TSTP Solution File: SWW634_2 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWW634_2 : TPTP v8.1.0. Released v6.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n002.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 20:59:30 EDT 2022
% Result : Theorem 0.22s 0.49s
% Output : Proof 0.47s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : SWW634_2 : TPTP v8.1.0. Released v6.1.0.
% 0.14/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.35 % Computer : n002.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 20:40:33 EDT 2022
% 0.14/0.35 % 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.
% 0.22/0.49 % SZS status Theorem
% 0.22/0.49 % SZS output start Proof
% 0.22/0.49 tff(eq_prefix1_type, type, (
% 0.22/0.49 eq_prefix1: ( ty * uni * uni * $int ) > $o)).
% 0.22/0.49 tff(t2tb2_type, type, (
% 0.22/0.49 t2tb2: map_int_int > uni)).
% 0.22/0.49 tff(tptp_fun_T_19_type, type, (
% 0.22/0.49 tptp_fun_T_19: map_int_int)).
% 0.22/0.49 tff(tptp_fun_Col1_14_type, type, (
% 0.22/0.49 tptp_fun_Col1_14: map_int_int)).
% 0.22/0.49 tff(int_type, type, (
% 0.22/0.49 int: ty)).
% 0.22/0.49 tff(tptp_fun_K1_15_type, type, (
% 0.22/0.49 tptp_fun_K1_15: $int)).
% 0.22/0.49 tff(tptp_fun_K_10_type, type, (
% 0.22/0.49 tptp_fun_K_10: $int)).
% 0.22/0.49 tff(partial_solution1_type, type, (
% 0.22/0.49 partial_solution1: ( $int * map_int_int ) > $o)).
% 0.22/0.49 tff(tptp_fun_Col_9_type, type, (
% 0.22/0.49 tptp_fun_Col_9: map_int_int)).
% 0.22/0.49 tff(tb2t1_type, type, (
% 0.22/0.49 tb2t1: uni > $int)).
% 0.22/0.49 tff(get_type, type, (
% 0.22/0.49 get: ( ty * ty * uni * uni ) > uni)).
% 0.22/0.49 tff(t2tb1_type, type, (
% 0.22/0.49 t2tb1: $int > uni)).
% 0.22/0.49 tff(tptp_fun_J_23_type, type, (
% 0.22/0.49 tptp_fun_J_23: $int > $int)).
% 0.22/0.49 tff(mem_type, type, (
% 0.22/0.49 mem: ( ty * uni * uni ) > $o)).
% 0.22/0.49 tff(empty_type, type, (
% 0.22/0.49 empty: ty > uni)).
% 0.22/0.49 tff(tptp_fun_J_22_type, type, (
% 0.22/0.49 tptp_fun_J_22: $int > $int)).
% 0.22/0.49 tff(tptp_fun_J_21_type, type, (
% 0.22/0.49 tptp_fun_J_21: $int > $int)).
% 0.22/0.49 tff(t2tb_type, type, (
% 0.22/0.49 t2tb: set_int > uni)).
% 0.22/0.49 tff(below1_type, type, (
% 0.22/0.49 below1: $int > set_int)).
% 0.22/0.49 tff(tptp_fun_Q_13_type, type, (
% 0.22/0.49 tptp_fun_Q_13: $int)).
% 0.22/0.49 tff(n1_type, type, (
% 0.22/0.49 n1: $int)).
% 0.22/0.49 tff(tptp_fun_S_12_type, type, (
% 0.22/0.49 tptp_fun_S_12: $int)).
% 0.22/0.49 tff(cardinal1_type, type, (
% 0.22/0.49 cardinal1: ( ty * uni ) > $int)).
% 0.22/0.49 tff(t2tb3_type, type, (
% 0.22/0.49 t2tb3: map_int_lpmap_int_intrp > uni)).
% 0.22/0.49 tff(tptp_fun_Sol1_16_type, type, (
% 0.22/0.49 tptp_fun_Sol1_16: map_int_lpmap_int_intrp)).
% 0.22/0.49 tff(map_type, type, (
% 0.22/0.49 map: ( ty * ty ) > ty)).
% 0.22/0.49 tff(tptp_fun_S1_17_type, type, (
% 0.22/0.49 tptp_fun_S1_17: $int)).
% 0.22/0.49 tff(tptp_fun_I_20_type, type, (
% 0.22/0.49 tptp_fun_I_20: $int)).
% 0.22/0.49 tff(sorted1_type, type, (
% 0.22/0.49 sorted1: ( map_int_lpmap_int_intrp * $int * $int ) > $o)).
% 0.22/0.49 tff(tptp_fun_Sol_11_type, type, (
% 0.22/0.49 tptp_fun_Sol_11: map_int_lpmap_int_intrp)).
% 0.22/0.49 tff(tptp_fun_I_18_type, type, (
% 0.22/0.49 tptp_fun_I_18: map_int_int > $int)).
% 0.22/0.49 tff(tptp_fun_K_3_type, type, (
% 0.22/0.49 tptp_fun_K_3: ( $int * uni * uni * ty ) > $int)).
% 0.22/0.49 tff(1,plain,
% 0.22/0.49 ((($lesseq($sum(S!12, $product(-1, S1!17)), 0) & ($sum(K!10, $product(-1, K1!15)) = 0) & sorted1(Sol1!16, S!12, S1!17) & ![T: map_int_int] : (((~(partial_solution1(n1, T) & eq_prefix1(int, t2tb2(Col1!14), t2tb2(T), K1!15))) | ($lesseq($sum(S!12, $product(-1, tptp_fun_I_18(T))), 0) & (~$lesseq($sum(S1!17, $product(-1, tptp_fun_I_18(T))), 0)) & eq_prefix1(int, t2tb2(T), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(tptp_fun_I_18(T))), n1))) & ((partial_solution1(n1, T) & eq_prefix1(int, t2tb2(Col1!14), t2tb2(T), K1!15)) | ![I: $int] : (~($greatereq($sum(I, $product(-1, S!12)), 0) & (~$greatereq($sum(I, $product(-1, S1!17)), 0)) & eq_prefix1(int, t2tb2(T), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(I)), n1))))) & eq_prefix1(int, t2tb2(Col!9), t2tb2(Col1!14), K1!15) & eq_prefix1(map(int, int), t2tb3(Sol!11), t2tb3(Sol1!16), S!12) & ((~(S!12 = 0)) | (~sorted1(Sol1!16, 0, S1!17)) | ((partial_solution1(n1, T!19) | ($greatereq(I!20, 0) & (~$greatereq($sum(S!12, $sum($product(-1, S1!17), I!20)), 0)) & eq_prefix1(int, t2tb2(T!19), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(I!20)), n1))) & ((~partial_solution1(n1, T!19)) | ![I: $int] : (~($greatereq(I, 0) & (~$greatereq($sum(I, $sum(S!12, $product(-1, S1!17))), 0)) & eq_prefix1(int, t2tb2(T!19), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(I)), n1))))))) & ($greatereq(Q!13, 0) & ($sum(n1, $product(-1, Q!13)) = 0) & (S!12 = 0) & (K!10 = 0)) & ($greatereq(K!10, 0) & ($sum(n1, $sum($product(-1, K!10), $product(-1, cardinal1(int, t2tb(below1(Q!13)))))) = 0) & $greatereq(S!12, 0) & ![I: $int] : (((~mem(int, t2tb1(I), t2tb(below1(Q!13)))) | ($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, n1)), 0)) & ![J: $int] : ((~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, K!10)), 0)))) | (~($sum(I, $product(-1, tb2t1(get(int, int, t2tb2(Col!9), t2tb1(J))))) = 0))))) & ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, n1)), 0) | mem(int, t2tb1(I), t2tb(below1(Q!13))) | (~((~($greatereq(tptp_fun_J_21(I), 0) & (~$lesseq($sum(K!10, $product(-1, tptp_fun_J_21(I))), 0)))) | (~($sum(I, $product(-1, tb2t1(get(int, int, t2tb2(Col!9), t2tb1(tptp_fun_J_21(I)))))) = 0)))))) & ![I: $int] : ((~$greatereq(I, 0)) | ((mem(int, t2tb1(I), empty(int)) | ![J: $int] : ((~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, K!10)), 0)))) | (~($sum(I, $sum(J, $sum($product(-1, K!10), $product(-1, tb2t1(get(int, int, t2tb2(Col!9), t2tb1(J))))))) = 0)))) & ((~mem(int, t2tb1(I), empty(int))) | (~((~($greatereq(tptp_fun_J_22(I), 0) & (~$lesseq($sum(K!10, $product(-1, tptp_fun_J_22(I))), 0)))) | (~($sum(I, $sum($product(-1, K!10), $sum(tptp_fun_J_22(I), $product(-1, tb2t1(get(int, int, t2tb2(Col!9), t2tb1(tptp_fun_J_22(I)))))))) = 0))))))) & ![I: $int] : ((~$greatereq(I, 0)) | ((mem(int, t2tb1(I), empty(int)) | ![J: $int] : ((~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, K!10)), 0)))) | (~($sum(I, $sum($product(-1, J), $sum(K!10, $product(-1, tb2t1(get(int, int, t2tb2(Col!9), t2tb1(J))))))) = 0)))) & ((~mem(int, t2tb1(I), empty(int))) | (~((~($greatereq(tptp_fun_J_23(I), 0) & (~$lesseq($sum(K!10, $product(-1, tptp_fun_J_23(I))), 0)))) | (~($sum(I, $sum(K!10, $sum($product(-1, tptp_fun_J_23(I)), $product(-1, tb2t1(get(int, int, t2tb2(Col!9), t2tb1(tptp_fun_J_23(I)))))))) = 0))))))) & partial_solution1(K!10, Col!9))) <=> ($lesseq($sum(S!12, $product(-1, S1!17)), 0) & ($sum(K!10, $product(-1, K1!15)) = 0) & sorted1(Sol1!16, S!12, S1!17) & ![T: map_int_int] : (((~(partial_solution1(n1, T) & eq_prefix1(int, t2tb2(Col1!14), t2tb2(T), K1!15))) | ($lesseq($sum(S!12, $product(-1, tptp_fun_I_18(T))), 0) & (~$lesseq($sum(S1!17, $product(-1, tptp_fun_I_18(T))), 0)) & eq_prefix1(int, t2tb2(T), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(tptp_fun_I_18(T))), n1))) & ((partial_solution1(n1, T) & eq_prefix1(int, t2tb2(Col1!14), t2tb2(T), K1!15)) | ![I: $int] : (~($greatereq($sum(I, $product(-1, S!12)), 0) & (~$greatereq($sum(I, $product(-1, S1!17)), 0)) & eq_prefix1(int, t2tb2(T), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(I)), n1))))) & eq_prefix1(int, t2tb2(Col!9), t2tb2(Col1!14), K1!15) & eq_prefix1(map(int, int), t2tb3(Sol!11), t2tb3(Sol1!16), S!12) & ((~(S!12 = 0)) | (~sorted1(Sol1!16, 0, S1!17)) | ((partial_solution1(n1, T!19) | ($greatereq(I!20, 0) & (~$greatereq($sum(S!12, $sum($product(-1, S1!17), I!20)), 0)) & eq_prefix1(int, t2tb2(T!19), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(I!20)), n1))) & ((~partial_solution1(n1, T!19)) | ![I: $int] : (~($greatereq(I, 0) & (~$greatereq($sum(I, $sum(S!12, $product(-1, S1!17))), 0)) & eq_prefix1(int, t2tb2(T!19), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(I)), n1)))))) & $greatereq(Q!13, 0) & ($sum(n1, $product(-1, Q!13)) = 0) & (S!12 = 0) & (K!10 = 0) & $greatereq(K!10, 0) & ($sum(n1, $sum($product(-1, K!10), $product(-1, cardinal1(int, t2tb(below1(Q!13)))))) = 0) & $greatereq(S!12, 0) & ![I: $int] : (((~mem(int, t2tb1(I), t2tb(below1(Q!13)))) | ($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, n1)), 0)) & ![J: $int] : ((~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, K!10)), 0)))) | (~($sum(I, $product(-1, tb2t1(get(int, int, t2tb2(Col!9), t2tb1(J))))) = 0))))) & ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, n1)), 0) | mem(int, t2tb1(I), t2tb(below1(Q!13))) | (~((~($greatereq(tptp_fun_J_21(I), 0) & (~$lesseq($sum(K!10, $product(-1, tptp_fun_J_21(I))), 0)))) | (~($sum(I, $product(-1, tb2t1(get(int, int, t2tb2(Col!9), t2tb1(tptp_fun_J_21(I)))))) = 0)))))) & ![I: $int] : ((~$greatereq(I, 0)) | ((mem(int, t2tb1(I), empty(int)) | ![J: $int] : ((~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, K!10)), 0)))) | (~($sum(I, $sum(J, $sum($product(-1, K!10), $product(-1, tb2t1(get(int, int, t2tb2(Col!9), t2tb1(J))))))) = 0)))) & ((~mem(int, t2tb1(I), empty(int))) | (~((~($greatereq(tptp_fun_J_22(I), 0) & (~$lesseq($sum(K!10, $product(-1, tptp_fun_J_22(I))), 0)))) | (~($sum(I, $sum($product(-1, K!10), $sum(tptp_fun_J_22(I), $product(-1, tb2t1(get(int, int, t2tb2(Col!9), t2tb1(tptp_fun_J_22(I)))))))) = 0))))))) & ![I: $int] : ((~$greatereq(I, 0)) | ((mem(int, t2tb1(I), empty(int)) | ![J: $int] : ((~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, K!10)), 0)))) | (~($sum(I, $sum($product(-1, J), $sum(K!10, $product(-1, tb2t1(get(int, int, t2tb2(Col!9), t2tb1(J))))))) = 0)))) & ((~mem(int, t2tb1(I), empty(int))) | (~((~($greatereq(tptp_fun_J_23(I), 0) & (~$lesseq($sum(K!10, $product(-1, tptp_fun_J_23(I))), 0)))) | (~($sum(I, $sum(K!10, $sum($product(-1, tptp_fun_J_23(I)), $product(-1, tb2t1(get(int, int, t2tb2(Col!9), t2tb1(tptp_fun_J_23(I)))))))) = 0))))))) & partial_solution1(K!10, Col!9))),
% 0.22/0.49 inference(rewrite,[status(thm)],[])).
% 0.22/0.49 tff(2,plain,
% 0.22/0.49 (($greatereq(K!10, 0) & ($sum(K!10, $sum($product(-1, n1), cardinal1(int, t2tb(below1(Q!13))))) = 0) & $greatereq(S!12, 0) & ![I: $int] : (((~mem(int, t2tb1(I), t2tb(below1(Q!13)))) | ($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, n1)), 0)) & ![J: $int] : ((~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, K!10)), 0)))) | (~($sum(I, $product(-1, tb2t1(get(int, int, t2tb2(Col!9), t2tb1(J))))) = 0))))) & (mem(int, t2tb1(I), t2tb(below1(Q!13))) | ((~$greatereq(I, 0)) | (~(~$greatereq($sum(I, $product(-1, n1)), 0))) | (~((~($greatereq(tptp_fun_J_21(I), 0) & (~$greatereq($sum(tptp_fun_J_21(I), $product(-1, K!10)), 0)))) | (~($sum(I, $product(-1, tb2t1(get(int, int, t2tb2(Col!9), t2tb1(tptp_fun_J_21(I)))))) = 0))))))) & ![I: $int] : ((~$greatereq(I, 0)) | (((~(~mem(int, t2tb1(I), empty(int)))) | ![J: $int] : ((~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, K!10)), 0)))) | (~($sum(I, $sum(J, $sum($product(-1, tb2t1(get(int, int, t2tb2(Col!9), t2tb1(J)))), $product(-1, K!10)))) = 0)))) & ((~mem(int, t2tb1(I), empty(int))) | (~((~($greatereq(tptp_fun_J_22(I), 0) & (~$greatereq($sum(tptp_fun_J_22(I), $product(-1, K!10)), 0)))) | (~($sum(I, $sum(tptp_fun_J_22(I), $sum($product(-1, tb2t1(get(int, int, t2tb2(Col!9), t2tb1(tptp_fun_J_22(I))))), $product(-1, K!10)))) = 0))))))) & ![I: $int] : ((~$greatereq(I, 0)) | (((~(~mem(int, t2tb1(I), empty(int)))) | ![J: $int] : ((~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, K!10)), 0)))) | (~($sum(I, $sum($product(-1, J), $sum($product(-1, tb2t1(get(int, int, t2tb2(Col!9), t2tb1(J)))), K!10))) = 0)))) & ((~mem(int, t2tb1(I), empty(int))) | (~((~($greatereq(tptp_fun_J_23(I), 0) & (~$greatereq($sum(tptp_fun_J_23(I), $product(-1, K!10)), 0)))) | (~($sum(I, $sum($product(-1, tptp_fun_J_23(I)), $sum($product(-1, tb2t1(get(int, int, t2tb2(Col!9), t2tb1(tptp_fun_J_23(I))))), K!10))) = 0))))))) & partial_solution1(K!10, Col!9)) <=> ($greatereq(K!10, 0) & ($sum(n1, $sum($product(-1, K!10), $product(-1, cardinal1(int, t2tb(below1(Q!13)))))) = 0) & $greatereq(S!12, 0) & ![I: $int] : (((~mem(int, t2tb1(I), t2tb(below1(Q!13)))) | ($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, n1)), 0)) & ![J: $int] : ((~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, K!10)), 0)))) | (~($sum(I, $product(-1, tb2t1(get(int, int, t2tb2(Col!9), t2tb1(J))))) = 0))))) & ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, n1)), 0) | mem(int, t2tb1(I), t2tb(below1(Q!13))) | (~((~($greatereq(tptp_fun_J_21(I), 0) & (~$lesseq($sum(K!10, $product(-1, tptp_fun_J_21(I))), 0)))) | (~($sum(I, $product(-1, tb2t1(get(int, int, t2tb2(Col!9), t2tb1(tptp_fun_J_21(I)))))) = 0)))))) & ![I: $int] : ((~$greatereq(I, 0)) | ((mem(int, t2tb1(I), empty(int)) | ![J: $int] : ((~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, K!10)), 0)))) | (~($sum(I, $sum(J, $sum($product(-1, K!10), $product(-1, tb2t1(get(int, int, t2tb2(Col!9), t2tb1(J))))))) = 0)))) & ((~mem(int, t2tb1(I), empty(int))) | (~((~($greatereq(tptp_fun_J_22(I), 0) & (~$lesseq($sum(K!10, $product(-1, tptp_fun_J_22(I))), 0)))) | (~($sum(I, $sum($product(-1, K!10), $sum(tptp_fun_J_22(I), $product(-1, tb2t1(get(int, int, t2tb2(Col!9), t2tb1(tptp_fun_J_22(I)))))))) = 0))))))) & ![I: $int] : ((~$greatereq(I, 0)) | ((mem(int, t2tb1(I), empty(int)) | ![J: $int] : ((~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, K!10)), 0)))) | (~($sum(I, $sum($product(-1, J), $sum(K!10, $product(-1, tb2t1(get(int, int, t2tb2(Col!9), t2tb1(J))))))) = 0)))) & ((~mem(int, t2tb1(I), empty(int))) | (~((~($greatereq(tptp_fun_J_23(I), 0) & (~$lesseq($sum(K!10, $product(-1, tptp_fun_J_23(I))), 0)))) | (~($sum(I, $sum(K!10, $sum($product(-1, tptp_fun_J_23(I)), $product(-1, tb2t1(get(int, int, t2tb2(Col!9), t2tb1(tptp_fun_J_23(I)))))))) = 0))))))) & partial_solution1(K!10, Col!9))),
% 0.22/0.50 inference(rewrite,[status(thm)],[])).
% 0.22/0.50 tff(3,plain,
% 0.22/0.50 ((~(~($greatereq(Q!13, 0) & ($sum(n1, $product(-1, Q!13)) = 0) & (S!12 = 0) & (K!10 = 0)))) <=> ($greatereq(Q!13, 0) & ($sum(n1, $product(-1, Q!13)) = 0) & (S!12 = 0) & (K!10 = 0))),
% 0.22/0.50 inference(rewrite,[status(thm)],[])).
% 0.22/0.50 tff(4,plain,
% 0.22/0.50 ((($lesseq($sum(S!12, $product(-1, S1!17)), 0) & ($sum(K!10, $product(-1, K1!15)) = 0) & sorted1(Sol1!16, S!12, S1!17) & ![T: map_int_int] : (((~(partial_solution1(n1, T) & eq_prefix1(int, t2tb2(Col1!14), t2tb2(T), K1!15))) | ($lesseq($sum(S!12, $product(-1, tptp_fun_I_18(T))), 0) & (~$lesseq($sum(S1!17, $product(-1, tptp_fun_I_18(T))), 0)) & eq_prefix1(int, t2tb2(T), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(tptp_fun_I_18(T))), n1))) & ((partial_solution1(n1, T) & eq_prefix1(int, t2tb2(Col1!14), t2tb2(T), K1!15)) | ![I: $int] : (~($greatereq($sum(I, $product(-1, S!12)), 0) & (~$greatereq($sum(I, $product(-1, S1!17)), 0)) & eq_prefix1(int, t2tb2(T), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(I)), n1))))) & eq_prefix1(int, t2tb2(Col!9), t2tb2(Col1!14), K1!15) & eq_prefix1(map(int, int), t2tb3(Sol!11), t2tb3(Sol1!16), S!12)) & ((~(S!12 = 0)) | (~sorted1(Sol1!16, 0, S1!17)) | ((partial_solution1(n1, T!19) | ($greatereq(I!20, 0) & (~$greatereq($sum(S!12, $sum($product(-1, S1!17), I!20)), 0)) & eq_prefix1(int, t2tb2(T!19), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(I!20)), n1))) & ((~partial_solution1(n1, T!19)) | ![I: $int] : (~($greatereq(I, 0) & (~$greatereq($sum(I, $sum(S!12, $product(-1, S1!17))), 0)) & eq_prefix1(int, t2tb2(T!19), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(I)), n1))))))) <=> ($lesseq($sum(S!12, $product(-1, S1!17)), 0) & ($sum(K!10, $product(-1, K1!15)) = 0) & sorted1(Sol1!16, S!12, S1!17) & ![T: map_int_int] : (((~(partial_solution1(n1, T) & eq_prefix1(int, t2tb2(Col1!14), t2tb2(T), K1!15))) | ($lesseq($sum(S!12, $product(-1, tptp_fun_I_18(T))), 0) & (~$lesseq($sum(S1!17, $product(-1, tptp_fun_I_18(T))), 0)) & eq_prefix1(int, t2tb2(T), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(tptp_fun_I_18(T))), n1))) & ((partial_solution1(n1, T) & eq_prefix1(int, t2tb2(Col1!14), t2tb2(T), K1!15)) | ![I: $int] : (~($greatereq($sum(I, $product(-1, S!12)), 0) & (~$greatereq($sum(I, $product(-1, S1!17)), 0)) & eq_prefix1(int, t2tb2(T), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(I)), n1))))) & eq_prefix1(int, t2tb2(Col!9), t2tb2(Col1!14), K1!15) & eq_prefix1(map(int, int), t2tb3(Sol!11), t2tb3(Sol1!16), S!12) & ((~(S!12 = 0)) | (~sorted1(Sol1!16, 0, S1!17)) | ((partial_solution1(n1, T!19) | ($greatereq(I!20, 0) & (~$greatereq($sum(S!12, $sum($product(-1, S1!17), I!20)), 0)) & eq_prefix1(int, t2tb2(T!19), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(I!20)), n1))) & ((~partial_solution1(n1, T!19)) | ![I: $int] : (~($greatereq(I, 0) & (~$greatereq($sum(I, $sum(S!12, $product(-1, S1!17))), 0)) & eq_prefix1(int, t2tb2(T!19), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(I)), n1)))))))),
% 0.22/0.50 inference(rewrite,[status(thm)],[])).
% 0.22/0.50 tff(5,plain,
% 0.22/0.50 (((~(S!12 = 0)) | (~sorted1(Sol1!16, 0, S1!17)) | ((partial_solution1(n1, T!19) | ($greatereq(I!20, 0) & (~$greatereq($sum(I!20, $sum(S!12, $product(-1, S1!17))), 0)) & eq_prefix1(int, t2tb2(T!19), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(I!20)), n1))) & ((~partial_solution1(n1, T!19)) | ![I: $int] : (~($greatereq(I, 0) & (~$greatereq($sum(I, $sum(S!12, $product(-1, S1!17))), 0)) & eq_prefix1(int, t2tb2(T!19), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(I)), n1)))))) <=> ((~(S!12 = 0)) | (~sorted1(Sol1!16, 0, S1!17)) | ((partial_solution1(n1, T!19) | ($greatereq(I!20, 0) & (~$greatereq($sum(S!12, $sum($product(-1, S1!17), I!20)), 0)) & eq_prefix1(int, t2tb2(T!19), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(I!20)), n1))) & ((~partial_solution1(n1, T!19)) | ![I: $int] : (~($greatereq(I, 0) & (~$greatereq($sum(I, $sum(S!12, $product(-1, S1!17))), 0)) & eq_prefix1(int, t2tb2(T!19), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(I)), n1))))))),
% 0.22/0.50 inference(rewrite,[status(thm)],[])).
% 0.22/0.50 tff(6,plain,
% 0.22/0.50 (($greatereq($sum(S1!17, $product(-1, S!12)), 0) & ($sum(K1!15, $product(-1, K!10)) = 0) & sorted1(Sol1!16, S!12, S1!17) & ![T: map_int_int] : (((~(partial_solution1(n1, T) & eq_prefix1(int, t2tb2(Col1!14), t2tb2(T), K1!15))) | ($greatereq($sum(tptp_fun_I_18(T), $product(-1, S!12)), 0) & (~$greatereq($sum(tptp_fun_I_18(T), $product(-1, S1!17)), 0)) & eq_prefix1(int, t2tb2(T), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(tptp_fun_I_18(T))), n1))) & ((partial_solution1(n1, T) & eq_prefix1(int, t2tb2(Col1!14), t2tb2(T), K1!15)) | ![I: $int] : (~($greatereq($sum(I, $product(-1, S!12)), 0) & (~$greatereq($sum(I, $product(-1, S1!17)), 0)) & eq_prefix1(int, t2tb2(T), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(I)), n1))))) & eq_prefix1(int, t2tb2(Col!9), t2tb2(Col1!14), K1!15) & eq_prefix1(map(int, int), t2tb3(Sol!11), t2tb3(Sol1!16), S!12)) <=> ($lesseq($sum(S!12, $product(-1, S1!17)), 0) & ($sum(K!10, $product(-1, K1!15)) = 0) & sorted1(Sol1!16, S!12, S1!17) & ![T: map_int_int] : (((~(partial_solution1(n1, T) & eq_prefix1(int, t2tb2(Col1!14), t2tb2(T), K1!15))) | ($lesseq($sum(S!12, $product(-1, tptp_fun_I_18(T))), 0) & (~$lesseq($sum(S1!17, $product(-1, tptp_fun_I_18(T))), 0)) & eq_prefix1(int, t2tb2(T), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(tptp_fun_I_18(T))), n1))) & ((partial_solution1(n1, T) & eq_prefix1(int, t2tb2(Col1!14), t2tb2(T), K1!15)) | ![I: $int] : (~($greatereq($sum(I, $product(-1, S!12)), 0) & (~$greatereq($sum(I, $product(-1, S1!17)), 0)) & eq_prefix1(int, t2tb2(T), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(I)), n1))))) & eq_prefix1(int, t2tb2(Col!9), t2tb2(Col1!14), K1!15) & eq_prefix1(map(int, int), t2tb3(Sol!11), t2tb3(Sol1!16), S!12))),
% 0.22/0.50 inference(rewrite,[status(thm)],[])).
% 0.22/0.50 tff(7,plain,
% 0.22/0.50 ((($greatereq($sum(S1!17, $product(-1, S!12)), 0) & ($sum(K1!15, $product(-1, K!10)) = 0) & sorted1(Sol1!16, S!12, S1!17) & ![T: map_int_int] : (((~(partial_solution1(n1, T) & eq_prefix1(int, t2tb2(Col1!14), t2tb2(T), K1!15))) | ($greatereq($sum(tptp_fun_I_18(T), $product(-1, S!12)), 0) & (~$greatereq($sum(tptp_fun_I_18(T), $product(-1, S1!17)), 0)) & eq_prefix1(int, t2tb2(T), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(tptp_fun_I_18(T))), n1))) & ((partial_solution1(n1, T) & eq_prefix1(int, t2tb2(Col1!14), t2tb2(T), K1!15)) | ![I: $int] : (~($greatereq($sum(I, $product(-1, S!12)), 0) & (~$greatereq($sum(I, $product(-1, S1!17)), 0)) & eq_prefix1(int, t2tb2(T), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(I)), n1))))) & eq_prefix1(int, t2tb2(Col!9), t2tb2(Col1!14), K1!15) & eq_prefix1(map(int, int), t2tb3(Sol!11), t2tb3(Sol1!16), S!12)) & ((~(S!12 = 0)) | (~sorted1(Sol1!16, 0, S1!17)) | ((partial_solution1(n1, T!19) | ($greatereq(I!20, 0) & (~$greatereq($sum(I!20, $sum(S!12, $product(-1, S1!17))), 0)) & eq_prefix1(int, t2tb2(T!19), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(I!20)), n1))) & ((~partial_solution1(n1, T!19)) | ![I: $int] : (~($greatereq(I, 0) & (~$greatereq($sum(I, $sum(S!12, $product(-1, S1!17))), 0)) & eq_prefix1(int, t2tb2(T!19), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(I)), n1))))))) <=> (($lesseq($sum(S!12, $product(-1, S1!17)), 0) & ($sum(K!10, $product(-1, K1!15)) = 0) & sorted1(Sol1!16, S!12, S1!17) & ![T: map_int_int] : (((~(partial_solution1(n1, T) & eq_prefix1(int, t2tb2(Col1!14), t2tb2(T), K1!15))) | ($lesseq($sum(S!12, $product(-1, tptp_fun_I_18(T))), 0) & (~$lesseq($sum(S1!17, $product(-1, tptp_fun_I_18(T))), 0)) & eq_prefix1(int, t2tb2(T), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(tptp_fun_I_18(T))), n1))) & ((partial_solution1(n1, T) & eq_prefix1(int, t2tb2(Col1!14), t2tb2(T), K1!15)) | ![I: $int] : (~($greatereq($sum(I, $product(-1, S!12)), 0) & (~$greatereq($sum(I, $product(-1, S1!17)), 0)) & eq_prefix1(int, t2tb2(T), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(I)), n1))))) & eq_prefix1(int, t2tb2(Col!9), t2tb2(Col1!14), K1!15) & eq_prefix1(map(int, int), t2tb3(Sol!11), t2tb3(Sol1!16), S!12)) & ((~(S!12 = 0)) | (~sorted1(Sol1!16, 0, S1!17)) | ((partial_solution1(n1, T!19) | ($greatereq(I!20, 0) & (~$greatereq($sum(S!12, $sum($product(-1, S1!17), I!20)), 0)) & eq_prefix1(int, t2tb2(T!19), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(I!20)), n1))) & ((~partial_solution1(n1, T!19)) | ![I: $int] : (~($greatereq(I, 0) & (~$greatereq($sum(I, $sum(S!12, $product(-1, S1!17))), 0)) & eq_prefix1(int, t2tb2(T!19), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(I)), n1)))))))),
% 0.22/0.50 inference(monotonicity,[status(thm)],[6, 5])).
% 0.22/0.50 tff(8,plain,
% 0.22/0.50 ((($greatereq($sum(S1!17, $product(-1, S!12)), 0) & ($sum(K1!15, $product(-1, K!10)) = 0) & sorted1(Sol1!16, S!12, S1!17) & ![T: map_int_int] : (((~(partial_solution1(n1, T) & eq_prefix1(int, t2tb2(Col1!14), t2tb2(T), K1!15))) | ($greatereq($sum(tptp_fun_I_18(T), $product(-1, S!12)), 0) & (~$greatereq($sum(tptp_fun_I_18(T), $product(-1, S1!17)), 0)) & eq_prefix1(int, t2tb2(T), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(tptp_fun_I_18(T))), n1))) & ((partial_solution1(n1, T) & eq_prefix1(int, t2tb2(Col1!14), t2tb2(T), K1!15)) | ![I: $int] : (~($greatereq($sum(I, $product(-1, S!12)), 0) & (~$greatereq($sum(I, $product(-1, S1!17)), 0)) & eq_prefix1(int, t2tb2(T), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(I)), n1))))) & eq_prefix1(int, t2tb2(Col!9), t2tb2(Col1!14), K1!15) & eq_prefix1(map(int, int), t2tb3(Sol!11), t2tb3(Sol1!16), S!12)) & ((~(S!12 = 0)) | (~sorted1(Sol1!16, 0, S1!17)) | ((partial_solution1(n1, T!19) | ($greatereq(I!20, 0) & (~$greatereq($sum(I!20, $sum(S!12, $product(-1, S1!17))), 0)) & eq_prefix1(int, t2tb2(T!19), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(I!20)), n1))) & ((~partial_solution1(n1, T!19)) | ![I: $int] : (~($greatereq(I, 0) & (~$greatereq($sum(I, $sum(S!12, $product(-1, S1!17))), 0)) & eq_prefix1(int, t2tb2(T!19), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(I)), n1))))))) <=> ($lesseq($sum(S!12, $product(-1, S1!17)), 0) & ($sum(K!10, $product(-1, K1!15)) = 0) & sorted1(Sol1!16, S!12, S1!17) & ![T: map_int_int] : (((~(partial_solution1(n1, T) & eq_prefix1(int, t2tb2(Col1!14), t2tb2(T), K1!15))) | ($lesseq($sum(S!12, $product(-1, tptp_fun_I_18(T))), 0) & (~$lesseq($sum(S1!17, $product(-1, tptp_fun_I_18(T))), 0)) & eq_prefix1(int, t2tb2(T), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(tptp_fun_I_18(T))), n1))) & ((partial_solution1(n1, T) & eq_prefix1(int, t2tb2(Col1!14), t2tb2(T), K1!15)) | ![I: $int] : (~($greatereq($sum(I, $product(-1, S!12)), 0) & (~$greatereq($sum(I, $product(-1, S1!17)), 0)) & eq_prefix1(int, t2tb2(T), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(I)), n1))))) & eq_prefix1(int, t2tb2(Col!9), t2tb2(Col1!14), K1!15) & eq_prefix1(map(int, int), t2tb3(Sol!11), t2tb3(Sol1!16), S!12) & ((~(S!12 = 0)) | (~sorted1(Sol1!16, 0, S1!17)) | ((partial_solution1(n1, T!19) | ($greatereq(I!20, 0) & (~$greatereq($sum(S!12, $sum($product(-1, S1!17), I!20)), 0)) & eq_prefix1(int, t2tb2(T!19), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(I!20)), n1))) & ((~partial_solution1(n1, T!19)) | ![I: $int] : (~($greatereq(I, 0) & (~$greatereq($sum(I, $sum(S!12, $product(-1, S1!17))), 0)) & eq_prefix1(int, t2tb2(T!19), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(I)), n1)))))))),
% 0.22/0.50 inference(transitivity,[status(thm)],[7, 4])).
% 0.22/0.50 tff(9,plain,
% 0.22/0.50 (((($greatereq($sum(S1!17, $product(-1, S!12)), 0) & ($sum(K1!15, $product(-1, K!10)) = 0) & sorted1(Sol1!16, S!12, S1!17) & ![T: map_int_int] : (((~(partial_solution1(n1, T) & eq_prefix1(int, t2tb2(Col1!14), t2tb2(T), K1!15))) | ($greatereq($sum(tptp_fun_I_18(T), $product(-1, S!12)), 0) & (~$greatereq($sum(tptp_fun_I_18(T), $product(-1, S1!17)), 0)) & eq_prefix1(int, t2tb2(T), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(tptp_fun_I_18(T))), n1))) & ((partial_solution1(n1, T) & eq_prefix1(int, t2tb2(Col1!14), t2tb2(T), K1!15)) | ![I: $int] : (~($greatereq($sum(I, $product(-1, S!12)), 0) & (~$greatereq($sum(I, $product(-1, S1!17)), 0)) & eq_prefix1(int, t2tb2(T), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(I)), n1))))) & eq_prefix1(int, t2tb2(Col!9), t2tb2(Col1!14), K1!15) & eq_prefix1(map(int, int), t2tb3(Sol!11), t2tb3(Sol1!16), S!12)) & ((~(S!12 = 0)) | (~sorted1(Sol1!16, 0, S1!17)) | ((partial_solution1(n1, T!19) | ($greatereq(I!20, 0) & (~$greatereq($sum(I!20, $sum(S!12, $product(-1, S1!17))), 0)) & eq_prefix1(int, t2tb2(T!19), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(I!20)), n1))) & ((~partial_solution1(n1, T!19)) | ![I: $int] : (~($greatereq(I, 0) & (~$greatereq($sum(I, $sum(S!12, $product(-1, S1!17))), 0)) & eq_prefix1(int, t2tb2(T!19), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(I)), n1))))))) & (~(~($greatereq(Q!13, 0) & ($sum(n1, $product(-1, Q!13)) = 0) & (S!12 = 0) & (K!10 = 0)))) & ($greatereq(K!10, 0) & ($sum(K!10, $sum($product(-1, n1), cardinal1(int, t2tb(below1(Q!13))))) = 0) & $greatereq(S!12, 0) & ![I: $int] : (((~mem(int, t2tb1(I), t2tb(below1(Q!13)))) | ($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, n1)), 0)) & ![J: $int] : ((~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, K!10)), 0)))) | (~($sum(I, $product(-1, tb2t1(get(int, int, t2tb2(Col!9), t2tb1(J))))) = 0))))) & (mem(int, t2tb1(I), t2tb(below1(Q!13))) | ((~$greatereq(I, 0)) | (~(~$greatereq($sum(I, $product(-1, n1)), 0))) | (~((~($greatereq(tptp_fun_J_21(I), 0) & (~$greatereq($sum(tptp_fun_J_21(I), $product(-1, K!10)), 0)))) | (~($sum(I, $product(-1, tb2t1(get(int, int, t2tb2(Col!9), t2tb1(tptp_fun_J_21(I)))))) = 0))))))) & ![I: $int] : ((~$greatereq(I, 0)) | (((~(~mem(int, t2tb1(I), empty(int)))) | ![J: $int] : ((~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, K!10)), 0)))) | (~($sum(I, $sum(J, $sum($product(-1, tb2t1(get(int, int, t2tb2(Col!9), t2tb1(J)))), $product(-1, K!10)))) = 0)))) & ((~mem(int, t2tb1(I), empty(int))) | (~((~($greatereq(tptp_fun_J_22(I), 0) & (~$greatereq($sum(tptp_fun_J_22(I), $product(-1, K!10)), 0)))) | (~($sum(I, $sum(tptp_fun_J_22(I), $sum($product(-1, tb2t1(get(int, int, t2tb2(Col!9), t2tb1(tptp_fun_J_22(I))))), $product(-1, K!10)))) = 0))))))) & ![I: $int] : ((~$greatereq(I, 0)) | (((~(~mem(int, t2tb1(I), empty(int)))) | ![J: $int] : ((~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, K!10)), 0)))) | (~($sum(I, $sum($product(-1, J), $sum($product(-1, tb2t1(get(int, int, t2tb2(Col!9), t2tb1(J)))), K!10))) = 0)))) & ((~mem(int, t2tb1(I), empty(int))) | (~((~($greatereq(tptp_fun_J_23(I), 0) & (~$greatereq($sum(tptp_fun_J_23(I), $product(-1, K!10)), 0)))) | (~($sum(I, $sum($product(-1, tptp_fun_J_23(I)), $sum($product(-1, tb2t1(get(int, int, t2tb2(Col!9), t2tb1(tptp_fun_J_23(I))))), K!10))) = 0))))))) & partial_solution1(K!10, Col!9))) <=> (($lesseq($sum(S!12, $product(-1, S1!17)), 0) & ($sum(K!10, $product(-1, K1!15)) = 0) & sorted1(Sol1!16, S!12, S1!17) & ![T: map_int_int] : (((~(partial_solution1(n1, T) & eq_prefix1(int, t2tb2(Col1!14), t2tb2(T), K1!15))) | ($lesseq($sum(S!12, $product(-1, tptp_fun_I_18(T))), 0) & (~$lesseq($sum(S1!17, $product(-1, tptp_fun_I_18(T))), 0)) & eq_prefix1(int, t2tb2(T), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(tptp_fun_I_18(T))), n1))) & ((partial_solution1(n1, T) & eq_prefix1(int, t2tb2(Col1!14), t2tb2(T), K1!15)) | ![I: $int] : (~($greatereq($sum(I, $product(-1, S!12)), 0) & (~$greatereq($sum(I, $product(-1, S1!17)), 0)) & eq_prefix1(int, t2tb2(T), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(I)), n1))))) & eq_prefix1(int, t2tb2(Col!9), t2tb2(Col1!14), K1!15) & eq_prefix1(map(int, int), t2tb3(Sol!11), t2tb3(Sol1!16), S!12) & ((~(S!12 = 0)) | (~sorted1(Sol1!16, 0, S1!17)) | ((partial_solution1(n1, T!19) | ($greatereq(I!20, 0) & (~$greatereq($sum(S!12, $sum($product(-1, S1!17), I!20)), 0)) & eq_prefix1(int, t2tb2(T!19), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(I!20)), n1))) & ((~partial_solution1(n1, T!19)) | ![I: $int] : (~($greatereq(I, 0) & (~$greatereq($sum(I, $sum(S!12, $product(-1, S1!17))), 0)) & eq_prefix1(int, t2tb2(T!19), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(I)), n1))))))) & ($greatereq(Q!13, 0) & ($sum(n1, $product(-1, Q!13)) = 0) & (S!12 = 0) & (K!10 = 0)) & ($greatereq(K!10, 0) & ($sum(n1, $sum($product(-1, K!10), $product(-1, cardinal1(int, t2tb(below1(Q!13)))))) = 0) & $greatereq(S!12, 0) & ![I: $int] : (((~mem(int, t2tb1(I), t2tb(below1(Q!13)))) | ($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, n1)), 0)) & ![J: $int] : ((~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, K!10)), 0)))) | (~($sum(I, $product(-1, tb2t1(get(int, int, t2tb2(Col!9), t2tb1(J))))) = 0))))) & ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, n1)), 0) | mem(int, t2tb1(I), t2tb(below1(Q!13))) | (~((~($greatereq(tptp_fun_J_21(I), 0) & (~$lesseq($sum(K!10, $product(-1, tptp_fun_J_21(I))), 0)))) | (~($sum(I, $product(-1, tb2t1(get(int, int, t2tb2(Col!9), t2tb1(tptp_fun_J_21(I)))))) = 0)))))) & ![I: $int] : ((~$greatereq(I, 0)) | ((mem(int, t2tb1(I), empty(int)) | ![J: $int] : ((~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, K!10)), 0)))) | (~($sum(I, $sum(J, $sum($product(-1, K!10), $product(-1, tb2t1(get(int, int, t2tb2(Col!9), t2tb1(J))))))) = 0)))) & ((~mem(int, t2tb1(I), empty(int))) | (~((~($greatereq(tptp_fun_J_22(I), 0) & (~$lesseq($sum(K!10, $product(-1, tptp_fun_J_22(I))), 0)))) | (~($sum(I, $sum($product(-1, K!10), $sum(tptp_fun_J_22(I), $product(-1, tb2t1(get(int, int, t2tb2(Col!9), t2tb1(tptp_fun_J_22(I)))))))) = 0))))))) & ![I: $int] : ((~$greatereq(I, 0)) | ((mem(int, t2tb1(I), empty(int)) | ![J: $int] : ((~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, K!10)), 0)))) | (~($sum(I, $sum($product(-1, J), $sum(K!10, $product(-1, tb2t1(get(int, int, t2tb2(Col!9), t2tb1(J))))))) = 0)))) & ((~mem(int, t2tb1(I), empty(int))) | (~((~($greatereq(tptp_fun_J_23(I), 0) & (~$lesseq($sum(K!10, $product(-1, tptp_fun_J_23(I))), 0)))) | (~($sum(I, $sum(K!10, $sum($product(-1, tptp_fun_J_23(I)), $product(-1, tb2t1(get(int, int, t2tb2(Col!9), t2tb1(tptp_fun_J_23(I)))))))) = 0))))))) & partial_solution1(K!10, Col!9)))),
% 0.22/0.51 inference(monotonicity,[status(thm)],[8, 3, 2])).
% 0.22/0.51 tff(10,plain,
% 0.22/0.51 (((($greatereq($sum(S1!17, $product(-1, S!12)), 0) & ($sum(K1!15, $product(-1, K!10)) = 0) & sorted1(Sol1!16, S!12, S1!17) & ![T: map_int_int] : (((~(partial_solution1(n1, T) & eq_prefix1(int, t2tb2(Col1!14), t2tb2(T), K1!15))) | ($greatereq($sum(tptp_fun_I_18(T), $product(-1, S!12)), 0) & (~$greatereq($sum(tptp_fun_I_18(T), $product(-1, S1!17)), 0)) & eq_prefix1(int, t2tb2(T), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(tptp_fun_I_18(T))), n1))) & ((partial_solution1(n1, T) & eq_prefix1(int, t2tb2(Col1!14), t2tb2(T), K1!15)) | ![I: $int] : (~($greatereq($sum(I, $product(-1, S!12)), 0) & (~$greatereq($sum(I, $product(-1, S1!17)), 0)) & eq_prefix1(int, t2tb2(T), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(I)), n1))))) & eq_prefix1(int, t2tb2(Col!9), t2tb2(Col1!14), K1!15) & eq_prefix1(map(int, int), t2tb3(Sol!11), t2tb3(Sol1!16), S!12)) & ((~(S!12 = 0)) | (~sorted1(Sol1!16, 0, S1!17)) | ((partial_solution1(n1, T!19) | ($greatereq(I!20, 0) & (~$greatereq($sum(I!20, $sum(S!12, $product(-1, S1!17))), 0)) & eq_prefix1(int, t2tb2(T!19), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(I!20)), n1))) & ((~partial_solution1(n1, T!19)) | ![I: $int] : (~($greatereq(I, 0) & (~$greatereq($sum(I, $sum(S!12, $product(-1, S1!17))), 0)) & eq_prefix1(int, t2tb2(T!19), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(I)), n1))))))) & (~(~($greatereq(Q!13, 0) & ($sum(n1, $product(-1, Q!13)) = 0) & (S!12 = 0) & (K!10 = 0)))) & ($greatereq(K!10, 0) & ($sum(K!10, $sum($product(-1, n1), cardinal1(int, t2tb(below1(Q!13))))) = 0) & $greatereq(S!12, 0) & ![I: $int] : (((~mem(int, t2tb1(I), t2tb(below1(Q!13)))) | ($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, n1)), 0)) & ![J: $int] : ((~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, K!10)), 0)))) | (~($sum(I, $product(-1, tb2t1(get(int, int, t2tb2(Col!9), t2tb1(J))))) = 0))))) & (mem(int, t2tb1(I), t2tb(below1(Q!13))) | ((~$greatereq(I, 0)) | (~(~$greatereq($sum(I, $product(-1, n1)), 0))) | (~((~($greatereq(tptp_fun_J_21(I), 0) & (~$greatereq($sum(tptp_fun_J_21(I), $product(-1, K!10)), 0)))) | (~($sum(I, $product(-1, tb2t1(get(int, int, t2tb2(Col!9), t2tb1(tptp_fun_J_21(I)))))) = 0))))))) & ![I: $int] : ((~$greatereq(I, 0)) | (((~(~mem(int, t2tb1(I), empty(int)))) | ![J: $int] : ((~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, K!10)), 0)))) | (~($sum(I, $sum(J, $sum($product(-1, tb2t1(get(int, int, t2tb2(Col!9), t2tb1(J)))), $product(-1, K!10)))) = 0)))) & ((~mem(int, t2tb1(I), empty(int))) | (~((~($greatereq(tptp_fun_J_22(I), 0) & (~$greatereq($sum(tptp_fun_J_22(I), $product(-1, K!10)), 0)))) | (~($sum(I, $sum(tptp_fun_J_22(I), $sum($product(-1, tb2t1(get(int, int, t2tb2(Col!9), t2tb1(tptp_fun_J_22(I))))), $product(-1, K!10)))) = 0))))))) & ![I: $int] : ((~$greatereq(I, 0)) | (((~(~mem(int, t2tb1(I), empty(int)))) | ![J: $int] : ((~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, K!10)), 0)))) | (~($sum(I, $sum($product(-1, J), $sum($product(-1, tb2t1(get(int, int, t2tb2(Col!9), t2tb1(J)))), K!10))) = 0)))) & ((~mem(int, t2tb1(I), empty(int))) | (~((~($greatereq(tptp_fun_J_23(I), 0) & (~$greatereq($sum(tptp_fun_J_23(I), $product(-1, K!10)), 0)))) | (~($sum(I, $sum($product(-1, tptp_fun_J_23(I)), $sum($product(-1, tb2t1(get(int, int, t2tb2(Col!9), t2tb1(tptp_fun_J_23(I))))), K!10))) = 0))))))) & partial_solution1(K!10, Col!9))) <=> ($lesseq($sum(S!12, $product(-1, S1!17)), 0) & ($sum(K!10, $product(-1, K1!15)) = 0) & sorted1(Sol1!16, S!12, S1!17) & ![T: map_int_int] : (((~(partial_solution1(n1, T) & eq_prefix1(int, t2tb2(Col1!14), t2tb2(T), K1!15))) | ($lesseq($sum(S!12, $product(-1, tptp_fun_I_18(T))), 0) & (~$lesseq($sum(S1!17, $product(-1, tptp_fun_I_18(T))), 0)) & eq_prefix1(int, t2tb2(T), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(tptp_fun_I_18(T))), n1))) & ((partial_solution1(n1, T) & eq_prefix1(int, t2tb2(Col1!14), t2tb2(T), K1!15)) | ![I: $int] : (~($greatereq($sum(I, $product(-1, S!12)), 0) & (~$greatereq($sum(I, $product(-1, S1!17)), 0)) & eq_prefix1(int, t2tb2(T), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(I)), n1))))) & eq_prefix1(int, t2tb2(Col!9), t2tb2(Col1!14), K1!15) & eq_prefix1(map(int, int), t2tb3(Sol!11), t2tb3(Sol1!16), S!12) & ((~(S!12 = 0)) | (~sorted1(Sol1!16, 0, S1!17)) | ((partial_solution1(n1, T!19) | ($greatereq(I!20, 0) & (~$greatereq($sum(S!12, $sum($product(-1, S1!17), I!20)), 0)) & eq_prefix1(int, t2tb2(T!19), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(I!20)), n1))) & ((~partial_solution1(n1, T!19)) | ![I: $int] : (~($greatereq(I, 0) & (~$greatereq($sum(I, $sum(S!12, $product(-1, S1!17))), 0)) & eq_prefix1(int, t2tb2(T!19), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(I)), n1)))))) & $greatereq(Q!13, 0) & ($sum(n1, $product(-1, Q!13)) = 0) & (S!12 = 0) & (K!10 = 0) & $greatereq(K!10, 0) & ($sum(n1, $sum($product(-1, K!10), $product(-1, cardinal1(int, t2tb(below1(Q!13)))))) = 0) & $greatereq(S!12, 0) & ![I: $int] : (((~mem(int, t2tb1(I), t2tb(below1(Q!13)))) | ($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, n1)), 0)) & ![J: $int] : ((~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, K!10)), 0)))) | (~($sum(I, $product(-1, tb2t1(get(int, int, t2tb2(Col!9), t2tb1(J))))) = 0))))) & ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, n1)), 0) | mem(int, t2tb1(I), t2tb(below1(Q!13))) | (~((~($greatereq(tptp_fun_J_21(I), 0) & (~$lesseq($sum(K!10, $product(-1, tptp_fun_J_21(I))), 0)))) | (~($sum(I, $product(-1, tb2t1(get(int, int, t2tb2(Col!9), t2tb1(tptp_fun_J_21(I)))))) = 0)))))) & ![I: $int] : ((~$greatereq(I, 0)) | ((mem(int, t2tb1(I), empty(int)) | ![J: $int] : ((~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, K!10)), 0)))) | (~($sum(I, $sum(J, $sum($product(-1, K!10), $product(-1, tb2t1(get(int, int, t2tb2(Col!9), t2tb1(J))))))) = 0)))) & ((~mem(int, t2tb1(I), empty(int))) | (~((~($greatereq(tptp_fun_J_22(I), 0) & (~$lesseq($sum(K!10, $product(-1, tptp_fun_J_22(I))), 0)))) | (~($sum(I, $sum($product(-1, K!10), $sum(tptp_fun_J_22(I), $product(-1, tb2t1(get(int, int, t2tb2(Col!9), t2tb1(tptp_fun_J_22(I)))))))) = 0))))))) & ![I: $int] : ((~$greatereq(I, 0)) | ((mem(int, t2tb1(I), empty(int)) | ![J: $int] : ((~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, K!10)), 0)))) | (~($sum(I, $sum($product(-1, J), $sum(K!10, $product(-1, tb2t1(get(int, int, t2tb2(Col!9), t2tb1(J))))))) = 0)))) & ((~mem(int, t2tb1(I), empty(int))) | (~((~($greatereq(tptp_fun_J_23(I), 0) & (~$lesseq($sum(K!10, $product(-1, tptp_fun_J_23(I))), 0)))) | (~($sum(I, $sum(K!10, $sum($product(-1, tptp_fun_J_23(I)), $product(-1, tb2t1(get(int, int, t2tb2(Col!9), t2tb1(tptp_fun_J_23(I)))))))) = 0))))))) & partial_solution1(K!10, Col!9))),
% 0.22/0.51 inference(transitivity,[status(thm)],[9, 1])).
% 0.22/0.51 tff(11,plain,
% 0.22/0.51 ((~![Q: $int, S: $int, Sol: map_int_lpmap_int_intrp, K: $int, Col: map_int_int] : (![S1: $int, Sol1: map_int_lpmap_int_intrp, K1: $int, Col1: map_int_int] : ((~($greatereq($sum(S1, $product(-1, S)), 0) & ($sum(K1, $product(-1, K)) = 0) & sorted1(Sol1, S, S1) & ![T: map_int_int] : ((partial_solution1(n1, T) & eq_prefix1(int, t2tb2(Col1), t2tb2(T), K1)) <=> ?[I: $int] : ($greatereq($sum(I, $product(-1, S)), 0) & (~$greatereq($sum(I, $product(-1, S1)), 0)) & eq_prefix1(int, t2tb2(T), get(map(int, int), int, t2tb3(Sol1), t2tb1(I)), n1))) & eq_prefix1(int, t2tb2(Col), t2tb2(Col1), K1) & eq_prefix1(map(int, int), t2tb3(Sol), t2tb3(Sol1), S))) | ((S = 0) & sorted1(Sol1, 0, S1) & ![T: map_int_int] : (partial_solution1(n1, T) <=> ?[I: $int] : ($greatereq(I, 0) & (~$greatereq($sum(I, $sum(S, $product(-1, S1))), 0)) & eq_prefix1(int, t2tb2(T), get(map(int, int), int, t2tb3(Sol1), t2tb1(I)), n1))))) | (~($greatereq(Q, 0) & ($sum(n1, $product(-1, Q)) = 0) & (S = 0) & (K = 0))) | (~($greatereq(K, 0) & ($sum(K, $sum($product(-1, n1), cardinal1(int, t2tb(below1(Q))))) = 0) & $greatereq(S, 0) & ![I: $int] : (mem(int, t2tb1(I), t2tb(below1(Q))) <=> ($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, n1)), 0)) & ![J: $int] : ((~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, K)), 0)))) | (~($sum(I, $product(-1, tb2t1(get(int, int, t2tb2(Col), t2tb1(J))))) = 0))))) & ![I: $int] : ((~$greatereq(I, 0)) | ((~mem(int, t2tb1(I), empty(int))) <=> ![J: $int] : ((~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, K)), 0)))) | (~($sum(I, $sum(J, $sum($product(-1, tb2t1(get(int, int, t2tb2(Col), t2tb1(J)))), $product(-1, K)))) = 0))))) & ![I: $int] : ((~$greatereq(I, 0)) | ((~mem(int, t2tb1(I), empty(int))) <=> ![J: $int] : ((~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, K)), 0)))) | (~($sum(I, $sum($product(-1, J), $sum($product(-1, tb2t1(get(int, int, t2tb2(Col), t2tb1(J)))), K))) = 0))))) & partial_solution1(K, Col))))) <=> (~![Q: $int, S: $int, Sol: map_int_lpmap_int_intrp, K: $int, Col: map_int_int] : (![S1: $int, Sol1: map_int_lpmap_int_intrp, K1: $int, Col1: map_int_int] : ((~($greatereq($sum(S1, $product(-1, S)), 0) & ($sum(K1, $product(-1, K)) = 0) & sorted1(Sol1, S, S1) & ![T: map_int_int] : ((partial_solution1(n1, T) & eq_prefix1(int, t2tb2(Col1), t2tb2(T), K1)) <=> ?[I: $int] : ($greatereq($sum(I, $product(-1, S)), 0) & (~$greatereq($sum(I, $product(-1, S1)), 0)) & eq_prefix1(int, t2tb2(T), get(map(int, int), int, t2tb3(Sol1), t2tb1(I)), n1))) & eq_prefix1(int, t2tb2(Col), t2tb2(Col1), K1) & eq_prefix1(map(int, int), t2tb3(Sol), t2tb3(Sol1), S))) | ((S = 0) & sorted1(Sol1, 0, S1) & ![T: map_int_int] : (partial_solution1(n1, T) <=> ?[I: $int] : ($greatereq(I, 0) & (~$greatereq($sum(I, $sum(S, $product(-1, S1))), 0)) & eq_prefix1(int, t2tb2(T), get(map(int, int), int, t2tb3(Sol1), t2tb1(I)), n1))))) | (~($greatereq(Q, 0) & ($sum(n1, $product(-1, Q)) = 0) & (S = 0) & (K = 0))) | (~($greatereq(K, 0) & ($sum(K, $sum($product(-1, n1), cardinal1(int, t2tb(below1(Q))))) = 0) & $greatereq(S, 0) & ![I: $int] : (mem(int, t2tb1(I), t2tb(below1(Q))) <=> ($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, n1)), 0)) & ![J: $int] : ((~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, K)), 0)))) | (~($sum(I, $product(-1, tb2t1(get(int, int, t2tb2(Col), t2tb1(J))))) = 0))))) & ![I: $int] : ((~$greatereq(I, 0)) | ((~mem(int, t2tb1(I), empty(int))) <=> ![J: $int] : ((~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, K)), 0)))) | (~($sum(I, $sum(J, $sum($product(-1, tb2t1(get(int, int, t2tb2(Col), t2tb1(J)))), $product(-1, K)))) = 0))))) & ![I: $int] : ((~$greatereq(I, 0)) | ((~mem(int, t2tb1(I), empty(int))) <=> ![J: $int] : ((~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, K)), 0)))) | (~($sum(I, $sum($product(-1, J), $sum($product(-1, tb2t1(get(int, int, t2tb2(Col), t2tb1(J)))), K))) = 0))))) & partial_solution1(K, Col)))))),
% 0.22/0.51 inference(rewrite,[status(thm)],[])).
% 0.22/0.51 tff(12,plain,
% 0.22/0.51 ((~![Q: $int, S: $int, Sol: map_int_lpmap_int_intrp, K: $int, Col: map_int_int] : (![S1: $int, Sol1: map_int_lpmap_int_intrp, K1: $int, Col1: map_int_int] : ((~($greatereq($sum(S1, $product(-1, S)), 0) & ($sum(K1, $product(-1, K)) = 0) & sorted1(Sol1, S, S1) & ![T: map_int_int] : ((partial_solution1(n1, T) & eq_prefix1(int, t2tb2(Col1), t2tb2(T), K1)) <=> ?[I: $int] : ($lesseq($sum(S, $product(-1, I)), 0) & (~$lesseq($sum(S1, $product(-1, I)), 0)) & eq_prefix1(int, t2tb2(T), get(map(int, int), int, t2tb3(Sol1), t2tb1(I)), n1))) & eq_prefix1(int, t2tb2(Col), t2tb2(Col1), K1) & eq_prefix1(map(int, int), t2tb3(Sol), t2tb3(Sol1), S))) | ((S = 0) & sorted1(Sol1, 0, S1) & ![T: map_int_int] : (partial_solution1(n1, T) <=> ?[I: $int] : ($greatereq(I, 0) & (~$lesseq($sum(S1, $sum($product(-1, S), $product(-1, I))), 0)) & eq_prefix1(int, t2tb2(T), get(map(int, int), int, t2tb3(Sol1), t2tb1(I)), n1))))) | (~($greatereq(Q, 0) & ($sum(Q, $product(-1, n1)) = 0) & (S = 0) & (K = 0))) | (~($greatereq(K, 0) & ($sum(K, $sum(cardinal1(int, t2tb(below1(Q))), $product(-1, n1))) = 0) & $greatereq(S, 0) & ![I: $int] : (mem(int, t2tb1(I), t2tb(below1(Q))) <=> ($greatereq(I, 0) & (~$lesseq($sum(n1, $product(-1, I)), 0)) & ![J: $int] : ((~($greatereq(J, 0) & (~$lesseq($sum(K, $product(-1, J)), 0)))) | (~($sum(tb2t1(get(int, int, t2tb2(Col), t2tb1(J))), $product(-1, I)) = 0))))) & ![I: $int] : ((~$greatereq(I, 0)) | ((~mem(int, t2tb1(I), empty(int))) <=> ![J: $int] : ((~($greatereq(J, 0) & (~$lesseq($sum(K, $product(-1, J)), 0)))) | (~($sum(tb2t1(get(int, int, t2tb2(Col), t2tb1(J))), $sum($product(-1, I), $sum($product(-1, J), K))) = 0))))) & ![I: $int] : ((~$greatereq(I, 0)) | ((~mem(int, t2tb1(I), empty(int))) <=> ![J: $int] : ((~($greatereq(J, 0) & (~$lesseq($sum(K, $product(-1, J)), 0)))) | (~($sum(tb2t1(get(int, int, t2tb2(Col), t2tb1(J))), $sum($product(-1, I), $sum($product(-1, K), J))) = 0))))) & partial_solution1(K, Col))))) <=> (~![Q: $int, S: $int, Sol: map_int_lpmap_int_intrp, K: $int, Col: map_int_int] : (![S1: $int, Sol1: map_int_lpmap_int_intrp, K1: $int, Col1: map_int_int] : ((~($greatereq($sum(S1, $product(-1, S)), 0) & ($sum(K1, $product(-1, K)) = 0) & sorted1(Sol1, S, S1) & ![T: map_int_int] : ((partial_solution1(n1, T) & eq_prefix1(int, t2tb2(Col1), t2tb2(T), K1)) <=> ?[I: $int] : ($greatereq($sum(I, $product(-1, S)), 0) & (~$greatereq($sum(I, $product(-1, S1)), 0)) & eq_prefix1(int, t2tb2(T), get(map(int, int), int, t2tb3(Sol1), t2tb1(I)), n1))) & eq_prefix1(int, t2tb2(Col), t2tb2(Col1), K1) & eq_prefix1(map(int, int), t2tb3(Sol), t2tb3(Sol1), S))) | ((S = 0) & sorted1(Sol1, 0, S1) & ![T: map_int_int] : (partial_solution1(n1, T) <=> ?[I: $int] : ($greatereq(I, 0) & (~$greatereq($sum(I, $sum(S, $product(-1, S1))), 0)) & eq_prefix1(int, t2tb2(T), get(map(int, int), int, t2tb3(Sol1), t2tb1(I)), n1))))) | (~($greatereq(Q, 0) & ($sum(n1, $product(-1, Q)) = 0) & (S = 0) & (K = 0))) | (~($greatereq(K, 0) & ($sum(K, $sum($product(-1, n1), cardinal1(int, t2tb(below1(Q))))) = 0) & $greatereq(S, 0) & ![I: $int] : (mem(int, t2tb1(I), t2tb(below1(Q))) <=> ($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, n1)), 0)) & ![J: $int] : ((~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, K)), 0)))) | (~($sum(I, $product(-1, tb2t1(get(int, int, t2tb2(Col), t2tb1(J))))) = 0))))) & ![I: $int] : ((~$greatereq(I, 0)) | ((~mem(int, t2tb1(I), empty(int))) <=> ![J: $int] : ((~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, K)), 0)))) | (~($sum(I, $sum(J, $sum($product(-1, tb2t1(get(int, int, t2tb2(Col), t2tb1(J)))), $product(-1, K)))) = 0))))) & ![I: $int] : ((~$greatereq(I, 0)) | ((~mem(int, t2tb1(I), empty(int))) <=> ![J: $int] : ((~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, K)), 0)))) | (~($sum(I, $sum($product(-1, J), $sum($product(-1, tb2t1(get(int, int, t2tb2(Col), t2tb1(J)))), K))) = 0))))) & partial_solution1(K, Col)))))),
% 0.22/0.51 inference(rewrite,[status(thm)],[])).
% 0.22/0.51 tff(13,plain,
% 0.22/0.51 ((~![Q: $int, S: $int, Sol: map_int_lpmap_int_intrp, K: $int, Col: map_int_int] : (![S1: $int, Sol1: map_int_lpmap_int_intrp, K1: $int, Col1: map_int_int] : ((~($lesseq(0, $sum(S1, $product(-1, S))) & (K1 = K) & sorted1(Sol1, S, S1) & ![T: map_int_int] : ((partial_solution1(n1, T) & eq_prefix1(int, t2tb2(Col1), t2tb2(T), K1)) <=> ?[I: $int] : ($lesseq(S, I) & (~$lesseq(S1, I)) & eq_prefix1(int, t2tb2(T), get(map(int, int), int, t2tb3(Sol1), t2tb1(I)), n1))) & eq_prefix1(int, t2tb2(Col), t2tb2(Col1), K1) & eq_prefix1(map(int, int), t2tb3(Sol), t2tb3(Sol1), S))) | ((S = 0) & sorted1(Sol1, 0, S1) & ![T: map_int_int] : (partial_solution1(n1, T) <=> ?[I: $int] : ($lesseq(0, I) & (~$lesseq($sum(S1, $product(-1, S)), I)) & eq_prefix1(int, t2tb2(T), get(map(int, int), int, t2tb3(Sol1), t2tb1(I)), n1))))) | (~($lesseq(0, K) & ($sum(K, cardinal1(int, t2tb(below1(Q)))) = n1) & $lesseq(0, S) & ![I: $int] : (mem(int, t2tb1(I), t2tb(below1(Q))) <=> ($lesseq(0, I) & (~$lesseq(n1, I)) & ![J: $int] : ((~($lesseq(0, J) & (~$lesseq(K, J)))) | (~(tb2t1(get(int, int, t2tb2(Col), t2tb1(J))) = I))))) & ![I: $int] : ((~$lesseq(0, I)) | ((~mem(int, t2tb1(I), empty(int))) <=> ![J: $int] : ((~($lesseq(0, J) & (~$lesseq(K, J)))) | (~(tb2t1(get(int, int, t2tb2(Col), t2tb1(J))) = $sum(I, $sum(J, $product(-1, K)))))))) & ![I: $int] : ((~$lesseq(0, I)) | ((~mem(int, t2tb1(I), empty(int))) <=> ![J: $int] : ((~($lesseq(0, J) & (~$lesseq(K, J)))) | (~(tb2t1(get(int, int, t2tb2(Col), t2tb1(J))) = $sum(I, $sum(K, $product(-1, J)))))))) & partial_solution1(K, Col))) | (~($lesseq(0, Q) & (Q = n1) & (S = 0) & (K = 0))))) <=> (~![Q: $int, S: $int, Sol: map_int_lpmap_int_intrp, K: $int, Col: map_int_int] : (![S1: $int, Sol1: map_int_lpmap_int_intrp, K1: $int, Col1: map_int_int] : ((~($greatereq($sum(S1, $product(-1, S)), 0) & ($sum(K1, $product(-1, K)) = 0) & sorted1(Sol1, S, S1) & ![T: map_int_int] : ((partial_solution1(n1, T) & eq_prefix1(int, t2tb2(Col1), t2tb2(T), K1)) <=> ?[I: $int] : ($lesseq($sum(S, $product(-1, I)), 0) & (~$lesseq($sum(S1, $product(-1, I)), 0)) & eq_prefix1(int, t2tb2(T), get(map(int, int), int, t2tb3(Sol1), t2tb1(I)), n1))) & eq_prefix1(int, t2tb2(Col), t2tb2(Col1), K1) & eq_prefix1(map(int, int), t2tb3(Sol), t2tb3(Sol1), S))) | ((S = 0) & sorted1(Sol1, 0, S1) & ![T: map_int_int] : (partial_solution1(n1, T) <=> ?[I: $int] : ($greatereq(I, 0) & (~$lesseq($sum(S1, $sum($product(-1, S), $product(-1, I))), 0)) & eq_prefix1(int, t2tb2(T), get(map(int, int), int, t2tb3(Sol1), t2tb1(I)), n1))))) | (~($greatereq(Q, 0) & ($sum(Q, $product(-1, n1)) = 0) & (S = 0) & (K = 0))) | (~($greatereq(K, 0) & ($sum(K, $sum(cardinal1(int, t2tb(below1(Q))), $product(-1, n1))) = 0) & $greatereq(S, 0) & ![I: $int] : (mem(int, t2tb1(I), t2tb(below1(Q))) <=> ($greatereq(I, 0) & (~$lesseq($sum(n1, $product(-1, I)), 0)) & ![J: $int] : ((~($greatereq(J, 0) & (~$lesseq($sum(K, $product(-1, J)), 0)))) | (~($sum(tb2t1(get(int, int, t2tb2(Col), t2tb1(J))), $product(-1, I)) = 0))))) & ![I: $int] : ((~$greatereq(I, 0)) | ((~mem(int, t2tb1(I), empty(int))) <=> ![J: $int] : ((~($greatereq(J, 0) & (~$lesseq($sum(K, $product(-1, J)), 0)))) | (~($sum(tb2t1(get(int, int, t2tb2(Col), t2tb1(J))), $sum($product(-1, I), $sum($product(-1, J), K))) = 0))))) & ![I: $int] : ((~$greatereq(I, 0)) | ((~mem(int, t2tb1(I), empty(int))) <=> ![J: $int] : ((~($greatereq(J, 0) & (~$lesseq($sum(K, $product(-1, J)), 0)))) | (~($sum(tb2t1(get(int, int, t2tb2(Col), t2tb1(J))), $sum($product(-1, I), $sum($product(-1, K), J))) = 0))))) & partial_solution1(K, Col)))))),
% 0.22/0.51 inference(rewrite,[status(thm)],[])).
% 0.22/0.51 tff(14,plain,
% 0.22/0.51 ((~![Q: $int, S: $int, Sol: map_int_lpmap_int_intrp, K: $int, Col: map_int_int] : (![S1: $int, Sol1: map_int_lpmap_int_intrp, K1: $int, Col1: map_int_int] : ((~($lesseq(0, $sum(S1, $product(-1, S))) & (K1 = K) & sorted1(Sol1, S, S1) & ![T: map_int_int] : ((partial_solution1(n1, T) & eq_prefix1(int, t2tb2(Col1), t2tb2(T), K1)) <=> ?[I: $int] : ($lesseq(S, I) & (~$lesseq(S1, I)) & eq_prefix1(int, t2tb2(T), get(map(int, int), int, t2tb3(Sol1), t2tb1(I)), n1))) & eq_prefix1(int, t2tb2(Col), t2tb2(Col1), K1) & eq_prefix1(map(int, int), t2tb3(Sol), t2tb3(Sol1), S))) | ((S = 0) & sorted1(Sol1, 0, S1) & ![T: map_int_int] : (partial_solution1(n1, T) <=> ?[I: $int] : ($lesseq(0, I) & (~$lesseq($sum(S1, $product(-1, S)), I)) & eq_prefix1(int, t2tb2(T), get(map(int, int), int, t2tb3(Sol1), t2tb1(I)), n1))))) | (~($lesseq(0, K) & ($sum(K, cardinal1(int, t2tb(below1(Q)))) = n1) & $lesseq(0, S) & ![I: $int] : (mem(int, t2tb1(I), t2tb(below1(Q))) <=> ($lesseq(0, I) & (~$lesseq(n1, I)) & ![J: $int] : ((~($lesseq(0, J) & (~$lesseq(K, J)))) | (~(tb2t1(get(int, int, t2tb2(Col), t2tb1(J))) = I))))) & ![I: $int] : ((~$lesseq(0, I)) | ((~mem(int, t2tb1(I), empty(int))) <=> ![J: $int] : ((~($lesseq(0, J) & (~$lesseq(K, J)))) | (~(tb2t1(get(int, int, t2tb2(Col), t2tb1(J))) = $sum(I, $sum(J, $product(-1, K)))))))) & ![I: $int] : ((~$lesseq(0, I)) | ((~mem(int, t2tb1(I), empty(int))) <=> ![J: $int] : ((~($lesseq(0, J) & (~$lesseq(K, J)))) | (~(tb2t1(get(int, int, t2tb2(Col), t2tb1(J))) = $sum(I, $sum(K, $product(-1, J)))))))) & partial_solution1(K, Col))) | (~($lesseq(0, Q) & (Q = n1) & (S = 0) & (K = 0))))) <=> (~![Q: $int, S: $int, Sol: map_int_lpmap_int_intrp, K: $int, Col: map_int_int] : (![S1: $int, Sol1: map_int_lpmap_int_intrp, K1: $int, Col1: map_int_int] : ((~($lesseq(0, $sum(S1, $product(-1, S))) & (K1 = K) & sorted1(Sol1, S, S1) & ![T: map_int_int] : ((partial_solution1(n1, T) & eq_prefix1(int, t2tb2(Col1), t2tb2(T), K1)) <=> ?[I: $int] : ($lesseq(S, I) & (~$lesseq(S1, I)) & eq_prefix1(int, t2tb2(T), get(map(int, int), int, t2tb3(Sol1), t2tb1(I)), n1))) & eq_prefix1(int, t2tb2(Col), t2tb2(Col1), K1) & eq_prefix1(map(int, int), t2tb3(Sol), t2tb3(Sol1), S))) | ((S = 0) & sorted1(Sol1, 0, S1) & ![T: map_int_int] : (partial_solution1(n1, T) <=> ?[I: $int] : ($lesseq(0, I) & (~$lesseq($sum(S1, $product(-1, S)), I)) & eq_prefix1(int, t2tb2(T), get(map(int, int), int, t2tb3(Sol1), t2tb1(I)), n1))))) | (~($lesseq(0, K) & ($sum(K, cardinal1(int, t2tb(below1(Q)))) = n1) & $lesseq(0, S) & ![I: $int] : (mem(int, t2tb1(I), t2tb(below1(Q))) <=> ($lesseq(0, I) & (~$lesseq(n1, I)) & ![J: $int] : ((~($lesseq(0, J) & (~$lesseq(K, J)))) | (~(tb2t1(get(int, int, t2tb2(Col), t2tb1(J))) = I))))) & ![I: $int] : ((~$lesseq(0, I)) | ((~mem(int, t2tb1(I), empty(int))) <=> ![J: $int] : ((~($lesseq(0, J) & (~$lesseq(K, J)))) | (~(tb2t1(get(int, int, t2tb2(Col), t2tb1(J))) = $sum(I, $sum(J, $product(-1, K)))))))) & ![I: $int] : ((~$lesseq(0, I)) | ((~mem(int, t2tb1(I), empty(int))) <=> ![J: $int] : ((~($lesseq(0, J) & (~$lesseq(K, J)))) | (~(tb2t1(get(int, int, t2tb2(Col), t2tb1(J))) = $sum(I, $sum(K, $product(-1, J)))))))) & partial_solution1(K, Col))) | (~($lesseq(0, Q) & (Q = n1) & (S = 0) & (K = 0)))))),
% 0.22/0.51 inference(rewrite,[status(thm)],[])).
% 0.22/0.51 tff(15,plain,
% 0.22/0.51 ((~![Q: $int, S: $int, Sol: map_int_lpmap_int_intrp, K: $int, Col: map_int_int] : (((($lesseq(0, Q) & (Q = n1)) & (S = 0)) & (K = 0)) => ((((((($lesseq(0, K) & ($sum(K, cardinal1(int, t2tb(below1(Q)))) = n1)) & $lesseq(0, S)) & ![I: $int] : (mem(int, t2tb1(I), t2tb(below1(Q))) <=> (($lesseq(0, I) & $less(I, n1)) & ![J: $int] : (($lesseq(0, J) & $less(J, K)) => (~(tb2t1(get(int, int, t2tb2(Col), t2tb1(J))) = I)))))) & ![I: $int] : ($lesseq(0, I) => ((~mem(int, t2tb1(I), empty(int))) <=> ![J: $int] : (($lesseq(0, J) & $less(J, K)) => (~(tb2t1(get(int, int, t2tb2(Col), t2tb1(J))) = $difference($sum(I, J), K))))))) & ![I: $int] : ($lesseq(0, I) => ((~mem(int, t2tb1(I), empty(int))) <=> ![J: $int] : (($lesseq(0, J) & $less(J, K)) => (~(tb2t1(get(int, int, t2tb2(Col), t2tb1(J))) = $difference($sum(I, K), J))))))) & partial_solution1(K, Col)) => ![S1: $int, Sol1: map_int_lpmap_int_intrp, K1: $int, Col1: map_int_int] : (((((($lesseq(0, $difference(S1, S)) & (K1 = K)) & sorted1(Sol1, S, S1)) & ![T: map_int_int] : ((partial_solution1(n1, T) & eq_prefix1(int, t2tb2(Col1), t2tb2(T), K1)) <=> ?[I: $int] : (($lesseq(S, I) & $less(I, S1)) & eq_prefix1(int, t2tb2(T), get(map(int, int), int, t2tb3(Sol1), t2tb1(I)), n1)))) & eq_prefix1(int, t2tb2(Col), t2tb2(Col1), K1)) & eq_prefix1(map(int, int), t2tb3(Sol), t2tb3(Sol1), S)) => ((($difference(S1, S) = S1) & sorted1(Sol1, 0, S1)) & ![T: map_int_int] : (partial_solution1(n1, T) <=> ?[I: $int] : (($lesseq(0, I) & $less(I, $difference(S1, S))) & eq_prefix1(int, t2tb2(T), get(map(int, int), int, t2tb3(Sol1), t2tb1(I)), n1)))))))) <=> (~![Q: $int, S: $int, Sol: map_int_lpmap_int_intrp, K: $int, Col: map_int_int] : (![S1: $int, Sol1: map_int_lpmap_int_intrp, K1: $int, Col1: map_int_int] : ((~($lesseq(0, $sum(S1, $product(-1, S))) & (K1 = K) & sorted1(Sol1, S, S1) & ![T: map_int_int] : ((partial_solution1(n1, T) & eq_prefix1(int, t2tb2(Col1), t2tb2(T), K1)) <=> ?[I: $int] : ($lesseq(S, I) & (~$lesseq(S1, I)) & eq_prefix1(int, t2tb2(T), get(map(int, int), int, t2tb3(Sol1), t2tb1(I)), n1))) & eq_prefix1(int, t2tb2(Col), t2tb2(Col1), K1) & eq_prefix1(map(int, int), t2tb3(Sol), t2tb3(Sol1), S))) | ((S = 0) & sorted1(Sol1, 0, S1) & ![T: map_int_int] : (partial_solution1(n1, T) <=> ?[I: $int] : ($lesseq(0, I) & (~$lesseq($sum(S1, $product(-1, S)), I)) & eq_prefix1(int, t2tb2(T), get(map(int, int), int, t2tb3(Sol1), t2tb1(I)), n1))))) | (~($lesseq(0, K) & ($sum(K, cardinal1(int, t2tb(below1(Q)))) = n1) & $lesseq(0, S) & ![I: $int] : (mem(int, t2tb1(I), t2tb(below1(Q))) <=> ($lesseq(0, I) & (~$lesseq(n1, I)) & ![J: $int] : ((~($lesseq(0, J) & (~$lesseq(K, J)))) | (~(tb2t1(get(int, int, t2tb2(Col), t2tb1(J))) = I))))) & ![I: $int] : ((~$lesseq(0, I)) | ((~mem(int, t2tb1(I), empty(int))) <=> ![J: $int] : ((~($lesseq(0, J) & (~$lesseq(K, J)))) | (~(tb2t1(get(int, int, t2tb2(Col), t2tb1(J))) = $sum(I, $sum(J, $product(-1, K)))))))) & ![I: $int] : ((~$lesseq(0, I)) | ((~mem(int, t2tb1(I), empty(int))) <=> ![J: $int] : ((~($lesseq(0, J) & (~$lesseq(K, J)))) | (~(tb2t1(get(int, int, t2tb2(Col), t2tb1(J))) = $sum(I, $sum(K, $product(-1, J)))))))) & partial_solution1(K, Col))) | (~($lesseq(0, Q) & (Q = n1) & (S = 0) & (K = 0)))))),
% 0.22/0.51 inference(rewrite,[status(thm)],[])).
% 0.22/0.51 tff(16,axiom,(~![Q: $int, S: $int, Sol: map_int_lpmap_int_intrp, K: $int, Col: map_int_int] : (((($lesseq(0, Q) & (Q = n1)) & (S = 0)) & (K = 0)) => ((((((($lesseq(0, K) & ($sum(K, cardinal1(int, t2tb(below1(Q)))) = n1)) & $lesseq(0, S)) & ![I: $int] : (mem(int, t2tb1(I), t2tb(below1(Q))) <=> (($lesseq(0, I) & $less(I, n1)) & ![J: $int] : (($lesseq(0, J) & $less(J, K)) => (~(tb2t1(get(int, int, t2tb2(Col), t2tb1(J))) = I)))))) & ![I: $int] : ($lesseq(0, I) => ((~mem(int, t2tb1(I), empty(int))) <=> ![J: $int] : (($lesseq(0, J) & $less(J, K)) => (~(tb2t1(get(int, int, t2tb2(Col), t2tb1(J))) = $difference($sum(I, J), K))))))) & ![I: $int] : ($lesseq(0, I) => ((~mem(int, t2tb1(I), empty(int))) <=> ![J: $int] : (($lesseq(0, J) & $less(J, K)) => (~(tb2t1(get(int, int, t2tb2(Col), t2tb1(J))) = $difference($sum(I, K), J))))))) & partial_solution1(K, Col)) => ![S1: $int, Sol1: map_int_lpmap_int_intrp, K1: $int, Col1: map_int_int] : (((((($lesseq(0, $difference(S1, S)) & (K1 = K)) & sorted1(Sol1, S, S1)) & ![T: map_int_int] : ((partial_solution1(n1, T) & eq_prefix1(int, t2tb2(Col1), t2tb2(T), K1)) <=> ?[I: $int] : (($lesseq(S, I) & $less(I, S1)) & eq_prefix1(int, t2tb2(T), get(map(int, int), int, t2tb3(Sol1), t2tb1(I)), n1)))) & eq_prefix1(int, t2tb2(Col), t2tb2(Col1), K1)) & eq_prefix1(map(int, int), t2tb3(Sol), t2tb3(Sol1), S)) => ((($difference(S1, S) = S1) & sorted1(Sol1, 0, S1)) & ![T: map_int_int] : (partial_solution1(n1, T) <=> ?[I: $int] : (($lesseq(0, I) & $less(I, $difference(S1, S))) & eq_prefix1(int, t2tb2(T), get(map(int, int), int, t2tb3(Sol1), t2tb1(I)), n1)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','wP_parameter_queens3')).
% 0.22/0.51 tff(17,plain,
% 0.22/0.51 (~![Q: $int, S: $int, Sol: map_int_lpmap_int_intrp, K: $int, Col: map_int_int] : (![S1: $int, Sol1: map_int_lpmap_int_intrp, K1: $int, Col1: map_int_int] : ((~($lesseq(0, $sum(S1, $product(-1, S))) & (K1 = K) & sorted1(Sol1, S, S1) & ![T: map_int_int] : ((partial_solution1(n1, T) & eq_prefix1(int, t2tb2(Col1), t2tb2(T), K1)) <=> ?[I: $int] : ($lesseq(S, I) & (~$lesseq(S1, I)) & eq_prefix1(int, t2tb2(T), get(map(int, int), int, t2tb3(Sol1), t2tb1(I)), n1))) & eq_prefix1(int, t2tb2(Col), t2tb2(Col1), K1) & eq_prefix1(map(int, int), t2tb3(Sol), t2tb3(Sol1), S))) | ((S = 0) & sorted1(Sol1, 0, S1) & ![T: map_int_int] : (partial_solution1(n1, T) <=> ?[I: $int] : ($lesseq(0, I) & (~$lesseq($sum(S1, $product(-1, S)), I)) & eq_prefix1(int, t2tb2(T), get(map(int, int), int, t2tb3(Sol1), t2tb1(I)), n1))))) | (~($lesseq(0, K) & ($sum(K, cardinal1(int, t2tb(below1(Q)))) = n1) & $lesseq(0, S) & ![I: $int] : (mem(int, t2tb1(I), t2tb(below1(Q))) <=> ($lesseq(0, I) & (~$lesseq(n1, I)) & ![J: $int] : ((~($lesseq(0, J) & (~$lesseq(K, J)))) | (~(tb2t1(get(int, int, t2tb2(Col), t2tb1(J))) = I))))) & ![I: $int] : ((~$lesseq(0, I)) | ((~mem(int, t2tb1(I), empty(int))) <=> ![J: $int] : ((~($lesseq(0, J) & (~$lesseq(K, J)))) | (~(tb2t1(get(int, int, t2tb2(Col), t2tb1(J))) = $sum(I, $sum(J, $product(-1, K)))))))) & ![I: $int] : ((~$lesseq(0, I)) | ((~mem(int, t2tb1(I), empty(int))) <=> ![J: $int] : ((~($lesseq(0, J) & (~$lesseq(K, J)))) | (~(tb2t1(get(int, int, t2tb2(Col), t2tb1(J))) = $sum(I, $sum(K, $product(-1, J)))))))) & partial_solution1(K, Col))) | (~($lesseq(0, Q) & (Q = n1) & (S = 0) & (K = 0))))),
% 0.22/0.52 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.22/0.52 tff(18,plain,
% 0.22/0.52 (~![Q: $int, S: $int, Sol: map_int_lpmap_int_intrp, K: $int, Col: map_int_int] : (![S1: $int, Sol1: map_int_lpmap_int_intrp, K1: $int, Col1: map_int_int] : ((~($lesseq(0, $sum(S1, $product(-1, S))) & (K1 = K) & sorted1(Sol1, S, S1) & ![T: map_int_int] : ((partial_solution1(n1, T) & eq_prefix1(int, t2tb2(Col1), t2tb2(T), K1)) <=> ?[I: $int] : ($lesseq(S, I) & (~$lesseq(S1, I)) & eq_prefix1(int, t2tb2(T), get(map(int, int), int, t2tb3(Sol1), t2tb1(I)), n1))) & eq_prefix1(int, t2tb2(Col), t2tb2(Col1), K1) & eq_prefix1(map(int, int), t2tb3(Sol), t2tb3(Sol1), S))) | ((S = 0) & sorted1(Sol1, 0, S1) & ![T: map_int_int] : (partial_solution1(n1, T) <=> ?[I: $int] : ($lesseq(0, I) & (~$lesseq($sum(S1, $product(-1, S)), I)) & eq_prefix1(int, t2tb2(T), get(map(int, int), int, t2tb3(Sol1), t2tb1(I)), n1))))) | (~($lesseq(0, K) & ($sum(K, cardinal1(int, t2tb(below1(Q)))) = n1) & $lesseq(0, S) & ![I: $int] : (mem(int, t2tb1(I), t2tb(below1(Q))) <=> ($lesseq(0, I) & (~$lesseq(n1, I)) & ![J: $int] : ((~($lesseq(0, J) & (~$lesseq(K, J)))) | (~(tb2t1(get(int, int, t2tb2(Col), t2tb1(J))) = I))))) & ![I: $int] : ((~$lesseq(0, I)) | ((~mem(int, t2tb1(I), empty(int))) <=> ![J: $int] : ((~($lesseq(0, J) & (~$lesseq(K, J)))) | (~(tb2t1(get(int, int, t2tb2(Col), t2tb1(J))) = $sum(I, $sum(J, $product(-1, K)))))))) & ![I: $int] : ((~$lesseq(0, I)) | ((~mem(int, t2tb1(I), empty(int))) <=> ![J: $int] : ((~($lesseq(0, J) & (~$lesseq(K, J)))) | (~(tb2t1(get(int, int, t2tb2(Col), t2tb1(J))) = $sum(I, $sum(K, $product(-1, J)))))))) & partial_solution1(K, Col))) | (~($lesseq(0, Q) & (Q = n1) & (S = 0) & (K = 0))))),
% 0.22/0.52 inference(modus_ponens,[status(thm)],[17, 14])).
% 0.22/0.52 tff(19,plain,
% 0.22/0.52 (~![Q: $int, S: $int, Sol: map_int_lpmap_int_intrp, K: $int, Col: map_int_int] : (![S1: $int, Sol1: map_int_lpmap_int_intrp, K1: $int, Col1: map_int_int] : ((~($lesseq(0, $sum(S1, $product(-1, S))) & (K1 = K) & sorted1(Sol1, S, S1) & ![T: map_int_int] : ((partial_solution1(n1, T) & eq_prefix1(int, t2tb2(Col1), t2tb2(T), K1)) <=> ?[I: $int] : ($lesseq(S, I) & (~$lesseq(S1, I)) & eq_prefix1(int, t2tb2(T), get(map(int, int), int, t2tb3(Sol1), t2tb1(I)), n1))) & eq_prefix1(int, t2tb2(Col), t2tb2(Col1), K1) & eq_prefix1(map(int, int), t2tb3(Sol), t2tb3(Sol1), S))) | ((S = 0) & sorted1(Sol1, 0, S1) & ![T: map_int_int] : (partial_solution1(n1, T) <=> ?[I: $int] : ($lesseq(0, I) & (~$lesseq($sum(S1, $product(-1, S)), I)) & eq_prefix1(int, t2tb2(T), get(map(int, int), int, t2tb3(Sol1), t2tb1(I)), n1))))) | (~($lesseq(0, K) & ($sum(K, cardinal1(int, t2tb(below1(Q)))) = n1) & $lesseq(0, S) & ![I: $int] : (mem(int, t2tb1(I), t2tb(below1(Q))) <=> ($lesseq(0, I) & (~$lesseq(n1, I)) & ![J: $int] : ((~($lesseq(0, J) & (~$lesseq(K, J)))) | (~(tb2t1(get(int, int, t2tb2(Col), t2tb1(J))) = I))))) & ![I: $int] : ((~$lesseq(0, I)) | ((~mem(int, t2tb1(I), empty(int))) <=> ![J: $int] : ((~($lesseq(0, J) & (~$lesseq(K, J)))) | (~(tb2t1(get(int, int, t2tb2(Col), t2tb1(J))) = $sum(I, $sum(J, $product(-1, K)))))))) & ![I: $int] : ((~$lesseq(0, I)) | ((~mem(int, t2tb1(I), empty(int))) <=> ![J: $int] : ((~($lesseq(0, J) & (~$lesseq(K, J)))) | (~(tb2t1(get(int, int, t2tb2(Col), t2tb1(J))) = $sum(I, $sum(K, $product(-1, J)))))))) & partial_solution1(K, Col))) | (~($lesseq(0, Q) & (Q = n1) & (S = 0) & (K = 0))))),
% 0.22/0.52 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.22/0.52 tff(20,plain,
% 0.22/0.52 (~![Q: $int, S: $int, Sol: map_int_lpmap_int_intrp, K: $int, Col: map_int_int] : (![S1: $int, Sol1: map_int_lpmap_int_intrp, K1: $int, Col1: map_int_int] : ((~($lesseq(0, $sum(S1, $product(-1, S))) & (K1 = K) & sorted1(Sol1, S, S1) & ![T: map_int_int] : ((partial_solution1(n1, T) & eq_prefix1(int, t2tb2(Col1), t2tb2(T), K1)) <=> ?[I: $int] : ($lesseq(S, I) & (~$lesseq(S1, I)) & eq_prefix1(int, t2tb2(T), get(map(int, int), int, t2tb3(Sol1), t2tb1(I)), n1))) & eq_prefix1(int, t2tb2(Col), t2tb2(Col1), K1) & eq_prefix1(map(int, int), t2tb3(Sol), t2tb3(Sol1), S))) | ((S = 0) & sorted1(Sol1, 0, S1) & ![T: map_int_int] : (partial_solution1(n1, T) <=> ?[I: $int] : ($lesseq(0, I) & (~$lesseq($sum(S1, $product(-1, S)), I)) & eq_prefix1(int, t2tb2(T), get(map(int, int), int, t2tb3(Sol1), t2tb1(I)), n1))))) | (~($lesseq(0, K) & ($sum(K, cardinal1(int, t2tb(below1(Q)))) = n1) & $lesseq(0, S) & ![I: $int] : (mem(int, t2tb1(I), t2tb(below1(Q))) <=> ($lesseq(0, I) & (~$lesseq(n1, I)) & ![J: $int] : ((~($lesseq(0, J) & (~$lesseq(K, J)))) | (~(tb2t1(get(int, int, t2tb2(Col), t2tb1(J))) = I))))) & ![I: $int] : ((~$lesseq(0, I)) | ((~mem(int, t2tb1(I), empty(int))) <=> ![J: $int] : ((~($lesseq(0, J) & (~$lesseq(K, J)))) | (~(tb2t1(get(int, int, t2tb2(Col), t2tb1(J))) = $sum(I, $sum(J, $product(-1, K)))))))) & ![I: $int] : ((~$lesseq(0, I)) | ((~mem(int, t2tb1(I), empty(int))) <=> ![J: $int] : ((~($lesseq(0, J) & (~$lesseq(K, J)))) | (~(tb2t1(get(int, int, t2tb2(Col), t2tb1(J))) = $sum(I, $sum(K, $product(-1, J)))))))) & partial_solution1(K, Col))) | (~($lesseq(0, Q) & (Q = n1) & (S = 0) & (K = 0))))),
% 0.22/0.52 inference(modus_ponens,[status(thm)],[19, 14])).
% 0.22/0.52 tff(21,plain,
% 0.22/0.52 (~![Q: $int, S: $int, Sol: map_int_lpmap_int_intrp, K: $int, Col: map_int_int] : (![S1: $int, Sol1: map_int_lpmap_int_intrp, K1: $int, Col1: map_int_int] : ((~($greatereq($sum(S1, $product(-1, S)), 0) & ($sum(K1, $product(-1, K)) = 0) & sorted1(Sol1, S, S1) & ![T: map_int_int] : ((partial_solution1(n1, T) & eq_prefix1(int, t2tb2(Col1), t2tb2(T), K1)) <=> ?[I: $int] : ($lesseq($sum(S, $product(-1, I)), 0) & (~$lesseq($sum(S1, $product(-1, I)), 0)) & eq_prefix1(int, t2tb2(T), get(map(int, int), int, t2tb3(Sol1), t2tb1(I)), n1))) & eq_prefix1(int, t2tb2(Col), t2tb2(Col1), K1) & eq_prefix1(map(int, int), t2tb3(Sol), t2tb3(Sol1), S))) | ((S = 0) & sorted1(Sol1, 0, S1) & ![T: map_int_int] : (partial_solution1(n1, T) <=> ?[I: $int] : ($greatereq(I, 0) & (~$lesseq($sum(S1, $sum($product(-1, S), $product(-1, I))), 0)) & eq_prefix1(int, t2tb2(T), get(map(int, int), int, t2tb3(Sol1), t2tb1(I)), n1))))) | (~($greatereq(Q, 0) & ($sum(Q, $product(-1, n1)) = 0) & (S = 0) & (K = 0))) | (~($greatereq(K, 0) & ($sum(K, $sum(cardinal1(int, t2tb(below1(Q))), $product(-1, n1))) = 0) & $greatereq(S, 0) & ![I: $int] : (mem(int, t2tb1(I), t2tb(below1(Q))) <=> ($greatereq(I, 0) & (~$lesseq($sum(n1, $product(-1, I)), 0)) & ![J: $int] : ((~($greatereq(J, 0) & (~$lesseq($sum(K, $product(-1, J)), 0)))) | (~($sum(tb2t1(get(int, int, t2tb2(Col), t2tb1(J))), $product(-1, I)) = 0))))) & ![I: $int] : ((~$greatereq(I, 0)) | ((~mem(int, t2tb1(I), empty(int))) <=> ![J: $int] : ((~($greatereq(J, 0) & (~$lesseq($sum(K, $product(-1, J)), 0)))) | (~($sum(tb2t1(get(int, int, t2tb2(Col), t2tb1(J))), $sum($product(-1, I), $sum($product(-1, J), K))) = 0))))) & ![I: $int] : ((~$greatereq(I, 0)) | ((~mem(int, t2tb1(I), empty(int))) <=> ![J: $int] : ((~($greatereq(J, 0) & (~$lesseq($sum(K, $product(-1, J)), 0)))) | (~($sum(tb2t1(get(int, int, t2tb2(Col), t2tb1(J))), $sum($product(-1, I), $sum($product(-1, K), J))) = 0))))) & partial_solution1(K, Col))))),
% 0.22/0.52 inference(modus_ponens,[status(thm)],[20, 13])).
% 0.22/0.52 tff(22,plain,
% 0.22/0.52 (~![Q: $int, S: $int, Sol: map_int_lpmap_int_intrp, K: $int, Col: map_int_int] : (![S1: $int, Sol1: map_int_lpmap_int_intrp, K1: $int, Col1: map_int_int] : ((~($greatereq($sum(S1, $product(-1, S)), 0) & ($sum(K1, $product(-1, K)) = 0) & sorted1(Sol1, S, S1) & ![T: map_int_int] : ((partial_solution1(n1, T) & eq_prefix1(int, t2tb2(Col1), t2tb2(T), K1)) <=> ?[I: $int] : ($greatereq($sum(I, $product(-1, S)), 0) & (~$greatereq($sum(I, $product(-1, S1)), 0)) & eq_prefix1(int, t2tb2(T), get(map(int, int), int, t2tb3(Sol1), t2tb1(I)), n1))) & eq_prefix1(int, t2tb2(Col), t2tb2(Col1), K1) & eq_prefix1(map(int, int), t2tb3(Sol), t2tb3(Sol1), S))) | ((S = 0) & sorted1(Sol1, 0, S1) & ![T: map_int_int] : (partial_solution1(n1, T) <=> ?[I: $int] : ($greatereq(I, 0) & (~$greatereq($sum(I, $sum(S, $product(-1, S1))), 0)) & eq_prefix1(int, t2tb2(T), get(map(int, int), int, t2tb3(Sol1), t2tb1(I)), n1))))) | (~($greatereq(Q, 0) & ($sum(n1, $product(-1, Q)) = 0) & (S = 0) & (K = 0))) | (~($greatereq(K, 0) & ($sum(K, $sum($product(-1, n1), cardinal1(int, t2tb(below1(Q))))) = 0) & $greatereq(S, 0) & ![I: $int] : (mem(int, t2tb1(I), t2tb(below1(Q))) <=> ($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, n1)), 0)) & ![J: $int] : ((~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, K)), 0)))) | (~($sum(I, $product(-1, tb2t1(get(int, int, t2tb2(Col), t2tb1(J))))) = 0))))) & ![I: $int] : ((~$greatereq(I, 0)) | ((~mem(int, t2tb1(I), empty(int))) <=> ![J: $int] : ((~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, K)), 0)))) | (~($sum(I, $sum(J, $sum($product(-1, tb2t1(get(int, int, t2tb2(Col), t2tb1(J)))), $product(-1, K)))) = 0))))) & ![I: $int] : ((~$greatereq(I, 0)) | ((~mem(int, t2tb1(I), empty(int))) <=> ![J: $int] : ((~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, K)), 0)))) | (~($sum(I, $sum($product(-1, J), $sum($product(-1, tb2t1(get(int, int, t2tb2(Col), t2tb1(J)))), K))) = 0))))) & partial_solution1(K, Col))))),
% 0.22/0.52 inference(modus_ponens,[status(thm)],[21, 12])).
% 0.22/0.52 tff(23,plain,
% 0.22/0.52 (~![Q: $int, S: $int, Sol: map_int_lpmap_int_intrp, K: $int, Col: map_int_int] : (![S1: $int, Sol1: map_int_lpmap_int_intrp, K1: $int, Col1: map_int_int] : ((~($greatereq($sum(S1, $product(-1, S)), 0) & ($sum(K1, $product(-1, K)) = 0) & sorted1(Sol1, S, S1) & ![T: map_int_int] : ((partial_solution1(n1, T) & eq_prefix1(int, t2tb2(Col1), t2tb2(T), K1)) <=> ?[I: $int] : ($greatereq($sum(I, $product(-1, S)), 0) & (~$greatereq($sum(I, $product(-1, S1)), 0)) & eq_prefix1(int, t2tb2(T), get(map(int, int), int, t2tb3(Sol1), t2tb1(I)), n1))) & eq_prefix1(int, t2tb2(Col), t2tb2(Col1), K1) & eq_prefix1(map(int, int), t2tb3(Sol), t2tb3(Sol1), S))) | ((S = 0) & sorted1(Sol1, 0, S1) & ![T: map_int_int] : (partial_solution1(n1, T) <=> ?[I: $int] : ($greatereq(I, 0) & (~$greatereq($sum(I, $sum(S, $product(-1, S1))), 0)) & eq_prefix1(int, t2tb2(T), get(map(int, int), int, t2tb3(Sol1), t2tb1(I)), n1))))) | (~($greatereq(Q, 0) & ($sum(n1, $product(-1, Q)) = 0) & (S = 0) & (K = 0))) | (~($greatereq(K, 0) & ($sum(K, $sum($product(-1, n1), cardinal1(int, t2tb(below1(Q))))) = 0) & $greatereq(S, 0) & ![I: $int] : (mem(int, t2tb1(I), t2tb(below1(Q))) <=> ($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, n1)), 0)) & ![J: $int] : ((~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, K)), 0)))) | (~($sum(I, $product(-1, tb2t1(get(int, int, t2tb2(Col), t2tb1(J))))) = 0))))) & ![I: $int] : ((~$greatereq(I, 0)) | ((~mem(int, t2tb1(I), empty(int))) <=> ![J: $int] : ((~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, K)), 0)))) | (~($sum(I, $sum(J, $sum($product(-1, tb2t1(get(int, int, t2tb2(Col), t2tb1(J)))), $product(-1, K)))) = 0))))) & ![I: $int] : ((~$greatereq(I, 0)) | ((~mem(int, t2tb1(I), empty(int))) <=> ![J: $int] : ((~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, K)), 0)))) | (~($sum(I, $sum($product(-1, J), $sum($product(-1, tb2t1(get(int, int, t2tb2(Col), t2tb1(J)))), K))) = 0))))) & partial_solution1(K, Col))))),
% 0.22/0.52 inference(modus_ponens,[status(thm)],[22, 11])).
% 0.22/0.52 tff(24,plain,
% 0.22/0.52 (~![Q: $int, S: $int, Sol: map_int_lpmap_int_intrp, K: $int, Col: map_int_int] : (![S1: $int, Sol1: map_int_lpmap_int_intrp, K1: $int, Col1: map_int_int] : ((~($greatereq($sum(S1, $product(-1, S)), 0) & ($sum(K1, $product(-1, K)) = 0) & sorted1(Sol1, S, S1) & ![T: map_int_int] : ((partial_solution1(n1, T) & eq_prefix1(int, t2tb2(Col1), t2tb2(T), K1)) <=> ?[I: $int] : ($greatereq($sum(I, $product(-1, S)), 0) & (~$greatereq($sum(I, $product(-1, S1)), 0)) & eq_prefix1(int, t2tb2(T), get(map(int, int), int, t2tb3(Sol1), t2tb1(I)), n1))) & eq_prefix1(int, t2tb2(Col), t2tb2(Col1), K1) & eq_prefix1(map(int, int), t2tb3(Sol), t2tb3(Sol1), S))) | ((S = 0) & sorted1(Sol1, 0, S1) & ![T: map_int_int] : (partial_solution1(n1, T) <=> ?[I: $int] : ($greatereq(I, 0) & (~$greatereq($sum(I, $sum(S, $product(-1, S1))), 0)) & eq_prefix1(int, t2tb2(T), get(map(int, int), int, t2tb3(Sol1), t2tb1(I)), n1))))) | (~($greatereq(Q, 0) & ($sum(n1, $product(-1, Q)) = 0) & (S = 0) & (K = 0))) | (~($greatereq(K, 0) & ($sum(K, $sum($product(-1, n1), cardinal1(int, t2tb(below1(Q))))) = 0) & $greatereq(S, 0) & ![I: $int] : (mem(int, t2tb1(I), t2tb(below1(Q))) <=> ($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, n1)), 0)) & ![J: $int] : ((~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, K)), 0)))) | (~($sum(I, $product(-1, tb2t1(get(int, int, t2tb2(Col), t2tb1(J))))) = 0))))) & ![I: $int] : ((~$greatereq(I, 0)) | ((~mem(int, t2tb1(I), empty(int))) <=> ![J: $int] : ((~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, K)), 0)))) | (~($sum(I, $sum(J, $sum($product(-1, tb2t1(get(int, int, t2tb2(Col), t2tb1(J)))), $product(-1, K)))) = 0))))) & ![I: $int] : ((~$greatereq(I, 0)) | ((~mem(int, t2tb1(I), empty(int))) <=> ![J: $int] : ((~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, K)), 0)))) | (~($sum(I, $sum($product(-1, J), $sum($product(-1, tb2t1(get(int, int, t2tb2(Col), t2tb1(J)))), K))) = 0))))) & partial_solution1(K, Col))))),
% 0.22/0.52 inference(modus_ponens,[status(thm)],[23, 11])).
% 0.22/0.52 tff(25,plain,
% 0.22/0.52 ($lesseq($sum(S!12, $product(-1, S1!17)), 0) & ($sum(K!10, $product(-1, K1!15)) = 0) & sorted1(Sol1!16, S!12, S1!17) & ![T: map_int_int] : (((~(partial_solution1(n1, T) & eq_prefix1(int, t2tb2(Col1!14), t2tb2(T), K1!15))) | ($lesseq($sum(S!12, $product(-1, tptp_fun_I_18(T))), 0) & (~$lesseq($sum(S1!17, $product(-1, tptp_fun_I_18(T))), 0)) & eq_prefix1(int, t2tb2(T), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(tptp_fun_I_18(T))), n1))) & ((partial_solution1(n1, T) & eq_prefix1(int, t2tb2(Col1!14), t2tb2(T), K1!15)) | ![I: $int] : (~($greatereq($sum(I, $product(-1, S!12)), 0) & (~$greatereq($sum(I, $product(-1, S1!17)), 0)) & eq_prefix1(int, t2tb2(T), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(I)), n1))))) & eq_prefix1(int, t2tb2(Col!9), t2tb2(Col1!14), K1!15) & eq_prefix1(map(int, int), t2tb3(Sol!11), t2tb3(Sol1!16), S!12) & ((~(S!12 = 0)) | (~sorted1(Sol1!16, 0, S1!17)) | ((partial_solution1(n1, T!19) | ($greatereq(I!20, 0) & (~$greatereq($sum(S!12, $sum($product(-1, S1!17), I!20)), 0)) & eq_prefix1(int, t2tb2(T!19), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(I!20)), n1))) & ((~partial_solution1(n1, T!19)) | ![I: $int] : (~($greatereq(I, 0) & (~$greatereq($sum(I, $sum(S!12, $product(-1, S1!17))), 0)) & eq_prefix1(int, t2tb2(T!19), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(I)), n1)))))) & $greatereq(Q!13, 0) & ($sum(n1, $product(-1, Q!13)) = 0) & (S!12 = 0) & (K!10 = 0) & $greatereq(K!10, 0) & ($sum(n1, $sum($product(-1, K!10), $product(-1, cardinal1(int, t2tb(below1(Q!13)))))) = 0) & $greatereq(S!12, 0) & ![I: $int] : (((~mem(int, t2tb1(I), t2tb(below1(Q!13)))) | ($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, n1)), 0)) & ![J: $int] : ((~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, K!10)), 0)))) | (~($sum(I, $product(-1, tb2t1(get(int, int, t2tb2(Col!9), t2tb1(J))))) = 0))))) & ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, n1)), 0) | mem(int, t2tb1(I), t2tb(below1(Q!13))) | (~((~($greatereq(tptp_fun_J_21(I), 0) & (~$lesseq($sum(K!10, $product(-1, tptp_fun_J_21(I))), 0)))) | (~($sum(I, $product(-1, tb2t1(get(int, int, t2tb2(Col!9), t2tb1(tptp_fun_J_21(I)))))) = 0)))))) & ![I: $int] : ((~$greatereq(I, 0)) | ((mem(int, t2tb1(I), empty(int)) | ![J: $int] : ((~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, K!10)), 0)))) | (~($sum(I, $sum(J, $sum($product(-1, K!10), $product(-1, tb2t1(get(int, int, t2tb2(Col!9), t2tb1(J))))))) = 0)))) & ((~mem(int, t2tb1(I), empty(int))) | (~((~($greatereq(tptp_fun_J_22(I), 0) & (~$lesseq($sum(K!10, $product(-1, tptp_fun_J_22(I))), 0)))) | (~($sum(I, $sum($product(-1, K!10), $sum(tptp_fun_J_22(I), $product(-1, tb2t1(get(int, int, t2tb2(Col!9), t2tb1(tptp_fun_J_22(I)))))))) = 0))))))) & ![I: $int] : ((~$greatereq(I, 0)) | ((mem(int, t2tb1(I), empty(int)) | ![J: $int] : ((~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, K!10)), 0)))) | (~($sum(I, $sum($product(-1, J), $sum(K!10, $product(-1, tb2t1(get(int, int, t2tb2(Col!9), t2tb1(J))))))) = 0)))) & ((~mem(int, t2tb1(I), empty(int))) | (~((~($greatereq(tptp_fun_J_23(I), 0) & (~$lesseq($sum(K!10, $product(-1, tptp_fun_J_23(I))), 0)))) | (~($sum(I, $sum(K!10, $sum($product(-1, tptp_fun_J_23(I)), $product(-1, tb2t1(get(int, int, t2tb2(Col!9), t2tb1(tptp_fun_J_23(I)))))))) = 0))))))) & partial_solution1(K!10, Col!9)),
% 0.22/0.52 inference(modus_ponens,[status(thm)],[24, 10])).
% 0.22/0.52 tff(26,plain,
% 0.22/0.52 ($sum(K!10, $product(-1, K1!15)) = 0),
% 0.22/0.52 inference(and_elim,[status(thm)],[25])).
% 0.22/0.52 tff(27,plain,
% 0.22/0.52 ((~($sum(K!10, $product(-1, K1!15)) = 0)) | $lesseq($sum(K!10, $product(-1, K1!15)), 0)),
% 0.22/0.52 inference(theory_lemma,[status(thm)],[])).
% 0.22/0.52 tff(28,plain,
% 0.22/0.52 ($lesseq($sum(K!10, $product(-1, K1!15)), 0)),
% 0.22/0.52 inference(unit_resolution,[status(thm)],[27, 26])).
% 0.22/0.52 tff(29,plain,
% 0.22/0.52 ((~($sum(K!10, $product(-1, K1!15)) = 0)) | $greatereq($sum(K!10, $product(-1, K1!15)), 0)),
% 0.22/0.52 inference(theory_lemma,[status(thm)],[])).
% 0.22/0.52 tff(30,plain,
% 0.22/0.52 ($greatereq($sum(K!10, $product(-1, K1!15)), 0)),
% 0.22/0.52 inference(unit_resolution,[status(thm)],[29, 26])).
% 0.22/0.52 tff(31,plain,
% 0.22/0.52 (K!10 = 0),
% 0.22/0.52 inference(and_elim,[status(thm)],[25])).
% 0.22/0.52 tff(32,plain,
% 0.22/0.52 ((~(K!10 = 0)) | $lesseq(K!10, 0)),
% 0.22/0.52 inference(theory_lemma,[status(thm)],[])).
% 0.22/0.52 tff(33,plain,
% 0.22/0.52 ($lesseq(K!10, 0)),
% 0.22/0.52 inference(unit_resolution,[status(thm)],[32, 31])).
% 0.22/0.52 tff(34,plain,
% 0.22/0.52 ($greatereq(K!10, 0)),
% 0.22/0.52 inference(and_elim,[status(thm)],[25])).
% 0.22/0.52 tff(35,plain,
% 0.22/0.52 (K1!15 = 0),
% 0.22/0.52 inference(theory_lemma,[status(thm)],[34, 33, 30, 28])).
% 0.22/0.52 tff(36,plain,
% 0.22/0.52 (0 = K1!15),
% 0.22/0.52 inference(symmetry,[status(thm)],[35])).
% 0.22/0.52 tff(37,plain,
% 0.22/0.52 (eq_prefix1(int, t2tb2(Col1!14), t2tb2(T!19), 0) <=> eq_prefix1(int, t2tb2(Col1!14), t2tb2(T!19), K1!15)),
% 0.22/0.52 inference(monotonicity,[status(thm)],[36])).
% 0.22/0.52 tff(38,plain,
% 0.22/0.52 (eq_prefix1(int, t2tb2(Col1!14), t2tb2(T!19), K1!15) <=> eq_prefix1(int, t2tb2(Col1!14), t2tb2(T!19), 0)),
% 0.22/0.52 inference(symmetry,[status(thm)],[37])).
% 0.22/0.52 tff(39,plain,
% 0.22/0.52 ((~eq_prefix1(int, t2tb2(Col1!14), t2tb2(T!19), K1!15)) <=> (~eq_prefix1(int, t2tb2(Col1!14), t2tb2(T!19), 0))),
% 0.22/0.52 inference(monotonicity,[status(thm)],[38])).
% 0.22/0.52 tff(40,plain,
% 0.22/0.52 (^[T: map_int_int] : refl((~((~((~partial_solution1(n1, T)) | (~eq_prefix1(int, t2tb2(Col1!14), t2tb2(T), K1!15)) | (~($lesseq($sum(S1!17, $product(-1, tptp_fun_I_18(T))), 0) | (~$lesseq($sum(S!12, $product(-1, tptp_fun_I_18(T))), 0)) | (~eq_prefix1(int, t2tb2(T), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(tptp_fun_I_18(T))), n1)))))) | (~((~((~partial_solution1(n1, T)) | (~eq_prefix1(int, t2tb2(Col1!14), t2tb2(T), K1!15)))) | ![I: $int] : ($greatereq($sum(I, $product(-1, S1!17)), 0) | (~$greatereq($sum(I, $product(-1, S!12)), 0)) | (~eq_prefix1(int, t2tb2(T), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(I)), n1))))))) <=> (~((~((~partial_solution1(n1, T)) | (~eq_prefix1(int, t2tb2(Col1!14), t2tb2(T), K1!15)) | (~($lesseq($sum(S1!17, $product(-1, tptp_fun_I_18(T))), 0) | (~$lesseq($sum(S!12, $product(-1, tptp_fun_I_18(T))), 0)) | (~eq_prefix1(int, t2tb2(T), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(tptp_fun_I_18(T))), n1)))))) | (~((~((~partial_solution1(n1, T)) | (~eq_prefix1(int, t2tb2(Col1!14), t2tb2(T), K1!15)))) | ![I: $int] : ($greatereq($sum(I, $product(-1, S1!17)), 0) | (~$greatereq($sum(I, $product(-1, S!12)), 0)) | (~eq_prefix1(int, t2tb2(T), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(I)), n1))))))))),
% 0.22/0.53 inference(bind,[status(th)],[])).
% 0.22/0.53 tff(41,plain,
% 0.22/0.53 (![T: map_int_int] : (~((~((~partial_solution1(n1, T)) | (~eq_prefix1(int, t2tb2(Col1!14), t2tb2(T), K1!15)) | (~($lesseq($sum(S1!17, $product(-1, tptp_fun_I_18(T))), 0) | (~$lesseq($sum(S!12, $product(-1, tptp_fun_I_18(T))), 0)) | (~eq_prefix1(int, t2tb2(T), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(tptp_fun_I_18(T))), n1)))))) | (~((~((~partial_solution1(n1, T)) | (~eq_prefix1(int, t2tb2(Col1!14), t2tb2(T), K1!15)))) | ![I: $int] : ($greatereq($sum(I, $product(-1, S1!17)), 0) | (~$greatereq($sum(I, $product(-1, S!12)), 0)) | (~eq_prefix1(int, t2tb2(T), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(I)), n1))))))) <=> ![T: map_int_int] : (~((~((~partial_solution1(n1, T)) | (~eq_prefix1(int, t2tb2(Col1!14), t2tb2(T), K1!15)) | (~($lesseq($sum(S1!17, $product(-1, tptp_fun_I_18(T))), 0) | (~$lesseq($sum(S!12, $product(-1, tptp_fun_I_18(T))), 0)) | (~eq_prefix1(int, t2tb2(T), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(tptp_fun_I_18(T))), n1)))))) | (~((~((~partial_solution1(n1, T)) | (~eq_prefix1(int, t2tb2(Col1!14), t2tb2(T), K1!15)))) | ![I: $int] : ($greatereq($sum(I, $product(-1, S1!17)), 0) | (~$greatereq($sum(I, $product(-1, S!12)), 0)) | (~eq_prefix1(int, t2tb2(T), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(I)), n1)))))))),
% 0.22/0.53 inference(quant_intro,[status(thm)],[40])).
% 0.22/0.53 tff(42,plain,
% 0.22/0.53 (^[T: map_int_int] : rewrite((~((~((~partial_solution1(n1, T)) | (~eq_prefix1(int, t2tb2(Col1!14), t2tb2(T), K1!15)) | (~($lesseq($sum(S1!17, $product(-1, tptp_fun_I_18(T))), 0) | (~$lesseq($sum(S!12, $product(-1, tptp_fun_I_18(T))), 0)) | (~eq_prefix1(int, t2tb2(T), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(tptp_fun_I_18(T))), n1)))))) | (~((~((~partial_solution1(n1, T)) | (~eq_prefix1(int, t2tb2(Col1!14), t2tb2(T), K1!15)))) | ![I: $int] : ($greatereq($sum(I, $product(-1, S1!17)), 0) | (~$greatereq($sum(I, $product(-1, S!12)), 0)) | (~eq_prefix1(int, t2tb2(T), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(I)), n1))))))) <=> (~((~((~partial_solution1(n1, T)) | (~eq_prefix1(int, t2tb2(Col1!14), t2tb2(T), K1!15)) | (~($lesseq($sum(S1!17, $product(-1, tptp_fun_I_18(T))), 0) | (~$lesseq($sum(S!12, $product(-1, tptp_fun_I_18(T))), 0)) | (~eq_prefix1(int, t2tb2(T), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(tptp_fun_I_18(T))), n1)))))) | (~((~((~partial_solution1(n1, T)) | (~eq_prefix1(int, t2tb2(Col1!14), t2tb2(T), K1!15)))) | ![I: $int] : ($greatereq($sum(I, $product(-1, S1!17)), 0) | (~$greatereq($sum(I, $product(-1, S!12)), 0)) | (~eq_prefix1(int, t2tb2(T), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(I)), n1))))))))),
% 0.22/0.53 inference(bind,[status(th)],[])).
% 0.22/0.53 tff(43,plain,
% 0.22/0.53 (![T: map_int_int] : (~((~((~partial_solution1(n1, T)) | (~eq_prefix1(int, t2tb2(Col1!14), t2tb2(T), K1!15)) | (~($lesseq($sum(S1!17, $product(-1, tptp_fun_I_18(T))), 0) | (~$lesseq($sum(S!12, $product(-1, tptp_fun_I_18(T))), 0)) | (~eq_prefix1(int, t2tb2(T), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(tptp_fun_I_18(T))), n1)))))) | (~((~((~partial_solution1(n1, T)) | (~eq_prefix1(int, t2tb2(Col1!14), t2tb2(T), K1!15)))) | ![I: $int] : ($greatereq($sum(I, $product(-1, S1!17)), 0) | (~$greatereq($sum(I, $product(-1, S!12)), 0)) | (~eq_prefix1(int, t2tb2(T), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(I)), n1))))))) <=> ![T: map_int_int] : (~((~((~partial_solution1(n1, T)) | (~eq_prefix1(int, t2tb2(Col1!14), t2tb2(T), K1!15)) | (~($lesseq($sum(S1!17, $product(-1, tptp_fun_I_18(T))), 0) | (~$lesseq($sum(S!12, $product(-1, tptp_fun_I_18(T))), 0)) | (~eq_prefix1(int, t2tb2(T), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(tptp_fun_I_18(T))), n1)))))) | (~((~((~partial_solution1(n1, T)) | (~eq_prefix1(int, t2tb2(Col1!14), t2tb2(T), K1!15)))) | ![I: $int] : ($greatereq($sum(I, $product(-1, S1!17)), 0) | (~$greatereq($sum(I, $product(-1, S!12)), 0)) | (~eq_prefix1(int, t2tb2(T), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(I)), n1)))))))),
% 0.22/0.53 inference(quant_intro,[status(thm)],[42])).
% 0.22/0.53 tff(44,plain,
% 0.22/0.53 (![T: map_int_int] : (~((~((~partial_solution1(n1, T)) | (~eq_prefix1(int, t2tb2(Col1!14), t2tb2(T), K1!15)) | (~($lesseq($sum(S1!17, $product(-1, tptp_fun_I_18(T))), 0) | (~$lesseq($sum(S!12, $product(-1, tptp_fun_I_18(T))), 0)) | (~eq_prefix1(int, t2tb2(T), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(tptp_fun_I_18(T))), n1)))))) | (~((~((~partial_solution1(n1, T)) | (~eq_prefix1(int, t2tb2(Col1!14), t2tb2(T), K1!15)))) | ![I: $int] : ($greatereq($sum(I, $product(-1, S1!17)), 0) | (~$greatereq($sum(I, $product(-1, S!12)), 0)) | (~eq_prefix1(int, t2tb2(T), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(I)), n1))))))) <=> ![T: map_int_int] : (~((~((~partial_solution1(n1, T)) | (~eq_prefix1(int, t2tb2(Col1!14), t2tb2(T), K1!15)) | (~($lesseq($sum(S1!17, $product(-1, tptp_fun_I_18(T))), 0) | (~$lesseq($sum(S!12, $product(-1, tptp_fun_I_18(T))), 0)) | (~eq_prefix1(int, t2tb2(T), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(tptp_fun_I_18(T))), n1)))))) | (~((~((~partial_solution1(n1, T)) | (~eq_prefix1(int, t2tb2(Col1!14), t2tb2(T), K1!15)))) | ![I: $int] : ($greatereq($sum(I, $product(-1, S1!17)), 0) | (~$greatereq($sum(I, $product(-1, S!12)), 0)) | (~eq_prefix1(int, t2tb2(T), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(I)), n1)))))))),
% 0.22/0.53 inference(transitivity,[status(thm)],[43, 41])).
% 0.22/0.53 tff(45,plain,
% 0.22/0.53 (^[T: map_int_int] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((partial_solution1(n1, T) & eq_prefix1(int, t2tb2(Col1!14), t2tb2(T), K1!15)) <=> (~((~partial_solution1(n1, T)) | (~eq_prefix1(int, t2tb2(Col1!14), t2tb2(T), K1!15))))), ((~(partial_solution1(n1, T) & eq_prefix1(int, t2tb2(Col1!14), t2tb2(T), K1!15))) <=> (~(~((~partial_solution1(n1, T)) | (~eq_prefix1(int, t2tb2(Col1!14), t2tb2(T), K1!15))))))), rewrite((~(~((~partial_solution1(n1, T)) | (~eq_prefix1(int, t2tb2(Col1!14), t2tb2(T), K1!15))))) <=> ((~partial_solution1(n1, T)) | (~eq_prefix1(int, t2tb2(Col1!14), t2tb2(T), K1!15)))), ((~(partial_solution1(n1, T) & eq_prefix1(int, t2tb2(Col1!14), t2tb2(T), K1!15))) <=> ((~partial_solution1(n1, T)) | (~eq_prefix1(int, t2tb2(Col1!14), t2tb2(T), K1!15))))), rewrite(($lesseq($sum(S!12, $product(-1, tptp_fun_I_18(T))), 0) & (~$lesseq($sum(S1!17, $product(-1, tptp_fun_I_18(T))), 0)) & eq_prefix1(int, t2tb2(T), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(tptp_fun_I_18(T))), n1)) <=> (~($lesseq($sum(S1!17, $product(-1, tptp_fun_I_18(T))), 0) | (~$lesseq($sum(S!12, $product(-1, tptp_fun_I_18(T))), 0)) | (~eq_prefix1(int, t2tb2(T), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(tptp_fun_I_18(T))), n1))))), (((~(partial_solution1(n1, T) & eq_prefix1(int, t2tb2(Col1!14), t2tb2(T), K1!15))) | ($lesseq($sum(S!12, $product(-1, tptp_fun_I_18(T))), 0) & (~$lesseq($sum(S1!17, $product(-1, tptp_fun_I_18(T))), 0)) & eq_prefix1(int, t2tb2(T), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(tptp_fun_I_18(T))), n1))) <=> (((~partial_solution1(n1, T)) | (~eq_prefix1(int, t2tb2(Col1!14), t2tb2(T), K1!15))) | (~($lesseq($sum(S1!17, $product(-1, tptp_fun_I_18(T))), 0) | (~$lesseq($sum(S!12, $product(-1, tptp_fun_I_18(T))), 0)) | (~eq_prefix1(int, t2tb2(T), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(tptp_fun_I_18(T))), n1))))))), rewrite((((~partial_solution1(n1, T)) | (~eq_prefix1(int, t2tb2(Col1!14), t2tb2(T), K1!15))) | (~($lesseq($sum(S1!17, $product(-1, tptp_fun_I_18(T))), 0) | (~$lesseq($sum(S!12, $product(-1, tptp_fun_I_18(T))), 0)) | (~eq_prefix1(int, t2tb2(T), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(tptp_fun_I_18(T))), n1))))) <=> ((~partial_solution1(n1, T)) | (~eq_prefix1(int, t2tb2(Col1!14), t2tb2(T), K1!15)) | (~($lesseq($sum(S1!17, $product(-1, tptp_fun_I_18(T))), 0) | (~$lesseq($sum(S!12, $product(-1, tptp_fun_I_18(T))), 0)) | (~eq_prefix1(int, t2tb2(T), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(tptp_fun_I_18(T))), n1)))))), (((~(partial_solution1(n1, T) & eq_prefix1(int, t2tb2(Col1!14), t2tb2(T), K1!15))) | ($lesseq($sum(S!12, $product(-1, tptp_fun_I_18(T))), 0) & (~$lesseq($sum(S1!17, $product(-1, tptp_fun_I_18(T))), 0)) & eq_prefix1(int, t2tb2(T), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(tptp_fun_I_18(T))), n1))) <=> ((~partial_solution1(n1, T)) | (~eq_prefix1(int, t2tb2(Col1!14), t2tb2(T), K1!15)) | (~($lesseq($sum(S1!17, $product(-1, tptp_fun_I_18(T))), 0) | (~$lesseq($sum(S!12, $product(-1, tptp_fun_I_18(T))), 0)) | (~eq_prefix1(int, t2tb2(T), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(tptp_fun_I_18(T))), n1))))))), rewrite(((partial_solution1(n1, T) & eq_prefix1(int, t2tb2(Col1!14), t2tb2(T), K1!15)) | ![I: $int] : (~($greatereq($sum(I, $product(-1, S!12)), 0) & (~$greatereq($sum(I, $product(-1, S1!17)), 0)) & eq_prefix1(int, t2tb2(T), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(I)), n1)))) <=> ((~((~partial_solution1(n1, T)) | (~eq_prefix1(int, t2tb2(Col1!14), t2tb2(T), K1!15)))) | ![I: $int] : ($greatereq($sum(I, $product(-1, S1!17)), 0) | (~$greatereq($sum(I, $product(-1, S!12)), 0)) | (~eq_prefix1(int, t2tb2(T), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(I)), n1))))), ((((~(partial_solution1(n1, T) & eq_prefix1(int, t2tb2(Col1!14), t2tb2(T), K1!15))) | ($lesseq($sum(S!12, $product(-1, tptp_fun_I_18(T))), 0) & (~$lesseq($sum(S1!17, $product(-1, tptp_fun_I_18(T))), 0)) & eq_prefix1(int, t2tb2(T), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(tptp_fun_I_18(T))), n1))) & ((partial_solution1(n1, T) & eq_prefix1(int, t2tb2(Col1!14), t2tb2(T), K1!15)) | ![I: $int] : (~($greatereq($sum(I, $product(-1, S!12)), 0) & (~$greatereq($sum(I, $product(-1, S1!17)), 0)) & eq_prefix1(int, t2tb2(T), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(I)), n1))))) <=> (((~partial_solution1(n1, T)) | (~eq_prefix1(int, t2tb2(Col1!14), t2tb2(T), K1!15)) | (~($lesseq($sum(S1!17, $product(-1, tptp_fun_I_18(T))), 0) | (~$lesseq($sum(S!12, $product(-1, tptp_fun_I_18(T))), 0)) | (~eq_prefix1(int, t2tb2(T), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(tptp_fun_I_18(T))), n1))))) & ((~((~partial_solution1(n1, T)) | (~eq_prefix1(int, t2tb2(Col1!14), t2tb2(T), K1!15)))) | ![I: $int] : ($greatereq($sum(I, $product(-1, S1!17)), 0) | (~$greatereq($sum(I, $product(-1, S!12)), 0)) | (~eq_prefix1(int, t2tb2(T), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(I)), n1))))))), rewrite((((~partial_solution1(n1, T)) | (~eq_prefix1(int, t2tb2(Col1!14), t2tb2(T), K1!15)) | (~($lesseq($sum(S1!17, $product(-1, tptp_fun_I_18(T))), 0) | (~$lesseq($sum(S!12, $product(-1, tptp_fun_I_18(T))), 0)) | (~eq_prefix1(int, t2tb2(T), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(tptp_fun_I_18(T))), n1))))) & ((~((~partial_solution1(n1, T)) | (~eq_prefix1(int, t2tb2(Col1!14), t2tb2(T), K1!15)))) | ![I: $int] : ($greatereq($sum(I, $product(-1, S1!17)), 0) | (~$greatereq($sum(I, $product(-1, S!12)), 0)) | (~eq_prefix1(int, t2tb2(T), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(I)), n1))))) <=> (~((~((~partial_solution1(n1, T)) | (~eq_prefix1(int, t2tb2(Col1!14), t2tb2(T), K1!15)) | (~($lesseq($sum(S1!17, $product(-1, tptp_fun_I_18(T))), 0) | (~$lesseq($sum(S!12, $product(-1, tptp_fun_I_18(T))), 0)) | (~eq_prefix1(int, t2tb2(T), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(tptp_fun_I_18(T))), n1)))))) | (~((~((~partial_solution1(n1, T)) | (~eq_prefix1(int, t2tb2(Col1!14), t2tb2(T), K1!15)))) | ![I: $int] : ($greatereq($sum(I, $product(-1, S1!17)), 0) | (~$greatereq($sum(I, $product(-1, S!12)), 0)) | (~eq_prefix1(int, t2tb2(T), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(I)), n1)))))))), ((((~(partial_solution1(n1, T) & eq_prefix1(int, t2tb2(Col1!14), t2tb2(T), K1!15))) | ($lesseq($sum(S!12, $product(-1, tptp_fun_I_18(T))), 0) & (~$lesseq($sum(S1!17, $product(-1, tptp_fun_I_18(T))), 0)) & eq_prefix1(int, t2tb2(T), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(tptp_fun_I_18(T))), n1))) & ((partial_solution1(n1, T) & eq_prefix1(int, t2tb2(Col1!14), t2tb2(T), K1!15)) | ![I: $int] : (~($greatereq($sum(I, $product(-1, S!12)), 0) & (~$greatereq($sum(I, $product(-1, S1!17)), 0)) & eq_prefix1(int, t2tb2(T), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(I)), n1))))) <=> (~((~((~partial_solution1(n1, T)) | (~eq_prefix1(int, t2tb2(Col1!14), t2tb2(T), K1!15)) | (~($lesseq($sum(S1!17, $product(-1, tptp_fun_I_18(T))), 0) | (~$lesseq($sum(S!12, $product(-1, tptp_fun_I_18(T))), 0)) | (~eq_prefix1(int, t2tb2(T), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(tptp_fun_I_18(T))), n1)))))) | (~((~((~partial_solution1(n1, T)) | (~eq_prefix1(int, t2tb2(Col1!14), t2tb2(T), K1!15)))) | ![I: $int] : ($greatereq($sum(I, $product(-1, S1!17)), 0) | (~$greatereq($sum(I, $product(-1, S!12)), 0)) | (~eq_prefix1(int, t2tb2(T), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(I)), n1)))))))))),
% 0.22/0.53 inference(bind,[status(th)],[])).
% 0.22/0.53 tff(46,plain,
% 0.22/0.53 (![T: map_int_int] : (((~(partial_solution1(n1, T) & eq_prefix1(int, t2tb2(Col1!14), t2tb2(T), K1!15))) | ($lesseq($sum(S!12, $product(-1, tptp_fun_I_18(T))), 0) & (~$lesseq($sum(S1!17, $product(-1, tptp_fun_I_18(T))), 0)) & eq_prefix1(int, t2tb2(T), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(tptp_fun_I_18(T))), n1))) & ((partial_solution1(n1, T) & eq_prefix1(int, t2tb2(Col1!14), t2tb2(T), K1!15)) | ![I: $int] : (~($greatereq($sum(I, $product(-1, S!12)), 0) & (~$greatereq($sum(I, $product(-1, S1!17)), 0)) & eq_prefix1(int, t2tb2(T), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(I)), n1))))) <=> ![T: map_int_int] : (~((~((~partial_solution1(n1, T)) | (~eq_prefix1(int, t2tb2(Col1!14), t2tb2(T), K1!15)) | (~($lesseq($sum(S1!17, $product(-1, tptp_fun_I_18(T))), 0) | (~$lesseq($sum(S!12, $product(-1, tptp_fun_I_18(T))), 0)) | (~eq_prefix1(int, t2tb2(T), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(tptp_fun_I_18(T))), n1)))))) | (~((~((~partial_solution1(n1, T)) | (~eq_prefix1(int, t2tb2(Col1!14), t2tb2(T), K1!15)))) | ![I: $int] : ($greatereq($sum(I, $product(-1, S1!17)), 0) | (~$greatereq($sum(I, $product(-1, S!12)), 0)) | (~eq_prefix1(int, t2tb2(T), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(I)), n1)))))))),
% 0.22/0.53 inference(quant_intro,[status(thm)],[45])).
% 0.22/0.53 tff(47,plain,
% 0.22/0.53 (![T: map_int_int] : (((~(partial_solution1(n1, T) & eq_prefix1(int, t2tb2(Col1!14), t2tb2(T), K1!15))) | ($lesseq($sum(S!12, $product(-1, tptp_fun_I_18(T))), 0) & (~$lesseq($sum(S1!17, $product(-1, tptp_fun_I_18(T))), 0)) & eq_prefix1(int, t2tb2(T), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(tptp_fun_I_18(T))), n1))) & ((partial_solution1(n1, T) & eq_prefix1(int, t2tb2(Col1!14), t2tb2(T), K1!15)) | ![I: $int] : (~($greatereq($sum(I, $product(-1, S!12)), 0) & (~$greatereq($sum(I, $product(-1, S1!17)), 0)) & eq_prefix1(int, t2tb2(T), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(I)), n1)))))),
% 0.22/0.53 inference(and_elim,[status(thm)],[25])).
% 0.22/0.53 tff(48,plain,
% 0.22/0.53 (![T: map_int_int] : (~((~((~partial_solution1(n1, T)) | (~eq_prefix1(int, t2tb2(Col1!14), t2tb2(T), K1!15)) | (~($lesseq($sum(S1!17, $product(-1, tptp_fun_I_18(T))), 0) | (~$lesseq($sum(S!12, $product(-1, tptp_fun_I_18(T))), 0)) | (~eq_prefix1(int, t2tb2(T), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(tptp_fun_I_18(T))), n1)))))) | (~((~((~partial_solution1(n1, T)) | (~eq_prefix1(int, t2tb2(Col1!14), t2tb2(T), K1!15)))) | ![I: $int] : ($greatereq($sum(I, $product(-1, S1!17)), 0) | (~$greatereq($sum(I, $product(-1, S!12)), 0)) | (~eq_prefix1(int, t2tb2(T), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(I)), n1)))))))),
% 0.22/0.53 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.22/0.53 tff(49,plain,
% 0.22/0.53 (![T: map_int_int] : (~((~((~partial_solution1(n1, T)) | (~eq_prefix1(int, t2tb2(Col1!14), t2tb2(T), K1!15)) | (~($lesseq($sum(S1!17, $product(-1, tptp_fun_I_18(T))), 0) | (~$lesseq($sum(S!12, $product(-1, tptp_fun_I_18(T))), 0)) | (~eq_prefix1(int, t2tb2(T), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(tptp_fun_I_18(T))), n1)))))) | (~((~((~partial_solution1(n1, T)) | (~eq_prefix1(int, t2tb2(Col1!14), t2tb2(T), K1!15)))) | ![I: $int] : ($greatereq($sum(I, $product(-1, S1!17)), 0) | (~$greatereq($sum(I, $product(-1, S!12)), 0)) | (~eq_prefix1(int, t2tb2(T), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(I)), n1)))))))),
% 0.22/0.53 inference(modus_ponens,[status(thm)],[48, 44])).
% 0.22/0.53 tff(50,plain,
% 0.22/0.53 ((~![T: map_int_int] : (~((~((~partial_solution1(n1, T)) | (~eq_prefix1(int, t2tb2(Col1!14), t2tb2(T), K1!15)) | (~($lesseq($sum(S1!17, $product(-1, tptp_fun_I_18(T))), 0) | (~$lesseq($sum(S!12, $product(-1, tptp_fun_I_18(T))), 0)) | (~eq_prefix1(int, t2tb2(T), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(tptp_fun_I_18(T))), n1)))))) | (~((~((~partial_solution1(n1, T)) | (~eq_prefix1(int, t2tb2(Col1!14), t2tb2(T), K1!15)))) | ![I: $int] : ($greatereq($sum(I, $product(-1, S1!17)), 0) | (~$greatereq($sum(I, $product(-1, S!12)), 0)) | (~eq_prefix1(int, t2tb2(T), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(I)), n1)))))))) | (~((~((~partial_solution1(n1, T!19)) | (~eq_prefix1(int, t2tb2(Col1!14), t2tb2(T!19), K1!15)) | (~($lesseq($sum(S1!17, $product(-1, tptp_fun_I_18(T!19))), 0) | (~$lesseq($sum(S!12, $product(-1, tptp_fun_I_18(T!19))), 0)) | (~eq_prefix1(int, t2tb2(T!19), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(tptp_fun_I_18(T!19))), n1)))))) | (~((~((~partial_solution1(n1, T!19)) | (~eq_prefix1(int, t2tb2(Col1!14), t2tb2(T!19), K1!15)))) | ![I: $int] : ($greatereq($sum(I, $product(-1, S1!17)), 0) | (~$greatereq($sum(I, $product(-1, S!12)), 0)) | (~eq_prefix1(int, t2tb2(T!19), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(I)), n1)))))))),
% 0.22/0.53 inference(quant_inst,[status(thm)],[])).
% 0.22/0.53 tff(51,plain,
% 0.22/0.53 (~((~((~partial_solution1(n1, T!19)) | (~eq_prefix1(int, t2tb2(Col1!14), t2tb2(T!19), K1!15)) | (~($lesseq($sum(S1!17, $product(-1, tptp_fun_I_18(T!19))), 0) | (~$lesseq($sum(S!12, $product(-1, tptp_fun_I_18(T!19))), 0)) | (~eq_prefix1(int, t2tb2(T!19), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(tptp_fun_I_18(T!19))), n1)))))) | (~((~((~partial_solution1(n1, T!19)) | (~eq_prefix1(int, t2tb2(Col1!14), t2tb2(T!19), K1!15)))) | ![I: $int] : ($greatereq($sum(I, $product(-1, S1!17)), 0) | (~$greatereq($sum(I, $product(-1, S!12)), 0)) | (~eq_prefix1(int, t2tb2(T!19), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(I)), n1))))))),
% 0.22/0.53 inference(unit_resolution,[status(thm)],[50, 49])).
% 0.22/0.53 tff(52,plain,
% 0.22/0.53 (((~((~partial_solution1(n1, T!19)) | (~eq_prefix1(int, t2tb2(Col1!14), t2tb2(T!19), K1!15)) | (~($lesseq($sum(S1!17, $product(-1, tptp_fun_I_18(T!19))), 0) | (~$lesseq($sum(S!12, $product(-1, tptp_fun_I_18(T!19))), 0)) | (~eq_prefix1(int, t2tb2(T!19), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(tptp_fun_I_18(T!19))), n1)))))) | (~((~((~partial_solution1(n1, T!19)) | (~eq_prefix1(int, t2tb2(Col1!14), t2tb2(T!19), K1!15)))) | ![I: $int] : ($greatereq($sum(I, $product(-1, S1!17)), 0) | (~$greatereq($sum(I, $product(-1, S!12)), 0)) | (~eq_prefix1(int, t2tb2(T!19), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(I)), n1)))))) | ((~partial_solution1(n1, T!19)) | (~eq_prefix1(int, t2tb2(Col1!14), t2tb2(T!19), K1!15)) | (~($lesseq($sum(S1!17, $product(-1, tptp_fun_I_18(T!19))), 0) | (~$lesseq($sum(S!12, $product(-1, tptp_fun_I_18(T!19))), 0)) | (~eq_prefix1(int, t2tb2(T!19), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(tptp_fun_I_18(T!19))), n1)))))),
% 0.22/0.53 inference(tautology,[status(thm)],[])).
% 0.22/0.53 tff(53,plain,
% 0.22/0.53 ((~partial_solution1(n1, T!19)) | (~eq_prefix1(int, t2tb2(Col1!14), t2tb2(T!19), K1!15)) | (~($lesseq($sum(S1!17, $product(-1, tptp_fun_I_18(T!19))), 0) | (~$lesseq($sum(S!12, $product(-1, tptp_fun_I_18(T!19))), 0)) | (~eq_prefix1(int, t2tb2(T!19), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(tptp_fun_I_18(T!19))), n1))))),
% 0.22/0.53 inference(unit_resolution,[status(thm)],[52, 51])).
% 0.22/0.53 tff(54,assumption,(~($lesseq($sum(S1!17, $product(-1, tptp_fun_I_18(T!19))), 0) | (~$lesseq($sum(S!12, $product(-1, tptp_fun_I_18(T!19))), 0)) | (~eq_prefix1(int, t2tb2(T!19), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(tptp_fun_I_18(T!19))), n1)))), introduced(assumption)).
% 0.22/0.53 tff(55,plain,
% 0.22/0.53 (($lesseq($sum(S1!17, $product(-1, tptp_fun_I_18(T!19))), 0) | (~$lesseq($sum(S!12, $product(-1, tptp_fun_I_18(T!19))), 0)) | (~eq_prefix1(int, t2tb2(T!19), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(tptp_fun_I_18(T!19))), n1))) | (~$lesseq($sum(S1!17, $product(-1, tptp_fun_I_18(T!19))), 0))),
% 0.22/0.53 inference(tautology,[status(thm)],[])).
% 0.22/0.53 tff(56,plain,
% 0.22/0.53 (~$lesseq($sum(S1!17, $product(-1, tptp_fun_I_18(T!19))), 0)),
% 0.22/0.53 inference(unit_resolution,[status(thm)],[55, 54])).
% 0.22/0.54 tff(57,plain,
% 0.22/0.54 (![J: uni] : (t2tb1(tb2t1(J)) = J) <=> ![J: uni] : (t2tb1(tb2t1(J)) = J)),
% 0.22/0.54 inference(rewrite,[status(thm)],[])).
% 0.22/0.54 tff(58,plain,
% 0.22/0.54 (![J: uni] : (t2tb1(tb2t1(J)) = J) <=> ![J: uni] : (t2tb1(tb2t1(J)) = J)),
% 0.22/0.54 inference(rewrite,[status(thm)],[])).
% 0.22/0.54 tff(59,axiom,(![J: uni] : (t2tb1(tb2t1(J)) = J)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bridgeR1')).
% 0.22/0.54 tff(60,plain,
% 0.22/0.54 (![J: uni] : (t2tb1(tb2t1(J)) = J)),
% 0.22/0.54 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.22/0.54 tff(61,plain,(
% 0.22/0.54 ![J: uni] : (t2tb1(tb2t1(J)) = J)),
% 0.22/0.54 inference(skolemize,[status(sab)],[60])).
% 0.22/0.54 tff(62,plain,
% 0.22/0.54 (![J: uni] : (t2tb1(tb2t1(J)) = J)),
% 0.22/0.54 inference(modus_ponens,[status(thm)],[61, 57])).
% 0.22/0.54 tff(63,plain,
% 0.22/0.54 ((~![J: uni] : (t2tb1(tb2t1(J)) = J)) | (t2tb1(tb2t1(t2tb1(tptp_fun_I_18(T!19)))) = t2tb1(tptp_fun_I_18(T!19)))),
% 0.22/0.54 inference(quant_inst,[status(thm)],[])).
% 0.22/0.54 tff(64,plain,
% 0.22/0.54 (t2tb1(tb2t1(t2tb1(tptp_fun_I_18(T!19)))) = t2tb1(tptp_fun_I_18(T!19))),
% 0.22/0.54 inference(unit_resolution,[status(thm)],[63, 62])).
% 0.22/0.54 tff(65,plain,
% 0.22/0.54 (get(map(int, int), int, t2tb3(Sol1!16), t2tb1(tb2t1(t2tb1(tptp_fun_I_18(T!19))))) = get(map(int, int), int, t2tb3(Sol1!16), t2tb1(tptp_fun_I_18(T!19)))),
% 0.22/0.54 inference(monotonicity,[status(thm)],[64])).
% 0.22/0.54 tff(66,plain,
% 0.22/0.54 (eq_prefix1(int, t2tb2(T!19), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(tb2t1(t2tb1(tptp_fun_I_18(T!19))))), n1) <=> eq_prefix1(int, t2tb2(T!19), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(tptp_fun_I_18(T!19))), n1)),
% 0.22/0.54 inference(monotonicity,[status(thm)],[65])).
% 0.22/0.54 tff(67,plain,
% 0.22/0.54 (eq_prefix1(int, t2tb2(T!19), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(tptp_fun_I_18(T!19))), n1) <=> eq_prefix1(int, t2tb2(T!19), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(tb2t1(t2tb1(tptp_fun_I_18(T!19))))), n1)),
% 0.22/0.54 inference(symmetry,[status(thm)],[66])).
% 0.22/0.54 tff(68,plain,
% 0.22/0.54 (($lesseq($sum(S1!17, $product(-1, tptp_fun_I_18(T!19))), 0) | (~$lesseq($sum(S!12, $product(-1, tptp_fun_I_18(T!19))), 0)) | (~eq_prefix1(int, t2tb2(T!19), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(tptp_fun_I_18(T!19))), n1))) | eq_prefix1(int, t2tb2(T!19), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(tptp_fun_I_18(T!19))), n1)),
% 0.22/0.54 inference(tautology,[status(thm)],[])).
% 0.22/0.54 tff(69,plain,
% 0.22/0.54 (eq_prefix1(int, t2tb2(T!19), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(tptp_fun_I_18(T!19))), n1)),
% 0.22/0.54 inference(unit_resolution,[status(thm)],[68, 54])).
% 0.22/0.54 tff(70,plain,
% 0.22/0.54 (eq_prefix1(int, t2tb2(T!19), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(tb2t1(t2tb1(tptp_fun_I_18(T!19))))), n1)),
% 0.22/0.54 inference(modus_ponens,[status(thm)],[69, 67])).
% 0.22/0.54 tff(71,plain,
% 0.22/0.54 ($greatereq(S!12, 0)),
% 0.22/0.54 inference(and_elim,[status(thm)],[25])).
% 0.22/0.54 tff(72,plain,
% 0.22/0.54 (($lesseq($sum(S1!17, $product(-1, tptp_fun_I_18(T!19))), 0) | (~$lesseq($sum(S!12, $product(-1, tptp_fun_I_18(T!19))), 0)) | (~eq_prefix1(int, t2tb2(T!19), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(tptp_fun_I_18(T!19))), n1))) | $lesseq($sum(S!12, $product(-1, tptp_fun_I_18(T!19))), 0)),
% 0.22/0.54 inference(tautology,[status(thm)],[])).
% 0.22/0.54 tff(73,plain,
% 0.22/0.54 ($lesseq($sum(S!12, $product(-1, tptp_fun_I_18(T!19))), 0)),
% 0.22/0.54 inference(unit_resolution,[status(thm)],[72, 54])).
% 0.22/0.54 tff(74,assumption,($lesseq($sum(S!12, $product(-1, tptp_fun_I_18(T!19))), 0)), introduced(assumption)).
% 0.22/0.54 tff(75,assumption,(~$lesseq($sum(S!12, $product(-1, tb2t1(t2tb1(tptp_fun_I_18(T!19))))), 0)), introduced(assumption)).
% 0.22/0.54 tff(76,plain,
% 0.22/0.54 (^[I: $int] : refl(($sum(I, $product(-1, tb2t1(t2tb1(I)))) = 0) <=> ($sum(I, $product(-1, tb2t1(t2tb1(I)))) = 0))),
% 0.22/0.54 inference(bind,[status(th)],[])).
% 0.22/0.54 tff(77,plain,
% 0.22/0.54 (![I: $int] : ($sum(I, $product(-1, tb2t1(t2tb1(I)))) = 0) <=> ![I: $int] : ($sum(I, $product(-1, tb2t1(t2tb1(I)))) = 0)),
% 0.22/0.54 inference(quant_intro,[status(thm)],[76])).
% 0.22/0.54 tff(78,plain,
% 0.22/0.54 (^[I: $int] : trans(monotonicity(rewrite($sum(tb2t1(t2tb1(I)), $product(-1, I)) = $sum($product(-1, I), tb2t1(t2tb1(I)))), (($sum(tb2t1(t2tb1(I)), $product(-1, I)) = 0) <=> ($sum($product(-1, I), tb2t1(t2tb1(I))) = 0))), rewrite(($sum($product(-1, I), tb2t1(t2tb1(I))) = 0) <=> ($sum(I, $product(-1, tb2t1(t2tb1(I)))) = 0)), (($sum(tb2t1(t2tb1(I)), $product(-1, I)) = 0) <=> ($sum(I, $product(-1, tb2t1(t2tb1(I)))) = 0)))),
% 0.22/0.54 inference(bind,[status(th)],[])).
% 0.22/0.54 tff(79,plain,
% 0.22/0.54 (![I: $int] : ($sum(tb2t1(t2tb1(I)), $product(-1, I)) = 0) <=> ![I: $int] : ($sum(I, $product(-1, tb2t1(t2tb1(I)))) = 0)),
% 0.22/0.54 inference(quant_intro,[status(thm)],[78])).
% 0.22/0.54 tff(80,plain,
% 0.22/0.54 (^[I: $int] : rewrite((tb2t1(t2tb1(I)) = I) <=> ($sum(tb2t1(t2tb1(I)), $product(-1, I)) = 0))),
% 0.22/0.54 inference(bind,[status(th)],[])).
% 0.22/0.54 tff(81,plain,
% 0.22/0.54 (![I: $int] : (tb2t1(t2tb1(I)) = I) <=> ![I: $int] : ($sum(tb2t1(t2tb1(I)), $product(-1, I)) = 0)),
% 0.22/0.54 inference(quant_intro,[status(thm)],[80])).
% 0.22/0.54 tff(82,plain,
% 0.22/0.54 (![I: $int] : (tb2t1(t2tb1(I)) = I) <=> ![I: $int] : (tb2t1(t2tb1(I)) = I)),
% 0.22/0.54 inference(rewrite,[status(thm)],[])).
% 0.22/0.54 tff(83,axiom,(![I: $int] : (tb2t1(t2tb1(I)) = I)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bridgeL1')).
% 0.22/0.54 tff(84,plain,
% 0.22/0.54 (![I: $int] : (tb2t1(t2tb1(I)) = I)),
% 0.22/0.54 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.22/0.54 tff(85,plain,
% 0.22/0.54 (![I: $int] : ($sum(tb2t1(t2tb1(I)), $product(-1, I)) = 0)),
% 0.22/0.54 inference(modus_ponens,[status(thm)],[84, 81])).
% 0.22/0.54 tff(86,plain,
% 0.22/0.54 (![I: $int] : ($sum(I, $product(-1, tb2t1(t2tb1(I)))) = 0)),
% 0.22/0.54 inference(modus_ponens,[status(thm)],[85, 79])).
% 0.22/0.54 tff(87,plain,(
% 0.22/0.54 ![I: $int] : ($sum(I, $product(-1, tb2t1(t2tb1(I)))) = 0)),
% 0.22/0.54 inference(skolemize,[status(sab)],[86])).
% 0.22/0.54 tff(88,plain,
% 0.22/0.54 (![I: $int] : ($sum(I, $product(-1, tb2t1(t2tb1(I)))) = 0)),
% 0.22/0.54 inference(modus_ponens,[status(thm)],[87, 77])).
% 0.22/0.54 tff(89,plain,
% 0.22/0.54 ((~![I: $int] : ($sum(I, $product(-1, tb2t1(t2tb1(I)))) = 0)) | ($sum(tptp_fun_I_18(T!19), $product(-1, tb2t1(t2tb1(tptp_fun_I_18(T!19))))) = 0)),
% 0.22/0.54 inference(quant_inst,[status(thm)],[])).
% 0.22/0.54 tff(90,plain,
% 0.22/0.54 ($sum(tptp_fun_I_18(T!19), $product(-1, tb2t1(t2tb1(tptp_fun_I_18(T!19))))) = 0),
% 0.22/0.54 inference(unit_resolution,[status(thm)],[89, 88])).
% 0.22/0.54 tff(91,plain,
% 0.22/0.54 ((~($sum(tptp_fun_I_18(T!19), $product(-1, tb2t1(t2tb1(tptp_fun_I_18(T!19))))) = 0)) | $lesseq($sum(tptp_fun_I_18(T!19), $product(-1, tb2t1(t2tb1(tptp_fun_I_18(T!19))))), 0)),
% 0.22/0.54 inference(theory_lemma,[status(thm)],[])).
% 0.22/0.54 tff(92,plain,
% 0.22/0.54 ($lesseq($sum(tptp_fun_I_18(T!19), $product(-1, tb2t1(t2tb1(tptp_fun_I_18(T!19))))), 0)),
% 0.22/0.54 inference(unit_resolution,[status(thm)],[91, 90])).
% 0.22/0.54 tff(93,plain,
% 0.22/0.54 ($false),
% 0.22/0.54 inference(theory_lemma,[status(thm)],[92, 75, 74])).
% 0.22/0.54 tff(94,plain,($lesseq($sum(S!12, $product(-1, tb2t1(t2tb1(tptp_fun_I_18(T!19))))), 0) | (~$lesseq($sum(S!12, $product(-1, tptp_fun_I_18(T!19))), 0))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.54 tff(95,plain,
% 0.22/0.54 ($lesseq($sum(S!12, $product(-1, tb2t1(t2tb1(tptp_fun_I_18(T!19))))), 0)),
% 0.22/0.54 inference(unit_resolution,[status(thm)],[94, 73])).
% 0.22/0.54 tff(96,plain,
% 0.22/0.54 ($greatereq(tb2t1(t2tb1(tptp_fun_I_18(T!19))), 0) | (~$greatereq(S!12, 0)) | (~$lesseq($sum(S!12, $product(-1, tb2t1(t2tb1(tptp_fun_I_18(T!19))))), 0))),
% 0.22/0.54 inference(theory_lemma,[status(thm)],[])).
% 0.22/0.54 tff(97,plain,
% 0.22/0.54 ($greatereq(tb2t1(t2tb1(tptp_fun_I_18(T!19))), 0)),
% 0.22/0.54 inference(unit_resolution,[status(thm)],[96, 95, 71])).
% 0.22/0.54 tff(98,assumption,(~partial_solution1(n1, T!19)), introduced(assumption)).
% 0.22/0.54 tff(99,plain,
% 0.22/0.54 (S!12 = 0),
% 0.22/0.54 inference(and_elim,[status(thm)],[25])).
% 0.22/0.54 tff(100,plain,
% 0.22/0.54 (sorted1(Sol1!16, S!12, S1!17) <=> sorted1(Sol1!16, 0, S1!17)),
% 0.22/0.54 inference(monotonicity,[status(thm)],[99])).
% 0.22/0.54 tff(101,plain,
% 0.22/0.54 (sorted1(Sol1!16, S!12, S1!17)),
% 0.22/0.54 inference(and_elim,[status(thm)],[25])).
% 0.22/0.54 tff(102,plain,
% 0.22/0.54 (sorted1(Sol1!16, 0, S1!17)),
% 0.22/0.54 inference(modus_ponens,[status(thm)],[101, 100])).
% 0.22/0.54 tff(103,plain,
% 0.22/0.54 (((~(S!12 = 0)) | (~sorted1(Sol1!16, 0, S1!17)) | (~((~(partial_solution1(n1, T!19) | (~($greatereq($sum(S!12, $sum($product(-1, S1!17), I!20)), 0) | (~$greatereq(I!20, 0)) | (~eq_prefix1(int, t2tb2(T!19), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(I!20)), n1)))))) | (~((~partial_solution1(n1, T!19)) | ![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $sum(S!12, $product(-1, S1!17))), 0) | (~eq_prefix1(int, t2tb2(T!19), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(I)), n1)))))))) <=> ((~(S!12 = 0)) | (~sorted1(Sol1!16, 0, S1!17)) | (~((~(partial_solution1(n1, T!19) | (~($greatereq($sum(S!12, $sum($product(-1, S1!17), I!20)), 0) | (~$greatereq(I!20, 0)) | (~eq_prefix1(int, t2tb2(T!19), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(I!20)), n1)))))) | (~((~partial_solution1(n1, T!19)) | ![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $sum(S!12, $product(-1, S1!17))), 0) | (~eq_prefix1(int, t2tb2(T!19), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(I)), n1))))))))),
% 0.22/0.54 inference(rewrite,[status(thm)],[])).
% 0.22/0.54 tff(104,plain,
% 0.22/0.54 (((~(S!12 = 0)) | (~sorted1(Sol1!16, 0, S1!17)) | ((partial_solution1(n1, T!19) | ($greatereq(I!20, 0) & (~$greatereq($sum(S!12, $sum($product(-1, S1!17), I!20)), 0)) & eq_prefix1(int, t2tb2(T!19), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(I!20)), n1))) & ((~partial_solution1(n1, T!19)) | ![I: $int] : (~($greatereq(I, 0) & (~$greatereq($sum(I, $sum(S!12, $product(-1, S1!17))), 0)) & eq_prefix1(int, t2tb2(T!19), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(I)), n1)))))) <=> ((~(S!12 = 0)) | (~sorted1(Sol1!16, 0, S1!17)) | (~((~(partial_solution1(n1, T!19) | (~($greatereq($sum(S!12, $sum($product(-1, S1!17), I!20)), 0) | (~$greatereq(I!20, 0)) | (~eq_prefix1(int, t2tb2(T!19), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(I!20)), n1)))))) | (~((~partial_solution1(n1, T!19)) | ![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $sum(S!12, $product(-1, S1!17))), 0) | (~eq_prefix1(int, t2tb2(T!19), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(I)), n1))))))))),
% 0.22/0.54 inference(rewrite,[status(thm)],[])).
% 0.22/0.54 tff(105,plain,
% 0.22/0.54 ((~(S!12 = 0)) | (~sorted1(Sol1!16, 0, S1!17)) | ((partial_solution1(n1, T!19) | ($greatereq(I!20, 0) & (~$greatereq($sum(S!12, $sum($product(-1, S1!17), I!20)), 0)) & eq_prefix1(int, t2tb2(T!19), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(I!20)), n1))) & ((~partial_solution1(n1, T!19)) | ![I: $int] : (~($greatereq(I, 0) & (~$greatereq($sum(I, $sum(S!12, $product(-1, S1!17))), 0)) & eq_prefix1(int, t2tb2(T!19), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(I)), n1)))))),
% 0.22/0.54 inference(and_elim,[status(thm)],[25])).
% 0.22/0.54 tff(106,plain,
% 0.22/0.54 ((~(S!12 = 0)) | (~sorted1(Sol1!16, 0, S1!17)) | (~((~(partial_solution1(n1, T!19) | (~($greatereq($sum(S!12, $sum($product(-1, S1!17), I!20)), 0) | (~$greatereq(I!20, 0)) | (~eq_prefix1(int, t2tb2(T!19), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(I!20)), n1)))))) | (~((~partial_solution1(n1, T!19)) | ![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $sum(S!12, $product(-1, S1!17))), 0) | (~eq_prefix1(int, t2tb2(T!19), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(I)), n1)))))))),
% 0.22/0.54 inference(modus_ponens,[status(thm)],[105, 104])).
% 0.22/0.54 tff(107,plain,
% 0.22/0.54 ((~(S!12 = 0)) | (~sorted1(Sol1!16, 0, S1!17)) | (~((~(partial_solution1(n1, T!19) | (~($greatereq($sum(S!12, $sum($product(-1, S1!17), I!20)), 0) | (~$greatereq(I!20, 0)) | (~eq_prefix1(int, t2tb2(T!19), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(I!20)), n1)))))) | (~((~partial_solution1(n1, T!19)) | ![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $sum(S!12, $product(-1, S1!17))), 0) | (~eq_prefix1(int, t2tb2(T!19), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(I)), n1)))))))),
% 0.22/0.54 inference(modus_ponens,[status(thm)],[106, 103])).
% 0.22/0.54 tff(108,plain,
% 0.22/0.54 (~((~(partial_solution1(n1, T!19) | (~($greatereq($sum(S!12, $sum($product(-1, S1!17), I!20)), 0) | (~$greatereq(I!20, 0)) | (~eq_prefix1(int, t2tb2(T!19), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(I!20)), n1)))))) | (~((~partial_solution1(n1, T!19)) | ![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $sum(S!12, $product(-1, S1!17))), 0) | (~eq_prefix1(int, t2tb2(T!19), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(I)), n1))))))),
% 0.22/0.54 inference(unit_resolution,[status(thm)],[107, 102, 99])).
% 0.22/0.54 tff(109,plain,
% 0.22/0.54 (((~(partial_solution1(n1, T!19) | (~($greatereq($sum(S!12, $sum($product(-1, S1!17), I!20)), 0) | (~$greatereq(I!20, 0)) | (~eq_prefix1(int, t2tb2(T!19), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(I!20)), n1)))))) | (~((~partial_solution1(n1, T!19)) | ![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $sum(S!12, $product(-1, S1!17))), 0) | (~eq_prefix1(int, t2tb2(T!19), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(I)), n1)))))) | (partial_solution1(n1, T!19) | (~($greatereq($sum(S!12, $sum($product(-1, S1!17), I!20)), 0) | (~$greatereq(I!20, 0)) | (~eq_prefix1(int, t2tb2(T!19), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(I!20)), n1)))))),
% 0.22/0.54 inference(tautology,[status(thm)],[])).
% 0.22/0.54 tff(110,plain,
% 0.22/0.54 (partial_solution1(n1, T!19) | (~($greatereq($sum(S!12, $sum($product(-1, S1!17), I!20)), 0) | (~$greatereq(I!20, 0)) | (~eq_prefix1(int, t2tb2(T!19), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(I!20)), n1))))),
% 0.22/0.54 inference(unit_resolution,[status(thm)],[109, 108])).
% 0.22/0.54 tff(111,plain,
% 0.22/0.54 ((~(partial_solution1(n1, T!19) | (~($greatereq($sum(S!12, $sum($product(-1, S1!17), I!20)), 0) | (~$greatereq(I!20, 0)) | (~eq_prefix1(int, t2tb2(T!19), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(I!20)), n1)))))) | partial_solution1(n1, T!19) | (~($greatereq($sum(S!12, $sum($product(-1, S1!17), I!20)), 0) | (~$greatereq(I!20, 0)) | (~eq_prefix1(int, t2tb2(T!19), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(I!20)), n1))))),
% 0.22/0.54 inference(tautology,[status(thm)],[])).
% 0.22/0.54 tff(112,plain,
% 0.22/0.54 (partial_solution1(n1, T!19) | (~($greatereq($sum(S!12, $sum($product(-1, S1!17), I!20)), 0) | (~$greatereq(I!20, 0)) | (~eq_prefix1(int, t2tb2(T!19), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(I!20)), n1))))),
% 0.22/0.54 inference(unit_resolution,[status(thm)],[111, 110])).
% 0.22/0.54 tff(113,plain,
% 0.22/0.54 (~($greatereq($sum(S!12, $sum($product(-1, S1!17), I!20)), 0) | (~$greatereq(I!20, 0)) | (~eq_prefix1(int, t2tb2(T!19), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(I!20)), n1)))),
% 0.22/0.54 inference(unit_resolution,[status(thm)],[112, 98])).
% 0.22/0.54 tff(114,plain,
% 0.22/0.54 (($greatereq($sum(S!12, $sum($product(-1, S1!17), I!20)), 0) | (~$greatereq(I!20, 0)) | (~eq_prefix1(int, t2tb2(T!19), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(I!20)), n1))) | (~$greatereq($sum(S!12, $sum($product(-1, S1!17), I!20)), 0))),
% 0.22/0.54 inference(tautology,[status(thm)],[])).
% 0.22/0.54 tff(115,plain,
% 0.22/0.54 (~$greatereq($sum(S!12, $sum($product(-1, S1!17), I!20)), 0)),
% 0.22/0.54 inference(unit_resolution,[status(thm)],[114, 113])).
% 0.22/0.54 tff(116,plain,
% 0.22/0.54 ((~$lesseq($sum(S1!17, $product(-1, I!20)), 0)) | (~$greatereq(S!12, 0)) | $greatereq($sum(S!12, $sum($product(-1, S1!17), I!20)), 0)),
% 0.22/0.54 inference(theory_lemma,[status(thm)],[])).
% 0.22/0.54 tff(117,plain,
% 0.22/0.54 (~$lesseq($sum(S1!17, $product(-1, I!20)), 0)),
% 0.22/0.54 inference(unit_resolution,[status(thm)],[116, 115, 71])).
% 0.22/0.54 tff(118,plain,
% 0.22/0.54 ((~(S!12 = 0)) | $lesseq(S!12, 0)),
% 0.22/0.54 inference(theory_lemma,[status(thm)],[])).
% 0.22/0.54 tff(119,plain,
% 0.22/0.54 ($lesseq(S!12, 0)),
% 0.22/0.54 inference(unit_resolution,[status(thm)],[118, 99])).
% 0.22/0.54 tff(120,plain,
% 0.22/0.54 (($greatereq($sum(S!12, $sum($product(-1, S1!17), I!20)), 0) | (~$greatereq(I!20, 0)) | (~eq_prefix1(int, t2tb2(T!19), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(I!20)), n1))) | $greatereq(I!20, 0)),
% 0.22/0.54 inference(tautology,[status(thm)],[])).
% 0.22/0.54 tff(121,plain,
% 0.22/0.54 ($greatereq(I!20, 0)),
% 0.22/0.54 inference(unit_resolution,[status(thm)],[120, 113])).
% 0.22/0.54 tff(122,plain,
% 0.22/0.54 ($lesseq($sum(S!12, $product(-1, I!20)), 0) | (~$lesseq(S!12, 0)) | (~$greatereq(I!20, 0))),
% 0.22/0.54 inference(theory_lemma,[status(thm)],[])).
% 0.22/0.54 tff(123,plain,
% 0.22/0.54 ($lesseq($sum(S!12, $product(-1, I!20)), 0)),
% 0.22/0.54 inference(unit_resolution,[status(thm)],[122, 121, 119])).
% 0.22/0.54 tff(124,plain,
% 0.22/0.54 (((~((~partial_solution1(n1, T!19)) | (~eq_prefix1(int, t2tb2(Col1!14), t2tb2(T!19), K1!15)) | (~($lesseq($sum(S1!17, $product(-1, tptp_fun_I_18(T!19))), 0) | (~$lesseq($sum(S!12, $product(-1, tptp_fun_I_18(T!19))), 0)) | (~eq_prefix1(int, t2tb2(T!19), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(tptp_fun_I_18(T!19))), n1)))))) | (~((~((~partial_solution1(n1, T!19)) | (~eq_prefix1(int, t2tb2(Col1!14), t2tb2(T!19), K1!15)))) | ![I: $int] : ($greatereq($sum(I, $product(-1, S1!17)), 0) | (~$greatereq($sum(I, $product(-1, S!12)), 0)) | (~eq_prefix1(int, t2tb2(T!19), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(I)), n1)))))) | ((~((~partial_solution1(n1, T!19)) | (~eq_prefix1(int, t2tb2(Col1!14), t2tb2(T!19), K1!15)))) | ![I: $int] : ($greatereq($sum(I, $product(-1, S1!17)), 0) | (~$greatereq($sum(I, $product(-1, S!12)), 0)) | (~eq_prefix1(int, t2tb2(T!19), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(I)), n1))))),
% 0.22/0.54 inference(tautology,[status(thm)],[])).
% 0.22/0.54 tff(125,plain,
% 0.22/0.54 ((~((~partial_solution1(n1, T!19)) | (~eq_prefix1(int, t2tb2(Col1!14), t2tb2(T!19), K1!15)))) | ![I: $int] : ($greatereq($sum(I, $product(-1, S1!17)), 0) | (~$greatereq($sum(I, $product(-1, S!12)), 0)) | (~eq_prefix1(int, t2tb2(T!19), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(I)), n1)))),
% 0.22/0.54 inference(unit_resolution,[status(thm)],[124, 51])).
% 0.22/0.54 tff(126,plain,
% 0.22/0.54 (((~partial_solution1(n1, T!19)) | (~eq_prefix1(int, t2tb2(Col1!14), t2tb2(T!19), K1!15))) | partial_solution1(n1, T!19)),
% 0.22/0.54 inference(tautology,[status(thm)],[])).
% 0.22/0.54 tff(127,plain,
% 0.22/0.54 ((~partial_solution1(n1, T!19)) | (~eq_prefix1(int, t2tb2(Col1!14), t2tb2(T!19), K1!15))),
% 0.22/0.54 inference(unit_resolution,[status(thm)],[126, 98])).
% 0.22/0.54 tff(128,plain,
% 0.22/0.54 ((~((~((~partial_solution1(n1, T!19)) | (~eq_prefix1(int, t2tb2(Col1!14), t2tb2(T!19), K1!15)))) | ![I: $int] : ($greatereq($sum(I, $product(-1, S1!17)), 0) | (~$greatereq($sum(I, $product(-1, S!12)), 0)) | (~eq_prefix1(int, t2tb2(T!19), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(I)), n1))))) | (~((~partial_solution1(n1, T!19)) | (~eq_prefix1(int, t2tb2(Col1!14), t2tb2(T!19), K1!15)))) | ![I: $int] : ($greatereq($sum(I, $product(-1, S1!17)), 0) | (~$greatereq($sum(I, $product(-1, S!12)), 0)) | (~eq_prefix1(int, t2tb2(T!19), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(I)), n1)))),
% 0.22/0.54 inference(tautology,[status(thm)],[])).
% 0.22/0.54 tff(129,plain,
% 0.22/0.54 ((~((~((~partial_solution1(n1, T!19)) | (~eq_prefix1(int, t2tb2(Col1!14), t2tb2(T!19), K1!15)))) | ![I: $int] : ($greatereq($sum(I, $product(-1, S1!17)), 0) | (~$greatereq($sum(I, $product(-1, S!12)), 0)) | (~eq_prefix1(int, t2tb2(T!19), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(I)), n1))))) | ![I: $int] : ($greatereq($sum(I, $product(-1, S1!17)), 0) | (~$greatereq($sum(I, $product(-1, S!12)), 0)) | (~eq_prefix1(int, t2tb2(T!19), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(I)), n1)))),
% 0.22/0.54 inference(unit_resolution,[status(thm)],[128, 127])).
% 0.22/0.54 tff(130,plain,
% 0.22/0.54 (![I: $int] : ($greatereq($sum(I, $product(-1, S1!17)), 0) | (~$greatereq($sum(I, $product(-1, S!12)), 0)) | (~eq_prefix1(int, t2tb2(T!19), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(I)), n1)))),
% 0.22/0.54 inference(unit_resolution,[status(thm)],[129, 125])).
% 0.22/0.54 tff(131,plain,
% 0.22/0.54 (($greatereq($sum(S!12, $sum($product(-1, S1!17), I!20)), 0) | (~$greatereq(I!20, 0)) | (~eq_prefix1(int, t2tb2(T!19), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(I!20)), n1))) | eq_prefix1(int, t2tb2(T!19), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(I!20)), n1)),
% 0.22/0.54 inference(tautology,[status(thm)],[])).
% 0.22/0.54 tff(132,plain,
% 0.22/0.54 (eq_prefix1(int, t2tb2(T!19), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(I!20)), n1)),
% 0.22/0.54 inference(unit_resolution,[status(thm)],[131, 113])).
% 0.22/0.54 tff(133,plain,
% 0.22/0.54 (((~![I: $int] : ($greatereq($sum(I, $product(-1, S1!17)), 0) | (~$greatereq($sum(I, $product(-1, S!12)), 0)) | (~eq_prefix1(int, t2tb2(T!19), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(I)), n1)))) | ((~eq_prefix1(int, t2tb2(T!19), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(I!20)), n1)) | $lesseq($sum(S1!17, $product(-1, I!20)), 0) | (~$lesseq($sum(S!12, $product(-1, I!20)), 0)))) <=> ((~![I: $int] : ($greatereq($sum(I, $product(-1, S1!17)), 0) | (~$greatereq($sum(I, $product(-1, S!12)), 0)) | (~eq_prefix1(int, t2tb2(T!19), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(I)), n1)))) | (~eq_prefix1(int, t2tb2(T!19), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(I!20)), n1)) | $lesseq($sum(S1!17, $product(-1, I!20)), 0) | (~$lesseq($sum(S!12, $product(-1, I!20)), 0)))),
% 0.22/0.54 inference(rewrite,[status(thm)],[])).
% 0.22/0.54 tff(134,plain,
% 0.22/0.54 (($lesseq($sum(S1!17, $product(-1, I!20)), 0) | (~$lesseq($sum(S!12, $product(-1, I!20)), 0)) | (~eq_prefix1(int, t2tb2(T!19), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(I!20)), n1))) <=> ((~eq_prefix1(int, t2tb2(T!19), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(I!20)), n1)) | $lesseq($sum(S1!17, $product(-1, I!20)), 0) | (~$lesseq($sum(S!12, $product(-1, I!20)), 0)))),
% 0.22/0.55 inference(rewrite,[status(thm)],[])).
% 0.22/0.55 tff(135,plain,
% 0.22/0.55 ((~$greatereq($sum(I!20, $product(-1, S!12)), 0)) <=> (~$lesseq($sum(S!12, $product(-1, I!20)), 0))),
% 0.22/0.55 inference(rewrite,[status(thm)],[])).
% 0.22/0.55 tff(136,plain,
% 0.22/0.55 ($greatereq($sum($product(-1, S1!17), I!20), 0) <=> $lesseq($sum(S1!17, $product(-1, I!20)), 0)),
% 0.22/0.55 inference(rewrite,[status(thm)],[])).
% 0.22/0.55 tff(137,plain,
% 0.22/0.55 ($sum(I!20, $product(-1, S1!17)) = $sum($product(-1, S1!17), I!20)),
% 0.22/0.55 inference(rewrite,[status(thm)],[])).
% 0.22/0.55 tff(138,plain,
% 0.22/0.55 ($greatereq($sum(I!20, $product(-1, S1!17)), 0) <=> $greatereq($sum($product(-1, S1!17), I!20), 0)),
% 0.22/0.55 inference(monotonicity,[status(thm)],[137])).
% 0.22/0.55 tff(139,plain,
% 0.22/0.55 ($greatereq($sum(I!20, $product(-1, S1!17)), 0) <=> $lesseq($sum(S1!17, $product(-1, I!20)), 0)),
% 0.22/0.55 inference(transitivity,[status(thm)],[138, 136])).
% 0.22/0.55 tff(140,plain,
% 0.22/0.55 (($greatereq($sum(I!20, $product(-1, S1!17)), 0) | (~$greatereq($sum(I!20, $product(-1, S!12)), 0)) | (~eq_prefix1(int, t2tb2(T!19), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(I!20)), n1))) <=> ($lesseq($sum(S1!17, $product(-1, I!20)), 0) | (~$lesseq($sum(S!12, $product(-1, I!20)), 0)) | (~eq_prefix1(int, t2tb2(T!19), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(I!20)), n1)))),
% 0.22/0.55 inference(monotonicity,[status(thm)],[139, 135])).
% 0.22/0.55 tff(141,plain,
% 0.22/0.55 (($greatereq($sum(I!20, $product(-1, S1!17)), 0) | (~$greatereq($sum(I!20, $product(-1, S!12)), 0)) | (~eq_prefix1(int, t2tb2(T!19), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(I!20)), n1))) <=> ((~eq_prefix1(int, t2tb2(T!19), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(I!20)), n1)) | $lesseq($sum(S1!17, $product(-1, I!20)), 0) | (~$lesseq($sum(S!12, $product(-1, I!20)), 0)))),
% 0.22/0.55 inference(transitivity,[status(thm)],[140, 134])).
% 0.22/0.55 tff(142,plain,
% 0.22/0.55 (((~![I: $int] : ($greatereq($sum(I, $product(-1, S1!17)), 0) | (~$greatereq($sum(I, $product(-1, S!12)), 0)) | (~eq_prefix1(int, t2tb2(T!19), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(I)), n1)))) | ($greatereq($sum(I!20, $product(-1, S1!17)), 0) | (~$greatereq($sum(I!20, $product(-1, S!12)), 0)) | (~eq_prefix1(int, t2tb2(T!19), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(I!20)), n1)))) <=> ((~![I: $int] : ($greatereq($sum(I, $product(-1, S1!17)), 0) | (~$greatereq($sum(I, $product(-1, S!12)), 0)) | (~eq_prefix1(int, t2tb2(T!19), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(I)), n1)))) | ((~eq_prefix1(int, t2tb2(T!19), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(I!20)), n1)) | $lesseq($sum(S1!17, $product(-1, I!20)), 0) | (~$lesseq($sum(S!12, $product(-1, I!20)), 0))))),
% 0.22/0.55 inference(monotonicity,[status(thm)],[141])).
% 0.22/0.55 tff(143,plain,
% 0.22/0.55 (((~![I: $int] : ($greatereq($sum(I, $product(-1, S1!17)), 0) | (~$greatereq($sum(I, $product(-1, S!12)), 0)) | (~eq_prefix1(int, t2tb2(T!19), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(I)), n1)))) | ($greatereq($sum(I!20, $product(-1, S1!17)), 0) | (~$greatereq($sum(I!20, $product(-1, S!12)), 0)) | (~eq_prefix1(int, t2tb2(T!19), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(I!20)), n1)))) <=> ((~![I: $int] : ($greatereq($sum(I, $product(-1, S1!17)), 0) | (~$greatereq($sum(I, $product(-1, S!12)), 0)) | (~eq_prefix1(int, t2tb2(T!19), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(I)), n1)))) | (~eq_prefix1(int, t2tb2(T!19), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(I!20)), n1)) | $lesseq($sum(S1!17, $product(-1, I!20)), 0) | (~$lesseq($sum(S!12, $product(-1, I!20)), 0)))),
% 0.22/0.55 inference(transitivity,[status(thm)],[142, 133])).
% 0.22/0.55 tff(144,plain,
% 0.22/0.55 ((~![I: $int] : ($greatereq($sum(I, $product(-1, S1!17)), 0) | (~$greatereq($sum(I, $product(-1, S!12)), 0)) | (~eq_prefix1(int, t2tb2(T!19), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(I)), n1)))) | ($greatereq($sum(I!20, $product(-1, S1!17)), 0) | (~$greatereq($sum(I!20, $product(-1, S!12)), 0)) | (~eq_prefix1(int, t2tb2(T!19), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(I!20)), n1)))),
% 0.22/0.55 inference(quant_inst,[status(thm)],[])).
% 0.22/0.55 tff(145,plain,
% 0.22/0.55 ((~![I: $int] : ($greatereq($sum(I, $product(-1, S1!17)), 0) | (~$greatereq($sum(I, $product(-1, S!12)), 0)) | (~eq_prefix1(int, t2tb2(T!19), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(I)), n1)))) | (~eq_prefix1(int, t2tb2(T!19), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(I!20)), n1)) | $lesseq($sum(S1!17, $product(-1, I!20)), 0) | (~$lesseq($sum(S!12, $product(-1, I!20)), 0))),
% 0.22/0.55 inference(modus_ponens,[status(thm)],[144, 143])).
% 0.22/0.55 tff(146,plain,
% 0.22/0.55 ($lesseq($sum(S1!17, $product(-1, I!20)), 0) | (~$lesseq($sum(S!12, $product(-1, I!20)), 0))),
% 0.22/0.55 inference(unit_resolution,[status(thm)],[145, 132, 130])).
% 0.22/0.55 tff(147,plain,
% 0.22/0.55 ($false),
% 0.22/0.55 inference(unit_resolution,[status(thm)],[146, 123, 117])).
% 0.22/0.55 tff(148,plain,(partial_solution1(n1, T!19)), inference(lemma,lemma(discharge,[]))).
% 0.22/0.55 tff(149,plain,
% 0.22/0.55 (((~(partial_solution1(n1, T!19) | (~($greatereq($sum(S!12, $sum($product(-1, S1!17), I!20)), 0) | (~$greatereq(I!20, 0)) | (~eq_prefix1(int, t2tb2(T!19), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(I!20)), n1)))))) | (~((~partial_solution1(n1, T!19)) | ![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $sum(S!12, $product(-1, S1!17))), 0) | (~eq_prefix1(int, t2tb2(T!19), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(I)), n1)))))) | ((~partial_solution1(n1, T!19)) | ![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $sum(S!12, $product(-1, S1!17))), 0) | (~eq_prefix1(int, t2tb2(T!19), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(I)), n1))))),
% 0.22/0.55 inference(tautology,[status(thm)],[])).
% 0.22/0.55 tff(150,plain,
% 0.22/0.55 ((~partial_solution1(n1, T!19)) | ![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $sum(S!12, $product(-1, S1!17))), 0) | (~eq_prefix1(int, t2tb2(T!19), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(I)), n1)))),
% 0.22/0.55 inference(unit_resolution,[status(thm)],[149, 108])).
% 0.22/0.55 tff(151,plain,
% 0.22/0.55 ((~((~partial_solution1(n1, T!19)) | ![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $sum(S!12, $product(-1, S1!17))), 0) | (~eq_prefix1(int, t2tb2(T!19), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(I)), n1))))) | (~partial_solution1(n1, T!19)) | ![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $sum(S!12, $product(-1, S1!17))), 0) | (~eq_prefix1(int, t2tb2(T!19), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(I)), n1)))),
% 0.22/0.55 inference(tautology,[status(thm)],[])).
% 0.22/0.55 tff(152,plain,
% 0.22/0.55 ((~partial_solution1(n1, T!19)) | ![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $sum(S!12, $product(-1, S1!17))), 0) | (~eq_prefix1(int, t2tb2(T!19), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(I)), n1)))),
% 0.22/0.55 inference(unit_resolution,[status(thm)],[151, 150])).
% 0.22/0.55 tff(153,plain,
% 0.22/0.55 (![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $sum(S!12, $product(-1, S1!17))), 0) | (~eq_prefix1(int, t2tb2(T!19), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(I)), n1)))),
% 0.22/0.55 inference(unit_resolution,[status(thm)],[152, 148])).
% 0.22/0.55 tff(154,plain,
% 0.22/0.55 (((~![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $sum(S!12, $product(-1, S1!17))), 0) | (~eq_prefix1(int, t2tb2(T!19), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(I)), n1)))) | ((~$greatereq(tb2t1(t2tb1(tptp_fun_I_18(T!19))), 0)) | (~eq_prefix1(int, t2tb2(T!19), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(tb2t1(t2tb1(tptp_fun_I_18(T!19))))), n1)) | $greatereq($sum(S!12, $sum($product(-1, S1!17), tb2t1(t2tb1(tptp_fun_I_18(T!19))))), 0))) <=> ((~![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $sum(S!12, $product(-1, S1!17))), 0) | (~eq_prefix1(int, t2tb2(T!19), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(I)), n1)))) | (~$greatereq(tb2t1(t2tb1(tptp_fun_I_18(T!19))), 0)) | (~eq_prefix1(int, t2tb2(T!19), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(tb2t1(t2tb1(tptp_fun_I_18(T!19))))), n1)) | $greatereq($sum(S!12, $sum($product(-1, S1!17), tb2t1(t2tb1(tptp_fun_I_18(T!19))))), 0))),
% 0.22/0.55 inference(rewrite,[status(thm)],[])).
% 0.22/0.55 tff(155,plain,
% 0.22/0.55 (((~$greatereq(tb2t1(t2tb1(tptp_fun_I_18(T!19))), 0)) | $greatereq($sum(S!12, $sum($product(-1, S1!17), tb2t1(t2tb1(tptp_fun_I_18(T!19))))), 0) | (~eq_prefix1(int, t2tb2(T!19), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(tb2t1(t2tb1(tptp_fun_I_18(T!19))))), n1))) <=> ((~$greatereq(tb2t1(t2tb1(tptp_fun_I_18(T!19))), 0)) | (~eq_prefix1(int, t2tb2(T!19), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(tb2t1(t2tb1(tptp_fun_I_18(T!19))))), n1)) | $greatereq($sum(S!12, $sum($product(-1, S1!17), tb2t1(t2tb1(tptp_fun_I_18(T!19))))), 0))),
% 0.22/0.55 inference(rewrite,[status(thm)],[])).
% 0.22/0.55 tff(156,plain,
% 0.22/0.55 ($greatereq($sum(tb2t1(t2tb1(tptp_fun_I_18(T!19))), $sum(S!12, $product(-1, S1!17))), 0) <=> $greatereq($sum(S!12, $sum($product(-1, S1!17), tb2t1(t2tb1(tptp_fun_I_18(T!19))))), 0)),
% 0.22/0.55 inference(rewrite,[status(thm)],[])).
% 0.22/0.55 tff(157,plain,
% 0.22/0.55 (((~$greatereq(tb2t1(t2tb1(tptp_fun_I_18(T!19))), 0)) | $greatereq($sum(tb2t1(t2tb1(tptp_fun_I_18(T!19))), $sum(S!12, $product(-1, S1!17))), 0) | (~eq_prefix1(int, t2tb2(T!19), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(tb2t1(t2tb1(tptp_fun_I_18(T!19))))), n1))) <=> ((~$greatereq(tb2t1(t2tb1(tptp_fun_I_18(T!19))), 0)) | $greatereq($sum(S!12, $sum($product(-1, S1!17), tb2t1(t2tb1(tptp_fun_I_18(T!19))))), 0) | (~eq_prefix1(int, t2tb2(T!19), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(tb2t1(t2tb1(tptp_fun_I_18(T!19))))), n1)))),
% 0.22/0.55 inference(monotonicity,[status(thm)],[156])).
% 0.22/0.55 tff(158,plain,
% 0.22/0.55 (((~$greatereq(tb2t1(t2tb1(tptp_fun_I_18(T!19))), 0)) | $greatereq($sum(tb2t1(t2tb1(tptp_fun_I_18(T!19))), $sum(S!12, $product(-1, S1!17))), 0) | (~eq_prefix1(int, t2tb2(T!19), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(tb2t1(t2tb1(tptp_fun_I_18(T!19))))), n1))) <=> ((~$greatereq(tb2t1(t2tb1(tptp_fun_I_18(T!19))), 0)) | (~eq_prefix1(int, t2tb2(T!19), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(tb2t1(t2tb1(tptp_fun_I_18(T!19))))), n1)) | $greatereq($sum(S!12, $sum($product(-1, S1!17), tb2t1(t2tb1(tptp_fun_I_18(T!19))))), 0))),
% 0.22/0.55 inference(transitivity,[status(thm)],[157, 155])).
% 0.22/0.55 tff(159,plain,
% 0.22/0.55 (((~![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $sum(S!12, $product(-1, S1!17))), 0) | (~eq_prefix1(int, t2tb2(T!19), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(I)), n1)))) | ((~$greatereq(tb2t1(t2tb1(tptp_fun_I_18(T!19))), 0)) | $greatereq($sum(tb2t1(t2tb1(tptp_fun_I_18(T!19))), $sum(S!12, $product(-1, S1!17))), 0) | (~eq_prefix1(int, t2tb2(T!19), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(tb2t1(t2tb1(tptp_fun_I_18(T!19))))), n1)))) <=> ((~![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $sum(S!12, $product(-1, S1!17))), 0) | (~eq_prefix1(int, t2tb2(T!19), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(I)), n1)))) | ((~$greatereq(tb2t1(t2tb1(tptp_fun_I_18(T!19))), 0)) | (~eq_prefix1(int, t2tb2(T!19), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(tb2t1(t2tb1(tptp_fun_I_18(T!19))))), n1)) | $greatereq($sum(S!12, $sum($product(-1, S1!17), tb2t1(t2tb1(tptp_fun_I_18(T!19))))), 0)))),
% 0.22/0.55 inference(monotonicity,[status(thm)],[158])).
% 0.22/0.55 tff(160,plain,
% 0.22/0.55 (((~![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $sum(S!12, $product(-1, S1!17))), 0) | (~eq_prefix1(int, t2tb2(T!19), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(I)), n1)))) | ((~$greatereq(tb2t1(t2tb1(tptp_fun_I_18(T!19))), 0)) | $greatereq($sum(tb2t1(t2tb1(tptp_fun_I_18(T!19))), $sum(S!12, $product(-1, S1!17))), 0) | (~eq_prefix1(int, t2tb2(T!19), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(tb2t1(t2tb1(tptp_fun_I_18(T!19))))), n1)))) <=> ((~![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $sum(S!12, $product(-1, S1!17))), 0) | (~eq_prefix1(int, t2tb2(T!19), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(I)), n1)))) | (~$greatereq(tb2t1(t2tb1(tptp_fun_I_18(T!19))), 0)) | (~eq_prefix1(int, t2tb2(T!19), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(tb2t1(t2tb1(tptp_fun_I_18(T!19))))), n1)) | $greatereq($sum(S!12, $sum($product(-1, S1!17), tb2t1(t2tb1(tptp_fun_I_18(T!19))))), 0))),
% 0.22/0.55 inference(transitivity,[status(thm)],[159, 154])).
% 0.22/0.55 tff(161,plain,
% 0.22/0.55 ((~![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $sum(S!12, $product(-1, S1!17))), 0) | (~eq_prefix1(int, t2tb2(T!19), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(I)), n1)))) | ((~$greatereq(tb2t1(t2tb1(tptp_fun_I_18(T!19))), 0)) | $greatereq($sum(tb2t1(t2tb1(tptp_fun_I_18(T!19))), $sum(S!12, $product(-1, S1!17))), 0) | (~eq_prefix1(int, t2tb2(T!19), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(tb2t1(t2tb1(tptp_fun_I_18(T!19))))), n1)))),
% 0.22/0.55 inference(quant_inst,[status(thm)],[])).
% 0.22/0.55 tff(162,plain,
% 0.22/0.55 ((~![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $sum(S!12, $product(-1, S1!17))), 0) | (~eq_prefix1(int, t2tb2(T!19), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(I)), n1)))) | (~$greatereq(tb2t1(t2tb1(tptp_fun_I_18(T!19))), 0)) | (~eq_prefix1(int, t2tb2(T!19), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(tb2t1(t2tb1(tptp_fun_I_18(T!19))))), n1)) | $greatereq($sum(S!12, $sum($product(-1, S1!17), tb2t1(t2tb1(tptp_fun_I_18(T!19))))), 0)),
% 0.22/0.55 inference(modus_ponens,[status(thm)],[161, 160])).
% 0.22/0.55 tff(163,plain,
% 0.22/0.55 ((~$greatereq(tb2t1(t2tb1(tptp_fun_I_18(T!19))), 0)) | (~eq_prefix1(int, t2tb2(T!19), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(tb2t1(t2tb1(tptp_fun_I_18(T!19))))), n1)) | $greatereq($sum(S!12, $sum($product(-1, S1!17), tb2t1(t2tb1(tptp_fun_I_18(T!19))))), 0)),
% 0.22/0.55 inference(unit_resolution,[status(thm)],[162, 153])).
% 0.22/0.55 tff(164,plain,
% 0.22/0.55 ($greatereq($sum(S!12, $sum($product(-1, S1!17), tb2t1(t2tb1(tptp_fun_I_18(T!19))))), 0)),
% 0.22/0.55 inference(unit_resolution,[status(thm)],[163, 97, 70])).
% 0.22/0.55 tff(165,plain,
% 0.22/0.55 ((~($sum(tptp_fun_I_18(T!19), $product(-1, tb2t1(t2tb1(tptp_fun_I_18(T!19))))) = 0)) | $greatereq($sum(tptp_fun_I_18(T!19), $product(-1, tb2t1(t2tb1(tptp_fun_I_18(T!19))))), 0)),
% 0.22/0.55 inference(theory_lemma,[status(thm)],[])).
% 0.22/0.55 tff(166,plain,
% 0.22/0.55 ($greatereq($sum(tptp_fun_I_18(T!19), $product(-1, tb2t1(t2tb1(tptp_fun_I_18(T!19))))), 0)),
% 0.22/0.55 inference(unit_resolution,[status(thm)],[165, 90])).
% 0.22/0.55 tff(167,plain,
% 0.22/0.55 ($false),
% 0.22/0.55 inference(theory_lemma,[status(thm)],[166, 119, 164, 56])).
% 0.22/0.55 tff(168,plain,($lesseq($sum(S1!17, $product(-1, tptp_fun_I_18(T!19))), 0) | (~$lesseq($sum(S!12, $product(-1, tptp_fun_I_18(T!19))), 0)) | (~eq_prefix1(int, t2tb2(T!19), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(tptp_fun_I_18(T!19))), n1))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.55 tff(169,plain,
% 0.22/0.55 ((~((~partial_solution1(n1, T!19)) | (~eq_prefix1(int, t2tb2(Col1!14), t2tb2(T!19), K1!15)) | (~($lesseq($sum(S1!17, $product(-1, tptp_fun_I_18(T!19))), 0) | (~$lesseq($sum(S!12, $product(-1, tptp_fun_I_18(T!19))), 0)) | (~eq_prefix1(int, t2tb2(T!19), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(tptp_fun_I_18(T!19))), n1)))))) | (~partial_solution1(n1, T!19)) | (~eq_prefix1(int, t2tb2(Col1!14), t2tb2(T!19), K1!15)) | (~($lesseq($sum(S1!17, $product(-1, tptp_fun_I_18(T!19))), 0) | (~$lesseq($sum(S!12, $product(-1, tptp_fun_I_18(T!19))), 0)) | (~eq_prefix1(int, t2tb2(T!19), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(tptp_fun_I_18(T!19))), n1))))),
% 0.22/0.55 inference(tautology,[status(thm)],[])).
% 0.22/0.55 tff(170,plain,
% 0.22/0.55 ((~((~partial_solution1(n1, T!19)) | (~eq_prefix1(int, t2tb2(Col1!14), t2tb2(T!19), K1!15)) | (~($lesseq($sum(S1!17, $product(-1, tptp_fun_I_18(T!19))), 0) | (~$lesseq($sum(S!12, $product(-1, tptp_fun_I_18(T!19))), 0)) | (~eq_prefix1(int, t2tb2(T!19), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(tptp_fun_I_18(T!19))), n1)))))) | (~eq_prefix1(int, t2tb2(Col1!14), t2tb2(T!19), K1!15)) | (~($lesseq($sum(S1!17, $product(-1, tptp_fun_I_18(T!19))), 0) | (~$lesseq($sum(S!12, $product(-1, tptp_fun_I_18(T!19))), 0)) | (~eq_prefix1(int, t2tb2(T!19), get(map(int, int), int, t2tb3(Sol1!16), t2tb1(tptp_fun_I_18(T!19))), n1))))),
% 0.22/0.55 inference(unit_resolution,[status(thm)],[169, 148])).
% 0.22/0.55 tff(171,plain,
% 0.22/0.55 (~eq_prefix1(int, t2tb2(Col1!14), t2tb2(T!19), K1!15)),
% 0.22/0.55 inference(unit_resolution,[status(thm)],[170, 168, 53])).
% 0.22/0.55 tff(172,plain,
% 0.22/0.55 (~eq_prefix1(int, t2tb2(Col1!14), t2tb2(T!19), 0)),
% 0.22/0.55 inference(modus_ponens,[status(thm)],[171, 39])).
% 0.22/0.55 tff(173,plain,
% 0.22/0.55 (^[A: ty, T: uni, U: uni, I: $int] : refl((~((~((~eq_prefix1(A, T, U, I)) | ![K: $int] : ((get(A, int, T, t2tb1(K)) = get(A, int, U, t2tb1(K))) | (~$greatereq(K, 0)) | $lesseq($sum(I, $product(-1, K)), 0)))) | (~(eq_prefix1(A, T, U, I) | (~($lesseq($sum(I, $product(-1, tptp_fun_K_3(I, U, T, A))), 0) | (get(A, int, T, t2tb1(tptp_fun_K_3(I, U, T, A))) = get(A, int, U, t2tb1(tptp_fun_K_3(I, U, T, A)))) | (~$greatereq(tptp_fun_K_3(I, U, T, A), 0)))))))) <=> (~((~((~eq_prefix1(A, T, U, I)) | ![K: $int] : ((get(A, int, T, t2tb1(K)) = get(A, int, U, t2tb1(K))) | (~$greatereq(K, 0)) | $lesseq($sum(I, $product(-1, K)), 0)))) | (~(eq_prefix1(A, T, U, I) | (~($lesseq($sum(I, $product(-1, tptp_fun_K_3(I, U, T, A))), 0) | (get(A, int, T, t2tb1(tptp_fun_K_3(I, U, T, A))) = get(A, int, U, t2tb1(tptp_fun_K_3(I, U, T, A)))) | (~$greatereq(tptp_fun_K_3(I, U, T, A), 0)))))))))),
% 0.22/0.55 inference(bind,[status(th)],[])).
% 0.22/0.55 tff(174,plain,
% 0.22/0.55 (![A: ty, T: uni, U: uni, I: $int] : (~((~((~eq_prefix1(A, T, U, I)) | ![K: $int] : ((get(A, int, T, t2tb1(K)) = get(A, int, U, t2tb1(K))) | (~$greatereq(K, 0)) | $lesseq($sum(I, $product(-1, K)), 0)))) | (~(eq_prefix1(A, T, U, I) | (~($lesseq($sum(I, $product(-1, tptp_fun_K_3(I, U, T, A))), 0) | (get(A, int, T, t2tb1(tptp_fun_K_3(I, U, T, A))) = get(A, int, U, t2tb1(tptp_fun_K_3(I, U, T, A)))) | (~$greatereq(tptp_fun_K_3(I, U, T, A), 0)))))))) <=> ![A: ty, T: uni, U: uni, I: $int] : (~((~((~eq_prefix1(A, T, U, I)) | ![K: $int] : ((get(A, int, T, t2tb1(K)) = get(A, int, U, t2tb1(K))) | (~$greatereq(K, 0)) | $lesseq($sum(I, $product(-1, K)), 0)))) | (~(eq_prefix1(A, T, U, I) | (~($lesseq($sum(I, $product(-1, tptp_fun_K_3(I, U, T, A))), 0) | (get(A, int, T, t2tb1(tptp_fun_K_3(I, U, T, A))) = get(A, int, U, t2tb1(tptp_fun_K_3(I, U, T, A)))) | (~$greatereq(tptp_fun_K_3(I, U, T, A), 0))))))))),
% 0.22/0.55 inference(quant_intro,[status(thm)],[173])).
% 0.22/0.55 tff(175,plain,
% 0.22/0.55 (^[A: ty, T: uni, U: uni, I: $int] : rewrite((~((~((~eq_prefix1(A, T, U, I)) | ![K: $int] : ((get(A, int, T, t2tb1(K)) = get(A, int, U, t2tb1(K))) | (~$greatereq(K, 0)) | $lesseq($sum(I, $product(-1, K)), 0)))) | (~(eq_prefix1(A, T, U, I) | (~($lesseq($sum(I, $product(-1, tptp_fun_K_3(I, U, T, A))), 0) | (get(A, int, T, t2tb1(tptp_fun_K_3(I, U, T, A))) = get(A, int, U, t2tb1(tptp_fun_K_3(I, U, T, A)))) | (~$greatereq(tptp_fun_K_3(I, U, T, A), 0)))))))) <=> (~((~((~eq_prefix1(A, T, U, I)) | ![K: $int] : ((get(A, int, T, t2tb1(K)) = get(A, int, U, t2tb1(K))) | (~$greatereq(K, 0)) | $lesseq($sum(I, $product(-1, K)), 0)))) | (~(eq_prefix1(A, T, U, I) | (~($lesseq($sum(I, $product(-1, tptp_fun_K_3(I, U, T, A))), 0) | (get(A, int, T, t2tb1(tptp_fun_K_3(I, U, T, A))) = get(A, int, U, t2tb1(tptp_fun_K_3(I, U, T, A)))) | (~$greatereq(tptp_fun_K_3(I, U, T, A), 0)))))))))),
% 0.22/0.55 inference(bind,[status(th)],[])).
% 0.22/0.55 tff(176,plain,
% 0.22/0.55 (![A: ty, T: uni, U: uni, I: $int] : (~((~((~eq_prefix1(A, T, U, I)) | ![K: $int] : ((get(A, int, T, t2tb1(K)) = get(A, int, U, t2tb1(K))) | (~$greatereq(K, 0)) | $lesseq($sum(I, $product(-1, K)), 0)))) | (~(eq_prefix1(A, T, U, I) | (~($lesseq($sum(I, $product(-1, tptp_fun_K_3(I, U, T, A))), 0) | (get(A, int, T, t2tb1(tptp_fun_K_3(I, U, T, A))) = get(A, int, U, t2tb1(tptp_fun_K_3(I, U, T, A)))) | (~$greatereq(tptp_fun_K_3(I, U, T, A), 0)))))))) <=> ![A: ty, T: uni, U: uni, I: $int] : (~((~((~eq_prefix1(A, T, U, I)) | ![K: $int] : ((get(A, int, T, t2tb1(K)) = get(A, int, U, t2tb1(K))) | (~$greatereq(K, 0)) | $lesseq($sum(I, $product(-1, K)), 0)))) | (~(eq_prefix1(A, T, U, I) | (~($lesseq($sum(I, $product(-1, tptp_fun_K_3(I, U, T, A))), 0) | (get(A, int, T, t2tb1(tptp_fun_K_3(I, U, T, A))) = get(A, int, U, t2tb1(tptp_fun_K_3(I, U, T, A)))) | (~$greatereq(tptp_fun_K_3(I, U, T, A), 0))))))))),
% 0.22/0.55 inference(quant_intro,[status(thm)],[175])).
% 0.22/0.55 tff(177,plain,
% 0.22/0.55 (![A: ty, T: uni, U: uni, I: $int] : (~((~((~eq_prefix1(A, T, U, I)) | ![K: $int] : ((get(A, int, T, t2tb1(K)) = get(A, int, U, t2tb1(K))) | (~$greatereq(K, 0)) | $lesseq($sum(I, $product(-1, K)), 0)))) | (~(eq_prefix1(A, T, U, I) | (~($lesseq($sum(I, $product(-1, tptp_fun_K_3(I, U, T, A))), 0) | (get(A, int, T, t2tb1(tptp_fun_K_3(I, U, T, A))) = get(A, int, U, t2tb1(tptp_fun_K_3(I, U, T, A)))) | (~$greatereq(tptp_fun_K_3(I, U, T, A), 0)))))))) <=> ![A: ty, T: uni, U: uni, I: $int] : (~((~((~eq_prefix1(A, T, U, I)) | ![K: $int] : ((get(A, int, T, t2tb1(K)) = get(A, int, U, t2tb1(K))) | (~$greatereq(K, 0)) | $lesseq($sum(I, $product(-1, K)), 0)))) | (~(eq_prefix1(A, T, U, I) | (~($lesseq($sum(I, $product(-1, tptp_fun_K_3(I, U, T, A))), 0) | (get(A, int, T, t2tb1(tptp_fun_K_3(I, U, T, A))) = get(A, int, U, t2tb1(tptp_fun_K_3(I, U, T, A)))) | (~$greatereq(tptp_fun_K_3(I, U, T, A), 0))))))))),
% 0.22/0.56 inference(transitivity,[status(thm)],[176, 174])).
% 0.22/0.56 tff(178,plain,
% 0.22/0.56 (^[A: ty, T: uni, U: uni, I: $int] : trans(monotonicity(rewrite(((~eq_prefix1(A, T, U, I)) | ![K: $int] : ((~($greatereq(K, 0) & (~$lesseq($sum(I, $product(-1, K)), 0)))) | (get(A, int, T, t2tb1(K)) = get(A, int, U, t2tb1(K))))) <=> ((~eq_prefix1(A, T, U, I)) | ![K: $int] : ((get(A, int, T, t2tb1(K)) = get(A, int, U, t2tb1(K))) | (~$greatereq(K, 0)) | $lesseq($sum(I, $product(-1, K)), 0)))), trans(monotonicity(rewrite((~((~($greatereq(tptp_fun_K_3(I, U, T, A), 0) & (~$lesseq($sum(I, $product(-1, tptp_fun_K_3(I, U, T, A))), 0)))) | (get(A, int, T, t2tb1(tptp_fun_K_3(I, U, T, A))) = get(A, int, U, t2tb1(tptp_fun_K_3(I, U, T, A)))))) <=> (~($lesseq($sum(I, $product(-1, tptp_fun_K_3(I, U, T, A))), 0) | (get(A, int, T, t2tb1(tptp_fun_K_3(I, U, T, A))) = get(A, int, U, t2tb1(tptp_fun_K_3(I, U, T, A)))) | (~$greatereq(tptp_fun_K_3(I, U, T, A), 0))))), ((eq_prefix1(A, T, U, I) | (~((~($greatereq(tptp_fun_K_3(I, U, T, A), 0) & (~$lesseq($sum(I, $product(-1, tptp_fun_K_3(I, U, T, A))), 0)))) | (get(A, int, T, t2tb1(tptp_fun_K_3(I, U, T, A))) = get(A, int, U, t2tb1(tptp_fun_K_3(I, U, T, A))))))) <=> (eq_prefix1(A, T, U, I) | (~($lesseq($sum(I, $product(-1, tptp_fun_K_3(I, U, T, A))), 0) | (get(A, int, T, t2tb1(tptp_fun_K_3(I, U, T, A))) = get(A, int, U, t2tb1(tptp_fun_K_3(I, U, T, A)))) | (~$greatereq(tptp_fun_K_3(I, U, T, A), 0))))))), rewrite((eq_prefix1(A, T, U, I) | (~($lesseq($sum(I, $product(-1, tptp_fun_K_3(I, U, T, A))), 0) | (get(A, int, T, t2tb1(tptp_fun_K_3(I, U, T, A))) = get(A, int, U, t2tb1(tptp_fun_K_3(I, U, T, A)))) | (~$greatereq(tptp_fun_K_3(I, U, T, A), 0))))) <=> (eq_prefix1(A, T, U, I) | (~($lesseq($sum(I, $product(-1, tptp_fun_K_3(I, U, T, A))), 0) | (get(A, int, T, t2tb1(tptp_fun_K_3(I, U, T, A))) = get(A, int, U, t2tb1(tptp_fun_K_3(I, U, T, A)))) | (~$greatereq(tptp_fun_K_3(I, U, T, A), 0)))))), ((eq_prefix1(A, T, U, I) | (~((~($greatereq(tptp_fun_K_3(I, U, T, A), 0) & (~$lesseq($sum(I, $product(-1, tptp_fun_K_3(I, U, T, A))), 0)))) | (get(A, int, T, t2tb1(tptp_fun_K_3(I, U, T, A))) = get(A, int, U, t2tb1(tptp_fun_K_3(I, U, T, A))))))) <=> (eq_prefix1(A, T, U, I) | (~($lesseq($sum(I, $product(-1, tptp_fun_K_3(I, U, T, A))), 0) | (get(A, int, T, t2tb1(tptp_fun_K_3(I, U, T, A))) = get(A, int, U, t2tb1(tptp_fun_K_3(I, U, T, A)))) | (~$greatereq(tptp_fun_K_3(I, U, T, A), 0))))))), ((((~eq_prefix1(A, T, U, I)) | ![K: $int] : ((~($greatereq(K, 0) & (~$lesseq($sum(I, $product(-1, K)), 0)))) | (get(A, int, T, t2tb1(K)) = get(A, int, U, t2tb1(K))))) & (eq_prefix1(A, T, U, I) | (~((~($greatereq(tptp_fun_K_3(I, U, T, A), 0) & (~$lesseq($sum(I, $product(-1, tptp_fun_K_3(I, U, T, A))), 0)))) | (get(A, int, T, t2tb1(tptp_fun_K_3(I, U, T, A))) = get(A, int, U, t2tb1(tptp_fun_K_3(I, U, T, A)))))))) <=> (((~eq_prefix1(A, T, U, I)) | ![K: $int] : ((get(A, int, T, t2tb1(K)) = get(A, int, U, t2tb1(K))) | (~$greatereq(K, 0)) | $lesseq($sum(I, $product(-1, K)), 0))) & (eq_prefix1(A, T, U, I) | (~($lesseq($sum(I, $product(-1, tptp_fun_K_3(I, U, T, A))), 0) | (get(A, int, T, t2tb1(tptp_fun_K_3(I, U, T, A))) = get(A, int, U, t2tb1(tptp_fun_K_3(I, U, T, A)))) | (~$greatereq(tptp_fun_K_3(I, U, T, A), 0)))))))), rewrite((((~eq_prefix1(A, T, U, I)) | ![K: $int] : ((get(A, int, T, t2tb1(K)) = get(A, int, U, t2tb1(K))) | (~$greatereq(K, 0)) | $lesseq($sum(I, $product(-1, K)), 0))) & (eq_prefix1(A, T, U, I) | (~($lesseq($sum(I, $product(-1, tptp_fun_K_3(I, U, T, A))), 0) | (get(A, int, T, t2tb1(tptp_fun_K_3(I, U, T, A))) = get(A, int, U, t2tb1(tptp_fun_K_3(I, U, T, A)))) | (~$greatereq(tptp_fun_K_3(I, U, T, A), 0)))))) <=> (~((~((~eq_prefix1(A, T, U, I)) | ![K: $int] : ((get(A, int, T, t2tb1(K)) = get(A, int, U, t2tb1(K))) | (~$greatereq(K, 0)) | $lesseq($sum(I, $product(-1, K)), 0)))) | (~(eq_prefix1(A, T, U, I) | (~($lesseq($sum(I, $product(-1, tptp_fun_K_3(I, U, T, A))), 0) | (get(A, int, T, t2tb1(tptp_fun_K_3(I, U, T, A))) = get(A, int, U, t2tb1(tptp_fun_K_3(I, U, T, A)))) | (~$greatereq(tptp_fun_K_3(I, U, T, A), 0))))))))), ((((~eq_prefix1(A, T, U, I)) | ![K: $int] : ((~($greatereq(K, 0) & (~$lesseq($sum(I, $product(-1, K)), 0)))) | (get(A, int, T, t2tb1(K)) = get(A, int, U, t2tb1(K))))) & (eq_prefix1(A, T, U, I) | (~((~($greatereq(tptp_fun_K_3(I, U, T, A), 0) & (~$lesseq($sum(I, $product(-1, tptp_fun_K_3(I, U, T, A))), 0)))) | (get(A, int, T, t2tb1(tptp_fun_K_3(I, U, T, A))) = get(A, int, U, t2tb1(tptp_fun_K_3(I, U, T, A)))))))) <=> (~((~((~eq_prefix1(A, T, U, I)) | ![K: $int] : ((get(A, int, T, t2tb1(K)) = get(A, int, U, t2tb1(K))) | (~$greatereq(K, 0)) | $lesseq($sum(I, $product(-1, K)), 0)))) | (~(eq_prefix1(A, T, U, I) | (~($lesseq($sum(I, $product(-1, tptp_fun_K_3(I, U, T, A))), 0) | (get(A, int, T, t2tb1(tptp_fun_K_3(I, U, T, A))) = get(A, int, U, t2tb1(tptp_fun_K_3(I, U, T, A)))) | (~$greatereq(tptp_fun_K_3(I, U, T, A), 0))))))))))),
% 0.22/0.56 inference(bind,[status(th)],[])).
% 0.22/0.56 tff(179,plain,
% 0.22/0.56 (![A: ty, T: uni, U: uni, I: $int] : (((~eq_prefix1(A, T, U, I)) | ![K: $int] : ((~($greatereq(K, 0) & (~$lesseq($sum(I, $product(-1, K)), 0)))) | (get(A, int, T, t2tb1(K)) = get(A, int, U, t2tb1(K))))) & (eq_prefix1(A, T, U, I) | (~((~($greatereq(tptp_fun_K_3(I, U, T, A), 0) & (~$lesseq($sum(I, $product(-1, tptp_fun_K_3(I, U, T, A))), 0)))) | (get(A, int, T, t2tb1(tptp_fun_K_3(I, U, T, A))) = get(A, int, U, t2tb1(tptp_fun_K_3(I, U, T, A)))))))) <=> ![A: ty, T: uni, U: uni, I: $int] : (~((~((~eq_prefix1(A, T, U, I)) | ![K: $int] : ((get(A, int, T, t2tb1(K)) = get(A, int, U, t2tb1(K))) | (~$greatereq(K, 0)) | $lesseq($sum(I, $product(-1, K)), 0)))) | (~(eq_prefix1(A, T, U, I) | (~($lesseq($sum(I, $product(-1, tptp_fun_K_3(I, U, T, A))), 0) | (get(A, int, T, t2tb1(tptp_fun_K_3(I, U, T, A))) = get(A, int, U, t2tb1(tptp_fun_K_3(I, U, T, A)))) | (~$greatereq(tptp_fun_K_3(I, U, T, A), 0))))))))),
% 0.22/0.56 inference(quant_intro,[status(thm)],[178])).
% 0.22/0.56 tff(180,plain,
% 0.22/0.56 (^[A: ty, T: uni, U: uni, I: $int] : rewrite((eq_prefix1(A, T, U, I) <=> ![K: $int] : ((~($lesseq(0, K) & (~$lesseq(I, K)))) | (get(A, int, T, t2tb1(K)) = get(A, int, U, t2tb1(K))))) <=> (eq_prefix1(A, T, U, I) <=> ![K: $int] : ((~($greatereq(K, 0) & (~$lesseq($sum(I, $product(-1, K)), 0)))) | (get(A, int, T, t2tb1(K)) = get(A, int, U, t2tb1(K))))))),
% 0.22/0.56 inference(bind,[status(th)],[])).
% 0.22/0.56 tff(181,plain,
% 0.22/0.56 (![A: ty, T: uni, U: uni, I: $int] : (eq_prefix1(A, T, U, I) <=> ![K: $int] : ((~($lesseq(0, K) & (~$lesseq(I, K)))) | (get(A, int, T, t2tb1(K)) = get(A, int, U, t2tb1(K))))) <=> ![A: ty, T: uni, U: uni, I: $int] : (eq_prefix1(A, T, U, I) <=> ![K: $int] : ((~($greatereq(K, 0) & (~$lesseq($sum(I, $product(-1, K)), 0)))) | (get(A, int, T, t2tb1(K)) = get(A, int, U, t2tb1(K)))))),
% 0.22/0.56 inference(quant_intro,[status(thm)],[180])).
% 0.22/0.56 tff(182,plain,
% 0.22/0.56 (![A: ty, T: uni, U: uni, I: $int] : (eq_prefix1(A, T, U, I) <=> ![K: $int] : ((~($lesseq(0, K) & (~$lesseq(I, K)))) | (get(A, int, T, t2tb1(K)) = get(A, int, U, t2tb1(K))))) <=> ![A: ty, T: uni, U: uni, I: $int] : (eq_prefix1(A, T, U, I) <=> ![K: $int] : ((~($lesseq(0, K) & (~$lesseq(I, K)))) | (get(A, int, T, t2tb1(K)) = get(A, int, U, t2tb1(K)))))),
% 0.22/0.56 inference(rewrite,[status(thm)],[])).
% 0.22/0.56 tff(183,plain,
% 0.22/0.56 (^[A: ty, T: uni, U: uni, I: $int] : rewrite((eq_prefix1(A, T, U, I) <=> ![K: $int] : (($lesseq(0, K) & $less(K, I)) => (get(A, int, T, t2tb1(K)) = get(A, int, U, t2tb1(K))))) <=> (eq_prefix1(A, T, U, I) <=> ![K: $int] : ((~($lesseq(0, K) & (~$lesseq(I, K)))) | (get(A, int, T, t2tb1(K)) = get(A, int, U, t2tb1(K))))))),
% 0.22/0.56 inference(bind,[status(th)],[])).
% 0.22/0.56 tff(184,plain,
% 0.22/0.56 (![A: ty, T: uni, U: uni, I: $int] : (eq_prefix1(A, T, U, I) <=> ![K: $int] : (($lesseq(0, K) & $less(K, I)) => (get(A, int, T, t2tb1(K)) = get(A, int, U, t2tb1(K))))) <=> ![A: ty, T: uni, U: uni, I: $int] : (eq_prefix1(A, T, U, I) <=> ![K: $int] : ((~($lesseq(0, K) & (~$lesseq(I, K)))) | (get(A, int, T, t2tb1(K)) = get(A, int, U, t2tb1(K)))))),
% 0.22/0.56 inference(quant_intro,[status(thm)],[183])).
% 0.22/0.56 tff(185,axiom,(![A: ty, T: uni, U: uni, I: $int] : (eq_prefix1(A, T, U, I) <=> ![K: $int] : (($lesseq(0, K) & $less(K, I)) => (get(A, int, T, t2tb1(K)) = get(A, int, U, t2tb1(K)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','eq_prefix_def')).
% 0.22/0.56 tff(186,plain,
% 0.22/0.56 (![A: ty, T: uni, U: uni, I: $int] : (eq_prefix1(A, T, U, I) <=> ![K: $int] : ((~($lesseq(0, K) & (~$lesseq(I, K)))) | (get(A, int, T, t2tb1(K)) = get(A, int, U, t2tb1(K)))))),
% 0.22/0.56 inference(modus_ponens,[status(thm)],[185, 184])).
% 0.22/0.56 tff(187,plain,
% 0.22/0.56 (![A: ty, T: uni, U: uni, I: $int] : (eq_prefix1(A, T, U, I) <=> ![K: $int] : ((~($lesseq(0, K) & (~$lesseq(I, K)))) | (get(A, int, T, t2tb1(K)) = get(A, int, U, t2tb1(K)))))),
% 0.22/0.56 inference(modus_ponens,[status(thm)],[186, 182])).
% 0.22/0.56 tff(188,plain,
% 0.22/0.56 (![A: ty, T: uni, U: uni, I: $int] : (eq_prefix1(A, T, U, I) <=> ![K: $int] : ((~($greatereq(K, 0) & (~$lesseq($sum(I, $product(-1, K)), 0)))) | (get(A, int, T, t2tb1(K)) = get(A, int, U, t2tb1(K)))))),
% 0.22/0.56 inference(modus_ponens,[status(thm)],[187, 181])).
% 0.22/0.56 tff(189,plain,(
% 0.22/0.56 ![A: ty, T: uni, U: uni, I: $int] : (((~eq_prefix1(A, T, U, I)) | ![K: $int] : ((~($greatereq(K, 0) & (~$lesseq($sum(I, $product(-1, K)), 0)))) | (get(A, int, T, t2tb1(K)) = get(A, int, U, t2tb1(K))))) & (eq_prefix1(A, T, U, I) | (~((~($greatereq(tptp_fun_K_3(I, U, T, A), 0) & (~$lesseq($sum(I, $product(-1, tptp_fun_K_3(I, U, T, A))), 0)))) | (get(A, int, T, t2tb1(tptp_fun_K_3(I, U, T, A))) = get(A, int, U, t2tb1(tptp_fun_K_3(I, U, T, A))))))))),
% 0.22/0.56 inference(skolemize,[status(sab)],[188])).
% 0.22/0.56 tff(190,plain,
% 0.22/0.56 (![A: ty, T: uni, U: uni, I: $int] : (~((~((~eq_prefix1(A, T, U, I)) | ![K: $int] : ((get(A, int, T, t2tb1(K)) = get(A, int, U, t2tb1(K))) | (~$greatereq(K, 0)) | $lesseq($sum(I, $product(-1, K)), 0)))) | (~(eq_prefix1(A, T, U, I) | (~($lesseq($sum(I, $product(-1, tptp_fun_K_3(I, U, T, A))), 0) | (get(A, int, T, t2tb1(tptp_fun_K_3(I, U, T, A))) = get(A, int, U, t2tb1(tptp_fun_K_3(I, U, T, A)))) | (~$greatereq(tptp_fun_K_3(I, U, T, A), 0))))))))),
% 0.22/0.56 inference(modus_ponens,[status(thm)],[189, 179])).
% 0.22/0.56 tff(191,plain,
% 0.22/0.56 (![A: ty, T: uni, U: uni, I: $int] : (~((~((~eq_prefix1(A, T, U, I)) | ![K: $int] : ((get(A, int, T, t2tb1(K)) = get(A, int, U, t2tb1(K))) | (~$greatereq(K, 0)) | $lesseq($sum(I, $product(-1, K)), 0)))) | (~(eq_prefix1(A, T, U, I) | (~($lesseq($sum(I, $product(-1, tptp_fun_K_3(I, U, T, A))), 0) | (get(A, int, T, t2tb1(tptp_fun_K_3(I, U, T, A))) = get(A, int, U, t2tb1(tptp_fun_K_3(I, U, T, A)))) | (~$greatereq(tptp_fun_K_3(I, U, T, A), 0))))))))),
% 0.22/0.56 inference(modus_ponens,[status(thm)],[190, 177])).
% 0.22/0.56 tff(192,plain,
% 0.22/0.56 (((~![A: ty, T: uni, U: uni, I: $int] : (~((~((~eq_prefix1(A, T, U, I)) | ![K: $int] : ((get(A, int, T, t2tb1(K)) = get(A, int, U, t2tb1(K))) | (~$greatereq(K, 0)) | $lesseq($sum(I, $product(-1, K)), 0)))) | (~(eq_prefix1(A, T, U, I) | (~($lesseq($sum(I, $product(-1, tptp_fun_K_3(I, U, T, A))), 0) | (get(A, int, T, t2tb1(tptp_fun_K_3(I, U, T, A))) = get(A, int, U, t2tb1(tptp_fun_K_3(I, U, T, A)))) | (~$greatereq(tptp_fun_K_3(I, U, T, A), 0))))))))) | eq_prefix1(int, t2tb2(Col1!14), t2tb2(T!19), 0)) <=> ((~![A: ty, T: uni, U: uni, I: $int] : (~((~((~eq_prefix1(A, T, U, I)) | ![K: $int] : ((get(A, int, T, t2tb1(K)) = get(A, int, U, t2tb1(K))) | (~$greatereq(K, 0)) | $lesseq($sum(I, $product(-1, K)), 0)))) | (~(eq_prefix1(A, T, U, I) | (~($lesseq($sum(I, $product(-1, tptp_fun_K_3(I, U, T, A))), 0) | (get(A, int, T, t2tb1(tptp_fun_K_3(I, U, T, A))) = get(A, int, U, t2tb1(tptp_fun_K_3(I, U, T, A)))) | (~$greatereq(tptp_fun_K_3(I, U, T, A), 0))))))))) | eq_prefix1(int, t2tb2(Col1!14), t2tb2(T!19), 0))),
% 0.22/0.56 inference(rewrite,[status(thm)],[])).
% 0.22/0.56 tff(193,plain,
% 0.22/0.56 ((~(~eq_prefix1(int, t2tb2(Col1!14), t2tb2(T!19), 0))) <=> eq_prefix1(int, t2tb2(Col1!14), t2tb2(T!19), 0)),
% 0.22/0.56 inference(rewrite,[status(thm)],[])).
% 0.22/0.56 tff(194,plain,
% 0.22/0.56 (($false | (~eq_prefix1(int, t2tb2(Col1!14), t2tb2(T!19), 0))) <=> (~eq_prefix1(int, t2tb2(Col1!14), t2tb2(T!19), 0))),
% 0.22/0.56 inference(rewrite,[status(thm)],[])).
% 0.22/0.56 tff(195,plain,
% 0.22/0.56 ((~(eq_prefix1(int, t2tb2(Col1!14), t2tb2(T!19), 0) | (~($lesseq($sum(0, $product(-1, tptp_fun_K_3(0, t2tb2(T!19), t2tb2(Col1!14), int))), 0) | (get(int, int, t2tb2(Col1!14), t2tb1(tptp_fun_K_3(0, t2tb2(T!19), t2tb2(Col1!14), int))) = get(int, int, t2tb2(T!19), t2tb1(tptp_fun_K_3(0, t2tb2(T!19), t2tb2(Col1!14), int)))) | (~$greatereq(tptp_fun_K_3(0, t2tb2(T!19), t2tb2(Col1!14), int), 0)))))) <=> (~eq_prefix1(int, t2tb2(Col1!14), t2tb2(T!19), 0))),
% 0.22/0.56 inference(rewrite,[status(thm)],[])).
% 0.22/0.56 tff(196,plain,
% 0.22/0.56 ((~$true) <=> $false),
% 0.22/0.56 inference(rewrite,[status(thm)],[])).
% 0.22/0.56 tff(197,plain,
% 0.22/0.56 (((~eq_prefix1(int, t2tb2(Col1!14), t2tb2(T!19), 0)) | $true) <=> $true),
% 0.22/0.56 inference(rewrite,[status(thm)],[])).
% 0.22/0.56 tff(198,plain,
% 0.22/0.56 (![K: $int] : $true <=> $true),
% 0.22/0.56 inference(elim_unused_vars,[status(thm)],[])).
% 0.22/0.56 tff(199,plain,
% 0.22/0.56 (^[K: $int] : trans(monotonicity(trans(monotonicity(rewrite($sum(0, $product(-1, K)) = $product(-1, K)), ($lesseq($sum(0, $product(-1, K)), 0) <=> $lesseq($product(-1, K), 0))), rewrite($lesseq($product(-1, K), 0) <=> $greatereq(K, 0)), ($lesseq($sum(0, $product(-1, K)), 0) <=> $greatereq(K, 0))), (((get(int, int, t2tb2(Col1!14), t2tb1(K)) = get(int, int, t2tb2(T!19), t2tb1(K))) | (~$greatereq(K, 0)) | $lesseq($sum(0, $product(-1, K)), 0)) <=> ((get(int, int, t2tb2(Col1!14), t2tb1(K)) = get(int, int, t2tb2(T!19), t2tb1(K))) | (~$greatereq(K, 0)) | $greatereq(K, 0)))), rewrite(((get(int, int, t2tb2(Col1!14), t2tb1(K)) = get(int, int, t2tb2(T!19), t2tb1(K))) | (~$greatereq(K, 0)) | $greatereq(K, 0)) <=> $true), (((get(int, int, t2tb2(Col1!14), t2tb1(K)) = get(int, int, t2tb2(T!19), t2tb1(K))) | (~$greatereq(K, 0)) | $lesseq($sum(0, $product(-1, K)), 0)) <=> $true))),
% 0.22/0.56 inference(bind,[status(th)],[])).
% 0.22/0.56 tff(200,plain,
% 0.22/0.56 (![K: $int] : ((get(int, int, t2tb2(Col1!14), t2tb1(K)) = get(int, int, t2tb2(T!19), t2tb1(K))) | (~$greatereq(K, 0)) | $lesseq($sum(0, $product(-1, K)), 0)) <=> ![K: $int] : $true),
% 0.22/0.56 inference(quant_intro,[status(thm)],[199])).
% 0.22/0.56 tff(201,plain,
% 0.22/0.56 (![K: $int] : ((get(int, int, t2tb2(Col1!14), t2tb1(K)) = get(int, int, t2tb2(T!19), t2tb1(K))) | (~$greatereq(K, 0)) | $lesseq($sum(0, $product(-1, K)), 0)) <=> $true),
% 0.22/0.56 inference(transitivity,[status(thm)],[200, 198])).
% 0.22/0.56 tff(202,plain,
% 0.22/0.56 (((~eq_prefix1(int, t2tb2(Col1!14), t2tb2(T!19), 0)) | ![K: $int] : ((get(int, int, t2tb2(Col1!14), t2tb1(K)) = get(int, int, t2tb2(T!19), t2tb1(K))) | (~$greatereq(K, 0)) | $lesseq($sum(0, $product(-1, K)), 0))) <=> ((~eq_prefix1(int, t2tb2(Col1!14), t2tb2(T!19), 0)) | $true)),
% 0.22/0.56 inference(monotonicity,[status(thm)],[201])).
% 0.22/0.56 tff(203,plain,
% 0.22/0.56 (((~eq_prefix1(int, t2tb2(Col1!14), t2tb2(T!19), 0)) | ![K: $int] : ((get(int, int, t2tb2(Col1!14), t2tb1(K)) = get(int, int, t2tb2(T!19), t2tb1(K))) | (~$greatereq(K, 0)) | $lesseq($sum(0, $product(-1, K)), 0))) <=> $true),
% 0.22/0.56 inference(transitivity,[status(thm)],[202, 197])).
% 0.22/0.56 tff(204,plain,
% 0.22/0.56 ((~((~eq_prefix1(int, t2tb2(Col1!14), t2tb2(T!19), 0)) | ![K: $int] : ((get(int, int, t2tb2(Col1!14), t2tb1(K)) = get(int, int, t2tb2(T!19), t2tb1(K))) | (~$greatereq(K, 0)) | $lesseq($sum(0, $product(-1, K)), 0)))) <=> (~$true)),
% 0.22/0.56 inference(monotonicity,[status(thm)],[203])).
% 0.22/0.56 tff(205,plain,
% 0.22/0.56 ((~((~eq_prefix1(int, t2tb2(Col1!14), t2tb2(T!19), 0)) | ![K: $int] : ((get(int, int, t2tb2(Col1!14), t2tb1(K)) = get(int, int, t2tb2(T!19), t2tb1(K))) | (~$greatereq(K, 0)) | $lesseq($sum(0, $product(-1, K)), 0)))) <=> $false),
% 0.22/0.56 inference(transitivity,[status(thm)],[204, 196])).
% 0.22/0.56 tff(206,plain,
% 0.22/0.56 (((~((~eq_prefix1(int, t2tb2(Col1!14), t2tb2(T!19), 0)) | ![K: $int] : ((get(int, int, t2tb2(Col1!14), t2tb1(K)) = get(int, int, t2tb2(T!19), t2tb1(K))) | (~$greatereq(K, 0)) | $lesseq($sum(0, $product(-1, K)), 0)))) | (~(eq_prefix1(int, t2tb2(Col1!14), t2tb2(T!19), 0) | (~($lesseq($sum(0, $product(-1, tptp_fun_K_3(0, t2tb2(T!19), t2tb2(Col1!14), int))), 0) | (get(int, int, t2tb2(Col1!14), t2tb1(tptp_fun_K_3(0, t2tb2(T!19), t2tb2(Col1!14), int))) = get(int, int, t2tb2(T!19), t2tb1(tptp_fun_K_3(0, t2tb2(T!19), t2tb2(Col1!14), int)))) | (~$greatereq(tptp_fun_K_3(0, t2tb2(T!19), t2tb2(Col1!14), int), 0))))))) <=> ($false | (~eq_prefix1(int, t2tb2(Col1!14), t2tb2(T!19), 0)))),
% 0.47/0.56 inference(monotonicity,[status(thm)],[205, 195])).
% 0.47/0.56 tff(207,plain,
% 0.47/0.56 (((~((~eq_prefix1(int, t2tb2(Col1!14), t2tb2(T!19), 0)) | ![K: $int] : ((get(int, int, t2tb2(Col1!14), t2tb1(K)) = get(int, int, t2tb2(T!19), t2tb1(K))) | (~$greatereq(K, 0)) | $lesseq($sum(0, $product(-1, K)), 0)))) | (~(eq_prefix1(int, t2tb2(Col1!14), t2tb2(T!19), 0) | (~($lesseq($sum(0, $product(-1, tptp_fun_K_3(0, t2tb2(T!19), t2tb2(Col1!14), int))), 0) | (get(int, int, t2tb2(Col1!14), t2tb1(tptp_fun_K_3(0, t2tb2(T!19), t2tb2(Col1!14), int))) = get(int, int, t2tb2(T!19), t2tb1(tptp_fun_K_3(0, t2tb2(T!19), t2tb2(Col1!14), int)))) | (~$greatereq(tptp_fun_K_3(0, t2tb2(T!19), t2tb2(Col1!14), int), 0))))))) <=> (~eq_prefix1(int, t2tb2(Col1!14), t2tb2(T!19), 0))),
% 0.47/0.56 inference(transitivity,[status(thm)],[206, 194])).
% 0.47/0.56 tff(208,plain,
% 0.47/0.56 ((~((~((~eq_prefix1(int, t2tb2(Col1!14), t2tb2(T!19), 0)) | ![K: $int] : ((get(int, int, t2tb2(Col1!14), t2tb1(K)) = get(int, int, t2tb2(T!19), t2tb1(K))) | (~$greatereq(K, 0)) | $lesseq($sum(0, $product(-1, K)), 0)))) | (~(eq_prefix1(int, t2tb2(Col1!14), t2tb2(T!19), 0) | (~($lesseq($sum(0, $product(-1, tptp_fun_K_3(0, t2tb2(T!19), t2tb2(Col1!14), int))), 0) | (get(int, int, t2tb2(Col1!14), t2tb1(tptp_fun_K_3(0, t2tb2(T!19), t2tb2(Col1!14), int))) = get(int, int, t2tb2(T!19), t2tb1(tptp_fun_K_3(0, t2tb2(T!19), t2tb2(Col1!14), int)))) | (~$greatereq(tptp_fun_K_3(0, t2tb2(T!19), t2tb2(Col1!14), int), 0)))))))) <=> (~(~eq_prefix1(int, t2tb2(Col1!14), t2tb2(T!19), 0)))),
% 0.47/0.56 inference(monotonicity,[status(thm)],[207])).
% 0.47/0.56 tff(209,plain,
% 0.47/0.56 ((~((~((~eq_prefix1(int, t2tb2(Col1!14), t2tb2(T!19), 0)) | ![K: $int] : ((get(int, int, t2tb2(Col1!14), t2tb1(K)) = get(int, int, t2tb2(T!19), t2tb1(K))) | (~$greatereq(K, 0)) | $lesseq($sum(0, $product(-1, K)), 0)))) | (~(eq_prefix1(int, t2tb2(Col1!14), t2tb2(T!19), 0) | (~($lesseq($sum(0, $product(-1, tptp_fun_K_3(0, t2tb2(T!19), t2tb2(Col1!14), int))), 0) | (get(int, int, t2tb2(Col1!14), t2tb1(tptp_fun_K_3(0, t2tb2(T!19), t2tb2(Col1!14), int))) = get(int, int, t2tb2(T!19), t2tb1(tptp_fun_K_3(0, t2tb2(T!19), t2tb2(Col1!14), int)))) | (~$greatereq(tptp_fun_K_3(0, t2tb2(T!19), t2tb2(Col1!14), int), 0)))))))) <=> eq_prefix1(int, t2tb2(Col1!14), t2tb2(T!19), 0)),
% 0.47/0.56 inference(transitivity,[status(thm)],[208, 193])).
% 0.47/0.56 tff(210,plain,
% 0.47/0.56 (((~![A: ty, T: uni, U: uni, I: $int] : (~((~((~eq_prefix1(A, T, U, I)) | ![K: $int] : ((get(A, int, T, t2tb1(K)) = get(A, int, U, t2tb1(K))) | (~$greatereq(K, 0)) | $lesseq($sum(I, $product(-1, K)), 0)))) | (~(eq_prefix1(A, T, U, I) | (~($lesseq($sum(I, $product(-1, tptp_fun_K_3(I, U, T, A))), 0) | (get(A, int, T, t2tb1(tptp_fun_K_3(I, U, T, A))) = get(A, int, U, t2tb1(tptp_fun_K_3(I, U, T, A)))) | (~$greatereq(tptp_fun_K_3(I, U, T, A), 0))))))))) | (~((~((~eq_prefix1(int, t2tb2(Col1!14), t2tb2(T!19), 0)) | ![K: $int] : ((get(int, int, t2tb2(Col1!14), t2tb1(K)) = get(int, int, t2tb2(T!19), t2tb1(K))) | (~$greatereq(K, 0)) | $lesseq($sum(0, $product(-1, K)), 0)))) | (~(eq_prefix1(int, t2tb2(Col1!14), t2tb2(T!19), 0) | (~($lesseq($sum(0, $product(-1, tptp_fun_K_3(0, t2tb2(T!19), t2tb2(Col1!14), int))), 0) | (get(int, int, t2tb2(Col1!14), t2tb1(tptp_fun_K_3(0, t2tb2(T!19), t2tb2(Col1!14), int))) = get(int, int, t2tb2(T!19), t2tb1(tptp_fun_K_3(0, t2tb2(T!19), t2tb2(Col1!14), int)))) | (~$greatereq(tptp_fun_K_3(0, t2tb2(T!19), t2tb2(Col1!14), int), 0))))))))) <=> ((~![A: ty, T: uni, U: uni, I: $int] : (~((~((~eq_prefix1(A, T, U, I)) | ![K: $int] : ((get(A, int, T, t2tb1(K)) = get(A, int, U, t2tb1(K))) | (~$greatereq(K, 0)) | $lesseq($sum(I, $product(-1, K)), 0)))) | (~(eq_prefix1(A, T, U, I) | (~($lesseq($sum(I, $product(-1, tptp_fun_K_3(I, U, T, A))), 0) | (get(A, int, T, t2tb1(tptp_fun_K_3(I, U, T, A))) = get(A, int, U, t2tb1(tptp_fun_K_3(I, U, T, A)))) | (~$greatereq(tptp_fun_K_3(I, U, T, A), 0))))))))) | eq_prefix1(int, t2tb2(Col1!14), t2tb2(T!19), 0))),
% 0.47/0.56 inference(monotonicity,[status(thm)],[209])).
% 0.47/0.56 tff(211,plain,
% 0.47/0.56 (((~![A: ty, T: uni, U: uni, I: $int] : (~((~((~eq_prefix1(A, T, U, I)) | ![K: $int] : ((get(A, int, T, t2tb1(K)) = get(A, int, U, t2tb1(K))) | (~$greatereq(K, 0)) | $lesseq($sum(I, $product(-1, K)), 0)))) | (~(eq_prefix1(A, T, U, I) | (~($lesseq($sum(I, $product(-1, tptp_fun_K_3(I, U, T, A))), 0) | (get(A, int, T, t2tb1(tptp_fun_K_3(I, U, T, A))) = get(A, int, U, t2tb1(tptp_fun_K_3(I, U, T, A)))) | (~$greatereq(tptp_fun_K_3(I, U, T, A), 0))))))))) | (~((~((~eq_prefix1(int, t2tb2(Col1!14), t2tb2(T!19), 0)) | ![K: $int] : ((get(int, int, t2tb2(Col1!14), t2tb1(K)) = get(int, int, t2tb2(T!19), t2tb1(K))) | (~$greatereq(K, 0)) | $lesseq($sum(0, $product(-1, K)), 0)))) | (~(eq_prefix1(int, t2tb2(Col1!14), t2tb2(T!19), 0) | (~($lesseq($sum(0, $product(-1, tptp_fun_K_3(0, t2tb2(T!19), t2tb2(Col1!14), int))), 0) | (get(int, int, t2tb2(Col1!14), t2tb1(tptp_fun_K_3(0, t2tb2(T!19), t2tb2(Col1!14), int))) = get(int, int, t2tb2(T!19), t2tb1(tptp_fun_K_3(0, t2tb2(T!19), t2tb2(Col1!14), int)))) | (~$greatereq(tptp_fun_K_3(0, t2tb2(T!19), t2tb2(Col1!14), int), 0))))))))) <=> ((~![A: ty, T: uni, U: uni, I: $int] : (~((~((~eq_prefix1(A, T, U, I)) | ![K: $int] : ((get(A, int, T, t2tb1(K)) = get(A, int, U, t2tb1(K))) | (~$greatereq(K, 0)) | $lesseq($sum(I, $product(-1, K)), 0)))) | (~(eq_prefix1(A, T, U, I) | (~($lesseq($sum(I, $product(-1, tptp_fun_K_3(I, U, T, A))), 0) | (get(A, int, T, t2tb1(tptp_fun_K_3(I, U, T, A))) = get(A, int, U, t2tb1(tptp_fun_K_3(I, U, T, A)))) | (~$greatereq(tptp_fun_K_3(I, U, T, A), 0))))))))) | eq_prefix1(int, t2tb2(Col1!14), t2tb2(T!19), 0))),
% 0.47/0.57 inference(transitivity,[status(thm)],[210, 192])).
% 0.47/0.57 tff(212,plain,
% 0.47/0.57 ((~![A: ty, T: uni, U: uni, I: $int] : (~((~((~eq_prefix1(A, T, U, I)) | ![K: $int] : ((get(A, int, T, t2tb1(K)) = get(A, int, U, t2tb1(K))) | (~$greatereq(K, 0)) | $lesseq($sum(I, $product(-1, K)), 0)))) | (~(eq_prefix1(A, T, U, I) | (~($lesseq($sum(I, $product(-1, tptp_fun_K_3(I, U, T, A))), 0) | (get(A, int, T, t2tb1(tptp_fun_K_3(I, U, T, A))) = get(A, int, U, t2tb1(tptp_fun_K_3(I, U, T, A)))) | (~$greatereq(tptp_fun_K_3(I, U, T, A), 0))))))))) | (~((~((~eq_prefix1(int, t2tb2(Col1!14), t2tb2(T!19), 0)) | ![K: $int] : ((get(int, int, t2tb2(Col1!14), t2tb1(K)) = get(int, int, t2tb2(T!19), t2tb1(K))) | (~$greatereq(K, 0)) | $lesseq($sum(0, $product(-1, K)), 0)))) | (~(eq_prefix1(int, t2tb2(Col1!14), t2tb2(T!19), 0) | (~($lesseq($sum(0, $product(-1, tptp_fun_K_3(0, t2tb2(T!19), t2tb2(Col1!14), int))), 0) | (get(int, int, t2tb2(Col1!14), t2tb1(tptp_fun_K_3(0, t2tb2(T!19), t2tb2(Col1!14), int))) = get(int, int, t2tb2(T!19), t2tb1(tptp_fun_K_3(0, t2tb2(T!19), t2tb2(Col1!14), int)))) | (~$greatereq(tptp_fun_K_3(0, t2tb2(T!19), t2tb2(Col1!14), int), 0))))))))),
% 0.47/0.57 inference(quant_inst,[status(thm)],[])).
% 0.47/0.57 tff(213,plain,
% 0.47/0.57 ((~![A: ty, T: uni, U: uni, I: $int] : (~((~((~eq_prefix1(A, T, U, I)) | ![K: $int] : ((get(A, int, T, t2tb1(K)) = get(A, int, U, t2tb1(K))) | (~$greatereq(K, 0)) | $lesseq($sum(I, $product(-1, K)), 0)))) | (~(eq_prefix1(A, T, U, I) | (~($lesseq($sum(I, $product(-1, tptp_fun_K_3(I, U, T, A))), 0) | (get(A, int, T, t2tb1(tptp_fun_K_3(I, U, T, A))) = get(A, int, U, t2tb1(tptp_fun_K_3(I, U, T, A)))) | (~$greatereq(tptp_fun_K_3(I, U, T, A), 0))))))))) | eq_prefix1(int, t2tb2(Col1!14), t2tb2(T!19), 0)),
% 0.47/0.57 inference(modus_ponens,[status(thm)],[212, 211])).
% 0.47/0.57 tff(214,plain,
% 0.47/0.57 (eq_prefix1(int, t2tb2(Col1!14), t2tb2(T!19), 0)),
% 0.47/0.57 inference(unit_resolution,[status(thm)],[213, 191])).
% 0.47/0.57 tff(215,plain,
% 0.47/0.57 ($false),
% 0.47/0.57 inference(unit_resolution,[status(thm)],[214, 172])).
% 0.47/0.57 % SZS output end Proof
%------------------------------------------------------------------------------