95 ($sum(tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))), $product(-1, tb2t(t2tb(tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))))) = 0),
% 0.98/0.95 inference(unit_resolution,[status(thm)],[429, 388])).
% 0.98/0.95 tff(431,plain,
% 0.98/0.95 ((~($sum(tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))), $product(-1, tb2t(t2tb(tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))))) = 0)) | $greatereq($sum(tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))), $product(-1, tb2t(t2tb(tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))))), 0)),
% 0.98/0.95 inference(theory_lemma,[status(thm)],[])).
% 0.98/0.95 tff(432,plain,
% 0.98/0.95 ($greatereq($sum(tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))), $product(-1, tb2t(t2tb(tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))))), 0)),
% 0.98/0.95 inference(unit_resolution,[status(thm)],[431, 430])).
% 0.98/0.95 tff(433,assumption,($lesseq($sum(tb2t(t2tb(Pos!4)), $product(-1, tb2t(t2tb(tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))))), 0)), introduced(assumption)).
% 0.98/0.95 tff(434,assumption,(~$lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))), 0)), introduced(assumption)).
% 0.98/0.95 tff(435,plain,
% 0.98/0.95 ($false),
% 0.98/0.95 inference(theory_lemma,[status(thm)],[434, 433, 392, 432])).
% 0.98/0.95 tff(436,plain,((~$lesseq($sum(tb2t(t2tb(Pos!4)), $product(-1, tb2t(t2tb(tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))))), 0)) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))), 0)), inference(lemma,lemma(discharge,[]))).
% 0.98/0.95 tff(437,plain,
% 0.98/0.95 (~$lesseq($sum(tb2t(t2tb(Pos!4)), $product(-1, tb2t(t2tb(tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))))), 0)),
% 0.98/0.95 inference(unit_resolution,[status(thm)],[436, 428])).
% 0.98/0.95 tff(438,plain,
% 0.98/0.95 ((~(tb2t(t2tb(Pos!4)) = tb2t(t2tb(tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))))) | $lesseq($sum(tb2t(t2tb(Pos!4)), $product(-1, tb2t(t2tb(tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))))), 0)),
% 0.98/0.95 inference(theory_lemma,[status(thm)],[])).
% 0.98/0.95 tff(439,plain,
% 0.98/0.95 (~(tb2t(t2tb(Pos!4)) = tb2t(t2tb(tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))))),
% 0.98/0.95 inference(unit_resolution,[status(thm)],[438, 437])).
% 0.98/0.95 tff(440,assumption,(t2tb(Pos!4) = t2tb(tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))), introduced(assumption)).
% 0.98/0.95 tff(441,plain,
% 0.98/0.95 (tb2t(t2tb(Pos!4)) = tb2t(t2tb(tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))))))),
% 0.98/0.95 inference(monotonicity,[status(thm)],[440])).
% 0.98/0.95 tff(442,assumption,(~(tb2t(t2tb(Pos!4)) = tb2t(t2tb(tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))))), introduced(assumption)).
% 0.98/0.95 tff(443,plain,
% 0.98/0.95 ($false),
% 0.98/0.95 inference(unit_resolution,[status(thm)],[442, 441])).
% 0.98/0.95 tff(444,plain,((~(t2tb(Pos!4) = t2tb(tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))))))) | (tb2t(t2tb(Pos!4)) = tb2t(t2tb(tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))))), inference(lemma,lemma(discharge,[]))).
% 0.98/0.95 tff(445,plain,
% 0.98/0.95 (~(t2tb(Pos!4) = t2tb(tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))))))),
% 0.98/0.95 inference(unit_resolution,[status(thm)],[444, 439])).
% 0.98/0.95 tff(446,plain,
% 0.98/0.95 (^[X: $int] : refl(sort1(int, t2tb(X)) <=> sort1(int, t2tb(X)))),
% 0.98/0.95 inference(bind,[status(th)],[])).
% 0.98/0.95 tff(447,plain,
% 0.98/0.95 (![X: $int] : sort1(int, t2tb(X)) <=> ![X: $int] : sort1(int, t2tb(X))),
% 0.98/0.95 inference(quant_intro,[status(thm)],[446])).
% 0.98/0.95 tff(448,plain,
% 0.98/0.95 (![X: $int] : sort1(int, t2tb(X)) <=> ![X: $int] : sort1(int, t2tb(X))),
% 0.98/0.95 inference(rewrite,[status(thm)],[])).
% 0.98/0.95 tff(449,axiom,(![X: $int] : sort1(int, t2tb(X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t2tb_sort')).
% 0.98/0.95 tff(450,plain,
% 0.98/0.95 (![X: $int] : sort1(int, t2tb(X))),
% 0.98/0.95 inference(modus_ponens,[status(thm)],[449, 448])).
% 0.98/0.95 tff(451,plain,(
% 0.98/0.95 ![X: $int] : sort1(int, t2tb(X))),
% 0.98/0.95 inference(skolemize,[status(sab)],[450])).
% 0.98/0.95 tff(452,plain,
% 0.98/0.95 (![X: $int] : sort1(int, t2tb(X))),
% 0.98/0.95 inference(modus_ponens,[status(thm)],[451, 447])).
% 0.98/0.95 tff(453,plain,
% 0.98/0.95 ((~![X: $int] : sort1(int, t2tb(X))) | sort1(int, t2tb(tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))))))),
% 0.98/0.95 inference(quant_inst,[status(thm)],[])).
% 0.98/0.95 tff(454,plain,
% 0.98/0.95 (sort1(int, t2tb(tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))))))),
% 0.98/0.95 inference(unit_resolution,[status(thm)],[453, 452])).
% 0.98/0.95 tff(455,plain,
% 0.98/0.95 ((~![X: $int] : sort1(int, t2tb(X))) | sort1(int, t2tb(Pos!4))),
% 0.98/0.95 inference(quant_inst,[status(thm)],[])).
% 0.98/0.95 tff(456,plain,
% 0.98/0.95 (sort1(int, t2tb(Pos!4))),
% 0.98/0.95 inference(unit_resolution,[status(thm)],[455, 452])).
% 0.98/0.95 tff(457,plain,
% 0.98/0.95 (^[A: ty, B: ty, M: uni, A1: uni, A2: uni] : rewrite((![B1: uni] : ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))) | (~sort1(A, A2)) | (~sort1(A, A1))) <=> ((~sort1(A, A2)) | (~sort1(A, A1)) | ![B1: uni] : ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2)))))),
% 0.98/0.95 inference(bind,[status(th)],[])).
% 0.98/0.95 tff(458,plain,
% 0.98/0.95 (![A: ty, B: ty, M: uni, A1: uni, A2: uni] : (![B1: uni] : ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))) | (~sort1(A, A2)) | (~sort1(A, A1))) <=> ![A: ty, B: ty, M: uni, A1: uni, A2: uni] : ((~sort1(A, A2)) | (~sort1(A, A1)) | ![B1: uni] : ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))))),
% 0.98/0.95 inference(quant_intro,[status(thm)],[457])).
% 0.98/0.95 tff(459,plain,
% 0.98/0.95 (^[A: ty, B: ty, M: uni, A1: uni, A2: uni] : refl((![B1: uni] : ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))) | (~sort1(A, A2)) | (~sort1(A, A1))) <=> (![B1: uni] : ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))) | (~sort1(A, A2)) | (~sort1(A, A1))))),
% 0.98/0.95 inference(bind,[status(th)],[])).
% 0.98/0.95 tff(460,plain,
% 0.98/0.95 (![A: ty, B: ty, M: uni, A1: uni, A2: uni] : (![B1: uni] : ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))) | (~sort1(A, A2)) | (~sort1(A, A1))) <=> ![A: ty, B: ty, M: uni, A1: uni, A2: uni] : (![B1: uni] : ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))) | (~sort1(A, A2)) | (~sort1(A, A1)))),
% 0.98/0.95 inference(quant_intro,[status(thm)],[459])).
% 0.98/0.95 tff(461,plain,
% 0.98/0.95 (^[A: ty, B: ty, M: uni, A1: uni, A2: uni] : rewrite((![B1: uni] : ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))) | (~sort1(A, A2)) | (~sort1(A, A1))) <=> (![B1: uni] : ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))) | (~sort1(A, A2)) | (~sort1(A, A1))))),
% 0.98/0.95 inference(bind,[status(th)],[])).
% 0.98/0.95 tff(462,plain,
% 0.98/0.95 (![A: ty, B: ty, M: uni, A1: uni, A2: uni] : (![B1: uni] : ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))) | (~sort1(A, A2)) | (~sort1(A, A1))) <=> ![A: ty, B: ty, M: uni, A1: uni, A2: uni] : (![B1: uni] : ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))) | (~sort1(A, A2)) | (~sort1(A, A1)))),
% 0.98/0.95 inference(quant_intro,[status(thm)],[461])).
% 0.98/0.95 tff(463,plain,
% 0.98/0.95 (![A: ty, B: ty, M: uni, A1: uni, A2: uni] : (![B1: uni] : ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))) | (~sort1(A, A2)) | (~sort1(A, A1))) <=> ![A: ty, B: ty, M: uni, A1: uni, A2: uni] : (![B1: uni] : ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))) | (~sort1(A, A2)) | (~sort1(A, A1)))),
% 0.98/0.95 inference(transitivity,[status(thm)],[462, 460])).
% 0.98/0.95 tff(464,plain,
% 0.98/0.95 (![A: ty, B: ty, M: uni, A1: uni, A2: uni] : (![B1: uni] : ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))) | (~sort1(A, A2)) | (~sort1(A, A1))) <=> ![A: ty, B: ty, M: uni, A1: uni, A2: uni] : (![B1: uni] : ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))) | (~sort1(A, A2)) | (~sort1(A, A1)))),
% 0.98/0.95 inference(rewrite,[status(thm)],[])).
% 0.98/0.95 tff(465,plain,
% 0.98/0.95 (^[A: ty, B: ty, M: uni, A1: uni, A2: uni] : trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[B1: uni] : rewrite(((~(A1 = A2)) => (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))) <=> ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))))), (![B1: uni] : ((~(A1 = A2)) => (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))) <=> ![B1: uni] : ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))))), ((sort1(A, A2) => ![B1: uni] : ((~(A1 = A2)) => (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2)))) <=> (sort1(A, A2) => ![B1: uni] : ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2)))))), rewrite((sort1(A, A2) => ![B1: uni] : ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2)))) <=> ((~sort1(A, A2)) | ![B1: uni] : ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))))), ((sort1(A, A2) => ![B1: uni] : ((~(A1 = A2)) => (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2)))) <=> ((~sort1(A, A2)) | ![B1: uni] : ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2)))))), ((sort1(A, A1) => (sort1(A, A2) => ![B1: uni] : ((~(A1 = A2)) => (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))))) <=> (sort1(A, A1) => ((~sort1(A, A2)) | ![B1: uni] : ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))))))), rewrite((sort1(A, A1) => ((~sort1(A, A2)) | ![B1: uni] : ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))))) <=> (![B1: uni] : ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))) | (~sort1(A, A2)) | (~sort1(A, A1)))), ((sort1(A, A1) => (sort1(A, A2) => ![B1: uni] : ((~(A1 = A2)) => (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))))) <=> (![B1: uni] : ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))) | (~sort1(A, A2)) | (~sort1(A, A1)))))),
% 0.98/0.95 inference(bind,[status(th)],[])).
% 0.98/0.95 tff(466,plain,
% 0.98/0.95 (![A: ty, B: ty, M: uni, A1: uni, A2: uni] : (sort1(A, A1) => (sort1(A, A2) => ![B1: uni] : ((~(A1 = A2)) => (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))))) <=> ![A: ty, B: ty, M: uni, A1: uni, A2: uni] : (![B1: uni] : ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))) | (~sort1(A, A2)) | (~sort1(A, A1)))),
% 0.98/0.95 inference(quant_intro,[status(thm)],[465])).
% 0.98/0.95 tff(467,axiom,(![A: ty, B: ty, M: uni, A1: uni, A2: uni] : (sort1(A, A1) => (sort1(A, A2) => ![B1: uni] : ((~(A1 = A2)) => (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','select_neq')).
% 0.98/0.95 tff(468,plain,
% 0.98/0.95 (![A: ty, B: ty, M: uni, A1: uni, A2: uni] : (![B1: uni] : ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))) | (~sort1(A, A2)) | (~sort1(A, A1)))),
% 0.98/0.95 inference(modus_ponens,[status(thm)],[467, 466])).
% 0.98/0.95 tff(469,plain,
% 0.98/0.95 (![A: ty, B: ty, M: uni, A1: uni, A2: uni] : (![B1: uni] : ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))) | (~sort1(A, A2)) | (~sort1(A, A1)))),
% 0.98/0.95 inference(modus_ponens,[status(thm)],[468, 464])).
% 0.98/0.95 tff(470,plain,(
% 0.98/0.95 ![A: ty, B: ty, M: uni, A1: uni, A2: uni] : (![B1: uni] : ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))) | (~sort1(A, A2)) | (~sort1(A, A1)))),
% 0.98/0.95 inference(skolemize,[status(sab)],[469])).
% 0.98/0.95 tff(471,plain,
% 0.98/0.95 (![A: ty, B: ty, M: uni, A1: uni, A2: uni] : (![B1: uni] : ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))) | (~sort1(A, A2)) | (~sort1(A, A1)))),
% 0.98/0.95 inference(modus_ponens,[status(thm)],[470, 463])).
% 0.98/0.95 tff(472,plain,
% 0.98/0.95 (![A: ty, B: ty, M: uni, A1: uni, A2: uni] : ((~sort1(A, A2)) | (~sort1(A, A1)) | ![B1: uni] : ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))))),
% 0.98/0.95 inference(modus_ponens,[status(thm)],[471, 458])).
% 0.98/0.95 tff(473,plain,
% 0.98/0.95 (((~![A: ty, B: ty, M: uni, A1: uni, A2: uni] : ((~sort1(A, A2)) | (~sort1(A, A1)) | ![B1: uni] : ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))))) | ((~sort1(int, t2tb(Pos!4))) | (~sort1(int, t2tb(tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))))))) | ![B1: uni] : ((t2tb(Pos!4) = t2tb(tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))) | (get(int, int, set(int, int, t2tb2(Board2!10), t2tb(Pos!4), B1), t2tb(tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))) = get(int, int, t2tb2(Board2!10), t2tb(tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))))))) <=> ((~![A: ty, B: ty, M: uni, A1: uni, A2: uni] : ((~sort1(A, A2)) | (~sort1(A, A1)) | ![B1: uni] : ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))))) | (~sort1(int, t2tb(Pos!4))) | (~sort1(int, t2tb(tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))))))) | ![B1: uni] : ((t2tb(Pos!4) = t2tb(tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))) | (get(int, int, set(int, int, t2tb2(Board2!10), t2tb(Pos!4), B1), t2tb(tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))) = get(int, int, t2tb2(Board2!10), t2tb(tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))))))),
% 0.98/0.95 inference(rewrite,[status(thm)],[])).
% 0.98/0.95 tff(474,plain,
% 0.98/0.95 (((~sort1(int, t2tb(tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))))))) | (~sort1(int, t2tb(Pos!4))) | ![B1: uni] : ((t2tb(Pos!4) = t2tb(tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))) | (get(int, int, set(int, int, t2tb2(Board2!10), t2tb(Pos!4), B1), t2tb(tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))) = get(int, int, t2tb2(Board2!10), t2tb(tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))))))))) <=> ((~sort1(int, t2tb(Pos!4))) | (~sort1(int, t2tb(tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))))))) | ![B1: uni] : ((t2tb(Pos!4) = t2tb(tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))) | (get(int, int, set(int, int, t2tb2(Board2!10), t2tb(Pos!4), B1), t2tb(tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))) = get(int, int, t2tb2(Board2!10), t2tb(tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))))))),
% 0.98/0.95 inference(rewrite,[status(thm)],[])).
% 0.98/0.95 tff(475,plain,
% 0.98/0.95 (((~![A: ty, B: ty, M: uni, A1: uni, A2: uni] : ((~sort1(A, A2)) | (~sort1(A, A1)) | ![B1: uni] : ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))))) | ((~sort1(int, t2tb(tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))))))) | (~sort1(int, t2tb(Pos!4))) | ![B1: uni] : ((t2tb(Pos!4) = t2tb(tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))) | (get(int, int, set(int, int, t2tb2(Board2!10), t2tb(Pos!4), B1), t2tb(tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))) = get(int, int, t2tb2(Board2!10), t2tb(tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))))))) <=> ((~![A: ty, B: ty, M: uni, A1: uni, A2: uni] : ((~sort1(A, A2)) | (~sort1(A, A1)) | ![B1: uni] : ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))))) | ((~sort1(int, t2tb(Pos!4))) | (~sort1(int, t2tb(tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))))))) | ![B1: uni] : ((t2tb(Pos!4) = t2tb(tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))) | (get(int, int, set(int, int, t2tb2(Board2!10), t2tb(Pos!4), B1), t2tb(tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))) = get(int, int, t2tb2(Board2!10), t2tb(tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))))))))))),
% 0.98/0.95 inference(monotonicity,[status(thm)],[474])).
% 0.98/0.95 tff(476,plain,
% 0.98/0.95 (((~![A: ty, B: ty, M: uni, A1: uni, A2: uni] : ((~sort1(A, A2)) | (~sort1(A, A1)) | ![B1: uni] : ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))))) | ((~sort1(int, t2tb(tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))))))) | (~sort1(int, t2tb(Pos!4))) | ![B1: uni] : ((t2tb(Pos!4) = t2tb(tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))) | (get(int, int, set(int, int, t2tb2(Board2!10), t2tb(Pos!4), B1), t2tb(tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))) = get(int, int, t2tb2(Board2!10), t2tb(tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))))))) <=> ((~![A: ty, B: ty, M: uni, A1: uni, A2: uni] : ((~sort1(A, A2)) | (~sort1(A, A1)) | ![B1: uni] : ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))))) | (~sort1(int, t2tb(Pos!4))) | (~sort1(int, t2tb(tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))))))) | ![B1: uni] : ((t2tb(Pos!4) = t2tb(tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))) | (get(int, int, set(int, int, t2tb2(Board2!10), t2tb(Pos!4), B1), t2tb(tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))) = get(int, int, t2tb2(Board2!10), t2tb(tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))))))),
% 0.98/0.95 inference(transitivity,[status(thm)],[475, 473])).
% 0.98/0.95 tff(477,plain,
% 0.98/0.95 ((~![A: ty, B: ty, M: uni, A1: uni, A2: uni] : ((~sort1(A, A2)) | (~sort1(A, A1)) | ![B1: uni] : ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))))) | ((~sort1(int, t2tb(tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))))))) | (~sort1(int, t2tb(Pos!4))) | ![B1: uni] : ((t2tb(Pos!4) = t2tb(tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))) | (get(int, int, set(int, int, t2tb2(Board2!10), t2tb(Pos!4), B1), t2tb(tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))) = get(int, int, t2tb2(Board2!10), t2tb(tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))))))),
% 0.98/0.95 inference(quant_inst,[status(thm)],[])).
% 0.98/0.95 tff(478,plain,
% 0.98/0.95 ((~![A: ty, B: ty, M: uni, A1: uni, A2: uni] : ((~sort1(A, A2)) | (~sort1(A, A1)) | ![B1: uni] : ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))))) | (~sort1(int, t2tb(Pos!4))) | (~sort1(int, t2tb(tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))))))) | ![B1: uni] : ((t2tb(Pos!4) = t2tb(tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))) | (get(int, int, set(int, int, t2tb2(Board2!10), t2tb(Pos!4), B1), t2tb(tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))) = get(int, int, t2tb2(Board2!10), t2tb(tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))))))))),
% 0.98/0.95 inference(modus_ponens,[status(thm)],[477, 476])).
% 0.98/0.95 tff(479,plain,
% 0.98/0.95 (![B1: uni] : ((t2tb(Pos!4) = t2tb(tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))) | (get(int, int, set(int, int, t2tb2(Board2!10), t2tb(Pos!4), B1), t2tb(tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))) = get(int, int, t2tb2(Board2!10), t2tb(tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))))))))),
% 0.98/0.95 inference(unit_resolution,[status(thm)],[478, 472, 456, 454])).
% 0.98/0.95 tff(480,plain,
% 0.98/0.95 (((~![B1: uni] : ((t2tb(Pos!4) = t2tb(tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))) | (get(int, int, set(int, int, t2tb2(Board2!10), t2tb(Pos!4), B1), t2tb(tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))) = get(int, int, t2tb2(Board2!10), t2tb(tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))))))))) | ((t2tb(Pos!4) = t2tb(tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))) | (get(int, int, set(int, int, t2tb2(Board2!10), t2tb(Pos!4), t2tb(I!11)), t2tb(tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))) = get(int, int, t2tb2(Board2!10), t2tb(tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))))))))) <=> ((~![B1: uni] : ((t2tb(Pos!4) = t2tb(tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))) | (get(int, int, set(int, int, t2tb2(Board2!10), t2tb(Pos!4), B1), t2tb(tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))) = get(int, int, t2tb2(Board2!10), t2tb(tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))))))))) | (t2tb(Pos!4) = t2tb(tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))) | (get(int, int, set(int, int, t2tb2(Board2!10), t2tb(Pos!4), t2tb(I!11)), t2tb(tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))) = get(int, int, t2tb2(Board2!10), t2tb(tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))))))))),
% 0.98/0.95 inference(rewrite,[status(thm)],[])).
% 0.98/0.95 tff(481,plain,
% 0.98/0.95 ((~![B1: uni] : ((t2tb(Pos!4) = t2tb(tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))) | (get(int, int, set(int, int, t2tb2(Board2!10), t2tb(Pos!4), B1), t2tb(tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))) = get(int, int, t2tb2(Board2!10), t2tb(tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))))))))) | ((t2tb(Pos!4) = t2tb(tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))) | (get(int, int, set(int, int, t2tb2(Board2!10), t2tb(Pos!4), t2tb(I!11)), t2tb(tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))) = get(int, int, t2tb2(Board2!10), t2tb(tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))))))))),
% 0.98/0.95 inference(quant_inst,[status(thm)],[])).
% 0.98/0.95 tff(482,plain,
% 0.98/0.95 ((~![B1: uni] : ((t2tb(Pos!4) = t2tb(tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))) | (get(int, int, set(int, int, t2tb2(Board2!10), t2tb(Pos!4), B1), t2tb(tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))) = get(int, int, t2tb2(Board2!10), t2tb(tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))))))))) | (t2tb(Pos!4) = t2tb(tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))) | (get(int, int, set(int, int, t2tb2(Board2!10), t2tb(Pos!4), t2tb(I!11)), t2tb(tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))) = get(int, int, t2tb2(Board2!10), t2tb(tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))))),
% 0.98/0.95 inference(modus_ponens,[status(thm)],[481, 480])).
% 0.98/0.95 tff(483,plain,
% 0.98/0.95 ((t2tb(Pos!4) = t2tb(tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))) | (get(int, int, set(int, int, t2tb2(Board2!10), t2tb(Pos!4), t2tb(I!11)), t2tb(tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))) = get(int, int, t2tb2(Board2!10), t2tb(tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))))),
% 0.98/0.96 inference(unit_resolution,[status(thm)],[482, 479])).
% 0.98/0.96 tff(484,plain,
% 0.98/0.96 (get(int, int, set(int, int, t2tb2(Board2!10), t2tb(Pos!4), t2tb(I!11)), t2tb(tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))) = get(int, int, t2tb2(Board2!10), t2tb(tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))))))),
% 0.98/0.96 inference(unit_resolution,[status(thm)],[483, 445])).
% 0.98/0.96 tff(485,plain,
% 0.98/0.96 (![J: uni] : (t2tb2(tb2t2(J)) = J) <=> ![J: uni] : (t2tb2(tb2t2(J)) = J)),
% 0.98/0.96 inference(rewrite,[status(thm)],[])).
% 0.98/0.96 tff(486,plain,
% 0.98/0.96 (![J: uni] : (t2tb2(tb2t2(J)) = J) <=> ![J: uni] : (t2tb2(tb2t2(J)) = J)),
% 0.98/0.96 inference(rewrite,[status(thm)],[])).
% 0.98/0.96 tff(487,axiom,(![J: uni] : (t2tb2(tb2t2(J)) = J)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bridgeR2')).
% 0.98/0.96 tff(488,plain,
% 0.98/0.96 (![J: uni] : (t2tb2(tb2t2(J)) = J)),
% 0.98/0.96 inference(modus_ponens,[status(thm)],[487, 486])).
% 0.98/0.96 tff(489,plain,(
% 0.98/0.96 ![J: uni] : (t2tb2(tb2t2(J)) = J)),
% 0.98/0.96 inference(skolemize,[status(sab)],[488])).
% 0.98/0.96 tff(490,plain,
% 0.98/0.96 (![J: uni] : (t2tb2(tb2t2(J)) = J)),
% 0.98/0.96 inference(modus_ponens,[status(thm)],[489, 485])).
% 0.98/0.96 tff(491,plain,
% 0.98/0.96 ((~![J: uni] : (t2tb2(tb2t2(J)) = J)) | (t2tb2(tb2t2(set(int, int, t2tb2(Board2!10), t2tb(Pos!4), t2tb(I!11)))) = set(int, int, t2tb2(Board2!10), t2tb(Pos!4), t2tb(I!11)))),
% 0.98/0.96 inference(quant_inst,[status(thm)],[])).
% 0.98/0.96 tff(492,plain,
% 0.98/0.96 (t2tb2(tb2t2(set(int, int, t2tb2(Board2!10), t2tb(Pos!4), t2tb(I!11)))) = set(int, int, t2tb2(Board2!10), t2tb(Pos!4), t2tb(I!11))),
% 0.98/0.96 inference(unit_resolution,[status(thm)],[491, 490])).
% 0.98/0.96 tff(493,assumption,(Board3!12 = tb2t2(set(int, int, t2tb2(Board2!10), t2tb(Pos!4), t2tb(I!11)))), introduced(assumption)).
% 0.98/0.96 tff(494,plain,
% 0.98/0.96 (t2tb2(Board3!12) = t2tb2(tb2t2(set(int, int, t2tb2(Board2!10), t2tb(Pos!4), t2tb(I!11))))),
% 0.98/0.96 inference(monotonicity,[status(thm)],[493])).
% 0.98/0.96 tff(495,plain,
% 0.98/0.96 (t2tb2(Board3!12) = set(int, int, t2tb2(Board2!10), t2tb(Pos!4), t2tb(I!11))),
% 0.98/0.96 inference(transitivity,[status(thm)],[494, 492])).
% 0.98/0.96 tff(496,plain,
% 0.98/0.96 (sort1(map(int, int), t2tb2(Board3!12)) <=> sort1(map(int, int), set(int, int, t2tb2(Board2!10), t2tb(Pos!4), t2tb(I!11)))),
% 0.98/0.96 inference(monotonicity,[status(thm)],[495])).
% 0.98/0.96 tff(497,plain,
% 0.98/0.96 (sort1(map(int, int), set(int, int, t2tb2(Board2!10), t2tb(Pos!4), t2tb(I!11))) <=> sort1(map(int, int), t2tb2(Board3!12))),
% 0.98/0.96 inference(symmetry,[status(thm)],[496])).
% 0.98/0.96 tff(498,plain,
% 0.98/0.96 (^[A: ty, B: ty, X: uni, X1: uni, X2: uni] : refl(sort1(map(A, B), set(B, A, X, X1, X2)) <=> sort1(map(A, B), set(B, A, X, X1, X2)))),
% 0.98/0.96 inference(bind,[status(th)],[])).
% 0.98/0.96 tff(499,plain,
% 0.98/0.96 (![A: ty, B: ty, X: uni, X1: uni, X2: uni] : sort1(map(A, B), set(B, A, X, X1, X2)) <=> ![A: ty, B: ty, X: uni, X1: uni, X2: uni] : sort1(map(A, B), set(B, A, X, X1, X2))),
% 0.98/0.96 inference(quant_intro,[status(thm)],[498])).
% 0.98/0.96 tff(500,plain,
% 0.98/0.96 (![A: ty, B: ty, X: uni, X1: uni, X2: uni] : sort1(map(A, B), set(B, A, X, X1, X2)) <=> ![A: ty, B: ty, X: uni, X1: uni, X2: uni] : sort1(map(A, B), set(B, A, X, X1, X2))),
% 0.98/0.96 inference(rewrite,[status(thm)],[])).
% 0.98/0.96 tff(501,axiom,(![A: ty, B: ty, X: uni, X1: uni, X2: uni] : sort1(map(A, B), set(B, A, X, X1, X2))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','set_sort2')).
% 0.98/0.96 tff(502,plain,
% 0.98/0.96 (![A: ty, B: ty, X: uni, X1: uni, X2: uni] : sort1(map(A, B), set(B, A, X, X1, X2))),
% 0.98/0.96 inference(modus_ponens,[status(thm)],[501, 500])).
% 0.98/0.96 tff(503,plain,(
% 0.98/0.96 ![A: ty, B: ty, X: uni, X1: uni, X2: uni] : sort1(map(A, B), set(B, A, X, X1, X2))),
% 0.98/0.96 inference(skolemize,[status(sab)],[502])).
% 0.98/0.96 tff(504,plain,
% 0.98/0.96 (![A: ty, B: ty, X: uni, X1: uni, X2: uni] : sort1(map(A, B), set(B, A, X, X1, X2))),
% 0.98/0.96 inference(modus_ponens,[status(thm)],[503, 499])).
% 0.98/0.96 tff(505,plain,
% 0.98/0.96 ((~![A: ty, B: ty, X: uni, X1: uni, X2: uni] : sort1(map(A, B), set(B, A, X, X1, X2))) | sort1(map(int, int), set(int, int, t2tb2(Board2!10), t2tb(Pos!4), t2tb(I!11)))),
% 0.98/0.96 inference(quant_inst,[status(thm)],[])).
% 0.98/0.96 tff(506,plain,
% 0.98/0.96 (sort1(map(int, int), set(int, int, t2tb2(Board2!10), t2tb(Pos!4), t2tb(I!11)))),
% 0.98/0.96 inference(unit_resolution,[status(thm)],[505, 504])).
% 0.98/0.96 tff(507,plain,
% 0.98/0.96 (sort1(map(int, int), t2tb2(Board3!12))),
% 0.98/0.96 inference(modus_ponens,[status(thm)],[506, 497])).
% 0.98/0.96 tff(508,plain,
% 0.98/0.96 (((~![A: ty, U: $int, U1: uni] : ((~sort1(map(int, A), U1)) | (elts(A, mk_array1(A, U, U1)) = U1))) | ((~sort1(map(int, int), t2tb2(Board3!12))) | (elts(int, mk_array1(int, N!5, t2tb2(Board3!12))) = t2tb2(Board3!12)))) <=> ((~![A: ty, U: $int, U1: uni] : ((~sort1(map(int, A), U1)) | (elts(A, mk_array1(A, U, U1)) = U1))) | (~sort1(map(int, int), t2tb2(Board3!12))) | (elts(int, mk_array1(int, N!5, t2tb2(Board3!12))) = t2tb2(Board3!12)))),
% 0.98/0.96 inference(rewrite,[status(thm)],[])).
% 0.98/0.96 tff(509,plain,
% 0.98/0.96 ((~![A: ty, U: $int, U1: uni] : ((~sort1(map(int, A), U1)) | (elts(A, mk_array1(A, U, U1)) = U1))) | ((~sort1(map(int, int), t2tb2(Board3!12))) | (elts(int, mk_array1(int, N!5, t2tb2(Board3!12))) = t2tb2(Board3!12)))),
% 0.98/0.96 inference(quant_inst,[status(thm)],[])).
% 0.98/0.96 tff(510,plain,
% 0.98/0.96 ((~![A: ty, U: $int, U1: uni] : ((~sort1(map(int, A), U1)) | (elts(A, mk_array1(A, U, U1)) = U1))) | (~sort1(map(int, int), t2tb2(Board3!12))) | (elts(int, mk_array1(int, N!5, t2tb2(Board3!12))) = t2tb2(Board3!12))),
% 0.98/0.96 inference(modus_ponens,[status(thm)],[509, 508])).
% 0.98/0.96 tff(511,plain,
% 0.98/0.96 ((~sort1(map(int, int), t2tb2(Board3!12))) | (elts(int, mk_array1(int, N!5, t2tb2(Board3!12))) = t2tb2(Board3!12))),
% 0.98/0.96 inference(unit_resolution,[status(thm)],[510, 187])).
% 0.98/0.96 tff(512,plain,
% 0.98/0.96 (elts(int, mk_array1(int, N!5, t2tb2(Board3!12))) = t2tb2(Board3!12)),
% 0.98/0.96 inference(unit_resolution,[status(thm)],[511, 507])).
% 0.98/0.96 tff(513,plain,
% 0.98/0.96 (mk_array1(int, N!5, t2tb2(Board3!12)) = mk_array1(int, Board!7, t2tb2(Board3!12))),
% 0.98/0.96 inference(monotonicity,[status(thm)],[370])).
% 0.98/0.96 tff(514,plain,
% 0.98/0.96 (mk_array1(int, Board!7, t2tb2(Board3!12)) = mk_array1(int, N!5, t2tb2(Board3!12))),
% 0.98/0.96 inference(symmetry,[status(thm)],[513])).
% 0.98/0.96 tff(515,plain,
% 0.98/0.96 (elts(int, mk_array1(int, Board!7, t2tb2(Board3!12))) = elts(int, mk_array1(int, N!5, t2tb2(Board3!12)))),
% 0.98/0.96 inference(monotonicity,[status(thm)],[514])).
% 0.98/0.96 tff(516,plain,
% 0.98/0.96 (elts(int, mk_array1(int, Board!7, t2tb2(Board3!12))) = set(int, int, t2tb2(Board2!10), t2tb(Pos!4), t2tb(I!11))),
% 0.98/0.96 inference(transitivity,[status(thm)],[515, 512, 494, 492])).
% 0.98/0.96 tff(517,plain,
% 0.98/0.96 (get(int, int, elts(int, mk_array1(int, Board!7, t2tb2(Board3!12))), t2tb(tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))) = get(int, int, set(int, int, t2tb2(Board2!10), t2tb(Pos!4), t2tb(I!11)), t2tb(tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))))))),
% 0.98/0.96 inference(monotonicity,[status(thm)],[516])).
% 0.98/0.96 tff(518,plain,
% 0.98/0.96 ((~![A: ty, A1: uni, I: $int] : (get2(A, A1, I) = get(A, int, elts(A, A1), t2tb(I)))) | (get2(int, mk_array1(int, Board!7, t2tb2(Board3!12)), tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))))) = get(int, int, elts(int, mk_array1(int, Board!7, t2tb2(Board3!12))), t2tb(tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))))),
% 0.98/0.96 inference(quant_inst,[status(thm)],[])).
% 0.98/0.96 tff(519,plain,
% 0.98/0.96 (get2(int, mk_array1(int, Board!7, t2tb2(Board3!12)), tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))))) = get(int, int, elts(int, mk_array1(int, Board!7, t2tb2(Board3!12))), t2tb(tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))))))),
% 0.98/0.96 inference(unit_resolution,[status(thm)],[518, 165])).
% 0.98/0.96 tff(520,plain,
% 0.98/0.96 ((~![J: uni] : (t2tb1(tb2t1(J)) = J)) | (t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))) = mk_array1(int, Board!7, t2tb2(Board3!12)))),
% 0.98/0.96 inference(quant_inst,[status(thm)],[])).
% 0.98/0.96 tff(521,plain,
% 0.98/0.96 (t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))) = mk_array1(int, Board!7, t2tb2(Board3!12))),
% 0.98/0.96 inference(unit_resolution,[status(thm)],[520, 154])).
% 0.98/0.96 tff(522,plain,
% 0.98/0.96 (get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))))) = get2(int, mk_array1(int, Board!7, t2tb2(Board3!12)), tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))),
% 0.98/0.96 inference(monotonicity,[status(thm)],[521])).
% 0.98/0.96 tff(523,plain,
% 0.98/0.96 (get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))))) = get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))), tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))),
% 0.98/0.96 inference(transitivity,[status(thm)],[522, 519, 517, 484, 421, 407, 404])).
% 0.98/0.96 tff(524,plain,
% 0.98/0.96 (tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))) = tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))), tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))))))),
% 0.98/0.96 inference(monotonicity,[status(thm)],[523])).
% 0.98/0.96 tff(525,plain,
% 0.98/0.96 ((~(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))) = tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))), tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))))) | $lesseq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))), tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))))), 0)),
% 0.98/0.96 inference(theory_lemma,[status(thm)],[])).
% 0.98/0.96 tff(526,plain,
% 0.98/0.96 ($lesseq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))), tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))))), 0)),
% 0.98/0.96 inference(unit_resolution,[status(thm)],[525, 524])).
% 0.98/0.96 tff(527,plain,
% 0.98/0.96 ((~(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))) = tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))), tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))))) | $greatereq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))), tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))))), 0)),
% 0.98/0.96 inference(theory_lemma,[status(thm)],[])).
% 0.98/0.96 tff(528,plain,
% 0.98/0.96 ($greatereq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))), tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))))), 0)),
% 0.98/0.96 inference(unit_resolution,[status(thm)],[527, 524])).
% 0.98/0.96 tff(529,plain,
% 0.98/0.96 (($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))), tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))))) = 0) | (~$lesseq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))), tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))))), 0)) | (~$greatereq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))), tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))))), 0))),
% 0.98/0.96 inference(theory_lemma,[status(thm)],[])).
% 0.98/0.96 tff(530,plain,
% 0.98/0.96 ($false),
% 0.98/0.96 inference(unit_resolution,[status(thm)],[529, 528, 526, 400])).
% 0.98/0.96 tff(531,plain,(($lesseq($sum(tb2t(t2tb(Pos!4)), $product(-1, tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))), 0) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))), tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))))) = 0) | (~$greatereq(tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))), 0))) | (~(Board3!12 = tb2t2(set(int, int, t2tb2(Board2!10), t2tb(Pos!4), t2tb(I!11)))))), inference(lemma,lemma(discharge,[]))).
% 0.98/0.96 tff(532,plain,
% 0.98/0.96 ($lesseq($sum(tb2t(t2tb(Pos!4)), $product(-1, tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))), 0) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))), tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))))) = 0) | (~$greatereq(tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))), 0))),
% 0.98/0.96 inference(unit_resolution,[status(thm)],[531, 365])).
% 0.98/0.96 tff(533,assumption,((~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t(t2tb(Pos!4)))) | ![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, tb2t(t2tb(Pos!4)))), 0) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))), Q)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)))) = 0)))) | (~(eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t(t2tb(Pos!4))) | (~($lesseq($sum(tb2t(t2tb(Pos!4)), $product(-1, tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))), 0) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))), tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))))) = 0) | (~$greatereq(tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))), 0))))))), introduced(assumption)).
% 0.98/0.96 tff(534,plain,
% 0.98/0.96 (((~![B1: array_int, B2: array_int, Pos: $int] : (~((~((~eq_board1(B1, B2, Pos)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0) | ($sum(tb2t(get2(int, t2tb1(B2), Q)), $product(-1, tb2t(get2(int, t2tb1(B1), Q)))) = 0)))) | (~(eq_board1(B1, B2, Pos) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_0(Pos, B2, B1))), 0) | ($sum(tb2t(get2(int, t2tb1(B2), tptp_fun_Q_0(Pos, B2, B1))), $product(-1, tb2t(get2(int, t2tb1(B1), tptp_fun_Q_0(Pos, B2, B1))))) = 0) | (~$greatereq(tptp_fun_Q_0(Pos, B2, B1), 0))))))))) | (~((~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t(t2tb(Pos!4)))) | ![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, tb2t(t2tb(Pos!4)))), 0) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))), Q)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)))) = 0)))) | (~(eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t(t2tb(Pos!4))) | (~($lesseq($sum(tb2t(t2tb(Pos!4)), $product(-1, tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))), 0) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))), tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))))) = 0) | (~$greatereq(tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))), 0))))))))) <=> ((~![B1: array_int, B2: array_int, Pos: $int] : (~((~((~eq_board1(B1, B2, Pos)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0) | ($sum(tb2t(get2(int, t2tb1(B2), Q)), $product(-1, tb2t(get2(int, t2tb1(B1), Q)))) = 0)))) | (~(eq_board1(B1, B2, Pos) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_0(Pos, B2, B1))), 0) | ($sum(tb2t(get2(int, t2tb1(B2), tptp_fun_Q_0(Pos, B2, B1))), $product(-1, tb2t(get2(int, t2tb1(B1), tptp_fun_Q_0(Pos, B2, B1))))) = 0) | (~$greatereq(tptp_fun_Q_0(Pos, B2, B1), 0))))))))) | (~((~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t(t2tb(Pos!4)))) | ![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, tb2t(t2tb(Pos!4)))), 0) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))), Q)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)))) = 0)))) | (~(eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t(t2tb(Pos!4))) | (~($lesseq($sum(tb2t(t2tb(Pos!4)), $product(-1, tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))), 0) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))), tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))))) = 0) | (~$greatereq(tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))), 0)))))))))),
% 0.98/0.96 inference(rewrite,[status(thm)],[])).
% 0.98/0.96 tff(535,plain,
% 0.98/0.96 ((~((~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t(t2tb(Pos!4)))) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(tb2t(t2tb(Pos!4)), $product(-1, Q)), 0) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))), Q)))) = 0)))) | (~(eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t(t2tb(Pos!4))) | (~($lesseq($sum(tb2t(t2tb(Pos!4)), $product(-1, tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))), 0) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))), tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))))) = 0) | (~$greatereq(tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))), 0)))))))) <=> (~((~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t(t2tb(Pos!4)))) | ![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, tb2t(t2tb(Pos!4)))), 0) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))), Q)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)))) = 0)))) | (~(eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t(t2tb(Pos!4))) | (~($lesseq($sum(tb2t(t2tb(Pos!4)), $product(-1, tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))), 0) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))), tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))))) = 0) | (~$greatereq(tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))), 0))))))))),
% 0.98/0.96 inference(rewrite,[status(thm)],[])).
% 0.98/0.96 tff(536,plain,
% 0.98/0.96 (((~![B1: array_int, B2: array_int, Pos: $int] : (~((~((~eq_board1(B1, B2, Pos)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0) | ($sum(tb2t(get2(int, t2tb1(B2), Q)), $product(-1, tb2t(get2(int, t2tb1(B1), Q)))) = 0)))) | (~(eq_board1(B1, B2, Pos) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_0(Pos, B2, B1))), 0) | ($sum(tb2t(get2(int, t2tb1(B2), tptp_fun_Q_0(Pos, B2, B1))), $product(-1, tb2t(get2(int, t2tb1(B1), tptp_fun_Q_0(Pos, B2, B1))))) = 0) | (~$greatereq(tptp_fun_Q_0(Pos, B2, B1), 0))))))))) | (~((~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t(t2tb(Pos!4)))) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(tb2t(t2tb(Pos!4)), $product(-1, Q)), 0) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))), Q)))) = 0)))) | (~(eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t(t2tb(Pos!4))) | (~($lesseq($sum(tb2t(t2tb(Pos!4)), $product(-1, tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))), 0) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))), tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))))) = 0) | (~$greatereq(tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))), 0))))))))) <=> ((~![B1: array_int, B2: array_int, Pos: $int] : (~((~((~eq_board1(B1, B2, Pos)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0) | ($sum(tb2t(get2(int, t2tb1(B2), Q)), $product(-1, tb2t(get2(int, t2tb1(B1), Q)))) = 0)))) | (~(eq_board1(B1, B2, Pos) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_0(Pos, B2, B1))), 0) | ($sum(tb2t(get2(int, t2tb1(B2), tptp_fun_Q_0(Pos, B2, B1))), $product(-1, tb2t(get2(int, t2tb1(B1), tptp_fun_Q_0(Pos, B2, B1))))) = 0) | (~$greatereq(tptp_fun_Q_0(Pos, B2, B1), 0))))))))) | (~((~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t(t2tb(Pos!4)))) | ![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, tb2t(t2tb(Pos!4)))), 0) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))), Q)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)))) = 0)))) | (~(eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t(t2tb(Pos!4))) | (~($lesseq($sum(tb2t(t2tb(Pos!4)), $product(-1, tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))), 0) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))), tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))))) = 0) | (~$greatereq(tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))), 0)))))))))),
% 0.98/0.96 inference(monotonicity,[status(thm)],[535])).
% 0.98/0.96 tff(537,plain,
% 0.98/0.96 (((~![B1: array_int, B2: array_int, Pos: $int] : (~((~((~eq_board1(B1, B2, Pos)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0) | ($sum(tb2t(get2(int, t2tb1(B2), Q)), $product(-1, tb2t(get2(int, t2tb1(B1), Q)))) = 0)))) | (~(eq_board1(B1, B2, Pos) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_0(Pos, B2, B1))), 0) | ($sum(tb2t(get2(int, t2tb1(B2), tptp_fun_Q_0(Pos, B2, B1))), $product(-1, tb2t(get2(int, t2tb1(B1), tptp_fun_Q_0(Pos, B2, B1))))) = 0) | (~$greatereq(tptp_fun_Q_0(Pos, B2, B1), 0))))))))) | (~((~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t(t2tb(Pos!4)))) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(tb2t(t2tb(Pos!4)), $product(-1, Q)), 0) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))), Q)))) = 0)))) | (~(eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t(t2tb(Pos!4))) | (~($lesseq($sum(tb2t(t2tb(Pos!4)), $product(-1, tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))), 0) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))), tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))))) = 0) | (~$greatereq(tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))), 0))))))))) <=> ((~![B1: array_int, B2: array_int, Pos: $int] : (~((~((~eq_board1(B1, B2, Pos)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0) | ($sum(tb2t(get2(int, t2tb1(B2), Q)), $product(-1, tb2t(get2(int, t2tb1(B1), Q)))) = 0)))) | (~(eq_board1(B1, B2, Pos) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_0(Pos, B2, B1))), 0) | ($sum(tb2t(get2(int, t2tb1(B2), tptp_fun_Q_0(Pos, B2, B1))), $product(-1, tb2t(get2(int, t2tb1(B1), tptp_fun_Q_0(Pos, B2, B1))))) = 0) | (~$greatereq(tptp_fun_Q_0(Pos, B2, B1), 0))))))))) | (~((~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t(t2tb(Pos!4)))) | ![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, tb2t(t2tb(Pos!4)))), 0) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))), Q)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)))) = 0)))) | (~(eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t(t2tb(Pos!4))) | (~($lesseq($sum(tb2t(t2tb(Pos!4)), $product(-1, tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))), 0) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))), tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))))) = 0) | (~$greatereq(tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))), 0)))))))))),
% 0.98/0.97 inference(transitivity,[status(thm)],[536, 534])).
% 0.98/0.97 tff(538,plain,
% 0.98/0.97 ((~![B1: array_int, B2: array_int, Pos: $int] : (~((~((~eq_board1(B1, B2, Pos)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0) | ($sum(tb2t(get2(int, t2tb1(B2), Q)), $product(-1, tb2t(get2(int, t2tb1(B1), Q)))) = 0)))) | (~(eq_board1(B1, B2, Pos) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_0(Pos, B2, B1))), 0) | ($sum(tb2t(get2(int, t2tb1(B2), tptp_fun_Q_0(Pos, B2, B1))), $product(-1, tb2t(get2(int, t2tb1(B1), tptp_fun_Q_0(Pos, B2, B1))))) = 0) | (~$greatereq(tptp_fun_Q_0(Pos, B2, B1), 0))))))))) | (~((~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t(t2tb(Pos!4)))) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(tb2t(t2tb(Pos!4)), $product(-1, Q)), 0) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))), Q)))) = 0)))) | (~(eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t(t2tb(Pos!4))) | (~($lesseq($sum(tb2t(t2tb(Pos!4)), $product(-1, tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))), 0) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))), tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))))) = 0) | (~$greatereq(tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))), 0))))))))),
% 0.98/0.97 inference(quant_inst,[status(thm)],[])).
% 0.98/0.97 tff(539,plain,
% 0.98/0.97 ((~![B1: array_int, B2: array_int, Pos: $int] : (~((~((~eq_board1(B1, B2, Pos)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0) | ($sum(tb2t(get2(int, t2tb1(B2), Q)), $product(-1, tb2t(get2(int, t2tb1(B1), Q)))) = 0)))) | (~(eq_board1(B1, B2, Pos) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_0(Pos, B2, B1))), 0) | ($sum(tb2t(get2(int, t2tb1(B2), tptp_fun_Q_0(Pos, B2, B1))), $product(-1, tb2t(get2(int, t2tb1(B1), tptp_fun_Q_0(Pos, B2, B1))))) = 0) | (~$greatereq(tptp_fun_Q_0(Pos, B2, B1), 0))))))))) | (~((~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t(t2tb(Pos!4)))) | ![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, tb2t(t2tb(Pos!4)))), 0) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))), Q)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)))) = 0)))) | (~(eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t(t2tb(Pos!4))) | (~($lesseq($sum(tb2t(t2tb(Pos!4)), $product(-1, tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))), 0) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))), tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))))) = 0) | (~$greatereq(tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))), 0))))))))),
% 0.98/0.97 inference(modus_ponens,[status(thm)],[538, 537])).
% 0.98/0.97 tff(540,plain,
% 0.98/0.97 ($false),
% 0.98/0.97 inference(unit_resolution,[status(thm)],[539, 297, 533])).
% 0.98/0.97 tff(541,plain,(~((~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t(t2tb(Pos!4)))) | ![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, tb2t(t2tb(Pos!4)))), 0) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))), Q)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)))) = 0)))) | (~(eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t(t2tb(Pos!4))) | (~($lesseq($sum(tb2t(t2tb(Pos!4)), $product(-1, tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))), 0) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))), tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))))) = 0) | (~$greatereq(tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))), 0)))))))), inference(lemma,lemma(discharge,[]))).
% 1.02/0.97 tff(542,plain,
% 1.02/0.97 (((~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t(t2tb(Pos!4)))) | ![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, tb2t(t2tb(Pos!4)))), 0) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))), Q)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)))) = 0)))) | (~(eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t(t2tb(Pos!4))) | (~($lesseq($sum(tb2t(t2tb(Pos!4)), $product(-1, tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))), 0) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))), tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))))) = 0) | (~$greatereq(tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))), 0))))))) | (eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t(t2tb(Pos!4))) | (~($lesseq($sum(tb2t(t2tb(Pos!4)), $product(-1, tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))), 0) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))), tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))))) = 0) | (~$greatereq(tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))), 0)))))),
% 1.02/0.97 inference(tautology,[status(thm)],[])).
% 1.02/0.97 tff(543,plain,
% 1.02/0.97 (eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t(t2tb(Pos!4))) | (~($lesseq($sum(tb2t(t2tb(Pos!4)), $product(-1, tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))), 0) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))), tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))))) = 0) | (~$greatereq(tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))), 0))))),
% 1.02/0.97 inference(unit_resolution,[status(thm)],[542, 541])).
% 1.02/0.97 tff(544,plain,
% 1.02/0.97 ((~(eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t(t2tb(Pos!4))) | (~($lesseq($sum(tb2t(t2tb(Pos!4)), $product(-1, tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))), 0) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))), tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))))) = 0) | (~$greatereq(tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))), 0)))))) | eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t(t2tb(Pos!4))) | (~($lesseq($sum(tb2t(t2tb(Pos!4)), $product(-1, tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))), 0) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))), tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))))) = 0) | (~$greatereq(tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))), 0))))),
% 1.02/0.97 inference(tautology,[status(thm)],[])).
% 1.02/0.97 tff(545,plain,
% 1.02/0.97 (eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t(t2tb(Pos!4))) | (~($lesseq($sum(tb2t(t2tb(Pos!4)), $product(-1, tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))), 0) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))), tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))))))) = 0) | (~$greatereq(tptp_fun_Q_0(tb2t(t2tb(Pos!4)), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))), 0))))),
% 1.02/0.97 inference(unit_resolution,[status(thm)],[544, 543])).
% 1.02/0.97 tff(546,plain,
% 1.02/0.97 (eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t(t2tb(Pos!4)))),
% 1.02/0.97 inference(unit_resolution,[status(thm)],[545, 532])).
% 1.02/0.97 tff(547,plain,
% 1.02/0.97 (eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, N!5, t2tb2(tb2t2(set(int, int, t2tb2(Board2!10), t2tb(Pos!4), t2tb(I!11)))))), Pos!4)),
% 1.02/0.97 inference(modus_ponens,[status(thm)],[546, 397])).
% 1.02/0.97 tff(548,plain,
% 1.02/0.97 (eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)),
% 1.02/0.97 inference(modus_ponens,[status(thm)],[547, 375])).
% 1.02/0.97 tff(549,assumption,(~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)), introduced(assumption)).
% 1.02/0.97 tff(550,plain,
% 1.02/0.97 ($false),
% 1.02/0.97 inference(unit_resolution,[status(thm)],[549, 548])).
% 1.02/0.97 tff(551,plain,(eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)), inference(lemma,lemma(discharge,[]))).
% 1.02/0.97 tff(552,plain,
% 1.02/0.97 (^[B1: array_int, B2: array_int, Pos: $int] : refl(((~eq_board1(B1, B2, Pos)) | eq_board1(B2, B1, Pos)) <=> ((~eq_board1(B1, B2, Pos)) | eq_board1(B2, B1, Pos)))),
% 1.02/0.97 inference(bind,[status(th)],[])).
% 1.02/0.97 tff(553,plain,
% 1.02/0.97 (![B1: array_int, B2: array_int, Pos: $int] : ((~eq_board1(B1, B2, Pos)) | eq_board1(B2, B1, Pos)) <=> ![B1: array_int, B2: array_int, Pos: $int] : ((~eq_board1(B1, B2, Pos)) | eq_board1(B2, B1, Pos))),
% 1.02/0.97 inference(quant_intro,[status(thm)],[552])).
% 1.02/0.97 tff(554,plain,
% 1.02/0.97 (![B1: array_int, B2: array_int, Pos: $int] : ((~eq_board1(B1, B2, Pos)) | eq_board1(B2, B1, Pos)) <=> ![B1: array_int, B2: array_int, Pos: $int] : ((~eq_board1(B1, B2, Pos)) | eq_board1(B2, B1, Pos))),
% 1.02/0.97 inference(rewrite,[status(thm)],[])).
% 1.02/0.97 tff(555,plain,
% 1.02/0.97 (^[B1: array_int, B2: array_int, Pos: $int] : rewrite((eq_board1(B1, B2, Pos) => eq_board1(B2, B1, Pos)) <=> ((~eq_board1(B1, B2, Pos)) | eq_board1(B2, B1, Pos)))),
% 1.02/0.97 inference(bind,[status(th)],[])).
% 1.02/0.97 tff(556,plain,
% 1.02/0.97 (![B1: array_int, B2: array_int, Pos: $int] : (eq_board1(B1, B2, Pos) => eq_board1(B2, B1, Pos)) <=> ![B1: array_int, B2: array_int, Pos: $int] : ((~eq_board1(B1, B2, Pos)) | eq_board1(B2, B1, Pos))),
% 1.02/0.97 inference(quant_intro,[status(thm)],[555])).
% 1.02/0.97 tff(557,axiom,(![B1: array_int, B2: array_int, Pos: $int] : (eq_board1(B1, B2, Pos) => eq_board1(B2, B1, Pos))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','eq_board_sym')).
% 1.02/0.97 tff(558,plain,
% 1.02/0.97 (![B1: array_int, B2: array_int, Pos: $int] : ((~eq_board1(B1, B2, Pos)) | eq_board1(B2, B1, Pos))),
% 1.02/0.97 inference(modus_ponens,[status(thm)],[557, 556])).
% 1.02/0.97 tff(559,plain,
% 1.02/0.97 (![B1: array_int, B2: array_int, Pos: $int] : ((~eq_board1(B1, B2, Pos)) | eq_board1(B2, B1, Pos))),
% 1.02/0.97 inference(modus_ponens,[status(thm)],[558, 554])).
% 1.02/0.97 tff(560,plain,(
% 1.02/0.97 ![B1: array_int, B2: array_int, Pos: $int] : ((~eq_board1(B1, B2, Pos)) | eq_board1(B2, B1, Pos))),
% 1.02/0.97 inference(skolemize,[status(sab)],[559])).
% 1.02/0.97 tff(561,plain,
% 1.02/0.97 (![B1: array_int, B2: array_int, Pos: $int] : ((~eq_board1(B1, B2, Pos)) | eq_board1(B2, B1, Pos))),
% 1.02/0.97 inference(modus_ponens,[status(thm)],[560, 553])).
% 1.02/0.97 tff(562,plain,
% 1.02/0.97 (((~![B1: array_int, B2: array_int, Pos: $int] : ((~eq_board1(B1, B2, Pos)) | eq_board1(B2, B1, Pos))) | ((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), Pos!4))) <=> ((~![B1: array_int, B2: array_int, Pos: $int] : ((~eq_board1(B1, B2, Pos)) | eq_board1(B2, B1, Pos))) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), Pos!4))),
% 1.02/0.97 inference(rewrite,[status(thm)],[])).
% 1.02/0.97 tff(563,plain,
% 1.02/0.97 ((~![B1: array_int, B2: array_int, Pos: $int] : ((~eq_board1(B1, B2, Pos)) | eq_board1(B2, B1, Pos))) | ((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), Pos!4))),
% 1.02/0.97 inference(quant_inst,[status(thm)],[])).
% 1.02/0.97 tff(564,plain,
% 1.02/0.97 ((~![B1: array_int, B2: array_int, Pos: $int] : ((~eq_board1(B1, B2, Pos)) | eq_board1(B2, B1, Pos))) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), Pos!4)),
% 1.02/0.97 inference(modus_ponens,[status(thm)],[563, 562])).
% 1.02/0.97 tff(565,plain,
% 1.02/0.97 (eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), Pos!4)),
% 1.02/0.97 inference(unit_resolution,[status(thm)],[564, 561, 551])).
% 1.02/0.97 tff(566,assumption,(~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)), introduced(assumption)).
% 1.02/0.97 tff(567,plain,
% 1.02/0.97 ($greatereq(N!5, 1)),
% 1.02/0.97 inference(unit_resolution,[status(thm)],[328, 48])).
% 1.02/0.97 tff(568,plain,
% 1.02/0.97 ($greatereq(N!5, 1) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!9, t2tb2(B1!8))), N!5)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, B!9, t2tb2(B1!8))), Pos!4)) | (~is_board1(tb2t1(mk_array1(int, B!9, t2tb2(B1!8))), N!5)) | (~($sum(N!5, $product(-1, B!9)) = 0))))))),
% 1.02/0.97 inference(unit_resolution,[status(thm)],[330, 567])).
% 1.02/0.97 tff(569,plain,
% 1.02/0.97 (~($sum(Pos!4, $product(-1, N!5)) = 0)),
% 1.02/0.97 inference(unit_resolution,[status(thm)],[332, 48])).
% 1.02/0.97 tff(570,plain,
% 1.02/0.97 ((~($sum(Pos!4, $product(-1, N!5)) = 0)) | solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), N!5)),
% 1.02/0.97 inference(unit_resolution,[status(thm)],[334, 569])).
% 1.02/0.97 tff(571,plain,
% 1.02/0.97 (~(($sum(Pos!4, $product(-1, N!5)) = 0) | (~((~($greatereq(N!5, 1) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!9, t2tb2(B1!8))), N!5)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, B!9, t2tb2(B1!8))), Pos!4)) | (~is_board1(tb2t1(mk_array1(int, B!9, t2tb2(B1!8))), N!5)) | (~($sum(N!5, $product(-1, B!9)) = 0)))))))) | (~((~$greatereq(N!5, 1)) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~$greatereq(I!11, 0)) | (~$greatereq($sum(N!5, $product(-1, I!11)), 1)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos!4)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), 0)) | $greatereq($sum(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), $product(-1, I!11)), 0))) | (~($greatereq($sum(Pos!4, $product(-1, Board!7)), 0) | (~$greatereq(Board!7, 0)) | (~$greatereq(Pos!4, 0)) | (~((~$greatereq(Board!7, 0)) | (~(Board3!12 = tb2t2(set(int, int, t2tb2(Board2!10), t2tb(Pos!4), t2tb(I!11))))) | (~($greatereq($sum(Pos!4, $product(-1, Board!7)), 0) | (~$greatereq(Pos!4, 0)) | (~(((~(Result!13 = true1)) <=> is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | (~((~((Result!13 = true1) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Pos!4)) | (~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~($sum(N!5, $product(-1, B!19)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))), 0)))))))) | (~((~(Result!13 = true1)) | (~((~$lesseq($sum(Pos!4, $product(-1, N!5)), 0)) | (~($sum(N!5, $product(-1, Board!7)) = 0)) | (~$greatereq(Pos!4, -1)) | (~$lesseq($sum(Pos!4, $product(-1, N!5)), -1)) | (~solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~((~$greatereq(Board!7, 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B, t2tb2(B1))), $sum(1, Pos!4))))) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), Pos!4)) | (~($sum(N!5, $product(-1, B!16)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))), 0)))))))))))))))))))))))) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~$greatereq(Board!7, 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), Pos!4)) | (~($sum(N!5, $product(-1, B!21)) = 0)))))) | (~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | $lesseq($sum(N!5, $product(-1, tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))))), 0) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos!4)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), 0)))))))))))))),
% 1.02/0.98 inference(unit_resolution,[status(thm)],[41, 570])).
% 1.02/0.98 tff(572,plain,
% 1.02/0.98 ((~($greatereq(N!5, 1) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!9, t2tb2(B1!8))), N!5)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, B!9, t2tb2(B1!8))), Pos!4)) | (~is_board1(tb2t1(mk_array1(int, B!9, t2tb2(B1!8))), N!5)) | (~($sum(N!5, $product(-1, B!9)) = 0)))))))) | (~((~$greatereq(N!5, 1)) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~$greatereq(I!11, 0)) | (~$greatereq($sum(N!5, $product(-1, I!11)), 1)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos!4)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), 0)) | $greatereq($sum(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), $product(-1, I!11)), 0))) | (~($greatereq($sum(Pos!4, $product(-1, Board!7)), 0) | (~$greatereq(Board!7, 0)) | (~$greatereq(Pos!4, 0)) | (~((~$greatereq(Board!7, 0)) | (~(Board3!12 = tb2t2(set(int, int, t2tb2(Board2!10), t2tb(Pos!4), t2tb(I!11))))) | (~($greatereq($sum(Pos!4, $product(-1, Board!7)), 0) | (~$greatereq(Pos!4, 0)) | (~(((~(Result!13 = true1)) <=> is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | (~((~((Result!13 = true1) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Pos!4)) | (~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~($sum(N!5, $product(-1, B!19)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))), 0)))))))) | (~((~(Result!13 = true1)) | (~((~$lesseq($sum(Pos!4, $product(-1, N!5)), 0)) | (~($sum(N!5, $product(-1, Board!7)) = 0)) | (~$greatereq(Pos!4, -1)) | (~$lesseq($sum(Pos!4, $product(-1, N!5)), -1)) | (~solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~((~$greatereq(Board!7, 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B, t2tb2(B1))), $sum(1, Pos!4))))) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), Pos!4)) | (~($sum(N!5, $product(-1, B!16)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))), 0)))))))))))))))))))))))) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~$greatereq(Board!7, 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), Pos!4)) | (~($sum(N!5, $product(-1, B!21)) = 0)))))) | (~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | $lesseq($sum(N!5, $product(-1, tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))))), 0) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos!4)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), 0))))))))))),
% 1.02/0.98 inference(unit_resolution,[status(thm)],[337, 571])).
% 1.02/0.98 tff(573,plain,
% 1.02/0.98 (~((~$greatereq(N!5, 1)) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~$greatereq(I!11, 0)) | (~$greatereq($sum(N!5, $product(-1, I!11)), 1)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos!4)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), 0)) | $greatereq($sum(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), $product(-1, I!11)), 0))) | (~($greatereq($sum(Pos!4, $product(-1, Board!7)), 0) | (~$greatereq(Board!7, 0)) | (~$greatereq(Pos!4, 0)) | (~((~$greatereq(Board!7, 0)) | (~(Board3!12 = tb2t2(set(int, int, t2tb2(Board2!10), t2tb(Pos!4), t2tb(I!11))))) | (~($greatereq($sum(Pos!4, $product(-1, Board!7)), 0) | (~$greatereq(Pos!4, 0)) | (~(((~(Result!13 = true1)) <=> is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | (~((~((Result!13 = true1) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Pos!4)) | (~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~($sum(N!5, $product(-1, B!19)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))), 0)))))))) | (~((~(Result!13 = true1)) | (~((~$lesseq($sum(Pos!4, $product(-1, N!5)), 0)) | (~($sum(N!5, $product(-1, Board!7)) = 0)) | (~$greatereq(Pos!4, -1)) | (~$lesseq($sum(Pos!4, $product(-1, N!5)), -1)) | (~solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~((~$greatereq(Board!7, 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B, t2tb2(B1))), $sum(1, Pos!4))))) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), Pos!4)) | (~($sum(N!5, $product(-1, B!16)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))), 0)))))))))))))))))))))))) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~$greatereq(Board!7, 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), Pos!4)) | (~($sum(N!5, $product(-1, B!21)) = 0)))))) | (~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | $lesseq($sum(N!5, $product(-1, tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))))), 0) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos!4)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), 0)))))))))),
% 1.02/0.98 inference(unit_resolution,[status(thm)],[339, 572, 568])).
% 1.02/0.98 tff(574,plain,
% 1.02/0.98 ((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~$greatereq(I!11, 0)) | (~$greatereq($sum(N!5, $product(-1, I!11)), 1)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos!4)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), 0)) | $greatereq($sum(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), $product(-1, I!11)), 0))) | (~($greatereq($sum(Pos!4, $product(-1, Board!7)), 0) | (~$greatereq(Board!7, 0)) | (~$greatereq(Pos!4, 0)) | (~((~$greatereq(Board!7, 0)) | (~(Board3!12 = tb2t2(set(int, int, t2tb2(Board2!10), t2tb(Pos!4), t2tb(I!11))))) | (~($greatereq($sum(Pos!4, $product(-1, Board!7)), 0) | (~$greatereq(Pos!4, 0)) | (~(((~(Result!13 = true1)) <=> is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | (~((~((Result!13 = true1) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Pos!4)) | (~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~($sum(N!5, $product(-1, B!19)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))), 0)))))))) | (~((~(Result!13 = true1)) | (~((~$lesseq($sum(Pos!4, $product(-1, N!5)), 0)) | (~($sum(N!5, $product(-1, Board!7)) = 0)) | (~$greatereq(Pos!4, -1)) | (~$lesseq($sum(Pos!4, $product(-1, N!5)), -1)) | (~solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~((~$greatereq(Board!7, 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B, t2tb2(B1))), $sum(1, Pos!4))))) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), Pos!4)) | (~($sum(N!5, $product(-1, B!16)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))), 0)))))))))))))))))))))))) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~$greatereq(Board!7, 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), N!5)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B!21, t2tb2(B1!20))), Pos!4)) | (~($sum(N!5, $product(-1, B!21)) = 0)))))) | (~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | $lesseq($sum(N!5, $product(-1, tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))))), 0) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos!4)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), 0))))))),
% 1.02/0.98 inference(unit_resolution,[status(thm)],[341, 573])).
% 1.02/0.98 tff(575,plain,
% 1.02/0.98 (~((~$greatereq(I!11, 0)) | (~$greatereq($sum(N!5, $product(-1, I!11)), 1)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos!4)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), 0)) | $greatereq($sum(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), $product(-1, I!11)), 0))) | (~($greatereq($sum(Pos!4, $product(-1, Board!7)), 0) | (~$greatereq(Board!7, 0)) | (~$greatereq(Pos!4, 0)) | (~((~$greatereq(Board!7, 0)) | (~(Board3!12 = tb2t2(set(int, int, t2tb2(Board2!10), t2tb(Pos!4), t2tb(I!11))))) | (~($greatereq($sum(Pos!4, $product(-1, Board!7)), 0) | (~$greatereq(Pos!4, 0)) | (~(((~(Result!13 = true1)) <=> is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | (~((~((Result!13 = true1) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Pos!4)) | (~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~($sum(N!5, $product(-1, B!19)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))), 0)))))))) | (~((~(Result!13 = true1)) | (~((~$lesseq($sum(Pos!4, $product(-1, N!5)), 0)) | (~($sum(N!5, $product(-1, Board!7)) = 0)) | (~$greatereq(Pos!4, -1)) | (~$lesseq($sum(Pos!4, $product(-1, N!5)), -1)) | (~solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~((~$greatereq(Board!7, 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B, t2tb2(B1))), $sum(1, Pos!4))))) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), Pos!4)) | (~($sum(N!5, $product(-1, B!16)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))), 0)))))))))))))))))))))))),
% 1.02/0.98 inference(unit_resolution,[status(thm)],[325, 574, 266])).
% 1.02/0.98 tff(576,plain,
% 1.02/0.98 (((~$greatereq(I!11, 0)) | (~$greatereq($sum(N!5, $product(-1, I!11)), 1)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos!4)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), 0)) | $greatereq($sum(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), $product(-1, I!11)), 0))) | (~($greatereq($sum(Pos!4, $product(-1, Board!7)), 0) | (~$greatereq(Board!7, 0)) | (~$greatereq(Pos!4, 0)) | (~((~$greatereq(Board!7, 0)) | (~(Board3!12 = tb2t2(set(int, int, t2tb2(Board2!10), t2tb(Pos!4), t2tb(I!11))))) | (~($greatereq($sum(Pos!4, $product(-1, Board!7)), 0) | (~$greatereq(Pos!4, 0)) | (~(((~(Result!13 = true1)) <=> is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | (~((~((Result!13 = true1) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Pos!4)) | (~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~($sum(N!5, $product(-1, B!19)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))), 0)))))))) | (~((~(Result!13 = true1)) | (~((~$lesseq($sum(Pos!4, $product(-1, N!5)), 0)) | (~($sum(N!5, $product(-1, Board!7)) = 0)) | (~$greatereq(Pos!4, -1)) | (~$lesseq($sum(Pos!4, $product(-1, N!5)), -1)) | (~solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~((~$greatereq(Board!7, 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B, t2tb2(B1))), $sum(1, Pos!4))))) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), Pos!4)) | (~($sum(N!5, $product(-1, B!16)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))), 0))))))))))))))))))))))) | eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)),
% 1.02/0.98 inference(tautology,[status(thm)],[])).
% 1.02/0.98 tff(577,plain,
% 1.02/0.98 (eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)),
% 1.02/0.98 inference(unit_resolution,[status(thm)],[576, 575])).
% 1.02/0.98 tff(578,plain,
% 1.02/0.98 (^[B1: array_int, B2: array_int, B3: array_int, Pos: $int] : refl((eq_board1(B1, B3, Pos) | (~eq_board1(B2, B3, Pos)) | (~eq_board1(B1, B2, Pos))) <=> (eq_board1(B1, B3, Pos) | (~eq_board1(B2, B3, Pos)) | (~eq_board1(B1, B2, Pos))))),
% 1.02/0.98 inference(bind,[status(th)],[])).
% 1.02/0.98 tff(579,plain,
% 1.02/0.98 (![B1: array_int, B2: array_int, B3: array_int, Pos: $int] : (eq_board1(B1, B3, Pos) | (~eq_board1(B2, B3, Pos)) | (~eq_board1(B1, B2, Pos))) <=> ![B1: array_int, B2: array_int, B3: array_int, Pos: $int] : (eq_board1(B1, B3, Pos) | (~eq_board1(B2, B3, Pos)) | (~eq_board1(B1, B2, Pos)))),
% 1.02/0.98 inference(quant_intro,[status(thm)],[578])).
% 1.02/0.98 tff(580,plain,
% 1.02/0.98 (![B1: array_int, B2: array_int, B3: array_int, Pos: $int] : (eq_board1(B1, B3, Pos) | (~eq_board1(B2, B3, Pos)) | (~eq_board1(B1, B2, Pos))) <=> ![B1: array_int, B2: array_int, B3: array_int, Pos: $int] : (eq_board1(B1, B3, Pos) | (~eq_board1(B2, B3, Pos)) | (~eq_board1(B1, B2, Pos)))),
% 1.02/0.98 inference(rewrite,[status(thm)],[])).
% 1.02/0.98 tff(581,plain,
% 1.02/0.98 (^[B1: array_int, B2: array_int, B3: array_int, Pos: $int] : trans(monotonicity(rewrite((eq_board1(B2, B3, Pos) => eq_board1(B1, B3, Pos)) <=> ((~eq_board1(B2, B3, Pos)) | eq_board1(B1, B3, Pos))), ((eq_board1(B1, B2, Pos) => (eq_board1(B2, B3, Pos) => eq_board1(B1, B3, Pos))) <=> (eq_board1(B1, B2, Pos) => ((~eq_board1(B2, B3, Pos)) | eq_board1(B1, B3, Pos))))), rewrite((eq_board1(B1, B2, Pos) => ((~eq_board1(B2, B3, Pos)) | eq_board1(B1, B3, Pos))) <=> (eq_board1(B1, B3, Pos) | (~eq_board1(B2, B3, Pos)) | (~eq_board1(B1, B2, Pos)))), ((eq_board1(B1, B2, Pos) => (eq_board1(B2, B3, Pos) => eq_board1(B1, B3, Pos))) <=> (eq_board1(B1, B3, Pos) | (~eq_board1(B2, B3, Pos)) | (~eq_board1(B1, B2, Pos)))))),
% 1.02/0.98 inference(bind,[status(th)],[])).
% 1.02/0.98 tff(582,plain,
% 1.02/0.98 (![B1: array_int, B2: array_int, B3: array_int, Pos: $int] : (eq_board1(B1, B2, Pos) => (eq_board1(B2, B3, Pos) => eq_board1(B1, B3, Pos))) <=> ![B1: array_int, B2: array_int, B3: array_int, Pos: $int] : (eq_board1(B1, B3, Pos) | (~eq_board1(B2, B3, Pos)) | (~eq_board1(B1, B2, Pos)))),
% 1.02/0.98 inference(quant_intro,[status(thm)],[581])).
% 1.02/0.98 tff(583,axiom,(![B1: array_int, B2: array_int, B3: array_int, Pos: $int] : (eq_board1(B1, B2, Pos) => (eq_board1(B2, B3, Pos) => eq_board1(B1, B3, Pos)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','eq_board_trans')).
% 1.02/0.98 tff(584,plain,
% 1.02/0.98 (![B1: array_int, B2: array_int, B3: array_int, Pos: $int] : (eq_board1(B1, B3, Pos) | (~eq_board1(B2, B3, Pos)) | (~eq_board1(B1, B2, Pos)))),
% 1.02/0.98 inference(modus_ponens,[status(thm)],[583, 582])).
% 1.02/0.98 tff(585,plain,
% 1.02/0.98 (![B1: array_int, B2: array_int, B3: array_int, Pos: $int] : (eq_board1(B1, B3, Pos) | (~eq_board1(B2, B3, Pos)) | (~eq_board1(B1, B2, Pos)))),
% 1.02/0.98 inference(modus_ponens,[status(thm)],[584, 580])).
% 1.02/0.98 tff(586,plain,(
% 1.02/0.98 ![B1: array_int, B2: array_int, B3: array_int, Pos: $int] : (eq_board1(B1, B3, Pos) | (~eq_board1(B2, B3, Pos)) | (~eq_board1(B1, B2, Pos)))),
% 1.02/0.98 inference(skolemize,[status(sab)],[585])).
% 1.02/0.98 tff(587,plain,
% 1.02/0.98 (![B1: array_int, B2: array_int, B3: array_int, Pos: $int] : (eq_board1(B1, B3, Pos) | (~eq_board1(B2, B3, Pos)) | (~eq_board1(B1, B2, Pos)))),
% 1.02/0.98 inference(modus_ponens,[status(thm)],[586, 579])).
% 1.02/0.98 tff(588,plain,
% 1.02/0.98 (((~![B1: array_int, B2: array_int, B3: array_int, Pos: $int] : (eq_board1(B1, B3, Pos) | (~eq_board1(B2, B3, Pos)) | (~eq_board1(B1, B2, Pos)))) | (eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), Pos!4)))) <=> ((~![B1: array_int, B2: array_int, B3: array_int, Pos: $int] : (eq_board1(B1, B3, Pos) | (~eq_board1(B2, B3, Pos)) | (~eq_board1(B1, B2, Pos)))) | eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), Pos!4)))),
% 1.02/0.98 inference(rewrite,[status(thm)],[])).
% 1.02/0.98 tff(589,plain,
% 1.02/0.98 ((~![B1: array_int, B2: array_int, B3: array_int, Pos: $int] : (eq_board1(B1, B3, Pos) | (~eq_board1(B2, B3, Pos)) | (~eq_board1(B1, B2, Pos)))) | (eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), Pos!4)))),
% 1.02/0.98 inference(quant_inst,[status(thm)],[])).
% 1.02/0.98 tff(590,plain,
% 1.02/0.98 ((~![B1: array_int, B2: array_int, B3: array_int, Pos: $int] : (eq_board1(B1, B3, Pos) | (~eq_board1(B2, B3, Pos)) | (~eq_board1(B1, B2, Pos)))) | eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), Pos!4))),
% 1.02/0.98 inference(modus_ponens,[status(thm)],[589, 588])).
% 1.02/0.98 tff(591,plain,
% 1.02/0.98 ($false),
% 1.02/0.98 inference(unit_resolution,[status(thm)],[590, 587, 577, 566, 565])).
% 1.02/0.98 tff(592,plain,(eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)), inference(lemma,lemma(discharge,[]))).
% 1.02/0.98 tff(593,plain,
% 1.02/0.98 ((~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Pos!4)) | (~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~($sum(N!5, $product(-1, B!19)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))), 0)))))) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Pos!4)) | (~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~($sum(N!5, $product(-1, B!19)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))), 0))))),
% 1.02/0.98 inference(tautology,[status(thm)],[])).
% 1.02/0.98 tff(594,plain,
% 1.02/0.98 ((~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Pos!4)) | (~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~($sum(N!5, $product(-1, B!19)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))), 0)))))) | (~((~solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Pos!4)) | (~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~($sum(N!5, $product(-1, B!19)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))), 0))))),
% 1.02/0.98 inference(unit_resolution,[status(thm)],[593, 592])).
% 1.02/0.98 tff(595,plain,
% 1.02/0.98 (~((~solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Pos!4)) | (~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~($sum(N!5, $product(-1, B!19)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))), 0)))),
% 1.02/0.99 inference(unit_resolution,[status(thm)],[594, 363])).
% 1.02/0.99 tff(596,plain,
% 1.02/0.99 (((~solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Pos!4)) | (~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~($sum(N!5, $product(-1, B!19)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))), 0))) | eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Pos!4)),
% 1.02/0.99 inference(tautology,[status(thm)],[])).
% 1.02/0.99 tff(597,plain,
% 1.02/0.99 (eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Pos!4)),
% 1.02/0.99 inference(unit_resolution,[status(thm)],[596, 595])).
% 1.02/0.99 tff(598,assumption,(~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Pos!4)), introduced(assumption)).
% 1.02/0.99 tff(599,assumption,(eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Pos!4)), introduced(assumption)).
% 1.02/0.99 tff(600,plain,
% 1.02/0.99 (((~![B1: array_int, B2: array_int, B3: array_int, Pos: $int] : (eq_board1(B1, B3, Pos) | (~eq_board1(B2, B3, Pos)) | (~eq_board1(B1, B2, Pos)))) | ((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Pos!4)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Pos!4))) <=> ((~![B1: array_int, B2: array_int, B3: array_int, Pos: $int] : (eq_board1(B1, B3, Pos) | (~eq_board1(B2, B3, Pos)) | (~eq_board1(B1, B2, Pos)))) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Pos!4)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Pos!4))),
% 1.02/0.99 inference(rewrite,[status(thm)],[])).
% 1.02/0.99 tff(601,plain,
% 1.02/0.99 ((eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Pos!4) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Pos!4)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4))) <=> ((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Pos!4)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Pos!4))),
% 1.02/0.99 inference(rewrite,[status(thm)],[])).
% 1.02/0.99 tff(602,plain,
% 1.02/0.99 (((~![B1: array_int, B2: array_int, B3: array_int, Pos: $int] : (eq_board1(B1, B3, Pos) | (~eq_board1(B2, B3, Pos)) | (~eq_board1(B1, B2, Pos)))) | (eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Pos!4) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Pos!4)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)))) <=> ((~![B1: array_int, B2: array_int, B3: array_int, Pos: $int] : (eq_board1(B1, B3, Pos) | (~eq_board1(B2, B3, Pos)) | (~eq_board1(B1, B2, Pos)))) | ((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Pos!4)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Pos!4)))),
% 1.02/0.99 inference(monotonicity,[status(thm)],[601])).
% 1.02/0.99 tff(603,plain,
% 1.02/0.99 (((~![B1: array_int, B2: array_int, B3: array_int, Pos: $int] : (eq_board1(B1, B3, Pos) | (~eq_board1(B2, B3, Pos)) | (~eq_board1(B1, B2, Pos)))) | (eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Pos!4) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Pos!4)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)))) <=> ((~![B1: array_int, B2: array_int, B3: array_int, Pos: $int] : (eq_board1(B1, B3, Pos) | (~eq_board1(B2, B3, Pos)) | (~eq_board1(B1, B2, Pos)))) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Pos!4)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Pos!4))),
% 1.02/0.99 inference(transitivity,[status(thm)],[602, 600])).
% 1.02/0.99 tff(604,plain,
% 1.02/0.99 ((~![B1: array_int, B2: array_int, B3: array_int, Pos: $int] : (eq_board1(B1, B3, Pos) | (~eq_board1(B2, B3, Pos)) | (~eq_board1(B1, B2, Pos)))) | (eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Pos!4) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Pos!4)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)))),
% 1.02/0.99 inference(quant_inst,[status(thm)],[])).
% 1.02/0.99 tff(605,plain,
% 1.02/0.99 ((~![B1: array_int, B2: array_int, B3: array_int, Pos: $int] : (eq_board1(B1, B3, Pos) | (~eq_board1(B2, B3, Pos)) | (~eq_board1(B1, B2, Pos)))) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Pos!4)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Pos!4)),
% 1.02/0.99 inference(modus_ponens,[status(thm)],[604, 603])).
% 1.02/0.99 tff(606,plain,
% 1.02/0.99 ($false),
% 1.02/0.99 inference(unit_resolution,[status(thm)],[605, 587, 599, 551, 598])).
% 1.02/0.99 tff(607,plain,(eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Pos!4) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Pos!4))), inference(lemma,lemma(discharge,[]))).
% 1.02/0.99 tff(608,plain,
% 1.02/0.99 (eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Pos!4)),
% 1.02/0.99 inference(unit_resolution,[status(thm)],[607, 597])).
% 1.02/0.99 tff(609,plain,
% 1.02/0.99 (((~solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Pos!4)) | (~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~($sum(N!5, $product(-1, B!19)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))), 0))) | $greatereq(tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))), 0)),
% 1.02/0.99 inference(tautology,[status(thm)],[])).
% 1.02/0.99 tff(610,plain,
% 1.02/0.99 ($greatereq(tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))), 0)),
% 1.02/0.99 inference(unit_resolution,[status(thm)],[609, 595])).
% 1.02/0.99 tff(611,plain,
% 1.02/0.99 (((~solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Pos!4)) | (~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~($sum(N!5, $product(-1, B!19)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))), 0))) | ($sum(N!5, $product(-1, B!19)) = 0)),
% 1.02/0.99 inference(tautology,[status(thm)],[])).
% 1.02/0.99 tff(612,plain,
% 1.02/0.99 ($sum(N!5, $product(-1, B!19)) = 0),
% 1.02/0.99 inference(unit_resolution,[status(thm)],[611, 595])).
% 1.02/0.99 tff(613,plain,
% 1.02/0.99 (((~solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Pos!4)) | (~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~($sum(N!5, $product(-1, B!19)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))), 0))) | is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)),
% 1.02/0.99 inference(tautology,[status(thm)],[])).
% 1.02/0.99 tff(614,plain,
% 1.02/0.99 (is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)),
% 1.02/0.99 inference(unit_resolution,[status(thm)],[613, 595])).
% 1.02/0.99 tff(615,plain,
% 1.02/0.99 (((~solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Pos!4)) | (~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~($sum(N!5, $product(-1, B!19)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))), 0))) | solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)),
% 1.02/0.99 inference(tautology,[status(thm)],[])).
% 1.02/0.99 tff(616,plain,
% 1.02/0.99 (solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)),
% 1.02/0.99 inference(unit_resolution,[status(thm)],[615, 595])).
% 1.02/0.99 tff(617,plain,
% 1.02/0.99 (((~$greatereq(I!11, 0)) | (~$greatereq($sum(N!5, $product(-1, I!11)), 1)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos!4)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), 0)) | $greatereq($sum(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), $product(-1, I!11)), 0))) | (~($greatereq($sum(Pos!4, $product(-1, Board!7)), 0) | (~$greatereq(Board!7, 0)) | (~$greatereq(Pos!4, 0)) | (~((~$greatereq(Board!7, 0)) | (~(Board3!12 = tb2t2(set(int, int, t2tb2(Board2!10), t2tb(Pos!4), t2tb(I!11))))) | (~($greatereq($sum(Pos!4, $product(-1, Board!7)), 0) | (~$greatereq(Pos!4, 0)) | (~(((~(Result!13 = true1)) <=> is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | (~((~((Result!13 = true1) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Pos!4)) | (~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~($sum(N!5, $product(-1, B!19)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))), 0)))))))) | (~((~(Result!13 = true1)) | (~((~$lesseq($sum(Pos!4, $product(-1, N!5)), 0)) | (~($sum(N!5, $product(-1, Board!7)) = 0)) | (~$greatereq(Pos!4, -1)) | (~$lesseq($sum(Pos!4, $product(-1, N!5)), -1)) | (~solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~((~$greatereq(Board!7, 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B, t2tb2(B1))), $sum(1, Pos!4))))) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), Pos!4)) | (~($sum(N!5, $product(-1, B!16)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))), 0))))))))))))))))))))))) | ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos!4)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), 0)) | $greatereq($sum(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), $product(-1, I!11)), 0))),
% 1.02/0.99 inference(tautology,[status(thm)],[])).
% 1.02/0.99 tff(618,plain,
% 1.02/0.99 (![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos!4)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), 0)) | $greatereq($sum(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), $product(-1, I!11)), 0))),
% 1.02/0.99 inference(unit_resolution,[status(thm)],[617, 575])).
% 1.02/0.99 tff(619,plain,
% 1.02/0.99 (((~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos!4)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), 0)) | $greatereq($sum(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), $product(-1, I!11)), 0))) | ((~solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~($sum(N!5, $product(-1, B!19)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))), 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Pos!4)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))))), 0))) <=> ((~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos!4)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), 0)) | $greatereq($sum(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), $product(-1, I!11)), 0))) | (~solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~($sum(N!5, $product(-1, B!19)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))), 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Pos!4)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))))), 0))),
% 1.02/0.99 inference(rewrite,[status(thm)],[])).
% 1.02/0.99 tff(620,plain,
% 1.02/0.99 (((~solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~($sum(N!5, $product(-1, B!19)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Pos!4)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))), 0)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))))), 0)) <=> ((~solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~($sum(N!5, $product(-1, B!19)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))), 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Pos!4)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))))), 0))),
% 1.02/0.99 inference(rewrite,[status(thm)],[])).
% 1.02/0.99 tff(621,plain,
% 1.02/0.99 ($greatereq($sum($product(-1, I!11), tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4)))), 0) <=> $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))))), 0)),
% 1.02/0.99 inference(rewrite,[status(thm)],[])).
% 1.02/0.99 tff(622,plain,
% 1.02/0.99 ($sum(tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))), $product(-1, I!11)) = $sum($product(-1, I!11), tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))))),
% 1.02/0.99 inference(rewrite,[status(thm)],[])).
% 1.02/0.99 tff(623,plain,
% 1.02/0.99 ($greatereq($sum(tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))), $product(-1, I!11)), 0) <=> $greatereq($sum($product(-1, I!11), tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4)))), 0)),
% 1.02/0.99 inference(monotonicity,[status(thm)],[622])).
% 1.02/0.99 tff(624,plain,
% 1.02/0.99 ($greatereq($sum(tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))), $product(-1, I!11)), 0) <=> $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))))), 0)),
% 1.02/0.99 inference(transitivity,[status(thm)],[623, 621])).
% 1.02/0.99 tff(625,plain,
% 1.02/0.99 ((~($sum(B!19, $product(-1, N!5)) = 0)) <=> (~($sum(N!5, $product(-1, B!19)) = 0))),
% 1.02/0.99 inference(rewrite,[status(thm)],[])).
% 1.02/0.99 tff(626,plain,
% 1.02/0.99 (((~solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~($sum(B!19, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Pos!4)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))), 0)) | $greatereq($sum(tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))), $product(-1, I!11)), 0)) <=> ((~solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~($sum(N!5, $product(-1, B!19)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Pos!4)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))), 0)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))))), 0))),
% 1.02/0.99 inference(monotonicity,[status(thm)],[625, 624])).
% 1.02/0.99 tff(627,plain,
% 1.02/0.99 (((~solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~($sum(B!19, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Pos!4)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))), 0)) | $greatereq($sum(tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))), $product(-1, I!11)), 0)) <=> ((~solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~($sum(N!5, $product(-1, B!19)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))), 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Pos!4)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))))), 0))),
% 1.02/0.99 inference(transitivity,[status(thm)],[626, 620])).
% 1.02/0.99 tff(628,plain,
% 1.02/0.99 (((~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos!4)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), 0)) | $greatereq($sum(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), $product(-1, I!11)), 0))) | ((~solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~($sum(B!19, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Pos!4)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))), 0)) | $greatereq($sum(tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))), $product(-1, I!11)), 0))) <=> ((~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos!4)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), 0)) | $greatereq($sum(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), $product(-1, I!11)), 0))) | ((~solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~($sum(N!5, $product(-1, B!19)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))), 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Pos!4)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))))), 0)))),
% 1.02/0.99 inference(monotonicity,[status(thm)],[627])).
% 1.02/0.99 tff(629,plain,
% 1.02/0.99 (((~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos!4)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), 0)) | $greatereq($sum(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), $product(-1, I!11)), 0))) | ((~solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~($sum(B!19, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Pos!4)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))), 0)) | $greatereq($sum(tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))), $product(-1, I!11)), 0))) <=> ((~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos!4)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), 0)) | $greatereq($sum(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), $product(-1, I!11)), 0))) | (~solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~($sum(N!5, $product(-1, B!19)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))), 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Pos!4)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))))), 0))),
% 1.02/0.99 inference(transitivity,[status(thm)],[628, 619])).
% 1.02/0.99 tff(630,plain,
% 1.02/0.99 ((~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos!4)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), 0)) | $greatereq($sum(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), $product(-1, I!11)), 0))) | ((~solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~($sum(B!19, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Pos!4)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))), 0)) | $greatereq($sum(tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))), $product(-1, I!11)), 0))),
% 1.02/0.99 inference(quant_inst,[status(thm)],[])).
% 1.02/0.99 tff(631,plain,
% 1.02/0.99 ((~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos!4)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), 0)) | $greatereq($sum(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), $product(-1, I!11)), 0))) | (~solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~($sum(N!5, $product(-1, B!19)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))), 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Pos!4)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))))), 0)),
% 1.02/1.00 inference(modus_ponens,[status(thm)],[630, 629])).
% 1.02/1.00 tff(632,plain,
% 1.02/1.00 ($lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))))), 0)),
% 1.02/1.00 inference(unit_resolution,[status(thm)],[631, 618, 616, 614, 612, 610, 608])).
% 1.02/1.00 tff(633,plain,
% 1.02/1.00 ((~![X: map_int_int] : sort1(map(int, int), t2tb2(X))) | sort1(map(int, int), t2tb2(B1!18))),
% 1.02/1.00 inference(quant_inst,[status(thm)],[])).
% 1.02/1.00 tff(634,plain,
% 1.02/1.00 (sort1(map(int, int), t2tb2(B1!18))),
% 1.02/1.00 inference(unit_resolution,[status(thm)],[633, 175])).
% 1.02/1.00 tff(635,plain,
% 1.02/1.00 (((~![A: ty, U: $int, U1: uni] : ((~sort1(map(int, A), U1)) | (elts(A, mk_array1(A, U, U1)) = U1))) | ((~sort1(map(int, int), t2tb2(B1!18))) | (elts(int, mk_array1(int, B!19, t2tb2(B1!18))) = t2tb2(B1!18)))) <=> ((~![A: ty, U: $int, U1: uni] : ((~sort1(map(int, A), U1)) | (elts(A, mk_array1(A, U, U1)) = U1))) | (~sort1(map(int, int), t2tb2(B1!18))) | (elts(int, mk_array1(int, B!19, t2tb2(B1!18))) = t2tb2(B1!18)))),
% 1.02/1.00 inference(rewrite,[status(thm)],[])).
% 1.02/1.00 tff(636,plain,
% 1.02/1.00 ((~![A: ty, U: $int, U1: uni] : ((~sort1(map(int, A), U1)) | (elts(A, mk_array1(A, U, U1)) = U1))) | ((~sort1(map(int, int), t2tb2(B1!18))) | (elts(int, mk_array1(int, B!19, t2tb2(B1!18))) = t2tb2(B1!18)))),
% 1.02/1.00 inference(quant_inst,[status(thm)],[])).
% 1.02/1.00 tff(637,plain,
% 1.02/1.00 ((~![A: ty, U: $int, U1: uni] : ((~sort1(map(int, A), U1)) | (elts(A, mk_array1(A, U, U1)) = U1))) | (~sort1(map(int, int), t2tb2(B1!18))) | (elts(int, mk_array1(int, B!19, t2tb2(B1!18))) = t2tb2(B1!18))),
% 1.02/1.00 inference(modus_ponens,[status(thm)],[636, 635])).
% 1.02/1.00 tff(638,plain,
% 1.02/1.00 ((~sort1(map(int, int), t2tb2(B1!18))) | (elts(int, mk_array1(int, B!19, t2tb2(B1!18))) = t2tb2(B1!18))),
% 1.02/1.00 inference(unit_resolution,[status(thm)],[637, 187])).
% 1.02/1.00 tff(639,plain,
% 1.02/1.00 (elts(int, mk_array1(int, B!19, t2tb2(B1!18))) = t2tb2(B1!18)),
% 1.02/1.00 inference(unit_resolution,[status(thm)],[638, 634])).
% 1.02/1.00 tff(640,plain,
% 1.02/1.00 (get(int, int, elts(int, mk_array1(int, B!19, t2tb2(B1!18))), t2tb(Pos!4)) = get(int, int, t2tb2(B1!18), t2tb(Pos!4))),
% 1.02/1.00 inference(monotonicity,[status(thm)],[639])).
% 1.02/1.00 tff(641,plain,
% 1.02/1.00 ((~![A: ty, A1: uni, I: $int] : (get2(A, A1, I) = get(A, int, elts(A, A1), t2tb(I)))) | (get2(int, mk_array1(int, B!19, t2tb2(B1!18)), Pos!4) = get(int, int, elts(int, mk_array1(int, B!19, t2tb2(B1!18))), t2tb(Pos!4)))),
% 1.02/1.00 inference(quant_inst,[status(thm)],[])).
% 1.02/1.00 tff(642,plain,
% 1.02/1.00 (get2(int, mk_array1(int, B!19, t2tb2(B1!18)), Pos!4) = get(int, int, elts(int, mk_array1(int, B!19, t2tb2(B1!18))), t2tb(Pos!4))),
% 1.02/1.00 inference(unit_resolution,[status(thm)],[641, 165])).
% 1.02/1.00 tff(643,plain,
% 1.02/1.00 ((~![J: uni] : (t2tb1(tb2t1(J)) = J)) | (t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))) = mk_array1(int, B!19, t2tb2(B1!18)))),
% 1.02/1.00 inference(quant_inst,[status(thm)],[])).
% 1.02/1.00 tff(644,plain,
% 1.02/1.00 (t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))) = mk_array1(int, B!19, t2tb2(B1!18))),
% 1.02/1.00 inference(unit_resolution,[status(thm)],[643, 154])).
% 1.02/1.00 tff(645,plain,
% 1.02/1.00 (get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), Pos!4) = get2(int, mk_array1(int, B!19, t2tb2(B1!18)), Pos!4)),
% 1.02/1.00 inference(monotonicity,[status(thm)],[644])).
% 1.02/1.00 tff(646,plain,
% 1.02/1.00 (get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), Pos!4) = get(int, int, t2tb2(B1!18), t2tb(Pos!4))),
% 1.02/1.00 inference(transitivity,[status(thm)],[645, 642, 640])).
% 1.02/1.00 tff(647,plain,
% 1.02/1.00 (tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), Pos!4)) = tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4)))),
% 1.02/1.00 inference(monotonicity,[status(thm)],[646])).
% 1.02/1.00 tff(648,plain,
% 1.02/1.00 (tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))) = tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), Pos!4))),
% 1.02/1.00 inference(symmetry,[status(thm)],[647])).
% 1.02/1.00 tff(649,plain,
% 1.02/1.00 ((~(tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))) = tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), Pos!4)))) | $lesseq($sum(tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), Pos!4)))), 0)),
% 1.02/1.00 inference(theory_lemma,[status(thm)],[])).
% 1.02/1.00 tff(650,plain,
% 1.02/1.00 ($lesseq($sum(tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), Pos!4)))), 0)),
% 1.02/1.00 inference(unit_resolution,[status(thm)],[649, 648])).
% 1.02/1.00 tff(651,plain,
% 1.02/1.00 ((~![I: $int] : ($sum(I, $product(-1, tb2t(t2tb(I)))) = 0)) | ($sum(I!11, $product(-1, tb2t(t2tb(I!11)))) = 0)),
% 1.02/1.00 inference(quant_inst,[status(thm)],[])).
% 1.02/1.00 tff(652,plain,
% 1.02/1.00 ($sum(I!11, $product(-1, tb2t(t2tb(I!11)))) = 0),
% 1.02/1.00 inference(unit_resolution,[status(thm)],[651, 388])).
% 1.02/1.00 tff(653,plain,
% 1.02/1.00 ((~($sum(I!11, $product(-1, tb2t(t2tb(I!11)))) = 0)) | $greatereq($sum(I!11, $product(-1, tb2t(t2tb(I!11)))), 0)),
% 1.02/1.00 inference(theory_lemma,[status(thm)],[])).
% 1.02/1.00 tff(654,plain,
% 1.02/1.00 ($greatereq($sum(I!11, $product(-1, tb2t(t2tb(I!11)))), 0)),
% 1.02/1.00 inference(unit_resolution,[status(thm)],[653, 652])).
% 1.02/1.00 tff(655,plain,
% 1.02/1.00 ((~![X: $int] : sort1(int, t2tb(X))) | sort1(int, t2tb(I!11))),
% 1.02/1.00 inference(quant_inst,[status(thm)],[])).
% 1.02/1.00 tff(656,plain,
% 1.02/1.00 (sort1(int, t2tb(I!11))),
% 1.02/1.00 inference(unit_resolution,[status(thm)],[655, 452])).
% 1.02/1.00 tff(657,plain,
% 1.02/1.00 (^[A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : refl(((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort1(B, B1))) <=> ((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort1(B, B1))))),
% 1.02/1.00 inference(bind,[status(th)],[])).
% 1.02/1.00 tff(658,plain,
% 1.02/1.00 (![A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : ((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort1(B, B1))) <=> ![A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : ((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort1(B, B1)))),
% 1.02/1.00 inference(quant_intro,[status(thm)],[657])).
% 1.02/1.00 tff(659,plain,
% 1.02/1.00 (![A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : ((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort1(B, B1))) <=> ![A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : ((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort1(B, B1)))),
% 1.02/1.00 inference(rewrite,[status(thm)],[])).
% 1.02/1.00 tff(660,plain,
% 1.02/1.00 (^[A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : trans(monotonicity(rewrite(((A1 = A2) => (get(B, A, set(B, A, M, A1, B1), A2) = B1)) <=> ((~(A1 = A2)) | (get(B, A, set(B, A, M, A1, B1), A2) = B1))), ((sort1(B, B1) => ((A1 = A2) => (get(B, A, set(B, A, M, A1, B1), A2) = B1))) <=> (sort1(B, B1) => ((~(A1 = A2)) | (get(B, A, set(B, A, M, A1, B1), A2) = B1))))), rewrite((sort1(B, B1) => ((~(A1 = A2)) | (get(B, A, set(B, A, M, A1, B1), A2) = B1))) <=> ((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort1(B, B1)))), ((sort1(B, B1) => ((A1 = A2) => (get(B, A, set(B, A, M, A1, B1), A2) = B1))) <=> ((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort1(B, B1)))))),
% 1.02/1.00 inference(bind,[status(th)],[])).
% 1.02/1.00 tff(661,plain,
% 1.02/1.00 (![A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : (sort1(B, B1) => ((A1 = A2) => (get(B, A, set(B, A, M, A1, B1), A2) = B1))) <=> ![A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : ((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort1(B, B1)))),
% 1.02/1.00 inference(quant_intro,[status(thm)],[660])).
% 1.02/1.00 tff(662,axiom,(![A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : (sort1(B, B1) => ((A1 = A2) => (get(B, A, set(B, A, M, A1, B1), A2) = B1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','select_eq')).
% 1.02/1.00 tff(663,plain,
% 1.02/1.00 (![A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : ((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort1(B, B1)))),
% 1.02/1.00 inference(modus_ponens,[status(thm)],[662, 661])).
% 1.02/1.00 tff(664,plain,
% 1.02/1.00 (![A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : ((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort1(B, B1)))),
% 1.02/1.00 inference(modus_ponens,[status(thm)],[663, 659])).
% 1.02/1.00 tff(665,plain,(
% 1.02/1.00 ![A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : ((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort1(B, B1)))),
% 1.02/1.00 inference(skolemize,[status(sab)],[664])).
% 1.02/1.00 tff(666,plain,
% 1.02/1.00 (![A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : ((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort1(B, B1)))),
% 1.02/1.00 inference(modus_ponens,[status(thm)],[665, 658])).
% 1.02/1.00 tff(667,plain,
% 1.02/1.00 (((~![A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : ((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort1(B, B1)))) | ((~sort1(int, t2tb(I!11))) | (get(int, int, set(int, int, t2tb2(Board2!10), t2tb(Pos!4), t2tb(I!11)), t2tb(Pos!4)) = t2tb(I!11)))) <=> ((~![A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : ((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort1(B, B1)))) | (~sort1(int, t2tb(I!11))) | (get(int, int, set(int, int, t2tb2(Board2!10), t2tb(Pos!4), t2tb(I!11)), t2tb(Pos!4)) = t2tb(I!11)))),
% 1.02/1.00 inference(rewrite,[status(thm)],[])).
% 1.02/1.00 tff(668,plain,
% 1.02/1.00 (((get(int, int, set(int, int, t2tb2(Board2!10), t2tb(Pos!4), t2tb(I!11)), t2tb(Pos!4)) = t2tb(I!11)) | $false | (~sort1(int, t2tb(I!11)))) <=> ((~sort1(int, t2tb(I!11))) | (get(int, int, set(int, int, t2tb2(Board2!10), t2tb(Pos!4), t2tb(I!11)), t2tb(Pos!4)) = t2tb(I!11)))),
% 1.02/1.00 inference(rewrite,[status(thm)],[])).
% 1.02/1.00 tff(669,plain,
% 1.02/1.00 ((t2tb(Pos!4) = t2tb(Pos!4)) <=> $true),
% 1.02/1.00 inference(rewrite,[status(thm)],[])).
% 1.02/1.00 tff(670,plain,
% 1.02/1.00 ((~(t2tb(Pos!4) = t2tb(Pos!4))) <=> (~$true)),
% 1.02/1.00 inference(monotonicity,[status(thm)],[669])).
% 1.02/1.00 tff(671,plain,
% 1.02/1.00 ((~(t2tb(Pos!4) = t2tb(Pos!4))) <=> $false),
% 1.02/1.00 inference(transitivity,[status(thm)],[670, 302])).
% 1.02/1.00 tff(672,plain,
% 1.02/1.00 (((get(int, int, set(int, int, t2tb2(Board2!10), t2tb(Pos!4), t2tb(I!11)), t2tb(Pos!4)) = t2tb(I!11)) | (~(t2tb(Pos!4) = t2tb(Pos!4))) | (~sort1(int, t2tb(I!11)))) <=> ((get(int, int, set(int, int, t2tb2(Board2!10), t2tb(Pos!4), t2tb(I!11)), t2tb(Pos!4)) = t2tb(I!11)) | $false | (~sort1(int, t2tb(I!11))))),
% 1.02/1.00 inference(monotonicity,[status(thm)],[671])).
% 1.02/1.00 tff(673,plain,
% 1.02/1.00 (((get(int, int, set(int, int, t2tb2(Board2!10), t2tb(Pos!4), t2tb(I!11)), t2tb(Pos!4)) = t2tb(I!11)) | (~(t2tb(Pos!4) = t2tb(Pos!4))) | (~sort1(int, t2tb(I!11)))) <=> ((~sort1(int, t2tb(I!11))) | (get(int, int, set(int, int, t2tb2(Board2!10), t2tb(Pos!4), t2tb(I!11)), t2tb(Pos!4)) = t2tb(I!11)))),
% 1.02/1.00 inference(transitivity,[status(thm)],[672, 668])).
% 1.02/1.00 tff(674,plain,
% 1.02/1.00 (((~![A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : ((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort1(B, B1)))) | ((get(int, int, set(int, int, t2tb2(Board2!10), t2tb(Pos!4), t2tb(I!11)), t2tb(Pos!4)) = t2tb(I!11)) | (~(t2tb(Pos!4) = t2tb(Pos!4))) | (~sort1(int, t2tb(I!11))))) <=> ((~![A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : ((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort1(B, B1)))) | ((~sort1(int, t2tb(I!11))) | (get(int, int, set(int, int, t2tb2(Board2!10), t2tb(Pos!4), t2tb(I!11)), t2tb(Pos!4)) = t2tb(I!11))))),
% 1.02/1.00 inference(monotonicity,[status(thm)],[673])).
% 1.02/1.00 tff(675,plain,
% 1.02/1.00 (((~![A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : ((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort1(B, B1)))) | ((get(int, int, set(int, int, t2tb2(Board2!10), t2tb(Pos!4), t2tb(I!11)), t2tb(Pos!4)) = t2tb(I!11)) | (~(t2tb(Pos!4) = t2tb(Pos!4))) | (~sort1(int, t2tb(I!11))))) <=> ((~![A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : ((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort1(B, B1)))) | (~sort1(int, t2tb(I!11))) | (get(int, int, set(int, int, t2tb2(Board2!10), t2tb(Pos!4), t2tb(I!11)), t2tb(Pos!4)) = t2tb(I!11)))),
% 1.02/1.00 inference(transitivity,[status(thm)],[674, 667])).
% 1.02/1.00 tff(676,plain,
% 1.02/1.00 ((~![A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : ((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort1(B, B1)))) | ((get(int, int, set(int, int, t2tb2(Board2!10), t2tb(Pos!4), t2tb(I!11)), t2tb(Pos!4)) = t2tb(I!11)) | (~(t2tb(Pos!4) = t2tb(Pos!4))) | (~sort1(int, t2tb(I!11))))),
% 1.02/1.00 inference(quant_inst,[status(thm)],[])).
% 1.02/1.00 tff(677,plain,
% 1.02/1.00 ((~![A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : ((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort1(B, B1)))) | (~sort1(int, t2tb(I!11))) | (get(int, int, set(int, int, t2tb2(Board2!10), t2tb(Pos!4), t2tb(I!11)), t2tb(Pos!4)) = t2tb(I!11))),
% 1.02/1.00 inference(modus_ponens,[status(thm)],[676, 675])).
% 1.02/1.00 tff(678,plain,
% 1.02/1.00 (get(int, int, set(int, int, t2tb2(Board2!10), t2tb(Pos!4), t2tb(I!11)), t2tb(Pos!4)) = t2tb(I!11)),
% 1.02/1.00 inference(unit_resolution,[status(thm)],[677, 666, 656])).
% 1.02/1.00 tff(679,plain,
% 1.02/1.00 (get(int, int, t2tb2(tb2t2(set(int, int, t2tb2(Board2!10), t2tb(Pos!4), t2tb(I!11)))), t2tb(Pos!4)) = get(int, int, set(int, int, t2tb2(Board2!10), t2tb(Pos!4), t2tb(I!11)), t2tb(Pos!4))),
% 1.02/1.00 inference(monotonicity,[status(thm)],[492])).
% 1.02/1.00 tff(680,plain,
% 1.02/1.00 (t2tb2(Board3!12) = set(int, int, t2tb2(Board2!10), t2tb(Pos!4), t2tb(I!11))),
% 1.02/1.00 inference(transitivity,[status(thm)],[366, 492])).
% 1.02/1.00 tff(681,plain,
% 1.02/1.00 (sort1(map(int, int), t2tb2(Board3!12)) <=> sort1(map(int, int), set(int, int, t2tb2(Board2!10), t2tb(Pos!4), t2tb(I!11)))),
% 1.02/1.00 inference(monotonicity,[status(thm)],[680])).
% 1.02/1.00 tff(682,plain,
% 1.02/1.00 (sort1(map(int, int), set(int, int, t2tb2(Board2!10), t2tb(Pos!4), t2tb(I!11))) <=> sort1(map(int, int), t2tb2(Board3!12))),
% 1.02/1.00 inference(symmetry,[status(thm)],[681])).
% 1.02/1.00 tff(683,plain,
% 1.02/1.00 (sort1(map(int, int), t2tb2(Board3!12))),
% 1.02/1.00 inference(modus_ponens,[status(thm)],[506, 682])).
% 1.02/1.00 tff(684,plain,
% 1.02/1.00 (elts(int, mk_array1(int, N!5, t2tb2(Board3!12))) = t2tb2(Board3!12)),
% 1.02/1.00 inference(unit_resolution,[status(thm)],[511, 683])).
% 1.02/1.00 tff(685,plain,
% 1.02/1.00 (elts(int, mk_array1(int, Board!7, t2tb2(Board3!12))) = t2tb2(tb2t2(set(int, int, t2tb2(Board2!10), t2tb(Pos!4), t2tb(I!11))))),
% 1.02/1.00 inference(transitivity,[status(thm)],[515, 684, 366])).
% 1.02/1.00 tff(686,plain,
% 1.02/1.00 (get(int, int, elts(int, mk_array1(int, Board!7, t2tb2(Board3!12))), t2tb(Pos!4)) = get(int, int, t2tb2(tb2t2(set(int, int, t2tb2(Board2!10), t2tb(Pos!4), t2tb(I!11)))), t2tb(Pos!4))),
% 1.02/1.00 inference(monotonicity,[status(thm)],[685])).
% 1.02/1.00 tff(687,plain,
% 1.02/1.00 ((~![A: ty, A1: uni, I: $int] : (get2(A, A1, I) = get(A, int, elts(A, A1), t2tb(I)))) | (get2(int, mk_array1(int, Board!7, t2tb2(Board3!12)), Pos!4) = get(int, int, elts(int, mk_array1(int, Board!7, t2tb2(Board3!12))), t2tb(Pos!4)))),
% 1.02/1.00 inference(quant_inst,[status(thm)],[])).
% 1.02/1.00 tff(688,plain,
% 1.02/1.00 (get2(int, mk_array1(int, Board!7, t2tb2(Board3!12)), Pos!4) = get(int, int, elts(int, mk_array1(int, Board!7, t2tb2(Board3!12))), t2tb(Pos!4))),
% 1.02/1.00 inference(unit_resolution,[status(thm)],[687, 165])).
% 1.02/1.00 tff(689,plain,
% 1.02/1.00 (get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Pos!4) = get2(int, mk_array1(int, Board!7, t2tb2(Board3!12)), Pos!4)),
% 1.02/1.00 inference(monotonicity,[status(thm)],[521])).
% 1.02/1.00 tff(690,plain,
% 1.02/1.00 (get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Pos!4) = t2tb(I!11)),
% 1.02/1.00 inference(transitivity,[status(thm)],[689, 688, 686, 679, 678])).
% 1.02/1.00 tff(691,plain,
% 1.02/1.00 (tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Pos!4)) = tb2t(t2tb(I!11))),
% 1.02/1.00 inference(monotonicity,[status(thm)],[690])).
% 1.02/1.00 tff(692,plain,
% 1.02/1.00 (tb2t(t2tb(I!11)) = tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Pos!4))),
% 1.02/1.00 inference(symmetry,[status(thm)],[691])).
% 1.02/1.00 tff(693,plain,
% 1.02/1.00 ((~(tb2t(t2tb(I!11)) = tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Pos!4)))) | $greatereq($sum(tb2t(t2tb(I!11)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Pos!4)))), 0)),
% 1.02/1.00 inference(theory_lemma,[status(thm)],[])).
% 1.02/1.00 tff(694,plain,
% 1.02/1.00 ($greatereq($sum(tb2t(t2tb(I!11)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Pos!4)))), 0)),
% 1.02/1.00 inference(unit_resolution,[status(thm)],[693, 692])).
% 1.02/1.00 tff(695,plain,
% 1.02/1.00 ($lesseq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Pos!4)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), Pos!4)))), 0) | (~$lesseq($sum(tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), Pos!4)))), 0)) | (~$lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))))), 0)) | (~$greatereq($sum(I!11, $product(-1, tb2t(t2tb(I!11)))), 0)) | (~$greatereq($sum(tb2t(t2tb(I!11)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Pos!4)))), 0))),
% 1.02/1.00 inference(theory_lemma,[status(thm)],[])).
% 1.02/1.00 tff(696,plain,
% 1.02/1.00 ($lesseq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Pos!4)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), Pos!4)))), 0) | (~$lesseq($sum(tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), Pos!4)))), 0)) | (~$lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))))), 0))),
% 1.02/1.00 inference(unit_resolution,[status(thm)],[695, 694, 654])).
% 1.02/1.00 tff(697,plain,
% 1.02/1.00 ($lesseq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Pos!4)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), Pos!4)))), 0)),
% 1.02/1.00 inference(unit_resolution,[status(thm)],[696, 650, 632])).
% 1.02/1.00 tff(698,plain,
% 1.02/1.00 (((~solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Pos!4)) | (~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~($sum(N!5, $product(-1, B!19)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))), 0))) | (~$lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))))), -1))),
% 1.02/1.00 inference(tautology,[status(thm)],[])).
% 1.02/1.00 tff(699,plain,
% 1.02/1.00 (~$lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))))), -1)),
% 1.02/1.00 inference(unit_resolution,[status(thm)],[698, 595])).
% 1.02/1.00 tff(700,plain,
% 1.02/1.00 ((~(tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))) = tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), Pos!4)))) | $greatereq($sum(tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), Pos!4)))), 0)),
% 1.02/1.00 inference(theory_lemma,[status(thm)],[])).
% 1.02/1.00 tff(701,plain,
% 1.02/1.00 ($greatereq($sum(tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), Pos!4)))), 0)),
% 1.02/1.00 inference(unit_resolution,[status(thm)],[700, 648])).
% 1.02/1.00 tff(702,plain,
% 1.02/1.00 ((~($sum(I!11, $product(-1, tb2t(t2tb(I!11)))) = 0)) | $lesseq($sum(I!11, $product(-1, tb2t(t2tb(I!11)))), 0)),
% 1.02/1.00 inference(theory_lemma,[status(thm)],[])).
% 1.02/1.00 tff(703,plain,
% 1.02/1.00 ($lesseq($sum(I!11, $product(-1, tb2t(t2tb(I!11)))), 0)),
% 1.02/1.00 inference(unit_resolution,[status(thm)],[702, 652])).
% 1.02/1.00 tff(704,plain,
% 1.02/1.00 ((~(tb2t(t2tb(I!11)) = tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Pos!4)))) | $lesseq($sum(tb2t(t2tb(I!11)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Pos!4)))), 0)),
% 1.02/1.00 inference(theory_lemma,[status(thm)],[])).
% 1.02/1.00 tff(705,plain,
% 1.02/1.00 ($lesseq($sum(tb2t(t2tb(I!11)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Pos!4)))), 0)),
% 1.02/1.00 inference(unit_resolution,[status(thm)],[704, 692])).
% 1.02/1.00 tff(706,plain,
% 1.02/1.00 ($greatereq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Pos!4)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), Pos!4)))), 0) | (~$greatereq($sum(tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), Pos!4)))), 0)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))))), -1) | (~$lesseq($sum(I!11, $product(-1, tb2t(t2tb(I!11)))), 0)) | (~$lesseq($sum(tb2t(t2tb(I!11)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Pos!4)))), 0))),
% 1.02/1.00 inference(theory_lemma,[status(thm)],[])).
% 1.02/1.00 tff(707,plain,
% 1.02/1.00 ($greatereq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Pos!4)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), Pos!4)))), 0) | (~$greatereq($sum(tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), Pos!4)))), 0)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))))), -1)),
% 1.02/1.00 inference(unit_resolution,[status(thm)],[706, 705, 703])).
% 1.02/1.00 tff(708,plain,
% 1.02/1.00 ($greatereq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Pos!4)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), Pos!4)))), 0)),
% 1.02/1.00 inference(unit_resolution,[status(thm)],[707, 701, 699])).
% 1.02/1.00 tff(709,plain,
% 1.02/1.00 (($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Pos!4)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), Pos!4)))) = 0) | (~$lesseq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Pos!4)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), Pos!4)))), 0)) | (~$greatereq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Pos!4)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), Pos!4)))), 0))),
% 1.02/1.00 inference(theory_lemma,[status(thm)],[])).
% 1.02/1.00 tff(710,plain,
% 1.02/1.00 ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Pos!4)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), Pos!4)))) = 0),
% 1.02/1.00 inference(unit_resolution,[status(thm)],[709, 708, 697])).
% 1.02/1.00 tff(711,plain,
% 1.02/1.00 (((~![B1: array_int, B2: array_int, Pos: $int] : ((~eq_board1(B1, B2, Pos)) | eq_board1(B2, B1, Pos))) | ((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Pos!4)) | eq_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4))) <=> ((~![B1: array_int, B2: array_int, Pos: $int] : ((~eq_board1(B1, B2, Pos)) | eq_board1(B2, B1, Pos))) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Pos!4)) | eq_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4))),
% 1.02/1.00 inference(rewrite,[status(thm)],[])).
% 1.02/1.00 tff(712,plain,
% 1.02/1.00 ((~![B1: array_int, B2: array_int, Pos: $int] : ((~eq_board1(B1, B2, Pos)) | eq_board1(B2, B1, Pos))) | ((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Pos!4)) | eq_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4))),
% 1.02/1.00 inference(quant_inst,[status(thm)],[])).
% 1.02/1.00 tff(713,plain,
% 1.02/1.00 ((~![B1: array_int, B2: array_int, Pos: $int] : ((~eq_board1(B1, B2, Pos)) | eq_board1(B2, B1, Pos))) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Pos!4)) | eq_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)),
% 1.02/1.00 inference(modus_ponens,[status(thm)],[712, 711])).
% 1.02/1.00 tff(714,plain,
% 1.02/1.00 (eq_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)),
% 1.02/1.00 inference(unit_resolution,[status(thm)],[713, 561, 597])).
% 1.02/1.00 tff(715,plain,
% 1.02/1.00 (^[B1: array_int, B2: array_int, Pos: $int] : refl(((~eq_board1(B1, B2, Pos)) | eq_board1(B1, B2, $sum(1, Pos)) | (~($sum(tb2t(get2(int, t2tb1(B1), Pos)), $product(-1, tb2t(get2(int, t2tb1(B2), Pos)))) = 0))) <=> ((~eq_board1(B1, B2, Pos)) | eq_board1(B1, B2, $sum(1, Pos)) | (~($sum(tb2t(get2(int, t2tb1(B1), Pos)), $product(-1, tb2t(get2(int, t2tb1(B2), Pos)))) = 0))))),
% 1.02/1.00 inference(bind,[status(th)],[])).
% 1.02/1.00 tff(716,plain,
% 1.02/1.00 (![B1: array_int, B2: array_int, Pos: $int] : ((~eq_board1(B1, B2, Pos)) | eq_board1(B1, B2, $sum(1, Pos)) | (~($sum(tb2t(get2(int, t2tb1(B1), Pos)), $product(-1, tb2t(get2(int, t2tb1(B2), Pos)))) = 0))) <=> ![B1: array_int, B2: array_int, Pos: $int] : ((~eq_board1(B1, B2, Pos)) | eq_board1(B1, B2, $sum(1, Pos)) | (~($sum(tb2t(get2(int, t2tb1(B1), Pos)), $product(-1, tb2t(get2(int, t2tb1(B2), Pos)))) = 0)))),
% 1.02/1.00 inference(quant_intro,[status(thm)],[715])).
% 1.02/1.00 tff(717,plain,
% 1.02/1.00 (^[B1: array_int, B2: array_int, Pos: $int] : trans(monotonicity(rewrite((~(tb2t(get2(int, t2tb1(B1), Pos)) = tb2t(get2(int, t2tb1(B2), Pos)))) <=> (~($sum(tb2t(get2(int, t2tb1(B1), Pos)), $product(-1, tb2t(get2(int, t2tb1(B2), Pos)))) = 0))), (((~eq_board1(B1, B2, Pos)) | eq_board1(B1, B2, $sum(1, Pos)) | (~(tb2t(get2(int, t2tb1(B1), Pos)) = tb2t(get2(int, t2tb1(B2), Pos))))) <=> ((~eq_board1(B1, B2, Pos)) | eq_board1(B1, B2, $sum(1, Pos)) | (~($sum(tb2t(get2(int, t2tb1(B1), Pos)), $product(-1, tb2t(get2(int, t2tb1(B2), Pos)))) = 0))))), rewrite(((~eq_board1(B1, B2, Pos)) | eq_board1(B1, B2, $sum(1, Pos)) | (~($sum(tb2t(get2(int, t2tb1(B1), Pos)), $product(-1, tb2t(get2(int, t2tb1(B2), Pos)))) = 0))) <=> ((~eq_board1(B1, B2, Pos)) | eq_board1(B1, B2, $sum(1, Pos)) | (~($sum(tb2t(get2(int, t2tb1(B1), Pos)), $product(-1, tb2t(get2(int, t2tb1(B2), Pos)))) = 0)))), (((~eq_board1(B1, B2, Pos)) | eq_board1(B1, B2, $sum(1, Pos)) | (~(tb2t(get2(int, t2tb1(B1), Pos)) = tb2t(get2(int, t2tb1(B2), Pos))))) <=> ((~eq_board1(B1, B2, Pos)) | eq_board1(B1, B2, $sum(1, Pos)) | (~($sum(tb2t(get2(int, t2tb1(B1), Pos)), $product(-1, tb2t(get2(int, t2tb1(B2), Pos)))) = 0)))))),
% 1.02/1.00 inference(bind,[status(th)],[])).
% 1.02/1.00 tff(718,plain,
% 1.02/1.00 (![B1: array_int, B2: array_int, Pos: $int] : ((~eq_board1(B1, B2, Pos)) | eq_board1(B1, B2, $sum(1, Pos)) | (~(tb2t(get2(int, t2tb1(B1), Pos)) = tb2t(get2(int, t2tb1(B2), Pos))))) <=> ![B1: array_int, B2: array_int, Pos: $int] : ((~eq_board1(B1, B2, Pos)) | eq_board1(B1, B2, $sum(1, Pos)) | (~($sum(tb2t(get2(int, t2tb1(B1), Pos)), $product(-1, tb2t(get2(int, t2tb1(B2), Pos)))) = 0)))),
% 1.02/1.00 inference(quant_intro,[status(thm)],[717])).
% 1.02/1.00 tff(719,plain,
% 1.02/1.00 (![B1: array_int, B2: array_int, Pos: $int] : ((~eq_board1(B1, B2, Pos)) | eq_board1(B1, B2, $sum(1, Pos)) | (~(tb2t(get2(int, t2tb1(B1), Pos)) = tb2t(get2(int, t2tb1(B2), Pos))))) <=> ![B1: array_int, B2: array_int, Pos: $int] : ((~eq_board1(B1, B2, Pos)) | eq_board1(B1, B2, $sum(1, Pos)) | (~(tb2t(get2(int, t2tb1(B1), Pos)) = tb2t(get2(int, t2tb1(B2), Pos)))))),
% 1.02/1.00 inference(rewrite,[status(thm)],[])).
% 1.02/1.00 tff(720,plain,
% 1.02/1.00 (^[B1: array_int, B2: array_int, Pos: $int] : trans(monotonicity(trans(monotonicity(rewrite(eq_board1(B1, B2, $sum(Pos, 1)) <=> eq_board1(B1, B2, $sum(1, Pos))), (((tb2t(get2(int, t2tb1(B1), Pos)) = tb2t(get2(int, t2tb1(B2), Pos))) => eq_board1(B1, B2, $sum(Pos, 1))) <=> ((tb2t(get2(int, t2tb1(B1), Pos)) = tb2t(get2(int, t2tb1(B2), Pos))) => eq_board1(B1, B2, $sum(1, Pos))))), rewrite(((tb2t(get2(int, t2tb1(B1), Pos)) = tb2t(get2(int, t2tb1(B2), Pos))) => eq_board1(B1, B2, $sum(1, Pos))) <=> ((~(tb2t(get2(int, t2tb1(B1), Pos)) = tb2t(get2(int, t2tb1(B2), Pos)))) | eq_board1(B1, B2, $sum(1, Pos)))), (((tb2t(get2(int, t2tb1(B1), Pos)) = tb2t(get2(int, t2tb1(B2), Pos))) => eq_board1(B1, B2, $sum(Pos, 1))) <=> ((~(tb2t(get2(int, t2tb1(B1), Pos)) = tb2t(get2(int, t2tb1(B2), Pos)))) | eq_board1(B1, B2, $sum(1, Pos))))), ((eq_board1(B1, B2, Pos) => ((tb2t(get2(int, t2tb1(B1), Pos)) = tb2t(get2(int, t2tb1(B2), Pos))) => eq_board1(B1, B2, $sum(Pos, 1)))) <=> (eq_board1(B1, B2, Pos) => ((~(tb2t(get2(int, t2tb1(B1), Pos)) = tb2t(get2(int, t2tb1(B2), Pos)))) | eq_board1(B1, B2, $sum(1, Pos)))))), rewrite((eq_board1(B1, B2, Pos) => ((~(tb2t(get2(int, t2tb1(B1), Pos)) = tb2t(get2(int, t2tb1(B2), Pos)))) | eq_board1(B1, B2, $sum(1, Pos)))) <=> ((~eq_board1(B1, B2, Pos)) | eq_board1(B1, B2, $sum(1, Pos)) | (~(tb2t(get2(int, t2tb1(B1), Pos)) = tb2t(get2(int, t2tb1(B2), Pos)))))), ((eq_board1(B1, B2, Pos) => ((tb2t(get2(int, t2tb1(B1), Pos)) = tb2t(get2(int, t2tb1(B2), Pos))) => eq_board1(B1, B2, $sum(Pos, 1)))) <=> ((~eq_board1(B1, B2, Pos)) | eq_board1(B1, B2, $sum(1, Pos)) | (~(tb2t(get2(int, t2tb1(B1), Pos)) = tb2t(get2(int, t2tb1(B2), Pos)))))))),
% 1.02/1.01 inference(bind,[status(th)],[])).
% 1.02/1.01 tff(721,plain,
% 1.02/1.01 (![B1: array_int, B2: array_int, Pos: $int] : (eq_board1(B1, B2, Pos) => ((tb2t(get2(int, t2tb1(B1), Pos)) = tb2t(get2(int, t2tb1(B2), Pos))) => eq_board1(B1, B2, $sum(Pos, 1)))) <=> ![B1: array_int, B2: array_int, Pos: $int] : ((~eq_board1(B1, B2, Pos)) | eq_board1(B1, B2, $sum(1, Pos)) | (~(tb2t(get2(int, t2tb1(B1), Pos)) = tb2t(get2(int, t2tb1(B2), Pos)))))),
% 1.02/1.01 inference(quant_intro,[status(thm)],[720])).
% 1.02/1.01 tff(722,axiom,(![B1: array_int, B2: array_int, Pos: $int] : (eq_board1(B1, B2, Pos) => ((tb2t(get2(int, t2tb1(B1), Pos)) = tb2t(get2(int, t2tb1(B2), Pos))) => eq_board1(B1, B2, $sum(Pos, 1))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','eq_board_extension')).
% 1.02/1.01 tff(723,plain,
% 1.02/1.01 (![B1: array_int, B2: array_int, Pos: $int] : ((~eq_board1(B1, B2, Pos)) | eq_board1(B1, B2, $sum(1, Pos)) | (~(tb2t(get2(int, t2tb1(B1), Pos)) = tb2t(get2(int, t2tb1(B2), Pos)))))),
% 1.02/1.01 inference(modus_ponens,[status(thm)],[722, 721])).
% 1.02/1.01 tff(724,plain,
% 1.02/1.01 (![B1: array_int, B2: array_int, Pos: $int] : ((~eq_board1(B1, B2, Pos)) | eq_board1(B1, B2, $sum(1, Pos)) | (~(tb2t(get2(int, t2tb1(B1), Pos)) = tb2t(get2(int, t2tb1(B2), Pos)))))),
% 1.02/1.01 inference(modus_ponens,[status(thm)],[723, 719])).
% 1.02/1.01 tff(725,plain,
% 1.02/1.01 (![B1: array_int, B2: array_int, Pos: $int] : ((~eq_board1(B1, B2, Pos)) | eq_board1(B1, B2, $sum(1, Pos)) | (~($sum(tb2t(get2(int, t2tb1(B1), Pos)), $product(-1, tb2t(get2(int, t2tb1(B2), Pos)))) = 0)))),
% 1.02/1.01 inference(modus_ponens,[status(thm)],[724, 718])).
% 1.02/1.01 tff(726,plain,(
% 1.02/1.01 ![B1: array_int, B2: array_int, Pos: $int] : ((~eq_board1(B1, B2, Pos)) | eq_board1(B1, B2, $sum(1, Pos)) | (~($sum(tb2t(get2(int, t2tb1(B1), Pos)), $product(-1, tb2t(get2(int, t2tb1(B2), Pos)))) = 0)))),
% 1.02/1.01 inference(skolemize,[status(sab)],[725])).
% 1.02/1.01 tff(727,plain,
% 1.02/1.01 (![B1: array_int, B2: array_int, Pos: $int] : ((~eq_board1(B1, B2, Pos)) | eq_board1(B1, B2, $sum(1, Pos)) | (~($sum(tb2t(get2(int, t2tb1(B1), Pos)), $product(-1, tb2t(get2(int, t2tb1(B2), Pos)))) = 0)))),
% 1.02/1.01 inference(modus_ponens,[status(thm)],[726, 716])).
% 1.02/1.01 tff(728,plain,
% 1.02/1.01 (((~![B1: array_int, B2: array_int, Pos: $int] : ((~eq_board1(B1, B2, Pos)) | eq_board1(B1, B2, $sum(1, Pos)) | (~($sum(tb2t(get2(int, t2tb1(B1), Pos)), $product(-1, tb2t(get2(int, t2tb1(B2), Pos)))) = 0)))) | ((~($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Pos!4)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), Pos!4)))) = 0)) | (~eq_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | eq_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4)))) <=> ((~![B1: array_int, B2: array_int, Pos: $int] : ((~eq_board1(B1, B2, Pos)) | eq_board1(B1, B2, $sum(1, Pos)) | (~($sum(tb2t(get2(int, t2tb1(B1), Pos)), $product(-1, tb2t(get2(int, t2tb1(B2), Pos)))) = 0)))) | (~($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Pos!4)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), Pos!4)))) = 0)) | (~eq_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | eq_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4)))),
% 1.02/1.01 inference(rewrite,[status(thm)],[])).
% 1.02/1.01 tff(729,plain,
% 1.02/1.01 (((~eq_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | eq_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4)) | (~($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Pos!4)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), Pos!4)))) = 0))) <=> ((~($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Pos!4)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), Pos!4)))) = 0)) | (~eq_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | eq_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4)))),
% 1.02/1.01 inference(rewrite,[status(thm)],[])).
% 1.02/1.01 tff(730,plain,
% 1.02/1.01 ((~($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), Pos!4)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Pos!4)))) = 0)) <=> (~($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Pos!4)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), Pos!4)))) = 0))),
% 1.02/1.01 inference(rewrite,[status(thm)],[])).
% 1.02/1.01 tff(731,plain,
% 1.02/1.01 (((~eq_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | eq_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4)) | (~($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), Pos!4)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Pos!4)))) = 0))) <=> ((~eq_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | eq_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4)) | (~($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Pos!4)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), Pos!4)))) = 0)))),
% 1.02/1.01 inference(monotonicity,[status(thm)],[730])).
% 1.02/1.01 tff(732,plain,
% 1.02/1.01 (((~eq_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | eq_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4)) | (~($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), Pos!4)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Pos!4)))) = 0))) <=> ((~($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Pos!4)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), Pos!4)))) = 0)) | (~eq_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | eq_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4)))),
% 1.02/1.01 inference(transitivity,[status(thm)],[731, 729])).
% 1.02/1.01 tff(733,plain,
% 1.02/1.01 (((~![B1: array_int, B2: array_int, Pos: $int] : ((~eq_board1(B1, B2, Pos)) | eq_board1(B1, B2, $sum(1, Pos)) | (~($sum(tb2t(get2(int, t2tb1(B1), Pos)), $product(-1, tb2t(get2(int, t2tb1(B2), Pos)))) = 0)))) | ((~eq_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | eq_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4)) | (~($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), Pos!4)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Pos!4)))) = 0)))) <=> ((~![B1: array_int, B2: array_int, Pos: $int] : ((~eq_board1(B1, B2, Pos)) | eq_board1(B1, B2, $sum(1, Pos)) | (~($sum(tb2t(get2(int, t2tb1(B1), Pos)), $product(-1, tb2t(get2(int, t2tb1(B2), Pos)))) = 0)))) | ((~($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Pos!4)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), Pos!4)))) = 0)) | (~eq_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | eq_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))))),
% 1.02/1.01 inference(monotonicity,[status(thm)],[732])).
% 1.02/1.01 tff(734,plain,
% 1.02/1.01 (((~![B1: array_int, B2: array_int, Pos: $int] : ((~eq_board1(B1, B2, Pos)) | eq_board1(B1, B2, $sum(1, Pos)) | (~($sum(tb2t(get2(int, t2tb1(B1), Pos)), $product(-1, tb2t(get2(int, t2tb1(B2), Pos)))) = 0)))) | ((~eq_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | eq_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4)) | (~($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), Pos!4)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Pos!4)))) = 0)))) <=> ((~![B1: array_int, B2: array_int, Pos: $int] : ((~eq_board1(B1, B2, Pos)) | eq_board1(B1, B2, $sum(1, Pos)) | (~($sum(tb2t(get2(int, t2tb1(B1), Pos)), $product(-1, tb2t(get2(int, t2tb1(B2), Pos)))) = 0)))) | (~($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Pos!4)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), Pos!4)))) = 0)) | (~eq_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | eq_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4)))),
% 1.02/1.01 inference(transitivity,[status(thm)],[733, 728])).
% 1.02/1.01 tff(735,plain,
% 1.02/1.01 ((~![B1: array_int, B2: array_int, Pos: $int] : ((~eq_board1(B1, B2, Pos)) | eq_board1(B1, B2, $sum(1, Pos)) | (~($sum(tb2t(get2(int, t2tb1(B1), Pos)), $product(-1, tb2t(get2(int, t2tb1(B2), Pos)))) = 0)))) | ((~eq_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | eq_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4)) | (~($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), Pos!4)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Pos!4)))) = 0)))),
% 1.02/1.01 inference(quant_inst,[status(thm)],[])).
% 1.02/1.01 tff(736,plain,
% 1.02/1.01 ((~![B1: array_int, B2: array_int, Pos: $int] : ((~eq_board1(B1, B2, Pos)) | eq_board1(B1, B2, $sum(1, Pos)) | (~($sum(tb2t(get2(int, t2tb1(B1), Pos)), $product(-1, tb2t(get2(int, t2tb1(B2), Pos)))) = 0)))) | (~($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Pos!4)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), Pos!4)))) = 0)) | (~eq_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | eq_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))),
% 1.02/1.01 inference(modus_ponens,[status(thm)],[735, 734])).
% 1.02/1.01 tff(737,plain,
% 1.02/1.01 ((~($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Pos!4)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), Pos!4)))) = 0)) | eq_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))),
% 1.02/1.01 inference(unit_resolution,[status(thm)],[736, 727, 714])).
% 1.02/1.01 tff(738,plain,
% 1.02/1.01 (eq_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))),
% 1.02/1.01 inference(unit_resolution,[status(thm)],[737, 710])).
% 1.02/1.01 tff(739,plain,
% 1.02/1.01 ((~![A: ty, U: $int, U1: uni] : ($sum(U, $product(-1, length1(A, mk_array1(A, U, U1)))) = 0)) | ($sum(B!19, $product(-1, length1(int, mk_array1(int, B!19, t2tb2(B1!18))))) = 0)),
% 1.02/1.01 inference(quant_inst,[status(thm)],[])).
% 1.02/1.01 tff(740,plain,
% 1.02/1.01 ($sum(B!19, $product(-1, length1(int, mk_array1(int, B!19, t2tb2(B1!18))))) = 0),
% 1.02/1.01 inference(unit_resolution,[status(thm)],[739, 234])).
% 1.02/1.01 tff(741,plain,
% 1.02/1.01 ((~($sum(B!19, $product(-1, length1(int, mk_array1(int, B!19, t2tb2(B1!18))))) = 0)) | $greatereq($sum(B!19, $product(-1, length1(int, mk_array1(int, B!19, t2tb2(B1!18))))), 0)),
% 1.02/1.01 inference(theory_lemma,[status(thm)],[])).
% 1.02/1.01 tff(742,plain,
% 1.02/1.01 ($greatereq($sum(B!19, $product(-1, length1(int, mk_array1(int, B!19, t2tb2(B1!18))))), 0)),
% 1.02/1.01 inference(unit_resolution,[status(thm)],[741, 740])).
% 1.02/1.01 tff(743,plain,
% 1.02/1.01 ((~($sum(N!5, $product(-1, B!19)) = 0)) | $greatereq($sum(N!5, $product(-1, B!19)), 0)),
% 1.02/1.01 inference(theory_lemma,[status(thm)],[])).
% 1.02/1.01 tff(744,plain,
% 1.02/1.01 ($greatereq($sum(N!5, $product(-1, B!19)), 0)),
% 1.02/1.01 inference(unit_resolution,[status(thm)],[743, 612])).
% 1.02/1.01 tff(745,plain,
% 1.02/1.01 (length1(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))) = length1(int, mk_array1(int, B!19, t2tb2(B1!18)))),
% 1.02/1.01 inference(monotonicity,[status(thm)],[644])).
% 1.02/1.01 tff(746,plain,
% 1.02/1.01 ((~(length1(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))) = length1(int, mk_array1(int, B!19, t2tb2(B1!18))))) | $lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))), $product(-1, length1(int, mk_array1(int, B!19, t2tb2(B1!18))))), 0)),
% 1.02/1.01 inference(theory_lemma,[status(thm)],[])).
% 1.02/1.01 tff(747,plain,
% 1.02/1.01 ($lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))), $product(-1, length1(int, mk_array1(int, B!19, t2tb2(B1!18))))), 0)),
% 1.02/1.01 inference(unit_resolution,[status(thm)],[746, 745])).
% 1.02/1.01 tff(748,plain,
% 1.02/1.01 ((~![A: ty, U: $int, U1: uni] : ($sum(U, $product(-1, length1(A, mk_array1(A, U, U1)))) = 0)) | ($sum(N!5, $product(-1, length1(int, mk_array1(int, N!5, t2tb2(Board3!12))))) = 0)),
% 1.02/1.01 inference(quant_inst,[status(thm)],[])).
% 1.02/1.01 tff(749,plain,
% 1.02/1.01 ($sum(N!5, $product(-1, length1(int, mk_array1(int, N!5, t2tb2(Board3!12))))) = 0),
% 1.02/1.01 inference(unit_resolution,[status(thm)],[748, 234])).
% 1.02/1.01 tff(750,plain,
% 1.02/1.01 ((~($sum(N!5, $product(-1, length1(int, mk_array1(int, N!5, t2tb2(Board3!12))))) = 0)) | $lesseq($sum(N!5, $product(-1, length1(int, mk_array1(int, N!5, t2tb2(Board3!12))))), 0)),
% 1.02/1.01 inference(theory_lemma,[status(thm)],[])).
% 1.02/1.01 tff(751,plain,
% 1.02/1.01 ($lesseq($sum(N!5, $product(-1, length1(int, mk_array1(int, N!5, t2tb2(Board3!12))))), 0)),
% 1.02/1.01 inference(unit_resolution,[status(thm)],[750, 749])).
% 1.02/1.01 tff(752,plain,
% 1.02/1.01 (t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))) = mk_array1(int, N!5, t2tb2(Board3!12))),
% 1.02/1.01 inference(transitivity,[status(thm)],[521, 514])).
% 1.02/1.01 tff(753,plain,
% 1.02/1.01 (length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))) = length1(int, mk_array1(int, N!5, t2tb2(Board3!12)))),
% 1.02/1.01 inference(monotonicity,[status(thm)],[752])).
% 1.02/1.01 tff(754,plain,
% 1.02/1.01 (length1(int, mk_array1(int, N!5, t2tb2(Board3!12))) = length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))),
% 1.02/1.01 inference(symmetry,[status(thm)],[753])).
% 1.02/1.01 tff(755,plain,
% 1.02/1.01 ((~(length1(int, mk_array1(int, N!5, t2tb2(Board3!12))) = length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))))) | $lesseq($sum(length1(int, mk_array1(int, N!5, t2tb2(Board3!12))), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))))), 0)),
% 1.02/1.01 inference(theory_lemma,[status(thm)],[])).
% 1.02/1.01 tff(756,plain,
% 1.02/1.01 ($lesseq($sum(length1(int, mk_array1(int, N!5, t2tb2(Board3!12))), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))))), 0)),
% 1.02/1.01 inference(unit_resolution,[status(thm)],[755, 754])).
% 1.02/1.01 tff(757,plain,
% 1.02/1.01 ($greatereq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))))), 0) | (~$lesseq($sum(length1(int, mk_array1(int, N!5, t2tb2(Board3!12))), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))))), 0)) | (~$lesseq($sum(N!5, $product(-1, length1(int, mk_array1(int, N!5, t2tb2(Board3!12))))), 0)) | (~$lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))), $product(-1, length1(int, mk_array1(int, B!19, t2tb2(B1!18))))), 0)) | (~$greatereq($sum(B!19, $product(-1, length1(int, mk_array1(int, B!19, t2tb2(B1!18))))), 0)) | (~$greatereq($sum(N!5, $product(-1, B!19)), 0))),
% 1.02/1.01 inference(theory_lemma,[status(thm)],[])).
% 1.02/1.01 tff(758,plain,
% 1.02/1.01 ($greatereq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))))), 0) | (~$lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))), $product(-1, length1(int, mk_array1(int, B!19, t2tb2(B1!18))))), 0)) | (~$greatereq($sum(B!19, $product(-1, length1(int, mk_array1(int, B!19, t2tb2(B1!18))))), 0)) | (~$greatereq($sum(N!5, $product(-1, B!19)), 0))),
% 1.02/1.01 inference(unit_resolution,[status(thm)],[757, 756, 751])).
% 1.02/1.01 tff(759,plain,
% 1.02/1.01 ($greatereq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))))), 0)),
% 1.02/1.01 inference(unit_resolution,[status(thm)],[758, 747, 744, 742])).
% 1.02/1.01 tff(760,plain,
% 1.02/1.01 ((~($sum(B!19, $product(-1, length1(int, mk_array1(int, B!19, t2tb2(B1!18))))) = 0)) | $lesseq($sum(B!19, $product(-1, length1(int, mk_array1(int, B!19, t2tb2(B1!18))))), 0)),
% 1.02/1.01 inference(theory_lemma,[status(thm)],[])).
% 1.02/1.01 tff(761,plain,
% 1.02/1.01 ($lesseq($sum(B!19, $product(-1, length1(int, mk_array1(int, B!19, t2tb2(B1!18))))), 0)),
% 1.02/1.01 inference(unit_resolution,[status(thm)],[760, 740])).
% 1.02/1.01 tff(762,plain,
% 1.02/1.01 ((~($sum(N!5, $product(-1, B!19)) = 0)) | $lesseq($sum(N!5, $product(-1, B!19)), 0)),
% 1.02/1.01 inference(theory_lemma,[status(thm)],[])).
% 1.02/1.01 tff(763,plain,
% 1.02/1.01 ($lesseq($sum(N!5, $product(-1, B!19)), 0)),
% 1.02/1.01 inference(unit_resolution,[status(thm)],[762, 612])).
% 1.02/1.01 tff(764,plain,
% 1.02/1.01 ((~(length1(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))) = length1(int, mk_array1(int, B!19, t2tb2(B1!18))))) | $greatereq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))), $product(-1, length1(int, mk_array1(int, B!19, t2tb2(B1!18))))), 0)),
% 1.02/1.01 inference(theory_lemma,[status(thm)],[])).
% 1.02/1.01 tff(765,plain,
% 1.02/1.01 ($greatereq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))), $product(-1, length1(int, mk_array1(int, B!19, t2tb2(B1!18))))), 0)),
% 1.02/1.01 inference(unit_resolution,[status(thm)],[764, 745])).
% 1.02/1.01 tff(766,plain,
% 1.02/1.01 ((~($sum(N!5, $product(-1, length1(int, mk_array1(int, N!5, t2tb2(Board3!12))))) = 0)) | $greatereq($sum(N!5, $product(-1, length1(int, mk_array1(int, N!5, t2tb2(Board3!12))))), 0)),
% 1.02/1.01 inference(theory_lemma,[status(thm)],[])).
% 1.02/1.01 tff(767,plain,
% 1.02/1.01 ($greatereq($sum(N!5, $product(-1, length1(int, mk_array1(int, N!5, t2tb2(Board3!12))))), 0)),
% 1.02/1.01 inference(unit_resolution,[status(thm)],[766, 749])).
% 1.02/1.01 tff(768,plain,
% 1.02/1.01 ((~(length1(int, mk_array1(int, N!5, t2tb2(Board3!12))) = length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))))) | $greatereq($sum(length1(int, mk_array1(int, N!5, t2tb2(Board3!12))), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))))), 0)),
% 1.02/1.01 inference(theory_lemma,[status(thm)],[])).
% 1.02/1.01 tff(769,plain,
% 1.02/1.01 ($greatereq($sum(length1(int, mk_array1(int, N!5, t2tb2(Board3!12))), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))))), 0)),
% 1.02/1.01 inference(unit_resolution,[status(thm)],[768, 754])).
% 1.02/1.01 tff(770,plain,
% 1.02/1.01 ($lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))))), 0) | (~$greatereq($sum(length1(int, mk_array1(int, N!5, t2tb2(Board3!12))), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))))), 0)) | (~$greatereq($sum(N!5, $product(-1, length1(int, mk_array1(int, N!5, t2tb2(Board3!12))))), 0)) | (~$greatereq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))), $product(-1, length1(int, mk_array1(int, B!19, t2tb2(B1!18))))), 0)) | (~$lesseq($sum(B!19, $product(-1, length1(int, mk_array1(int, B!19, t2tb2(B1!18))))), 0)) | (~$lesseq($sum(N!5, $product(-1, B!19)), 0))),
% 1.02/1.01 inference(theory_lemma,[status(thm)],[])).
% 1.02/1.01 tff(771,plain,
% 1.02/1.01 ($lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))))), 0) | (~$greatereq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))), $product(-1, length1(int, mk_array1(int, B!19, t2tb2(B1!18))))), 0)) | (~$lesseq($sum(B!19, $product(-1, length1(int, mk_array1(int, B!19, t2tb2(B1!18))))), 0)) | (~$lesseq($sum(N!5, $product(-1, B!19)), 0))),
% 1.02/1.01 inference(unit_resolution,[status(thm)],[770, 769, 767])).
% 1.02/1.01 tff(772,plain,
% 1.02/1.01 ($lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))))), 0)),
% 1.02/1.01 inference(unit_resolution,[status(thm)],[771, 765, 763, 761])).
% 1.02/1.01 tff(773,plain,
% 1.02/1.01 (($sum(length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))))) = 0) | (~$lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))))), 0)) | (~$greatereq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))))), 0))),
% 1.02/1.01 inference(theory_lemma,[status(thm)],[])).
% 1.02/1.01 tff(774,plain,
% 1.02/1.01 ($sum(length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))))) = 0),
% 1.02/1.01 inference(unit_resolution,[status(thm)],[773, 772, 759])).
% 1.02/1.01 tff(775,assumption,(![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 1) | is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Q))), introduced(assumption)).
% 1.02/1.01 tff(776,plain,
% 1.02/1.01 (((~![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 1) | is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Q))) | ((~$greatereq(Pos!4, 0)) | is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4))) <=> ((~![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 1) | is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Q))) | (~$greatereq(Pos!4, 0)) | is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4))),
% 1.02/1.01 inference(rewrite,[status(thm)],[])).
% 1.02/1.01 tff(777,plain,
% 1.02/1.01 (((~$greatereq(Pos!4, 0)) | $false | is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) <=> ((~$greatereq(Pos!4, 0)) | is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4))),
% 1.02/1.01 inference(rewrite,[status(thm)],[])).
% 1.02/1.01 tff(778,plain,
% 1.02/1.01 ($greatereq(0, 1) <=> $false),
% 1.02/1.01 inference(rewrite,[status(thm)],[])).
% 1.02/1.01 tff(779,plain,
% 1.02/1.01 ($sum(Pos!4, $product(-1, Pos!4)) = 0),
% 1.02/1.01 inference(rewrite,[status(thm)],[])).
% 1.02/1.01 tff(780,plain,
% 1.02/1.01 ($greatereq($sum(Pos!4, $product(-1, Pos!4)), 1) <=> $greatereq(0, 1)),
% 1.02/1.01 inference(monotonicity,[status(thm)],[779])).
% 1.02/1.01 tff(781,plain,
% 1.02/1.01 ($greatereq($sum(Pos!4, $product(-1, Pos!4)), 1) <=> $false),
% 1.02/1.01 inference(transitivity,[status(thm)],[780, 778])).
% 1.02/1.01 tff(782,plain,
% 1.02/1.01 (((~$greatereq(Pos!4, 0)) | $greatereq($sum(Pos!4, $product(-1, Pos!4)), 1) | is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) <=> ((~$greatereq(Pos!4, 0)) | $false | is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4))),
% 1.02/1.01 inference(monotonicity,[status(thm)],[781])).
% 1.02/1.01 tff(783,plain,
% 1.02/1.01 (((~$greatereq(Pos!4, 0)) | $greatereq($sum(Pos!4, $product(-1, Pos!4)), 1) | is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) <=> ((~$greatereq(Pos!4, 0)) | is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4))),
% 1.02/1.01 inference(transitivity,[status(thm)],[782, 777])).
% 1.02/1.01 tff(784,plain,
% 1.02/1.01 (((~![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 1) | is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Q))) | ((~$greatereq(Pos!4, 0)) | $greatereq($sum(Pos!4, $product(-1, Pos!4)), 1) | is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4))) <=> ((~![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 1) | is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Q))) | ((~$greatereq(Pos!4, 0)) | is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)))),
% 1.02/1.01 inference(monotonicity,[status(thm)],[783])).
% 1.02/1.01 tff(785,plain,
% 1.02/1.01 (((~![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 1) | is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Q))) | ((~$greatereq(Pos!4, 0)) | $greatereq($sum(Pos!4, $product(-1, Pos!4)), 1) | is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4))) <=> ((~![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 1) | is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Q))) | (~$greatereq(Pos!4, 0)) | is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4))),
% 1.02/1.01 inference(transitivity,[status(thm)],[784, 776])).
% 1.02/1.01 tff(786,plain,
% 1.02/1.01 ((~![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 1) | is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Q))) | ((~$greatereq(Pos!4, 0)) | $greatereq($sum(Pos!4, $product(-1, Pos!4)), 1) | is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4))),
% 1.02/1.01 inference(quant_inst,[status(thm)],[])).
% 1.02/1.01 tff(787,plain,
% 1.02/1.01 ((~![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 1) | is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Q))) | (~$greatereq(Pos!4, 0)) | is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)),
% 1.02/1.01 inference(modus_ponens,[status(thm)],[786, 785])).
% 1.02/1.01 tff(788,plain,
% 1.02/1.01 ($false),
% 1.02/1.01 inference(unit_resolution,[status(thm)],[787, 260, 117, 775])).
% 1.02/1.01 tff(789,plain,((~![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 1) | is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Q))) | is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)), inference(lemma,lemma(discharge,[]))).
% 1.02/1.01 tff(790,plain,
% 1.02/1.01 (~![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 1) | is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Q))),
% 1.02/1.01 inference(unit_resolution,[status(thm)],[789, 117])).
% 1.02/1.01 tff(791,plain,
% 1.02/1.01 (((~is_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 1) | is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Q)))) | ![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 1) | is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Q))),
% 1.02/1.01 inference(tautology,[status(thm)],[])).
% 1.02/1.01 tff(792,plain,
% 1.02/1.01 ((~is_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 1) | is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Q)))),
% 1.02/1.01 inference(unit_resolution,[status(thm)],[791, 790])).
% 1.02/1.01 tff(793,assumption,((~(solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4)) | (~is_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~((~$greatereq(tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0)) | is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), -1))))) | (~((~solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~((~is_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 1) | is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Q)))))))), introduced(assumption)).
% 1.02/1.01 tff(794,plain,
% 1.02/1.01 (((~![Board: array_int, Pos: $int] : (~((~(solution1(Board, Pos) | (~is_board1(Board, Pos)) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_3(Pos, Board))), 0) | is_consistent1(Board, tptp_fun_Q_3(Pos, Board)) | (~$greatereq(tptp_fun_Q_3(Pos, Board), 0)))))) | (~((~solution1(Board, Pos)) | (~((~is_board1(Board, Pos)) | (~![Q: $int] : (is_consistent1(Board, Q) | (~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0)))))))))) | (~((~(solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4)) | (~is_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~((~$greatereq(tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0)) | is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), -1))))) | (~((~solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~((~is_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 1) | is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Q)))))))))) <=> ((~![Board: array_int, Pos: $int] : (~((~(solution1(Board, Pos) | (~is_board1(Board, Pos)) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_3(Pos, Board))), 0) | is_consistent1(Board, tptp_fun_Q_3(Pos, Board)) | (~$greatereq(tptp_fun_Q_3(Pos, Board), 0)))))) | (~((~solution1(Board, Pos)) | (~((~is_board1(Board, Pos)) | (~![Q: $int] : (is_consistent1(Board, Q) | (~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0)))))))))) | (~((~(solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4)) | (~is_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~((~$greatereq(tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0)) | is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), -1))))) | (~((~solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~((~is_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 1) | is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Q))))))))))),
% 1.02/1.02 inference(rewrite,[status(thm)],[])).
% 1.02/1.02 tff(795,plain,
% 1.02/1.02 ((~((~(solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4)) | (~is_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~($lesseq($sum($sum(1, Pos!4), $product(-1, tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), 0) | is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))) | (~$greatereq(tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0)))))) | (~((~solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~((~is_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~![Q: $int] : (is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Q) | (~$greatereq(Q, 0)) | $lesseq($sum($sum(1, Pos!4), $product(-1, Q)), 0))))))))) <=> (~((~(solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4)) | (~is_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~((~$greatereq(tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0)) | is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), -1))))) | (~((~solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~((~is_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 1) | is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Q)))))))))),
% 1.02/1.02 inference(rewrite,[status(thm)],[])).
% 1.02/1.02 tff(796,plain,
% 1.02/1.02 (((~![Board: array_int, Pos: $int] : (~((~(solution1(Board, Pos) | (~is_board1(Board, Pos)) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_3(Pos, Board))), 0) | is_consistent1(Board, tptp_fun_Q_3(Pos, Board)) | (~$greatereq(tptp_fun_Q_3(Pos, Board), 0)))))) | (~((~solution1(Board, Pos)) | (~((~is_board1(Board, Pos)) | (~![Q: $int] : (is_consistent1(Board, Q) | (~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0)))))))))) | (~((~(solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4)) | (~is_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~($lesseq($sum($sum(1, Pos!4), $product(-1, tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), 0) | is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))) | (~$greatereq(tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0)))))) | (~((~solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~((~is_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~![Q: $int] : (is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Q) | (~$greatereq(Q, 0)) | $lesseq($sum($sum(1, Pos!4), $product(-1, Q)), 0)))))))))) <=> ((~![Board: array_int, Pos: $int] : (~((~(solution1(Board, Pos) | (~is_board1(Board, Pos)) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_3(Pos, Board))), 0) | is_consistent1(Board, tptp_fun_Q_3(Pos, Board)) | (~$greatereq(tptp_fun_Q_3(Pos, Board), 0)))))) | (~((~solution1(Board, Pos)) | (~((~is_board1(Board, Pos)) | (~![Q: $int] : (is_consistent1(Board, Q) | (~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0)))))))))) | (~((~(solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4)) | (~is_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~((~$greatereq(tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0)) | is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), -1))))) | (~((~solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~((~is_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 1) | is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Q))))))))))),
% 1.02/1.02 inference(monotonicity,[status(thm)],[795])).
% 1.02/1.02 tff(797,plain,
% 1.02/1.02 (((~![Board: array_int, Pos: $int] : (~((~(solution1(Board, Pos) | (~is_board1(Board, Pos)) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_3(Pos, Board))), 0) | is_consistent1(Board, tptp_fun_Q_3(Pos, Board)) | (~$greatereq(tptp_fun_Q_3(Pos, Board), 0)))))) | (~((~solution1(Board, Pos)) | (~((~is_board1(Board, Pos)) | (~![Q: $int] : (is_consistent1(Board, Q) | (~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0)))))))))) | (~((~(solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4)) | (~is_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~($lesseq($sum($sum(1, Pos!4), $product(-1, tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), 0) | is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))) | (~$greatereq(tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0)))))) | (~((~solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~((~is_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~![Q: $int] : (is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Q) | (~$greatereq(Q, 0)) | $lesseq($sum($sum(1, Pos!4), $product(-1, Q)), 0)))))))))) <=> ((~![Board: array_int, Pos: $int] : (~((~(solution1(Board, Pos) | (~is_board1(Board, Pos)) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_3(Pos, Board))), 0) | is_consistent1(Board, tptp_fun_Q_3(Pos, Board)) | (~$greatereq(tptp_fun_Q_3(Pos, Board), 0)))))) | (~((~solution1(Board, Pos)) | (~((~is_board1(Board, Pos)) | (~![Q: $int] : (is_consistent1(Board, Q) | (~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0)))))))))) | (~((~(solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4)) | (~is_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~((~$greatereq(tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0)) | is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), -1))))) | (~((~solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~((~is_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 1) | is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Q))))))))))),
% 1.02/1.02 inference(transitivity,[status(thm)],[796, 794])).
% 1.02/1.02 tff(798,plain,
% 1.02/1.02 ((~![Board: array_int, Pos: $int] : (~((~(solution1(Board, Pos) | (~is_board1(Board, Pos)) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_3(Pos, Board))), 0) | is_consistent1(Board, tptp_fun_Q_3(Pos, Board)) | (~$greatereq(tptp_fun_Q_3(Pos, Board), 0)))))) | (~((~solution1(Board, Pos)) | (~((~is_board1(Board, Pos)) | (~![Q: $int] : (is_consistent1(Board, Q) | (~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0)))))))))) | (~((~(solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4)) | (~is_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~($lesseq($sum($sum(1, Pos!4), $product(-1, tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), 0) | is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))) | (~$greatereq(tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0)))))) | (~((~solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~((~is_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~![Q: $int] : (is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Q) | (~$greatereq(Q, 0)) | $lesseq($sum($sum(1, Pos!4), $product(-1, Q)), 0)))))))))),
% 1.02/1.02 inference(quant_inst,[status(thm)],[])).
% 1.02/1.02 tff(799,plain,
% 1.02/1.02 ((~![Board: array_int, Pos: $int] : (~((~(solution1(Board, Pos) | (~is_board1(Board, Pos)) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_3(Pos, Board))), 0) | is_consistent1(Board, tptp_fun_Q_3(Pos, Board)) | (~$greatereq(tptp_fun_Q_3(Pos, Board), 0)))))) | (~((~solution1(Board, Pos)) | (~((~is_board1(Board, Pos)) | (~![Q: $int] : (is_consistent1(Board, Q) | (~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0)))))))))) | (~((~(solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4)) | (~is_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~((~$greatereq(tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0)) | is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), -1))))) | (~((~solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~((~is_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 1) | is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Q)))))))))),
% 1.02/1.02 inference(modus_ponens,[status(thm)],[798, 797])).
% 1.02/1.02 tff(800,plain,
% 1.02/1.02 ($false),
% 1.02/1.02 inference(unit_resolution,[status(thm)],[799, 107, 793])).
% 1.02/1.02 tff(801,plain,(~((~(solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4)) | (~is_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~((~$greatereq(tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0)) | is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), -1))))) | (~((~solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~((~is_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 1) | is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Q))))))))), inference(lemma,lemma(discharge,[]))).
% 1.02/1.02 tff(802,plain,
% 1.02/1.02 (((~(solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4)) | (~is_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~((~$greatereq(tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0)) | is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), -1))))) | (~((~solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~((~is_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 1) | is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Q)))))))) | ((~solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~((~is_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 1) | is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Q))))))),
% 1.02/1.02 inference(tautology,[status(thm)],[])).
% 1.02/1.02 tff(803,plain,
% 1.02/1.02 ((~solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~((~is_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 1) | is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Q)))))),
% 1.02/1.02 inference(unit_resolution,[status(thm)],[802, 801])).
% 1.02/1.02 tff(804,plain,
% 1.02/1.02 ((~((~solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~((~is_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 1) | is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Q))))))) | (~solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~((~is_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 1) | is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Q)))))),
% 1.02/1.02 inference(tautology,[status(thm)],[])).
% 1.02/1.02 tff(805,plain,
% 1.02/1.02 ((~solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~((~is_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 1) | is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Q)))))),
% 1.02/1.02 inference(unit_resolution,[status(thm)],[804, 803])).
% 1.02/1.02 tff(806,plain,
% 1.02/1.02 (~solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))),
% 1.02/1.02 inference(unit_resolution,[status(thm)],[805, 792])).
% 1.02/1.02 tff(807,plain,
% 1.02/1.02 (^[B1: array_int, B2: array_int, Pos: $int] : refl((solution1(B2, Pos) | (~eq_board1(B1, B2, Pos)) | (~solution1(B1, Pos)) | (~($sum(length1(int, t2tb1(B1)), $product(-1, length1(int, t2tb1(B2)))) = 0))) <=> (solution1(B2, Pos) | (~eq_board1(B1, B2, Pos)) | (~solution1(B1, Pos)) | (~($sum(length1(int, t2tb1(B1)), $product(-1, length1(int, t2tb1(B2)))) = 0))))),
% 1.02/1.02 inference(bind,[status(th)],[])).
% 1.02/1.02 tff(808,plain,
% 1.02/1.02 (![B1: array_int, B2: array_int, Pos: $int] : (solution1(B2, Pos) | (~eq_board1(B1, B2, Pos)) | (~solution1(B1, Pos)) | (~($sum(length1(int, t2tb1(B1)), $product(-1, length1(int, t2tb1(B2)))) = 0))) <=> ![B1: array_int, B2: array_int, Pos: $int] : (solution1(B2, Pos) | (~eq_board1(B1, B2, Pos)) | (~solution1(B1, Pos)) | (~($sum(length1(int, t2tb1(B1)), $product(-1, length1(int, t2tb1(B2)))) = 0)))),
% 1.02/1.02 inference(quant_intro,[status(thm)],[807])).
% 1.02/1.02 tff(809,plain,
% 1.02/1.02 (^[B1: array_int, B2: array_int, Pos: $int] : trans(monotonicity(rewrite((~(length1(int, t2tb1(B1)) = length1(int, t2tb1(B2)))) <=> (~($sum(length1(int, t2tb1(B1)), $product(-1, length1(int, t2tb1(B2)))) = 0))), ((solution1(B2, Pos) | (~eq_board1(B1, B2, Pos)) | (~solution1(B1, Pos)) | (~(length1(int, t2tb1(B1)) = length1(int, t2tb1(B2))))) <=> (solution1(B2, Pos) | (~eq_board1(B1, B2, Pos)) | (~solution1(B1, Pos)) | (~($sum(length1(int, t2tb1(B1)), $product(-1, length1(int, t2tb1(B2)))) = 0))))), rewrite((solution1(B2, Pos) | (~eq_board1(B1, B2, Pos)) | (~solution1(B1, Pos)) | (~($sum(length1(int, t2tb1(B1)), $product(-1, length1(int, t2tb1(B2)))) = 0))) <=> (solution1(B2, Pos) | (~eq_board1(B1, B2, Pos)) | (~solution1(B1, Pos)) | (~($sum(length1(int, t2tb1(B1)), $product(-1, length1(int, t2tb1(B2)))) = 0)))), ((solution1(B2, Pos) | (~eq_board1(B1, B2, Pos)) | (~solution1(B1, Pos)) | (~(length1(int, t2tb1(B1)) = length1(int, t2tb1(B2))))) <=> (solution1(B2, Pos) | (~eq_board1(B1, B2, Pos)) | (~solution1(B1, Pos)) | (~($sum(length1(int, t2tb1(B1)), $product(-1, length1(int, t2tb1(B2)))) = 0)))))),
% 1.02/1.02 inference(bind,[status(th)],[])).
% 1.02/1.02 tff(810,plain,
% 1.02/1.02 (![B1: array_int, B2: array_int, Pos: $int] : (solution1(B2, Pos) | (~eq_board1(B1, B2, Pos)) | (~solution1(B1, Pos)) | (~(length1(int, t2tb1(B1)) = length1(int, t2tb1(B2))))) <=> ![B1: array_int, B2: array_int, Pos: $int] : (solution1(B2, Pos) | (~eq_board1(B1, B2, Pos)) | (~solution1(B1, Pos)) | (~($sum(length1(int, t2tb1(B1)), $product(-1, length1(int, t2tb1(B2)))) = 0)))),
% 1.02/1.02 inference(quant_intro,[status(thm)],[809])).
% 1.02/1.02 tff(811,plain,
% 1.02/1.02 (![B1: array_int, B2: array_int, Pos: $int] : (solution1(B2, Pos) | (~eq_board1(B1, B2, Pos)) | (~solution1(B1, Pos)) | (~(length1(int, t2tb1(B1)) = length1(int, t2tb1(B2))))) <=> ![B1: array_int, B2: array_int, Pos: $int] : (solution1(B2, Pos) | (~eq_board1(B1, B2, Pos)) | (~solution1(B1, Pos)) | (~(length1(int, t2tb1(B1)) = length1(int, t2tb1(B2)))))),
% 1.02/1.02 inference(rewrite,[status(thm)],[])).
% 1.02/1.02 tff(812,plain,
% 1.02/1.02 (^[B1: array_int, B2: array_int, Pos: $int] : trans(monotonicity(trans(monotonicity(rewrite((solution1(B1, Pos) => solution1(B2, Pos)) <=> ((~solution1(B1, Pos)) | solution1(B2, Pos))), ((eq_board1(B1, B2, Pos) => (solution1(B1, Pos) => solution1(B2, Pos))) <=> (eq_board1(B1, B2, Pos) => ((~solution1(B1, Pos)) | solution1(B2, Pos))))), rewrite((eq_board1(B1, B2, Pos) => ((~solution1(B1, Pos)) | solution1(B2, Pos))) <=> (solution1(B2, Pos) | (~eq_board1(B1, B2, Pos)) | (~solution1(B1, Pos)))), ((eq_board1(B1, B2, Pos) => (solution1(B1, Pos) => solution1(B2, Pos))) <=> (solution1(B2, Pos) | (~eq_board1(B1, B2, Pos)) | (~solution1(B1, Pos))))), (((length1(int, t2tb1(B1)) = length1(int, t2tb1(B2))) => (eq_board1(B1, B2, Pos) => (solution1(B1, Pos) => solution1(B2, Pos)))) <=> ((length1(int, t2tb1(B1)) = length1(int, t2tb1(B2))) => (solution1(B2, Pos) | (~eq_board1(B1, B2, Pos)) | (~solution1(B1, Pos)))))), rewrite(((length1(int, t2tb1(B1)) = length1(int, t2tb1(B2))) => (solution1(B2, Pos) | (~eq_board1(B1, B2, Pos)) | (~solution1(B1, Pos)))) <=> (solution1(B2, Pos) | (~eq_board1(B1, B2, Pos)) | (~solution1(B1, Pos)) | (~(length1(int, t2tb1(B1)) = length1(int, t2tb1(B2)))))), (((length1(int, t2tb1(B1)) = length1(int, t2tb1(B2))) => (eq_board1(B1, B2, Pos) => (solution1(B1, Pos) => solution1(B2, Pos)))) <=> (solution1(B2, Pos) | (~eq_board1(B1, B2, Pos)) | (~solution1(B1, Pos)) | (~(length1(int, t2tb1(B1)) = length1(int, t2tb1(B2)))))))),
% 1.02/1.02 inference(bind,[status(th)],[])).
% 1.02/1.02 tff(813,plain,
% 1.02/1.02 (![B1: array_int, B2: array_int, Pos: $int] : ((length1(int, t2tb1(B1)) = length1(int, t2tb1(B2))) => (eq_board1(B1, B2, Pos) => (solution1(B1, Pos) => solution1(B2, Pos)))) <=> ![B1: array_int, B2: array_int, Pos: $int] : (solution1(B2, Pos) | (~eq_board1(B1, B2, Pos)) | (~solution1(B1, Pos)) | (~(length1(int, t2tb1(B1)) = length1(int, t2tb1(B2)))))),
% 1.02/1.02 inference(quant_intro,[status(thm)],[812])).
% 1.02/1.02 tff(814,axiom,(![B1: array_int, B2: array_int, Pos: $int] : ((length1(int, t2tb1(B1)) = length1(int, t2tb1(B2))) => (eq_board1(B1, B2, Pos) => (solution1(B1, Pos) => solution1(B2, Pos))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','solution_eq_board')).
% 1.02/1.02 tff(815,plain,
% 1.02/1.02 (![B1: array_int, B2: array_int, Pos: $int] : (solution1(B2, Pos) | (~eq_board1(B1, B2, Pos)) | (~solution1(B1, Pos)) | (~(length1(int, t2tb1(B1)) = length1(int, t2tb1(B2)))))),
% 1.02/1.02 inference(modus_ponens,[status(thm)],[814, 813])).
% 1.02/1.02 tff(816,plain,
% 1.02/1.02 (![B1: array_int, B2: array_int, Pos: $int] : (solution1(B2, Pos) | (~eq_board1(B1, B2, Pos)) | (~solution1(B1, Pos)) | (~(length1(int, t2tb1(B1)) = length1(int, t2tb1(B2)))))),
% 1.02/1.02 inference(modus_ponens,[status(thm)],[815, 811])).
% 1.02/1.02 tff(817,plain,
% 1.02/1.02 (![B1: array_int, B2: array_int, Pos: $int] : (solution1(B2, Pos) | (~eq_board1(B1, B2, Pos)) | (~solution1(B1, Pos)) | (~($sum(length1(int, t2tb1(B1)), $product(-1, length1(int, t2tb1(B2)))) = 0)))),
% 1.02/1.02 inference(modus_ponens,[status(thm)],[816, 810])).
% 1.02/1.02 tff(818,plain,(
% 1.02/1.02 ![B1: array_int, B2: array_int, Pos: $int] : (solution1(B2, Pos) | (~eq_board1(B1, B2, Pos)) | (~solution1(B1, Pos)) | (~($sum(length1(int, t2tb1(B1)), $product(-1, length1(int, t2tb1(B2)))) = 0)))),
% 1.02/1.02 inference(skolemize,[status(sab)],[817])).
% 1.02/1.02 tff(819,plain,
% 1.02/1.02 (![B1: array_int, B2: array_int, Pos: $int] : (solution1(B2, Pos) | (~eq_board1(B1, B2, Pos)) | (~solution1(B1, Pos)) | (~($sum(length1(int, t2tb1(B1)), $product(-1, length1(int, t2tb1(B2)))) = 0)))),
% 1.02/1.02 inference(modus_ponens,[status(thm)],[818, 808])).
% 1.02/1.02 tff(820,plain,
% 1.02/1.02 (((~![B1: array_int, B2: array_int, Pos: $int] : (solution1(B2, Pos) | (~eq_board1(B1, B2, Pos)) | (~solution1(B1, Pos)) | (~($sum(length1(int, t2tb1(B1)), $product(-1, length1(int, t2tb1(B2)))) = 0)))) | (solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4)) | (~($sum(length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))))) = 0)) | (~eq_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), $sum(1, Pos!4))))) <=> ((~![B1: array_int, B2: array_int, Pos: $int] : (solution1(B2, Pos) | (~eq_board1(B1, B2, Pos)) | (~solution1(B1, Pos)) | (~($sum(length1(int, t2tb1(B1)), $product(-1, length1(int, t2tb1(B2)))) = 0)))) | solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4)) | (~($sum(length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))))) = 0)) | (~eq_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), $sum(1, Pos!4))))),
% 1.02/1.02 inference(rewrite,[status(thm)],[])).
% 1.02/1.02 tff(821,plain,
% 1.02/1.02 ((solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4)) | (~eq_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), $sum(1, Pos!4))) | (~($sum(length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))))) = 0))) <=> (solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4)) | (~($sum(length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))))) = 0)) | (~eq_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), $sum(1, Pos!4))))),
% 1.02/1.02 inference(rewrite,[status(thm)],[])).
% 1.02/1.02 tff(822,plain,
% 1.02/1.02 ((~($sum(length1(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))))) = 0)) <=> (~($sum(length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))))) = 0))),
% 1.02/1.02 inference(rewrite,[status(thm)],[])).
% 1.02/1.02 tff(823,plain,
% 1.02/1.02 ((solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4)) | (~eq_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), $sum(1, Pos!4))) | (~($sum(length1(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))))) = 0))) <=> (solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4)) | (~eq_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), $sum(1, Pos!4))) | (~($sum(length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))))) = 0)))),
% 1.02/1.02 inference(monotonicity,[status(thm)],[822])).
% 1.02/1.02 tff(824,plain,
% 1.02/1.02 ((solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4)) | (~eq_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), $sum(1, Pos!4))) | (~($sum(length1(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))))) = 0))) <=> (solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4)) | (~($sum(length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))))) = 0)) | (~eq_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), $sum(1, Pos!4))))),
% 1.02/1.02 inference(transitivity,[status(thm)],[823, 821])).
% 1.02/1.02 tff(825,plain,
% 1.02/1.02 (((~![B1: array_int, B2: array_int, Pos: $int] : (solution1(B2, Pos) | (~eq_board1(B1, B2, Pos)) | (~solution1(B1, Pos)) | (~($sum(length1(int, t2tb1(B1)), $product(-1, length1(int, t2tb1(B2)))) = 0)))) | (solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4)) | (~eq_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), $sum(1, Pos!4))) | (~($sum(length1(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))))) = 0)))) <=> ((~![B1: array_int, B2: array_int, Pos: $int] : (solution1(B2, Pos) | (~eq_board1(B1, B2, Pos)) | (~solution1(B1, Pos)) | (~($sum(length1(int, t2tb1(B1)), $product(-1, length1(int, t2tb1(B2)))) = 0)))) | (solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4)) | (~($sum(length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))))) = 0)) | (~eq_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), $sum(1, Pos!4)))))),
% 1.02/1.02 inference(monotonicity,[status(thm)],[824])).
% 1.02/1.02 tff(826,plain,
% 1.02/1.02 (((~![B1: array_int, B2: array_int, Pos: $int] : (solution1(B2, Pos) | (~eq_board1(B1, B2, Pos)) | (~solution1(B1, Pos)) | (~($sum(length1(int, t2tb1(B1)), $product(-1, length1(int, t2tb1(B2)))) = 0)))) | (solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4)) | (~eq_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), $sum(1, Pos!4))) | (~($sum(length1(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))))) = 0)))) <=> ((~![B1: array_int, B2: array_int, Pos: $int] : (solution1(B2, Pos) | (~eq_board1(B1, B2, Pos)) | (~solution1(B1, Pos)) | (~($sum(length1(int, t2tb1(B1)), $product(-1, length1(int, t2tb1(B2)))) = 0)))) | solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4)) | (~($sum(length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))))) = 0)) | (~eq_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), $sum(1, Pos!4))))),
% 1.02/1.02 inference(transitivity,[status(thm)],[825, 820])).
% 1.02/1.02 tff(827,plain,
% 1.02/1.02 ((~![B1: array_int, B2: array_int, Pos: $int] : (solution1(B2, Pos) | (~eq_board1(B1, B2, Pos)) | (~solution1(B1, Pos)) | (~($sum(length1(int, t2tb1(B1)), $product(-1, length1(int, t2tb1(B2)))) = 0)))) | (solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4)) | (~eq_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), $sum(1, Pos!4))) | (~($sum(length1(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))))) = 0)))),
% 1.02/1.02 inference(quant_inst,[status(thm)],[])).
% 1.02/1.02 tff(828,plain,
% 1.02/1.02 ((~![B1: array_int, B2: array_int, Pos: $int] : (solution1(B2, Pos) | (~eq_board1(B1, B2, Pos)) | (~solution1(B1, Pos)) | (~($sum(length1(int, t2tb1(B1)), $product(-1, length1(int, t2tb1(B2)))) = 0)))) | solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4)) | (~($sum(length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))))) = 0)) | (~eq_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), $sum(1, Pos!4)))),
% 1.02/1.02 inference(modus_ponens,[status(thm)],[827, 826])).
% 1.02/1.02 tff(829,plain,
% 1.02/1.02 (~solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), $sum(1, Pos!4))),
% 1.02/1.02 inference(unit_resolution,[status(thm)],[828, 819, 806, 774, 738])).
% 1.02/1.02 tff(830,plain,
% 1.02/1.02 (((~![Board: array_int, Pos: $int] : (~((~(solution1(Board, Pos) | (~is_board1(Board, Pos)) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_3(Pos, Board))), 0) | is_consistent1(Board, tptp_fun_Q_3(Pos, Board)) | (~$greatereq(tptp_fun_Q_3(Pos, Board), 0)))))) | (~((~solution1(Board, Pos)) | (~((~is_board1(Board, Pos)) | (~![Q: $int] : (is_consistent1(Board, Q) | (~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0)))))))))) | (~((~(solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5) | (~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~(is_consistent1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), tptp_fun_Q_3(N!5, tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))) | $lesseq($sum(N!5, $product(-1, tptp_fun_Q_3(N!5, tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), 0) | (~$greatereq(tptp_fun_Q_3(N!5, tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), 0)))))) | (~((~solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~((~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, N!5)), 0) | is_consistent1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Q)))))))))) <=> ((~![Board: array_int, Pos: $int] : (~((~(solution1(Board, Pos) | (~is_board1(Board, Pos)) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_3(Pos, Board))), 0) | is_consistent1(Board, tptp_fun_Q_3(Pos, Board)) | (~$greatereq(tptp_fun_Q_3(Pos, Board), 0)))))) | (~((~solution1(Board, Pos)) | (~((~is_board1(Board, Pos)) | (~![Q: $int] : (is_consistent1(Board, Q) | (~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0)))))))))) | (~((~(solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5) | (~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~(is_consistent1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), tptp_fun_Q_3(N!5, tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))) | $lesseq($sum(N!5, $product(-1, tptp_fun_Q_3(N!5, tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), 0) | (~$greatereq(tptp_fun_Q_3(N!5, tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), 0)))))) | (~((~solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~((~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, N!5)), 0) | is_consistent1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Q))))))))))),
% 1.02/1.02 inference(rewrite,[status(thm)],[])).
% 1.02/1.02 tff(831,plain,
% 1.02/1.02 ((~((~(solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5) | (~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~($lesseq($sum(N!5, $product(-1, tptp_fun_Q_3(N!5, tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), 0) | is_consistent1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), tptp_fun_Q_3(N!5, tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))) | (~$greatereq(tptp_fun_Q_3(N!5, tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), 0)))))) | (~((~solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~((~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~![Q: $int] : (is_consistent1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Q) | (~$greatereq(Q, 0)) | $lesseq($sum(N!5, $product(-1, Q)), 0))))))))) <=> (~((~(solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5) | (~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~(is_consistent1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), tptp_fun_Q_3(N!5, tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))) | $lesseq($sum(N!5, $product(-1, tptp_fun_Q_3(N!5, tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), 0) | (~$greatereq(tptp_fun_Q_3(N!5, tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), 0)))))) | (~((~solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~((~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, N!5)), 0) | is_consistent1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Q)))))))))),
% 1.02/1.02 inference(rewrite,[status(thm)],[])).
% 1.02/1.02 tff(832,plain,
% 1.02/1.02 (((~![Board: array_int, Pos: $int] : (~((~(solution1(Board, Pos) | (~is_board1(Board, Pos)) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_3(Pos, Board))), 0) | is_consistent1(Board, tptp_fun_Q_3(Pos, Board)) | (~$greatereq(tptp_fun_Q_3(Pos, Board), 0)))))) | (~((~solution1(Board, Pos)) | (~((~is_board1(Board, Pos)) | (~![Q: $int] : (is_consistent1(Board, Q) | (~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0)))))))))) | (~((~(solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5) | (~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~($lesseq($sum(N!5, $product(-1, tptp_fun_Q_3(N!5, tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), 0) | is_consistent1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), tptp_fun_Q_3(N!5, tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))) | (~$greatereq(tptp_fun_Q_3(N!5, tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), 0)))))) | (~((~solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~((~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~![Q: $int] : (is_consistent1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Q) | (~$greatereq(Q, 0)) | $lesseq($sum(N!5, $product(-1, Q)), 0)))))))))) <=> ((~![Board: array_int, Pos: $int] : (~((~(solution1(Board, Pos) | (~is_board1(Board, Pos)) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_3(Pos, Board))), 0) | is_consistent1(Board, tptp_fun_Q_3(Pos, Board)) | (~$greatereq(tptp_fun_Q_3(Pos, Board), 0)))))) | (~((~solution1(Board, Pos)) | (~((~is_board1(Board, Pos)) | (~![Q: $int] : (is_consistent1(Board, Q) | (~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0)))))))))) | (~((~(solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5) | (~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~(is_consistent1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), tptp_fun_Q_3(N!5, tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))) | $lesseq($sum(N!5, $product(-1, tptp_fun_Q_3(N!5, tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), 0) | (~$greatereq(tptp_fun_Q_3(N!5, tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), 0)))))) | (~((~solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~((~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, N!5)), 0) | is_consistent1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Q))))))))))),
% 1.02/1.03 inference(monotonicity,[status(thm)],[831])).
% 1.02/1.03 tff(833,plain,
% 1.02/1.03 (((~![Board: array_int, Pos: $int] : (~((~(solution1(Board, Pos) | (~is_board1(Board, Pos)) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_3(Pos, Board))), 0) | is_consistent1(Board, tptp_fun_Q_3(Pos, Board)) | (~$greatereq(tptp_fun_Q_3(Pos, Board), 0)))))) | (~((~solution1(Board, Pos)) | (~((~is_board1(Board, Pos)) | (~![Q: $int] : (is_consistent1(Board, Q) | (~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0)))))))))) | (~((~(solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5) | (~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~($lesseq($sum(N!5, $product(-1, tptp_fun_Q_3(N!5, tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), 0) | is_consistent1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), tptp_fun_Q_3(N!5, tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))) | (~$greatereq(tptp_fun_Q_3(N!5, tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), 0)))))) | (~((~solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~((~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~![Q: $int] : (is_consistent1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Q) | (~$greatereq(Q, 0)) | $lesseq($sum(N!5, $product(-1, Q)), 0)))))))))) <=> ((~![Board: array_int, Pos: $int] : (~((~(solution1(Board, Pos) | (~is_board1(Board, Pos)) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_3(Pos, Board))), 0) | is_consistent1(Board, tptp_fun_Q_3(Pos, Board)) | (~$greatereq(tptp_fun_Q_3(Pos, Board), 0)))))) | (~((~solution1(Board, Pos)) | (~((~is_board1(Board, Pos)) | (~![Q: $int] : (is_consistent1(Board, Q) | (~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0)))))))))) | (~((~(solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5) | (~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~(is_consistent1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), tptp_fun_Q_3(N!5, tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))) | $lesseq($sum(N!5, $product(-1, tptp_fun_Q_3(N!5, tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), 0) | (~$greatereq(tptp_fun_Q_3(N!5, tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), 0)))))) | (~((~solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~((~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, N!5)), 0) | is_consistent1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Q))))))))))),
% 1.02/1.03 inference(transitivity,[status(thm)],[832, 830])).
% 1.02/1.03 tff(834,plain,
% 1.02/1.03 ((~![Board: array_int, Pos: $int] : (~((~(solution1(Board, Pos) | (~is_board1(Board, Pos)) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_3(Pos, Board))), 0) | is_consistent1(Board, tptp_fun_Q_3(Pos, Board)) | (~$greatereq(tptp_fun_Q_3(Pos, Board), 0)))))) | (~((~solution1(Board, Pos)) | (~((~is_board1(Board, Pos)) | (~![Q: $int] : (is_consistent1(Board, Q) | (~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0)))))))))) | (~((~(solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5) | (~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~($lesseq($sum(N!5, $product(-1, tptp_fun_Q_3(N!5, tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), 0) | is_consistent1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), tptp_fun_Q_3(N!5, tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))) | (~$greatereq(tptp_fun_Q_3(N!5, tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), 0)))))) | (~((~solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~((~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~![Q: $int] : (is_consistent1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Q) | (~$greatereq(Q, 0)) | $lesseq($sum(N!5, $product(-1, Q)), 0)))))))))),
% 1.02/1.03 inference(quant_inst,[status(thm)],[])).
% 1.02/1.03 tff(835,plain,
% 1.02/1.03 ((~![Board: array_int, Pos: $int] : (~((~(solution1(Board, Pos) | (~is_board1(Board, Pos)) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_3(Pos, Board))), 0) | is_consistent1(Board, tptp_fun_Q_3(Pos, Board)) | (~$greatereq(tptp_fun_Q_3(Pos, Board), 0)))))) | (~((~solution1(Board, Pos)) | (~((~is_board1(Board, Pos)) | (~![Q: $int] : (is_consistent1(Board, Q) | (~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0)))))))))) | (~((~(solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5) | (~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~(is_consistent1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), tptp_fun_Q_3(N!5, tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))) | $lesseq($sum(N!5, $product(-1, tptp_fun_Q_3(N!5, tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), 0) | (~$greatereq(tptp_fun_Q_3(N!5, tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), 0)))))) | (~((~solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~((~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, N!5)), 0) | is_consistent1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Q)))))))))),
% 1.02/1.03 inference(modus_ponens,[status(thm)],[834, 833])).
% 1.02/1.03 tff(836,plain,
% 1.02/1.03 (~((~(solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5) | (~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~(is_consistent1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), tptp_fun_Q_3(N!5, tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))) | $lesseq($sum(N!5, $product(-1, tptp_fun_Q_3(N!5, tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), 0) | (~$greatereq(tptp_fun_Q_3(N!5, tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), 0)))))) | (~((~solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~((~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, N!5)), 0) | is_consistent1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Q))))))))),
% 1.02/1.03 inference(unit_resolution,[status(thm)],[835, 107])).
% 1.02/1.03 tff(837,plain,
% 1.02/1.03 (((~(solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5) | (~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~(is_consistent1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), tptp_fun_Q_3(N!5, tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))) | $lesseq($sum(N!5, $product(-1, tptp_fun_Q_3(N!5, tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), 0) | (~$greatereq(tptp_fun_Q_3(N!5, tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), 0)))))) | (~((~solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~((~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, N!5)), 0) | is_consistent1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Q)))))))) | ((~solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~((~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, N!5)), 0) | is_consistent1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Q))))))),
% 1.02/1.03 inference(tautology,[status(thm)],[])).
% 1.02/1.03 tff(838,plain,
% 1.02/1.03 ((~solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~((~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, N!5)), 0) | is_consistent1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Q)))))),
% 1.02/1.03 inference(unit_resolution,[status(thm)],[837, 836])).
% 1.02/1.03 tff(839,plain,
% 1.02/1.03 ((~((~solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~((~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, N!5)), 0) | is_consistent1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Q))))))) | (~solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~((~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, N!5)), 0) | is_consistent1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Q)))))),
% 1.02/1.03 inference(tautology,[status(thm)],[])).
% 1.02/1.03 tff(840,plain,
% 1.02/1.03 ((~((~solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~((~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, N!5)), 0) | is_consistent1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Q))))))) | (~((~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, N!5)), 0) | is_consistent1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Q)))))),
% 1.02/1.03 inference(unit_resolution,[status(thm)],[839, 616])).
% 1.02/1.03 tff(841,plain,
% 1.02/1.03 (~((~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, N!5)), 0) | is_consistent1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Q))))),
% 1.02/1.03 inference(unit_resolution,[status(thm)],[840, 838])).
% 1.02/1.03 tff(842,plain,
% 1.02/1.03 (((~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, N!5)), 0) | is_consistent1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Q)))) | ![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, N!5)), 0) | is_consistent1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Q))),
% 1.02/1.03 inference(tautology,[status(thm)],[])).
% 1.02/1.03 tff(843,plain,
% 1.02/1.03 (![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, N!5)), 0) | is_consistent1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Q))),
% 1.02/1.03 inference(unit_resolution,[status(thm)],[842, 841])).
% 1.02/1.03 tff(844,assumption,(![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, N!5)), 0) | is_consistent1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Q))), introduced(assumption)).
% 1.02/1.03 tff(845,assumption,(~(is_consistent1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))) | (~$greatereq(tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), 0)) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), -1))), introduced(assumption)).
% 1.02/1.03 tff(846,plain,
% 1.02/1.03 ((is_consistent1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))) | (~$greatereq(tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), 0)) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), -1)) | $greatereq(tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), 0)),
% 1.02/1.03 inference(tautology,[status(thm)],[])).
% 1.02/1.03 tff(847,plain,
% 1.02/1.03 ($greatereq(tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), 0)),
% 1.02/1.03 inference(unit_resolution,[status(thm)],[846, 845])).
% 1.02/1.03 tff(848,plain,
% 1.02/1.03 ((is_consistent1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))) | (~$greatereq(tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), 0)) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), -1)) | (~is_consistent1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))))),
% 1.02/1.03 inference(tautology,[status(thm)],[])).
% 1.02/1.03 tff(849,plain,
% 1.02/1.03 (~is_consistent1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))),
% 1.02/1.03 inference(unit_resolution,[status(thm)],[848, 845])).
% 1.02/1.03 tff(850,plain,
% 1.02/1.03 (((~![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, N!5)), 0) | is_consistent1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Q))) | (is_consistent1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))) | (~$greatereq(tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), 0)) | $lesseq($sum(N!5, $product(-1, tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), 0))) <=> ((~![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, N!5)), 0) | is_consistent1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Q))) | is_consistent1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))) | (~$greatereq(tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), 0)) | $lesseq($sum(N!5, $product(-1, tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), 0))),
% 1.02/1.03 inference(rewrite,[status(thm)],[])).
% 1.02/1.03 tff(851,plain,
% 1.02/1.03 (((~$greatereq(tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), 0)) | $lesseq($sum(N!5, $product(-1, tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), 0) | is_consistent1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))) <=> (is_consistent1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))) | (~$greatereq(tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), 0)) | $lesseq($sum(N!5, $product(-1, tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), 0))),
% 1.02/1.03 inference(rewrite,[status(thm)],[])).
% 1.02/1.03 tff(852,plain,
% 1.02/1.03 ($greatereq($sum($product(-1, N!5), tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))), 0) <=> $lesseq($sum(N!5, $product(-1, tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), 0)),
% 1.02/1.03 inference(rewrite,[status(thm)],[])).
% 1.02/1.03 tff(853,plain,
% 1.02/1.03 ($sum(tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), $product(-1, N!5)) = $sum($product(-1, N!5), tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))),
% 1.02/1.03 inference(rewrite,[status(thm)],[])).
% 1.02/1.03 tff(854,plain,
% 1.02/1.03 ($greatereq($sum(tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), $product(-1, N!5)), 0) <=> $greatereq($sum($product(-1, N!5), tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))), 0)),
% 1.02/1.03 inference(monotonicity,[status(thm)],[853])).
% 1.02/1.03 tff(855,plain,
% 1.02/1.03 ($greatereq($sum(tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), $product(-1, N!5)), 0) <=> $lesseq($sum(N!5, $product(-1, tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), 0)),
% 1.02/1.03 inference(transitivity,[status(thm)],[854, 852])).
% 1.02/1.03 tff(856,plain,
% 1.02/1.03 (((~$greatereq(tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), 0)) | $greatereq($sum(tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), $product(-1, N!5)), 0) | is_consistent1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))) <=> ((~$greatereq(tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), 0)) | $lesseq($sum(N!5, $product(-1, tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), 0) | is_consistent1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))))),
% 1.02/1.03 inference(monotonicity,[status(thm)],[855])).
% 1.02/1.03 tff(857,plain,
% 1.02/1.03 (((~$greatereq(tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), 0)) | $greatereq($sum(tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), $product(-1, N!5)), 0) | is_consistent1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))) <=> (is_consistent1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))) | (~$greatereq(tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), 0)) | $lesseq($sum(N!5, $product(-1, tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), 0))),
% 1.02/1.03 inference(transitivity,[status(thm)],[856, 851])).
% 1.02/1.03 tff(858,plain,
% 1.02/1.03 (((~![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, N!5)), 0) | is_consistent1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Q))) | ((~$greatereq(tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), 0)) | $greatereq($sum(tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), $product(-1, N!5)), 0) | is_consistent1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))))) <=> ((~![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, N!5)), 0) | is_consistent1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Q))) | (is_consistent1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))) | (~$greatereq(tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), 0)) | $lesseq($sum(N!5, $product(-1, tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), 0)))),
% 1.08/1.03 inference(monotonicity,[status(thm)],[857])).
% 1.08/1.03 tff(859,plain,
% 1.08/1.03 (((~![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, N!5)), 0) | is_consistent1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Q))) | ((~$greatereq(tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), 0)) | $greatereq($sum(tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), $product(-1, N!5)), 0) | is_consistent1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))))) <=> ((~![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, N!5)), 0) | is_consistent1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Q))) | is_consistent1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))) | (~$greatereq(tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), 0)) | $lesseq($sum(N!5, $product(-1, tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), 0))),
% 1.08/1.03 inference(transitivity,[status(thm)],[858, 850])).
% 1.08/1.03 tff(860,plain,
% 1.08/1.03 ((~![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, N!5)), 0) | is_consistent1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Q))) | ((~$greatereq(tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), 0)) | $greatereq($sum(tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), $product(-1, N!5)), 0) | is_consistent1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))))),
% 1.08/1.03 inference(quant_inst,[status(thm)],[])).
% 1.08/1.03 tff(861,plain,
% 1.08/1.03 ((~![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, N!5)), 0) | is_consistent1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Q))) | is_consistent1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))) | (~$greatereq(tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), 0)) | $lesseq($sum(N!5, $product(-1, tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), 0)),
% 1.08/1.03 inference(modus_ponens,[status(thm)],[860, 859])).
% 1.08/1.03 tff(862,plain,
% 1.08/1.03 ($lesseq($sum(N!5, $product(-1, tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), 0)),
% 1.08/1.03 inference(unit_resolution,[status(thm)],[861, 849, 847, 844])).
% 1.08/1.03 tff(863,plain,
% 1.08/1.03 ((is_consistent1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))) | (~$greatereq(tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), 0)) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), -1)) | (~$lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), -1))),
% 1.08/1.03 inference(tautology,[status(thm)],[])).
% 1.08/1.03 tff(864,plain,
% 1.08/1.03 (~$lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), -1)),
% 1.08/1.03 inference(unit_resolution,[status(thm)],[863, 845])).
% 1.08/1.03 tff(865,plain,
% 1.08/1.03 ($false),
% 1.08/1.03 inference(theory_lemma,[status(thm)],[48, 864, 862])).
% 1.08/1.03 tff(866,plain,((is_consistent1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))) | (~$greatereq(tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), 0)) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), -1)) | (~![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, N!5)), 0) | is_consistent1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Q)))), inference(lemma,lemma(discharge,[]))).
% 1.08/1.03 tff(867,plain,
% 1.08/1.03 (is_consistent1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))) | (~$greatereq(tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), 0)) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), -1)),
% 1.08/1.03 inference(unit_resolution,[status(thm)],[866, 843])).
% 1.08/1.03 tff(868,plain,
% 1.08/1.03 ((~(solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), $sum(1, Pos!4)) | (~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), $sum(1, Pos!4))) | (~(is_consistent1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))) | (~$greatereq(tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), 0)) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), -1))))) | solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), $sum(1, Pos!4)) | (~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), $sum(1, Pos!4))) | (~(is_consistent1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))) | (~$greatereq(tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), 0)) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), -1)))),
% 1.08/1.03 inference(tautology,[status(thm)],[])).
% 1.08/1.03 tff(869,plain,
% 1.08/1.03 ((~(solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), $sum(1, Pos!4)) | (~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), $sum(1, Pos!4))) | (~(is_consistent1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))) | (~$greatereq(tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), 0)) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), -1))))) | (~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), $sum(1, Pos!4)))),
% 1.08/1.03 inference(unit_resolution,[status(thm)],[868, 867, 829])).
% 1.08/1.03 tff(870,plain,
% 1.08/1.03 (~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), $sum(1, Pos!4))),
% 1.08/1.03 inference(unit_resolution,[status(thm)],[869, 116])).
% 1.08/1.03 tff(871,plain,
% 1.08/1.03 ((~(is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), $sum(1, Pos!4)) | (~((~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), 0)) | $lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))))), 0))) | (~$greatereq(tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), 0)) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), -1))))) | is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), $sum(1, Pos!4)) | (~((~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), 0)) | $lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))))), 0))) | (~$greatereq(tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), 0)) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), -1)))),
% 1.08/1.03 inference(tautology,[status(thm)],[])).
% 1.08/1.03 tff(872,plain,
% 1.08/1.03 ((~(is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), $sum(1, Pos!4)) | (~((~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), 0)) | $lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))))), 0))) | (~$greatereq(tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), 0)) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), -1))))) | (~((~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), 0)) | $lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))))), 0))) | (~$greatereq(tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), 0)) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), -1)))),
% 1.08/1.03 inference(unit_resolution,[status(thm)],[871, 870])).
% 1.08/1.03 tff(873,plain,
% 1.08/1.03 (~((~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), 0)) | $lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))))), 0))) | (~$greatereq(tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), 0)) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), -1))),
% 1.08/1.03 inference(unit_resolution,[status(thm)],[872, 82])).
% 1.08/1.03 tff(874,plain,
% 1.08/1.03 (((~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), 0)) | $lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))))), 0))) | (~$greatereq(tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), 0)) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), -1)) | $greatereq(tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), 0)),
% 1.08/1.03 inference(tautology,[status(thm)],[])).
% 1.08/1.03 tff(875,plain,
% 1.08/1.03 ($greatereq(tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), 0)),
% 1.08/1.03 inference(unit_resolution,[status(thm)],[874, 873])).
% 1.08/1.03 tff(876,plain,
% 1.08/1.03 (((~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), 0)) | $lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))))), 0))) | (~$greatereq(tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), 0)) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), -1)) | ((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), 0)) | $lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))))), 0))),
% 1.08/1.04 inference(tautology,[status(thm)],[])).
% 1.08/1.04 tff(877,plain,
% 1.08/1.04 ((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), 0)) | $lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))))), 0)),
% 1.08/1.04 inference(unit_resolution,[status(thm)],[876, 873])).
% 1.08/1.04 tff(878,plain,
% 1.08/1.04 (((~![Board: array_int, Pos: $int] : (~((~((~is_board1(Board, Pos)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(Board), Q)), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(Board), Q)), $product(-1, length1(int, t2tb1(Board)))), 0)))))) | (~(is_board1(Board, Pos) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_2(Pos, Board))), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(Board), tptp_fun_Q_2(Pos, Board))), 0)) | $lesseq($sum(length1(int, t2tb1(Board)), $product(-1, tb2t(get2(int, t2tb1(Board), tptp_fun_Q_2(Pos, Board))))), 0))) | (~$greatereq(tptp_fun_Q_2(Pos, Board), 0))))))))) | (~((~((~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, N!5)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), Q)), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), Q)), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))))), 0)))))) | (~(is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5) | (~($lesseq($sum(N!5, $product(-1, tptp_fun_Q_2(N!5, tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), tptp_fun_Q_2(N!5, tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), 0)) | $lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), tptp_fun_Q_2(N!5, tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))))), 0))) | (~$greatereq(tptp_fun_Q_2(N!5, tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), 0))))))))) <=> ((~![Board: array_int, Pos: $int] : (~((~((~is_board1(Board, Pos)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(Board), Q)), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(Board), Q)), $product(-1, length1(int, t2tb1(Board)))), 0)))))) | (~(is_board1(Board, Pos) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_2(Pos, Board))), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(Board), tptp_fun_Q_2(Pos, Board))), 0)) | $lesseq($sum(length1(int, t2tb1(Board)), $product(-1, tb2t(get2(int, t2tb1(Board), tptp_fun_Q_2(Pos, Board))))), 0))) | (~$greatereq(tptp_fun_Q_2(Pos, Board), 0))))))))) | (~((~((~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, N!5)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), Q)), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), Q)), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))))), 0)))))) | (~(is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5) | (~($lesseq($sum(N!5, $product(-1, tptp_fun_Q_2(N!5, tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), tptp_fun_Q_2(N!5, tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), 0)) | $lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), tptp_fun_Q_2(N!5, tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))))), 0))) | (~$greatereq(tptp_fun_Q_2(N!5, tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), 0)))))))))),
% 1.08/1.04 inference(rewrite,[status(thm)],[])).
% 1.08/1.04 tff(879,plain,
% 1.08/1.04 ((~((~((~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(N!5, $product(-1, Q)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), Q)), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), Q)), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))))), 0)))))) | (~(is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5) | (~($lesseq($sum(N!5, $product(-1, tptp_fun_Q_2(N!5, tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), tptp_fun_Q_2(N!5, tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), 0)) | $lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), tptp_fun_Q_2(N!5, tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))))), 0))) | (~$greatereq(tptp_fun_Q_2(N!5, tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), 0)))))))) <=> (~((~((~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, N!5)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), Q)), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), Q)), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))))), 0)))))) | (~(is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5) | (~($lesseq($sum(N!5, $product(-1, tptp_fun_Q_2(N!5, tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), tptp_fun_Q_2(N!5, tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), 0)) | $lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), tptp_fun_Q_2(N!5, tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))))), 0))) | (~$greatereq(tptp_fun_Q_2(N!5, tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), 0))))))))),
% 1.08/1.04 inference(rewrite,[status(thm)],[])).
% 1.08/1.04 tff(880,plain,
% 1.08/1.04 (((~![Board: array_int, Pos: $int] : (~((~((~is_board1(Board, Pos)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(Board), Q)), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(Board), Q)), $product(-1, length1(int, t2tb1(Board)))), 0)))))) | (~(is_board1(Board, Pos) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_2(Pos, Board))), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(Board), tptp_fun_Q_2(Pos, Board))), 0)) | $lesseq($sum(length1(int, t2tb1(Board)), $product(-1, tb2t(get2(int, t2tb1(Board), tptp_fun_Q_2(Pos, Board))))), 0))) | (~$greatereq(tptp_fun_Q_2(Pos, Board), 0))))))))) | (~((~((~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(N!5, $product(-1, Q)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), Q)), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), Q)), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))))), 0)))))) | (~(is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5) | (~($lesseq($sum(N!5, $product(-1, tptp_fun_Q_2(N!5, tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), tptp_fun_Q_2(N!5, tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), 0)) | $lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), tptp_fun_Q_2(N!5, tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))))), 0))) | (~$greatereq(tptp_fun_Q_2(N!5, tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), 0))))))))) <=> ((~![Board: array_int, Pos: $int] : (~((~((~is_board1(Board, Pos)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(Board), Q)), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(Board), Q)), $product(-1, length1(int, t2tb1(Board)))), 0)))))) | (~(is_board1(Board, Pos) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_2(Pos, Board))), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(Board), tptp_fun_Q_2(Pos, Board))), 0)) | $lesseq($sum(length1(int, t2tb1(Board)), $product(-1, tb2t(get2(int, t2tb1(Board), tptp_fun_Q_2(Pos, Board))))), 0))) | (~$greatereq(tptp_fun_Q_2(Pos, Board), 0))))))))) | (~((~((~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, N!5)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), Q)), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), Q)), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))))), 0)))))) | (~(is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5) | (~($lesseq($sum(N!5, $product(-1, tptp_fun_Q_2(N!5, tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), tptp_fun_Q_2(N!5, tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), 0)) | $lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), tptp_fun_Q_2(N!5, tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))))), 0))) | (~$greatereq(tptp_fun_Q_2(N!5, tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), 0)))))))))),
% 1.08/1.04 inference(monotonicity,[status(thm)],[879])).
% 1.08/1.04 tff(881,plain,
% 1.08/1.04 (((~![Board: array_int, Pos: $int] : (~((~((~is_board1(Board, Pos)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(Board), Q)), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(Board), Q)), $product(-1, length1(int, t2tb1(Board)))), 0)))))) | (~(is_board1(Board, Pos) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_2(Pos, Board))), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(Board), tptp_fun_Q_2(Pos, Board))), 0)) | $lesseq($sum(length1(int, t2tb1(Board)), $product(-1, tb2t(get2(int, t2tb1(Board), tptp_fun_Q_2(Pos, Board))))), 0))) | (~$greatereq(tptp_fun_Q_2(Pos, Board), 0))))))))) | (~((~((~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(N!5, $product(-1, Q)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), Q)), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), Q)), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))))), 0)))))) | (~(is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5) | (~($lesseq($sum(N!5, $product(-1, tptp_fun_Q_2(N!5, tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), tptp_fun_Q_2(N!5, tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), 0)) | $lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), tptp_fun_Q_2(N!5, tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))))), 0))) | (~$greatereq(tptp_fun_Q_2(N!5, tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), 0))))))))) <=> ((~![Board: array_int, Pos: $int] : (~((~((~is_board1(Board, Pos)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(Board), Q)), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(Board), Q)), $product(-1, length1(int, t2tb1(Board)))), 0)))))) | (~(is_board1(Board, Pos) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_2(Pos, Board))), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(Board), tptp_fun_Q_2(Pos, Board))), 0)) | $lesseq($sum(length1(int, t2tb1(Board)), $product(-1, tb2t(get2(int, t2tb1(Board), tptp_fun_Q_2(Pos, Board))))), 0))) | (~$greatereq(tptp_fun_Q_2(Pos, Board), 0))))))))) | (~((~((~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, N!5)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), Q)), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), Q)), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))))), 0)))))) | (~(is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5) | (~($lesseq($sum(N!5, $product(-1, tptp_fun_Q_2(N!5, tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), tptp_fun_Q_2(N!5, tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), 0)) | $lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), tptp_fun_Q_2(N!5, tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))))), 0))) | (~$greatereq(tptp_fun_Q_2(N!5, tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), 0)))))))))),
% 1.08/1.04 inference(transitivity,[status(thm)],[880, 878])).
% 1.08/1.04 tff(882,plain,
% 1.08/1.04 ((~![Board: array_int, Pos: $int] : (~((~((~is_board1(Board, Pos)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(Board), Q)), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(Board), Q)), $product(-1, length1(int, t2tb1(Board)))), 0)))))) | (~(is_board1(Board, Pos) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_2(Pos, Board))), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(Board), tptp_fun_Q_2(Pos, Board))), 0)) | $lesseq($sum(length1(int, t2tb1(Board)), $product(-1, tb2t(get2(int, t2tb1(Board), tptp_fun_Q_2(Pos, Board))))), 0))) | (~$greatereq(tptp_fun_Q_2(Pos, Board), 0))))))))) | (~((~((~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(N!5, $product(-1, Q)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), Q)), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), Q)), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))))), 0)))))) | (~(is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5) | (~($lesseq($sum(N!5, $product(-1, tptp_fun_Q_2(N!5, tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), tptp_fun_Q_2(N!5, tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), 0)) | $lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), tptp_fun_Q_2(N!5, tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))))), 0))) | (~$greatereq(tptp_fun_Q_2(N!5, tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), 0))))))))),
% 1.08/1.04 inference(quant_inst,[status(thm)],[])).
% 1.08/1.04 tff(883,plain,
% 1.08/1.04 ((~![Board: array_int, Pos: $int] : (~((~((~is_board1(Board, Pos)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(Board), Q)), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(Board), Q)), $product(-1, length1(int, t2tb1(Board)))), 0)))))) | (~(is_board1(Board, Pos) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_2(Pos, Board))), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(Board), tptp_fun_Q_2(Pos, Board))), 0)) | $lesseq($sum(length1(int, t2tb1(Board)), $product(-1, tb2t(get2(int, t2tb1(Board), tptp_fun_Q_2(Pos, Board))))), 0))) | (~$greatereq(tptp_fun_Q_2(Pos, Board), 0))))))))) | (~((~((~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, N!5)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), Q)), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), Q)), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))))), 0)))))) | (~(is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5) | (~($lesseq($sum(N!5, $product(-1, tptp_fun_Q_2(N!5, tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), tptp_fun_Q_2(N!5, tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), 0)) | $lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), tptp_fun_Q_2(N!5, tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))))), 0))) | (~$greatereq(tptp_fun_Q_2(N!5, tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), 0))))))))),
% 1.08/1.04 inference(modus_ponens,[status(thm)],[882, 881])).
% 1.08/1.04 tff(884,plain,
% 1.08/1.04 (~((~((~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, N!5)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), Q)), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), Q)), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))))), 0)))))) | (~(is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5) | (~($lesseq($sum(N!5, $product(-1, tptp_fun_Q_2(N!5, tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), tptp_fun_Q_2(N!5, tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), 0)) | $lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), tptp_fun_Q_2(N!5, tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))))), 0))) | (~$greatereq(tptp_fun_Q_2(N!5, tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), 0)))))))),
% 1.08/1.04 inference(unit_resolution,[status(thm)],[883, 73])).
% 1.08/1.04 tff(885,plain,
% 1.08/1.04 (((~((~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, N!5)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), Q)), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), Q)), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))))), 0)))))) | (~(is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5) | (~($lesseq($sum(N!5, $product(-1, tptp_fun_Q_2(N!5, tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), tptp_fun_Q_2(N!5, tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), 0)) | $lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), tptp_fun_Q_2(N!5, tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))))), 0))) | (~$greatereq(tptp_fun_Q_2(N!5, tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), 0))))))) | ((~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, N!5)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), Q)), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), Q)), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))))), 0)))))),
% 1.08/1.04 inference(tautology,[status(thm)],[])).
% 1.08/1.04 tff(886,plain,
% 1.08/1.04 ((~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, N!5)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), Q)), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), Q)), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))))), 0))))),
% 1.08/1.04 inference(unit_resolution,[status(thm)],[885, 884])).
% 1.08/1.04 tff(887,plain,
% 1.08/1.04 ((~((~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, N!5)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), Q)), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), Q)), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))))), 0)))))) | (~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, N!5)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), Q)), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), Q)), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))))), 0))))),
% 1.08/1.04 inference(tautology,[status(thm)],[])).
% 1.08/1.04 tff(888,plain,
% 1.08/1.04 ((~((~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, N!5)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), Q)), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), Q)), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))))), 0)))))) | ![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, N!5)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), Q)), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), Q)), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))))), 0))))),
% 1.08/1.04 inference(unit_resolution,[status(thm)],[887, 614])).
% 1.08/1.04 tff(889,plain,
% 1.08/1.04 (![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, N!5)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), Q)), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), Q)), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))))), 0))))),
% 1.08/1.04 inference(unit_resolution,[status(thm)],[888, 886])).
% 1.08/1.04 tff(890,assumption,($greatereq(tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), 0)), introduced(assumption)).
% 1.08/1.04 tff(891,assumption,((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), 0)) | $lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))))), 0)), introduced(assumption)).
% 1.08/1.04 tff(892,assumption,(![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, N!5)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), Q)), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), Q)), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))))), 0))))), introduced(assumption)).
% 1.08/1.04 tff(893,assumption,(~$lesseq($sum(N!5, $product(-1, tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), 0)), introduced(assumption)).
% 1.08/1.04 tff(894,plain,
% 1.08/1.04 (((~![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, N!5)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), Q)), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), Q)), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))))), 0))))) | ((~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), 0)) | $lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))))), 0))) | (~$greatereq(tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), 0)) | $lesseq($sum(N!5, $product(-1, tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), 0))) <=> ((~![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, N!5)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), Q)), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), Q)), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))))), 0))))) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), 0)) | $lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))))), 0))) | (~$greatereq(tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), 0)) | $lesseq($sum(N!5, $product(-1, tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), 0))),
% 1.08/1.04 inference(rewrite,[status(thm)],[])).
% 1.08/1.04 tff(895,plain,
% 1.08/1.04 (((~$greatereq(tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), 0)) | $lesseq($sum(N!5, $product(-1, tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), 0)) | $lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))))), 0)))) <=> ((~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), 0)) | $lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))))), 0))) | (~$greatereq(tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), 0)) | $lesseq($sum(N!5, $product(-1, tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), 0))),
% 1.08/1.04 inference(rewrite,[status(thm)],[])).
% 1.08/1.04 tff(896,plain,
% 1.08/1.04 ((~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))))), 0))) <=> (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), 0)) | $lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))))), 0)))),
% 1.08/1.04 inference(rewrite,[status(thm)],[])).
% 1.08/1.04 tff(897,plain,
% 1.08/1.04 ($greatereq($sum($product(-1, N!5), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))), 0) <=> $lesseq($sum(N!5, $product(-1, tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), 0)),
% 1.08/1.04 inference(rewrite,[status(thm)],[])).
% 1.08/1.04 tff(898,plain,
% 1.08/1.04 ($sum(tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), $product(-1, N!5)) = $sum($product(-1, N!5), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))),
% 1.08/1.04 inference(rewrite,[status(thm)],[])).
% 1.08/1.04 tff(899,plain,
% 1.08/1.04 ($greatereq($sum(tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), $product(-1, N!5)), 0) <=> $greatereq($sum($product(-1, N!5), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))), 0)),
% 1.08/1.04 inference(monotonicity,[status(thm)],[898])).
% 1.08/1.04 tff(900,plain,
% 1.08/1.04 ($greatereq($sum(tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), $product(-1, N!5)), 0) <=> $lesseq($sum(N!5, $product(-1, tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), 0)),
% 1.08/1.04 inference(transitivity,[status(thm)],[899, 897])).
% 1.08/1.04 tff(901,plain,
% 1.08/1.04 (((~$greatereq(tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), 0)) | $greatereq($sum(tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), $product(-1, N!5)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))))), 0)))) <=> ((~$greatereq(tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), 0)) | $lesseq($sum(N!5, $product(-1, tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), 0)) | $lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))))), 0))))),
% 1.08/1.05 inference(monotonicity,[status(thm)],[900, 896])).
% 1.08/1.05 tff(902,plain,
% 1.08/1.05 (((~$greatereq(tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), 0)) | $greatereq($sum(tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), $product(-1, N!5)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))))), 0)))) <=> ((~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), 0)) | $lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))))), 0))) | (~$greatereq(tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), 0)) | $lesseq($sum(N!5, $product(-1, tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), 0))),
% 1.08/1.05 inference(transitivity,[status(thm)],[901, 895])).
% 1.08/1.05 tff(903,plain,
% 1.08/1.05 (((~![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, N!5)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), Q)), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), Q)), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))))), 0))))) | ((~$greatereq(tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), 0)) | $greatereq($sum(tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), $product(-1, N!5)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))))), 0))))) <=> ((~![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, N!5)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), Q)), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), Q)), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))))), 0))))) | ((~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), 0)) | $lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))))), 0))) | (~$greatereq(tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), 0)) | $lesseq($sum(N!5, $product(-1, tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), 0)))),
% 1.08/1.05 inference(monotonicity,[status(thm)],[902])).
% 1.08/1.05 tff(904,plain,
% 1.08/1.05 (((~![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, N!5)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), Q)), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), Q)), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))))), 0))))) | ((~$greatereq(tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), 0)) | $greatereq($sum(tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), $product(-1, N!5)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))))), 0))))) <=> ((~![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, N!5)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), Q)), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), Q)), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))))), 0))))) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), 0)) | $lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))))), 0))) | (~$greatereq(tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), 0)) | $lesseq($sum(N!5, $product(-1, tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), 0))),
% 1.08/1.05 inference(transitivity,[status(thm)],[903, 894])).
% 1.08/1.05 tff(905,plain,
% 1.08/1.05 ((~![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, N!5)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), Q)), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), Q)), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))))), 0))))) | ((~$greatereq(tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), 0)) | $greatereq($sum(tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), $product(-1, N!5)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))))), 0))))),
% 1.08/1.05 inference(quant_inst,[status(thm)],[])).
% 1.08/1.05 tff(906,plain,
% 1.08/1.05 ((~![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, N!5)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), Q)), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), Q)), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))))), 0))))) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), 0)) | $lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))))), 0))) | (~$greatereq(tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), 0)) | $lesseq($sum(N!5, $product(-1, tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), 0)),
% 1.08/1.05 inference(modus_ponens,[status(thm)],[905, 904])).
% 1.08/1.05 tff(907,plain,
% 1.08/1.05 ($false),
% 1.08/1.05 inference(unit_resolution,[status(thm)],[906, 893, 892, 891, 890])).
% 1.08/1.05 tff(908,plain,($lesseq($sum(N!5, $product(-1, tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), 0) | (~![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, N!5)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), Q)), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), Q)), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))))), 0))))) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), 0)) | $lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))))), 0))) | (~$greatereq(tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), 0))), inference(lemma,lemma(discharge,[]))).
% 1.08/1.05 tff(909,plain,
% 1.08/1.05 ($lesseq($sum(N!5, $product(-1, tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), 0)),
% 1.08/1.05 inference(unit_resolution,[status(thm)],[908, 889, 877, 875])).
% 1.08/1.05 tff(910,plain,
% 1.08/1.05 (((~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), 0)) | $lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))))), 0))) | (~$greatereq(tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))), 0)) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), -1)) | (~$lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), -1))),
% 1.08/1.05 inference(tautology,[status(thm)],[])).
% 1.08/1.05 tff(911,plain,
% 1.08/1.05 (~$lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, B!19, t2tb2(B1!18)))))), -1)),
% 1.08/1.05 inference(unit_resolution,[status(thm)],[910, 873])).
% 1.08/1.05 tff(912,plain,
% 1.08/1.05 ($false),
% 1.08/1.05 inference(theory_lemma,[status(thm)],[911, 909, 48])).
% 1.08/1.05 tff(913,plain,(is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)), inference(lemma,lemma(discharge,[]))).
% 1.08/1.05 tff(914,plain,
% 1.08/1.05 (((~(Result!13 = true1)) <=> is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | (Result!13 = true1) | (~is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4))),
% 1.08/1.05 inference(tautology,[status(thm)],[])).
% 1.08/1.05 tff(915,plain,
% 1.08/1.05 ((Result!13 = true1) | (~is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4))),
% 1.08/1.05 inference(unit_resolution,[status(thm)],[914, 351])).
% 1.08/1.05 tff(916,plain,
% 1.08/1.05 (Result!13 = true1),
% 1.08/1.05 inference(unit_resolution,[status(thm)],[915, 913])).
% 1.08/1.05 tff(917,plain,
% 1.08/1.05 (((Result!13 = true1) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Pos!4)) | (~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~($sum(N!5, $product(-1, B!19)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))), 0))))))) | (~(Result!13 = true1))),
% 1.08/1.05 inference(tautology,[status(thm)],[])).
% 1.08/1.05 tff(918,plain,
% 1.08/1.05 ((Result!13 = true1) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Pos!4)) | (~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~($sum(N!5, $product(-1, B!19)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))), 0))))))),
% 1.08/1.05 inference(unit_resolution,[status(thm)],[917, 916])).
% 1.08/1.05 tff(919,plain,
% 1.08/1.05 (~((~(Result!13 = true1)) | (~((~$lesseq($sum(Pos!4, $product(-1, N!5)), 0)) | (~($sum(N!5, $product(-1, Board!7)) = 0)) | (~$greatereq(Pos!4, -1)) | (~$lesseq($sum(Pos!4, $product(-1, N!5)), -1)) | (~solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~((~$greatereq(Board!7, 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B, t2tb2(B1))), $sum(1, Pos!4))))) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), Pos!4)) | (~($sum(N!5, $product(-1, B!16)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))), 0)))))))))))),
% 1.08/1.05 inference(unit_resolution,[status(thm)],[360, 918])).
% 1.08/1.05 tff(920,assumption,(~((~$greatereq(tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0)) | is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), -1))), introduced(assumption)).
% 1.08/1.05 tff(921,plain,
% 1.08/1.05 (((~$greatereq(tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0)) | is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), -1)) | (~is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))))),
% 1.08/1.05 inference(tautology,[status(thm)],[])).
% 1.08/1.05 tff(922,plain,
% 1.08/1.05 (~is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))),
% 1.08/1.05 inference(unit_resolution,[status(thm)],[921, 920])).
% 1.08/1.05 tff(923,plain,
% 1.08/1.05 (((~$greatereq(tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0)) | is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), -1)) | $greatereq(tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0)),
% 1.08/1.05 inference(tautology,[status(thm)],[])).
% 1.08/1.05 tff(924,plain,
% 1.08/1.05 ($greatereq(tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0)),
% 1.08/1.05 inference(unit_resolution,[status(thm)],[923, 920])).
% 1.08/1.05 tff(925,plain,
% 1.08/1.05 (((~![Board: array_int, Pos: $int] : (~((~(solution1(Board, Pos) | (~is_board1(Board, Pos)) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_3(Pos, Board))), 0) | is_consistent1(Board, tptp_fun_Q_3(Pos, Board)) | (~$greatereq(tptp_fun_Q_3(Pos, Board), 0)))))) | (~((~solution1(Board, Pos)) | (~((~is_board1(Board, Pos)) | (~![Q: $int] : (is_consistent1(Board, Q) | (~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0)))))))))) | (~((~((~is_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | (~($lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_3(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), 0) | is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tptp_fun_Q_3(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))) | (~$greatereq(tptp_fun_Q_3(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0)))) | solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4))) | (~((~solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | (~((~is_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | (~![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 0) | is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Q)))))))))) <=> ((~![Board: array_int, Pos: $int] : (~((~(solution1(Board, Pos) | (~is_board1(Board, Pos)) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_3(Pos, Board))), 0) | is_consistent1(Board, tptp_fun_Q_3(Pos, Board)) | (~$greatereq(tptp_fun_Q_3(Pos, Board), 0)))))) | (~((~solution1(Board, Pos)) | (~((~is_board1(Board, Pos)) | (~![Q: $int] : (is_consistent1(Board, Q) | (~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0)))))))))) | (~((~((~is_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | (~($lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_3(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), 0) | is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tptp_fun_Q_3(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))) | (~$greatereq(tptp_fun_Q_3(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0)))) | solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4))) | (~((~solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | (~((~is_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | (~![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 0) | is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Q))))))))))),
% 1.08/1.05 inference(rewrite,[status(thm)],[])).
% 1.08/1.05 tff(926,plain,
% 1.08/1.05 ((~((~(solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4) | (~is_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | (~($lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_3(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), 0) | is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tptp_fun_Q_3(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))) | (~$greatereq(tptp_fun_Q_3(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0)))))) | (~((~solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | (~((~is_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | (~![Q: $int] : (is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Q) | (~$greatereq(Q, 0)) | $lesseq($sum(Pos!4, $product(-1, Q)), 0))))))))) <=> (~((~((~is_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | (~($lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_3(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), 0) | is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tptp_fun_Q_3(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))) | (~$greatereq(tptp_fun_Q_3(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0)))) | solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4))) | (~((~solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | (~((~is_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | (~![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 0) | is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Q)))))))))),
% 1.08/1.05 inference(rewrite,[status(thm)],[])).
% 1.08/1.05 tff(927,plain,
% 1.08/1.05 (((~![Board: array_int, Pos: $int] : (~((~(solution1(Board, Pos) | (~is_board1(Board, Pos)) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_3(Pos, Board))), 0) | is_consistent1(Board, tptp_fun_Q_3(Pos, Board)) | (~$greatereq(tptp_fun_Q_3(Pos, Board), 0)))))) | (~((~solution1(Board, Pos)) | (~((~is_board1(Board, Pos)) | (~![Q: $int] : (is_consistent1(Board, Q) | (~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0)))))))))) | (~((~(solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4) | (~is_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | (~($lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_3(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), 0) | is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tptp_fun_Q_3(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))) | (~$greatereq(tptp_fun_Q_3(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0)))))) | (~((~solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | (~((~is_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | (~![Q: $int] : (is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Q) | (~$greatereq(Q, 0)) | $lesseq($sum(Pos!4, $product(-1, Q)), 0)))))))))) <=> ((~![Board: array_int, Pos: $int] : (~((~(solution1(Board, Pos) | (~is_board1(Board, Pos)) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_3(Pos, Board))), 0) | is_consistent1(Board, tptp_fun_Q_3(Pos, Board)) | (~$greatereq(tptp_fun_Q_3(Pos, Board), 0)))))) | (~((~solution1(Board, Pos)) | (~((~is_board1(Board, Pos)) | (~![Q: $int] : (is_consistent1(Board, Q) | (~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0)))))))))) | (~((~((~is_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | (~($lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_3(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), 0) | is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tptp_fun_Q_3(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))) | (~$greatereq(tptp_fun_Q_3(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0)))) | solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4))) | (~((~solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | (~((~is_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | (~![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 0) | is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Q))))))))))),
% 1.08/1.05 inference(monotonicity,[status(thm)],[926])).
% 1.08/1.05 tff(928,plain,
% 1.08/1.05 (((~![Board: array_int, Pos: $int] : (~((~(solution1(Board, Pos) | (~is_board1(Board, Pos)) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_3(Pos, Board))), 0) | is_consistent1(Board, tptp_fun_Q_3(Pos, Board)) | (~$greatereq(tptp_fun_Q_3(Pos, Board), 0)))))) | (~((~solution1(Board, Pos)) | (~((~is_board1(Board, Pos)) | (~![Q: $int] : (is_consistent1(Board, Q) | (~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0)))))))))) | (~((~(solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4) | (~is_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | (~($lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_3(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), 0) | is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tptp_fun_Q_3(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))) | (~$greatereq(tptp_fun_Q_3(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0)))))) | (~((~solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | (~((~is_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | (~![Q: $int] : (is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Q) | (~$greatereq(Q, 0)) | $lesseq($sum(Pos!4, $product(-1, Q)), 0)))))))))) <=> ((~![Board: array_int, Pos: $int] : (~((~(solution1(Board, Pos) | (~is_board1(Board, Pos)) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_3(Pos, Board))), 0) | is_consistent1(Board, tptp_fun_Q_3(Pos, Board)) | (~$greatereq(tptp_fun_Q_3(Pos, Board), 0)))))) | (~((~solution1(Board, Pos)) | (~((~is_board1(Board, Pos)) | (~![Q: $int] : (is_consistent1(Board, Q) | (~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0)))))))))) | (~((~((~is_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | (~($lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_3(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), 0) | is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tptp_fun_Q_3(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))) | (~$greatereq(tptp_fun_Q_3(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0)))) | solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4))) | (~((~solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | (~((~is_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | (~![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 0) | is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Q))))))))))),
% 1.08/1.05 inference(transitivity,[status(thm)],[927, 925])).
% 1.08/1.05 tff(929,plain,
% 1.08/1.05 ((~![Board: array_int, Pos: $int] : (~((~(solution1(Board, Pos) | (~is_board1(Board, Pos)) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_3(Pos, Board))), 0) | is_consistent1(Board, tptp_fun_Q_3(Pos, Board)) | (~$greatereq(tptp_fun_Q_3(Pos, Board), 0)))))) | (~((~solution1(Board, Pos)) | (~((~is_board1(Board, Pos)) | (~![Q: $int] : (is_consistent1(Board, Q) | (~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0)))))))))) | (~((~(solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4) | (~is_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | (~($lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_3(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), 0) | is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tptp_fun_Q_3(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))) | (~$greatereq(tptp_fun_Q_3(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0)))))) | (~((~solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | (~((~is_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | (~![Q: $int] : (is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Q) | (~$greatereq(Q, 0)) | $lesseq($sum(Pos!4, $product(-1, Q)), 0)))))))))),
% 1.08/1.05 inference(quant_inst,[status(thm)],[])).
% 1.08/1.05 tff(930,plain,
% 1.08/1.05 ((~![Board: array_int, Pos: $int] : (~((~(solution1(Board, Pos) | (~is_board1(Board, Pos)) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_3(Pos, Board))), 0) | is_consistent1(Board, tptp_fun_Q_3(Pos, Board)) | (~$greatereq(tptp_fun_Q_3(Pos, Board), 0)))))) | (~((~solution1(Board, Pos)) | (~((~is_board1(Board, Pos)) | (~![Q: $int] : (is_consistent1(Board, Q) | (~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0)))))))))) | (~((~((~is_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | (~($lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_3(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), 0) | is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tptp_fun_Q_3(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))) | (~$greatereq(tptp_fun_Q_3(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0)))) | solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4))) | (~((~solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | (~((~is_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | (~![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 0) | is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Q)))))))))),
% 1.08/1.05 inference(modus_ponens,[status(thm)],[929, 928])).
% 1.08/1.05 tff(931,plain,
% 1.08/1.05 (~((~((~is_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | (~($lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_3(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), 0) | is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tptp_fun_Q_3(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))) | (~$greatereq(tptp_fun_Q_3(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0)))) | solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4))) | (~((~solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | (~((~is_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | (~![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 0) | is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Q))))))))),
% 1.08/1.06 inference(unit_resolution,[status(thm)],[930, 107])).
% 1.08/1.06 tff(932,plain,
% 1.08/1.06 (((~((~is_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | (~($lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_3(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), 0) | is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tptp_fun_Q_3(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))) | (~$greatereq(tptp_fun_Q_3(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0)))) | solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4))) | (~((~solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | (~((~is_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | (~![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 0) | is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Q)))))))) | ((~solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | (~((~is_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | (~![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 0) | is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Q))))))),
% 1.08/1.06 inference(tautology,[status(thm)],[])).
% 1.08/1.06 tff(933,plain,
% 1.08/1.06 ((~solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | (~((~is_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | (~![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 0) | is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Q)))))),
% 1.08/1.06 inference(unit_resolution,[status(thm)],[932, 931])).
% 1.08/1.06 tff(934,plain,
% 1.08/1.06 ((~![A: ty, U: $int, U1: uni] : ($sum(U, $product(-1, length1(A, mk_array1(A, U, U1)))) = 0)) | ($sum(N!5, $product(-1, length1(int, mk_array1(int, N!5, t2tb2(Board2!10))))) = 0)),
% 1.08/1.06 inference(quant_inst,[status(thm)],[])).
% 1.08/1.06 tff(935,plain,
% 1.08/1.06 ($sum(N!5, $product(-1, length1(int, mk_array1(int, N!5, t2tb2(Board2!10))))) = 0),
% 1.08/1.06 inference(unit_resolution,[status(thm)],[934, 234])).
% 1.08/1.06 tff(936,plain,
% 1.08/1.06 ((~($sum(N!5, $product(-1, length1(int, mk_array1(int, N!5, t2tb2(Board2!10))))) = 0)) | $lesseq($sum(N!5, $product(-1, length1(int, mk_array1(int, N!5, t2tb2(Board2!10))))), 0)),
% 1.08/1.06 inference(theory_lemma,[status(thm)],[])).
% 1.08/1.06 tff(937,plain,
% 1.08/1.06 ($lesseq($sum(N!5, $product(-1, length1(int, mk_array1(int, N!5, t2tb2(Board2!10))))), 0)),
% 1.08/1.06 inference(unit_resolution,[status(thm)],[936, 935])).
% 1.08/1.06 tff(938,plain,
% 1.08/1.06 (t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10)))) = mk_array1(int, N!5, t2tb2(Board2!10))),
% 1.08/1.06 inference(transitivity,[status(thm)],[402, 409])).
% 1.08/1.06 tff(939,plain,
% 1.08/1.06 (length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))))) = length1(int, mk_array1(int, N!5, t2tb2(Board2!10)))),
% 1.08/1.06 inference(monotonicity,[status(thm)],[938])).
% 1.08/1.06 tff(940,plain,
% 1.08/1.06 ((~(length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))))) = length1(int, mk_array1(int, N!5, t2tb2(Board2!10))))) | $greatereq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))))), $product(-1, length1(int, mk_array1(int, N!5, t2tb2(Board2!10))))), 0)),
% 1.08/1.06 inference(theory_lemma,[status(thm)],[])).
% 1.08/1.06 tff(941,plain,
% 1.08/1.06 ($greatereq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))))), $product(-1, length1(int, mk_array1(int, N!5, t2tb2(Board2!10))))), 0)),
% 1.08/1.06 inference(unit_resolution,[status(thm)],[940, 939])).
% 1.08/1.06 tff(942,plain,
% 1.08/1.06 ($greatereq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))))), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))))), 0) | (~$greatereq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))))), $product(-1, length1(int, mk_array1(int, N!5, t2tb2(Board2!10))))), 0)) | (~$lesseq($sum(N!5, $product(-1, length1(int, mk_array1(int, N!5, t2tb2(Board2!10))))), 0)) | (~$greatereq($sum(length1(int, mk_array1(int, N!5, t2tb2(Board3!12))), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))))), 0)) | (~$greatereq($sum(N!5, $product(-1, length1(int, mk_array1(int, N!5, t2tb2(Board3!12))))), 0))),
% 1.08/1.06 inference(theory_lemma,[status(thm)],[])).
% 1.08/1.06 tff(943,plain,
% 1.08/1.06 ($greatereq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))))), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))))), 0)),
% 1.08/1.06 inference(unit_resolution,[status(thm)],[942, 941, 767, 937, 769])).
% 1.08/1.06 tff(944,plain,
% 1.08/1.06 ((~($sum(N!5, $product(-1, length1(int, mk_array1(int, N!5, t2tb2(Board2!10))))) = 0)) | $greatereq($sum(N!5, $product(-1, length1(int, mk_array1(int, N!5, t2tb2(Board2!10))))), 0)),
% 1.08/1.06 inference(theory_lemma,[status(thm)],[])).
% 1.08/1.06 tff(945,plain,
% 1.08/1.06 ($greatereq($sum(N!5, $product(-1, length1(int, mk_array1(int, N!5, t2tb2(Board2!10))))), 0)),
% 1.08/1.06 inference(unit_resolution,[status(thm)],[944, 935])).
% 1.08/1.06 tff(946,plain,
% 1.08/1.06 ((~(length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))))) = length1(int, mk_array1(int, N!5, t2tb2(Board2!10))))) | $lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))))), $product(-1, length1(int, mk_array1(int, N!5, t2tb2(Board2!10))))), 0)),
% 1.08/1.06 inference(theory_lemma,[status(thm)],[])).
% 1.08/1.06 tff(947,plain,
% 1.08/1.06 ($lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))))), $product(-1, length1(int, mk_array1(int, N!5, t2tb2(Board2!10))))), 0)),
% 1.08/1.06 inference(unit_resolution,[status(thm)],[946, 939])).
% 1.08/1.06 tff(948,plain,
% 1.08/1.06 ($lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))))), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))))), 0) | (~$lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))))), $product(-1, length1(int, mk_array1(int, N!5, t2tb2(Board2!10))))), 0)) | (~$greatereq($sum(N!5, $product(-1, length1(int, mk_array1(int, N!5, t2tb2(Board2!10))))), 0)) | (~$lesseq($sum(length1(int, mk_array1(int, N!5, t2tb2(Board3!12))), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))))), 0)) | (~$lesseq($sum(N!5, $product(-1, length1(int, mk_array1(int, N!5, t2tb2(Board3!12))))), 0))),
% 1.08/1.06 inference(theory_lemma,[status(thm)],[])).
% 1.08/1.06 tff(949,plain,
% 1.08/1.06 ($lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))))), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))))), 0)),
% 1.08/1.06 inference(unit_resolution,[status(thm)],[948, 947, 751, 945, 756])).
% 1.08/1.06 tff(950,plain,
% 1.08/1.06 (($sum(length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))))), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))))) = 0) | (~$lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))))), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))))), 0)) | (~$greatereq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))))), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))))), 0))),
% 1.08/1.06 inference(theory_lemma,[status(thm)],[])).
% 1.08/1.06 tff(951,plain,
% 1.08/1.06 ($sum(length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))))), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))))) = 0),
% 1.08/1.06 inference(unit_resolution,[status(thm)],[950, 949, 943])).
% 1.08/1.06 tff(952,plain,
% 1.08/1.06 ((~![A: ty, U: $int, U1: uni] : ($sum(U, $product(-1, length1(A, mk_array1(A, U, U1)))) = 0)) | ($sum(Board!7, $product(-1, length1(int, mk_array1(int, Board!7, t2tb2(Board1!6))))) = 0)),
% 1.08/1.06 inference(quant_inst,[status(thm)],[])).
% 1.08/1.06 tff(953,plain,
% 1.08/1.06 ($sum(Board!7, $product(-1, length1(int, mk_array1(int, Board!7, t2tb2(Board1!6))))) = 0),
% 1.08/1.06 inference(unit_resolution,[status(thm)],[952, 234])).
% 1.08/1.06 tff(954,plain,
% 1.08/1.06 ((~($sum(Board!7, $product(-1, length1(int, mk_array1(int, Board!7, t2tb2(Board1!6))))) = 0)) | $lesseq($sum(Board!7, $product(-1, length1(int, mk_array1(int, Board!7, t2tb2(Board1!6))))), 0)),
% 1.08/1.06 inference(theory_lemma,[status(thm)],[])).
% 1.08/1.06 tff(955,plain,
% 1.08/1.06 ($lesseq($sum(Board!7, $product(-1, length1(int, mk_array1(int, Board!7, t2tb2(Board1!6))))), 0)),
% 1.08/1.06 inference(unit_resolution,[status(thm)],[954, 953])).
% 1.08/1.06 tff(956,plain,
% 1.08/1.06 ((~![J: uni] : (t2tb1(tb2t1(J)) = J)) | (t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6)))) = mk_array1(int, Board!7, t2tb2(Board1!6)))),
% 1.08/1.06 inference(quant_inst,[status(thm)],[])).
% 1.08/1.06 tff(957,plain,
% 1.08/1.06 (t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6)))) = mk_array1(int, Board!7, t2tb2(Board1!6))),
% 1.08/1.06 inference(unit_resolution,[status(thm)],[956, 154])).
% 1.08/1.06 tff(958,plain,
% 1.08/1.06 (length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))))) = length1(int, mk_array1(int, Board!7, t2tb2(Board1!6)))),
% 1.08/1.06 inference(monotonicity,[status(thm)],[957])).
% 1.08/1.06 tff(959,plain,
% 1.08/1.06 (length1(int, mk_array1(int, Board!7, t2tb2(Board1!6))) = length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6)))))),
% 1.08/1.06 inference(symmetry,[status(thm)],[958])).
% 1.08/1.06 tff(960,plain,
% 1.08/1.06 ((~(length1(int, mk_array1(int, Board!7, t2tb2(Board1!6))) = length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))))))) | $lesseq($sum(length1(int, mk_array1(int, Board!7, t2tb2(Board1!6))), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))))))), 0)),
% 1.08/1.06 inference(theory_lemma,[status(thm)],[])).
% 1.08/1.06 tff(961,plain,
% 1.08/1.06 ($lesseq($sum(length1(int, mk_array1(int, Board!7, t2tb2(Board1!6))), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))))))), 0)),
% 1.08/1.06 inference(unit_resolution,[status(thm)],[960, 959])).
% 1.08/1.06 tff(962,plain,
% 1.08/1.06 ($greatereq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))))), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))))))), 0) | (~$lesseq($sum(length1(int, mk_array1(int, Board!7, t2tb2(Board1!6))), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))))))), 0)) | (~$lesseq($sum(Board!7, $product(-1, length1(int, mk_array1(int, Board!7, t2tb2(Board1!6))))), 0)) | (~$lesseq($sum(N!5, $product(-1, Board!7)), 0)) | (~$lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))))), $product(-1, length1(int, mk_array1(int, N!5, t2tb2(Board2!10))))), 0)) | (~$greatereq($sum(N!5, $product(-1, length1(int, mk_array1(int, N!5, t2tb2(Board2!10))))), 0))),
% 1.08/1.06 inference(theory_lemma,[status(thm)],[])).
% 1.08/1.06 tff(963,plain,
% 1.08/1.06 ($greatereq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))))), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))))))), 0) | (~$lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))))), $product(-1, length1(int, mk_array1(int, N!5, t2tb2(Board2!10))))), 0)) | (~$greatereq($sum(N!5, $product(-1, length1(int, mk_array1(int, N!5, t2tb2(Board2!10))))), 0))),
% 1.08/1.06 inference(unit_resolution,[status(thm)],[962, 961, 955, 120])).
% 1.08/1.06 tff(964,plain,
% 1.08/1.06 ($greatereq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))))), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))))))), 0)),
% 1.08/1.06 inference(unit_resolution,[status(thm)],[963, 947, 945])).
% 1.08/1.06 tff(965,plain,
% 1.08/1.06 ((~($sum(Board!7, $product(-1, length1(int, mk_array1(int, Board!7, t2tb2(Board1!6))))) = 0)) | $greatereq($sum(Board!7, $product(-1, length1(int, mk_array1(int, Board!7, t2tb2(Board1!6))))), 0)),
% 1.08/1.06 inference(theory_lemma,[status(thm)],[])).
% 1.08/1.06 tff(966,plain,
% 1.08/1.06 ($greatereq($sum(Board!7, $product(-1, length1(int, mk_array1(int, Board!7, t2tb2(Board1!6))))), 0)),
% 1.08/1.06 inference(unit_resolution,[status(thm)],[965, 953])).
% 1.08/1.06 tff(967,plain,
% 1.08/1.06 ((~(length1(int, mk_array1(int, Board!7, t2tb2(Board1!6))) = length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))))))) | $greatereq($sum(length1(int, mk_array1(int, Board!7, t2tb2(Board1!6))), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))))))), 0)),
% 1.08/1.06 inference(theory_lemma,[status(thm)],[])).
% 1.08/1.06 tff(968,plain,
% 1.08/1.06 ($greatereq($sum(length1(int, mk_array1(int, Board!7, t2tb2(Board1!6))), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))))))), 0)),
% 1.08/1.06 inference(unit_resolution,[status(thm)],[967, 959])).
% 1.08/1.06 tff(969,plain,
% 1.08/1.06 ($lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))))), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))))))), 0) | (~$greatereq($sum(length1(int, mk_array1(int, Board!7, t2tb2(Board1!6))), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))))))), 0)) | (~$greatereq($sum(Board!7, $product(-1, length1(int, mk_array1(int, Board!7, t2tb2(Board1!6))))), 0)) | (~$greatereq($sum(N!5, $product(-1, Board!7)), 0)) | (~$greatereq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))))), $product(-1, length1(int, mk_array1(int, N!5, t2tb2(Board2!10))))), 0)) | (~$lesseq($sum(N!5, $product(-1, length1(int, mk_array1(int, N!5, t2tb2(Board2!10))))), 0))),
% 1.08/1.06 inference(theory_lemma,[status(thm)],[])).
% 1.08/1.06 tff(970,plain,
% 1.08/1.06 ($lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))))), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))))))), 0) | (~$greatereq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))))), $product(-1, length1(int, mk_array1(int, N!5, t2tb2(Board2!10))))), 0)) | (~$lesseq($sum(N!5, $product(-1, length1(int, mk_array1(int, N!5, t2tb2(Board2!10))))), 0))),
% 1.08/1.06 inference(unit_resolution,[status(thm)],[969, 968, 966, 369])).
% 1.08/1.06 tff(971,plain,
% 1.08/1.06 ($lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))))), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))))))), 0)),
% 1.08/1.06 inference(unit_resolution,[status(thm)],[970, 941, 937])).
% 1.08/1.06 tff(972,plain,
% 1.08/1.06 (($sum(length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))))), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))))))) = 0) | (~$lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))))), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))))))), 0)) | (~$greatereq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))))), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))))))), 0))),
% 1.08/1.06 inference(theory_lemma,[status(thm)],[])).
% 1.08/1.06 tff(973,plain,
% 1.08/1.06 ($sum(length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))))), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))))))) = 0),
% 1.08/1.06 inference(unit_resolution,[status(thm)],[972, 971, 964])).
% 1.08/1.06 tff(974,plain,
% 1.08/1.06 (((~![B1: array_int, B2: array_int, Pos: $int] : ((~eq_board1(B1, B2, Pos)) | eq_board1(B2, B1, Pos))) | ((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), Pos!4))) <=> ((~![B1: array_int, B2: array_int, Pos: $int] : ((~eq_board1(B1, B2, Pos)) | eq_board1(B2, B1, Pos))) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), Pos!4))),
% 1.08/1.06 inference(rewrite,[status(thm)],[])).
% 1.08/1.06 tff(975,plain,
% 1.08/1.06 ((~![B1: array_int, B2: array_int, Pos: $int] : ((~eq_board1(B1, B2, Pos)) | eq_board1(B2, B1, Pos))) | ((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), Pos!4))),
% 1.08/1.06 inference(quant_inst,[status(thm)],[])).
% 1.08/1.06 tff(976,plain,
% 1.08/1.06 ((~![B1: array_int, B2: array_int, Pos: $int] : ((~eq_board1(B1, B2, Pos)) | eq_board1(B2, B1, Pos))) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), Pos!4)),
% 1.08/1.06 inference(modus_ponens,[status(thm)],[975, 974])).
% 1.08/1.06 tff(977,plain,
% 1.08/1.06 (eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), Pos!4)),
% 1.08/1.06 inference(unit_resolution,[status(thm)],[976, 561, 577])).
% 1.08/1.06 tff(978,plain,
% 1.08/1.06 (((~![B1: array_int, B2: array_int, Pos: $int] : (solution1(B2, Pos) | (~eq_board1(B1, B2, Pos)) | (~solution1(B1, Pos)) | (~($sum(length1(int, t2tb1(B1)), $product(-1, length1(int, t2tb1(B2)))) = 0)))) | ((~solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), Pos!4) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), Pos!4)) | (~($sum(length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))))), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))))))) = 0)))) <=> ((~![B1: array_int, B2: array_int, Pos: $int] : (solution1(B2, Pos) | (~eq_board1(B1, B2, Pos)) | (~solution1(B1, Pos)) | (~($sum(length1(int, t2tb1(B1)), $product(-1, length1(int, t2tb1(B2)))) = 0)))) | (~solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), Pos!4) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), Pos!4)) | (~($sum(length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))))), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))))))) = 0)))),
% 1.08/1.06 inference(rewrite,[status(thm)],[])).
% 1.08/1.06 tff(979,plain,
% 1.08/1.06 ((solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), Pos!4) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), Pos!4)) | (~solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~($sum(length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))))), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))))))) = 0))) <=> ((~solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), Pos!4) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), Pos!4)) | (~($sum(length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))))), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))))))) = 0)))),
% 1.08/1.06 inference(rewrite,[status(thm)],[])).
% 1.08/1.06 tff(980,plain,
% 1.08/1.06 (((~![B1: array_int, B2: array_int, Pos: $int] : (solution1(B2, Pos) | (~eq_board1(B1, B2, Pos)) | (~solution1(B1, Pos)) | (~($sum(length1(int, t2tb1(B1)), $product(-1, length1(int, t2tb1(B2)))) = 0)))) | (solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), Pos!4) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), Pos!4)) | (~solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~($sum(length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))))), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))))))) = 0)))) <=> ((~![B1: array_int, B2: array_int, Pos: $int] : (solution1(B2, Pos) | (~eq_board1(B1, B2, Pos)) | (~solution1(B1, Pos)) | (~($sum(length1(int, t2tb1(B1)), $product(-1, length1(int, t2tb1(B2)))) = 0)))) | ((~solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), Pos!4) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), Pos!4)) | (~($sum(length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))))), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))))))) = 0))))),
% 1.08/1.06 inference(monotonicity,[status(thm)],[979])).
% 1.08/1.06 tff(981,plain,
% 1.08/1.06 (((~![B1: array_int, B2: array_int, Pos: $int] : (solution1(B2, Pos) | (~eq_board1(B1, B2, Pos)) | (~solution1(B1, Pos)) | (~($sum(length1(int, t2tb1(B1)), $product(-1, length1(int, t2tb1(B2)))) = 0)))) | (solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), Pos!4) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), Pos!4)) | (~solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~($sum(length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))))), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))))))) = 0)))) <=> ((~![B1: array_int, B2: array_int, Pos: $int] : (solution1(B2, Pos) | (~eq_board1(B1, B2, Pos)) | (~solution1(B1, Pos)) | (~($sum(length1(int, t2tb1(B1)), $product(-1, length1(int, t2tb1(B2)))) = 0)))) | (~solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), Pos!4) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), Pos!4)) | (~($sum(length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))))), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))))))) = 0)))),
% 1.08/1.06 inference(transitivity,[status(thm)],[980, 978])).
% 1.08/1.06 tff(982,plain,
% 1.08/1.06 ((~![B1: array_int, B2: array_int, Pos: $int] : (solution1(B2, Pos) | (~eq_board1(B1, B2, Pos)) | (~solution1(B1, Pos)) | (~($sum(length1(int, t2tb1(B1)), $product(-1, length1(int, t2tb1(B2)))) = 0)))) | (solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), Pos!4) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), Pos!4)) | (~solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~($sum(length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))))), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))))))) = 0)))),
% 1.08/1.06 inference(quant_inst,[status(thm)],[])).
% 1.08/1.06 tff(983,plain,
% 1.08/1.06 ((~![B1: array_int, B2: array_int, Pos: $int] : (solution1(B2, Pos) | (~eq_board1(B1, B2, Pos)) | (~solution1(B1, Pos)) | (~($sum(length1(int, t2tb1(B1)), $product(-1, length1(int, t2tb1(B2)))) = 0)))) | (~solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), Pos!4) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), Pos!4)) | (~($sum(length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))))), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))))))) = 0))),
% 1.08/1.06 inference(modus_ponens,[status(thm)],[982, 981])).
% 1.08/1.06 tff(984,plain,
% 1.08/1.06 (solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), Pos!4) | (~($sum(length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))))), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))))))) = 0))),
% 1.08/1.06 inference(unit_resolution,[status(thm)],[983, 819, 46, 977])).
% 1.08/1.06 tff(985,plain,
% 1.08/1.06 (solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), Pos!4)),
% 1.08/1.06 inference(unit_resolution,[status(thm)],[984, 973])).
% 1.08/1.06 tff(986,plain,
% 1.08/1.06 (((~![B1: array_int, B2: array_int, Pos: $int] : (solution1(B2, Pos) | (~eq_board1(B1, B2, Pos)) | (~solution1(B1, Pos)) | (~($sum(length1(int, t2tb1(B1)), $product(-1, length1(int, t2tb1(B2)))) = 0)))) | ((~solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), Pos!4)) | solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4) | (~($sum(length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))))), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))))) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)))) <=> ((~![B1: array_int, B2: array_int, Pos: $int] : (solution1(B2, Pos) | (~eq_board1(B1, B2, Pos)) | (~solution1(B1, Pos)) | (~($sum(length1(int, t2tb1(B1)), $product(-1, length1(int, t2tb1(B2)))) = 0)))) | (~solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), Pos!4)) | solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4) | (~($sum(length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))))), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))))) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)))),
% 1.08/1.06 inference(rewrite,[status(thm)],[])).
% 1.08/1.06 tff(987,plain,
% 1.08/1.06 ((solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | (~solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), Pos!4)) | (~($sum(length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))))), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))))) = 0))) <=> ((~solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), Pos!4)) | solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4) | (~($sum(length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))))), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))))) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)))),
% 1.08/1.06 inference(rewrite,[status(thm)],[])).
% 1.08/1.06 tff(988,plain,
% 1.08/1.06 (((~![B1: array_int, B2: array_int, Pos: $int] : (solution1(B2, Pos) | (~eq_board1(B1, B2, Pos)) | (~solution1(B1, Pos)) | (~($sum(length1(int, t2tb1(B1)), $product(-1, length1(int, t2tb1(B2)))) = 0)))) | (solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | (~solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), Pos!4)) | (~($sum(length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))))), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))))) = 0)))) <=> ((~![B1: array_int, B2: array_int, Pos: $int] : (solution1(B2, Pos) | (~eq_board1(B1, B2, Pos)) | (~solution1(B1, Pos)) | (~($sum(length1(int, t2tb1(B1)), $product(-1, length1(int, t2tb1(B2)))) = 0)))) | ((~solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), Pos!4)) | solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4) | (~($sum(length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))))), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))))) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4))))),
% 1.08/1.07 inference(monotonicity,[status(thm)],[987])).
% 1.08/1.07 tff(989,plain,
% 1.08/1.07 (((~![B1: array_int, B2: array_int, Pos: $int] : (solution1(B2, Pos) | (~eq_board1(B1, B2, Pos)) | (~solution1(B1, Pos)) | (~($sum(length1(int, t2tb1(B1)), $product(-1, length1(int, t2tb1(B2)))) = 0)))) | (solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | (~solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), Pos!4)) | (~($sum(length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))))), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))))) = 0)))) <=> ((~![B1: array_int, B2: array_int, Pos: $int] : (solution1(B2, Pos) | (~eq_board1(B1, B2, Pos)) | (~solution1(B1, Pos)) | (~($sum(length1(int, t2tb1(B1)), $product(-1, length1(int, t2tb1(B2)))) = 0)))) | (~solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), Pos!4)) | solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4) | (~($sum(length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))))), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))))) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)))),
% 1.08/1.07 inference(transitivity,[status(thm)],[988, 986])).
% 1.08/1.07 tff(990,plain,
% 1.08/1.07 ((~![B1: array_int, B2: array_int, Pos: $int] : (solution1(B2, Pos) | (~eq_board1(B1, B2, Pos)) | (~solution1(B1, Pos)) | (~($sum(length1(int, t2tb1(B1)), $product(-1, length1(int, t2tb1(B2)))) = 0)))) | (solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | (~solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), Pos!4)) | (~($sum(length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))))), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))))) = 0)))),
% 1.08/1.07 inference(quant_inst,[status(thm)],[])).
% 1.08/1.07 tff(991,plain,
% 1.08/1.07 ((~![B1: array_int, B2: array_int, Pos: $int] : (solution1(B2, Pos) | (~eq_board1(B1, B2, Pos)) | (~solution1(B1, Pos)) | (~($sum(length1(int, t2tb1(B1)), $product(-1, length1(int, t2tb1(B2)))) = 0)))) | (~solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), Pos!4)) | solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4) | (~($sum(length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))))), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))))) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4))),
% 1.08/1.07 inference(modus_ponens,[status(thm)],[990, 989])).
% 1.08/1.07 tff(992,plain,
% 1.08/1.07 (solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4) | (~($sum(length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))))), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))))) = 0))),
% 1.08/1.07 inference(unit_resolution,[status(thm)],[991, 819, 985, 551])).
% 1.08/1.07 tff(993,plain,
% 1.08/1.07 (solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)),
% 1.08/1.07 inference(unit_resolution,[status(thm)],[992, 951])).
% 1.08/1.07 tff(994,plain,
% 1.08/1.07 ((~((~solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | (~((~is_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | (~![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 0) | is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Q))))))) | (~solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | (~((~is_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | (~![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 0) | is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Q)))))),
% 1.08/1.07 inference(tautology,[status(thm)],[])).
% 1.08/1.07 tff(995,plain,
% 1.08/1.07 ((~((~solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | (~((~is_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | (~![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 0) | is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Q))))))) | (~((~is_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | (~![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 0) | is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Q)))))),
% 1.08/1.07 inference(unit_resolution,[status(thm)],[994, 993])).
% 1.08/1.07 tff(996,plain,
% 1.08/1.07 (~((~is_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | (~![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 0) | is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Q))))),
% 1.08/1.07 inference(unit_resolution,[status(thm)],[995, 933])).
% 1.08/1.07 tff(997,plain,
% 1.08/1.07 (((~is_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | (~![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 0) | is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Q)))) | ![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 0) | is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Q))),
% 1.08/1.07 inference(tautology,[status(thm)],[])).
% 1.08/1.07 tff(998,plain,
% 1.08/1.07 (![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 0) | is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Q))),
% 1.08/1.07 inference(unit_resolution,[status(thm)],[997, 996])).
% 1.08/1.07 tff(999,plain,
% 1.08/1.07 (((~![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 0) | is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Q))) | ((~$greatereq(tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0)) | is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), 0))) <=> ((~![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 0) | is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Q))) | (~$greatereq(tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0)) | is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), 0))),
% 1.08/1.07 inference(rewrite,[status(thm)],[])).
% 1.08/1.07 tff(1000,plain,
% 1.08/1.07 (((~$greatereq(tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0)) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), 0) | is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))) <=> ((~$greatereq(tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0)) | is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), 0))),
% 1.08/1.07 inference(rewrite,[status(thm)],[])).
% 1.08/1.07 tff(1001,plain,
% 1.08/1.07 ($greatereq($sum($product(-1, Pos!4), tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))), 0) <=> $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), 0)),
% 1.08/1.07 inference(rewrite,[status(thm)],[])).
% 1.08/1.07 tff(1002,plain,
% 1.08/1.07 ($sum(tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), $product(-1, Pos!4)) = $sum($product(-1, Pos!4), tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))),
% 1.08/1.07 inference(rewrite,[status(thm)],[])).
% 1.08/1.07 tff(1003,plain,
% 1.08/1.07 ($greatereq($sum(tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), $product(-1, Pos!4)), 0) <=> $greatereq($sum($product(-1, Pos!4), tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))), 0)),
% 1.08/1.07 inference(monotonicity,[status(thm)],[1002])).
% 1.08/1.07 tff(1004,plain,
% 1.08/1.07 ($greatereq($sum(tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), $product(-1, Pos!4)), 0) <=> $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), 0)),
% 1.08/1.07 inference(transitivity,[status(thm)],[1003, 1001])).
% 1.08/1.07 tff(1005,plain,
% 1.08/1.07 (((~$greatereq(tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0)) | $greatereq($sum(tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), $product(-1, Pos!4)), 0) | is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))) <=> ((~$greatereq(tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0)) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), 0) | is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))))),
% 1.08/1.07 inference(monotonicity,[status(thm)],[1004])).
% 1.08/1.07 tff(1006,plain,
% 1.08/1.07 (((~$greatereq(tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0)) | $greatereq($sum(tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), $product(-1, Pos!4)), 0) | is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))) <=> ((~$greatereq(tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0)) | is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), 0))),
% 1.08/1.07 inference(transitivity,[status(thm)],[1005, 1000])).
% 1.08/1.07 tff(1007,plain,
% 1.08/1.07 (((~![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 0) | is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Q))) | ((~$greatereq(tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0)) | $greatereq($sum(tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), $product(-1, Pos!4)), 0) | is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))))) <=> ((~![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 0) | is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Q))) | ((~$greatereq(tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0)) | is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), 0)))),
% 1.08/1.07 inference(monotonicity,[status(thm)],[1006])).
% 1.08/1.07 tff(1008,plain,
% 1.08/1.07 (((~![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 0) | is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Q))) | ((~$greatereq(tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0)) | $greatereq($sum(tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), $product(-1, Pos!4)), 0) | is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))))) <=> ((~![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 0) | is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Q))) | (~$greatereq(tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0)) | is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), 0))),
% 1.08/1.07 inference(transitivity,[status(thm)],[1007, 999])).
% 1.08/1.07 tff(1009,plain,
% 1.08/1.07 ((~![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 0) | is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Q))) | ((~$greatereq(tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0)) | $greatereq($sum(tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), $product(-1, Pos!4)), 0) | is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))))),
% 1.08/1.07 inference(quant_inst,[status(thm)],[])).
% 1.08/1.07 tff(1010,plain,
% 1.08/1.07 ((~![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 0) | is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Q))) | (~$greatereq(tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0)) | is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), 0)),
% 1.08/1.07 inference(modus_ponens,[status(thm)],[1009, 1008])).
% 1.08/1.07 tff(1011,plain,
% 1.08/1.07 ($lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), 0)),
% 1.08/1.07 inference(unit_resolution,[status(thm)],[1010, 998, 924, 922])).
% 1.08/1.07 tff(1012,plain,
% 1.08/1.07 (((~$greatereq(tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0)) | is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), -1)) | (~$lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), -1))),
% 1.08/1.07 inference(tautology,[status(thm)],[])).
% 1.08/1.07 tff(1013,plain,
% 1.08/1.07 (~$lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), -1)),
% 1.08/1.07 inference(unit_resolution,[status(thm)],[1012, 920])).
% 1.08/1.07 tff(1014,plain,
% 1.08/1.07 (Pos!4 = tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))),
% 1.08/1.07 inference(theory_lemma,[status(thm)],[1013, 1011])).
% 1.08/1.07 tff(1015,plain,
% 1.08/1.07 (tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))) = Pos!4),
% 1.08/1.07 inference(symmetry,[status(thm)],[1014])).
% 1.08/1.07 tff(1016,plain,
% 1.08/1.07 (is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))) <=> is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)),
% 1.08/1.07 inference(monotonicity,[status(thm)],[1015])).
% 1.08/1.07 tff(1017,plain,
% 1.08/1.07 (is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4) <=> is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))),
% 1.08/1.07 inference(symmetry,[status(thm)],[1016])).
% 1.08/1.07 tff(1018,assumption,(is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)), introduced(assumption)).
% 1.08/1.07 tff(1019,plain,
% 1.08/1.07 (is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))),
% 1.08/1.07 inference(modus_ponens,[status(thm)],[1018, 1017])).
% 1.08/1.07 tff(1020,plain,
% 1.08/1.07 ($false),
% 1.08/1.07 inference(unit_resolution,[status(thm)],[922, 1019])).
% 1.08/1.07 tff(1021,plain,(((~$greatereq(tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0)) | is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), -1)) | (~is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4))), inference(lemma,lemma(discharge,[]))).
% 1.08/1.07 tff(1022,plain,
% 1.08/1.07 ((~$greatereq(tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0)) | is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), -1)),
% 1.08/1.07 inference(unit_resolution,[status(thm)],[1021, 913])).
% 1.08/1.07 tff(1023,plain,
% 1.08/1.07 (((~(solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4)) | (~is_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~((~$greatereq(tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0)) | is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), -1))))) | (~((~solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~((~is_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 1) | is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Q)))))))) | (solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4)) | (~is_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~((~$greatereq(tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0)) | is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), -1))))),
% 1.08/1.07 inference(tautology,[status(thm)],[])).
% 1.08/1.07 tff(1024,plain,
% 1.08/1.07 (solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4)) | (~is_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~((~$greatereq(tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0)) | is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), -1)))),
% 1.08/1.07 inference(unit_resolution,[status(thm)],[1023, 801])).
% 1.08/1.07 tff(1025,assumption,((~((~is_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | ![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 1) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))))), 0)))))) | (~(is_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4)) | (~((~$greatereq(tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0)) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), 0)) | $lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))), 0))) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), -1)))))), introduced(assumption)).
% 1.08/1.07 tff(1026,plain,
% 1.08/1.07 (((~![Board: array_int, Pos: $int] : (~((~((~is_board1(Board, Pos)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(Board), Q)), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(Board), Q)), $product(-1, length1(int, t2tb1(Board)))), 0)))))) | (~(is_board1(Board, Pos) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_2(Pos, Board))), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(Board), tptp_fun_Q_2(Pos, Board))), 0)) | $lesseq($sum(length1(int, t2tb1(Board)), $product(-1, tb2t(get2(int, t2tb1(Board), tptp_fun_Q_2(Pos, Board))))), 0))) | (~$greatereq(tptp_fun_Q_2(Pos, Board), 0))))))))) | (~((~((~is_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | ![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 1) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))))), 0)))))) | (~(is_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4)) | (~((~$greatereq(tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0)) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), 0)) | $lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))), 0))) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), -1)))))))) <=> ((~![Board: array_int, Pos: $int] : (~((~((~is_board1(Board, Pos)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(Board), Q)), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(Board), Q)), $product(-1, length1(int, t2tb1(Board)))), 0)))))) | (~(is_board1(Board, Pos) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_2(Pos, Board))), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(Board), tptp_fun_Q_2(Pos, Board))), 0)) | $lesseq($sum(length1(int, t2tb1(Board)), $product(-1, tb2t(get2(int, t2tb1(Board), tptp_fun_Q_2(Pos, Board))))), 0))) | (~$greatereq(tptp_fun_Q_2(Pos, Board), 0))))))))) | (~((~((~is_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | ![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 1) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))))), 0)))))) | (~(is_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4)) | (~((~$greatereq(tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0)) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), 0)) | $lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))), 0))) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), -1))))))))),
% 1.08/1.07 inference(rewrite,[status(thm)],[])).
% 1.08/1.07 tff(1027,plain,
% 1.08/1.07 ((~((~((~is_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum($sum(1, Pos!4), $product(-1, Q)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))))), 0)))))) | (~(is_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4)) | (~($lesseq($sum($sum(1, Pos!4), $product(-1, tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), 0)) | $lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))), 0))) | (~$greatereq(tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0)))))))) <=> (~((~((~is_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | ![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 1) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))))), 0)))))) | (~(is_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4)) | (~((~$greatereq(tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0)) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), 0)) | $lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))), 0))) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), -1)))))))),
% 1.08/1.07 inference(rewrite,[status(thm)],[])).
% 1.08/1.07 tff(1028,plain,
% 1.08/1.07 (((~![Board: array_int, Pos: $int] : (~((~((~is_board1(Board, Pos)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(Board), Q)), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(Board), Q)), $product(-1, length1(int, t2tb1(Board)))), 0)))))) | (~(is_board1(Board, Pos) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_2(Pos, Board))), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(Board), tptp_fun_Q_2(Pos, Board))), 0)) | $lesseq($sum(length1(int, t2tb1(Board)), $product(-1, tb2t(get2(int, t2tb1(Board), tptp_fun_Q_2(Pos, Board))))), 0))) | (~$greatereq(tptp_fun_Q_2(Pos, Board), 0))))))))) | (~((~((~is_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum($sum(1, Pos!4), $product(-1, Q)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))))), 0)))))) | (~(is_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4)) | (~($lesseq($sum($sum(1, Pos!4), $product(-1, tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), 0)) | $lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))), 0))) | (~$greatereq(tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0))))))))) <=> ((~![Board: array_int, Pos: $int] : (~((~((~is_board1(Board, Pos)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(Board), Q)), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(Board), Q)), $product(-1, length1(int, t2tb1(Board)))), 0)))))) | (~(is_board1(Board, Pos) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_2(Pos, Board))), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(Board), tptp_fun_Q_2(Pos, Board))), 0)) | $lesseq($sum(length1(int, t2tb1(Board)), $product(-1, tb2t(get2(int, t2tb1(Board), tptp_fun_Q_2(Pos, Board))))), 0))) | (~$greatereq(tptp_fun_Q_2(Pos, Board), 0))))))))) | (~((~((~is_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | ![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 1) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))))), 0)))))) | (~(is_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4)) | (~((~$greatereq(tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0)) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), 0)) | $lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))), 0))) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), -1))))))))),
% 1.12/1.08 inference(monotonicity,[status(thm)],[1027])).
% 1.12/1.08 tff(1029,plain,
% 1.12/1.08 (((~![Board: array_int, Pos: $int] : (~((~((~is_board1(Board, Pos)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(Board), Q)), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(Board), Q)), $product(-1, length1(int, t2tb1(Board)))), 0)))))) | (~(is_board1(Board, Pos) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_2(Pos, Board))), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(Board), tptp_fun_Q_2(Pos, Board))), 0)) | $lesseq($sum(length1(int, t2tb1(Board)), $product(-1, tb2t(get2(int, t2tb1(Board), tptp_fun_Q_2(Pos, Board))))), 0))) | (~$greatereq(tptp_fun_Q_2(Pos, Board), 0))))))))) | (~((~((~is_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum($sum(1, Pos!4), $product(-1, Q)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))))), 0)))))) | (~(is_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4)) | (~($lesseq($sum($sum(1, Pos!4), $product(-1, tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), 0)) | $lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))), 0))) | (~$greatereq(tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0))))))))) <=> ((~![Board: array_int, Pos: $int] : (~((~((~is_board1(Board, Pos)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(Board), Q)), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(Board), Q)), $product(-1, length1(int, t2tb1(Board)))), 0)))))) | (~(is_board1(Board, Pos) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_2(Pos, Board))), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(Board), tptp_fun_Q_2(Pos, Board))), 0)) | $lesseq($sum(length1(int, t2tb1(Board)), $product(-1, tb2t(get2(int, t2tb1(Board), tptp_fun_Q_2(Pos, Board))))), 0))) | (~$greatereq(tptp_fun_Q_2(Pos, Board), 0))))))))) | (~((~((~is_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | ![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 1) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))))), 0)))))) | (~(is_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4)) | (~((~$greatereq(tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0)) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), 0)) | $lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))), 0))) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), -1))))))))),
% 1.12/1.08 inference(transitivity,[status(thm)],[1028, 1026])).
% 1.12/1.08 tff(1030,plain,
% 1.12/1.08 ((~![Board: array_int, Pos: $int] : (~((~((~is_board1(Board, Pos)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(Board), Q)), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(Board), Q)), $product(-1, length1(int, t2tb1(Board)))), 0)))))) | (~(is_board1(Board, Pos) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_2(Pos, Board))), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(Board), tptp_fun_Q_2(Pos, Board))), 0)) | $lesseq($sum(length1(int, t2tb1(Board)), $product(-1, tb2t(get2(int, t2tb1(Board), tptp_fun_Q_2(Pos, Board))))), 0))) | (~$greatereq(tptp_fun_Q_2(Pos, Board), 0))))))))) | (~((~((~is_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum($sum(1, Pos!4), $product(-1, Q)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))))), 0)))))) | (~(is_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4)) | (~($lesseq($sum($sum(1, Pos!4), $product(-1, tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), 0)) | $lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))), 0))) | (~$greatereq(tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0))))))))),
% 1.12/1.08 inference(quant_inst,[status(thm)],[])).
% 1.12/1.08 tff(1031,plain,
% 1.12/1.08 ((~![Board: array_int, Pos: $int] : (~((~((~is_board1(Board, Pos)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(Board), Q)), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(Board), Q)), $product(-1, length1(int, t2tb1(Board)))), 0)))))) | (~(is_board1(Board, Pos) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_2(Pos, Board))), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(Board), tptp_fun_Q_2(Pos, Board))), 0)) | $lesseq($sum(length1(int, t2tb1(Board)), $product(-1, tb2t(get2(int, t2tb1(Board), tptp_fun_Q_2(Pos, Board))))), 0))) | (~$greatereq(tptp_fun_Q_2(Pos, Board), 0))))))))) | (~((~((~is_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | ![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 1) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))))), 0)))))) | (~(is_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4)) | (~((~$greatereq(tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0)) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), 0)) | $lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))), 0))) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), -1)))))))),
% 1.12/1.08 inference(modus_ponens,[status(thm)],[1030, 1029])).
% 1.12/1.08 tff(1032,plain,
% 1.12/1.08 ($false),
% 1.12/1.08 inference(unit_resolution,[status(thm)],[1031, 73, 1025])).
% 1.12/1.08 tff(1033,plain,(~((~((~is_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | ![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 1) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))))), 0)))))) | (~(is_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4)) | (~((~$greatereq(tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0)) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), 0)) | $lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))), 0))) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), -1))))))), inference(lemma,lemma(discharge,[]))).
% 1.12/1.08 tff(1034,plain,
% 1.12/1.08 (((~((~is_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | ![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 1) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))))), 0)))))) | (~(is_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4)) | (~((~$greatereq(tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0)) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), 0)) | $lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))), 0))) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), -1)))))) | (is_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4)) | (~((~$greatereq(tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0)) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), 0)) | $lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))), 0))) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), -1))))),
% 1.12/1.08 inference(tautology,[status(thm)],[])).
% 1.12/1.08 tff(1035,plain,
% 1.12/1.08 (is_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4)) | (~((~$greatereq(tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0)) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), 0)) | $lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))), 0))) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), -1)))),
% 1.12/1.08 inference(unit_resolution,[status(thm)],[1034, 1033])).
% 1.12/1.08 tff(1036,plain,
% 1.12/1.08 (((~$greatereq(I!11, 0)) | (~$greatereq($sum(N!5, $product(-1, I!11)), 1)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos!4)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), 0)) | $greatereq($sum(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), $product(-1, I!11)), 0))) | (~($greatereq($sum(Pos!4, $product(-1, Board!7)), 0) | (~$greatereq(Board!7, 0)) | (~$greatereq(Pos!4, 0)) | (~((~$greatereq(Board!7, 0)) | (~(Board3!12 = tb2t2(set(int, int, t2tb2(Board2!10), t2tb(Pos!4), t2tb(I!11))))) | (~($greatereq($sum(Pos!4, $product(-1, Board!7)), 0) | (~$greatereq(Pos!4, 0)) | (~(((~(Result!13 = true1)) <=> is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | (~((~((Result!13 = true1) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Pos!4)) | (~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~($sum(N!5, $product(-1, B!19)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))), 0)))))))) | (~((~(Result!13 = true1)) | (~((~$lesseq($sum(Pos!4, $product(-1, N!5)), 0)) | (~($sum(N!5, $product(-1, Board!7)) = 0)) | (~$greatereq(Pos!4, -1)) | (~$lesseq($sum(Pos!4, $product(-1, N!5)), -1)) | (~solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~((~$greatereq(Board!7, 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B, t2tb2(B1))), $sum(1, Pos!4))))) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), Pos!4)) | (~($sum(N!5, $product(-1, B!16)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))), 0))))))))))))))))))))))) | $greatereq($sum(N!5, $product(-1, I!11)), 1)),
% 1.12/1.08 inference(tautology,[status(thm)],[])).
% 1.12/1.08 tff(1037,plain,
% 1.12/1.08 ($greatereq($sum(N!5, $product(-1, I!11)), 1)),
% 1.12/1.08 inference(unit_resolution,[status(thm)],[1036, 575])).
% 1.12/1.08 tff(1038,assumption,(~((~$greatereq(tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0)) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), 0)) | $lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))), 0))) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), -1))), introduced(assumption)).
% 1.12/1.08 tff(1039,plain,
% 1.12/1.08 (((~$greatereq(tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0)) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), 0)) | $lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))), 0))) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), -1)) | ((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), 0)) | $lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))), 0))),
% 1.12/1.08 inference(tautology,[status(thm)],[])).
% 1.12/1.08 tff(1040,plain,
% 1.12/1.08 ((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), 0)) | $lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))), 0)),
% 1.12/1.08 inference(unit_resolution,[status(thm)],[1039, 1038])).
% 1.12/1.08 tff(1041,plain,
% 1.12/1.08 (((~$greatereq(tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0)) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), 0)) | $lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))), 0))) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), -1)) | $greatereq(tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0)),
% 1.12/1.08 inference(tautology,[status(thm)],[])).
% 1.12/1.08 tff(1042,plain,
% 1.12/1.08 ($greatereq(tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0)),
% 1.12/1.08 inference(unit_resolution,[status(thm)],[1041, 1038])).
% 1.12/1.08 tff(1043,plain,
% 1.12/1.08 (((~$greatereq(tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0)) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), 0)) | $lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))), 0))) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), -1)) | (~$lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), -1))),
% 1.12/1.08 inference(tautology,[status(thm)],[])).
% 1.12/1.08 tff(1044,plain,
% 1.12/1.08 (~$lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), -1)),
% 1.12/1.08 inference(unit_resolution,[status(thm)],[1043, 1038])).
% 1.12/1.08 tff(1045,assumption,((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), 0)) | $lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))), 0)), introduced(assumption)).
% 1.12/1.08 tff(1046,assumption,($greatereq(tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0)), introduced(assumption)).
% 1.12/1.08 tff(1047,plain,
% 1.12/1.08 (((~![Board: array_int, Pos: $int] : (~((~((~is_board1(Board, Pos)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(Board), Q)), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(Board), Q)), $product(-1, length1(int, t2tb1(Board)))), 0)))))) | (~(is_board1(Board, Pos) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_2(Pos, Board))), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(Board), tptp_fun_Q_2(Pos, Board))), 0)) | $lesseq($sum(length1(int, t2tb1(Board)), $product(-1, tb2t(get2(int, t2tb1(Board), tptp_fun_Q_2(Pos, Board))))), 0))) | (~$greatereq(tptp_fun_Q_2(Pos, Board), 0))))))))) | (~((~((~is_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))))), 0)))))) | (~(is_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4) | (~($lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_2(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_2(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), 0)) | $lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_2(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))), 0))) | (~$greatereq(tptp_fun_Q_2(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0))))))))) <=> ((~![Board: array_int, Pos: $int] : (~((~((~is_board1(Board, Pos)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(Board), Q)), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(Board), Q)), $product(-1, length1(int, t2tb1(Board)))), 0)))))) | (~(is_board1(Board, Pos) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_2(Pos, Board))), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(Board), tptp_fun_Q_2(Pos, Board))), 0)) | $lesseq($sum(length1(int, t2tb1(Board)), $product(-1, tb2t(get2(int, t2tb1(Board), tptp_fun_Q_2(Pos, Board))))), 0))) | (~$greatereq(tptp_fun_Q_2(Pos, Board), 0))))))))) | (~((~((~is_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))))), 0)))))) | (~(is_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4) | (~($lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_2(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_2(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), 0)) | $lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_2(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))), 0))) | (~$greatereq(tptp_fun_Q_2(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0)))))))))),
% 1.12/1.08 inference(rewrite,[status(thm)],[])).
% 1.12/1.08 tff(1048,plain,
% 1.12/1.08 ((~((~((~is_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos!4, $product(-1, Q)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))))), 0)))))) | (~(is_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4) | (~($lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_2(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_2(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), 0)) | $lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_2(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))), 0))) | (~$greatereq(tptp_fun_Q_2(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0)))))))) <=> (~((~((~is_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))))), 0)))))) | (~(is_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4) | (~($lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_2(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_2(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), 0)) | $lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_2(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))), 0))) | (~$greatereq(tptp_fun_Q_2(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0))))))))),
% 1.12/1.08 inference(rewrite,[status(thm)],[])).
% 1.12/1.08 tff(1049,plain,
% 1.12/1.08 (((~![Board: array_int, Pos: $int] : (~((~((~is_board1(Board, Pos)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(Board), Q)), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(Board), Q)), $product(-1, length1(int, t2tb1(Board)))), 0)))))) | (~(is_board1(Board, Pos) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_2(Pos, Board))), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(Board), tptp_fun_Q_2(Pos, Board))), 0)) | $lesseq($sum(length1(int, t2tb1(Board)), $product(-1, tb2t(get2(int, t2tb1(Board), tptp_fun_Q_2(Pos, Board))))), 0))) | (~$greatereq(tptp_fun_Q_2(Pos, Board), 0))))))))) | (~((~((~is_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos!4, $product(-1, Q)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))))), 0)))))) | (~(is_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4) | (~($lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_2(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_2(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), 0)) | $lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_2(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))), 0))) | (~$greatereq(tptp_fun_Q_2(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0))))))))) <=> ((~![Board: array_int, Pos: $int] : (~((~((~is_board1(Board, Pos)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(Board), Q)), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(Board), Q)), $product(-1, length1(int, t2tb1(Board)))), 0)))))) | (~(is_board1(Board, Pos) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_2(Pos, Board))), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(Board), tptp_fun_Q_2(Pos, Board))), 0)) | $lesseq($sum(length1(int, t2tb1(Board)), $product(-1, tb2t(get2(int, t2tb1(Board), tptp_fun_Q_2(Pos, Board))))), 0))) | (~$greatereq(tptp_fun_Q_2(Pos, Board), 0))))))))) | (~((~((~is_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))))), 0)))))) | (~(is_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4) | (~($lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_2(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_2(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), 0)) | $lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_2(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))), 0))) | (~$greatereq(tptp_fun_Q_2(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0)))))))))),
% 1.12/1.09 inference(monotonicity,[status(thm)],[1048])).
% 1.12/1.09 tff(1050,plain,
% 1.12/1.09 (((~![Board: array_int, Pos: $int] : (~((~((~is_board1(Board, Pos)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(Board), Q)), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(Board), Q)), $product(-1, length1(int, t2tb1(Board)))), 0)))))) | (~(is_board1(Board, Pos) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_2(Pos, Board))), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(Board), tptp_fun_Q_2(Pos, Board))), 0)) | $lesseq($sum(length1(int, t2tb1(Board)), $product(-1, tb2t(get2(int, t2tb1(Board), tptp_fun_Q_2(Pos, Board))))), 0))) | (~$greatereq(tptp_fun_Q_2(Pos, Board), 0))))))))) | (~((~((~is_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos!4, $product(-1, Q)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))))), 0)))))) | (~(is_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4) | (~($lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_2(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_2(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), 0)) | $lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_2(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))), 0))) | (~$greatereq(tptp_fun_Q_2(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0))))))))) <=> ((~![Board: array_int, Pos: $int] : (~((~((~is_board1(Board, Pos)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(Board), Q)), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(Board), Q)), $product(-1, length1(int, t2tb1(Board)))), 0)))))) | (~(is_board1(Board, Pos) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_2(Pos, Board))), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(Board), tptp_fun_Q_2(Pos, Board))), 0)) | $lesseq($sum(length1(int, t2tb1(Board)), $product(-1, tb2t(get2(int, t2tb1(Board), tptp_fun_Q_2(Pos, Board))))), 0))) | (~$greatereq(tptp_fun_Q_2(Pos, Board), 0))))))))) | (~((~((~is_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))))), 0)))))) | (~(is_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4) | (~($lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_2(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_2(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), 0)) | $lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_2(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))), 0))) | (~$greatereq(tptp_fun_Q_2(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0)))))))))),
% 1.12/1.09 inference(transitivity,[status(thm)],[1049, 1047])).
% 1.12/1.09 tff(1051,plain,
% 1.12/1.09 ((~![Board: array_int, Pos: $int] : (~((~((~is_board1(Board, Pos)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(Board), Q)), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(Board), Q)), $product(-1, length1(int, t2tb1(Board)))), 0)))))) | (~(is_board1(Board, Pos) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_2(Pos, Board))), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(Board), tptp_fun_Q_2(Pos, Board))), 0)) | $lesseq($sum(length1(int, t2tb1(Board)), $product(-1, tb2t(get2(int, t2tb1(Board), tptp_fun_Q_2(Pos, Board))))), 0))) | (~$greatereq(tptp_fun_Q_2(Pos, Board), 0))))))))) | (~((~((~is_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos!4, $product(-1, Q)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))))), 0)))))) | (~(is_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4) | (~($lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_2(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_2(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), 0)) | $lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_2(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))), 0))) | (~$greatereq(tptp_fun_Q_2(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0))))))))),
% 1.12/1.09 inference(quant_inst,[status(thm)],[])).
% 1.12/1.09 tff(1052,plain,
% 1.12/1.09 ((~![Board: array_int, Pos: $int] : (~((~((~is_board1(Board, Pos)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(Board), Q)), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(Board), Q)), $product(-1, length1(int, t2tb1(Board)))), 0)))))) | (~(is_board1(Board, Pos) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_2(Pos, Board))), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(Board), tptp_fun_Q_2(Pos, Board))), 0)) | $lesseq($sum(length1(int, t2tb1(Board)), $product(-1, tb2t(get2(int, t2tb1(Board), tptp_fun_Q_2(Pos, Board))))), 0))) | (~$greatereq(tptp_fun_Q_2(Pos, Board), 0))))))))) | (~((~((~is_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))))), 0)))))) | (~(is_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4) | (~($lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_2(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_2(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), 0)) | $lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_2(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))), 0))) | (~$greatereq(tptp_fun_Q_2(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0))))))))),
% 1.12/1.09 inference(modus_ponens,[status(thm)],[1051, 1050])).
% 1.12/1.09 tff(1053,plain,
% 1.12/1.09 (~((~((~is_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))))), 0)))))) | (~(is_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4) | (~($lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_2(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_2(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), 0)) | $lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_2(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))), 0))) | (~$greatereq(tptp_fun_Q_2(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0)))))))),
% 1.12/1.09 inference(unit_resolution,[status(thm)],[1052, 73])).
% 1.12/1.09 tff(1054,plain,
% 1.12/1.09 (((~((~is_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))))), 0)))))) | (~(is_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4) | (~($lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_2(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_2(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), 0)) | $lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_2(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))), 0))) | (~$greatereq(tptp_fun_Q_2(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0))))))) | ((~is_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))))), 0)))))),
% 1.12/1.09 inference(tautology,[status(thm)],[])).
% 1.12/1.09 tff(1055,plain,
% 1.12/1.09 ((~is_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))))), 0))))),
% 1.12/1.09 inference(unit_resolution,[status(thm)],[1054, 1053])).
% 1.12/1.09 tff(1056,plain,
% 1.12/1.09 (((~is_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | (~![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 0) | is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Q)))) | is_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)),
% 1.12/1.09 inference(tautology,[status(thm)],[])).
% 1.12/1.09 tff(1057,plain,
% 1.12/1.09 (is_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)),
% 1.12/1.09 inference(unit_resolution,[status(thm)],[1056, 996])).
% 1.12/1.09 tff(1058,plain,
% 1.12/1.09 ((~((~is_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))))), 0)))))) | (~is_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))))), 0))))),
% 1.12/1.09 inference(tautology,[status(thm)],[])).
% 1.12/1.09 tff(1059,plain,
% 1.12/1.09 ((~((~is_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))))), 0)))))) | ![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))))), 0))))),
% 1.12/1.09 inference(unit_resolution,[status(thm)],[1058, 1057])).
% 1.12/1.09 tff(1060,plain,
% 1.12/1.09 (![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))))), 0))))),
% 1.12/1.09 inference(unit_resolution,[status(thm)],[1059, 1055])).
% 1.12/1.09 tff(1061,plain,
% 1.12/1.09 (((~![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))))), 0))))) | ((~$greatereq(tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0)) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), 0)) | $lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))), 0))) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), 0))) <=> ((~![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))))), 0))))) | (~$greatereq(tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0)) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), 0)) | $lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))), 0))) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), 0))),
% 1.12/1.09 inference(rewrite,[status(thm)],[])).
% 1.12/1.09 tff(1062,plain,
% 1.12/1.09 (((~$greatereq(tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0)) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), 0)) | $lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))), 0)))) <=> ((~$greatereq(tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0)) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), 0)) | $lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))), 0))) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), 0))),
% 1.12/1.09 inference(rewrite,[status(thm)],[])).
% 1.12/1.09 tff(1063,plain,
% 1.12/1.09 ((~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))))), 0))) <=> (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), 0)) | $lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))), 0)))),
% 1.12/1.09 inference(rewrite,[status(thm)],[])).
% 1.12/1.09 tff(1064,plain,
% 1.12/1.09 ($greatereq($sum($product(-1, Pos!4), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))), 0) <=> $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), 0)),
% 1.12/1.09 inference(rewrite,[status(thm)],[])).
% 1.12/1.09 tff(1065,plain,
% 1.12/1.09 ($sum(tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), $product(-1, Pos!4)) = $sum($product(-1, Pos!4), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))),
% 1.12/1.09 inference(rewrite,[status(thm)],[])).
% 1.12/1.09 tff(1066,plain,
% 1.12/1.09 ($greatereq($sum(tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), $product(-1, Pos!4)), 0) <=> $greatereq($sum($product(-1, Pos!4), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))), 0)),
% 1.12/1.09 inference(monotonicity,[status(thm)],[1065])).
% 1.12/1.09 tff(1067,plain,
% 1.12/1.09 ($greatereq($sum(tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), $product(-1, Pos!4)), 0) <=> $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), 0)),
% 1.12/1.09 inference(transitivity,[status(thm)],[1066, 1064])).
% 1.12/1.09 tff(1068,plain,
% 1.12/1.09 (((~$greatereq(tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0)) | $greatereq($sum(tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), $product(-1, Pos!4)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))))), 0)))) <=> ((~$greatereq(tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0)) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), 0)) | $lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))), 0))))),
% 1.12/1.09 inference(monotonicity,[status(thm)],[1067, 1063])).
% 1.12/1.09 tff(1069,plain,
% 1.12/1.09 (((~$greatereq(tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0)) | $greatereq($sum(tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), $product(-1, Pos!4)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))))), 0)))) <=> ((~$greatereq(tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0)) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), 0)) | $lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))), 0))) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), 0))),
% 1.12/1.09 inference(transitivity,[status(thm)],[1068, 1062])).
% 1.12/1.09 tff(1070,plain,
% 1.12/1.09 (((~![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))))), 0))))) | ((~$greatereq(tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0)) | $greatereq($sum(tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), $product(-1, Pos!4)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))))), 0))))) <=> ((~![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))))), 0))))) | ((~$greatereq(tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0)) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), 0)) | $lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))), 0))) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), 0)))),
% 1.12/1.09 inference(monotonicity,[status(thm)],[1069])).
% 1.12/1.09 tff(1071,plain,
% 1.12/1.09 (((~![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))))), 0))))) | ((~$greatereq(tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0)) | $greatereq($sum(tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), $product(-1, Pos!4)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))))), 0))))) <=> ((~![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))))), 0))))) | (~$greatereq(tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0)) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), 0)) | $lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))), 0))) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), 0))),
% 1.12/1.09 inference(transitivity,[status(thm)],[1070, 1061])).
% 1.12/1.09 tff(1072,plain,
% 1.12/1.09 ((~![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))))), 0))))) | ((~$greatereq(tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0)) | $greatereq($sum(tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), $product(-1, Pos!4)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))))), 0))))),
% 1.12/1.10 inference(quant_inst,[status(thm)],[])).
% 1.12/1.10 tff(1073,plain,
% 1.12/1.10 ((~![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 0) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))))), 0))))) | (~$greatereq(tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0)) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), 0)) | $lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))), 0))) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), 0)),
% 1.12/1.10 inference(modus_ponens,[status(thm)],[1072, 1071])).
% 1.12/1.10 tff(1074,plain,
% 1.12/1.10 ($lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), 0)),
% 1.12/1.10 inference(unit_resolution,[status(thm)],[1073, 1060, 1046, 1045])).
% 1.12/1.10 tff(1075,assumption,(~$lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), -1)), introduced(assumption)).
% 1.12/1.10 tff(1076,plain,
% 1.12/1.10 (Pos!4 = tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))),
% 1.12/1.10 inference(theory_lemma,[status(thm)],[1075, 1074])).
% 1.12/1.10 tff(1077,plain,
% 1.12/1.10 (tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))) = Pos!4),
% 1.12/1.10 inference(symmetry,[status(thm)],[1076])).
% 1.12/1.10 tff(1078,plain,
% 1.12/1.10 (get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))) = get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Pos!4)),
% 1.12/1.10 inference(monotonicity,[status(thm)],[1077])).
% 1.12/1.10 tff(1079,plain,
% 1.12/1.10 (get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))) = t2tb(I!11)),
% 1.12/1.10 inference(transitivity,[status(thm)],[1078, 689, 688, 686, 679, 678])).
% 1.12/1.10 tff(1080,plain,
% 1.12/1.10 (tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))) = tb2t(t2tb(I!11))),
% 1.12/1.10 inference(monotonicity,[status(thm)],[1079])).
% 1.12/1.10 tff(1081,plain,
% 1.12/1.10 (tb2t(t2tb(I!11)) = tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))))),
% 1.12/1.10 inference(symmetry,[status(thm)],[1080])).
% 1.12/1.10 tff(1082,plain,
% 1.12/1.10 ((~(tb2t(t2tb(I!11)) = tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))) | $lesseq($sum(tb2t(t2tb(I!11)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))), 0)),
% 1.12/1.10 inference(theory_lemma,[status(thm)],[])).
% 1.12/1.10 tff(1083,plain,
% 1.12/1.10 ($lesseq($sum(tb2t(t2tb(I!11)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))), 0)),
% 1.12/1.10 inference(unit_resolution,[status(thm)],[1082, 1081])).
% 1.12/1.10 tff(1084,assumption,(~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), 0)), introduced(assumption)).
% 1.12/1.10 tff(1085,plain,
% 1.12/1.10 (((~$greatereq(I!11, 0)) | (~$greatereq($sum(N!5, $product(-1, I!11)), 1)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos!4)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), 0)) | $greatereq($sum(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), $product(-1, I!11)), 0))) | (~($greatereq($sum(Pos!4, $product(-1, Board!7)), 0) | (~$greatereq(Board!7, 0)) | (~$greatereq(Pos!4, 0)) | (~((~$greatereq(Board!7, 0)) | (~(Board3!12 = tb2t2(set(int, int, t2tb2(Board2!10), t2tb(Pos!4), t2tb(I!11))))) | (~($greatereq($sum(Pos!4, $product(-1, Board!7)), 0) | (~$greatereq(Pos!4, 0)) | (~(((~(Result!13 = true1)) <=> is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | (~((~((Result!13 = true1) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), Pos!4)) | (~is_board1(tb2t1(mk_array1(int, B!19, t2tb2(B1!18))), N!5)) | (~($sum(N!5, $product(-1, B!19)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!18), t2tb(Pos!4))), 0)))))))) | (~((~(Result!13 = true1)) | (~((~$lesseq($sum(Pos!4, $product(-1, N!5)), 0)) | (~($sum(N!5, $product(-1, Board!7)) = 0)) | (~$greatereq(Pos!4, -1)) | (~$lesseq($sum(Pos!4, $product(-1, N!5)), -1)) | (~solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~((~$greatereq(Board!7, 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B, t2tb2(B1))), $sum(1, Pos!4))))) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), Pos!4)) | (~($sum(N!5, $product(-1, B!16)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))), 0))))))))))))))))))))))) | $greatereq(I!11, 0)),
% 1.12/1.10 inference(tautology,[status(thm)],[])).
% 1.12/1.10 tff(1086,plain,
% 1.12/1.10 ($greatereq(I!11, 0)),
% 1.12/1.10 inference(unit_resolution,[status(thm)],[1085, 575])).
% 1.12/1.10 tff(1087,plain,
% 1.12/1.10 ($false),
% 1.12/1.10 inference(theory_lemma,[status(thm)],[1086, 1084, 1083, 703])).
% 1.12/1.10 tff(1088,plain,($greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), 0) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), -1) | (~$greatereq(tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0)) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), 0)) | $lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))), 0)))), inference(lemma,lemma(discharge,[]))).
% 1.12/1.10 tff(1089,plain,
% 1.12/1.10 ($greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), 0)),
% 1.12/1.10 inference(unit_resolution,[status(thm)],[1088, 1044, 1042, 1040])).
% 1.12/1.10 tff(1090,plain,
% 1.12/1.10 ((~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), 0)) | $lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))), 0))) | (~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), 0)) | $lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))), 0)),
% 1.12/1.10 inference(tautology,[status(thm)],[])).
% 1.12/1.10 tff(1091,plain,
% 1.12/1.10 ($lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))), 0)),
% 1.12/1.10 inference(unit_resolution,[status(thm)],[1090, 1089, 1040])).
% 1.12/1.10 tff(1092,plain,
% 1.12/1.10 ($lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), 0)),
% 1.12/1.10 inference(unit_resolution,[status(thm)],[1073, 1060, 1042, 1040])).
% 1.12/1.10 tff(1093,plain,
% 1.12/1.10 (Pos!4 = tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))),
% 1.12/1.10 inference(theory_lemma,[status(thm)],[1044, 1092])).
% 1.12/1.10 tff(1094,plain,
% 1.12/1.10 (tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))) = Pos!4),
% 1.12/1.10 inference(symmetry,[status(thm)],[1093])).
% 1.12/1.10 tff(1095,plain,
% 1.12/1.10 (get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))) = get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Pos!4)),
% 1.12/1.10 inference(monotonicity,[status(thm)],[1094])).
% 1.12/1.10 tff(1096,plain,
% 1.12/1.10 (get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))) = t2tb(I!11)),
% 1.12/1.10 inference(transitivity,[status(thm)],[1095, 689, 688, 686, 679, 678])).
% 1.12/1.10 tff(1097,plain,
% 1.12/1.10 (tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))) = tb2t(t2tb(I!11))),
% 1.12/1.10 inference(monotonicity,[status(thm)],[1096])).
% 1.12/1.10 tff(1098,plain,
% 1.12/1.10 (tb2t(t2tb(I!11)) = tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))))),
% 1.12/1.10 inference(symmetry,[status(thm)],[1097])).
% 1.12/1.10 tff(1099,plain,
% 1.12/1.10 ((~(tb2t(t2tb(I!11)) = tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))) | $greatereq($sum(tb2t(t2tb(I!11)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))), 0)),
% 1.12/1.10 inference(theory_lemma,[status(thm)],[])).
% 1.12/1.10 tff(1100,plain,
% 1.12/1.10 ($greatereq($sum(tb2t(t2tb(I!11)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))), 0)),
% 1.12/1.10 inference(unit_resolution,[status(thm)],[1099, 1098])).
% 1.12/1.10 tff(1101,plain,
% 1.12/1.10 ($false),
% 1.12/1.10 inference(theory_lemma,[status(thm)],[654, 1100, 1091, 756, 751, 1037])).
% 1.12/1.10 tff(1102,plain,((~$greatereq(tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0)) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), 0)) | $lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))), 0))) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), -1)), inference(lemma,lemma(discharge,[]))).
% 1.12/1.10 tff(1103,plain,
% 1.12/1.10 ((~(is_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4)) | (~((~$greatereq(tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0)) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), 0)) | $lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))), 0))) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), -1))))) | is_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4)) | (~((~$greatereq(tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0)) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), 0)) | $lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))), 0))) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), -1)))),
% 1.12/1.10 inference(tautology,[status(thm)],[])).
% 1.12/1.10 tff(1104,plain,
% 1.12/1.10 ((~(is_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4)) | (~((~$greatereq(tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0)) | (~((~$greatereq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), 0)) | $lesseq($sum(length1(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))), 0))) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_2($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), -1))))) | is_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))),
% 1.12/1.10 inference(unit_resolution,[status(thm)],[1103, 1102])).
% 1.12/1.10 tff(1105,plain,
% 1.12/1.10 (is_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))),
% 1.12/1.10 inference(unit_resolution,[status(thm)],[1104, 1035])).
% 1.12/1.10 tff(1106,plain,
% 1.12/1.10 ((~(solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4)) | (~is_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~((~$greatereq(tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0)) | is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), -1))))) | solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4)) | (~is_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~((~$greatereq(tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0)) | is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), -1)))),
% 1.12/1.10 inference(tautology,[status(thm)],[])).
% 1.12/1.10 tff(1107,plain,
% 1.12/1.10 ((~(solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4)) | (~is_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~((~$greatereq(tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0)) | is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), -1))))) | solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4)) | (~((~$greatereq(tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0)) | is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), -1)))),
% 1.12/1.10 inference(unit_resolution,[status(thm)],[1106, 1105])).
% 1.12/1.10 tff(1108,plain,
% 1.12/1.10 (solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4)) | (~((~$greatereq(tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0)) | is_consistent1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_3($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), -1)))),
% 1.12/1.10 inference(unit_resolution,[status(thm)],[1107, 1024])).
% 1.12/1.10 tff(1109,plain,
% 1.12/1.10 (solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))),
% 1.12/1.10 inference(unit_resolution,[status(thm)],[1108, 1022])).
% 1.12/1.10 tff(1110,plain,
% 1.12/1.10 (((~![B1: array_int, B2: array_int, Pos: $int] : (~((~((~eq_board1(B1, B2, Pos)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0) | ($sum(tb2t(get2(int, t2tb1(B2), Q)), $product(-1, tb2t(get2(int, t2tb1(B1), Q)))) = 0)))) | (~(eq_board1(B1, B2, Pos) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_0(Pos, B2, B1))), 0) | ($sum(tb2t(get2(int, t2tb1(B2), tptp_fun_Q_0(Pos, B2, B1))), $product(-1, tb2t(get2(int, t2tb1(B1), tptp_fun_Q_0(Pos, B2, B1))))) = 0) | (~$greatereq(tptp_fun_Q_0(Pos, B2, B1), 0))))))))) | (~((~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), $sum(1, Pos!4))) | ![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 1) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), Q)))) = 0)))) | (~(eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), $sum(1, Pos!4)) | (~(($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))) = 0) | (~$greatereq(tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0)) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), -1)))))))) <=> ((~![B1: array_int, B2: array_int, Pos: $int] : (~((~((~eq_board1(B1, B2, Pos)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0) | ($sum(tb2t(get2(int, t2tb1(B2), Q)), $product(-1, tb2t(get2(int, t2tb1(B1), Q)))) = 0)))) | (~(eq_board1(B1, B2, Pos) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_0(Pos, B2, B1))), 0) | ($sum(tb2t(get2(int, t2tb1(B2), tptp_fun_Q_0(Pos, B2, B1))), $product(-1, tb2t(get2(int, t2tb1(B1), tptp_fun_Q_0(Pos, B2, B1))))) = 0) | (~$greatereq(tptp_fun_Q_0(Pos, B2, B1), 0))))))))) | (~((~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), $sum(1, Pos!4))) | ![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 1) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), Q)))) = 0)))) | (~(eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), $sum(1, Pos!4)) | (~(($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))) = 0) | (~$greatereq(tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0)) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), -1))))))))),
% 1.12/1.10 inference(rewrite,[status(thm)],[])).
% 1.12/1.10 tff(1111,plain,
% 1.12/1.10 ((~((~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), $sum(1, Pos!4))) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum($sum(1, Pos!4), $product(-1, Q)), 0) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), Q)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)))) = 0)))) | (~(eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), $sum(1, Pos!4)) | (~($lesseq($sum($sum(1, Pos!4), $product(-1, tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), 0) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))) = 0) | (~$greatereq(tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0)))))))) <=> (~((~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), $sum(1, Pos!4))) | ![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 1) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), Q)))) = 0)))) | (~(eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), $sum(1, Pos!4)) | (~(($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))) = 0) | (~$greatereq(tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0)) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), -1)))))))),
% 1.12/1.10 inference(rewrite,[status(thm)],[])).
% 1.12/1.10 tff(1112,plain,
% 1.12/1.10 (((~![B1: array_int, B2: array_int, Pos: $int] : (~((~((~eq_board1(B1, B2, Pos)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0) | ($sum(tb2t(get2(int, t2tb1(B2), Q)), $product(-1, tb2t(get2(int, t2tb1(B1), Q)))) = 0)))) | (~(eq_board1(B1, B2, Pos) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_0(Pos, B2, B1))), 0) | ($sum(tb2t(get2(int, t2tb1(B2), tptp_fun_Q_0(Pos, B2, B1))), $product(-1, tb2t(get2(int, t2tb1(B1), tptp_fun_Q_0(Pos, B2, B1))))) = 0) | (~$greatereq(tptp_fun_Q_0(Pos, B2, B1), 0))))))))) | (~((~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), $sum(1, Pos!4))) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum($sum(1, Pos!4), $product(-1, Q)), 0) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), Q)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)))) = 0)))) | (~(eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), $sum(1, Pos!4)) | (~($lesseq($sum($sum(1, Pos!4), $product(-1, tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), 0) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))) = 0) | (~$greatereq(tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0))))))))) <=> ((~![B1: array_int, B2: array_int, Pos: $int] : (~((~((~eq_board1(B1, B2, Pos)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0) | ($sum(tb2t(get2(int, t2tb1(B2), Q)), $product(-1, tb2t(get2(int, t2tb1(B1), Q)))) = 0)))) | (~(eq_board1(B1, B2, Pos) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_0(Pos, B2, B1))), 0) | ($sum(tb2t(get2(int, t2tb1(B2), tptp_fun_Q_0(Pos, B2, B1))), $product(-1, tb2t(get2(int, t2tb1(B1), tptp_fun_Q_0(Pos, B2, B1))))) = 0) | (~$greatereq(tptp_fun_Q_0(Pos, B2, B1), 0))))))))) | (~((~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), $sum(1, Pos!4))) | ![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 1) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), Q)))) = 0)))) | (~(eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), $sum(1, Pos!4)) | (~(($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))) = 0) | (~$greatereq(tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0)) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), -1))))))))),
% 1.12/1.10 inference(monotonicity,[status(thm)],[1111])).
% 1.12/1.10 tff(1113,plain,
% 1.12/1.10 (((~![B1: array_int, B2: array_int, Pos: $int] : (~((~((~eq_board1(B1, B2, Pos)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0) | ($sum(tb2t(get2(int, t2tb1(B2), Q)), $product(-1, tb2t(get2(int, t2tb1(B1), Q)))) = 0)))) | (~(eq_board1(B1, B2, Pos) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_0(Pos, B2, B1))), 0) | ($sum(tb2t(get2(int, t2tb1(B2), tptp_fun_Q_0(Pos, B2, B1))), $product(-1, tb2t(get2(int, t2tb1(B1), tptp_fun_Q_0(Pos, B2, B1))))) = 0) | (~$greatereq(tptp_fun_Q_0(Pos, B2, B1), 0))))))))) | (~((~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), $sum(1, Pos!4))) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum($sum(1, Pos!4), $product(-1, Q)), 0) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), Q)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)))) = 0)))) | (~(eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), $sum(1, Pos!4)) | (~($lesseq($sum($sum(1, Pos!4), $product(-1, tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), 0) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))) = 0) | (~$greatereq(tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0))))))))) <=> ((~![B1: array_int, B2: array_int, Pos: $int] : (~((~((~eq_board1(B1, B2, Pos)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0) | ($sum(tb2t(get2(int, t2tb1(B2), Q)), $product(-1, tb2t(get2(int, t2tb1(B1), Q)))) = 0)))) | (~(eq_board1(B1, B2, Pos) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_0(Pos, B2, B1))), 0) | ($sum(tb2t(get2(int, t2tb1(B2), tptp_fun_Q_0(Pos, B2, B1))), $product(-1, tb2t(get2(int, t2tb1(B1), tptp_fun_Q_0(Pos, B2, B1))))) = 0) | (~$greatereq(tptp_fun_Q_0(Pos, B2, B1), 0))))))))) | (~((~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), $sum(1, Pos!4))) | ![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 1) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), Q)))) = 0)))) | (~(eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), $sum(1, Pos!4)) | (~(($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))) = 0) | (~$greatereq(tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0)) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), -1))))))))),
% 1.12/1.11 inference(transitivity,[status(thm)],[1112, 1110])).
% 1.12/1.11 tff(1114,plain,
% 1.12/1.11 ((~![B1: array_int, B2: array_int, Pos: $int] : (~((~((~eq_board1(B1, B2, Pos)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0) | ($sum(tb2t(get2(int, t2tb1(B2), Q)), $product(-1, tb2t(get2(int, t2tb1(B1), Q)))) = 0)))) | (~(eq_board1(B1, B2, Pos) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_0(Pos, B2, B1))), 0) | ($sum(tb2t(get2(int, t2tb1(B2), tptp_fun_Q_0(Pos, B2, B1))), $product(-1, tb2t(get2(int, t2tb1(B1), tptp_fun_Q_0(Pos, B2, B1))))) = 0) | (~$greatereq(tptp_fun_Q_0(Pos, B2, B1), 0))))))))) | (~((~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), $sum(1, Pos!4))) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum($sum(1, Pos!4), $product(-1, Q)), 0) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), Q)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)))) = 0)))) | (~(eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), $sum(1, Pos!4)) | (~($lesseq($sum($sum(1, Pos!4), $product(-1, tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), 0) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))) = 0) | (~$greatereq(tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0))))))))),
% 1.12/1.11 inference(quant_inst,[status(thm)],[])).
% 1.12/1.11 tff(1115,plain,
% 1.12/1.11 ((~![B1: array_int, B2: array_int, Pos: $int] : (~((~((~eq_board1(B1, B2, Pos)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0) | ($sum(tb2t(get2(int, t2tb1(B2), Q)), $product(-1, tb2t(get2(int, t2tb1(B1), Q)))) = 0)))) | (~(eq_board1(B1, B2, Pos) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_0(Pos, B2, B1))), 0) | ($sum(tb2t(get2(int, t2tb1(B2), tptp_fun_Q_0(Pos, B2, B1))), $product(-1, tb2t(get2(int, t2tb1(B1), tptp_fun_Q_0(Pos, B2, B1))))) = 0) | (~$greatereq(tptp_fun_Q_0(Pos, B2, B1), 0))))))))) | (~((~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), $sum(1, Pos!4))) | ![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 1) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), Q)))) = 0)))) | (~(eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), $sum(1, Pos!4)) | (~(($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))) = 0) | (~$greatereq(tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0)) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), -1)))))))),
% 1.12/1.11 inference(modus_ponens,[status(thm)],[1114, 1113])).
% 1.12/1.11 tff(1116,plain,
% 1.12/1.11 (~((~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), $sum(1, Pos!4))) | ![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 1) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), Q)))) = 0)))) | (~(eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), $sum(1, Pos!4)) | (~(($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))) = 0) | (~$greatereq(tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0)) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), -1))))))),
% 1.12/1.11 inference(unit_resolution,[status(thm)],[1115, 297])).
% 1.12/1.11 tff(1117,plain,
% 1.12/1.11 (((~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), $sum(1, Pos!4))) | ![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 1) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), Q)))) = 0)))) | (~(eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), $sum(1, Pos!4)) | (~(($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))) = 0) | (~$greatereq(tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0)) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), -1)))))) | (eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), $sum(1, Pos!4)) | (~(($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))) = 0) | (~$greatereq(tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0)) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), -1))))),
% 1.12/1.11 inference(tautology,[status(thm)],[])).
% 1.12/1.11 tff(1118,plain,
% 1.12/1.11 (eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), $sum(1, Pos!4)) | (~(($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))) = 0) | (~$greatereq(tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0)) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), -1)))),
% 1.12/1.11 inference(unit_resolution,[status(thm)],[1117, 1116])).
% 1.12/1.11 tff(1119,assumption,(~((~$greatereq(Board!7, 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B, t2tb2(B1))), $sum(1, Pos!4))))) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), Pos!4)) | (~($sum(N!5, $product(-1, B!16)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))), 0)))))))), introduced(assumption)).
% 1.12/1.11 tff(1120,plain,
% 1.12/1.11 (((~$greatereq(Board!7, 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B, t2tb2(B1))), $sum(1, Pos!4))))) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), Pos!4)) | (~($sum(N!5, $product(-1, B!16)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))), 0))))))) | ((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), Pos!4)) | (~($sum(N!5, $product(-1, B!16)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))), 0)))))),
% 1.12/1.11 inference(tautology,[status(thm)],[])).
% 1.12/1.11 tff(1121,plain,
% 1.12/1.11 ((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), Pos!4)) | (~($sum(N!5, $product(-1, B!16)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))), 0))))),
% 1.12/1.11 inference(unit_resolution,[status(thm)],[1120, 1119])).
% 1.12/1.11 tff(1122,plain,
% 1.12/1.11 (((~![B1: array_int, B2: array_int, Pos: $int] : (~((~((~eq_board1(B1, B2, Pos)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0) | ($sum(tb2t(get2(int, t2tb1(B2), Q)), $product(-1, tb2t(get2(int, t2tb1(B1), Q)))) = 0)))) | (~(eq_board1(B1, B2, Pos) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_0(Pos, B2, B1))), 0) | ($sum(tb2t(get2(int, t2tb1(B2), tptp_fun_Q_0(Pos, B2, B1))), $product(-1, tb2t(get2(int, t2tb1(B1), tptp_fun_Q_0(Pos, B2, B1))))) = 0) | (~$greatereq(tptp_fun_Q_0(Pos, B2, B1), 0))))))))) | (~((~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | ![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 1) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), Q)))) = 0)))) | (~(eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4)) | (~(($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))))))) = 0) | (~$greatereq(tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), 0)) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))))), -1)))))))) <=> ((~![B1: array_int, B2: array_int, Pos: $int] : (~((~((~eq_board1(B1, B2, Pos)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0) | ($sum(tb2t(get2(int, t2tb1(B2), Q)), $product(-1, tb2t(get2(int, t2tb1(B1), Q)))) = 0)))) | (~(eq_board1(B1, B2, Pos) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_0(Pos, B2, B1))), 0) | ($sum(tb2t(get2(int, t2tb1(B2), tptp_fun_Q_0(Pos, B2, B1))), $product(-1, tb2t(get2(int, t2tb1(B1), tptp_fun_Q_0(Pos, B2, B1))))) = 0) | (~$greatereq(tptp_fun_Q_0(Pos, B2, B1), 0))))))))) | (~((~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | ![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 1) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), Q)))) = 0)))) | (~(eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4)) | (~(($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))))))) = 0) | (~$greatereq(tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), 0)) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))))), -1))))))))),
% 1.12/1.11 inference(rewrite,[status(thm)],[])).
% 1.12/1.11 tff(1123,plain,
% 1.12/1.11 ((~((~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum($sum(1, Pos!4), $product(-1, Q)), 0) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), Q)))) = 0)))) | (~(eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4)) | (~($lesseq($sum($sum(1, Pos!4), $product(-1, tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))))), 0) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))))))) = 0) | (~$greatereq(tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), 0)))))))) <=> (~((~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | ![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 1) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), Q)))) = 0)))) | (~(eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4)) | (~(($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))))))) = 0) | (~$greatereq(tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), 0)) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))))), -1)))))))),
% 1.12/1.11 inference(rewrite,[status(thm)],[])).
% 1.12/1.11 tff(1124,plain,
% 1.12/1.11 (((~![B1: array_int, B2: array_int, Pos: $int] : (~((~((~eq_board1(B1, B2, Pos)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0) | ($sum(tb2t(get2(int, t2tb1(B2), Q)), $product(-1, tb2t(get2(int, t2tb1(B1), Q)))) = 0)))) | (~(eq_board1(B1, B2, Pos) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_0(Pos, B2, B1))), 0) | ($sum(tb2t(get2(int, t2tb1(B2), tptp_fun_Q_0(Pos, B2, B1))), $product(-1, tb2t(get2(int, t2tb1(B1), tptp_fun_Q_0(Pos, B2, B1))))) = 0) | (~$greatereq(tptp_fun_Q_0(Pos, B2, B1), 0))))))))) | (~((~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum($sum(1, Pos!4), $product(-1, Q)), 0) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), Q)))) = 0)))) | (~(eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4)) | (~($lesseq($sum($sum(1, Pos!4), $product(-1, tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))))), 0) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))))))) = 0) | (~$greatereq(tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), 0))))))))) <=> ((~![B1: array_int, B2: array_int, Pos: $int] : (~((~((~eq_board1(B1, B2, Pos)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0) | ($sum(tb2t(get2(int, t2tb1(B2), Q)), $product(-1, tb2t(get2(int, t2tb1(B1), Q)))) = 0)))) | (~(eq_board1(B1, B2, Pos) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_0(Pos, B2, B1))), 0) | ($sum(tb2t(get2(int, t2tb1(B2), tptp_fun_Q_0(Pos, B2, B1))), $product(-1, tb2t(get2(int, t2tb1(B1), tptp_fun_Q_0(Pos, B2, B1))))) = 0) | (~$greatereq(tptp_fun_Q_0(Pos, B2, B1), 0))))))))) | (~((~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | ![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 1) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), Q)))) = 0)))) | (~(eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4)) | (~(($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))))))) = 0) | (~$greatereq(tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), 0)) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))))), -1))))))))),
% 1.12/1.12 inference(monotonicity,[status(thm)],[1123])).
% 1.12/1.12 tff(1125,plain,
% 1.12/1.12 (((~![B1: array_int, B2: array_int, Pos: $int] : (~((~((~eq_board1(B1, B2, Pos)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0) | ($sum(tb2t(get2(int, t2tb1(B2), Q)), $product(-1, tb2t(get2(int, t2tb1(B1), Q)))) = 0)))) | (~(eq_board1(B1, B2, Pos) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_0(Pos, B2, B1))), 0) | ($sum(tb2t(get2(int, t2tb1(B2), tptp_fun_Q_0(Pos, B2, B1))), $product(-1, tb2t(get2(int, t2tb1(B1), tptp_fun_Q_0(Pos, B2, B1))))) = 0) | (~$greatereq(tptp_fun_Q_0(Pos, B2, B1), 0))))))))) | (~((~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum($sum(1, Pos!4), $product(-1, Q)), 0) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), Q)))) = 0)))) | (~(eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4)) | (~($lesseq($sum($sum(1, Pos!4), $product(-1, tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))))), 0) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))))))) = 0) | (~$greatereq(tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), 0))))))))) <=> ((~![B1: array_int, B2: array_int, Pos: $int] : (~((~((~eq_board1(B1, B2, Pos)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0) | ($sum(tb2t(get2(int, t2tb1(B2), Q)), $product(-1, tb2t(get2(int, t2tb1(B1), Q)))) = 0)))) | (~(eq_board1(B1, B2, Pos) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_0(Pos, B2, B1))), 0) | ($sum(tb2t(get2(int, t2tb1(B2), tptp_fun_Q_0(Pos, B2, B1))), $product(-1, tb2t(get2(int, t2tb1(B1), tptp_fun_Q_0(Pos, B2, B1))))) = 0) | (~$greatereq(tptp_fun_Q_0(Pos, B2, B1), 0))))))))) | (~((~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | ![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 1) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), Q)))) = 0)))) | (~(eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4)) | (~(($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))))))) = 0) | (~$greatereq(tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), 0)) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))))), -1))))))))),
% 1.12/1.12 inference(transitivity,[status(thm)],[1124, 1122])).
% 1.12/1.12 tff(1126,plain,
% 1.12/1.12 ((~![B1: array_int, B2: array_int, Pos: $int] : (~((~((~eq_board1(B1, B2, Pos)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0) | ($sum(tb2t(get2(int, t2tb1(B2), Q)), $product(-1, tb2t(get2(int, t2tb1(B1), Q)))) = 0)))) | (~(eq_board1(B1, B2, Pos) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_0(Pos, B2, B1))), 0) | ($sum(tb2t(get2(int, t2tb1(B2), tptp_fun_Q_0(Pos, B2, B1))), $product(-1, tb2t(get2(int, t2tb1(B1), tptp_fun_Q_0(Pos, B2, B1))))) = 0) | (~$greatereq(tptp_fun_Q_0(Pos, B2, B1), 0))))))))) | (~((~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum($sum(1, Pos!4), $product(-1, Q)), 0) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), Q)))) = 0)))) | (~(eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4)) | (~($lesseq($sum($sum(1, Pos!4), $product(-1, tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))))), 0) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))))))) = 0) | (~$greatereq(tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), 0))))))))),
% 1.12/1.12 inference(quant_inst,[status(thm)],[])).
% 1.12/1.12 tff(1127,plain,
% 1.12/1.12 ((~![B1: array_int, B2: array_int, Pos: $int] : (~((~((~eq_board1(B1, B2, Pos)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0) | ($sum(tb2t(get2(int, t2tb1(B2), Q)), $product(-1, tb2t(get2(int, t2tb1(B1), Q)))) = 0)))) | (~(eq_board1(B1, B2, Pos) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_0(Pos, B2, B1))), 0) | ($sum(tb2t(get2(int, t2tb1(B2), tptp_fun_Q_0(Pos, B2, B1))), $product(-1, tb2t(get2(int, t2tb1(B1), tptp_fun_Q_0(Pos, B2, B1))))) = 0) | (~$greatereq(tptp_fun_Q_0(Pos, B2, B1), 0))))))))) | (~((~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | ![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 1) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), Q)))) = 0)))) | (~(eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4)) | (~(($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))))))) = 0) | (~$greatereq(tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), 0)) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))))), -1)))))))),
% 1.12/1.12 inference(modus_ponens,[status(thm)],[1126, 1125])).
% 1.12/1.12 tff(1128,plain,
% 1.12/1.12 (~((~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | ![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 1) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), Q)))) = 0)))) | (~(eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4)) | (~(($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))))))) = 0) | (~$greatereq(tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), 0)) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))))), -1))))))),
% 1.12/1.12 inference(unit_resolution,[status(thm)],[1127, 297])).
% 1.12/1.12 tff(1129,plain,
% 1.12/1.12 (((~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | ![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 1) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), Q)))) = 0)))) | (~(eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4)) | (~(($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))))))) = 0) | (~$greatereq(tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), 0)) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))))), -1)))))) | ((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | ![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 1) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), Q)))) = 0)))),
% 1.12/1.12 inference(tautology,[status(thm)],[])).
% 1.12/1.12 tff(1130,plain,
% 1.12/1.12 ((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | ![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 1) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), Q)))) = 0))),
% 1.12/1.12 inference(unit_resolution,[status(thm)],[1129, 1128])).
% 1.12/1.12 tff(1131,plain,
% 1.12/1.12 (((~$greatereq(Board!7, 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B, t2tb2(B1))), $sum(1, Pos!4))))) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), Pos!4)) | (~($sum(N!5, $product(-1, B!16)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))), 0))))))) | eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))),
% 1.12/1.12 inference(tautology,[status(thm)],[])).
% 1.12/1.12 tff(1132,plain,
% 1.12/1.12 (eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))),
% 1.12/1.12 inference(unit_resolution,[status(thm)],[1131, 1119])).
% 1.12/1.12 tff(1133,plain,
% 1.12/1.12 ((~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | ![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 1) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), Q)))) = 0)))) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | ![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 1) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), Q)))) = 0))),
% 1.12/1.12 inference(tautology,[status(thm)],[])).
% 1.12/1.12 tff(1134,plain,
% 1.12/1.12 ((~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | ![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 1) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), Q)))) = 0)))) | ![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 1) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), Q)))) = 0))),
% 1.12/1.12 inference(unit_resolution,[status(thm)],[1133, 1132])).
% 1.12/1.12 tff(1135,plain,
% 1.12/1.12 (![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 1) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), Q)))) = 0))),
% 1.12/1.12 inference(unit_resolution,[status(thm)],[1134, 1130])).
% 1.12/1.12 tff(1136,assumption,(~($lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))))), 0) | (~$greatereq(tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), 0)) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))))))) = 0))), introduced(assumption)).
% 1.12/1.12 tff(1137,plain,
% 1.12/1.12 (($lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))))), 0) | (~$greatereq(tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), 0)) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))))))) = 0)) | (~$lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))))), 0))),
% 1.12/1.12 inference(tautology,[status(thm)],[])).
% 1.12/1.12 tff(1138,plain,
% 1.12/1.12 (~$lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))))), 0)),
% 1.12/1.12 inference(unit_resolution,[status(thm)],[1137, 1136])).
% 1.12/1.12 tff(1139,plain,
% 1.12/1.12 ((~$lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))))), -1)) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))))), 0)),
% 1.12/1.12 inference(theory_lemma,[status(thm)],[])).
% 1.12/1.12 tff(1140,plain,
% 1.12/1.12 (~$lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))))), -1)),
% 1.12/1.12 inference(unit_resolution,[status(thm)],[1139, 1138])).
% 1.12/1.12 tff(1141,plain,
% 1.12/1.12 (($lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))))), 0) | (~$greatereq(tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), 0)) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))))))) = 0)) | (~($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))))))) = 0))),
% 1.12/1.12 inference(tautology,[status(thm)],[])).
% 1.12/1.12 tff(1142,plain,
% 1.12/1.12 (~($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))))))) = 0)),
% 1.12/1.12 inference(unit_resolution,[status(thm)],[1141, 1136])).
% 1.12/1.12 tff(1143,plain,
% 1.12/1.12 (($lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))))), 0) | (~$greatereq(tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), 0)) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))))))) = 0)) | $greatereq(tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), 0)),
% 1.12/1.12 inference(tautology,[status(thm)],[])).
% 1.12/1.12 tff(1144,plain,
% 1.12/1.12 ($greatereq(tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), 0)),
% 1.12/1.12 inference(unit_resolution,[status(thm)],[1143, 1136])).
% 1.12/1.12 tff(1145,assumption,(![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 1) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), Q)))) = 0))), introduced(assumption)).
% 1.12/1.12 tff(1146,plain,
% 1.12/1.12 (((~![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 1) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), Q)))) = 0))) | ((~$greatereq(tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), 0)) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))))), -1) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))))))) = 0))) <=> ((~![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 1) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), Q)))) = 0))) | (~$greatereq(tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), 0)) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))))), -1) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))))))) = 0))),
% 1.12/1.12 inference(rewrite,[status(thm)],[])).
% 1.12/1.12 tff(1147,plain,
% 1.12/1.12 (((~$greatereq(tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), 0)) | $greatereq($sum(tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), $product(-1, Pos!4)), 1) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))))))) = 0)) <=> ((~$greatereq(tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), 0)) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))))), -1) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))))))) = 0))),
% 1.12/1.12 inference(rewrite,[status(thm)],[])).
% 1.12/1.12 tff(1148,plain,
% 1.12/1.12 (((~![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 1) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), Q)))) = 0))) | ((~$greatereq(tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), 0)) | $greatereq($sum(tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), $product(-1, Pos!4)), 1) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))))))) = 0))) <=> ((~![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 1) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), Q)))) = 0))) | ((~$greatereq(tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), 0)) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))))), -1) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))))))) = 0)))),
% 1.12/1.12 inference(monotonicity,[status(thm)],[1147])).
% 1.12/1.12 tff(1149,plain,
% 1.12/1.12 (((~![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 1) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), Q)))) = 0))) | ((~$greatereq(tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), 0)) | $greatereq($sum(tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), $product(-1, Pos!4)), 1) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))))))) = 0))) <=> ((~![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 1) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), Q)))) = 0))) | (~$greatereq(tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), 0)) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))))), -1) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))))))) = 0))),
% 1.12/1.12 inference(transitivity,[status(thm)],[1148, 1146])).
% 1.12/1.12 tff(1150,plain,
% 1.12/1.12 ((~![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 1) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), Q)))) = 0))) | ((~$greatereq(tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), 0)) | $greatereq($sum(tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), $product(-1, Pos!4)), 1) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))))))) = 0))),
% 1.12/1.13 inference(quant_inst,[status(thm)],[])).
% 1.12/1.13 tff(1151,plain,
% 1.12/1.13 ((~![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 1) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), Q)))) = 0))) | (~$greatereq(tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), 0)) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))))), -1) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))))))) = 0)),
% 1.12/1.13 inference(modus_ponens,[status(thm)],[1150, 1149])).
% 1.12/1.13 tff(1152,plain,
% 1.12/1.13 ($false),
% 1.12/1.13 inference(unit_resolution,[status(thm)],[1151, 1145, 1144, 1142, 1140])).
% 1.12/1.13 tff(1153,plain,(($lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))))), 0) | (~$greatereq(tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), 0)) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))))))) = 0)) | (~![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 1) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), Q)))) = 0)))), inference(lemma,lemma(discharge,[]))).
% 1.12/1.13 tff(1154,plain,
% 1.12/1.13 ($lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))))), 0) | (~$greatereq(tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), 0)) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))))))) = 0)),
% 1.12/1.13 inference(unit_resolution,[status(thm)],[1153, 1135])).
% 1.12/1.13 tff(1155,assumption,((~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 0) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), Q)))) = 0)))) | (~(eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4) | (~($lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))))), 0) | (~$greatereq(tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), 0)) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))))))) = 0)))))), introduced(assumption)).
% 1.12/1.13 tff(1156,plain,
% 1.12/1.13 (((~![B1: array_int, B2: array_int, Pos: $int] : (~((~((~eq_board1(B1, B2, Pos)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0) | ($sum(tb2t(get2(int, t2tb1(B2), Q)), $product(-1, tb2t(get2(int, t2tb1(B1), Q)))) = 0)))) | (~(eq_board1(B1, B2, Pos) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_0(Pos, B2, B1))), 0) | ($sum(tb2t(get2(int, t2tb1(B2), tptp_fun_Q_0(Pos, B2, B1))), $product(-1, tb2t(get2(int, t2tb1(B1), tptp_fun_Q_0(Pos, B2, B1))))) = 0) | (~$greatereq(tptp_fun_Q_0(Pos, B2, B1), 0))))))))) | (~((~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 0) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), Q)))) = 0)))) | (~(eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4) | (~($lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))))), 0) | (~$greatereq(tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), 0)) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))))))) = 0)))))))) <=> ((~![B1: array_int, B2: array_int, Pos: $int] : (~((~((~eq_board1(B1, B2, Pos)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0) | ($sum(tb2t(get2(int, t2tb1(B2), Q)), $product(-1, tb2t(get2(int, t2tb1(B1), Q)))) = 0)))) | (~(eq_board1(B1, B2, Pos) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_0(Pos, B2, B1))), 0) | ($sum(tb2t(get2(int, t2tb1(B2), tptp_fun_Q_0(Pos, B2, B1))), $product(-1, tb2t(get2(int, t2tb1(B1), tptp_fun_Q_0(Pos, B2, B1))))) = 0) | (~$greatereq(tptp_fun_Q_0(Pos, B2, B1), 0))))))))) | (~((~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 0) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), Q)))) = 0)))) | (~(eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4) | (~($lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))))), 0) | (~$greatereq(tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), 0)) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))))))) = 0))))))))),
% 1.12/1.13 inference(rewrite,[status(thm)],[])).
% 1.12/1.13 tff(1157,plain,
% 1.12/1.13 ((~((~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos!4, $product(-1, Q)), 0) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), Q)))) = 0)))) | (~(eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4) | (~($lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))))), 0) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))))))) = 0) | (~$greatereq(tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), 0)))))))) <=> (~((~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 0) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), Q)))) = 0)))) | (~(eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4) | (~($lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))))), 0) | (~$greatereq(tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), 0)) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))))))) = 0)))))))),
% 1.12/1.13 inference(rewrite,[status(thm)],[])).
% 1.12/1.13 tff(1158,plain,
% 1.12/1.13 (((~![B1: array_int, B2: array_int, Pos: $int] : (~((~((~eq_board1(B1, B2, Pos)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0) | ($sum(tb2t(get2(int, t2tb1(B2), Q)), $product(-1, tb2t(get2(int, t2tb1(B1), Q)))) = 0)))) | (~(eq_board1(B1, B2, Pos) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_0(Pos, B2, B1))), 0) | ($sum(tb2t(get2(int, t2tb1(B2), tptp_fun_Q_0(Pos, B2, B1))), $product(-1, tb2t(get2(int, t2tb1(B1), tptp_fun_Q_0(Pos, B2, B1))))) = 0) | (~$greatereq(tptp_fun_Q_0(Pos, B2, B1), 0))))))))) | (~((~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos!4, $product(-1, Q)), 0) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), Q)))) = 0)))) | (~(eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4) | (~($lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))))), 0) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))))))) = 0) | (~$greatereq(tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), 0))))))))) <=> ((~![B1: array_int, B2: array_int, Pos: $int] : (~((~((~eq_board1(B1, B2, Pos)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0) | ($sum(tb2t(get2(int, t2tb1(B2), Q)), $product(-1, tb2t(get2(int, t2tb1(B1), Q)))) = 0)))) | (~(eq_board1(B1, B2, Pos) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_0(Pos, B2, B1))), 0) | ($sum(tb2t(get2(int, t2tb1(B2), tptp_fun_Q_0(Pos, B2, B1))), $product(-1, tb2t(get2(int, t2tb1(B1), tptp_fun_Q_0(Pos, B2, B1))))) = 0) | (~$greatereq(tptp_fun_Q_0(Pos, B2, B1), 0))))))))) | (~((~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 0) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), Q)))) = 0)))) | (~(eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4) | (~($lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))))), 0) | (~$greatereq(tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), 0)) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))))))) = 0))))))))),
% 1.12/1.13 inference(monotonicity,[status(thm)],[1157])).
% 1.12/1.13 tff(1159,plain,
% 1.12/1.13 (((~![B1: array_int, B2: array_int, Pos: $int] : (~((~((~eq_board1(B1, B2, Pos)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0) | ($sum(tb2t(get2(int, t2tb1(B2), Q)), $product(-1, tb2t(get2(int, t2tb1(B1), Q)))) = 0)))) | (~(eq_board1(B1, B2, Pos) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_0(Pos, B2, B1))), 0) | ($sum(tb2t(get2(int, t2tb1(B2), tptp_fun_Q_0(Pos, B2, B1))), $product(-1, tb2t(get2(int, t2tb1(B1), tptp_fun_Q_0(Pos, B2, B1))))) = 0) | (~$greatereq(tptp_fun_Q_0(Pos, B2, B1), 0))))))))) | (~((~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos!4, $product(-1, Q)), 0) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), Q)))) = 0)))) | (~(eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4) | (~($lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))))), 0) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))))))) = 0) | (~$greatereq(tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), 0))))))))) <=> ((~![B1: array_int, B2: array_int, Pos: $int] : (~((~((~eq_board1(B1, B2, Pos)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0) | ($sum(tb2t(get2(int, t2tb1(B2), Q)), $product(-1, tb2t(get2(int, t2tb1(B1), Q)))) = 0)))) | (~(eq_board1(B1, B2, Pos) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_0(Pos, B2, B1))), 0) | ($sum(tb2t(get2(int, t2tb1(B2), tptp_fun_Q_0(Pos, B2, B1))), $product(-1, tb2t(get2(int, t2tb1(B1), tptp_fun_Q_0(Pos, B2, B1))))) = 0) | (~$greatereq(tptp_fun_Q_0(Pos, B2, B1), 0))))))))) | (~((~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 0) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), Q)))) = 0)))) | (~(eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4) | (~($lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))))), 0) | (~$greatereq(tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), 0)) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))))))) = 0))))))))),
% 1.12/1.13 inference(transitivity,[status(thm)],[1158, 1156])).
% 1.12/1.13 tff(1160,plain,
% 1.12/1.13 ((~![B1: array_int, B2: array_int, Pos: $int] : (~((~((~eq_board1(B1, B2, Pos)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0) | ($sum(tb2t(get2(int, t2tb1(B2), Q)), $product(-1, tb2t(get2(int, t2tb1(B1), Q)))) = 0)))) | (~(eq_board1(B1, B2, Pos) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_0(Pos, B2, B1))), 0) | ($sum(tb2t(get2(int, t2tb1(B2), tptp_fun_Q_0(Pos, B2, B1))), $product(-1, tb2t(get2(int, t2tb1(B1), tptp_fun_Q_0(Pos, B2, B1))))) = 0) | (~$greatereq(tptp_fun_Q_0(Pos, B2, B1), 0))))))))) | (~((~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos!4, $product(-1, Q)), 0) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), Q)))) = 0)))) | (~(eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4) | (~($lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))))), 0) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))))))) = 0) | (~$greatereq(tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), 0))))))))),
% 1.12/1.13 inference(quant_inst,[status(thm)],[])).
% 1.12/1.13 tff(1161,plain,
% 1.12/1.13 ((~![B1: array_int, B2: array_int, Pos: $int] : (~((~((~eq_board1(B1, B2, Pos)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0) | ($sum(tb2t(get2(int, t2tb1(B2), Q)), $product(-1, tb2t(get2(int, t2tb1(B1), Q)))) = 0)))) | (~(eq_board1(B1, B2, Pos) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_0(Pos, B2, B1))), 0) | ($sum(tb2t(get2(int, t2tb1(B2), tptp_fun_Q_0(Pos, B2, B1))), $product(-1, tb2t(get2(int, t2tb1(B1), tptp_fun_Q_0(Pos, B2, B1))))) = 0) | (~$greatereq(tptp_fun_Q_0(Pos, B2, B1), 0))))))))) | (~((~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 0) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), Q)))) = 0)))) | (~(eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4) | (~($lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))))), 0) | (~$greatereq(tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), 0)) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))))))) = 0)))))))),
% 1.12/1.13 inference(modus_ponens,[status(thm)],[1160, 1159])).
% 1.12/1.13 tff(1162,plain,
% 1.12/1.13 ($false),
% 1.12/1.13 inference(unit_resolution,[status(thm)],[1161, 297, 1155])).
% 1.12/1.13 tff(1163,plain,(~((~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 0) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), Q)))) = 0)))) | (~(eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4) | (~($lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))))), 0) | (~$greatereq(tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), 0)) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))))))) = 0))))))), inference(lemma,lemma(discharge,[]))).
% 1.12/1.13 tff(1164,plain,
% 1.12/1.13 (((~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 0) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), Q)))) = 0)))) | (~(eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4) | (~($lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))))), 0) | (~$greatereq(tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), 0)) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))))))) = 0)))))) | (eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4) | (~($lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))))), 0) | (~$greatereq(tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), 0)) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))))))) = 0))))),
% 1.12/1.13 inference(tautology,[status(thm)],[])).
% 1.12/1.13 tff(1165,plain,
% 1.12/1.13 (eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4) | (~($lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))))), 0) | (~$greatereq(tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), 0)) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))))))) = 0)))),
% 1.12/1.13 inference(unit_resolution,[status(thm)],[1164, 1163])).
% 1.12/1.13 tff(1166,plain,
% 1.12/1.13 ((~(eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4) | (~($lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))))), 0) | (~$greatereq(tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), 0)) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))))))) = 0))))) | eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4) | (~($lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))))), 0) | (~$greatereq(tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), 0)) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))))))) = 0)))),
% 1.12/1.13 inference(tautology,[status(thm)],[])).
% 1.12/1.13 tff(1167,plain,
% 1.12/1.13 (eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4) | (~($lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))))), 0) | (~$greatereq(tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), 0)) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))))))) = 0)))),
% 1.12/1.14 inference(unit_resolution,[status(thm)],[1166, 1165])).
% 1.12/1.14 tff(1168,plain,
% 1.12/1.14 (eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)),
% 1.12/1.14 inference(unit_resolution,[status(thm)],[1167, 1154])).
% 1.12/1.14 tff(1169,assumption,(~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), Pos!4)), introduced(assumption)).
% 1.12/1.14 tff(1170,assumption,(eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)), introduced(assumption)).
% 1.12/1.14 tff(1171,plain,
% 1.12/1.14 (((~![B1: array_int, B2: array_int, B3: array_int, Pos: $int] : (eq_board1(B1, B3, Pos) | (~eq_board1(B2, B3, Pos)) | (~eq_board1(B1, B2, Pos)))) | ((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), Pos!4)) | eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), Pos!4) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)))) <=> ((~![B1: array_int, B2: array_int, B3: array_int, Pos: $int] : (eq_board1(B1, B3, Pos) | (~eq_board1(B2, B3, Pos)) | (~eq_board1(B1, B2, Pos)))) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), Pos!4)) | eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), Pos!4) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)))),
% 1.12/1.14 inference(rewrite,[status(thm)],[])).
% 1.12/1.14 tff(1172,plain,
% 1.12/1.14 ((eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), Pos!4) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), Pos!4)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4))) <=> ((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), Pos!4)) | eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), Pos!4) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)))),
% 1.12/1.14 inference(rewrite,[status(thm)],[])).
% 1.12/1.14 tff(1173,plain,
% 1.12/1.14 (((~![B1: array_int, B2: array_int, B3: array_int, Pos: $int] : (eq_board1(B1, B3, Pos) | (~eq_board1(B2, B3, Pos)) | (~eq_board1(B1, B2, Pos)))) | (eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), Pos!4) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), Pos!4)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)))) <=> ((~![B1: array_int, B2: array_int, B3: array_int, Pos: $int] : (eq_board1(B1, B3, Pos) | (~eq_board1(B2, B3, Pos)) | (~eq_board1(B1, B2, Pos)))) | ((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), Pos!4)) | eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), Pos!4) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4))))),
% 1.12/1.14 inference(monotonicity,[status(thm)],[1172])).
% 1.12/1.14 tff(1174,plain,
% 1.12/1.14 (((~![B1: array_int, B2: array_int, B3: array_int, Pos: $int] : (eq_board1(B1, B3, Pos) | (~eq_board1(B2, B3, Pos)) | (~eq_board1(B1, B2, Pos)))) | (eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), Pos!4) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), Pos!4)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)))) <=> ((~![B1: array_int, B2: array_int, B3: array_int, Pos: $int] : (eq_board1(B1, B3, Pos) | (~eq_board1(B2, B3, Pos)) | (~eq_board1(B1, B2, Pos)))) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), Pos!4)) | eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), Pos!4) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)))),
% 1.12/1.14 inference(transitivity,[status(thm)],[1173, 1171])).
% 1.12/1.14 tff(1175,plain,
% 1.12/1.14 ((~![B1: array_int, B2: array_int, B3: array_int, Pos: $int] : (eq_board1(B1, B3, Pos) | (~eq_board1(B2, B3, Pos)) | (~eq_board1(B1, B2, Pos)))) | (eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), Pos!4) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), Pos!4)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4)))),
% 1.12/1.14 inference(quant_inst,[status(thm)],[])).
% 1.12/1.14 tff(1176,plain,
% 1.12/1.14 ((~![B1: array_int, B2: array_int, B3: array_int, Pos: $int] : (eq_board1(B1, B3, Pos) | (~eq_board1(B2, B3, Pos)) | (~eq_board1(B1, B2, Pos)))) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), Pos!4)) | eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), Pos!4) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4))),
% 1.12/1.14 inference(modus_ponens,[status(thm)],[1175, 1174])).
% 1.12/1.14 tff(1177,plain,
% 1.12/1.14 ($false),
% 1.12/1.14 inference(unit_resolution,[status(thm)],[1176, 587, 565, 1170, 1169])).
% 1.12/1.14 tff(1178,plain,(eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), Pos!4) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), Pos!4))), inference(lemma,lemma(discharge,[]))).
% 1.12/1.14 tff(1179,plain,
% 1.12/1.14 (eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), Pos!4)),
% 1.12/1.14 inference(unit_resolution,[status(thm)],[1178, 1168])).
% 1.12/1.14 tff(1180,assumption,(eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), Pos!4)), introduced(assumption)).
% 1.12/1.14 tff(1181,assumption,(~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)), introduced(assumption)).
% 1.12/1.14 tff(1182,plain,
% 1.12/1.14 (((~![B1: array_int, B2: array_int, B3: array_int, Pos: $int] : (eq_board1(B1, B3, Pos) | (~eq_board1(B2, B3, Pos)) | (~eq_board1(B1, B2, Pos)))) | (eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), Pos!4)))) <=> ((~![B1: array_int, B2: array_int, B3: array_int, Pos: $int] : (eq_board1(B1, B3, Pos) | (~eq_board1(B2, B3, Pos)) | (~eq_board1(B1, B2, Pos)))) | eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), Pos!4)))),
% 1.12/1.14 inference(rewrite,[status(thm)],[])).
% 1.12/1.14 tff(1183,plain,
% 1.12/1.14 ((~![B1: array_int, B2: array_int, B3: array_int, Pos: $int] : (eq_board1(B1, B3, Pos) | (~eq_board1(B2, B3, Pos)) | (~eq_board1(B1, B2, Pos)))) | (eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), Pos!4)))),
% 1.12/1.14 inference(quant_inst,[status(thm)],[])).
% 1.12/1.14 tff(1184,plain,
% 1.12/1.14 ((~![B1: array_int, B2: array_int, B3: array_int, Pos: $int] : (eq_board1(B1, B3, Pos) | (~eq_board1(B2, B3, Pos)) | (~eq_board1(B1, B2, Pos)))) | eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), Pos!4))),
% 1.12/1.14 inference(modus_ponens,[status(thm)],[1183, 1182])).
% 1.12/1.14 tff(1185,plain,
% 1.12/1.14 ($false),
% 1.12/1.14 inference(unit_resolution,[status(thm)],[1184, 587, 577, 1181, 1180])).
% 1.12/1.14 tff(1186,plain,(eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), Pos!4))), inference(lemma,lemma(discharge,[]))).
% 1.12/1.14 tff(1187,plain,
% 1.12/1.14 (eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)),
% 1.12/1.14 inference(unit_resolution,[status(thm)],[1186, 1179])).
% 1.12/1.14 tff(1188,plain,
% 1.12/1.14 ((~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), Pos!4)) | (~($sum(N!5, $product(-1, B!16)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))), 0)))))) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), Pos!4)) | (~($sum(N!5, $product(-1, B!16)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))), 0))))),
% 1.12/1.14 inference(tautology,[status(thm)],[])).
% 1.12/1.14 tff(1189,plain,
% 1.12/1.14 (~((~solution1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), Pos!4)) | (~($sum(N!5, $product(-1, B!16)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))), 0)))),
% 1.12/1.14 inference(unit_resolution,[status(thm)],[1188, 1187, 1121])).
% 1.12/1.14 tff(1190,plain,
% 1.12/1.14 (((~solution1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), Pos!4)) | (~($sum(N!5, $product(-1, B!16)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))), 0))) | ($sum(N!5, $product(-1, B!16)) = 0)),
% 1.12/1.14 inference(tautology,[status(thm)],[])).
% 1.12/1.14 tff(1191,plain,
% 1.12/1.14 ($sum(N!5, $product(-1, B!16)) = 0),
% 1.19/1.14 inference(unit_resolution,[status(thm)],[1190, 1189])).
% 1.19/1.14 tff(1192,plain,
% 1.19/1.14 (((~solution1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), Pos!4)) | (~($sum(N!5, $product(-1, B!16)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))), 0))) | is_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)),
% 1.19/1.14 inference(tautology,[status(thm)],[])).
% 1.19/1.14 tff(1193,plain,
% 1.19/1.14 (is_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)),
% 1.19/1.14 inference(unit_resolution,[status(thm)],[1192, 1189])).
% 1.19/1.14 tff(1194,plain,
% 1.19/1.14 (((~solution1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), Pos!4)) | (~($sum(N!5, $product(-1, B!16)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))), 0))) | solution1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)),
% 1.19/1.14 inference(tautology,[status(thm)],[])).
% 1.19/1.14 tff(1195,plain,
% 1.19/1.14 (solution1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)),
% 1.19/1.14 inference(unit_resolution,[status(thm)],[1194, 1189])).
% 1.19/1.14 tff(1196,plain,
% 1.19/1.14 (((~$greatereq(Board!7, 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B, t2tb2(B1))), $sum(1, Pos!4))))) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), Pos!4)) | (~($sum(N!5, $product(-1, B!16)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))), 0))))))) | ![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B, t2tb2(B1))), $sum(1, Pos!4))))),
% 1.19/1.14 inference(tautology,[status(thm)],[])).
% 1.19/1.14 tff(1197,plain,
% 1.19/1.14 (![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B, t2tb2(B1))), $sum(1, Pos!4))))),
% 1.19/1.14 inference(unit_resolution,[status(thm)],[1196, 1119])).
% 1.19/1.14 tff(1198,plain,
% 1.19/1.14 (((~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B, t2tb2(B1))), $sum(1, Pos!4))))) | ((~solution1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~($sum(N!5, $product(-1, B!16)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), $sum(1, Pos!4))))) <=> ((~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B, t2tb2(B1))), $sum(1, Pos!4))))) | (~solution1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~($sum(N!5, $product(-1, B!16)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), $sum(1, Pos!4))))),
% 1.19/1.14 inference(rewrite,[status(thm)],[])).
% 1.19/1.14 tff(1199,plain,
% 1.19/1.14 (((~solution1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~($sum(N!5, $product(-1, B!16)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), $sum(1, Pos!4)))) <=> ((~solution1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~($sum(N!5, $product(-1, B!16)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), $sum(1, Pos!4))))),
% 1.19/1.14 inference(rewrite,[status(thm)],[])).
% 1.19/1.14 tff(1200,plain,
% 1.19/1.14 ((~($sum(B!16, $product(-1, N!5)) = 0)) <=> (~($sum(N!5, $product(-1, B!16)) = 0))),
% 1.19/1.14 inference(rewrite,[status(thm)],[])).
% 1.19/1.14 tff(1201,plain,
% 1.19/1.14 (((~solution1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~($sum(B!16, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), $sum(1, Pos!4)))) <=> ((~solution1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~($sum(N!5, $product(-1, B!16)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), $sum(1, Pos!4))))),
% 1.19/1.14 inference(monotonicity,[status(thm)],[1200])).
% 1.19/1.14 tff(1202,plain,
% 1.19/1.14 (((~solution1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~($sum(B!16, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), $sum(1, Pos!4)))) <=> ((~solution1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~($sum(N!5, $product(-1, B!16)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), $sum(1, Pos!4))))),
% 1.19/1.14 inference(transitivity,[status(thm)],[1201, 1199])).
% 1.19/1.14 tff(1203,plain,
% 1.19/1.14 (((~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B, t2tb2(B1))), $sum(1, Pos!4))))) | ((~solution1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~($sum(B!16, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), $sum(1, Pos!4))))) <=> ((~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B, t2tb2(B1))), $sum(1, Pos!4))))) | ((~solution1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~($sum(N!5, $product(-1, B!16)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), $sum(1, Pos!4)))))),
% 1.19/1.14 inference(monotonicity,[status(thm)],[1202])).
% 1.19/1.14 tff(1204,plain,
% 1.19/1.14 (((~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B, t2tb2(B1))), $sum(1, Pos!4))))) | ((~solution1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~($sum(B!16, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), $sum(1, Pos!4))))) <=> ((~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B, t2tb2(B1))), $sum(1, Pos!4))))) | (~solution1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~($sum(N!5, $product(-1, B!16)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), $sum(1, Pos!4))))),
% 1.19/1.14 inference(transitivity,[status(thm)],[1203, 1198])).
% 1.19/1.14 tff(1205,plain,
% 1.19/1.14 ((~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B, t2tb2(B1))), $sum(1, Pos!4))))) | ((~solution1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~($sum(B!16, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), $sum(1, Pos!4))))),
% 1.19/1.14 inference(quant_inst,[status(thm)],[])).
% 1.19/1.14 tff(1206,plain,
% 1.19/1.14 ((~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B, t2tb2(B1))), $sum(1, Pos!4))))) | (~solution1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~($sum(N!5, $product(-1, B!16)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), $sum(1, Pos!4)))),
% 1.19/1.14 inference(modus_ponens,[status(thm)],[1205, 1204])).
% 1.19/1.14 tff(1207,plain,
% 1.19/1.14 (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), $sum(1, Pos!4))),
% 1.19/1.14 inference(unit_resolution,[status(thm)],[1206, 1197, 1195, 1193, 1191])).
% 1.19/1.14 tff(1208,plain,
% 1.19/1.14 (((~![B1: array_int, B2: array_int, Pos: $int] : ((~eq_board1(B1, B2, Pos)) | eq_board1(B2, B1, Pos))) | ((~eq_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), $sum(1, Pos!4))) | eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), $sum(1, Pos!4)))) <=> ((~![B1: array_int, B2: array_int, Pos: $int] : ((~eq_board1(B1, B2, Pos)) | eq_board1(B2, B1, Pos))) | (~eq_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), $sum(1, Pos!4))) | eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), $sum(1, Pos!4)))),
% 1.19/1.14 inference(rewrite,[status(thm)],[])).
% 1.19/1.14 tff(1209,plain,
% 1.19/1.14 ((~![B1: array_int, B2: array_int, Pos: $int] : ((~eq_board1(B1, B2, Pos)) | eq_board1(B2, B1, Pos))) | ((~eq_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), $sum(1, Pos!4))) | eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), $sum(1, Pos!4)))),
% 1.19/1.14 inference(quant_inst,[status(thm)],[])).
% 1.19/1.14 tff(1210,plain,
% 1.19/1.14 ((~![B1: array_int, B2: array_int, Pos: $int] : ((~eq_board1(B1, B2, Pos)) | eq_board1(B2, B1, Pos))) | (~eq_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), $sum(1, Pos!4))) | eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), $sum(1, Pos!4))),
% 1.19/1.15 inference(modus_ponens,[status(thm)],[1209, 1208])).
% 1.19/1.15 tff(1211,plain,
% 1.19/1.15 (~eq_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), $sum(1, Pos!4))),
% 1.19/1.15 inference(unit_resolution,[status(thm)],[1210, 561, 1207])).
% 1.19/1.15 tff(1212,plain,
% 1.19/1.15 (((~![B1: array_int, B2: array_int, Pos: $int] : ((~eq_board1(B1, B2, Pos)) | eq_board1(B2, B1, Pos))) | ((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), $sum(1, Pos!4)))) <=> ((~![B1: array_int, B2: array_int, Pos: $int] : ((~eq_board1(B1, B2, Pos)) | eq_board1(B2, B1, Pos))) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), $sum(1, Pos!4)))),
% 1.19/1.15 inference(rewrite,[status(thm)],[])).
% 1.19/1.15 tff(1213,plain,
% 1.19/1.15 ((~![B1: array_int, B2: array_int, Pos: $int] : ((~eq_board1(B1, B2, Pos)) | eq_board1(B2, B1, Pos))) | ((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), $sum(1, Pos!4)))),
% 1.19/1.15 inference(quant_inst,[status(thm)],[])).
% 1.19/1.15 tff(1214,plain,
% 1.19/1.15 ((~![B1: array_int, B2: array_int, Pos: $int] : ((~eq_board1(B1, B2, Pos)) | eq_board1(B2, B1, Pos))) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), $sum(1, Pos!4))),
% 1.19/1.15 inference(modus_ponens,[status(thm)],[1213, 1212])).
% 1.19/1.15 tff(1215,plain,
% 1.19/1.15 (eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), $sum(1, Pos!4))),
% 1.19/1.15 inference(unit_resolution,[status(thm)],[1214, 561, 1132])).
% 1.19/1.15 tff(1216,plain,
% 1.19/1.15 (((~![B1: array_int, B2: array_int, B3: array_int, Pos: $int] : (eq_board1(B1, B3, Pos) | (~eq_board1(B2, B3, Pos)) | (~eq_board1(B1, B2, Pos)))) | ((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), $sum(1, Pos!4))) | eq_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), $sum(1, Pos!4)) | (~eq_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))))) <=> ((~![B1: array_int, B2: array_int, B3: array_int, Pos: $int] : (eq_board1(B1, B3, Pos) | (~eq_board1(B2, B3, Pos)) | (~eq_board1(B1, B2, Pos)))) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), $sum(1, Pos!4))) | eq_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), $sum(1, Pos!4)) | (~eq_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))))),
% 1.19/1.15 inference(rewrite,[status(thm)],[])).
% 1.19/1.15 tff(1217,plain,
% 1.19/1.15 ((eq_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), $sum(1, Pos!4)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), $sum(1, Pos!4))) | (~eq_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4)))) <=> ((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), $sum(1, Pos!4))) | eq_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), $sum(1, Pos!4)) | (~eq_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))))),
% 1.19/1.15 inference(rewrite,[status(thm)],[])).
% 1.19/1.15 tff(1218,plain,
% 1.19/1.15 (((~![B1: array_int, B2: array_int, B3: array_int, Pos: $int] : (eq_board1(B1, B3, Pos) | (~eq_board1(B2, B3, Pos)) | (~eq_board1(B1, B2, Pos)))) | (eq_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), $sum(1, Pos!4)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), $sum(1, Pos!4))) | (~eq_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))))) <=> ((~![B1: array_int, B2: array_int, B3: array_int, Pos: $int] : (eq_board1(B1, B3, Pos) | (~eq_board1(B2, B3, Pos)) | (~eq_board1(B1, B2, Pos)))) | ((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), $sum(1, Pos!4))) | eq_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), $sum(1, Pos!4)) | (~eq_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4)))))),
% 1.19/1.15 inference(monotonicity,[status(thm)],[1217])).
% 1.19/1.15 tff(1219,plain,
% 1.19/1.15 (((~![B1: array_int, B2: array_int, B3: array_int, Pos: $int] : (eq_board1(B1, B3, Pos) | (~eq_board1(B2, B3, Pos)) | (~eq_board1(B1, B2, Pos)))) | (eq_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), $sum(1, Pos!4)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), $sum(1, Pos!4))) | (~eq_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))))) <=> ((~![B1: array_int, B2: array_int, B3: array_int, Pos: $int] : (eq_board1(B1, B3, Pos) | (~eq_board1(B2, B3, Pos)) | (~eq_board1(B1, B2, Pos)))) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), $sum(1, Pos!4))) | eq_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), $sum(1, Pos!4)) | (~eq_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))))),
% 1.19/1.15 inference(transitivity,[status(thm)],[1218, 1216])).
% 1.19/1.15 tff(1220,plain,
% 1.19/1.15 ((~![B1: array_int, B2: array_int, B3: array_int, Pos: $int] : (eq_board1(B1, B3, Pos) | (~eq_board1(B2, B3, Pos)) | (~eq_board1(B1, B2, Pos)))) | (eq_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), $sum(1, Pos!4)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), $sum(1, Pos!4))) | (~eq_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))))),
% 1.19/1.15 inference(quant_inst,[status(thm)],[])).
% 1.19/1.15 tff(1221,plain,
% 1.19/1.15 ((~![B1: array_int, B2: array_int, B3: array_int, Pos: $int] : (eq_board1(B1, B3, Pos) | (~eq_board1(B2, B3, Pos)) | (~eq_board1(B1, B2, Pos)))) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), $sum(1, Pos!4))) | eq_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), $sum(1, Pos!4)) | (~eq_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4)))),
% 1.19/1.15 inference(modus_ponens,[status(thm)],[1220, 1219])).
% 1.19/1.15 tff(1222,plain,
% 1.19/1.15 (~eq_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))),
% 1.19/1.15 inference(unit_resolution,[status(thm)],[1221, 587, 1215, 1211])).
% 1.19/1.15 tff(1223,plain,
% 1.19/1.15 (((~![B1: array_int, B2: array_int, Pos: $int] : ((~eq_board1(B1, B2, Pos)) | eq_board1(B2, B1, Pos))) | ((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), $sum(1, Pos!4))) | eq_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4)))) <=> ((~![B1: array_int, B2: array_int, Pos: $int] : ((~eq_board1(B1, B2, Pos)) | eq_board1(B2, B1, Pos))) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), $sum(1, Pos!4))) | eq_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4)))),
% 1.19/1.15 inference(rewrite,[status(thm)],[])).
% 1.19/1.15 tff(1224,plain,
% 1.19/1.15 ((~![B1: array_int, B2: array_int, Pos: $int] : ((~eq_board1(B1, B2, Pos)) | eq_board1(B2, B1, Pos))) | ((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), $sum(1, Pos!4))) | eq_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4)))),
% 1.19/1.15 inference(quant_inst,[status(thm)],[])).
% 1.19/1.15 tff(1225,plain,
% 1.19/1.15 ((~![B1: array_int, B2: array_int, Pos: $int] : ((~eq_board1(B1, B2, Pos)) | eq_board1(B2, B1, Pos))) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), $sum(1, Pos!4))) | eq_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))),
% 1.19/1.15 inference(modus_ponens,[status(thm)],[1224, 1223])).
% 1.19/1.15 tff(1226,plain,
% 1.19/1.15 (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), $sum(1, Pos!4))),
% 1.19/1.15 inference(unit_resolution,[status(thm)],[1225, 561, 1222])).
% 1.19/1.15 tff(1227,plain,
% 1.19/1.15 ((~(eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), $sum(1, Pos!4)) | (~(($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))) = 0) | (~$greatereq(tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0)) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), -1))))) | eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), $sum(1, Pos!4)) | (~(($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))) = 0) | (~$greatereq(tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0)) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), -1)))),
% 1.19/1.15 inference(tautology,[status(thm)],[])).
% 1.19/1.15 tff(1228,plain,
% 1.19/1.15 ((~(eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), $sum(1, Pos!4)) | (~(($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))) = 0) | (~$greatereq(tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0)) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), -1))))) | (~(($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))) = 0) | (~$greatereq(tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0)) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), -1)))),
% 1.19/1.15 inference(unit_resolution,[status(thm)],[1227, 1226])).
% 1.19/1.15 tff(1229,plain,
% 1.19/1.15 (~(($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))) = 0) | (~$greatereq(tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0)) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), -1))),
% 1.19/1.15 inference(unit_resolution,[status(thm)],[1228, 1118])).
% 1.19/1.15 tff(1230,plain,
% 1.19/1.15 ((($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))) = 0) | (~$greatereq(tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0)) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), -1)) | $greatereq(tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0)),
% 1.19/1.15 inference(tautology,[status(thm)],[])).
% 1.19/1.15 tff(1231,plain,
% 1.19/1.15 ($greatereq(tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0)),
% 1.19/1.15 inference(unit_resolution,[status(thm)],[1230, 1229])).
% 1.19/1.15 tff(1232,plain,
% 1.19/1.15 ((($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))) = 0) | (~$greatereq(tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0)) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), -1)) | (~$lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), -1))),
% 1.19/1.15 inference(tautology,[status(thm)],[])).
% 1.19/1.15 tff(1233,plain,
% 1.19/1.15 (~$lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), -1)),
% 1.19/1.15 inference(unit_resolution,[status(thm)],[1232, 1229])).
% 1.19/1.15 tff(1234,plain,
% 1.19/1.15 (((~![B1: array_int, B2: array_int, Pos: $int] : (~((~((~eq_board1(B1, B2, Pos)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0) | ($sum(tb2t(get2(int, t2tb1(B2), Q)), $product(-1, tb2t(get2(int, t2tb1(B1), Q)))) = 0)))) | (~(eq_board1(B1, B2, Pos) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_0(Pos, B2, B1))), 0) | ($sum(tb2t(get2(int, t2tb1(B2), tptp_fun_Q_0(Pos, B2, B1))), $product(-1, tb2t(get2(int, t2tb1(B1), tptp_fun_Q_0(Pos, B2, B1))))) = 0) | (~$greatereq(tptp_fun_Q_0(Pos, B2, B1), 0))))))))) | (~((~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), $sum(1, Pos!4))) | ![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 1) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), Q)))) = 0)))) | (~(eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), $sum(1, Pos!4)) | (~((~$greatereq(tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0)) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))) = 0) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), -1)))))))) <=> ((~![B1: array_int, B2: array_int, Pos: $int] : (~((~((~eq_board1(B1, B2, Pos)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0) | ($sum(tb2t(get2(int, t2tb1(B2), Q)), $product(-1, tb2t(get2(int, t2tb1(B1), Q)))) = 0)))) | (~(eq_board1(B1, B2, Pos) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_0(Pos, B2, B1))), 0) | ($sum(tb2t(get2(int, t2tb1(B2), tptp_fun_Q_0(Pos, B2, B1))), $product(-1, tb2t(get2(int, t2tb1(B1), tptp_fun_Q_0(Pos, B2, B1))))) = 0) | (~$greatereq(tptp_fun_Q_0(Pos, B2, B1), 0))))))))) | (~((~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), $sum(1, Pos!4))) | ![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 1) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), Q)))) = 0)))) | (~(eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), $sum(1, Pos!4)) | (~((~$greatereq(tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0)) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))) = 0) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), -1))))))))),
% 1.19/1.15 inference(rewrite,[status(thm)],[])).
% 1.19/1.15 tff(1235,plain,
% 1.19/1.15 ((~((~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), $sum(1, Pos!4))) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum($sum(1, Pos!4), $product(-1, Q)), 0) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), Q)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)))) = 0)))) | (~(eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), $sum(1, Pos!4)) | (~($lesseq($sum($sum(1, Pos!4), $product(-1, tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), 0) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))) = 0) | (~$greatereq(tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0)))))))) <=> (~((~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), $sum(1, Pos!4))) | ![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 1) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), Q)))) = 0)))) | (~(eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), $sum(1, Pos!4)) | (~((~$greatereq(tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0)) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))) = 0) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), -1)))))))),
% 1.19/1.15 inference(rewrite,[status(thm)],[])).
% 1.19/1.15 tff(1236,plain,
% 1.19/1.15 (((~![B1: array_int, B2: array_int, Pos: $int] : (~((~((~eq_board1(B1, B2, Pos)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0) | ($sum(tb2t(get2(int, t2tb1(B2), Q)), $product(-1, tb2t(get2(int, t2tb1(B1), Q)))) = 0)))) | (~(eq_board1(B1, B2, Pos) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_0(Pos, B2, B1))), 0) | ($sum(tb2t(get2(int, t2tb1(B2), tptp_fun_Q_0(Pos, B2, B1))), $product(-1, tb2t(get2(int, t2tb1(B1), tptp_fun_Q_0(Pos, B2, B1))))) = 0) | (~$greatereq(tptp_fun_Q_0(Pos, B2, B1), 0))))))))) | (~((~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), $sum(1, Pos!4))) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum($sum(1, Pos!4), $product(-1, Q)), 0) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), Q)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)))) = 0)))) | (~(eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), $sum(1, Pos!4)) | (~($lesseq($sum($sum(1, Pos!4), $product(-1, tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), 0) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))) = 0) | (~$greatereq(tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0))))))))) <=> ((~![B1: array_int, B2: array_int, Pos: $int] : (~((~((~eq_board1(B1, B2, Pos)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0) | ($sum(tb2t(get2(int, t2tb1(B2), Q)), $product(-1, tb2t(get2(int, t2tb1(B1), Q)))) = 0)))) | (~(eq_board1(B1, B2, Pos) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_0(Pos, B2, B1))), 0) | ($sum(tb2t(get2(int, t2tb1(B2), tptp_fun_Q_0(Pos, B2, B1))), $product(-1, tb2t(get2(int, t2tb1(B1), tptp_fun_Q_0(Pos, B2, B1))))) = 0) | (~$greatereq(tptp_fun_Q_0(Pos, B2, B1), 0))))))))) | (~((~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), $sum(1, Pos!4))) | ![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 1) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), Q)))) = 0)))) | (~(eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), $sum(1, Pos!4)) | (~((~$greatereq(tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0)) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))) = 0) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), -1))))))))),
% 1.19/1.15 inference(monotonicity,[status(thm)],[1235])).
% 1.19/1.15 tff(1237,plain,
% 1.19/1.15 (((~![B1: array_int, B2: array_int, Pos: $int] : (~((~((~eq_board1(B1, B2, Pos)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0) | ($sum(tb2t(get2(int, t2tb1(B2), Q)), $product(-1, tb2t(get2(int, t2tb1(B1), Q)))) = 0)))) | (~(eq_board1(B1, B2, Pos) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_0(Pos, B2, B1))), 0) | ($sum(tb2t(get2(int, t2tb1(B2), tptp_fun_Q_0(Pos, B2, B1))), $product(-1, tb2t(get2(int, t2tb1(B1), tptp_fun_Q_0(Pos, B2, B1))))) = 0) | (~$greatereq(tptp_fun_Q_0(Pos, B2, B1), 0))))))))) | (~((~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), $sum(1, Pos!4))) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum($sum(1, Pos!4), $product(-1, Q)), 0) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), Q)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)))) = 0)))) | (~(eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), $sum(1, Pos!4)) | (~($lesseq($sum($sum(1, Pos!4), $product(-1, tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), 0) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))) = 0) | (~$greatereq(tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0))))))))) <=> ((~![B1: array_int, B2: array_int, Pos: $int] : (~((~((~eq_board1(B1, B2, Pos)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0) | ($sum(tb2t(get2(int, t2tb1(B2), Q)), $product(-1, tb2t(get2(int, t2tb1(B1), Q)))) = 0)))) | (~(eq_board1(B1, B2, Pos) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_0(Pos, B2, B1))), 0) | ($sum(tb2t(get2(int, t2tb1(B2), tptp_fun_Q_0(Pos, B2, B1))), $product(-1, tb2t(get2(int, t2tb1(B1), tptp_fun_Q_0(Pos, B2, B1))))) = 0) | (~$greatereq(tptp_fun_Q_0(Pos, B2, B1), 0))))))))) | (~((~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), $sum(1, Pos!4))) | ![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 1) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), Q)))) = 0)))) | (~(eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), $sum(1, Pos!4)) | (~((~$greatereq(tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0)) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))) = 0) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), -1))))))))),
% 1.19/1.16 inference(transitivity,[status(thm)],[1236, 1234])).
% 1.19/1.16 tff(1238,plain,
% 1.19/1.16 ((~![B1: array_int, B2: array_int, Pos: $int] : (~((~((~eq_board1(B1, B2, Pos)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0) | ($sum(tb2t(get2(int, t2tb1(B2), Q)), $product(-1, tb2t(get2(int, t2tb1(B1), Q)))) = 0)))) | (~(eq_board1(B1, B2, Pos) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_0(Pos, B2, B1))), 0) | ($sum(tb2t(get2(int, t2tb1(B2), tptp_fun_Q_0(Pos, B2, B1))), $product(-1, tb2t(get2(int, t2tb1(B1), tptp_fun_Q_0(Pos, B2, B1))))) = 0) | (~$greatereq(tptp_fun_Q_0(Pos, B2, B1), 0))))))))) | (~((~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), $sum(1, Pos!4))) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum($sum(1, Pos!4), $product(-1, Q)), 0) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), Q)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)))) = 0)))) | (~(eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), $sum(1, Pos!4)) | (~($lesseq($sum($sum(1, Pos!4), $product(-1, tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), 0) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))) = 0) | (~$greatereq(tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0))))))))),
% 1.19/1.16 inference(quant_inst,[status(thm)],[])).
% 1.19/1.16 tff(1239,plain,
% 1.19/1.16 ((~![B1: array_int, B2: array_int, Pos: $int] : (~((~((~eq_board1(B1, B2, Pos)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0) | ($sum(tb2t(get2(int, t2tb1(B2), Q)), $product(-1, tb2t(get2(int, t2tb1(B1), Q)))) = 0)))) | (~(eq_board1(B1, B2, Pos) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_0(Pos, B2, B1))), 0) | ($sum(tb2t(get2(int, t2tb1(B2), tptp_fun_Q_0(Pos, B2, B1))), $product(-1, tb2t(get2(int, t2tb1(B1), tptp_fun_Q_0(Pos, B2, B1))))) = 0) | (~$greatereq(tptp_fun_Q_0(Pos, B2, B1), 0))))))))) | (~((~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), $sum(1, Pos!4))) | ![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 1) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), Q)))) = 0)))) | (~(eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), $sum(1, Pos!4)) | (~((~$greatereq(tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0)) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))) = 0) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), -1)))))))),
% 1.19/1.16 inference(modus_ponens,[status(thm)],[1238, 1237])).
% 1.19/1.16 tff(1240,plain,
% 1.19/1.16 (~((~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), $sum(1, Pos!4))) | ![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 1) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), Q)))) = 0)))) | (~(eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), $sum(1, Pos!4)) | (~((~$greatereq(tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0)) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))) = 0) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), -1))))))),
% 1.19/1.16 inference(unit_resolution,[status(thm)],[1239, 297])).
% 1.19/1.16 tff(1241,plain,
% 1.19/1.16 (((~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), $sum(1, Pos!4))) | ![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 1) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), Q)))) = 0)))) | (~(eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), $sum(1, Pos!4)) | (~((~$greatereq(tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0)) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))) = 0) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), -1)))))) | ((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), $sum(1, Pos!4))) | ![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 1) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), Q)))) = 0)))),
% 1.19/1.16 inference(tautology,[status(thm)],[])).
% 1.19/1.16 tff(1242,plain,
% 1.19/1.16 ((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), $sum(1, Pos!4))) | ![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 1) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), Q)))) = 0))),
% 1.19/1.16 inference(unit_resolution,[status(thm)],[1241, 1240])).
% 1.19/1.16 tff(1243,plain,
% 1.19/1.16 ((~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), $sum(1, Pos!4))) | ![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 1) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), Q)))) = 0)))) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), $sum(1, Pos!4))) | ![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 1) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), Q)))) = 0))),
% 1.19/1.16 inference(tautology,[status(thm)],[])).
% 1.19/1.16 tff(1244,plain,
% 1.19/1.16 ((~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), $sum(1, Pos!4))) | ![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 1) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), Q)))) = 0)))) | ![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 1) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), Q)))) = 0))),
% 1.19/1.16 inference(unit_resolution,[status(thm)],[1243, 1215])).
% 1.19/1.16 tff(1245,plain,
% 1.19/1.16 (![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 1) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), Q)))) = 0))),
% 1.19/1.16 inference(unit_resolution,[status(thm)],[1244, 1242])).
% 1.19/1.16 tff(1246,plain,
% 1.19/1.16 (((~![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 1) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), Q)))) = 0))) | ((~$greatereq(tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0)) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), -1) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))) = 0))) <=> ((~![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 1) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), Q)))) = 0))) | (~$greatereq(tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0)) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), -1) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))) = 0))),
% 1.19/1.16 inference(rewrite,[status(thm)],[])).
% 1.19/1.16 tff(1247,plain,
% 1.19/1.16 (((~$greatereq(tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0)) | $greatereq($sum(tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), $product(-1, Pos!4)), 1) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))) = 0)) <=> ((~$greatereq(tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0)) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), -1) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))) = 0))),
% 1.19/1.16 inference(rewrite,[status(thm)],[])).
% 1.19/1.16 tff(1248,plain,
% 1.19/1.16 (((~![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 1) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), Q)))) = 0))) | ((~$greatereq(tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0)) | $greatereq($sum(tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), $product(-1, Pos!4)), 1) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))) = 0))) <=> ((~![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 1) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), Q)))) = 0))) | ((~$greatereq(tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0)) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), -1) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))) = 0)))),
% 1.19/1.16 inference(monotonicity,[status(thm)],[1247])).
% 1.19/1.16 tff(1249,plain,
% 1.19/1.16 (((~![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 1) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), Q)))) = 0))) | ((~$greatereq(tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0)) | $greatereq($sum(tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), $product(-1, Pos!4)), 1) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))) = 0))) <=> ((~![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 1) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), Q)))) = 0))) | (~$greatereq(tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0)) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), -1) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))) = 0))),
% 1.19/1.16 inference(transitivity,[status(thm)],[1248, 1246])).
% 1.19/1.16 tff(1250,plain,
% 1.19/1.16 ((~![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 1) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), Q)))) = 0))) | ((~$greatereq(tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0)) | $greatereq($sum(tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), $product(-1, Pos!4)), 1) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))) = 0))),
% 1.19/1.16 inference(quant_inst,[status(thm)],[])).
% 1.19/1.16 tff(1251,plain,
% 1.19/1.16 ((~![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 1) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), Q)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), Q)))) = 0))) | (~$greatereq(tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0)) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), -1) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))) = 0)),
% 1.19/1.16 inference(modus_ponens,[status(thm)],[1250, 1249])).
% 1.19/1.16 tff(1252,plain,
% 1.19/1.16 ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))) = 0),
% 1.19/1.16 inference(unit_resolution,[status(thm)],[1251, 1245, 1233, 1231])).
% 1.19/1.16 tff(1253,plain,
% 1.19/1.16 ((~($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))) = 0)) | $lesseq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))), 0)),
% 1.19/1.16 inference(theory_lemma,[status(thm)],[])).
% 1.19/1.16 tff(1254,plain,
% 1.19/1.16 ($lesseq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))), 0)),
% 1.19/1.16 inference(unit_resolution,[status(thm)],[1253, 1252])).
% 1.19/1.16 tff(1255,plain,
% 1.19/1.16 ((($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))) = 0) | (~$greatereq(tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0)) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), -1)) | (~($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))) = 0))),
% 1.19/1.16 inference(tautology,[status(thm)],[])).
% 1.19/1.16 tff(1256,plain,
% 1.19/1.16 (~($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))) = 0)),
% 1.19/1.16 inference(unit_resolution,[status(thm)],[1255, 1229])).
% 1.19/1.16 tff(1257,plain,
% 1.19/1.16 ((~($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))) = 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))), 0)),
% 1.19/1.17 inference(theory_lemma,[status(thm)],[])).
% 1.19/1.17 tff(1258,plain,
% 1.19/1.17 ($greatereq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))), 0)),
% 1.19/1.17 inference(unit_resolution,[status(thm)],[1257, 1252])).
% 1.19/1.17 tff(1259,assumption,($lesseq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))), 0)), introduced(assumption)).
% 1.19/1.17 tff(1260,assumption,(~($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))) = 0)), introduced(assumption)).
% 1.19/1.17 tff(1261,assumption,($greatereq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))), 0)), introduced(assumption)).
% 1.19/1.17 tff(1262,assumption,($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))) = 0), introduced(assumption)).
% 1.19/1.17 tff(1263,plain,
% 1.19/1.17 ((~($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))) = 0)) | $lesseq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))), 0)),
% 1.19/1.17 inference(theory_lemma,[status(thm)],[])).
% 1.19/1.17 tff(1264,plain,
% 1.19/1.17 ($lesseq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))), 0)),
% 1.19/1.17 inference(unit_resolution,[status(thm)],[1263, 1262])).
% 1.19/1.17 tff(1265,assumption,(~$lesseq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))), 0)), introduced(assumption)).
% 1.19/1.17 tff(1266,assumption,($lesseq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))), 0)), introduced(assumption)).
% 1.19/1.17 tff(1267,plain,
% 1.19/1.17 ($false),
% 1.19/1.17 inference(theory_lemma,[status(thm)],[1266, 1265, 1261])).
% 1.19/1.17 tff(1268,plain,($lesseq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))), 0) | (~$lesseq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))), 0)) | (~$greatereq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))), 0))), inference(lemma,lemma(discharge,[]))).
% 1.19/1.17 tff(1269,plain,
% 1.19/1.17 ($lesseq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))), 0)),
% 1.19/1.17 inference(unit_resolution,[status(thm)],[1268, 1264, 1261])).
% 1.19/1.17 tff(1270,plain,
% 1.19/1.17 (($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))) = 0) | (~$lesseq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))), 0)) | (~$greatereq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))), 0))),
% 1.19/1.17 inference(theory_lemma,[status(thm)],[])).
% 1.19/1.17 tff(1271,plain,
% 1.19/1.17 (~$greatereq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))), 0)),
% 1.19/1.17 inference(unit_resolution,[status(thm)],[1270, 1269, 1260])).
% 1.19/1.17 tff(1272,plain,
% 1.19/1.17 ((~($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))) = 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))), 0)),
% 1.19/1.17 inference(theory_lemma,[status(thm)],[])).
% 1.19/1.17 tff(1273,plain,
% 1.19/1.17 ($greatereq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))), 0)),
% 1.19/1.17 inference(unit_resolution,[status(thm)],[1272, 1262])).
% 1.19/1.17 tff(1274,plain,
% 1.19/1.17 ($false),
% 1.19/1.17 inference(theory_lemma,[status(thm)],[1273, 1271, 1259])).
% 1.19/1.17 tff(1275,plain,((~($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))) = 0)) | (~$lesseq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))), 0)) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))) = 0) | (~$greatereq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))), 0))), inference(lemma,lemma(discharge,[]))).
% 1.19/1.17 tff(1276,plain,
% 1.19/1.17 (~($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))) = 0)),
% 1.19/1.17 inference(unit_resolution,[status(thm)],[1275, 1258, 1256, 1254])).
% 1.19/1.17 tff(1277,plain,
% 1.19/1.17 (((~![B1: array_int, B2: array_int, Pos: $int] : (~((~((~eq_board1(B1, B2, Pos)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0) | ($sum(tb2t(get2(int, t2tb1(B2), Q)), $product(-1, tb2t(get2(int, t2tb1(B1), Q)))) = 0)))) | (~(eq_board1(B1, B2, Pos) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_0(Pos, B2, B1))), 0) | ($sum(tb2t(get2(int, t2tb1(B2), tptp_fun_Q_0(Pos, B2, B1))), $product(-1, tb2t(get2(int, t2tb1(B1), tptp_fun_Q_0(Pos, B2, B1))))) = 0) | (~$greatereq(tptp_fun_Q_0(Pos, B2, B1), 0))))))))) | (~((~((~eq_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), Pos!4)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 0) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), Q)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), Q)))) = 0)))) | (~(eq_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), Pos!4) | (~($lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))))), 0) | (~$greatereq(tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), 0)) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))))))) = 0)))))))) <=> ((~![B1: array_int, B2: array_int, Pos: $int] : (~((~((~eq_board1(B1, B2, Pos)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0) | ($sum(tb2t(get2(int, t2tb1(B2), Q)), $product(-1, tb2t(get2(int, t2tb1(B1), Q)))) = 0)))) | (~(eq_board1(B1, B2, Pos) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_0(Pos, B2, B1))), 0) | ($sum(tb2t(get2(int, t2tb1(B2), tptp_fun_Q_0(Pos, B2, B1))), $product(-1, tb2t(get2(int, t2tb1(B1), tptp_fun_Q_0(Pos, B2, B1))))) = 0) | (~$greatereq(tptp_fun_Q_0(Pos, B2, B1), 0))))))))) | (~((~((~eq_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), Pos!4)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 0) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), Q)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), Q)))) = 0)))) | (~(eq_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), Pos!4) | (~($lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))))), 0) | (~$greatereq(tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), 0)) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))))))) = 0))))))))),
% 1.19/1.17 inference(rewrite,[status(thm)],[])).
% 1.19/1.17 tff(1278,plain,
% 1.19/1.17 ((~((~((~eq_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), Pos!4)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos!4, $product(-1, Q)), 0) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), Q)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), Q)))) = 0)))) | (~(eq_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), Pos!4) | (~($lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))))), 0) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))))))) = 0) | (~$greatereq(tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), 0)))))))) <=> (~((~((~eq_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), Pos!4)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 0) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), Q)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), Q)))) = 0)))) | (~(eq_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), Pos!4) | (~($lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))))), 0) | (~$greatereq(tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), 0)) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))))))) = 0)))))))),
% 1.19/1.17 inference(rewrite,[status(thm)],[])).
% 1.19/1.17 tff(1279,plain,
% 1.19/1.17 (((~![B1: array_int, B2: array_int, Pos: $int] : (~((~((~eq_board1(B1, B2, Pos)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0) | ($sum(tb2t(get2(int, t2tb1(B2), Q)), $product(-1, tb2t(get2(int, t2tb1(B1), Q)))) = 0)))) | (~(eq_board1(B1, B2, Pos) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_0(Pos, B2, B1))), 0) | ($sum(tb2t(get2(int, t2tb1(B2), tptp_fun_Q_0(Pos, B2, B1))), $product(-1, tb2t(get2(int, t2tb1(B1), tptp_fun_Q_0(Pos, B2, B1))))) = 0) | (~$greatereq(tptp_fun_Q_0(Pos, B2, B1), 0))))))))) | (~((~((~eq_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), Pos!4)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos!4, $product(-1, Q)), 0) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), Q)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), Q)))) = 0)))) | (~(eq_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), Pos!4) | (~($lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))))), 0) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))))))) = 0) | (~$greatereq(tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), 0))))))))) <=> ((~![B1: array_int, B2: array_int, Pos: $int] : (~((~((~eq_board1(B1, B2, Pos)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0) | ($sum(tb2t(get2(int, t2tb1(B2), Q)), $product(-1, tb2t(get2(int, t2tb1(B1), Q)))) = 0)))) | (~(eq_board1(B1, B2, Pos) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_0(Pos, B2, B1))), 0) | ($sum(tb2t(get2(int, t2tb1(B2), tptp_fun_Q_0(Pos, B2, B1))), $product(-1, tb2t(get2(int, t2tb1(B1), tptp_fun_Q_0(Pos, B2, B1))))) = 0) | (~$greatereq(tptp_fun_Q_0(Pos, B2, B1), 0))))))))) | (~((~((~eq_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), Pos!4)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 0) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), Q)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), Q)))) = 0)))) | (~(eq_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), Pos!4) | (~($lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))))), 0) | (~$greatereq(tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), 0)) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))))))) = 0))))))))),
% 1.19/1.17 inference(monotonicity,[status(thm)],[1278])).
% 1.19/1.17 tff(1280,plain,
% 1.19/1.17 (((~![B1: array_int, B2: array_int, Pos: $int] : (~((~((~eq_board1(B1, B2, Pos)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0) | ($sum(tb2t(get2(int, t2tb1(B2), Q)), $product(-1, tb2t(get2(int, t2tb1(B1), Q)))) = 0)))) | (~(eq_board1(B1, B2, Pos) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_0(Pos, B2, B1))), 0) | ($sum(tb2t(get2(int, t2tb1(B2), tptp_fun_Q_0(Pos, B2, B1))), $product(-1, tb2t(get2(int, t2tb1(B1), tptp_fun_Q_0(Pos, B2, B1))))) = 0) | (~$greatereq(tptp_fun_Q_0(Pos, B2, B1), 0))))))))) | (~((~((~eq_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), Pos!4)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos!4, $product(-1, Q)), 0) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), Q)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), Q)))) = 0)))) | (~(eq_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), Pos!4) | (~($lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))))), 0) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))))))) = 0) | (~$greatereq(tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), 0))))))))) <=> ((~![B1: array_int, B2: array_int, Pos: $int] : (~((~((~eq_board1(B1, B2, Pos)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0) | ($sum(tb2t(get2(int, t2tb1(B2), Q)), $product(-1, tb2t(get2(int, t2tb1(B1), Q)))) = 0)))) | (~(eq_board1(B1, B2, Pos) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_0(Pos, B2, B1))), 0) | ($sum(tb2t(get2(int, t2tb1(B2), tptp_fun_Q_0(Pos, B2, B1))), $product(-1, tb2t(get2(int, t2tb1(B1), tptp_fun_Q_0(Pos, B2, B1))))) = 0) | (~$greatereq(tptp_fun_Q_0(Pos, B2, B1), 0))))))))) | (~((~((~eq_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), Pos!4)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 0) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), Q)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), Q)))) = 0)))) | (~(eq_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), Pos!4) | (~($lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))))), 0) | (~$greatereq(tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), 0)) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))))))) = 0))))))))),
% 1.19/1.17 inference(transitivity,[status(thm)],[1279, 1277])).
% 1.19/1.17 tff(1281,plain,
% 1.19/1.17 ((~![B1: array_int, B2: array_int, Pos: $int] : (~((~((~eq_board1(B1, B2, Pos)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0) | ($sum(tb2t(get2(int, t2tb1(B2), Q)), $product(-1, tb2t(get2(int, t2tb1(B1), Q)))) = 0)))) | (~(eq_board1(B1, B2, Pos) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_0(Pos, B2, B1))), 0) | ($sum(tb2t(get2(int, t2tb1(B2), tptp_fun_Q_0(Pos, B2, B1))), $product(-1, tb2t(get2(int, t2tb1(B1), tptp_fun_Q_0(Pos, B2, B1))))) = 0) | (~$greatereq(tptp_fun_Q_0(Pos, B2, B1), 0))))))))) | (~((~((~eq_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), Pos!4)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos!4, $product(-1, Q)), 0) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), Q)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), Q)))) = 0)))) | (~(eq_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), Pos!4) | (~($lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))))), 0) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))))))) = 0) | (~$greatereq(tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), 0))))))))),
% 1.19/1.17 inference(quant_inst,[status(thm)],[])).
% 1.19/1.17 tff(1282,plain,
% 1.19/1.17 ((~![B1: array_int, B2: array_int, Pos: $int] : (~((~((~eq_board1(B1, B2, Pos)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $lesseq($sum(Pos, $product(-1, Q)), 0) | ($sum(tb2t(get2(int, t2tb1(B2), Q)), $product(-1, tb2t(get2(int, t2tb1(B1), Q)))) = 0)))) | (~(eq_board1(B1, B2, Pos) | (~($lesseq($sum(Pos, $product(-1, tptp_fun_Q_0(Pos, B2, B1))), 0) | ($sum(tb2t(get2(int, t2tb1(B2), tptp_fun_Q_0(Pos, B2, B1))), $product(-1, tb2t(get2(int, t2tb1(B1), tptp_fun_Q_0(Pos, B2, B1))))) = 0) | (~$greatereq(tptp_fun_Q_0(Pos, B2, B1), 0))))))))) | (~((~((~eq_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), Pos!4)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 0) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), Q)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), Q)))) = 0)))) | (~(eq_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), Pos!4) | (~($lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))))), 0) | (~$greatereq(tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), 0)) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))))))) = 0)))))))),
% 1.19/1.18 inference(modus_ponens,[status(thm)],[1281, 1280])).
% 1.19/1.18 tff(1283,plain,
% 1.19/1.18 (~((~((~eq_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), Pos!4)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 0) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), Q)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), Q)))) = 0)))) | (~(eq_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), Pos!4) | (~($lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))))), 0) | (~$greatereq(tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), 0)) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))))))) = 0))))))),
% 1.19/1.18 inference(unit_resolution,[status(thm)],[1282, 297])).
% 1.19/1.18 tff(1284,plain,
% 1.19/1.18 (((~((~eq_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), Pos!4)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 0) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), Q)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), Q)))) = 0)))) | (~(eq_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), Pos!4) | (~($lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))))), 0) | (~$greatereq(tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), 0)) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), tptp_fun_Q_0(Pos!4, tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))))))) = 0)))))) | ((~eq_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), Pos!4)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 0) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), Q)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), Q)))) = 0)))),
% 1.19/1.18 inference(tautology,[status(thm)],[])).
% 1.19/1.18 tff(1285,plain,
% 1.19/1.18 ((~eq_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), Pos!4)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 0) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), Q)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), Q)))) = 0))),
% 1.19/1.18 inference(unit_resolution,[status(thm)],[1284, 1283])).
% 1.19/1.18 tff(1286,plain,
% 1.19/1.18 (((~solution1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), Pos!4)) | (~($sum(N!5, $product(-1, B!16)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))), 0))) | eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), Pos!4)),
% 1.19/1.18 inference(tautology,[status(thm)],[])).
% 1.19/1.18 tff(1287,plain,
% 1.19/1.18 (eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), Pos!4)),
% 1.19/1.18 inference(unit_resolution,[status(thm)],[1286, 1189])).
% 1.19/1.18 tff(1288,plain,
% 1.19/1.18 (((~![B1: array_int, B2: array_int, Pos: $int] : ((~eq_board1(B1, B2, Pos)) | eq_board1(B2, B1, Pos))) | ((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), Pos!4)) | eq_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), Pos!4))) <=> ((~![B1: array_int, B2: array_int, Pos: $int] : ((~eq_board1(B1, B2, Pos)) | eq_board1(B2, B1, Pos))) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), Pos!4)) | eq_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), Pos!4))),
% 1.23/1.18 inference(rewrite,[status(thm)],[])).
% 1.23/1.18 tff(1289,plain,
% 1.23/1.18 ((~![B1: array_int, B2: array_int, Pos: $int] : ((~eq_board1(B1, B2, Pos)) | eq_board1(B2, B1, Pos))) | ((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), Pos!4)) | eq_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), Pos!4))),
% 1.23/1.18 inference(quant_inst,[status(thm)],[])).
% 1.23/1.18 tff(1290,plain,
% 1.23/1.18 ((~![B1: array_int, B2: array_int, Pos: $int] : ((~eq_board1(B1, B2, Pos)) | eq_board1(B2, B1, Pos))) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), Pos!4)) | eq_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), Pos!4)),
% 1.23/1.18 inference(modus_ponens,[status(thm)],[1289, 1288])).
% 1.23/1.18 tff(1291,plain,
% 1.23/1.18 (eq_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), Pos!4)),
% 1.23/1.18 inference(unit_resolution,[status(thm)],[1290, 561, 1287])).
% 1.23/1.18 tff(1292,plain,
% 1.23/1.18 ((~((~eq_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), Pos!4)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 0) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), Q)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), Q)))) = 0)))) | (~eq_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), Pos!4)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 0) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), Q)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), Q)))) = 0))),
% 1.23/1.18 inference(tautology,[status(thm)],[])).
% 1.23/1.18 tff(1293,plain,
% 1.23/1.18 ((~((~eq_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), Pos!4)) | ![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 0) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), Q)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), Q)))) = 0)))) | ![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 0) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), Q)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), Q)))) = 0))),
% 1.23/1.18 inference(unit_resolution,[status(thm)],[1292, 1291])).
% 1.23/1.18 tff(1294,plain,
% 1.23/1.18 (![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 0) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), Q)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), Q)))) = 0))),
% 1.23/1.18 inference(unit_resolution,[status(thm)],[1293, 1285])).
% 1.23/1.18 tff(1295,plain,
% 1.23/1.18 (((~![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 0) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), Q)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), Q)))) = 0))) | ((~$greatereq(tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0)) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), 0) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))) = 0))) <=> ((~![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 0) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), Q)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), Q)))) = 0))) | (~$greatereq(tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0)) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), 0) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))) = 0))),
% 1.23/1.18 inference(rewrite,[status(thm)],[])).
% 1.23/1.18 tff(1296,plain,
% 1.23/1.18 (((~$greatereq(tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0)) | $greatereq($sum(tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), $product(-1, Pos!4)), 0) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))) = 0)) <=> ((~$greatereq(tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0)) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), 0) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))) = 0))),
% 1.23/1.18 inference(rewrite,[status(thm)],[])).
% 1.23/1.18 tff(1297,plain,
% 1.23/1.18 (((~![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 0) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), Q)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), Q)))) = 0))) | ((~$greatereq(tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0)) | $greatereq($sum(tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), $product(-1, Pos!4)), 0) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))) = 0))) <=> ((~![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 0) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), Q)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), Q)))) = 0))) | ((~$greatereq(tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0)) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), 0) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))) = 0)))),
% 1.23/1.18 inference(monotonicity,[status(thm)],[1296])).
% 1.23/1.18 tff(1298,plain,
% 1.23/1.18 (((~![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 0) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), Q)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), Q)))) = 0))) | ((~$greatereq(tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0)) | $greatereq($sum(tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), $product(-1, Pos!4)), 0) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))) = 0))) <=> ((~![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 0) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), Q)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), Q)))) = 0))) | (~$greatereq(tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0)) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), 0) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))) = 0))),
% 1.23/1.18 inference(transitivity,[status(thm)],[1297, 1295])).
% 1.23/1.18 tff(1299,plain,
% 1.23/1.18 ((~![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 0) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), Q)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), Q)))) = 0))) | ((~$greatereq(tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0)) | $greatereq($sum(tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), $product(-1, Pos!4)), 0) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))) = 0))),
% 1.23/1.18 inference(quant_inst,[status(thm)],[])).
% 1.23/1.18 tff(1300,plain,
% 1.23/1.18 ((~![Q: $int] : ((~$greatereq(Q, 0)) | $greatereq($sum(Q, $product(-1, Pos!4)), 0) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), Q)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), Q)))) = 0))) | (~$greatereq(tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), 0)) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), 0) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))) = 0)),
% 1.23/1.18 inference(modus_ponens,[status(thm)],[1299, 1298])).
% 1.23/1.18 tff(1301,plain,
% 1.23/1.18 ($lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), 0) | ($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))) = 0)),
% 1.23/1.18 inference(unit_resolution,[status(thm)],[1300, 1294, 1231])).
% 1.23/1.18 tff(1302,plain,
% 1.23/1.18 ($lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), 0)),
% 1.23/1.18 inference(unit_resolution,[status(thm)],[1301, 1276])).
% 1.23/1.18 tff(1303,plain,
% 1.23/1.18 (Pos!4 = tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))),
% 1.23/1.18 inference(theory_lemma,[status(thm)],[1233, 1302])).
% 1.23/1.18 tff(1304,plain,
% 1.23/1.18 (tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))) = Pos!4),
% 1.23/1.18 inference(symmetry,[status(thm)],[1303])).
% 1.23/1.18 tff(1305,plain,
% 1.23/1.18 (get2(int, t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))) = get2(int, t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), Pos!4)),
% 1.23/1.18 inference(monotonicity,[status(thm)],[1304])).
% 1.23/1.18 tff(1306,plain,
% 1.23/1.18 (tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))) = tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), Pos!4))),
% 1.23/1.18 inference(monotonicity,[status(thm)],[1305])).
% 1.23/1.18 tff(1307,plain,
% 1.23/1.18 (tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), Pos!4)) = tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))))),
% 1.23/1.18 inference(symmetry,[status(thm)],[1306])).
% 1.23/1.18 tff(1308,plain,
% 1.23/1.18 ((~(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), Pos!4)) = tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))) | $lesseq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), Pos!4)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))), 0)),
% 1.23/1.18 inference(theory_lemma,[status(thm)],[])).
% 1.23/1.18 tff(1309,plain,
% 1.23/1.18 ($lesseq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), Pos!4)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))), 0)),
% 1.23/1.18 inference(unit_resolution,[status(thm)],[1308, 1307])).
% 1.23/1.18 tff(1310,plain,
% 1.23/1.18 (![J: uni] : (t2tb(tb2t(J)) = J) <=> ![J: uni] : (t2tb(tb2t(J)) = J)),
% 1.23/1.18 inference(rewrite,[status(thm)],[])).
% 1.23/1.18 tff(1311,plain,
% 1.23/1.18 (![J: uni] : (t2tb(tb2t(J)) = J) <=> ![J: uni] : (t2tb(tb2t(J)) = J)),
% 1.23/1.18 inference(rewrite,[status(thm)],[])).
% 1.23/1.18 tff(1312,axiom,(![J: uni] : (t2tb(tb2t(J)) = J)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bridgeR')).
% 1.23/1.18 tff(1313,plain,
% 1.23/1.18 (![J: uni] : (t2tb(tb2t(J)) = J)),
% 1.23/1.18 inference(modus_ponens,[status(thm)],[1312, 1311])).
% 1.23/1.18 tff(1314,plain,(
% 1.23/1.18 ![J: uni] : (t2tb(tb2t(J)) = J)),
% 1.23/1.18 inference(skolemize,[status(sab)],[1313])).
% 1.23/1.18 tff(1315,plain,
% 1.23/1.18 (![J: uni] : (t2tb(tb2t(J)) = J)),
% 1.23/1.18 inference(modus_ponens,[status(thm)],[1314, 1310])).
% 1.23/1.18 tff(1316,plain,
% 1.23/1.18 ((~![J: uni] : (t2tb(tb2t(J)) = J)) | (t2tb(tb2t(t2tb(tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))))) = t2tb(tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))))),
% 1.23/1.18 inference(quant_inst,[status(thm)],[])).
% 1.23/1.18 tff(1317,plain,
% 1.23/1.18 (t2tb(tb2t(t2tb(tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))))) = t2tb(tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))),
% 1.23/1.18 inference(unit_resolution,[status(thm)],[1316, 1315])).
% 1.23/1.18 tff(1318,assumption,($lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), 0)), introduced(assumption)).
% 1.23/1.18 tff(1319,assumption,(~$lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), -1)), introduced(assumption)).
% 1.23/1.18 tff(1320,plain,
% 1.23/1.18 (Pos!4 = tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))),
% 1.23/1.18 inference(theory_lemma,[status(thm)],[1319, 1318])).
% 1.23/1.18 tff(1321,plain,
% 1.23/1.18 (tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))) = Pos!4),
% 1.23/1.18 inference(symmetry,[status(thm)],[1320])).
% 1.23/1.18 tff(1322,plain,
% 1.23/1.18 ((~![I: $int] : ($sum(I, $product(-1, tb2t(t2tb(I)))) = 0)) | ($sum(tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), $product(-1, tb2t(t2tb(tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))) = 0)),
% 1.23/1.18 inference(quant_inst,[status(thm)],[])).
% 1.23/1.18 tff(1323,plain,
% 1.23/1.18 ($sum(tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), $product(-1, tb2t(t2tb(tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))) = 0),
% 1.23/1.19 inference(unit_resolution,[status(thm)],[1322, 388])).
% 1.23/1.19 tff(1324,plain,
% 1.23/1.19 ((~($sum(tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), $product(-1, tb2t(t2tb(tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))) = 0)) | $lesseq($sum(tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), $product(-1, tb2t(t2tb(tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))), 0)),
% 1.23/1.19 inference(theory_lemma,[status(thm)],[])).
% 1.23/1.19 tff(1325,plain,
% 1.23/1.19 ($lesseq($sum(tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), $product(-1, tb2t(t2tb(tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))), 0)),
% 1.23/1.19 inference(unit_resolution,[status(thm)],[1324, 1323])).
% 1.23/1.19 tff(1326,plain,
% 1.23/1.19 ((~($sum(tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), $product(-1, tb2t(t2tb(tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))) = 0)) | $greatereq($sum(tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), $product(-1, tb2t(t2tb(tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))), 0)),
% 1.23/1.19 inference(theory_lemma,[status(thm)],[])).
% 1.23/1.19 tff(1327,plain,
% 1.23/1.19 ($greatereq($sum(tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), $product(-1, tb2t(t2tb(tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))), 0)),
% 1.23/1.19 inference(unit_resolution,[status(thm)],[1326, 1323])).
% 1.23/1.19 tff(1328,plain,
% 1.23/1.19 (tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))) = tb2t(t2tb(tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))))),
% 1.23/1.19 inference(theory_lemma,[status(thm)],[1327, 1325])).
% 1.23/1.19 tff(1329,plain,
% 1.23/1.19 (tb2t(t2tb(tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))) = tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))),
% 1.23/1.19 inference(symmetry,[status(thm)],[1328])).
% 1.23/1.19 tff(1330,plain,
% 1.23/1.19 (tb2t(t2tb(tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))) = Pos!4),
% 1.23/1.19 inference(transitivity,[status(thm)],[1329, 1321])).
% 1.23/1.19 tff(1331,plain,
% 1.23/1.19 (t2tb(tb2t(t2tb(tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))))) = t2tb(Pos!4)),
% 1.23/1.19 inference(monotonicity,[status(thm)],[1330])).
% 1.23/1.19 tff(1332,plain,
% 1.23/1.19 (t2tb(Pos!4) = t2tb(tb2t(t2tb(tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))),
% 1.23/1.19 inference(symmetry,[status(thm)],[1331])).
% 1.23/1.19 tff(1333,plain,
% 1.23/1.19 (t2tb(Pos!4) = t2tb(tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))),
% 1.23/1.19 inference(transitivity,[status(thm)],[1332, 1317])).
% 1.23/1.19 tff(1334,assumption,(~(t2tb(Pos!4) = t2tb(tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))))), introduced(assumption)).
% 1.23/1.19 tff(1335,plain,
% 1.23/1.19 ($false),
% 1.23/1.19 inference(unit_resolution,[status(thm)],[1334, 1333])).
% 1.23/1.19 tff(1336,plain,((~$lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), 0)) | (t2tb(Pos!4) = t2tb(tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))) | $lesseq($sum(Pos!4, $product(-1, tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), -1)), inference(lemma,lemma(discharge,[]))).
% 1.23/1.19 tff(1337,plain,
% 1.23/1.19 (t2tb(Pos!4) = t2tb(tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))),
% 1.23/1.19 inference(unit_resolution,[status(thm)],[1336, 1302, 1233])).
% 1.23/1.19 tff(1338,plain,
% 1.23/1.19 (((~![A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : ((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort1(B, B1)))) | ((~sort1(int, t2tb(I!11))) | (get(int, int, set(int, int, t2tb2(Board2!10), t2tb(Pos!4), t2tb(I!11)), t2tb(tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))) = t2tb(I!11)) | (~(t2tb(Pos!4) = t2tb(tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))))))) <=> ((~![A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : ((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort1(B, B1)))) | (~sort1(int, t2tb(I!11))) | (get(int, int, set(int, int, t2tb2(Board2!10), t2tb(Pos!4), t2tb(I!11)), t2tb(tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))) = t2tb(I!11)) | (~(t2tb(Pos!4) = t2tb(tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))))))),
% 1.23/1.19 inference(rewrite,[status(thm)],[])).
% 1.23/1.19 tff(1339,plain,
% 1.23/1.19 (((get(int, int, set(int, int, t2tb2(Board2!10), t2tb(Pos!4), t2tb(I!11)), t2tb(tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))) = t2tb(I!11)) | (~(t2tb(Pos!4) = t2tb(tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))))) | (~sort1(int, t2tb(I!11)))) <=> ((~sort1(int, t2tb(I!11))) | (get(int, int, set(int, int, t2tb2(Board2!10), t2tb(Pos!4), t2tb(I!11)), t2tb(tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))) = t2tb(I!11)) | (~(t2tb(Pos!4) = t2tb(tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))))))),
% 1.23/1.19 inference(rewrite,[status(thm)],[])).
% 1.23/1.19 tff(1340,plain,
% 1.23/1.19 (((~![A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : ((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort1(B, B1)))) | ((get(int, int, set(int, int, t2tb2(Board2!10), t2tb(Pos!4), t2tb(I!11)), t2tb(tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))) = t2tb(I!11)) | (~(t2tb(Pos!4) = t2tb(tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))))) | (~sort1(int, t2tb(I!11))))) <=> ((~![A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : ((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort1(B, B1)))) | ((~sort1(int, t2tb(I!11))) | (get(int, int, set(int, int, t2tb2(Board2!10), t2tb(Pos!4), t2tb(I!11)), t2tb(tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))) = t2tb(I!11)) | (~(t2tb(Pos!4) = t2tb(tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))))),
% 1.23/1.19 inference(monotonicity,[status(thm)],[1339])).
% 1.23/1.19 tff(1341,plain,
% 1.23/1.19 (((~![A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : ((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort1(B, B1)))) | ((get(int, int, set(int, int, t2tb2(Board2!10), t2tb(Pos!4), t2tb(I!11)), t2tb(tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))) = t2tb(I!11)) | (~(t2tb(Pos!4) = t2tb(tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))))) | (~sort1(int, t2tb(I!11))))) <=> ((~![A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : ((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort1(B, B1)))) | (~sort1(int, t2tb(I!11))) | (get(int, int, set(int, int, t2tb2(Board2!10), t2tb(Pos!4), t2tb(I!11)), t2tb(tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))) = t2tb(I!11)) | (~(t2tb(Pos!4) = t2tb(tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))))))),
% 1.23/1.19 inference(transitivity,[status(thm)],[1340, 1338])).
% 1.23/1.19 tff(1342,plain,
% 1.23/1.19 ((~![A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : ((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort1(B, B1)))) | ((get(int, int, set(int, int, t2tb2(Board2!10), t2tb(Pos!4), t2tb(I!11)), t2tb(tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))) = t2tb(I!11)) | (~(t2tb(Pos!4) = t2tb(tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))))) | (~sort1(int, t2tb(I!11))))),
% 1.23/1.19 inference(quant_inst,[status(thm)],[])).
% 1.23/1.19 tff(1343,plain,
% 1.23/1.19 ((~![A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : ((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort1(B, B1)))) | (~sort1(int, t2tb(I!11))) | (get(int, int, set(int, int, t2tb2(Board2!10), t2tb(Pos!4), t2tb(I!11)), t2tb(tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))) = t2tb(I!11)) | (~(t2tb(Pos!4) = t2tb(tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))),
% 1.23/1.19 inference(modus_ponens,[status(thm)],[1342, 1341])).
% 1.23/1.19 tff(1344,plain,
% 1.23/1.19 (get(int, int, set(int, int, t2tb2(Board2!10), t2tb(Pos!4), t2tb(I!11)), t2tb(tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))) = t2tb(I!11)),
% 1.23/1.19 inference(unit_resolution,[status(thm)],[1343, 666, 656, 1337])).
% 1.23/1.19 tff(1345,plain,
% 1.23/1.19 (elts(int, mk_array1(int, Board!7, t2tb2(Board3!12))) = set(int, int, t2tb2(Board2!10), t2tb(Pos!4), t2tb(I!11))),
% 1.23/1.19 inference(transitivity,[status(thm)],[515, 684, 366, 492])).
% 1.23/1.19 tff(1346,plain,
% 1.23/1.19 (get(int, int, elts(int, mk_array1(int, Board!7, t2tb2(Board3!12))), t2tb(tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))) = get(int, int, set(int, int, t2tb2(Board2!10), t2tb(Pos!4), t2tb(I!11)), t2tb(tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))))),
% 1.23/1.19 inference(monotonicity,[status(thm)],[1345])).
% 1.23/1.19 tff(1347,plain,
% 1.23/1.19 ((~![A: ty, A1: uni, I: $int] : (get2(A, A1, I) = get(A, int, elts(A, A1), t2tb(I)))) | (get2(int, mk_array1(int, Board!7, t2tb2(Board3!12)), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))) = get(int, int, elts(int, mk_array1(int, Board!7, t2tb2(Board3!12))), t2tb(tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))),
% 1.23/1.19 inference(quant_inst,[status(thm)],[])).
% 1.23/1.19 tff(1348,plain,
% 1.23/1.19 (get2(int, mk_array1(int, Board!7, t2tb2(Board3!12)), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))) = get(int, int, elts(int, mk_array1(int, Board!7, t2tb2(Board3!12))), t2tb(tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))))),
% 1.23/1.19 inference(unit_resolution,[status(thm)],[1347, 165])).
% 1.23/1.19 tff(1349,plain,
% 1.23/1.19 (get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))) = get2(int, mk_array1(int, Board!7, t2tb2(Board3!12)), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))),
% 1.23/1.19 inference(monotonicity,[status(thm)],[521])).
% 1.23/1.19 tff(1350,plain,
% 1.23/1.19 (get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))) = t2tb(I!11)),
% 1.23/1.19 inference(transitivity,[status(thm)],[1349, 1348, 1346, 1344])).
% 1.23/1.19 tff(1351,plain,
% 1.23/1.19 (tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))) = tb2t(t2tb(I!11))),
% 1.23/1.19 inference(monotonicity,[status(thm)],[1350])).
% 1.23/1.19 tff(1352,plain,
% 1.23/1.19 (tb2t(t2tb(I!11)) = tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))))))),
% 1.23/1.19 inference(symmetry,[status(thm)],[1351])).
% 1.23/1.19 tff(1353,plain,
% 1.23/1.19 ((~(tb2t(t2tb(I!11)) = tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))) | $greatereq($sum(tb2t(t2tb(I!11)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))), 0)),
% 1.23/1.19 inference(theory_lemma,[status(thm)],[])).
% 1.23/1.19 tff(1354,plain,
% 1.23/1.19 ($greatereq($sum(tb2t(t2tb(I!11)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))), 0)),
% 1.23/1.19 inference(unit_resolution,[status(thm)],[1353, 1352])).
% 1.23/1.19 tff(1355,plain,
% 1.23/1.19 ((~![X: map_int_int] : sort1(map(int, int), t2tb2(X))) | sort1(map(int, int), t2tb2(B1!15))),
% 1.23/1.19 inference(quant_inst,[status(thm)],[])).
% 1.23/1.19 tff(1356,plain,
% 1.23/1.19 (sort1(map(int, int), t2tb2(B1!15))),
% 1.23/1.19 inference(unit_resolution,[status(thm)],[1355, 175])).
% 1.23/1.19 tff(1357,plain,
% 1.23/1.19 (((~![A: ty, U: $int, U1: uni] : ((~sort1(map(int, A), U1)) | (elts(A, mk_array1(A, U, U1)) = U1))) | ((~sort1(map(int, int), t2tb2(B1!15))) | (elts(int, mk_array1(int, B!16, t2tb2(B1!15))) = t2tb2(B1!15)))) <=> ((~![A: ty, U: $int, U1: uni] : ((~sort1(map(int, A), U1)) | (elts(A, mk_array1(A, U, U1)) = U1))) | (~sort1(map(int, int), t2tb2(B1!15))) | (elts(int, mk_array1(int, B!16, t2tb2(B1!15))) = t2tb2(B1!15)))),
% 1.23/1.19 inference(rewrite,[status(thm)],[])).
% 1.23/1.19 tff(1358,plain,
% 1.23/1.19 ((~![A: ty, U: $int, U1: uni] : ((~sort1(map(int, A), U1)) | (elts(A, mk_array1(A, U, U1)) = U1))) | ((~sort1(map(int, int), t2tb2(B1!15))) | (elts(int, mk_array1(int, B!16, t2tb2(B1!15))) = t2tb2(B1!15)))),
% 1.23/1.19 inference(quant_inst,[status(thm)],[])).
% 1.23/1.19 tff(1359,plain,
% 1.23/1.19 ((~![A: ty, U: $int, U1: uni] : ((~sort1(map(int, A), U1)) | (elts(A, mk_array1(A, U, U1)) = U1))) | (~sort1(map(int, int), t2tb2(B1!15))) | (elts(int, mk_array1(int, B!16, t2tb2(B1!15))) = t2tb2(B1!15))),
% 1.23/1.19 inference(modus_ponens,[status(thm)],[1358, 1357])).
% 1.23/1.19 tff(1360,plain,
% 1.23/1.19 ((~sort1(map(int, int), t2tb2(B1!15))) | (elts(int, mk_array1(int, B!16, t2tb2(B1!15))) = t2tb2(B1!15))),
% 1.23/1.19 inference(unit_resolution,[status(thm)],[1359, 187])).
% 1.23/1.19 tff(1361,plain,
% 1.23/1.19 (elts(int, mk_array1(int, B!16, t2tb2(B1!15))) = t2tb2(B1!15)),
% 1.23/1.19 inference(unit_resolution,[status(thm)],[1360, 1356])).
% 1.23/1.19 tff(1362,plain,
% 1.23/1.19 (t2tb2(B1!15) = elts(int, mk_array1(int, B!16, t2tb2(B1!15)))),
% 1.23/1.19 inference(symmetry,[status(thm)],[1361])).
% 1.23/1.19 tff(1363,plain,
% 1.23/1.19 (get(int, int, t2tb2(B1!15), t2tb(Pos!4)) = get(int, int, elts(int, mk_array1(int, B!16, t2tb2(B1!15))), t2tb(Pos!4))),
% 1.23/1.19 inference(monotonicity,[status(thm)],[1362])).
% 1.23/1.19 tff(1364,plain,
% 1.23/1.19 (get(int, int, elts(int, mk_array1(int, B!16, t2tb2(B1!15))), t2tb(Pos!4)) = get(int, int, t2tb2(B1!15), t2tb(Pos!4))),
% 1.23/1.19 inference(symmetry,[status(thm)],[1363])).
% 1.23/1.19 tff(1365,plain,
% 1.23/1.19 ((~![A: ty, A1: uni, I: $int] : (get2(A, A1, I) = get(A, int, elts(A, A1), t2tb(I)))) | (get2(int, mk_array1(int, B!16, t2tb2(B1!15)), Pos!4) = get(int, int, elts(int, mk_array1(int, B!16, t2tb2(B1!15))), t2tb(Pos!4)))),
% 1.23/1.19 inference(quant_inst,[status(thm)],[])).
% 1.23/1.19 tff(1366,plain,
% 1.23/1.19 (get2(int, mk_array1(int, B!16, t2tb2(B1!15)), Pos!4) = get(int, int, elts(int, mk_array1(int, B!16, t2tb2(B1!15))), t2tb(Pos!4))),
% 1.23/1.19 inference(unit_resolution,[status(thm)],[1365, 165])).
% 1.23/1.19 tff(1367,plain,
% 1.23/1.19 ((~![J: uni] : (t2tb1(tb2t1(J)) = J)) | (t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))) = mk_array1(int, B!16, t2tb2(B1!15)))),
% 1.23/1.19 inference(quant_inst,[status(thm)],[])).
% 1.23/1.19 tff(1368,plain,
% 1.23/1.19 (t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))) = mk_array1(int, B!16, t2tb2(B1!15))),
% 1.23/1.19 inference(unit_resolution,[status(thm)],[1367, 154])).
% 1.23/1.19 tff(1369,plain,
% 1.23/1.19 (mk_array1(int, B!16, t2tb2(B1!15)) = t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))))),
% 1.23/1.19 inference(symmetry,[status(thm)],[1368])).
% 1.23/1.19 tff(1370,plain,
% 1.23/1.19 (get2(int, mk_array1(int, B!16, t2tb2(B1!15)), Pos!4) = get2(int, t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), Pos!4)),
% 1.23/1.19 inference(monotonicity,[status(thm)],[1369])).
% 1.23/1.19 tff(1371,plain,
% 1.23/1.19 (get2(int, t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), Pos!4) = get2(int, mk_array1(int, B!16, t2tb2(B1!15)), Pos!4)),
% 1.23/1.19 inference(symmetry,[status(thm)],[1370])).
% 1.23/1.19 tff(1372,plain,
% 1.23/1.19 (get2(int, t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), Pos!4) = get(int, int, t2tb2(B1!15), t2tb(Pos!4))),
% 1.23/1.19 inference(transitivity,[status(thm)],[1371, 1366, 1364])).
% 1.23/1.19 tff(1373,plain,
% 1.23/1.19 (tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), Pos!4)) = tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4)))),
% 1.23/1.19 inference(monotonicity,[status(thm)],[1372])).
% 1.23/1.19 tff(1374,plain,
% 1.23/1.19 (tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))) = tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), Pos!4))),
% 1.23/1.19 inference(symmetry,[status(thm)],[1373])).
% 1.23/1.19 tff(1375,plain,
% 1.23/1.19 ((~(tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))) = tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), Pos!4)))) | $lesseq($sum(tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), Pos!4)))), 0)),
% 1.23/1.19 inference(theory_lemma,[status(thm)],[])).
% 1.23/1.19 tff(1376,plain,
% 1.23/1.19 ($lesseq($sum(tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), Pos!4)))), 0)),
% 1.23/1.19 inference(unit_resolution,[status(thm)],[1375, 1374])).
% 1.23/1.19 tff(1377,plain,
% 1.23/1.19 ((~(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), Pos!4)) = tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))) | $greatereq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), Pos!4)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))), 0)),
% 1.23/1.19 inference(theory_lemma,[status(thm)],[])).
% 1.23/1.19 tff(1378,plain,
% 1.23/1.19 ($greatereq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), Pos!4)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))), 0)),
% 1.23/1.19 inference(unit_resolution,[status(thm)],[1377, 1307])).
% 1.23/1.19 tff(1379,plain,
% 1.23/1.19 (((~solution1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), Pos!4)) | (~($sum(N!5, $product(-1, B!16)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))), 0))) | (~$lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))))), -1))),
% 1.23/1.19 inference(tautology,[status(thm)],[])).
% 1.23/1.19 tff(1380,plain,
% 1.23/1.19 (~$lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))))), -1)),
% 1.23/1.19 inference(unit_resolution,[status(thm)],[1379, 1189])).
% 1.23/1.19 tff(1381,plain,
% 1.23/1.19 ((~(tb2t(t2tb(I!11)) = tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))) | $lesseq($sum(tb2t(t2tb(I!11)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))), 0)),
% 1.23/1.19 inference(theory_lemma,[status(thm)],[])).
% 1.23/1.19 tff(1382,plain,
% 1.23/1.19 ($lesseq($sum(tb2t(t2tb(I!11)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))), 0)),
% 1.23/1.19 inference(unit_resolution,[status(thm)],[1381, 1352])).
% 1.23/1.19 tff(1383,assumption,(~$lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))))), -1)), introduced(assumption)).
% 1.23/1.19 tff(1384,assumption,($lesseq($sum(tb2t(t2tb(I!11)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))), 0)), introduced(assumption)).
% 1.23/1.19 tff(1385,assumption,(~$lesseq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))), 0)), introduced(assumption)).
% 1.23/1.19 tff(1386,assumption,($greatereq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), Pos!4)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))), 0)), introduced(assumption)).
% 1.23/1.19 tff(1387,plain,
% 1.23/1.19 ((~(tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))) = tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), Pos!4)))) | $greatereq($sum(tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), Pos!4)))), 0)),
% 1.23/1.19 inference(theory_lemma,[status(thm)],[])).
% 1.23/1.19 tff(1388,plain,
% 1.23/1.19 ($greatereq($sum(tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), Pos!4)))), 0)),
% 1.23/1.19 inference(unit_resolution,[status(thm)],[1387, 1374])).
% 1.23/1.19 tff(1389,plain,
% 1.23/1.19 ($false),
% 1.23/1.19 inference(theory_lemma,[status(thm)],[703, 1388, 1386, 1259, 1385, 1384, 1383])).
% 1.23/1.19 tff(1390,plain,($lesseq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))), 0) | (~$greatereq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), Pos!4)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))), 0)) | (~$lesseq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))), 0)) | (~$lesseq($sum(tb2t(t2tb(I!11)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))), 0)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))))), -1)), inference(lemma,lemma(discharge,[]))).
% 1.23/1.20 tff(1391,plain,
% 1.23/1.20 ($lesseq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))), 0)),
% 1.23/1.20 inference(unit_resolution,[status(thm)],[1390, 1382, 1380, 1254, 1378])).
% 1.23/1.20 tff(1392,plain,
% 1.23/1.20 (($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))) = 0) | (~$lesseq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))), 0)) | (~$greatereq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))), 0))),
% 1.23/1.20 inference(theory_lemma,[status(thm)],[])).
% 1.23/1.20 tff(1393,plain,
% 1.23/1.20 (~$greatereq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))), 0)),
% 1.23/1.20 inference(unit_resolution,[status(thm)],[1392, 1391, 1276])).
% 1.23/1.20 tff(1394,plain,
% 1.23/1.20 ((~$lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))))), 0)) | (~$greatereq($sum(I!11, $product(-1, tb2t(t2tb(I!11)))), 0)) | (~$lesseq($sum(tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), Pos!4)))), 0)) | (~$lesseq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), Pos!4)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))), 0)) | (~$greatereq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))), 0)) | $greatereq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))), 0) | (~$greatereq($sum(tb2t(t2tb(I!11)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))), tptp_fun_Q_0($sum(1, Pos!4), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12)))))))), 0))),
% 1.23/1.20 inference(theory_lemma,[status(thm)],[])).
% 1.23/1.20 tff(1395,plain,
% 1.23/1.20 (~$lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))))), 0)),
% 1.23/1.20 inference(unit_resolution,[status(thm)],[1394, 1393, 1376, 1354, 1258, 1309, 654])).
% 1.23/1.20 tff(1396,plain,
% 1.23/1.20 (((~solution1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), Pos!4)) | (~($sum(N!5, $product(-1, B!16)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))), 0))) | $greatereq(tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))), 0)),
% 1.23/1.20 inference(tautology,[status(thm)],[])).
% 1.23/1.20 tff(1397,plain,
% 1.23/1.20 ($greatereq(tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))), 0)),
% 1.23/1.20 inference(unit_resolution,[status(thm)],[1396, 1189])).
% 1.23/1.20 tff(1398,plain,
% 1.23/1.20 (((~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos!4)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), 0)) | $greatereq($sum(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), $product(-1, I!11)), 0))) | ((~solution1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~($sum(N!5, $product(-1, B!16)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))), 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), Pos!4)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))))), 0))) <=> ((~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos!4)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), 0)) | $greatereq($sum(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), $product(-1, I!11)), 0))) | (~solution1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~($sum(N!5, $product(-1, B!16)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))), 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), Pos!4)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))))), 0))),
% 1.23/1.20 inference(rewrite,[status(thm)],[])).
% 1.23/1.20 tff(1399,plain,
% 1.23/1.20 (((~solution1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~($sum(N!5, $product(-1, B!16)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), Pos!4)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))), 0)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))))), 0)) <=> ((~solution1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~($sum(N!5, $product(-1, B!16)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))), 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), Pos!4)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))))), 0))),
% 1.23/1.20 inference(rewrite,[status(thm)],[])).
% 1.23/1.20 tff(1400,plain,
% 1.23/1.20 ($greatereq($sum($product(-1, I!11), tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4)))), 0) <=> $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))))), 0)),
% 1.23/1.20 inference(rewrite,[status(thm)],[])).
% 1.23/1.20 tff(1401,plain,
% 1.23/1.20 ($sum(tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))), $product(-1, I!11)) = $sum($product(-1, I!11), tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))))),
% 1.23/1.20 inference(rewrite,[status(thm)],[])).
% 1.23/1.20 tff(1402,plain,
% 1.23/1.20 ($greatereq($sum(tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))), $product(-1, I!11)), 0) <=> $greatereq($sum($product(-1, I!11), tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4)))), 0)),
% 1.23/1.20 inference(monotonicity,[status(thm)],[1401])).
% 1.23/1.20 tff(1403,plain,
% 1.23/1.20 ($greatereq($sum(tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))), $product(-1, I!11)), 0) <=> $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))))), 0)),
% 1.23/1.20 inference(transitivity,[status(thm)],[1402, 1400])).
% 1.23/1.20 tff(1404,plain,
% 1.23/1.20 (((~solution1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~($sum(B!16, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), Pos!4)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))), 0)) | $greatereq($sum(tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))), $product(-1, I!11)), 0)) <=> ((~solution1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~($sum(N!5, $product(-1, B!16)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), Pos!4)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))), 0)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))))), 0))),
% 1.23/1.20 inference(monotonicity,[status(thm)],[1200, 1403])).
% 1.23/1.20 tff(1405,plain,
% 1.23/1.20 (((~solution1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~($sum(B!16, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), Pos!4)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))), 0)) | $greatereq($sum(tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))), $product(-1, I!11)), 0)) <=> ((~solution1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~($sum(N!5, $product(-1, B!16)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))), 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), Pos!4)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))))), 0))),
% 1.23/1.20 inference(transitivity,[status(thm)],[1404, 1399])).
% 1.23/1.20 tff(1406,plain,
% 1.23/1.20 (((~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos!4)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), 0)) | $greatereq($sum(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), $product(-1, I!11)), 0))) | ((~solution1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~($sum(B!16, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), Pos!4)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))), 0)) | $greatereq($sum(tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))), $product(-1, I!11)), 0))) <=> ((~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos!4)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), 0)) | $greatereq($sum(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), $product(-1, I!11)), 0))) | ((~solution1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~($sum(N!5, $product(-1, B!16)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))), 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), Pos!4)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))))), 0)))),
% 1.23/1.20 inference(monotonicity,[status(thm)],[1405])).
% 1.23/1.20 tff(1407,plain,
% 1.23/1.20 (((~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos!4)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), 0)) | $greatereq($sum(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), $product(-1, I!11)), 0))) | ((~solution1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~($sum(B!16, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), Pos!4)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))), 0)) | $greatereq($sum(tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))), $product(-1, I!11)), 0))) <=> ((~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos!4)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), 0)) | $greatereq($sum(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), $product(-1, I!11)), 0))) | (~solution1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~($sum(N!5, $product(-1, B!16)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))), 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), Pos!4)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))))), 0))),
% 1.23/1.20 inference(transitivity,[status(thm)],[1406, 1398])).
% 1.23/1.20 tff(1408,plain,
% 1.23/1.20 ((~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos!4)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), 0)) | $greatereq($sum(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), $product(-1, I!11)), 0))) | ((~solution1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~($sum(B!16, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), Pos!4)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))), 0)) | $greatereq($sum(tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))), $product(-1, I!11)), 0))),
% 1.23/1.20 inference(quant_inst,[status(thm)],[])).
% 1.23/1.20 tff(1409,plain,
% 1.23/1.20 ((~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B, t2tb2(B1))), Pos!4)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), 0)) | $greatereq($sum(tb2t(get(int, int, t2tb2(B1), t2tb(Pos!4))), $product(-1, I!11)), 0))) | (~solution1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~($sum(N!5, $product(-1, B!16)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))), 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), Pos!4)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))))), 0)),
% 1.23/1.20 inference(modus_ponens,[status(thm)],[1408, 1407])).
% 1.23/1.20 tff(1410,plain,
% 1.23/1.20 ((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), Pos!4)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))))), 0)),
% 1.23/1.20 inference(unit_resolution,[status(thm)],[1409, 618, 1195, 1193, 1191, 1397])).
% 1.23/1.20 tff(1411,plain,
% 1.23/1.20 (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), Pos!4)),
% 1.23/1.20 inference(unit_resolution,[status(thm)],[1410, 1395])).
% 1.23/1.20 tff(1412,plain,
% 1.23/1.20 (((~![B1: array_int, B2: array_int, Pos: $int] : ((~eq_board1(B1, B2, Pos)) | eq_board1(B2, B1, Pos))) | ((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), Pos!4)) | eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), Pos!4))) <=> ((~![B1: array_int, B2: array_int, Pos: $int] : ((~eq_board1(B1, B2, Pos)) | eq_board1(B2, B1, Pos))) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), Pos!4)) | eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), Pos!4))),
% 1.23/1.20 inference(rewrite,[status(thm)],[])).
% 1.23/1.20 tff(1413,plain,
% 1.23/1.20 ((~![B1: array_int, B2: array_int, Pos: $int] : ((~eq_board1(B1, B2, Pos)) | eq_board1(B2, B1, Pos))) | ((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), Pos!4)) | eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), Pos!4))),
% 1.23/1.20 inference(quant_inst,[status(thm)],[])).
% 1.23/1.20 tff(1414,plain,
% 1.23/1.20 ((~![B1: array_int, B2: array_int, Pos: $int] : ((~eq_board1(B1, B2, Pos)) | eq_board1(B2, B1, Pos))) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), Pos!4)) | eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), Pos!4)),
% 1.23/1.20 inference(modus_ponens,[status(thm)],[1413, 1412])).
% 1.23/1.20 tff(1415,plain,
% 1.23/1.20 (eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), Pos!4)),
% 1.23/1.20 inference(unit_resolution,[status(thm)],[1414, 561, 1179])).
% 1.23/1.20 tff(1416,plain,
% 1.23/1.20 (((~![B1: array_int, B2: array_int, B3: array_int, Pos: $int] : (eq_board1(B1, B3, Pos) | (~eq_board1(B2, B3, Pos)) | (~eq_board1(B1, B2, Pos)))) | ((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), Pos!4)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), Pos!4)) | eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), Pos!4))) <=> ((~![B1: array_int, B2: array_int, B3: array_int, Pos: $int] : (eq_board1(B1, B3, Pos) | (~eq_board1(B2, B3, Pos)) | (~eq_board1(B1, B2, Pos)))) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), Pos!4)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), Pos!4)) | eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), Pos!4))),
% 1.23/1.20 inference(rewrite,[status(thm)],[])).
% 1.23/1.20 tff(1417,plain,
% 1.23/1.20 ((eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), Pos!4) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), Pos!4)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), Pos!4))) <=> ((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), Pos!4)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), Pos!4)) | eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), Pos!4))),
% 1.23/1.20 inference(rewrite,[status(thm)],[])).
% 1.23/1.20 tff(1418,plain,
% 1.23/1.20 (((~![B1: array_int, B2: array_int, B3: array_int, Pos: $int] : (eq_board1(B1, B3, Pos) | (~eq_board1(B2, B3, Pos)) | (~eq_board1(B1, B2, Pos)))) | (eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), Pos!4) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), Pos!4)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), Pos!4)))) <=> ((~![B1: array_int, B2: array_int, B3: array_int, Pos: $int] : (eq_board1(B1, B3, Pos) | (~eq_board1(B2, B3, Pos)) | (~eq_board1(B1, B2, Pos)))) | ((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), Pos!4)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), Pos!4)) | eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), Pos!4)))),
% 1.23/1.20 inference(monotonicity,[status(thm)],[1417])).
% 1.23/1.20 tff(1419,plain,
% 1.23/1.20 (((~![B1: array_int, B2: array_int, B3: array_int, Pos: $int] : (eq_board1(B1, B3, Pos) | (~eq_board1(B2, B3, Pos)) | (~eq_board1(B1, B2, Pos)))) | (eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), Pos!4) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), Pos!4)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), Pos!4)))) <=> ((~![B1: array_int, B2: array_int, B3: array_int, Pos: $int] : (eq_board1(B1, B3, Pos) | (~eq_board1(B2, B3, Pos)) | (~eq_board1(B1, B2, Pos)))) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), Pos!4)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), Pos!4)) | eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), Pos!4))),
% 1.23/1.20 inference(transitivity,[status(thm)],[1418, 1416])).
% 1.23/1.20 tff(1420,plain,
% 1.23/1.20 ((~![B1: array_int, B2: array_int, B3: array_int, Pos: $int] : (eq_board1(B1, B3, Pos) | (~eq_board1(B2, B3, Pos)) | (~eq_board1(B1, B2, Pos)))) | (eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), Pos!4) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), Pos!4)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), Pos!4)))),
% 1.23/1.20 inference(quant_inst,[status(thm)],[])).
% 1.23/1.20 tff(1421,plain,
% 1.23/1.20 ((~![B1: array_int, B2: array_int, B3: array_int, Pos: $int] : (eq_board1(B1, B3, Pos) | (~eq_board1(B2, B3, Pos)) | (~eq_board1(B1, B2, Pos)))) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), Pos!4)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), Pos!4)) | eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board2!10))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), Pos!4)),
% 1.23/1.20 inference(modus_ponens,[status(thm)],[1420, 1419])).
% 1.23/1.20 tff(1422,plain,
% 1.23/1.20 ($false),
% 1.23/1.20 inference(unit_resolution,[status(thm)],[1421, 587, 1287, 1415, 1411])).
% 1.23/1.20 tff(1423,plain,((~$greatereq(Board!7, 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B, t2tb2(B1))), $sum(1, Pos!4))))) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), Pos!4)) | (~($sum(N!5, $product(-1, B!16)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))), 0))))))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.21 tff(1424,plain,
% 1.23/1.21 ($lesseq($sum(Pos!4, $product(-1, N!5)), -1) | $greatereq($sum(Pos!4, $product(-1, N!5)), 0)),
% 1.23/1.21 inference(theory_lemma,[status(thm)],[])).
% 1.23/1.21 tff(1425,plain,
% 1.23/1.21 ($lesseq($sum(Pos!4, $product(-1, N!5)), -1)),
% 1.23/1.21 inference(unit_resolution,[status(thm)],[1424, 48])).
% 1.23/1.21 tff(1426,plain,
% 1.23/1.21 ($greatereq(Pos!4, -1) | (~$greatereq(Pos!4, 0))),
% 1.23/1.21 inference(theory_lemma,[status(thm)],[])).
% 1.23/1.21 tff(1427,plain,
% 1.23/1.21 ($greatereq(Pos!4, -1)),
% 1.23/1.21 inference(unit_resolution,[status(thm)],[1426, 260])).
% 1.23/1.21 tff(1428,plain,
% 1.23/1.21 ((~((~$lesseq($sum(Pos!4, $product(-1, N!5)), 0)) | (~($sum(N!5, $product(-1, Board!7)) = 0)) | (~$greatereq(Pos!4, -1)) | (~$lesseq($sum(Pos!4, $product(-1, N!5)), -1)) | (~solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~((~$greatereq(Board!7, 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B, t2tb2(B1))), $sum(1, Pos!4))))) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), Pos!4)) | (~($sum(N!5, $product(-1, B!16)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))), 0)))))))))) | (~$lesseq($sum(Pos!4, $product(-1, N!5)), 0)) | (~($sum(N!5, $product(-1, Board!7)) = 0)) | (~$greatereq(Pos!4, -1)) | (~$lesseq($sum(Pos!4, $product(-1, N!5)), -1)) | (~solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~((~$greatereq(Board!7, 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B, t2tb2(B1))), $sum(1, Pos!4))))) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), Pos!4)) | (~($sum(N!5, $product(-1, B!16)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))), 0))))))))),
% 1.23/1.21 inference(tautology,[status(thm)],[])).
% 1.23/1.21 tff(1429,plain,
% 1.23/1.21 ((~((~$lesseq($sum(Pos!4, $product(-1, N!5)), 0)) | (~($sum(N!5, $product(-1, Board!7)) = 0)) | (~$greatereq(Pos!4, -1)) | (~$lesseq($sum(Pos!4, $product(-1, N!5)), -1)) | (~solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~((~$greatereq(Board!7, 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B, t2tb2(B1))), $sum(1, Pos!4))))) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), Pos!4)) | (~($sum(N!5, $product(-1, B!16)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))), 0)))))))))) | (~$greatereq(Pos!4, -1)) | (~$lesseq($sum(Pos!4, $product(-1, N!5)), -1)) | (~solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~((~$greatereq(Board!7, 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B, t2tb2(B1))), $sum(1, Pos!4))))) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), Pos!4)) | (~($sum(N!5, $product(-1, B!16)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))), 0))))))))),
% 1.23/1.21 inference(unit_resolution,[status(thm)],[1428, 118, 24])).
% 1.23/1.21 tff(1430,plain,
% 1.23/1.21 ((~((~$lesseq($sum(Pos!4, $product(-1, N!5)), 0)) | (~($sum(N!5, $product(-1, Board!7)) = 0)) | (~$greatereq(Pos!4, -1)) | (~$lesseq($sum(Pos!4, $product(-1, N!5)), -1)) | (~solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~((~$greatereq(Board!7, 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B, t2tb2(B1))), $sum(1, Pos!4))))) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), Pos!4)) | (~($sum(N!5, $product(-1, B!16)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))), 0)))))))))) | (~$lesseq($sum(Pos!4, $product(-1, N!5)), -1)) | (~solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~((~$greatereq(Board!7, 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B, t2tb2(B1))), $sum(1, Pos!4))))) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), Pos!4)) | (~($sum(N!5, $product(-1, B!16)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))), 0))))))))),
% 1.23/1.21 inference(unit_resolution,[status(thm)],[1429, 1427])).
% 1.23/1.21 tff(1431,plain,
% 1.23/1.21 ((~((~$lesseq($sum(Pos!4, $product(-1, N!5)), 0)) | (~($sum(N!5, $product(-1, Board!7)) = 0)) | (~$greatereq(Pos!4, -1)) | (~$lesseq($sum(Pos!4, $product(-1, N!5)), -1)) | (~solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~((~$greatereq(Board!7, 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B, t2tb2(B1))), $sum(1, Pos!4))))) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), Pos!4)) | (~($sum(N!5, $product(-1, B!16)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))), 0)))))))))) | (~solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~((~$greatereq(Board!7, 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B, t2tb2(B1))), $sum(1, Pos!4))))) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), Pos!4)) | (~($sum(N!5, $product(-1, B!16)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))), 0))))))))),
% 1.23/1.21 inference(unit_resolution,[status(thm)],[1430, 1425])).
% 1.23/1.21 tff(1432,plain,
% 1.23/1.21 ((~((~$lesseq($sum(Pos!4, $product(-1, N!5)), 0)) | (~($sum(N!5, $product(-1, Board!7)) = 0)) | (~$greatereq(Pos!4, -1)) | (~$lesseq($sum(Pos!4, $product(-1, N!5)), -1)) | (~solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~((~$greatereq(Board!7, 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B, t2tb2(B1))), $sum(1, Pos!4))))) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), Pos!4)) | (~($sum(N!5, $product(-1, B!16)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))), 0)))))))))) | (~solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4)))),
% 1.23/1.21 inference(unit_resolution,[status(thm)],[1431, 1423])).
% 1.23/1.21 tff(1433,plain,
% 1.23/1.21 (~((~$lesseq($sum(Pos!4, $product(-1, N!5)), 0)) | (~($sum(N!5, $product(-1, Board!7)) = 0)) | (~$greatereq(Pos!4, -1)) | (~$lesseq($sum(Pos!4, $product(-1, N!5)), -1)) | (~solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~((~$greatereq(Board!7, 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B, t2tb2(B1))), $sum(1, Pos!4))))) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), Pos!4)) | (~($sum(N!5, $product(-1, B!16)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))), 0)))))))))),
% 1.23/1.21 inference(unit_resolution,[status(thm)],[1432, 1109])).
% 1.23/1.21 tff(1434,plain,
% 1.23/1.21 (((~(Result!13 = true1)) | (~((~$lesseq($sum(Pos!4, $product(-1, N!5)), 0)) | (~($sum(N!5, $product(-1, Board!7)) = 0)) | (~$greatereq(Pos!4, -1)) | (~$lesseq($sum(Pos!4, $product(-1, N!5)), -1)) | (~solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~((~$greatereq(Board!7, 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B, t2tb2(B1))), $sum(1, Pos!4))))) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), Pos!4)) | (~($sum(N!5, $product(-1, B!16)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))), 0))))))))))) | ((~$lesseq($sum(Pos!4, $product(-1, N!5)), 0)) | (~($sum(N!5, $product(-1, Board!7)) = 0)) | (~$greatereq(Pos!4, -1)) | (~$lesseq($sum(Pos!4, $product(-1, N!5)), -1)) | (~solution1(tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~((~$greatereq(Board!7, 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board3!12))), $sum(1, Pos!4))) | (~![B: $int, B1: map_int_int] : ((~solution1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B, t2tb2(B1))), N!5)) | (~($sum(B, $product(-1, N!5)) = 0)) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B, t2tb2(B1))), $sum(1, Pos!4))))) | (~((~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, Board!7, t2tb2(Board1!6))), Pos!4)) | (~((~solution1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | (~is_board1(tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), N!5)) | $lesseq($sum(I!11, $product(-1, tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))))), -1) | (~eq_board1(tb2t1(mk_array1(int, Board!7, t2tb2(Board4!14))), tb2t1(mk_array1(int, B!16, t2tb2(B1!15))), Pos!4)) | (~($sum(N!5, $product(-1, B!16)) = 0)) | (~$greatereq(tb2t(get(int, int, t2tb2(B1!15), t2tb(Pos!4))), 0)))))))))),
% 1.23/1.22 inference(tautology,[status(thm)],[])).
% 1.23/1.22 tff(1435,plain,
% 1.23/1.22 ($false),
% 1.23/1.22 inference(unit_resolution,[status(thm)],[1434, 1433, 919])).
% 1.23/1.22 % SZS output end Proof
%------------------------------------------------------------------------------