TSTP Solution File: SWW599_2 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWW599_2 : TPTP v8.1.0. Released v6.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n016.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 20:59:24 EDT 2022
% Result : Theorem 0.22s 0.44s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWW599_2 : TPTP v8.1.0. Released v6.1.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.15/0.35 % Computer : n016.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Sun Sep 4 20:38:09 EDT 2022
% 0.15/0.35 % CPUTime :
% 0.15/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.15/0.35 Usage: tptp [options] [-file:]file
% 0.15/0.35 -h, -? prints this message.
% 0.15/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.15/0.35 -m, -model generate model.
% 0.15/0.35 -p, -proof generate proof.
% 0.15/0.35 -c, -core generate unsat core of named formulas.
% 0.15/0.35 -st, -statistics display statistics.
% 0.15/0.35 -t:timeout set timeout (in second).
% 0.15/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.15/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.15/0.35 -<param>:<value> configuration parameter and value.
% 0.15/0.35 -o:<output-file> file to place output in.
% 0.22/0.44 % SZS status Theorem
% 0.22/0.44 % SZS output start Proof
% 0.22/0.44 tff(tptp_fun_I_0_type, type, (
% 0.22/0.44 tptp_fun_I_0: ( $int * $int * array_int ) > $int)).
% 0.22/0.44 tff(tb2t1_type, type, (
% 0.22/0.44 tb2t1: uni > array_int)).
% 0.22/0.44 tff(mk_array1_type, type, (
% 0.22/0.44 mk_array1: ( ty * $int * uni ) > uni)).
% 0.22/0.44 tff(t2tb2_type, type, (
% 0.22/0.44 t2tb2: map_int_int > uni)).
% 0.22/0.44 tff(tptp_fun_A1_3_type, type, (
% 0.22/0.44 tptp_fun_A1_3: map_int_int)).
% 0.22/0.44 tff(tptp_fun_A_4_type, type, (
% 0.22/0.44 tptp_fun_A_4: $int)).
% 0.22/0.44 tff(int_type, type, (
% 0.22/0.44 int: ty)).
% 0.22/0.44 tff(tptp_fun_V2_6_type, type, (
% 0.22/0.44 tptp_fun_V2_6: $int)).
% 0.22/0.44 tff(tptp_fun_N_2_type, type, (
% 0.22/0.44 tptp_fun_N_2: $int)).
% 0.22/0.44 tff(tptp_fun_J_1_type, type, (
% 0.22/0.44 tptp_fun_J_1: ( $int * $int * array_int ) > $int)).
% 0.22/0.44 tff(tb2t_type, type, (
% 0.22/0.44 tb2t: uni > $int)).
% 0.22/0.44 tff(get2_type, type, (
% 0.22/0.44 get2: ( ty * uni * $int ) > uni)).
% 0.22/0.44 tff(t2tb1_type, type, (
% 0.22/0.44 t2tb1: array_int > uni)).
% 0.22/0.44 tff(appear_twice1_type, type, (
% 0.22/0.44 appear_twice1: ( array_int * $int * $int ) > $o)).
% 0.22/0.44 tff(tptp_fun_V1_8_type, type, (
% 0.22/0.44 tptp_fun_V1_8: $int)).
% 0.22/0.44 tff(tptp_fun_V2_9_type, type, (
% 0.22/0.44 tptp_fun_V2_9: $int)).
% 0.22/0.44 tff(get_type, type, (
% 0.22/0.44 get: ( ty * ty * uni * uni ) > uni)).
% 0.22/0.44 tff(t2tb_type, type, (
% 0.22/0.44 t2tb: $int > uni)).
% 0.22/0.44 tff(tptp_fun_J_10_type, type, (
% 0.22/0.44 tptp_fun_J_10: $int > $int)).
% 0.22/0.44 tff(true1_type, type, (
% 0.22/0.44 true1: bool1)).
% 0.22/0.44 tff(tb2t3_type, type, (
% 0.22/0.44 tb2t3: uni > bool1)).
% 0.22/0.44 tff(t2tb4_type, type, (
% 0.22/0.44 t2tb4: map_int_bool > uni)).
% 0.22/0.44 tff(tptp_fun_Deja_vu_7_type, type, (
% 0.22/0.44 tptp_fun_Deja_vu_7: map_int_bool)).
% 0.22/0.44 tff(bool_type, type, (
% 0.22/0.44 bool: ty)).
% 0.22/0.44 tff(tptp_fun_V1_5_type, type, (
% 0.22/0.44 tptp_fun_V1_5: $int)).
% 0.22/0.44 tff(elts_type, type, (
% 0.22/0.44 elts: ( ty * uni ) > uni)).
% 0.22/0.44 tff(sort1_type, type, (
% 0.22/0.44 sort1: ( ty * uni ) > $o)).
% 0.22/0.44 tff(map_type, type, (
% 0.22/0.44 map: ( ty * ty ) > ty)).
% 0.22/0.44 tff(1,plain,
% 0.22/0.44 (^[A: array_int, V: $int, U: $int] : refl((~((~((~appear_twice1(A, V, U)) | (~($lesseq($sum(U, $product(-1, tptp_fun_I_0(U, V, A))), 0) | $lesseq($sum(U, $product(-1, tptp_fun_J_1(U, V, A))), 0) | ($sum(tptp_fun_I_0(U, V, A), $product(-1, tptp_fun_J_1(U, V, A))) = 0) | (~$greatereq(tptp_fun_I_0(U, V, A), 0)) | (~($sum(V, $product(-1, tb2t(get2(int, t2tb1(A), tptp_fun_I_0(U, V, A))))) = 0)) | (~$greatereq(tptp_fun_J_1(U, V, A), 0)) | (~($sum(V, $product(-1, tb2t(get2(int, t2tb1(A), tptp_fun_J_1(U, V, A))))) = 0)))))) | (~(appear_twice1(A, V, U) | ![I: $int] : ((~$greatereq(I, 0)) | $lesseq($sum(U, $product(-1, I)), 0) | (~($sum(V, $product(-1, tb2t(get2(int, t2tb1(A), I)))) = 0)) | ![J: $int] : ((~$greatereq(J, 0)) | $lesseq($sum(U, $product(-1, J)), 0) | ($sum(I, $product(-1, J)) = 0) | (~($sum(V, $product(-1, tb2t(get2(int, t2tb1(A), J)))) = 0)))))))) <=> (~((~((~appear_twice1(A, V, U)) | (~($lesseq($sum(U, $product(-1, tptp_fun_I_0(U, V, A))), 0) | $lesseq($sum(U, $product(-1, tptp_fun_J_1(U, V, A))), 0) | ($sum(tptp_fun_I_0(U, V, A), $product(-1, tptp_fun_J_1(U, V, A))) = 0) | (~$greatereq(tptp_fun_I_0(U, V, A), 0)) | (~($sum(V, $product(-1, tb2t(get2(int, t2tb1(A), tptp_fun_I_0(U, V, A))))) = 0)) | (~$greatereq(tptp_fun_J_1(U, V, A), 0)) | (~($sum(V, $product(-1, tb2t(get2(int, t2tb1(A), tptp_fun_J_1(U, V, A))))) = 0)))))) | (~(appear_twice1(A, V, U) | ![I: $int] : ((~$greatereq(I, 0)) | $lesseq($sum(U, $product(-1, I)), 0) | (~($sum(V, $product(-1, tb2t(get2(int, t2tb1(A), I)))) = 0)) | ![J: $int] : ((~$greatereq(J, 0)) | $lesseq($sum(U, $product(-1, J)), 0) | ($sum(I, $product(-1, J)) = 0) | (~($sum(V, $product(-1, tb2t(get2(int, t2tb1(A), J)))) = 0)))))))))),
% 0.22/0.44 inference(bind,[status(th)],[])).
% 0.22/0.44 tff(2,plain,
% 0.22/0.44 (![A: array_int, V: $int, U: $int] : (~((~((~appear_twice1(A, V, U)) | (~($lesseq($sum(U, $product(-1, tptp_fun_I_0(U, V, A))), 0) | $lesseq($sum(U, $product(-1, tptp_fun_J_1(U, V, A))), 0) | ($sum(tptp_fun_I_0(U, V, A), $product(-1, tptp_fun_J_1(U, V, A))) = 0) | (~$greatereq(tptp_fun_I_0(U, V, A), 0)) | (~($sum(V, $product(-1, tb2t(get2(int, t2tb1(A), tptp_fun_I_0(U, V, A))))) = 0)) | (~$greatereq(tptp_fun_J_1(U, V, A), 0)) | (~($sum(V, $product(-1, tb2t(get2(int, t2tb1(A), tptp_fun_J_1(U, V, A))))) = 0)))))) | (~(appear_twice1(A, V, U) | ![I: $int] : ((~$greatereq(I, 0)) | $lesseq($sum(U, $product(-1, I)), 0) | (~($sum(V, $product(-1, tb2t(get2(int, t2tb1(A), I)))) = 0)) | ![J: $int] : ((~$greatereq(J, 0)) | $lesseq($sum(U, $product(-1, J)), 0) | ($sum(I, $product(-1, J)) = 0) | (~($sum(V, $product(-1, tb2t(get2(int, t2tb1(A), J)))) = 0)))))))) <=> ![A: array_int, V: $int, U: $int] : (~((~((~appear_twice1(A, V, U)) | (~($lesseq($sum(U, $product(-1, tptp_fun_I_0(U, V, A))), 0) | $lesseq($sum(U, $product(-1, tptp_fun_J_1(U, V, A))), 0) | ($sum(tptp_fun_I_0(U, V, A), $product(-1, tptp_fun_J_1(U, V, A))) = 0) | (~$greatereq(tptp_fun_I_0(U, V, A), 0)) | (~($sum(V, $product(-1, tb2t(get2(int, t2tb1(A), tptp_fun_I_0(U, V, A))))) = 0)) | (~$greatereq(tptp_fun_J_1(U, V, A), 0)) | (~($sum(V, $product(-1, tb2t(get2(int, t2tb1(A), tptp_fun_J_1(U, V, A))))) = 0)))))) | (~(appear_twice1(A, V, U) | ![I: $int] : ((~$greatereq(I, 0)) | $lesseq($sum(U, $product(-1, I)), 0) | (~($sum(V, $product(-1, tb2t(get2(int, t2tb1(A), I)))) = 0)) | ![J: $int] : ((~$greatereq(J, 0)) | $lesseq($sum(U, $product(-1, J)), 0) | ($sum(I, $product(-1, J)) = 0) | (~($sum(V, $product(-1, tb2t(get2(int, t2tb1(A), J)))) = 0))))))))),
% 0.22/0.45 inference(quant_intro,[status(thm)],[1])).
% 0.22/0.45 tff(3,plain,
% 0.22/0.45 (^[A: array_int, V: $int, U: $int] : rewrite((~((~((~appear_twice1(A, V, U)) | (~($lesseq($sum(U, $product(-1, tptp_fun_I_0(U, V, A))), 0) | $lesseq($sum(U, $product(-1, tptp_fun_J_1(U, V, A))), 0) | ($sum(tptp_fun_I_0(U, V, A), $product(-1, tptp_fun_J_1(U, V, A))) = 0) | (~$greatereq(tptp_fun_I_0(U, V, A), 0)) | (~($sum(V, $product(-1, tb2t(get2(int, t2tb1(A), tptp_fun_I_0(U, V, A))))) = 0)) | (~$greatereq(tptp_fun_J_1(U, V, A), 0)) | (~($sum(V, $product(-1, tb2t(get2(int, t2tb1(A), tptp_fun_J_1(U, V, A))))) = 0)))))) | (~(appear_twice1(A, V, U) | ![I: $int] : ((~$greatereq(I, 0)) | $lesseq($sum(U, $product(-1, I)), 0) | (~($sum(V, $product(-1, tb2t(get2(int, t2tb1(A), I)))) = 0)) | ![J: $int] : ((~$greatereq(J, 0)) | $lesseq($sum(U, $product(-1, J)), 0) | ($sum(I, $product(-1, J)) = 0) | (~($sum(V, $product(-1, tb2t(get2(int, t2tb1(A), J)))) = 0)))))))) <=> (~((~((~appear_twice1(A, V, U)) | (~($lesseq($sum(U, $product(-1, tptp_fun_I_0(U, V, A))), 0) | $lesseq($sum(U, $product(-1, tptp_fun_J_1(U, V, A))), 0) | ($sum(tptp_fun_I_0(U, V, A), $product(-1, tptp_fun_J_1(U, V, A))) = 0) | (~$greatereq(tptp_fun_I_0(U, V, A), 0)) | (~($sum(V, $product(-1, tb2t(get2(int, t2tb1(A), tptp_fun_I_0(U, V, A))))) = 0)) | (~$greatereq(tptp_fun_J_1(U, V, A), 0)) | (~($sum(V, $product(-1, tb2t(get2(int, t2tb1(A), tptp_fun_J_1(U, V, A))))) = 0)))))) | (~(appear_twice1(A, V, U) | ![I: $int] : ((~$greatereq(I, 0)) | $lesseq($sum(U, $product(-1, I)), 0) | (~($sum(V, $product(-1, tb2t(get2(int, t2tb1(A), I)))) = 0)) | ![J: $int] : ((~$greatereq(J, 0)) | $lesseq($sum(U, $product(-1, J)), 0) | ($sum(I, $product(-1, J)) = 0) | (~($sum(V, $product(-1, tb2t(get2(int, t2tb1(A), J)))) = 0)))))))))),
% 0.22/0.45 inference(bind,[status(th)],[])).
% 0.22/0.45 tff(4,plain,
% 0.22/0.45 (![A: array_int, V: $int, U: $int] : (~((~((~appear_twice1(A, V, U)) | (~($lesseq($sum(U, $product(-1, tptp_fun_I_0(U, V, A))), 0) | $lesseq($sum(U, $product(-1, tptp_fun_J_1(U, V, A))), 0) | ($sum(tptp_fun_I_0(U, V, A), $product(-1, tptp_fun_J_1(U, V, A))) = 0) | (~$greatereq(tptp_fun_I_0(U, V, A), 0)) | (~($sum(V, $product(-1, tb2t(get2(int, t2tb1(A), tptp_fun_I_0(U, V, A))))) = 0)) | (~$greatereq(tptp_fun_J_1(U, V, A), 0)) | (~($sum(V, $product(-1, tb2t(get2(int, t2tb1(A), tptp_fun_J_1(U, V, A))))) = 0)))))) | (~(appear_twice1(A, V, U) | ![I: $int] : ((~$greatereq(I, 0)) | $lesseq($sum(U, $product(-1, I)), 0) | (~($sum(V, $product(-1, tb2t(get2(int, t2tb1(A), I)))) = 0)) | ![J: $int] : ((~$greatereq(J, 0)) | $lesseq($sum(U, $product(-1, J)), 0) | ($sum(I, $product(-1, J)) = 0) | (~($sum(V, $product(-1, tb2t(get2(int, t2tb1(A), J)))) = 0)))))))) <=> ![A: array_int, V: $int, U: $int] : (~((~((~appear_twice1(A, V, U)) | (~($lesseq($sum(U, $product(-1, tptp_fun_I_0(U, V, A))), 0) | $lesseq($sum(U, $product(-1, tptp_fun_J_1(U, V, A))), 0) | ($sum(tptp_fun_I_0(U, V, A), $product(-1, tptp_fun_J_1(U, V, A))) = 0) | (~$greatereq(tptp_fun_I_0(U, V, A), 0)) | (~($sum(V, $product(-1, tb2t(get2(int, t2tb1(A), tptp_fun_I_0(U, V, A))))) = 0)) | (~$greatereq(tptp_fun_J_1(U, V, A), 0)) | (~($sum(V, $product(-1, tb2t(get2(int, t2tb1(A), tptp_fun_J_1(U, V, A))))) = 0)))))) | (~(appear_twice1(A, V, U) | ![I: $int] : ((~$greatereq(I, 0)) | $lesseq($sum(U, $product(-1, I)), 0) | (~($sum(V, $product(-1, tb2t(get2(int, t2tb1(A), I)))) = 0)) | ![J: $int] : ((~$greatereq(J, 0)) | $lesseq($sum(U, $product(-1, J)), 0) | ($sum(I, $product(-1, J)) = 0) | (~($sum(V, $product(-1, tb2t(get2(int, t2tb1(A), J)))) = 0))))))))),
% 0.22/0.45 inference(quant_intro,[status(thm)],[3])).
% 0.22/0.45 tff(5,plain,
% 0.22/0.45 (![A: array_int, V: $int, U: $int] : (~((~((~appear_twice1(A, V, U)) | (~($lesseq($sum(U, $product(-1, tptp_fun_I_0(U, V, A))), 0) | $lesseq($sum(U, $product(-1, tptp_fun_J_1(U, V, A))), 0) | ($sum(tptp_fun_I_0(U, V, A), $product(-1, tptp_fun_J_1(U, V, A))) = 0) | (~$greatereq(tptp_fun_I_0(U, V, A), 0)) | (~($sum(V, $product(-1, tb2t(get2(int, t2tb1(A), tptp_fun_I_0(U, V, A))))) = 0)) | (~$greatereq(tptp_fun_J_1(U, V, A), 0)) | (~($sum(V, $product(-1, tb2t(get2(int, t2tb1(A), tptp_fun_J_1(U, V, A))))) = 0)))))) | (~(appear_twice1(A, V, U) | ![I: $int] : ((~$greatereq(I, 0)) | $lesseq($sum(U, $product(-1, I)), 0) | (~($sum(V, $product(-1, tb2t(get2(int, t2tb1(A), I)))) = 0)) | ![J: $int] : ((~$greatereq(J, 0)) | $lesseq($sum(U, $product(-1, J)), 0) | ($sum(I, $product(-1, J)) = 0) | (~($sum(V, $product(-1, tb2t(get2(int, t2tb1(A), J)))) = 0)))))))) <=> ![A: array_int, V: $int, U: $int] : (~((~((~appear_twice1(A, V, U)) | (~($lesseq($sum(U, $product(-1, tptp_fun_I_0(U, V, A))), 0) | $lesseq($sum(U, $product(-1, tptp_fun_J_1(U, V, A))), 0) | ($sum(tptp_fun_I_0(U, V, A), $product(-1, tptp_fun_J_1(U, V, A))) = 0) | (~$greatereq(tptp_fun_I_0(U, V, A), 0)) | (~($sum(V, $product(-1, tb2t(get2(int, t2tb1(A), tptp_fun_I_0(U, V, A))))) = 0)) | (~$greatereq(tptp_fun_J_1(U, V, A), 0)) | (~($sum(V, $product(-1, tb2t(get2(int, t2tb1(A), tptp_fun_J_1(U, V, A))))) = 0)))))) | (~(appear_twice1(A, V, U) | ![I: $int] : ((~$greatereq(I, 0)) | $lesseq($sum(U, $product(-1, I)), 0) | (~($sum(V, $product(-1, tb2t(get2(int, t2tb1(A), I)))) = 0)) | ![J: $int] : ((~$greatereq(J, 0)) | $lesseq($sum(U, $product(-1, J)), 0) | ($sum(I, $product(-1, J)) = 0) | (~($sum(V, $product(-1, tb2t(get2(int, t2tb1(A), J)))) = 0))))))))),
% 0.22/0.45 inference(transitivity,[status(thm)],[4, 2])).
% 0.22/0.45 tff(6,plain,
% 0.22/0.45 (^[A: array_int, V: $int, U: $int] : trans(monotonicity(rewrite(((~appear_twice1(A, V, U)) | ($greatereq(tptp_fun_I_0(U, V, A), 0) & (~$lesseq($sum(U, $product(-1, tptp_fun_I_0(U, V, A))), 0)) & ($sum(V, $product(-1, tb2t(get2(int, t2tb1(A), tptp_fun_I_0(U, V, A))))) = 0) & $greatereq(tptp_fun_J_1(U, V, A), 0) & (~$lesseq($sum(U, $product(-1, tptp_fun_J_1(U, V, A))), 0)) & (~($sum(tptp_fun_I_0(U, V, A), $product(-1, tptp_fun_J_1(U, V, A))) = 0)) & ($sum(V, $product(-1, tb2t(get2(int, t2tb1(A), tptp_fun_J_1(U, V, A))))) = 0))) <=> ((~appear_twice1(A, V, U)) | (~($lesseq($sum(U, $product(-1, tptp_fun_I_0(U, V, A))), 0) | $lesseq($sum(U, $product(-1, tptp_fun_J_1(U, V, A))), 0) | ($sum(tptp_fun_I_0(U, V, A), $product(-1, tptp_fun_J_1(U, V, A))) = 0) | (~$greatereq(tptp_fun_I_0(U, V, A), 0)) | (~($sum(V, $product(-1, tb2t(get2(int, t2tb1(A), tptp_fun_I_0(U, V, A))))) = 0)) | (~$greatereq(tptp_fun_J_1(U, V, A), 0)) | (~($sum(V, $product(-1, tb2t(get2(int, t2tb1(A), tptp_fun_J_1(U, V, A))))) = 0)))))), rewrite((appear_twice1(A, V, U) | ![I: $int] : ((~$greatereq(I, 0)) | $lesseq($sum(U, $product(-1, I)), 0) | (~($sum(V, $product(-1, tb2t(get2(int, t2tb1(A), I)))) = 0)) | ![J: $int] : (~($greatereq(J, 0) & (~$lesseq($sum(U, $product(-1, J)), 0)) & (~($sum(I, $product(-1, J)) = 0)) & ($sum(V, $product(-1, tb2t(get2(int, t2tb1(A), J)))) = 0))))) <=> (appear_twice1(A, V, U) | ![I: $int] : ((~$greatereq(I, 0)) | $lesseq($sum(U, $product(-1, I)), 0) | (~($sum(V, $product(-1, tb2t(get2(int, t2tb1(A), I)))) = 0)) | ![J: $int] : ((~$greatereq(J, 0)) | $lesseq($sum(U, $product(-1, J)), 0) | ($sum(I, $product(-1, J)) = 0) | (~($sum(V, $product(-1, tb2t(get2(int, t2tb1(A), J)))) = 0)))))), ((((~appear_twice1(A, V, U)) | ($greatereq(tptp_fun_I_0(U, V, A), 0) & (~$lesseq($sum(U, $product(-1, tptp_fun_I_0(U, V, A))), 0)) & ($sum(V, $product(-1, tb2t(get2(int, t2tb1(A), tptp_fun_I_0(U, V, A))))) = 0) & $greatereq(tptp_fun_J_1(U, V, A), 0) & (~$lesseq($sum(U, $product(-1, tptp_fun_J_1(U, V, A))), 0)) & (~($sum(tptp_fun_I_0(U, V, A), $product(-1, tptp_fun_J_1(U, V, A))) = 0)) & ($sum(V, $product(-1, tb2t(get2(int, t2tb1(A), tptp_fun_J_1(U, V, A))))) = 0))) & (appear_twice1(A, V, U) | ![I: $int] : ((~$greatereq(I, 0)) | $lesseq($sum(U, $product(-1, I)), 0) | (~($sum(V, $product(-1, tb2t(get2(int, t2tb1(A), I)))) = 0)) | ![J: $int] : (~($greatereq(J, 0) & (~$lesseq($sum(U, $product(-1, J)), 0)) & (~($sum(I, $product(-1, J)) = 0)) & ($sum(V, $product(-1, tb2t(get2(int, t2tb1(A), J)))) = 0)))))) <=> (((~appear_twice1(A, V, U)) | (~($lesseq($sum(U, $product(-1, tptp_fun_I_0(U, V, A))), 0) | $lesseq($sum(U, $product(-1, tptp_fun_J_1(U, V, A))), 0) | ($sum(tptp_fun_I_0(U, V, A), $product(-1, tptp_fun_J_1(U, V, A))) = 0) | (~$greatereq(tptp_fun_I_0(U, V, A), 0)) | (~($sum(V, $product(-1, tb2t(get2(int, t2tb1(A), tptp_fun_I_0(U, V, A))))) = 0)) | (~$greatereq(tptp_fun_J_1(U, V, A), 0)) | (~($sum(V, $product(-1, tb2t(get2(int, t2tb1(A), tptp_fun_J_1(U, V, A))))) = 0))))) & (appear_twice1(A, V, U) | ![I: $int] : ((~$greatereq(I, 0)) | $lesseq($sum(U, $product(-1, I)), 0) | (~($sum(V, $product(-1, tb2t(get2(int, t2tb1(A), I)))) = 0)) | ![J: $int] : ((~$greatereq(J, 0)) | $lesseq($sum(U, $product(-1, J)), 0) | ($sum(I, $product(-1, J)) = 0) | (~($sum(V, $product(-1, tb2t(get2(int, t2tb1(A), J)))) = 0)))))))), rewrite((((~appear_twice1(A, V, U)) | (~($lesseq($sum(U, $product(-1, tptp_fun_I_0(U, V, A))), 0) | $lesseq($sum(U, $product(-1, tptp_fun_J_1(U, V, A))), 0) | ($sum(tptp_fun_I_0(U, V, A), $product(-1, tptp_fun_J_1(U, V, A))) = 0) | (~$greatereq(tptp_fun_I_0(U, V, A), 0)) | (~($sum(V, $product(-1, tb2t(get2(int, t2tb1(A), tptp_fun_I_0(U, V, A))))) = 0)) | (~$greatereq(tptp_fun_J_1(U, V, A), 0)) | (~($sum(V, $product(-1, tb2t(get2(int, t2tb1(A), tptp_fun_J_1(U, V, A))))) = 0))))) & (appear_twice1(A, V, U) | ![I: $int] : ((~$greatereq(I, 0)) | $lesseq($sum(U, $product(-1, I)), 0) | (~($sum(V, $product(-1, tb2t(get2(int, t2tb1(A), I)))) = 0)) | ![J: $int] : ((~$greatereq(J, 0)) | $lesseq($sum(U, $product(-1, J)), 0) | ($sum(I, $product(-1, J)) = 0) | (~($sum(V, $product(-1, tb2t(get2(int, t2tb1(A), J)))) = 0)))))) <=> (~((~((~appear_twice1(A, V, U)) | (~($lesseq($sum(U, $product(-1, tptp_fun_I_0(U, V, A))), 0) | $lesseq($sum(U, $product(-1, tptp_fun_J_1(U, V, A))), 0) | ($sum(tptp_fun_I_0(U, V, A), $product(-1, tptp_fun_J_1(U, V, A))) = 0) | (~$greatereq(tptp_fun_I_0(U, V, A), 0)) | (~($sum(V, $product(-1, tb2t(get2(int, t2tb1(A), tptp_fun_I_0(U, V, A))))) = 0)) | (~$greatereq(tptp_fun_J_1(U, V, A), 0)) | (~($sum(V, $product(-1, tb2t(get2(int, t2tb1(A), tptp_fun_J_1(U, V, A))))) = 0)))))) | (~(appear_twice1(A, V, U) | ![I: $int] : ((~$greatereq(I, 0)) | $lesseq($sum(U, $product(-1, I)), 0) | (~($sum(V, $product(-1, tb2t(get2(int, t2tb1(A), I)))) = 0)) | ![J: $int] : ((~$greatereq(J, 0)) | $lesseq($sum(U, $product(-1, J)), 0) | ($sum(I, $product(-1, J)) = 0) | (~($sum(V, $product(-1, tb2t(get2(int, t2tb1(A), J)))) = 0))))))))), ((((~appear_twice1(A, V, U)) | ($greatereq(tptp_fun_I_0(U, V, A), 0) & (~$lesseq($sum(U, $product(-1, tptp_fun_I_0(U, V, A))), 0)) & ($sum(V, $product(-1, tb2t(get2(int, t2tb1(A), tptp_fun_I_0(U, V, A))))) = 0) & $greatereq(tptp_fun_J_1(U, V, A), 0) & (~$lesseq($sum(U, $product(-1, tptp_fun_J_1(U, V, A))), 0)) & (~($sum(tptp_fun_I_0(U, V, A), $product(-1, tptp_fun_J_1(U, V, A))) = 0)) & ($sum(V, $product(-1, tb2t(get2(int, t2tb1(A), tptp_fun_J_1(U, V, A))))) = 0))) & (appear_twice1(A, V, U) | ![I: $int] : ((~$greatereq(I, 0)) | $lesseq($sum(U, $product(-1, I)), 0) | (~($sum(V, $product(-1, tb2t(get2(int, t2tb1(A), I)))) = 0)) | ![J: $int] : (~($greatereq(J, 0) & (~$lesseq($sum(U, $product(-1, J)), 0)) & (~($sum(I, $product(-1, J)) = 0)) & ($sum(V, $product(-1, tb2t(get2(int, t2tb1(A), J)))) = 0)))))) <=> (~((~((~appear_twice1(A, V, U)) | (~($lesseq($sum(U, $product(-1, tptp_fun_I_0(U, V, A))), 0) | $lesseq($sum(U, $product(-1, tptp_fun_J_1(U, V, A))), 0) | ($sum(tptp_fun_I_0(U, V, A), $product(-1, tptp_fun_J_1(U, V, A))) = 0) | (~$greatereq(tptp_fun_I_0(U, V, A), 0)) | (~($sum(V, $product(-1, tb2t(get2(int, t2tb1(A), tptp_fun_I_0(U, V, A))))) = 0)) | (~$greatereq(tptp_fun_J_1(U, V, A), 0)) | (~($sum(V, $product(-1, tb2t(get2(int, t2tb1(A), tptp_fun_J_1(U, V, A))))) = 0)))))) | (~(appear_twice1(A, V, U) | ![I: $int] : ((~$greatereq(I, 0)) | $lesseq($sum(U, $product(-1, I)), 0) | (~($sum(V, $product(-1, tb2t(get2(int, t2tb1(A), I)))) = 0)) | ![J: $int] : ((~$greatereq(J, 0)) | $lesseq($sum(U, $product(-1, J)), 0) | ($sum(I, $product(-1, J)) = 0) | (~($sum(V, $product(-1, tb2t(get2(int, t2tb1(A), J)))) = 0))))))))))),
% 0.22/0.45 inference(bind,[status(th)],[])).
% 0.22/0.45 tff(7,plain,
% 0.22/0.45 (![A: array_int, V: $int, U: $int] : (((~appear_twice1(A, V, U)) | ($greatereq(tptp_fun_I_0(U, V, A), 0) & (~$lesseq($sum(U, $product(-1, tptp_fun_I_0(U, V, A))), 0)) & ($sum(V, $product(-1, tb2t(get2(int, t2tb1(A), tptp_fun_I_0(U, V, A))))) = 0) & $greatereq(tptp_fun_J_1(U, V, A), 0) & (~$lesseq($sum(U, $product(-1, tptp_fun_J_1(U, V, A))), 0)) & (~($sum(tptp_fun_I_0(U, V, A), $product(-1, tptp_fun_J_1(U, V, A))) = 0)) & ($sum(V, $product(-1, tb2t(get2(int, t2tb1(A), tptp_fun_J_1(U, V, A))))) = 0))) & (appear_twice1(A, V, U) | ![I: $int] : ((~$greatereq(I, 0)) | $lesseq($sum(U, $product(-1, I)), 0) | (~($sum(V, $product(-1, tb2t(get2(int, t2tb1(A), I)))) = 0)) | ![J: $int] : (~($greatereq(J, 0) & (~$lesseq($sum(U, $product(-1, J)), 0)) & (~($sum(I, $product(-1, J)) = 0)) & ($sum(V, $product(-1, tb2t(get2(int, t2tb1(A), J)))) = 0)))))) <=> ![A: array_int, V: $int, U: $int] : (~((~((~appear_twice1(A, V, U)) | (~($lesseq($sum(U, $product(-1, tptp_fun_I_0(U, V, A))), 0) | $lesseq($sum(U, $product(-1, tptp_fun_J_1(U, V, A))), 0) | ($sum(tptp_fun_I_0(U, V, A), $product(-1, tptp_fun_J_1(U, V, A))) = 0) | (~$greatereq(tptp_fun_I_0(U, V, A), 0)) | (~($sum(V, $product(-1, tb2t(get2(int, t2tb1(A), tptp_fun_I_0(U, V, A))))) = 0)) | (~$greatereq(tptp_fun_J_1(U, V, A), 0)) | (~($sum(V, $product(-1, tb2t(get2(int, t2tb1(A), tptp_fun_J_1(U, V, A))))) = 0)))))) | (~(appear_twice1(A, V, U) | ![I: $int] : ((~$greatereq(I, 0)) | $lesseq($sum(U, $product(-1, I)), 0) | (~($sum(V, $product(-1, tb2t(get2(int, t2tb1(A), I)))) = 0)) | ![J: $int] : ((~$greatereq(J, 0)) | $lesseq($sum(U, $product(-1, J)), 0) | ($sum(I, $product(-1, J)) = 0) | (~($sum(V, $product(-1, tb2t(get2(int, t2tb1(A), J)))) = 0))))))))),
% 0.22/0.45 inference(quant_intro,[status(thm)],[6])).
% 0.22/0.45 tff(8,plain,
% 0.22/0.45 (^[A: array_int, V: $int, U: $int] : rewrite((((~appear_twice1(A, V, U)) | ($greatereq(tptp_fun_I_0(U, V, A), 0) & (~$lesseq($sum(U, $product(-1, tptp_fun_I_0(U, V, A))), 0)) & ($sum(V, $product(-1, tb2t(get2(int, t2tb1(A), tptp_fun_I_0(U, V, A))))) = 0) & ($greatereq(tptp_fun_J_1(U, V, A), 0) & (~$lesseq($sum(U, $product(-1, tptp_fun_J_1(U, V, A))), 0)) & (~($sum(tptp_fun_I_0(U, V, A), $product(-1, tptp_fun_J_1(U, V, A))) = 0)) & ($sum(V, $product(-1, tb2t(get2(int, t2tb1(A), tptp_fun_J_1(U, V, A))))) = 0)))) & (appear_twice1(A, V, U) | ![I: $int] : ((~$greatereq(I, 0)) | (~(~$lesseq($sum(U, $product(-1, I)), 0))) | (~($sum(V, $product(-1, tb2t(get2(int, t2tb1(A), I)))) = 0)) | ![J: $int] : (~($greatereq(J, 0) & (~$lesseq($sum(U, $product(-1, J)), 0)) & (~($sum(I, $product(-1, J)) = 0)) & ($sum(V, $product(-1, tb2t(get2(int, t2tb1(A), J)))) = 0)))))) <=> (((~appear_twice1(A, V, U)) | ($greatereq(tptp_fun_I_0(U, V, A), 0) & (~$lesseq($sum(U, $product(-1, tptp_fun_I_0(U, V, A))), 0)) & ($sum(V, $product(-1, tb2t(get2(int, t2tb1(A), tptp_fun_I_0(U, V, A))))) = 0) & $greatereq(tptp_fun_J_1(U, V, A), 0) & (~$lesseq($sum(U, $product(-1, tptp_fun_J_1(U, V, A))), 0)) & (~($sum(tptp_fun_I_0(U, V, A), $product(-1, tptp_fun_J_1(U, V, A))) = 0)) & ($sum(V, $product(-1, tb2t(get2(int, t2tb1(A), tptp_fun_J_1(U, V, A))))) = 0))) & (appear_twice1(A, V, U) | ![I: $int] : ((~$greatereq(I, 0)) | $lesseq($sum(U, $product(-1, I)), 0) | (~($sum(V, $product(-1, tb2t(get2(int, t2tb1(A), I)))) = 0)) | ![J: $int] : (~($greatereq(J, 0) & (~$lesseq($sum(U, $product(-1, J)), 0)) & (~($sum(I, $product(-1, J)) = 0)) & ($sum(V, $product(-1, tb2t(get2(int, t2tb1(A), J)))) = 0)))))))),
% 0.22/0.45 inference(bind,[status(th)],[])).
% 0.22/0.45 tff(9,plain,
% 0.22/0.45 (![A: array_int, V: $int, U: $int] : (((~appear_twice1(A, V, U)) | ($greatereq(tptp_fun_I_0(U, V, A), 0) & (~$lesseq($sum(U, $product(-1, tptp_fun_I_0(U, V, A))), 0)) & ($sum(V, $product(-1, tb2t(get2(int, t2tb1(A), tptp_fun_I_0(U, V, A))))) = 0) & ($greatereq(tptp_fun_J_1(U, V, A), 0) & (~$lesseq($sum(U, $product(-1, tptp_fun_J_1(U, V, A))), 0)) & (~($sum(tptp_fun_I_0(U, V, A), $product(-1, tptp_fun_J_1(U, V, A))) = 0)) & ($sum(V, $product(-1, tb2t(get2(int, t2tb1(A), tptp_fun_J_1(U, V, A))))) = 0)))) & (appear_twice1(A, V, U) | ![I: $int] : ((~$greatereq(I, 0)) | (~(~$lesseq($sum(U, $product(-1, I)), 0))) | (~($sum(V, $product(-1, tb2t(get2(int, t2tb1(A), I)))) = 0)) | ![J: $int] : (~($greatereq(J, 0) & (~$lesseq($sum(U, $product(-1, J)), 0)) & (~($sum(I, $product(-1, J)) = 0)) & ($sum(V, $product(-1, tb2t(get2(int, t2tb1(A), J)))) = 0)))))) <=> ![A: array_int, V: $int, U: $int] : (((~appear_twice1(A, V, U)) | ($greatereq(tptp_fun_I_0(U, V, A), 0) & (~$lesseq($sum(U, $product(-1, tptp_fun_I_0(U, V, A))), 0)) & ($sum(V, $product(-1, tb2t(get2(int, t2tb1(A), tptp_fun_I_0(U, V, A))))) = 0) & $greatereq(tptp_fun_J_1(U, V, A), 0) & (~$lesseq($sum(U, $product(-1, tptp_fun_J_1(U, V, A))), 0)) & (~($sum(tptp_fun_I_0(U, V, A), $product(-1, tptp_fun_J_1(U, V, A))) = 0)) & ($sum(V, $product(-1, tb2t(get2(int, t2tb1(A), tptp_fun_J_1(U, V, A))))) = 0))) & (appear_twice1(A, V, U) | ![I: $int] : ((~$greatereq(I, 0)) | $lesseq($sum(U, $product(-1, I)), 0) | (~($sum(V, $product(-1, tb2t(get2(int, t2tb1(A), I)))) = 0)) | ![J: $int] : (~($greatereq(J, 0) & (~$lesseq($sum(U, $product(-1, J)), 0)) & (~($sum(I, $product(-1, J)) = 0)) & ($sum(V, $product(-1, tb2t(get2(int, t2tb1(A), J)))) = 0))))))),
% 0.22/0.45 inference(quant_intro,[status(thm)],[8])).
% 0.22/0.45 tff(10,plain,
% 0.22/0.45 (^[A: array_int, V: $int, U: $int] : rewrite((appear_twice1(A, V, U) <=> ?[I: $int] : ($greatereq(I, 0) & (~$lesseq($sum(U, $product(-1, I)), 0)) & ($sum(tb2t(get2(int, t2tb1(A), I)), $product(-1, V)) = 0) & ?[J: $int] : ($greatereq(J, 0) & (~$lesseq($sum(U, $product(-1, J)), 0)) & (~($sum(J, $product(-1, I)) = 0)) & ($sum(tb2t(get2(int, t2tb1(A), J)), $product(-1, V)) = 0)))) <=> (appear_twice1(A, V, U) <=> ?[I: $int] : ($greatereq(I, 0) & (~$lesseq($sum(U, $product(-1, I)), 0)) & ($sum(V, $product(-1, tb2t(get2(int, t2tb1(A), I)))) = 0) & ?[J: $int] : ($greatereq(J, 0) & (~$lesseq($sum(U, $product(-1, J)), 0)) & (~($sum(I, $product(-1, J)) = 0)) & ($sum(V, $product(-1, tb2t(get2(int, t2tb1(A), J)))) = 0)))))),
% 0.22/0.45 inference(bind,[status(th)],[])).
% 0.22/0.45 tff(11,plain,
% 0.22/0.45 (![A: array_int, V: $int, U: $int] : (appear_twice1(A, V, U) <=> ?[I: $int] : ($greatereq(I, 0) & (~$lesseq($sum(U, $product(-1, I)), 0)) & ($sum(tb2t(get2(int, t2tb1(A), I)), $product(-1, V)) = 0) & ?[J: $int] : ($greatereq(J, 0) & (~$lesseq($sum(U, $product(-1, J)), 0)) & (~($sum(J, $product(-1, I)) = 0)) & ($sum(tb2t(get2(int, t2tb1(A), J)), $product(-1, V)) = 0)))) <=> ![A: array_int, V: $int, U: $int] : (appear_twice1(A, V, U) <=> ?[I: $int] : ($greatereq(I, 0) & (~$lesseq($sum(U, $product(-1, I)), 0)) & ($sum(V, $product(-1, tb2t(get2(int, t2tb1(A), I)))) = 0) & ?[J: $int] : ($greatereq(J, 0) & (~$lesseq($sum(U, $product(-1, J)), 0)) & (~($sum(I, $product(-1, J)) = 0)) & ($sum(V, $product(-1, tb2t(get2(int, t2tb1(A), J)))) = 0))))),
% 0.22/0.45 inference(quant_intro,[status(thm)],[10])).
% 0.22/0.45 tff(12,plain,
% 0.22/0.45 (^[A: array_int, V: $int, U: $int] : rewrite((appear_twice1(A, V, U) <=> ?[I: $int] : ($lesseq(0, I) & (~$lesseq(U, I)) & (tb2t(get2(int, t2tb1(A), I)) = V) & ?[J: $int] : ($lesseq(0, J) & (~$lesseq(U, J)) & (~(J = I)) & (tb2t(get2(int, t2tb1(A), J)) = V)))) <=> (appear_twice1(A, V, U) <=> ?[I: $int] : ($greatereq(I, 0) & (~$lesseq($sum(U, $product(-1, I)), 0)) & ($sum(tb2t(get2(int, t2tb1(A), I)), $product(-1, V)) = 0) & ?[J: $int] : ($greatereq(J, 0) & (~$lesseq($sum(U, $product(-1, J)), 0)) & (~($sum(J, $product(-1, I)) = 0)) & ($sum(tb2t(get2(int, t2tb1(A), J)), $product(-1, V)) = 0)))))),
% 0.22/0.45 inference(bind,[status(th)],[])).
% 0.22/0.45 tff(13,plain,
% 0.22/0.45 (![A: array_int, V: $int, U: $int] : (appear_twice1(A, V, U) <=> ?[I: $int] : ($lesseq(0, I) & (~$lesseq(U, I)) & (tb2t(get2(int, t2tb1(A), I)) = V) & ?[J: $int] : ($lesseq(0, J) & (~$lesseq(U, J)) & (~(J = I)) & (tb2t(get2(int, t2tb1(A), J)) = V)))) <=> ![A: array_int, V: $int, U: $int] : (appear_twice1(A, V, U) <=> ?[I: $int] : ($greatereq(I, 0) & (~$lesseq($sum(U, $product(-1, I)), 0)) & ($sum(tb2t(get2(int, t2tb1(A), I)), $product(-1, V)) = 0) & ?[J: $int] : ($greatereq(J, 0) & (~$lesseq($sum(U, $product(-1, J)), 0)) & (~($sum(J, $product(-1, I)) = 0)) & ($sum(tb2t(get2(int, t2tb1(A), J)), $product(-1, V)) = 0))))),
% 0.22/0.45 inference(quant_intro,[status(thm)],[12])).
% 0.22/0.45 tff(14,plain,
% 0.22/0.45 (![A: array_int, V: $int, U: $int] : (appear_twice1(A, V, U) <=> ?[I: $int] : ($lesseq(0, I) & (~$lesseq(U, I)) & (tb2t(get2(int, t2tb1(A), I)) = V) & ?[J: $int] : ($lesseq(0, J) & (~$lesseq(U, J)) & (~(J = I)) & (tb2t(get2(int, t2tb1(A), J)) = V)))) <=> ![A: array_int, V: $int, U: $int] : (appear_twice1(A, V, U) <=> ?[I: $int] : ($lesseq(0, I) & (~$lesseq(U, I)) & (tb2t(get2(int, t2tb1(A), I)) = V) & ?[J: $int] : ($lesseq(0, J) & (~$lesseq(U, J)) & (~(J = I)) & (tb2t(get2(int, t2tb1(A), J)) = V))))),
% 0.22/0.45 inference(rewrite,[status(thm)],[])).
% 0.22/0.45 tff(15,plain,
% 0.22/0.45 (^[A: array_int, V: $int, U: $int] : rewrite((appear_twice1(A, V, U) <=> ?[I: $int] : ((($lesseq(0, I) & $less(I, U)) & (tb2t(get2(int, t2tb1(A), I)) = V)) & ?[J: $int] : ((($lesseq(0, J) & $less(J, U)) & (~(J = I))) & (tb2t(get2(int, t2tb1(A), J)) = V)))) <=> (appear_twice1(A, V, U) <=> ?[I: $int] : ($lesseq(0, I) & (~$lesseq(U, I)) & (tb2t(get2(int, t2tb1(A), I)) = V) & ?[J: $int] : ($lesseq(0, J) & (~$lesseq(U, J)) & (~(J = I)) & (tb2t(get2(int, t2tb1(A), J)) = V)))))),
% 0.22/0.45 inference(bind,[status(th)],[])).
% 0.22/0.45 tff(16,plain,
% 0.22/0.45 (![A: array_int, V: $int, U: $int] : (appear_twice1(A, V, U) <=> ?[I: $int] : ((($lesseq(0, I) & $less(I, U)) & (tb2t(get2(int, t2tb1(A), I)) = V)) & ?[J: $int] : ((($lesseq(0, J) & $less(J, U)) & (~(J = I))) & (tb2t(get2(int, t2tb1(A), J)) = V)))) <=> ![A: array_int, V: $int, U: $int] : (appear_twice1(A, V, U) <=> ?[I: $int] : ($lesseq(0, I) & (~$lesseq(U, I)) & (tb2t(get2(int, t2tb1(A), I)) = V) & ?[J: $int] : ($lesseq(0, J) & (~$lesseq(U, J)) & (~(J = I)) & (tb2t(get2(int, t2tb1(A), J)) = V))))),
% 0.22/0.45 inference(quant_intro,[status(thm)],[15])).
% 0.22/0.45 tff(17,axiom,(![A: array_int, V: $int, U: $int] : (appear_twice1(A, V, U) <=> ?[I: $int] : ((($lesseq(0, I) & $less(I, U)) & (tb2t(get2(int, t2tb1(A), I)) = V)) & ?[J: $int] : ((($lesseq(0, J) & $less(J, U)) & (~(J = I))) & (tb2t(get2(int, t2tb1(A), J)) = V))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','appear_twice_def')).
% 0.22/0.45 tff(18,plain,
% 0.22/0.45 (![A: array_int, V: $int, U: $int] : (appear_twice1(A, V, U) <=> ?[I: $int] : ($lesseq(0, I) & (~$lesseq(U, I)) & (tb2t(get2(int, t2tb1(A), I)) = V) & ?[J: $int] : ($lesseq(0, J) & (~$lesseq(U, J)) & (~(J = I)) & (tb2t(get2(int, t2tb1(A), J)) = V))))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.22/0.45 tff(19,plain,
% 0.22/0.45 (![A: array_int, V: $int, U: $int] : (appear_twice1(A, V, U) <=> ?[I: $int] : ($lesseq(0, I) & (~$lesseq(U, I)) & (tb2t(get2(int, t2tb1(A), I)) = V) & ?[J: $int] : ($lesseq(0, J) & (~$lesseq(U, J)) & (~(J = I)) & (tb2t(get2(int, t2tb1(A), J)) = V))))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.22/0.45 tff(20,plain,
% 0.22/0.45 (![A: array_int, V: $int, U: $int] : (appear_twice1(A, V, U) <=> ?[I: $int] : ($greatereq(I, 0) & (~$lesseq($sum(U, $product(-1, I)), 0)) & ($sum(tb2t(get2(int, t2tb1(A), I)), $product(-1, V)) = 0) & ?[J: $int] : ($greatereq(J, 0) & (~$lesseq($sum(U, $product(-1, J)), 0)) & (~($sum(J, $product(-1, I)) = 0)) & ($sum(tb2t(get2(int, t2tb1(A), J)), $product(-1, V)) = 0))))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[19, 13])).
% 0.22/0.45 tff(21,plain,
% 0.22/0.45 (![A: array_int, V: $int, U: $int] : (appear_twice1(A, V, U) <=> ?[I: $int] : ($greatereq(I, 0) & (~$lesseq($sum(U, $product(-1, I)), 0)) & ($sum(V, $product(-1, tb2t(get2(int, t2tb1(A), I)))) = 0) & ?[J: $int] : ($greatereq(J, 0) & (~$lesseq($sum(U, $product(-1, J)), 0)) & (~($sum(I, $product(-1, J)) = 0)) & ($sum(V, $product(-1, tb2t(get2(int, t2tb1(A), J)))) = 0))))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[20, 11])).
% 0.22/0.45 tff(22,plain,(
% 0.22/0.45 ![A: array_int, V: $int, U: $int] : (((~appear_twice1(A, V, U)) | ($greatereq(tptp_fun_I_0(U, V, A), 0) & (~$lesseq($sum(U, $product(-1, tptp_fun_I_0(U, V, A))), 0)) & ($sum(V, $product(-1, tb2t(get2(int, t2tb1(A), tptp_fun_I_0(U, V, A))))) = 0) & ($greatereq(tptp_fun_J_1(U, V, A), 0) & (~$lesseq($sum(U, $product(-1, tptp_fun_J_1(U, V, A))), 0)) & (~($sum(tptp_fun_I_0(U, V, A), $product(-1, tptp_fun_J_1(U, V, A))) = 0)) & ($sum(V, $product(-1, tb2t(get2(int, t2tb1(A), tptp_fun_J_1(U, V, A))))) = 0)))) & (appear_twice1(A, V, U) | ![I: $int] : ((~$greatereq(I, 0)) | (~(~$lesseq($sum(U, $product(-1, I)), 0))) | (~($sum(V, $product(-1, tb2t(get2(int, t2tb1(A), I)))) = 0)) | ![J: $int] : (~($greatereq(J, 0) & (~$lesseq($sum(U, $product(-1, J)), 0)) & (~($sum(I, $product(-1, J)) = 0)) & ($sum(V, $product(-1, tb2t(get2(int, t2tb1(A), J)))) = 0))))))),
% 0.22/0.45 inference(skolemize,[status(sab)],[21])).
% 0.22/0.45 tff(23,plain,
% 0.22/0.45 (![A: array_int, V: $int, U: $int] : (((~appear_twice1(A, V, U)) | ($greatereq(tptp_fun_I_0(U, V, A), 0) & (~$lesseq($sum(U, $product(-1, tptp_fun_I_0(U, V, A))), 0)) & ($sum(V, $product(-1, tb2t(get2(int, t2tb1(A), tptp_fun_I_0(U, V, A))))) = 0) & $greatereq(tptp_fun_J_1(U, V, A), 0) & (~$lesseq($sum(U, $product(-1, tptp_fun_J_1(U, V, A))), 0)) & (~($sum(tptp_fun_I_0(U, V, A), $product(-1, tptp_fun_J_1(U, V, A))) = 0)) & ($sum(V, $product(-1, tb2t(get2(int, t2tb1(A), tptp_fun_J_1(U, V, A))))) = 0))) & (appear_twice1(A, V, U) | ![I: $int] : ((~$greatereq(I, 0)) | $lesseq($sum(U, $product(-1, I)), 0) | (~($sum(V, $product(-1, tb2t(get2(int, t2tb1(A), I)))) = 0)) | ![J: $int] : (~($greatereq(J, 0) & (~$lesseq($sum(U, $product(-1, J)), 0)) & (~($sum(I, $product(-1, J)) = 0)) & ($sum(V, $product(-1, tb2t(get2(int, t2tb1(A), J)))) = 0))))))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[22, 9])).
% 0.22/0.45 tff(24,plain,
% 0.22/0.45 (![A: array_int, V: $int, U: $int] : (~((~((~appear_twice1(A, V, U)) | (~($lesseq($sum(U, $product(-1, tptp_fun_I_0(U, V, A))), 0) | $lesseq($sum(U, $product(-1, tptp_fun_J_1(U, V, A))), 0) | ($sum(tptp_fun_I_0(U, V, A), $product(-1, tptp_fun_J_1(U, V, A))) = 0) | (~$greatereq(tptp_fun_I_0(U, V, A), 0)) | (~($sum(V, $product(-1, tb2t(get2(int, t2tb1(A), tptp_fun_I_0(U, V, A))))) = 0)) | (~$greatereq(tptp_fun_J_1(U, V, A), 0)) | (~($sum(V, $product(-1, tb2t(get2(int, t2tb1(A), tptp_fun_J_1(U, V, A))))) = 0)))))) | (~(appear_twice1(A, V, U) | ![I: $int] : ((~$greatereq(I, 0)) | $lesseq($sum(U, $product(-1, I)), 0) | (~($sum(V, $product(-1, tb2t(get2(int, t2tb1(A), I)))) = 0)) | ![J: $int] : ((~$greatereq(J, 0)) | $lesseq($sum(U, $product(-1, J)), 0) | ($sum(I, $product(-1, J)) = 0) | (~($sum(V, $product(-1, tb2t(get2(int, t2tb1(A), J)))) = 0))))))))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[23, 7])).
% 0.22/0.45 tff(25,plain,
% 0.22/0.45 (![A: array_int, V: $int, U: $int] : (~((~((~appear_twice1(A, V, U)) | (~($lesseq($sum(U, $product(-1, tptp_fun_I_0(U, V, A))), 0) | $lesseq($sum(U, $product(-1, tptp_fun_J_1(U, V, A))), 0) | ($sum(tptp_fun_I_0(U, V, A), $product(-1, tptp_fun_J_1(U, V, A))) = 0) | (~$greatereq(tptp_fun_I_0(U, V, A), 0)) | (~($sum(V, $product(-1, tb2t(get2(int, t2tb1(A), tptp_fun_I_0(U, V, A))))) = 0)) | (~$greatereq(tptp_fun_J_1(U, V, A), 0)) | (~($sum(V, $product(-1, tb2t(get2(int, t2tb1(A), tptp_fun_J_1(U, V, A))))) = 0)))))) | (~(appear_twice1(A, V, U) | ![I: $int] : ((~$greatereq(I, 0)) | $lesseq($sum(U, $product(-1, I)), 0) | (~($sum(V, $product(-1, tb2t(get2(int, t2tb1(A), I)))) = 0)) | ![J: $int] : ((~$greatereq(J, 0)) | $lesseq($sum(U, $product(-1, J)), 0) | ($sum(I, $product(-1, J)) = 0) | (~($sum(V, $product(-1, tb2t(get2(int, t2tb1(A), J)))) = 0))))))))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[24, 5])).
% 0.22/0.45 tff(26,plain,
% 0.22/0.45 (((~![A: array_int, V: $int, U: $int] : (~((~((~appear_twice1(A, V, U)) | (~($lesseq($sum(U, $product(-1, tptp_fun_I_0(U, V, A))), 0) | $lesseq($sum(U, $product(-1, tptp_fun_J_1(U, V, A))), 0) | ($sum(tptp_fun_I_0(U, V, A), $product(-1, tptp_fun_J_1(U, V, A))) = 0) | (~$greatereq(tptp_fun_I_0(U, V, A), 0)) | (~($sum(V, $product(-1, tb2t(get2(int, t2tb1(A), tptp_fun_I_0(U, V, A))))) = 0)) | (~$greatereq(tptp_fun_J_1(U, V, A), 0)) | (~($sum(V, $product(-1, tb2t(get2(int, t2tb1(A), tptp_fun_J_1(U, V, A))))) = 0)))))) | (~(appear_twice1(A, V, U) | ![I: $int] : ((~$greatereq(I, 0)) | $lesseq($sum(U, $product(-1, I)), 0) | (~($sum(V, $product(-1, tb2t(get2(int, t2tb1(A), I)))) = 0)) | ![J: $int] : ((~$greatereq(J, 0)) | $lesseq($sum(U, $product(-1, J)), 0) | ($sum(I, $product(-1, J)) = 0) | (~($sum(V, $product(-1, tb2t(get2(int, t2tb1(A), J)))) = 0))))))))) | (~((~((~appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V2!6, $sum(2, N!2))) | (~(($sum(tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), $product(-1, tptp_fun_J_1($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))) = 0) | (~$greatereq(tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), 0)) | (~($sum(V2!6, $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))))) = 0)) | (~$greatereq(tptp_fun_J_1($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), 0)) | (~($sum(V2!6, $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), tptp_fun_J_1($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))))) = 0)) | $lesseq($sum(N!2, $product(-1, tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))), -2) | $lesseq($sum(N!2, $product(-1, tptp_fun_J_1($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))), -2))))) | (~(appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V2!6, $sum(2, N!2)) | ![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!2)), 2) | (~($sum(V2!6, $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), I)))) = 0)) | ![J: $int] : ((~$greatereq(J, 0)) | ($sum(I, $product(-1, J)) = 0) | $greatereq($sum(J, $product(-1, N!2)), 2) | (~($sum(V2!6, $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), J)))) = 0))))))))) <=> ((~![A: array_int, V: $int, U: $int] : (~((~((~appear_twice1(A, V, U)) | (~($lesseq($sum(U, $product(-1, tptp_fun_I_0(U, V, A))), 0) | $lesseq($sum(U, $product(-1, tptp_fun_J_1(U, V, A))), 0) | ($sum(tptp_fun_I_0(U, V, A), $product(-1, tptp_fun_J_1(U, V, A))) = 0) | (~$greatereq(tptp_fun_I_0(U, V, A), 0)) | (~($sum(V, $product(-1, tb2t(get2(int, t2tb1(A), tptp_fun_I_0(U, V, A))))) = 0)) | (~$greatereq(tptp_fun_J_1(U, V, A), 0)) | (~($sum(V, $product(-1, tb2t(get2(int, t2tb1(A), tptp_fun_J_1(U, V, A))))) = 0)))))) | (~(appear_twice1(A, V, U) | ![I: $int] : ((~$greatereq(I, 0)) | $lesseq($sum(U, $product(-1, I)), 0) | (~($sum(V, $product(-1, tb2t(get2(int, t2tb1(A), I)))) = 0)) | ![J: $int] : ((~$greatereq(J, 0)) | $lesseq($sum(U, $product(-1, J)), 0) | ($sum(I, $product(-1, J)) = 0) | (~($sum(V, $product(-1, tb2t(get2(int, t2tb1(A), J)))) = 0))))))))) | (~((~((~appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V2!6, $sum(2, N!2))) | (~(($sum(tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), $product(-1, tptp_fun_J_1($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))) = 0) | (~$greatereq(tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), 0)) | (~($sum(V2!6, $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))))) = 0)) | (~$greatereq(tptp_fun_J_1($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), 0)) | (~($sum(V2!6, $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), tptp_fun_J_1($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))))) = 0)) | $lesseq($sum(N!2, $product(-1, tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))), -2) | $lesseq($sum(N!2, $product(-1, tptp_fun_J_1($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))), -2))))) | (~(appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V2!6, $sum(2, N!2)) | ![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!2)), 2) | (~($sum(V2!6, $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), I)))) = 0)) | ![J: $int] : ((~$greatereq(J, 0)) | ($sum(I, $product(-1, J)) = 0) | $greatereq($sum(J, $product(-1, N!2)), 2) | (~($sum(V2!6, $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), J)))) = 0)))))))))),
% 0.22/0.46 inference(rewrite,[status(thm)],[])).
% 0.22/0.46 tff(27,plain,
% 0.22/0.46 ((~((~((~appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V2!6, $sum(2, N!2))) | (~($lesseq($sum($sum(2, N!2), $product(-1, tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))), 0) | $lesseq($sum($sum(2, N!2), $product(-1, tptp_fun_J_1($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))), 0) | ($sum(tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), $product(-1, tptp_fun_J_1($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))) = 0) | (~$greatereq(tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), 0)) | (~($sum(V2!6, $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))))) = 0)) | (~$greatereq(tptp_fun_J_1($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), 0)) | (~($sum(V2!6, $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), tptp_fun_J_1($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))))) = 0)))))) | (~(appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V2!6, $sum(2, N!2)) | ![I: $int] : ((~$greatereq(I, 0)) | $lesseq($sum($sum(2, N!2), $product(-1, I)), 0) | (~($sum(V2!6, $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), I)))) = 0)) | ![J: $int] : ((~$greatereq(J, 0)) | $lesseq($sum($sum(2, N!2), $product(-1, J)), 0) | ($sum(I, $product(-1, J)) = 0) | (~($sum(V2!6, $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), J)))) = 0)))))))) <=> (~((~((~appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V2!6, $sum(2, N!2))) | (~(($sum(tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), $product(-1, tptp_fun_J_1($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))) = 0) | (~$greatereq(tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), 0)) | (~($sum(V2!6, $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))))) = 0)) | (~$greatereq(tptp_fun_J_1($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), 0)) | (~($sum(V2!6, $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), tptp_fun_J_1($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))))) = 0)) | $lesseq($sum(N!2, $product(-1, tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))), -2) | $lesseq($sum(N!2, $product(-1, tptp_fun_J_1($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))), -2))))) | (~(appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V2!6, $sum(2, N!2)) | ![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!2)), 2) | (~($sum(V2!6, $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), I)))) = 0)) | ![J: $int] : ((~$greatereq(J, 0)) | ($sum(I, $product(-1, J)) = 0) | $greatereq($sum(J, $product(-1, N!2)), 2) | (~($sum(V2!6, $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), J)))) = 0))))))))),
% 0.22/0.46 inference(rewrite,[status(thm)],[])).
% 0.22/0.46 tff(28,plain,
% 0.22/0.46 (((~![A: array_int, V: $int, U: $int] : (~((~((~appear_twice1(A, V, U)) | (~($lesseq($sum(U, $product(-1, tptp_fun_I_0(U, V, A))), 0) | $lesseq($sum(U, $product(-1, tptp_fun_J_1(U, V, A))), 0) | ($sum(tptp_fun_I_0(U, V, A), $product(-1, tptp_fun_J_1(U, V, A))) = 0) | (~$greatereq(tptp_fun_I_0(U, V, A), 0)) | (~($sum(V, $product(-1, tb2t(get2(int, t2tb1(A), tptp_fun_I_0(U, V, A))))) = 0)) | (~$greatereq(tptp_fun_J_1(U, V, A), 0)) | (~($sum(V, $product(-1, tb2t(get2(int, t2tb1(A), tptp_fun_J_1(U, V, A))))) = 0)))))) | (~(appear_twice1(A, V, U) | ![I: $int] : ((~$greatereq(I, 0)) | $lesseq($sum(U, $product(-1, I)), 0) | (~($sum(V, $product(-1, tb2t(get2(int, t2tb1(A), I)))) = 0)) | ![J: $int] : ((~$greatereq(J, 0)) | $lesseq($sum(U, $product(-1, J)), 0) | ($sum(I, $product(-1, J)) = 0) | (~($sum(V, $product(-1, tb2t(get2(int, t2tb1(A), J)))) = 0))))))))) | (~((~((~appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V2!6, $sum(2, N!2))) | (~($lesseq($sum($sum(2, N!2), $product(-1, tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))), 0) | $lesseq($sum($sum(2, N!2), $product(-1, tptp_fun_J_1($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))), 0) | ($sum(tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), $product(-1, tptp_fun_J_1($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))) = 0) | (~$greatereq(tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), 0)) | (~($sum(V2!6, $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))))) = 0)) | (~$greatereq(tptp_fun_J_1($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), 0)) | (~($sum(V2!6, $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), tptp_fun_J_1($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))))) = 0)))))) | (~(appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V2!6, $sum(2, N!2)) | ![I: $int] : ((~$greatereq(I, 0)) | $lesseq($sum($sum(2, N!2), $product(-1, I)), 0) | (~($sum(V2!6, $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), I)))) = 0)) | ![J: $int] : ((~$greatereq(J, 0)) | $lesseq($sum($sum(2, N!2), $product(-1, J)), 0) | ($sum(I, $product(-1, J)) = 0) | (~($sum(V2!6, $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), J)))) = 0))))))))) <=> ((~![A: array_int, V: $int, U: $int] : (~((~((~appear_twice1(A, V, U)) | (~($lesseq($sum(U, $product(-1, tptp_fun_I_0(U, V, A))), 0) | $lesseq($sum(U, $product(-1, tptp_fun_J_1(U, V, A))), 0) | ($sum(tptp_fun_I_0(U, V, A), $product(-1, tptp_fun_J_1(U, V, A))) = 0) | (~$greatereq(tptp_fun_I_0(U, V, A), 0)) | (~($sum(V, $product(-1, tb2t(get2(int, t2tb1(A), tptp_fun_I_0(U, V, A))))) = 0)) | (~$greatereq(tptp_fun_J_1(U, V, A), 0)) | (~($sum(V, $product(-1, tb2t(get2(int, t2tb1(A), tptp_fun_J_1(U, V, A))))) = 0)))))) | (~(appear_twice1(A, V, U) | ![I: $int] : ((~$greatereq(I, 0)) | $lesseq($sum(U, $product(-1, I)), 0) | (~($sum(V, $product(-1, tb2t(get2(int, t2tb1(A), I)))) = 0)) | ![J: $int] : ((~$greatereq(J, 0)) | $lesseq($sum(U, $product(-1, J)), 0) | ($sum(I, $product(-1, J)) = 0) | (~($sum(V, $product(-1, tb2t(get2(int, t2tb1(A), J)))) = 0))))))))) | (~((~((~appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V2!6, $sum(2, N!2))) | (~(($sum(tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), $product(-1, tptp_fun_J_1($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))) = 0) | (~$greatereq(tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), 0)) | (~($sum(V2!6, $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))))) = 0)) | (~$greatereq(tptp_fun_J_1($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), 0)) | (~($sum(V2!6, $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), tptp_fun_J_1($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))))) = 0)) | $lesseq($sum(N!2, $product(-1, tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))), -2) | $lesseq($sum(N!2, $product(-1, tptp_fun_J_1($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))), -2))))) | (~(appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V2!6, $sum(2, N!2)) | ![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!2)), 2) | (~($sum(V2!6, $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), I)))) = 0)) | ![J: $int] : ((~$greatereq(J, 0)) | ($sum(I, $product(-1, J)) = 0) | $greatereq($sum(J, $product(-1, N!2)), 2) | (~($sum(V2!6, $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), J)))) = 0)))))))))),
% 0.22/0.47 inference(monotonicity,[status(thm)],[27])).
% 0.22/0.47 tff(29,plain,
% 0.22/0.47 (((~![A: array_int, V: $int, U: $int] : (~((~((~appear_twice1(A, V, U)) | (~($lesseq($sum(U, $product(-1, tptp_fun_I_0(U, V, A))), 0) | $lesseq($sum(U, $product(-1, tptp_fun_J_1(U, V, A))), 0) | ($sum(tptp_fun_I_0(U, V, A), $product(-1, tptp_fun_J_1(U, V, A))) = 0) | (~$greatereq(tptp_fun_I_0(U, V, A), 0)) | (~($sum(V, $product(-1, tb2t(get2(int, t2tb1(A), tptp_fun_I_0(U, V, A))))) = 0)) | (~$greatereq(tptp_fun_J_1(U, V, A), 0)) | (~($sum(V, $product(-1, tb2t(get2(int, t2tb1(A), tptp_fun_J_1(U, V, A))))) = 0)))))) | (~(appear_twice1(A, V, U) | ![I: $int] : ((~$greatereq(I, 0)) | $lesseq($sum(U, $product(-1, I)), 0) | (~($sum(V, $product(-1, tb2t(get2(int, t2tb1(A), I)))) = 0)) | ![J: $int] : ((~$greatereq(J, 0)) | $lesseq($sum(U, $product(-1, J)), 0) | ($sum(I, $product(-1, J)) = 0) | (~($sum(V, $product(-1, tb2t(get2(int, t2tb1(A), J)))) = 0))))))))) | (~((~((~appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V2!6, $sum(2, N!2))) | (~($lesseq($sum($sum(2, N!2), $product(-1, tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))), 0) | $lesseq($sum($sum(2, N!2), $product(-1, tptp_fun_J_1($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))), 0) | ($sum(tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), $product(-1, tptp_fun_J_1($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))) = 0) | (~$greatereq(tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), 0)) | (~($sum(V2!6, $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))))) = 0)) | (~$greatereq(tptp_fun_J_1($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), 0)) | (~($sum(V2!6, $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), tptp_fun_J_1($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))))) = 0)))))) | (~(appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V2!6, $sum(2, N!2)) | ![I: $int] : ((~$greatereq(I, 0)) | $lesseq($sum($sum(2, N!2), $product(-1, I)), 0) | (~($sum(V2!6, $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), I)))) = 0)) | ![J: $int] : ((~$greatereq(J, 0)) | $lesseq($sum($sum(2, N!2), $product(-1, J)), 0) | ($sum(I, $product(-1, J)) = 0) | (~($sum(V2!6, $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), J)))) = 0))))))))) <=> ((~![A: array_int, V: $int, U: $int] : (~((~((~appear_twice1(A, V, U)) | (~($lesseq($sum(U, $product(-1, tptp_fun_I_0(U, V, A))), 0) | $lesseq($sum(U, $product(-1, tptp_fun_J_1(U, V, A))), 0) | ($sum(tptp_fun_I_0(U, V, A), $product(-1, tptp_fun_J_1(U, V, A))) = 0) | (~$greatereq(tptp_fun_I_0(U, V, A), 0)) | (~($sum(V, $product(-1, tb2t(get2(int, t2tb1(A), tptp_fun_I_0(U, V, A))))) = 0)) | (~$greatereq(tptp_fun_J_1(U, V, A), 0)) | (~($sum(V, $product(-1, tb2t(get2(int, t2tb1(A), tptp_fun_J_1(U, V, A))))) = 0)))))) | (~(appear_twice1(A, V, U) | ![I: $int] : ((~$greatereq(I, 0)) | $lesseq($sum(U, $product(-1, I)), 0) | (~($sum(V, $product(-1, tb2t(get2(int, t2tb1(A), I)))) = 0)) | ![J: $int] : ((~$greatereq(J, 0)) | $lesseq($sum(U, $product(-1, J)), 0) | ($sum(I, $product(-1, J)) = 0) | (~($sum(V, $product(-1, tb2t(get2(int, t2tb1(A), J)))) = 0))))))))) | (~((~((~appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V2!6, $sum(2, N!2))) | (~(($sum(tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), $product(-1, tptp_fun_J_1($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))) = 0) | (~$greatereq(tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), 0)) | (~($sum(V2!6, $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))))) = 0)) | (~$greatereq(tptp_fun_J_1($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), 0)) | (~($sum(V2!6, $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), tptp_fun_J_1($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))))) = 0)) | $lesseq($sum(N!2, $product(-1, tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))), -2) | $lesseq($sum(N!2, $product(-1, tptp_fun_J_1($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))), -2))))) | (~(appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V2!6, $sum(2, N!2)) | ![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!2)), 2) | (~($sum(V2!6, $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), I)))) = 0)) | ![J: $int] : ((~$greatereq(J, 0)) | ($sum(I, $product(-1, J)) = 0) | $greatereq($sum(J, $product(-1, N!2)), 2) | (~($sum(V2!6, $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), J)))) = 0)))))))))),
% 0.22/0.47 inference(transitivity,[status(thm)],[28, 26])).
% 0.22/0.47 tff(30,plain,
% 0.22/0.47 ((~![A: array_int, V: $int, U: $int] : (~((~((~appear_twice1(A, V, U)) | (~($lesseq($sum(U, $product(-1, tptp_fun_I_0(U, V, A))), 0) | $lesseq($sum(U, $product(-1, tptp_fun_J_1(U, V, A))), 0) | ($sum(tptp_fun_I_0(U, V, A), $product(-1, tptp_fun_J_1(U, V, A))) = 0) | (~$greatereq(tptp_fun_I_0(U, V, A), 0)) | (~($sum(V, $product(-1, tb2t(get2(int, t2tb1(A), tptp_fun_I_0(U, V, A))))) = 0)) | (~$greatereq(tptp_fun_J_1(U, V, A), 0)) | (~($sum(V, $product(-1, tb2t(get2(int, t2tb1(A), tptp_fun_J_1(U, V, A))))) = 0)))))) | (~(appear_twice1(A, V, U) | ![I: $int] : ((~$greatereq(I, 0)) | $lesseq($sum(U, $product(-1, I)), 0) | (~($sum(V, $product(-1, tb2t(get2(int, t2tb1(A), I)))) = 0)) | ![J: $int] : ((~$greatereq(J, 0)) | $lesseq($sum(U, $product(-1, J)), 0) | ($sum(I, $product(-1, J)) = 0) | (~($sum(V, $product(-1, tb2t(get2(int, t2tb1(A), J)))) = 0))))))))) | (~((~((~appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V2!6, $sum(2, N!2))) | (~($lesseq($sum($sum(2, N!2), $product(-1, tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))), 0) | $lesseq($sum($sum(2, N!2), $product(-1, tptp_fun_J_1($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))), 0) | ($sum(tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), $product(-1, tptp_fun_J_1($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))) = 0) | (~$greatereq(tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), 0)) | (~($sum(V2!6, $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))))) = 0)) | (~$greatereq(tptp_fun_J_1($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), 0)) | (~($sum(V2!6, $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), tptp_fun_J_1($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))))) = 0)))))) | (~(appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V2!6, $sum(2, N!2)) | ![I: $int] : ((~$greatereq(I, 0)) | $lesseq($sum($sum(2, N!2), $product(-1, I)), 0) | (~($sum(V2!6, $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), I)))) = 0)) | ![J: $int] : ((~$greatereq(J, 0)) | $lesseq($sum($sum(2, N!2), $product(-1, J)), 0) | ($sum(I, $product(-1, J)) = 0) | (~($sum(V2!6, $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), J)))) = 0))))))))),
% 0.22/0.47 inference(quant_inst,[status(thm)],[])).
% 0.22/0.47 tff(31,plain,
% 0.22/0.47 ((~![A: array_int, V: $int, U: $int] : (~((~((~appear_twice1(A, V, U)) | (~($lesseq($sum(U, $product(-1, tptp_fun_I_0(U, V, A))), 0) | $lesseq($sum(U, $product(-1, tptp_fun_J_1(U, V, A))), 0) | ($sum(tptp_fun_I_0(U, V, A), $product(-1, tptp_fun_J_1(U, V, A))) = 0) | (~$greatereq(tptp_fun_I_0(U, V, A), 0)) | (~($sum(V, $product(-1, tb2t(get2(int, t2tb1(A), tptp_fun_I_0(U, V, A))))) = 0)) | (~$greatereq(tptp_fun_J_1(U, V, A), 0)) | (~($sum(V, $product(-1, tb2t(get2(int, t2tb1(A), tptp_fun_J_1(U, V, A))))) = 0)))))) | (~(appear_twice1(A, V, U) | ![I: $int] : ((~$greatereq(I, 0)) | $lesseq($sum(U, $product(-1, I)), 0) | (~($sum(V, $product(-1, tb2t(get2(int, t2tb1(A), I)))) = 0)) | ![J: $int] : ((~$greatereq(J, 0)) | $lesseq($sum(U, $product(-1, J)), 0) | ($sum(I, $product(-1, J)) = 0) | (~($sum(V, $product(-1, tb2t(get2(int, t2tb1(A), J)))) = 0))))))))) | (~((~((~appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V2!6, $sum(2, N!2))) | (~(($sum(tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), $product(-1, tptp_fun_J_1($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))) = 0) | (~$greatereq(tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), 0)) | (~($sum(V2!6, $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))))) = 0)) | (~$greatereq(tptp_fun_J_1($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), 0)) | (~($sum(V2!6, $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), tptp_fun_J_1($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))))) = 0)) | $lesseq($sum(N!2, $product(-1, tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))), -2) | $lesseq($sum(N!2, $product(-1, tptp_fun_J_1($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))), -2))))) | (~(appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V2!6, $sum(2, N!2)) | ![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!2)), 2) | (~($sum(V2!6, $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), I)))) = 0)) | ![J: $int] : ((~$greatereq(J, 0)) | ($sum(I, $product(-1, J)) = 0) | $greatereq($sum(J, $product(-1, N!2)), 2) | (~($sum(V2!6, $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), J)))) = 0))))))))),
% 0.22/0.47 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.22/0.47 tff(32,plain,
% 0.22/0.47 (~((~((~appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V2!6, $sum(2, N!2))) | (~(($sum(tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), $product(-1, tptp_fun_J_1($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))) = 0) | (~$greatereq(tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), 0)) | (~($sum(V2!6, $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))))) = 0)) | (~$greatereq(tptp_fun_J_1($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), 0)) | (~($sum(V2!6, $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), tptp_fun_J_1($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))))) = 0)) | $lesseq($sum(N!2, $product(-1, tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))), -2) | $lesseq($sum(N!2, $product(-1, tptp_fun_J_1($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))), -2))))) | (~(appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V2!6, $sum(2, N!2)) | ![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!2)), 2) | (~($sum(V2!6, $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), I)))) = 0)) | ![J: $int] : ((~$greatereq(J, 0)) | ($sum(I, $product(-1, J)) = 0) | $greatereq($sum(J, $product(-1, N!2)), 2) | (~($sum(V2!6, $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), J)))) = 0)))))))),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[31, 25])).
% 0.22/0.47 tff(33,plain,
% 0.22/0.47 (((~((~appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V2!6, $sum(2, N!2))) | (~(($sum(tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), $product(-1, tptp_fun_J_1($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))) = 0) | (~$greatereq(tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), 0)) | (~($sum(V2!6, $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))))) = 0)) | (~$greatereq(tptp_fun_J_1($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), 0)) | (~($sum(V2!6, $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), tptp_fun_J_1($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))))) = 0)) | $lesseq($sum(N!2, $product(-1, tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))), -2) | $lesseq($sum(N!2, $product(-1, tptp_fun_J_1($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))), -2))))) | (~(appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V2!6, $sum(2, N!2)) | ![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!2)), 2) | (~($sum(V2!6, $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), I)))) = 0)) | ![J: $int] : ((~$greatereq(J, 0)) | ($sum(I, $product(-1, J)) = 0) | $greatereq($sum(J, $product(-1, N!2)), 2) | (~($sum(V2!6, $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), J)))) = 0))))))) | ((~appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V2!6, $sum(2, N!2))) | (~(($sum(tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), $product(-1, tptp_fun_J_1($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))) = 0) | (~$greatereq(tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), 0)) | (~($sum(V2!6, $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))))) = 0)) | (~$greatereq(tptp_fun_J_1($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), 0)) | (~($sum(V2!6, $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), tptp_fun_J_1($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))))) = 0)) | $lesseq($sum(N!2, $product(-1, tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))), -2) | $lesseq($sum(N!2, $product(-1, tptp_fun_J_1($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))), -2))))),
% 0.22/0.48 inference(tautology,[status(thm)],[])).
% 0.22/0.48 tff(34,plain,
% 0.22/0.48 ((~appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V2!6, $sum(2, N!2))) | (~(($sum(tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), $product(-1, tptp_fun_J_1($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))) = 0) | (~$greatereq(tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), 0)) | (~($sum(V2!6, $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))))) = 0)) | (~$greatereq(tptp_fun_J_1($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), 0)) | (~($sum(V2!6, $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), tptp_fun_J_1($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))))) = 0)) | $lesseq($sum(N!2, $product(-1, tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))), -2) | $lesseq($sum(N!2, $product(-1, tptp_fun_J_1($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))), -2)))),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[33, 32])).
% 0.22/0.48 tff(35,plain,
% 0.22/0.48 (($greatereq(N!2, 0) & $greatereq(N!2, -1) & ($greatereq(A!4, 0) & ($sum(N!2, $product(-1, A!4)) = -2) & $greatereq(N!2, 2) & ![I: $int] : ((~($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, A!4)), 0)))) | ($greatereq(tb2t(get(int, int, t2tb2(A1!3), t2tb(I))), 0) & (~$lesseq($sum(N!2, $product(-1, tb2t(get(int, int, t2tb2(A1!3), t2tb(I))))), 0)))) & appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V1!5, $sum(2, N!2)) & appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V2!6, $sum(2, N!2)) & (~($sum(V1!5, $product(-1, V2!6)) = 0))) & (((~(V1!8 = -1)) | (V2!9 = -1)) & ((V1!8 = -1) | appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V1!8, $sum(2, N!2))) & ((V2!9 = -1) | (appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V2!9, $sum(2, N!2)) & (~($sum(V1!8, $product(-1, V2!9)) = 0)))) & ![V: $int] : ((~($greatereq(V, 0) & (~$greatereq($sum(V, $product(-1, N!2)), 0)))) | ((~(tb2t3(get(bool, int, t2tb4(Deja_vu!7), t2tb(V))) = true1)) & ![J: $int] : ((~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, N!2)), 2)))) | (~($sum(V, $product(-1, tb2t(get(int, int, t2tb2(A1!3), t2tb(J))))) = 0)))) | ((tb2t3(get(bool, int, t2tb4(Deja_vu!7), t2tb(V))) = true1) & $greatereq(tptp_fun_J_10(V), 0) & (~$lesseq($sum(N!2, $product(-1, tptp_fun_J_10(V))), -2)) & ($sum(V, $product(-1, tb2t(get(int, int, t2tb2(A1!3), t2tb(tptp_fun_J_10(V)))))) = 0))) & ((~(V1!8 = -1)) | ![V: $int] : ((~appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V, $sum(2, N!2))) | (~($greatereq(V, 0) & (~$greatereq($sum(V, $product(-1, N!2)), 0)))))) & ((~(V2!9 = -1)) | ![V: $int] : ((~appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V, $sum(2, N!2))) | (~($greatereq(V, 0) & (~$greatereq($sum(V, $product(-1, N!2)), 0)))) | ($sum(V, $product(-1, V1!8)) = 0))) & (~appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V1!8, $sum(2, N!2))))) <=> ($greatereq(N!2, 0) & $greatereq(N!2, -1) & $greatereq(A!4, 0) & ($sum(N!2, $product(-1, A!4)) = -2) & $greatereq(N!2, 2) & ![I: $int] : ((~($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, A!4)), 0)))) | ($greatereq(tb2t(get(int, int, t2tb2(A1!3), t2tb(I))), 0) & (~$lesseq($sum(N!2, $product(-1, tb2t(get(int, int, t2tb2(A1!3), t2tb(I))))), 0)))) & appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V1!5, $sum(2, N!2)) & appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V2!6, $sum(2, N!2)) & (~($sum(V1!5, $product(-1, V2!6)) = 0)) & ((~(V1!8 = -1)) | (V2!9 = -1)) & ((V1!8 = -1) | appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V1!8, $sum(2, N!2))) & ((V2!9 = -1) | (appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V2!9, $sum(2, N!2)) & (~($sum(V1!8, $product(-1, V2!9)) = 0)))) & ![V: $int] : ((~($greatereq(V, 0) & (~$greatereq($sum(V, $product(-1, N!2)), 0)))) | ((~(tb2t3(get(bool, int, t2tb4(Deja_vu!7), t2tb(V))) = true1)) & ![J: $int] : ((~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, N!2)), 2)))) | (~($sum(V, $product(-1, tb2t(get(int, int, t2tb2(A1!3), t2tb(J))))) = 0)))) | ((tb2t3(get(bool, int, t2tb4(Deja_vu!7), t2tb(V))) = true1) & $greatereq(tptp_fun_J_10(V), 0) & (~$lesseq($sum(N!2, $product(-1, tptp_fun_J_10(V))), -2)) & ($sum(V, $product(-1, tb2t(get(int, int, t2tb2(A1!3), t2tb(tptp_fun_J_10(V)))))) = 0))) & ((~(V1!8 = -1)) | ![V: $int] : ((~appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V, $sum(2, N!2))) | (~($greatereq(V, 0) & (~$greatereq($sum(V, $product(-1, N!2)), 0)))))) & ((~(V2!9 = -1)) | ![V: $int] : ((~appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V, $sum(2, N!2))) | (~($greatereq(V, 0) & (~$greatereq($sum(V, $product(-1, N!2)), 0)))) | ($sum(V, $product(-1, V1!8)) = 0))) & (~appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V1!8, $sum(2, N!2))))),
% 0.22/0.48 inference(rewrite,[status(thm)],[])).
% 0.22/0.48 tff(36,plain,
% 0.22/0.48 (((((~(V1!8 = -1)) | (V2!9 = -1)) & ((V1!8 = -1) | appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V1!8, $sum(2, N!2))) & ((V2!9 = -1) | (appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V2!9, $sum(2, N!2)) & (~($sum(V1!8, $product(-1, V2!9)) = 0)))) & ![V: $int] : ((~($greatereq(V, 0) & (~$greatereq($sum(V, $product(-1, N!2)), 0)))) | ((~(tb2t3(get(bool, int, t2tb4(Deja_vu!7), t2tb(V))) = true1)) & ![J: $int] : ((~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, N!2)), 2)))) | (~($sum(V, $product(-1, tb2t(get(int, int, t2tb2(A1!3), t2tb(J))))) = 0)))) | ((tb2t3(get(bool, int, t2tb4(Deja_vu!7), t2tb(V))) = true1) & $greatereq(tptp_fun_J_10(V), 0) & (~$lesseq($sum(N!2, $product(-1, tptp_fun_J_10(V))), -2)) & ($sum(V, $product(-1, tb2t(get(int, int, t2tb2(A1!3), t2tb(tptp_fun_J_10(V)))))) = 0))) & ((~(V1!8 = -1)) | ![V: $int] : ((~appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V, $sum(2, N!2))) | (~($greatereq(V, 0) & (~$greatereq($sum(V, $product(-1, N!2)), 0)))))) & ((~(V2!9 = -1)) | ![V: $int] : ((~appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V, $sum(2, N!2))) | (~($greatereq(V, 0) & (~$greatereq($sum(V, $product(-1, N!2)), 0)))) | ($sum(V, $product(-1, V1!8)) = 0)))) & (~appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V1!8, $sum(2, N!2)))) <=> (((~(V1!8 = -1)) | (V2!9 = -1)) & ((V1!8 = -1) | appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V1!8, $sum(2, N!2))) & ((V2!9 = -1) | (appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V2!9, $sum(2, N!2)) & (~($sum(V1!8, $product(-1, V2!9)) = 0)))) & ![V: $int] : ((~($greatereq(V, 0) & (~$greatereq($sum(V, $product(-1, N!2)), 0)))) | ((~(tb2t3(get(bool, int, t2tb4(Deja_vu!7), t2tb(V))) = true1)) & ![J: $int] : ((~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, N!2)), 2)))) | (~($sum(V, $product(-1, tb2t(get(int, int, t2tb2(A1!3), t2tb(J))))) = 0)))) | ((tb2t3(get(bool, int, t2tb4(Deja_vu!7), t2tb(V))) = true1) & $greatereq(tptp_fun_J_10(V), 0) & (~$lesseq($sum(N!2, $product(-1, tptp_fun_J_10(V))), -2)) & ($sum(V, $product(-1, tb2t(get(int, int, t2tb2(A1!3), t2tb(tptp_fun_J_10(V)))))) = 0))) & ((~(V1!8 = -1)) | ![V: $int] : ((~appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V, $sum(2, N!2))) | (~($greatereq(V, 0) & (~$greatereq($sum(V, $product(-1, N!2)), 0)))))) & ((~(V2!9 = -1)) | ![V: $int] : ((~appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V, $sum(2, N!2))) | (~($greatereq(V, 0) & (~$greatereq($sum(V, $product(-1, N!2)), 0)))) | ($sum(V, $product(-1, V1!8)) = 0))) & (~appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V1!8, $sum(2, N!2))))),
% 0.22/0.48 inference(rewrite,[status(thm)],[])).
% 0.22/0.48 tff(37,plain,
% 0.22/0.48 ((((~(V1!8 = -1)) | (V2!9 = -1)) & ((V1!8 = -1) | appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V1!8, $sum(2, N!2))) & ((V2!9 = -1) | (appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V2!9, $sum(2, N!2)) & (~($sum(V2!9, $product(-1, V1!8)) = 0)))) & ![V: $int] : ((~($greatereq(V, 0) & (~$greatereq($sum(V, $product(-1, N!2)), 0)))) | ((tb2t3(get(bool, int, t2tb4(Deja_vu!7), t2tb(V))) = true1) & ($greatereq(tptp_fun_J_10(V), 0) & (~$greatereq($sum(tptp_fun_J_10(V), $product(-1, N!2)), 2)) & ($sum(V, $product(-1, tb2t(get(int, int, t2tb2(A1!3), t2tb(tptp_fun_J_10(V)))))) = 0))) | ((~(tb2t3(get(bool, int, t2tb4(Deja_vu!7), t2tb(V))) = true1)) & ![J: $int] : ((~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, N!2)), 2)))) | (~($sum(V, $product(-1, tb2t(get(int, int, t2tb2(A1!3), t2tb(J))))) = 0))))) & ((~(V1!8 = -1)) | ![V: $int] : ((~appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V, $sum(2, N!2))) | (~($greatereq(V, 0) & (~$greatereq($sum(V, $product(-1, N!2)), 0)))))) & ((~(V2!9 = -1)) | ![V: $int] : ((~appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V, $sum(2, N!2))) | (~($greatereq(V, 0) & (~$greatereq($sum(V, $product(-1, N!2)), 0)))) | ($sum(V1!8, $product(-1, V)) = 0)))) <=> (((~(V1!8 = -1)) | (V2!9 = -1)) & ((V1!8 = -1) | appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V1!8, $sum(2, N!2))) & ((V2!9 = -1) | (appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V2!9, $sum(2, N!2)) & (~($sum(V1!8, $product(-1, V2!9)) = 0)))) & ![V: $int] : ((~($greatereq(V, 0) & (~$greatereq($sum(V, $product(-1, N!2)), 0)))) | ((~(tb2t3(get(bool, int, t2tb4(Deja_vu!7), t2tb(V))) = true1)) & ![J: $int] : ((~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, N!2)), 2)))) | (~($sum(V, $product(-1, tb2t(get(int, int, t2tb2(A1!3), t2tb(J))))) = 0)))) | ((tb2t3(get(bool, int, t2tb4(Deja_vu!7), t2tb(V))) = true1) & $greatereq(tptp_fun_J_10(V), 0) & (~$lesseq($sum(N!2, $product(-1, tptp_fun_J_10(V))), -2)) & ($sum(V, $product(-1, tb2t(get(int, int, t2tb2(A1!3), t2tb(tptp_fun_J_10(V)))))) = 0))) & ((~(V1!8 = -1)) | ![V: $int] : ((~appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V, $sum(2, N!2))) | (~($greatereq(V, 0) & (~$greatereq($sum(V, $product(-1, N!2)), 0)))))) & ((~(V2!9 = -1)) | ![V: $int] : ((~appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V, $sum(2, N!2))) | (~($greatereq(V, 0) & (~$greatereq($sum(V, $product(-1, N!2)), 0)))) | ($sum(V, $product(-1, V1!8)) = 0))))),
% 0.22/0.48 inference(rewrite,[status(thm)],[])).
% 0.22/0.48 tff(38,plain,
% 0.22/0.48 (((((~(V1!8 = -1)) | (V2!9 = -1)) & ((V1!8 = -1) | appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V1!8, $sum(2, N!2))) & ((V2!9 = -1) | (appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V2!9, $sum(2, N!2)) & (~($sum(V2!9, $product(-1, V1!8)) = 0)))) & ![V: $int] : ((~($greatereq(V, 0) & (~$greatereq($sum(V, $product(-1, N!2)), 0)))) | ((tb2t3(get(bool, int, t2tb4(Deja_vu!7), t2tb(V))) = true1) & ($greatereq(tptp_fun_J_10(V), 0) & (~$greatereq($sum(tptp_fun_J_10(V), $product(-1, N!2)), 2)) & ($sum(V, $product(-1, tb2t(get(int, int, t2tb2(A1!3), t2tb(tptp_fun_J_10(V)))))) = 0))) | ((~(tb2t3(get(bool, int, t2tb4(Deja_vu!7), t2tb(V))) = true1)) & ![J: $int] : ((~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, N!2)), 2)))) | (~($sum(V, $product(-1, tb2t(get(int, int, t2tb2(A1!3), t2tb(J))))) = 0))))) & ((~(V1!8 = -1)) | ![V: $int] : ((~appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V, $sum(2, N!2))) | (~($greatereq(V, 0) & (~$greatereq($sum(V, $product(-1, N!2)), 0)))))) & ((~(V2!9 = -1)) | ![V: $int] : ((~appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V, $sum(2, N!2))) | (~($greatereq(V, 0) & (~$greatereq($sum(V, $product(-1, N!2)), 0)))) | ($sum(V1!8, $product(-1, V)) = 0)))) & (~appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V1!8, $sum(2, N!2)))) <=> ((((~(V1!8 = -1)) | (V2!9 = -1)) & ((V1!8 = -1) | appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V1!8, $sum(2, N!2))) & ((V2!9 = -1) | (appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V2!9, $sum(2, N!2)) & (~($sum(V1!8, $product(-1, V2!9)) = 0)))) & ![V: $int] : ((~($greatereq(V, 0) & (~$greatereq($sum(V, $product(-1, N!2)), 0)))) | ((~(tb2t3(get(bool, int, t2tb4(Deja_vu!7), t2tb(V))) = true1)) & ![J: $int] : ((~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, N!2)), 2)))) | (~($sum(V, $product(-1, tb2t(get(int, int, t2tb2(A1!3), t2tb(J))))) = 0)))) | ((tb2t3(get(bool, int, t2tb4(Deja_vu!7), t2tb(V))) = true1) & $greatereq(tptp_fun_J_10(V), 0) & (~$lesseq($sum(N!2, $product(-1, tptp_fun_J_10(V))), -2)) & ($sum(V, $product(-1, tb2t(get(int, int, t2tb2(A1!3), t2tb(tptp_fun_J_10(V)))))) = 0))) & ((~(V1!8 = -1)) | ![V: $int] : ((~appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V, $sum(2, N!2))) | (~($greatereq(V, 0) & (~$greatereq($sum(V, $product(-1, N!2)), 0)))))) & ((~(V2!9 = -1)) | ![V: $int] : ((~appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V, $sum(2, N!2))) | (~($greatereq(V, 0) & (~$greatereq($sum(V, $product(-1, N!2)), 0)))) | ($sum(V, $product(-1, V1!8)) = 0)))) & (~appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V1!8, $sum(2, N!2))))),
% 0.22/0.48 inference(monotonicity,[status(thm)],[37])).
% 0.22/0.48 tff(39,plain,
% 0.22/0.48 (((((~(V1!8 = -1)) | (V2!9 = -1)) & ((V1!8 = -1) | appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V1!8, $sum(2, N!2))) & ((V2!9 = -1) | (appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V2!9, $sum(2, N!2)) & (~($sum(V2!9, $product(-1, V1!8)) = 0)))) & ![V: $int] : ((~($greatereq(V, 0) & (~$greatereq($sum(V, $product(-1, N!2)), 0)))) | ((tb2t3(get(bool, int, t2tb4(Deja_vu!7), t2tb(V))) = true1) & ($greatereq(tptp_fun_J_10(V), 0) & (~$greatereq($sum(tptp_fun_J_10(V), $product(-1, N!2)), 2)) & ($sum(V, $product(-1, tb2t(get(int, int, t2tb2(A1!3), t2tb(tptp_fun_J_10(V)))))) = 0))) | ((~(tb2t3(get(bool, int, t2tb4(Deja_vu!7), t2tb(V))) = true1)) & ![J: $int] : ((~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, N!2)), 2)))) | (~($sum(V, $product(-1, tb2t(get(int, int, t2tb2(A1!3), t2tb(J))))) = 0))))) & ((~(V1!8 = -1)) | ![V: $int] : ((~appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V, $sum(2, N!2))) | (~($greatereq(V, 0) & (~$greatereq($sum(V, $product(-1, N!2)), 0)))))) & ((~(V2!9 = -1)) | ![V: $int] : ((~appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V, $sum(2, N!2))) | (~($greatereq(V, 0) & (~$greatereq($sum(V, $product(-1, N!2)), 0)))) | ($sum(V1!8, $product(-1, V)) = 0)))) & (~appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V1!8, $sum(2, N!2)))) <=> (((~(V1!8 = -1)) | (V2!9 = -1)) & ((V1!8 = -1) | appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V1!8, $sum(2, N!2))) & ((V2!9 = -1) | (appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V2!9, $sum(2, N!2)) & (~($sum(V1!8, $product(-1, V2!9)) = 0)))) & ![V: $int] : ((~($greatereq(V, 0) & (~$greatereq($sum(V, $product(-1, N!2)), 0)))) | ((~(tb2t3(get(bool, int, t2tb4(Deja_vu!7), t2tb(V))) = true1)) & ![J: $int] : ((~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, N!2)), 2)))) | (~($sum(V, $product(-1, tb2t(get(int, int, t2tb2(A1!3), t2tb(J))))) = 0)))) | ((tb2t3(get(bool, int, t2tb4(Deja_vu!7), t2tb(V))) = true1) & $greatereq(tptp_fun_J_10(V), 0) & (~$lesseq($sum(N!2, $product(-1, tptp_fun_J_10(V))), -2)) & ($sum(V, $product(-1, tb2t(get(int, int, t2tb2(A1!3), t2tb(tptp_fun_J_10(V)))))) = 0))) & ((~(V1!8 = -1)) | ![V: $int] : ((~appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V, $sum(2, N!2))) | (~($greatereq(V, 0) & (~$greatereq($sum(V, $product(-1, N!2)), 0)))))) & ((~(V2!9 = -1)) | ![V: $int] : ((~appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V, $sum(2, N!2))) | (~($greatereq(V, 0) & (~$greatereq($sum(V, $product(-1, N!2)), 0)))) | ($sum(V, $product(-1, V1!8)) = 0))) & (~appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V1!8, $sum(2, N!2))))),
% 0.22/0.48 inference(transitivity,[status(thm)],[38, 36])).
% 0.22/0.48 tff(40,plain,
% 0.22/0.48 (($greatereq(A!4, 0) & ($sum(N!2, $product(-1, A!4)) = -2) & $greatereq(N!2, 2) & ![I: $int] : ((~($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, A!4)), 0)))) | ($greatereq(tb2t(get(int, int, t2tb2(A1!3), t2tb(I))), 0) & (~$lesseq($sum(N!2, $product(-1, tb2t(get(int, int, t2tb2(A1!3), t2tb(I))))), 0)))) & (appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V1!5, $sum(2, N!2)) & appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V2!6, $sum(2, N!2)) & (~($sum(V1!5, $product(-1, V2!6)) = 0)))) <=> ($greatereq(A!4, 0) & ($sum(N!2, $product(-1, A!4)) = -2) & $greatereq(N!2, 2) & ![I: $int] : ((~($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, A!4)), 0)))) | ($greatereq(tb2t(get(int, int, t2tb2(A1!3), t2tb(I))), 0) & (~$lesseq($sum(N!2, $product(-1, tb2t(get(int, int, t2tb2(A1!3), t2tb(I))))), 0)))) & appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V1!5, $sum(2, N!2)) & appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V2!6, $sum(2, N!2)) & (~($sum(V1!5, $product(-1, V2!6)) = 0)))),
% 0.22/0.48 inference(rewrite,[status(thm)],[])).
% 0.22/0.48 tff(41,plain,
% 0.22/0.48 ((appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V1!5, $sum(2, N!2)) & (appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V2!6, $sum(2, N!2)) & (~($sum(V1!5, $product(-1, V2!6)) = 0)))) <=> (appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V1!5, $sum(2, N!2)) & appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V2!6, $sum(2, N!2)) & (~($sum(V1!5, $product(-1, V2!6)) = 0)))),
% 0.22/0.48 inference(rewrite,[status(thm)],[])).
% 0.22/0.48 tff(42,plain,
% 0.22/0.48 (($sum($product(-1, N!2), A!4) = 2) <=> ($sum(N!2, $product(-1, A!4)) = -2)),
% 0.22/0.48 inference(rewrite,[status(thm)],[])).
% 0.22/0.48 tff(43,plain,
% 0.22/0.48 ($sum(A!4, $product(-1, N!2)) = $sum($product(-1, N!2), A!4)),
% 0.22/0.48 inference(rewrite,[status(thm)],[])).
% 0.22/0.48 tff(44,plain,
% 0.22/0.48 (($sum(A!4, $product(-1, N!2)) = 2) <=> ($sum($product(-1, N!2), A!4) = 2)),
% 0.22/0.48 inference(monotonicity,[status(thm)],[43])).
% 0.22/0.48 tff(45,plain,
% 0.22/0.48 (($sum(A!4, $product(-1, N!2)) = 2) <=> ($sum(N!2, $product(-1, A!4)) = -2)),
% 0.22/0.48 inference(transitivity,[status(thm)],[44, 42])).
% 0.22/0.48 tff(46,plain,
% 0.22/0.48 (($greatereq(A!4, 0) & ($sum(A!4, $product(-1, N!2)) = 2) & $greatereq(N!2, 2) & ![I: $int] : ((~($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, A!4)), 0)))) | ($greatereq(tb2t(get(int, int, t2tb2(A1!3), t2tb(I))), 0) & (~$lesseq($sum(N!2, $product(-1, tb2t(get(int, int, t2tb2(A1!3), t2tb(I))))), 0)))) & (appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V1!5, $sum(2, N!2)) & (appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V2!6, $sum(2, N!2)) & (~($sum(V1!5, $product(-1, V2!6)) = 0))))) <=> ($greatereq(A!4, 0) & ($sum(N!2, $product(-1, A!4)) = -2) & $greatereq(N!2, 2) & ![I: $int] : ((~($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, A!4)), 0)))) | ($greatereq(tb2t(get(int, int, t2tb2(A1!3), t2tb(I))), 0) & (~$lesseq($sum(N!2, $product(-1, tb2t(get(int, int, t2tb2(A1!3), t2tb(I))))), 0)))) & (appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V1!5, $sum(2, N!2)) & appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V2!6, $sum(2, N!2)) & (~($sum(V1!5, $product(-1, V2!6)) = 0))))),
% 0.22/0.49 inference(monotonicity,[status(thm)],[45, 41])).
% 0.22/0.49 tff(47,plain,
% 0.22/0.49 (($greatereq(A!4, 0) & ($sum(A!4, $product(-1, N!2)) = 2) & $greatereq(N!2, 2) & ![I: $int] : ((~($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, A!4)), 0)))) | ($greatereq(tb2t(get(int, int, t2tb2(A1!3), t2tb(I))), 0) & (~$lesseq($sum(N!2, $product(-1, tb2t(get(int, int, t2tb2(A1!3), t2tb(I))))), 0)))) & (appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V1!5, $sum(2, N!2)) & (appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V2!6, $sum(2, N!2)) & (~($sum(V1!5, $product(-1, V2!6)) = 0))))) <=> ($greatereq(A!4, 0) & ($sum(N!2, $product(-1, A!4)) = -2) & $greatereq(N!2, 2) & ![I: $int] : ((~($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, A!4)), 0)))) | ($greatereq(tb2t(get(int, int, t2tb2(A1!3), t2tb(I))), 0) & (~$lesseq($sum(N!2, $product(-1, tb2t(get(int, int, t2tb2(A1!3), t2tb(I))))), 0)))) & appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V1!5, $sum(2, N!2)) & appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V2!6, $sum(2, N!2)) & (~($sum(V1!5, $product(-1, V2!6)) = 0)))),
% 0.22/0.49 inference(transitivity,[status(thm)],[46, 40])).
% 0.22/0.49 tff(48,plain,
% 0.22/0.49 ((~(~$greatereq(N!2, -1))) <=> $greatereq(N!2, -1)),
% 0.22/0.49 inference(rewrite,[status(thm)],[])).
% 0.22/0.49 tff(49,plain,
% 0.22/0.49 ((~(~$greatereq(N!2, 0))) <=> $greatereq(N!2, 0)),
% 0.22/0.49 inference(rewrite,[status(thm)],[])).
% 0.22/0.49 tff(50,plain,
% 0.22/0.49 (((~(~$greatereq(N!2, 0))) & (~(~$greatereq(N!2, -1))) & ($greatereq(A!4, 0) & ($sum(A!4, $product(-1, N!2)) = 2) & $greatereq(N!2, 2) & ![I: $int] : ((~($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, A!4)), 0)))) | ($greatereq(tb2t(get(int, int, t2tb2(A1!3), t2tb(I))), 0) & (~$lesseq($sum(N!2, $product(-1, tb2t(get(int, int, t2tb2(A1!3), t2tb(I))))), 0)))) & (appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V1!5, $sum(2, N!2)) & (appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V2!6, $sum(2, N!2)) & (~($sum(V1!5, $product(-1, V2!6)) = 0))))) & ((((~(V1!8 = -1)) | (V2!9 = -1)) & ((V1!8 = -1) | appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V1!8, $sum(2, N!2))) & ((V2!9 = -1) | (appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V2!9, $sum(2, N!2)) & (~($sum(V2!9, $product(-1, V1!8)) = 0)))) & ![V: $int] : ((~($greatereq(V, 0) & (~$greatereq($sum(V, $product(-1, N!2)), 0)))) | ((tb2t3(get(bool, int, t2tb4(Deja_vu!7), t2tb(V))) = true1) & ($greatereq(tptp_fun_J_10(V), 0) & (~$greatereq($sum(tptp_fun_J_10(V), $product(-1, N!2)), 2)) & ($sum(V, $product(-1, tb2t(get(int, int, t2tb2(A1!3), t2tb(tptp_fun_J_10(V)))))) = 0))) | ((~(tb2t3(get(bool, int, t2tb4(Deja_vu!7), t2tb(V))) = true1)) & ![J: $int] : ((~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, N!2)), 2)))) | (~($sum(V, $product(-1, tb2t(get(int, int, t2tb2(A1!3), t2tb(J))))) = 0))))) & ((~(V1!8 = -1)) | ![V: $int] : ((~appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V, $sum(2, N!2))) | (~($greatereq(V, 0) & (~$greatereq($sum(V, $product(-1, N!2)), 0)))))) & ((~(V2!9 = -1)) | ![V: $int] : ((~appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V, $sum(2, N!2))) | (~($greatereq(V, 0) & (~$greatereq($sum(V, $product(-1, N!2)), 0)))) | ($sum(V1!8, $product(-1, V)) = 0)))) & (~appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V1!8, $sum(2, N!2))))) <=> ($greatereq(N!2, 0) & $greatereq(N!2, -1) & ($greatereq(A!4, 0) & ($sum(N!2, $product(-1, A!4)) = -2) & $greatereq(N!2, 2) & ![I: $int] : ((~($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, A!4)), 0)))) | ($greatereq(tb2t(get(int, int, t2tb2(A1!3), t2tb(I))), 0) & (~$lesseq($sum(N!2, $product(-1, tb2t(get(int, int, t2tb2(A1!3), t2tb(I))))), 0)))) & appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V1!5, $sum(2, N!2)) & appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V2!6, $sum(2, N!2)) & (~($sum(V1!5, $product(-1, V2!6)) = 0))) & (((~(V1!8 = -1)) | (V2!9 = -1)) & ((V1!8 = -1) | appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V1!8, $sum(2, N!2))) & ((V2!9 = -1) | (appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V2!9, $sum(2, N!2)) & (~($sum(V1!8, $product(-1, V2!9)) = 0)))) & ![V: $int] : ((~($greatereq(V, 0) & (~$greatereq($sum(V, $product(-1, N!2)), 0)))) | ((~(tb2t3(get(bool, int, t2tb4(Deja_vu!7), t2tb(V))) = true1)) & ![J: $int] : ((~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, N!2)), 2)))) | (~($sum(V, $product(-1, tb2t(get(int, int, t2tb2(A1!3), t2tb(J))))) = 0)))) | ((tb2t3(get(bool, int, t2tb4(Deja_vu!7), t2tb(V))) = true1) & $greatereq(tptp_fun_J_10(V), 0) & (~$lesseq($sum(N!2, $product(-1, tptp_fun_J_10(V))), -2)) & ($sum(V, $product(-1, tb2t(get(int, int, t2tb2(A1!3), t2tb(tptp_fun_J_10(V)))))) = 0))) & ((~(V1!8 = -1)) | ![V: $int] : ((~appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V, $sum(2, N!2))) | (~($greatereq(V, 0) & (~$greatereq($sum(V, $product(-1, N!2)), 0)))))) & ((~(V2!9 = -1)) | ![V: $int] : ((~appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V, $sum(2, N!2))) | (~($greatereq(V, 0) & (~$greatereq($sum(V, $product(-1, N!2)), 0)))) | ($sum(V, $product(-1, V1!8)) = 0))) & (~appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V1!8, $sum(2, N!2)))))),
% 0.22/0.49 inference(monotonicity,[status(thm)],[49, 48, 47, 39])).
% 0.22/0.49 tff(51,plain,
% 0.22/0.49 (((~(~$greatereq(N!2, 0))) & (~(~$greatereq(N!2, -1))) & ($greatereq(A!4, 0) & ($sum(A!4, $product(-1, N!2)) = 2) & $greatereq(N!2, 2) & ![I: $int] : ((~($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, A!4)), 0)))) | ($greatereq(tb2t(get(int, int, t2tb2(A1!3), t2tb(I))), 0) & (~$lesseq($sum(N!2, $product(-1, tb2t(get(int, int, t2tb2(A1!3), t2tb(I))))), 0)))) & (appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V1!5, $sum(2, N!2)) & (appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V2!6, $sum(2, N!2)) & (~($sum(V1!5, $product(-1, V2!6)) = 0))))) & ((((~(V1!8 = -1)) | (V2!9 = -1)) & ((V1!8 = -1) | appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V1!8, $sum(2, N!2))) & ((V2!9 = -1) | (appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V2!9, $sum(2, N!2)) & (~($sum(V2!9, $product(-1, V1!8)) = 0)))) & ![V: $int] : ((~($greatereq(V, 0) & (~$greatereq($sum(V, $product(-1, N!2)), 0)))) | ((tb2t3(get(bool, int, t2tb4(Deja_vu!7), t2tb(V))) = true1) & ($greatereq(tptp_fun_J_10(V), 0) & (~$greatereq($sum(tptp_fun_J_10(V), $product(-1, N!2)), 2)) & ($sum(V, $product(-1, tb2t(get(int, int, t2tb2(A1!3), t2tb(tptp_fun_J_10(V)))))) = 0))) | ((~(tb2t3(get(bool, int, t2tb4(Deja_vu!7), t2tb(V))) = true1)) & ![J: $int] : ((~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, N!2)), 2)))) | (~($sum(V, $product(-1, tb2t(get(int, int, t2tb2(A1!3), t2tb(J))))) = 0))))) & ((~(V1!8 = -1)) | ![V: $int] : ((~appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V, $sum(2, N!2))) | (~($greatereq(V, 0) & (~$greatereq($sum(V, $product(-1, N!2)), 0)))))) & ((~(V2!9 = -1)) | ![V: $int] : ((~appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V, $sum(2, N!2))) | (~($greatereq(V, 0) & (~$greatereq($sum(V, $product(-1, N!2)), 0)))) | ($sum(V1!8, $product(-1, V)) = 0)))) & (~appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V1!8, $sum(2, N!2))))) <=> ($greatereq(N!2, 0) & $greatereq(N!2, -1) & $greatereq(A!4, 0) & ($sum(N!2, $product(-1, A!4)) = -2) & $greatereq(N!2, 2) & ![I: $int] : ((~($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, A!4)), 0)))) | ($greatereq(tb2t(get(int, int, t2tb2(A1!3), t2tb(I))), 0) & (~$lesseq($sum(N!2, $product(-1, tb2t(get(int, int, t2tb2(A1!3), t2tb(I))))), 0)))) & appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V1!5, $sum(2, N!2)) & appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V2!6, $sum(2, N!2)) & (~($sum(V1!5, $product(-1, V2!6)) = 0)) & ((~(V1!8 = -1)) | (V2!9 = -1)) & ((V1!8 = -1) | appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V1!8, $sum(2, N!2))) & ((V2!9 = -1) | (appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V2!9, $sum(2, N!2)) & (~($sum(V1!8, $product(-1, V2!9)) = 0)))) & ![V: $int] : ((~($greatereq(V, 0) & (~$greatereq($sum(V, $product(-1, N!2)), 0)))) | ((~(tb2t3(get(bool, int, t2tb4(Deja_vu!7), t2tb(V))) = true1)) & ![J: $int] : ((~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, N!2)), 2)))) | (~($sum(V, $product(-1, tb2t(get(int, int, t2tb2(A1!3), t2tb(J))))) = 0)))) | ((tb2t3(get(bool, int, t2tb4(Deja_vu!7), t2tb(V))) = true1) & $greatereq(tptp_fun_J_10(V), 0) & (~$lesseq($sum(N!2, $product(-1, tptp_fun_J_10(V))), -2)) & ($sum(V, $product(-1, tb2t(get(int, int, t2tb2(A1!3), t2tb(tptp_fun_J_10(V)))))) = 0))) & ((~(V1!8 = -1)) | ![V: $int] : ((~appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V, $sum(2, N!2))) | (~($greatereq(V, 0) & (~$greatereq($sum(V, $product(-1, N!2)), 0)))))) & ((~(V2!9 = -1)) | ![V: $int] : ((~appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V, $sum(2, N!2))) | (~($greatereq(V, 0) & (~$greatereq($sum(V, $product(-1, N!2)), 0)))) | ($sum(V, $product(-1, V1!8)) = 0))) & (~appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V1!8, $sum(2, N!2))))),
% 0.22/0.49 inference(transitivity,[status(thm)],[50, 35])).
% 0.22/0.49 tff(52,plain,
% 0.22/0.49 ((~![A: $int, A1: map_int_int, N: $int] : ((~$greatereq(N, 0)) | (~$greatereq(N, -1)) | (~($greatereq(A, 0) & ($sum(A, $product(-1, N)) = 2) & $greatereq(N, 2) & ![I: $int] : ((~($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, A)), 0)))) | ($greatereq(tb2t(get(int, int, t2tb2(A1), t2tb(I))), 0) & (~$lesseq($sum(N, $product(-1, tb2t(get(int, int, t2tb2(A1), t2tb(I))))), 0)))) & ?[V1: $int] : (appear_twice1(tb2t1(mk_array1(int, A, t2tb2(A1))), V1, $sum(2, N)) & ?[V2: $int] : (appear_twice1(tb2t1(mk_array1(int, A, t2tb2(A1))), V2, $sum(2, N)) & (~($sum(V1, $product(-1, V2)) = 0)))))) | ![V2: $int, V1: $int, Deja_vu: map_int_bool] : ((~(((~(V1 = -1)) | (V2 = -1)) & ((V1 = -1) | appear_twice1(tb2t1(mk_array1(int, A, t2tb2(A1))), V1, $sum(2, N))) & ((V2 = -1) | (appear_twice1(tb2t1(mk_array1(int, A, t2tb2(A1))), V2, $sum(2, N)) & (~($sum(V2, $product(-1, V1)) = 0)))) & ![V: $int] : ((~($greatereq(V, 0) & (~$greatereq($sum(V, $product(-1, N)), 0)))) | ((tb2t3(get(bool, int, t2tb4(Deja_vu), t2tb(V))) = true1) & ?[J: $int] : ($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, N)), 2)) & ($sum(V, $product(-1, tb2t(get(int, int, t2tb2(A1), t2tb(J))))) = 0))) | ((~(tb2t3(get(bool, int, t2tb4(Deja_vu), t2tb(V))) = true1)) & ![J: $int] : ((~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, N)), 2)))) | (~($sum(V, $product(-1, tb2t(get(int, int, t2tb2(A1), t2tb(J))))) = 0))))) & ((~(V1 = -1)) | ![V: $int] : ((~appear_twice1(tb2t1(mk_array1(int, A, t2tb2(A1))), V, $sum(2, N))) | (~($greatereq(V, 0) & (~$greatereq($sum(V, $product(-1, N)), 0)))))) & ((~(V2 = -1)) | ![V: $int] : ((~appear_twice1(tb2t1(mk_array1(int, A, t2tb2(A1))), V, $sum(2, N))) | (~($greatereq(V, 0) & (~$greatereq($sum(V, $product(-1, N)), 0)))) | ($sum(V1, $product(-1, V)) = 0))))) | appear_twice1(tb2t1(mk_array1(int, A, t2tb2(A1))), V1, $sum(2, N))))) <=> (~![A: $int, A1: map_int_int, N: $int] : ((~$greatereq(N, 0)) | (~$greatereq(N, -1)) | (~($greatereq(A, 0) & ($sum(A, $product(-1, N)) = 2) & $greatereq(N, 2) & ![I: $int] : ((~($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, A)), 0)))) | ($greatereq(tb2t(get(int, int, t2tb2(A1), t2tb(I))), 0) & (~$lesseq($sum(N, $product(-1, tb2t(get(int, int, t2tb2(A1), t2tb(I))))), 0)))) & ?[V1: $int] : (appear_twice1(tb2t1(mk_array1(int, A, t2tb2(A1))), V1, $sum(2, N)) & ?[V2: $int] : (appear_twice1(tb2t1(mk_array1(int, A, t2tb2(A1))), V2, $sum(2, N)) & (~($sum(V1, $product(-1, V2)) = 0)))))) | ![V2: $int, V1: $int, Deja_vu: map_int_bool] : ((~(((~(V1 = -1)) | (V2 = -1)) & ((V1 = -1) | appear_twice1(tb2t1(mk_array1(int, A, t2tb2(A1))), V1, $sum(2, N))) & ((V2 = -1) | (appear_twice1(tb2t1(mk_array1(int, A, t2tb2(A1))), V2, $sum(2, N)) & (~($sum(V2, $product(-1, V1)) = 0)))) & ![V: $int] : ((~($greatereq(V, 0) & (~$greatereq($sum(V, $product(-1, N)), 0)))) | ((tb2t3(get(bool, int, t2tb4(Deja_vu), t2tb(V))) = true1) & ?[J: $int] : ($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, N)), 2)) & ($sum(V, $product(-1, tb2t(get(int, int, t2tb2(A1), t2tb(J))))) = 0))) | ((~(tb2t3(get(bool, int, t2tb4(Deja_vu), t2tb(V))) = true1)) & ![J: $int] : ((~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, N)), 2)))) | (~($sum(V, $product(-1, tb2t(get(int, int, t2tb2(A1), t2tb(J))))) = 0))))) & ((~(V1 = -1)) | ![V: $int] : ((~appear_twice1(tb2t1(mk_array1(int, A, t2tb2(A1))), V, $sum(2, N))) | (~($greatereq(V, 0) & (~$greatereq($sum(V, $product(-1, N)), 0)))))) & ((~(V2 = -1)) | ![V: $int] : ((~appear_twice1(tb2t1(mk_array1(int, A, t2tb2(A1))), V, $sum(2, N))) | (~($greatereq(V, 0) & (~$greatereq($sum(V, $product(-1, N)), 0)))) | ($sum(V1, $product(-1, V)) = 0))))) | appear_twice1(tb2t1(mk_array1(int, A, t2tb2(A1))), V1, $sum(2, N)))))),
% 0.22/0.49 inference(rewrite,[status(thm)],[])).
% 0.22/0.49 tff(53,plain,
% 0.22/0.49 ((~![A: $int, A1: map_int_int, N: $int] : ((~$greatereq(N, 0)) | (~$greatereq(N, -1)) | (~($greatereq(A, 0) & ($sum(A, $product(-1, N)) = 2) & $greatereq(N, 2) & ![I: $int] : ((~($greatereq(I, 0) & (~$lesseq($sum(A, $product(-1, I)), 0)))) | ($greatereq(tb2t(get(int, int, t2tb2(A1), t2tb(I))), 0) & (~$lesseq($sum(N, $product(-1, tb2t(get(int, int, t2tb2(A1), t2tb(I))))), 0)))) & ?[V1: $int] : (appear_twice1(tb2t1(mk_array1(int, A, t2tb2(A1))), V1, $sum(2, N)) & ?[V2: $int] : (appear_twice1(tb2t1(mk_array1(int, A, t2tb2(A1))), V2, $sum(2, N)) & (~($sum(V2, $product(-1, V1)) = 0)))))) | ![V2: $int, V1: $int, Deja_vu: map_int_bool] : ((~(((~(V1 = -1)) | (V2 = -1)) & ((V1 = -1) | appear_twice1(tb2t1(mk_array1(int, A, t2tb2(A1))), V1, $sum(2, N))) & ((V2 = -1) | (appear_twice1(tb2t1(mk_array1(int, A, t2tb2(A1))), V2, $sum(2, N)) & (~($sum(V2, $product(-1, V1)) = 0)))) & ![V: $int] : ((~($greatereq(V, 0) & (~$lesseq($sum(N, $product(-1, V)), 0)))) | ((~(tb2t3(get(bool, int, t2tb4(Deja_vu), t2tb(V))) = true1)) & ![J: $int] : ((~($sum(tb2t(get(int, int, t2tb2(A1), t2tb(J))), $product(-1, V)) = 0)) | (~($greatereq(J, 0) & (~$lesseq($sum(N, $product(-1, J)), -2)))))) | ((tb2t3(get(bool, int, t2tb4(Deja_vu), t2tb(V))) = true1) & ?[J: $int] : ($greatereq(J, 0) & (~$lesseq($sum(N, $product(-1, J)), -2)) & ($sum(tb2t(get(int, int, t2tb2(A1), t2tb(J))), $product(-1, V)) = 0)))) & ((~(V1 = -1)) | ![V: $int] : ((~appear_twice1(tb2t1(mk_array1(int, A, t2tb2(A1))), V, $sum(2, N))) | (~($greatereq(V, 0) & (~$lesseq($sum(N, $product(-1, V)), 0)))))) & ((~(V2 = -1)) | ![V: $int] : ((~appear_twice1(tb2t1(mk_array1(int, A, t2tb2(A1))), V, $sum(2, N))) | (~($greatereq(V, 0) & (~$lesseq($sum(N, $product(-1, V)), 0)))) | ($sum(V, $product(-1, V1)) = 0))))) | appear_twice1(tb2t1(mk_array1(int, A, t2tb2(A1))), V1, $sum(2, N))))) <=> (~![A: $int, A1: map_int_int, N: $int] : ((~$greatereq(N, 0)) | (~$greatereq(N, -1)) | (~($greatereq(A, 0) & ($sum(A, $product(-1, N)) = 2) & $greatereq(N, 2) & ![I: $int] : ((~($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, A)), 0)))) | ($greatereq(tb2t(get(int, int, t2tb2(A1), t2tb(I))), 0) & (~$lesseq($sum(N, $product(-1, tb2t(get(int, int, t2tb2(A1), t2tb(I))))), 0)))) & ?[V1: $int] : (appear_twice1(tb2t1(mk_array1(int, A, t2tb2(A1))), V1, $sum(2, N)) & ?[V2: $int] : (appear_twice1(tb2t1(mk_array1(int, A, t2tb2(A1))), V2, $sum(2, N)) & (~($sum(V1, $product(-1, V2)) = 0)))))) | ![V2: $int, V1: $int, Deja_vu: map_int_bool] : ((~(((~(V1 = -1)) | (V2 = -1)) & ((V1 = -1) | appear_twice1(tb2t1(mk_array1(int, A, t2tb2(A1))), V1, $sum(2, N))) & ((V2 = -1) | (appear_twice1(tb2t1(mk_array1(int, A, t2tb2(A1))), V2, $sum(2, N)) & (~($sum(V2, $product(-1, V1)) = 0)))) & ![V: $int] : ((~($greatereq(V, 0) & (~$greatereq($sum(V, $product(-1, N)), 0)))) | ((tb2t3(get(bool, int, t2tb4(Deja_vu), t2tb(V))) = true1) & ?[J: $int] : ($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, N)), 2)) & ($sum(V, $product(-1, tb2t(get(int, int, t2tb2(A1), t2tb(J))))) = 0))) | ((~(tb2t3(get(bool, int, t2tb4(Deja_vu), t2tb(V))) = true1)) & ![J: $int] : ((~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, N)), 2)))) | (~($sum(V, $product(-1, tb2t(get(int, int, t2tb2(A1), t2tb(J))))) = 0))))) & ((~(V1 = -1)) | ![V: $int] : ((~appear_twice1(tb2t1(mk_array1(int, A, t2tb2(A1))), V, $sum(2, N))) | (~($greatereq(V, 0) & (~$greatereq($sum(V, $product(-1, N)), 0)))))) & ((~(V2 = -1)) | ![V: $int] : ((~appear_twice1(tb2t1(mk_array1(int, A, t2tb2(A1))), V, $sum(2, N))) | (~($greatereq(V, 0) & (~$greatereq($sum(V, $product(-1, N)), 0)))) | ($sum(V1, $product(-1, V)) = 0))))) | appear_twice1(tb2t1(mk_array1(int, A, t2tb2(A1))), V1, $sum(2, N)))))),
% 0.22/0.49 inference(rewrite,[status(thm)],[])).
% 0.22/0.49 tff(54,plain,
% 0.22/0.49 ((~![A: $int, A1: map_int_int, N: $int] : ((~$lesseq(0, N)) | (~$lesseq(-1, N)) | ![V2: $int, V1: $int, Deja_vu: map_int_bool] : ((~(((~(V1 = -1)) | (V2 = -1)) & ((V1 = -1) | appear_twice1(tb2t1(mk_array1(int, A, t2tb2(A1))), V1, $sum(2, N))) & ((V2 = -1) | (appear_twice1(tb2t1(mk_array1(int, A, t2tb2(A1))), V2, $sum(2, N)) & (~(V2 = V1)))) & ![V: $int] : ((~($lesseq(0, V) & (~$lesseq(N, V)))) | ((~(tb2t3(get(bool, int, t2tb4(Deja_vu), t2tb(V))) = true1)) & ![J: $int] : ((~(tb2t(get(int, int, t2tb2(A1), t2tb(J))) = V)) | (~($lesseq(0, J) & (~$lesseq(N, $sum(-2, J))))))) | ((tb2t3(get(bool, int, t2tb4(Deja_vu), t2tb(V))) = true1) & ?[J: $int] : ($lesseq(0, J) & (~$lesseq(N, $sum(-2, J))) & (tb2t(get(int, int, t2tb2(A1), t2tb(J))) = V)))) & ((~(V1 = -1)) | ![V: $int] : ((~($lesseq(0, V) & (~$lesseq(N, V)))) | (~appear_twice1(tb2t1(mk_array1(int, A, t2tb2(A1))), V, $sum(2, N))))) & ((~(V2 = -1)) | ![V: $int] : ((V = V1) | (~($lesseq(0, V) & (~$lesseq(N, V)))) | (~appear_twice1(tb2t1(mk_array1(int, A, t2tb2(A1))), V, $sum(2, N))))))) | appear_twice1(tb2t1(mk_array1(int, A, t2tb2(A1))), V1, $sum(2, N))) | (~($lesseq(0, A) & (A = $sum(2, N)) & $lesseq(2, N) & ![I: $int] : ((~($lesseq(0, I) & (~$lesseq(A, I)))) | ($lesseq(0, tb2t(get(int, int, t2tb2(A1), t2tb(I)))) & (~$lesseq(N, tb2t(get(int, int, t2tb2(A1), t2tb(I))))))) & ?[V1: $int] : (appear_twice1(tb2t1(mk_array1(int, A, t2tb2(A1))), V1, $sum(2, N)) & ?[V2: $int] : (appear_twice1(tb2t1(mk_array1(int, A, t2tb2(A1))), V2, $sum(2, N)) & (~(V2 = V1)))))))) <=> (~![A: $int, A1: map_int_int, N: $int] : ((~$greatereq(N, 0)) | (~$greatereq(N, -1)) | (~($greatereq(A, 0) & ($sum(A, $product(-1, N)) = 2) & $greatereq(N, 2) & ![I: $int] : ((~($greatereq(I, 0) & (~$lesseq($sum(A, $product(-1, I)), 0)))) | ($greatereq(tb2t(get(int, int, t2tb2(A1), t2tb(I))), 0) & (~$lesseq($sum(N, $product(-1, tb2t(get(int, int, t2tb2(A1), t2tb(I))))), 0)))) & ?[V1: $int] : (appear_twice1(tb2t1(mk_array1(int, A, t2tb2(A1))), V1, $sum(2, N)) & ?[V2: $int] : (appear_twice1(tb2t1(mk_array1(int, A, t2tb2(A1))), V2, $sum(2, N)) & (~($sum(V2, $product(-1, V1)) = 0)))))) | ![V2: $int, V1: $int, Deja_vu: map_int_bool] : ((~(((~(V1 = -1)) | (V2 = -1)) & ((V1 = -1) | appear_twice1(tb2t1(mk_array1(int, A, t2tb2(A1))), V1, $sum(2, N))) & ((V2 = -1) | (appear_twice1(tb2t1(mk_array1(int, A, t2tb2(A1))), V2, $sum(2, N)) & (~($sum(V2, $product(-1, V1)) = 0)))) & ![V: $int] : ((~($greatereq(V, 0) & (~$lesseq($sum(N, $product(-1, V)), 0)))) | ((~(tb2t3(get(bool, int, t2tb4(Deja_vu), t2tb(V))) = true1)) & ![J: $int] : ((~($sum(tb2t(get(int, int, t2tb2(A1), t2tb(J))), $product(-1, V)) = 0)) | (~($greatereq(J, 0) & (~$lesseq($sum(N, $product(-1, J)), -2)))))) | ((tb2t3(get(bool, int, t2tb4(Deja_vu), t2tb(V))) = true1) & ?[J: $int] : ($greatereq(J, 0) & (~$lesseq($sum(N, $product(-1, J)), -2)) & ($sum(tb2t(get(int, int, t2tb2(A1), t2tb(J))), $product(-1, V)) = 0)))) & ((~(V1 = -1)) | ![V: $int] : ((~appear_twice1(tb2t1(mk_array1(int, A, t2tb2(A1))), V, $sum(2, N))) | (~($greatereq(V, 0) & (~$lesseq($sum(N, $product(-1, V)), 0)))))) & ((~(V2 = -1)) | ![V: $int] : ((~appear_twice1(tb2t1(mk_array1(int, A, t2tb2(A1))), V, $sum(2, N))) | (~($greatereq(V, 0) & (~$lesseq($sum(N, $product(-1, V)), 0)))) | ($sum(V, $product(-1, V1)) = 0))))) | appear_twice1(tb2t1(mk_array1(int, A, t2tb2(A1))), V1, $sum(2, N)))))),
% 0.22/0.49 inference(rewrite,[status(thm)],[])).
% 0.22/0.49 tff(55,plain,
% 0.22/0.49 ((~![A: $int, A1: map_int_int, N: $int] : ((~$lesseq(0, N)) | (~$lesseq(-1, N)) | ![V2: $int, V1: $int, Deja_vu: map_int_bool] : ((~(((~(V1 = -1)) | (V2 = -1)) & ((V1 = -1) | appear_twice1(tb2t1(mk_array1(int, A, t2tb2(A1))), V1, $sum(2, N))) & ((V2 = -1) | (appear_twice1(tb2t1(mk_array1(int, A, t2tb2(A1))), V2, $sum(2, N)) & (~(V2 = V1)))) & ![V: $int] : ((~($lesseq(0, V) & (~$lesseq(N, V)))) | ((~(tb2t3(get(bool, int, t2tb4(Deja_vu), t2tb(V))) = true1)) & ![J: $int] : ((~(tb2t(get(int, int, t2tb2(A1), t2tb(J))) = V)) | (~($lesseq(0, J) & (~$lesseq(N, $sum(-2, J))))))) | ((tb2t3(get(bool, int, t2tb4(Deja_vu), t2tb(V))) = true1) & ?[J: $int] : ($lesseq(0, J) & (~$lesseq(N, $sum(-2, J))) & (tb2t(get(int, int, t2tb2(A1), t2tb(J))) = V)))) & ((~(V1 = -1)) | ![V: $int] : ((~($lesseq(0, V) & (~$lesseq(N, V)))) | (~appear_twice1(tb2t1(mk_array1(int, A, t2tb2(A1))), V, $sum(2, N))))) & ((~(V2 = -1)) | ![V: $int] : ((V = V1) | (~($lesseq(0, V) & (~$lesseq(N, V)))) | (~appear_twice1(tb2t1(mk_array1(int, A, t2tb2(A1))), V, $sum(2, N))))))) | appear_twice1(tb2t1(mk_array1(int, A, t2tb2(A1))), V1, $sum(2, N))) | (~($lesseq(0, A) & (A = $sum(2, N)) & $lesseq(2, N) & ![I: $int] : ((~($lesseq(0, I) & (~$lesseq(A, I)))) | ($lesseq(0, tb2t(get(int, int, t2tb2(A1), t2tb(I)))) & (~$lesseq(N, tb2t(get(int, int, t2tb2(A1), t2tb(I))))))) & ?[V1: $int] : (appear_twice1(tb2t1(mk_array1(int, A, t2tb2(A1))), V1, $sum(2, N)) & ?[V2: $int] : (appear_twice1(tb2t1(mk_array1(int, A, t2tb2(A1))), V2, $sum(2, N)) & (~(V2 = V1)))))))) <=> (~![A: $int, A1: map_int_int, N: $int] : ((~$lesseq(0, N)) | (~$lesseq(-1, N)) | ![V2: $int, V1: $int, Deja_vu: map_int_bool] : ((~(((~(V1 = -1)) | (V2 = -1)) & ((V1 = -1) | appear_twice1(tb2t1(mk_array1(int, A, t2tb2(A1))), V1, $sum(2, N))) & ((V2 = -1) | (appear_twice1(tb2t1(mk_array1(int, A, t2tb2(A1))), V2, $sum(2, N)) & (~(V2 = V1)))) & ![V: $int] : ((~($lesseq(0, V) & (~$lesseq(N, V)))) | ((~(tb2t3(get(bool, int, t2tb4(Deja_vu), t2tb(V))) = true1)) & ![J: $int] : ((~(tb2t(get(int, int, t2tb2(A1), t2tb(J))) = V)) | (~($lesseq(0, J) & (~$lesseq(N, $sum(-2, J))))))) | ((tb2t3(get(bool, int, t2tb4(Deja_vu), t2tb(V))) = true1) & ?[J: $int] : ($lesseq(0, J) & (~$lesseq(N, $sum(-2, J))) & (tb2t(get(int, int, t2tb2(A1), t2tb(J))) = V)))) & ((~(V1 = -1)) | ![V: $int] : ((~($lesseq(0, V) & (~$lesseq(N, V)))) | (~appear_twice1(tb2t1(mk_array1(int, A, t2tb2(A1))), V, $sum(2, N))))) & ((~(V2 = -1)) | ![V: $int] : ((V = V1) | (~($lesseq(0, V) & (~$lesseq(N, V)))) | (~appear_twice1(tb2t1(mk_array1(int, A, t2tb2(A1))), V, $sum(2, N))))))) | appear_twice1(tb2t1(mk_array1(int, A, t2tb2(A1))), V1, $sum(2, N))) | (~($lesseq(0, A) & (A = $sum(2, N)) & $lesseq(2, N) & ![I: $int] : ((~($lesseq(0, I) & (~$lesseq(A, I)))) | ($lesseq(0, tb2t(get(int, int, t2tb2(A1), t2tb(I)))) & (~$lesseq(N, tb2t(get(int, int, t2tb2(A1), t2tb(I))))))) & ?[V1: $int] : (appear_twice1(tb2t1(mk_array1(int, A, t2tb2(A1))), V1, $sum(2, N)) & ?[V2: $int] : (appear_twice1(tb2t1(mk_array1(int, A, t2tb2(A1))), V2, $sum(2, N)) & (~(V2 = V1))))))))),
% 0.22/0.49 inference(rewrite,[status(thm)],[])).
% 0.22/0.49 tff(56,plain,
% 0.22/0.49 ((~![A: $int, A1: map_int_int, N: $int] : ((((($lesseq(0, A) & (A = $sum(N, 2))) & $lesseq(2, N)) & ![I: $int] : (($lesseq(0, I) & $less(I, A)) => ($lesseq(0, tb2t(get(int, int, t2tb2(A1), t2tb(I)))) & $less(tb2t(get(int, int, t2tb2(A1), t2tb(I))), N)))) & ?[V1: $int] : (appear_twice1(tb2t1(mk_array1(int, A, t2tb2(A1))), V1, $sum(N, 2)) & ?[V2: $int] : (appear_twice1(tb2t1(mk_array1(int, A, t2tb2(A1))), V2, $sum(N, 2)) & (~(V2 = V1))))) => ($lesseq(0, N) => ($lesseq(0, N) => ($lesseq(0, $sum(N, 1)) => ![V2: $int, V1: $int, Deja_vu: map_int_bool] : ((((((((V1 = $uminus(1)) => (V2 = $uminus(1))) & ((~(V1 = $uminus(1))) => appear_twice1(tb2t1(mk_array1(int, A, t2tb2(A1))), V1, $sum($sum(N, 1), 1)))) & ((~(V2 = $uminus(1))) => (appear_twice1(tb2t1(mk_array1(int, A, t2tb2(A1))), V2, $sum($sum(N, 1), 1)) & (~(V2 = V1))))) & ![V: $int] : (($lesseq(0, V) & $less(V, N)) => (((tb2t3(get(bool, int, t2tb4(Deja_vu), t2tb(V))) = true1) & ?[J: $int] : (($lesseq(0, J) & $less(J, $sum($sum(N, 1), 1))) & (tb2t(get(int, int, t2tb2(A1), t2tb(J))) = V))) | ((~(tb2t3(get(bool, int, t2tb4(Deja_vu), t2tb(V))) = true1)) & ![J: $int] : (($lesseq(0, J) & $less(J, $sum($sum(N, 1), 1))) => (~(tb2t(get(int, int, t2tb2(A1), t2tb(J))) = V))))))) & ((V1 = $uminus(1)) => ![V: $int] : (($lesseq(0, V) & $less(V, N)) => (~appear_twice1(tb2t1(mk_array1(int, A, t2tb2(A1))), V, $sum($sum(N, 1), 1)))))) & ((V2 = $uminus(1)) => ![V: $int] : (($lesseq(0, V) & $less(V, N)) => ((~(V = V1)) => (~appear_twice1(tb2t1(mk_array1(int, A, t2tb2(A1))), V, $sum($sum(N, 1), 1))))))) => appear_twice1(tb2t1(mk_array1(int, A, t2tb2(A1))), V1, $sum(N, 2)))))))) <=> (~![A: $int, A1: map_int_int, N: $int] : ((~$lesseq(0, N)) | (~$lesseq(-1, N)) | ![V2: $int, V1: $int, Deja_vu: map_int_bool] : ((~(((~(V1 = -1)) | (V2 = -1)) & ((V1 = -1) | appear_twice1(tb2t1(mk_array1(int, A, t2tb2(A1))), V1, $sum(2, N))) & ((V2 = -1) | (appear_twice1(tb2t1(mk_array1(int, A, t2tb2(A1))), V2, $sum(2, N)) & (~(V2 = V1)))) & ![V: $int] : ((~($lesseq(0, V) & (~$lesseq(N, V)))) | ((~(tb2t3(get(bool, int, t2tb4(Deja_vu), t2tb(V))) = true1)) & ![J: $int] : ((~(tb2t(get(int, int, t2tb2(A1), t2tb(J))) = V)) | (~($lesseq(0, J) & (~$lesseq(N, $sum(-2, J))))))) | ((tb2t3(get(bool, int, t2tb4(Deja_vu), t2tb(V))) = true1) & ?[J: $int] : ($lesseq(0, J) & (~$lesseq(N, $sum(-2, J))) & (tb2t(get(int, int, t2tb2(A1), t2tb(J))) = V)))) & ((~(V1 = -1)) | ![V: $int] : ((~($lesseq(0, V) & (~$lesseq(N, V)))) | (~appear_twice1(tb2t1(mk_array1(int, A, t2tb2(A1))), V, $sum(2, N))))) & ((~(V2 = -1)) | ![V: $int] : ((V = V1) | (~($lesseq(0, V) & (~$lesseq(N, V)))) | (~appear_twice1(tb2t1(mk_array1(int, A, t2tb2(A1))), V, $sum(2, N))))))) | appear_twice1(tb2t1(mk_array1(int, A, t2tb2(A1))), V1, $sum(2, N))) | (~($lesseq(0, A) & (A = $sum(2, N)) & $lesseq(2, N) & ![I: $int] : ((~($lesseq(0, I) & (~$lesseq(A, I)))) | ($lesseq(0, tb2t(get(int, int, t2tb2(A1), t2tb(I)))) & (~$lesseq(N, tb2t(get(int, int, t2tb2(A1), t2tb(I))))))) & ?[V1: $int] : (appear_twice1(tb2t1(mk_array1(int, A, t2tb2(A1))), V1, $sum(2, N)) & ?[V2: $int] : (appear_twice1(tb2t1(mk_array1(int, A, t2tb2(A1))), V2, $sum(2, N)) & (~(V2 = V1))))))))),
% 0.22/0.49 inference(rewrite,[status(thm)],[])).
% 0.22/0.49 tff(57,axiom,(~![A: $int, A1: map_int_int, N: $int] : ((((($lesseq(0, A) & (A = $sum(N, 2))) & $lesseq(2, N)) & ![I: $int] : (($lesseq(0, I) & $less(I, A)) => ($lesseq(0, tb2t(get(int, int, t2tb2(A1), t2tb(I)))) & $less(tb2t(get(int, int, t2tb2(A1), t2tb(I))), N)))) & ?[V1: $int] : (appear_twice1(tb2t1(mk_array1(int, A, t2tb2(A1))), V1, $sum(N, 2)) & ?[V2: $int] : (appear_twice1(tb2t1(mk_array1(int, A, t2tb2(A1))), V2, $sum(N, 2)) & (~(V2 = V1))))) => ($lesseq(0, N) => ($lesseq(0, N) => ($lesseq(0, $sum(N, 1)) => ![V2: $int, V1: $int, Deja_vu: map_int_bool] : ((((((((V1 = $uminus(1)) => (V2 = $uminus(1))) & ((~(V1 = $uminus(1))) => appear_twice1(tb2t1(mk_array1(int, A, t2tb2(A1))), V1, $sum($sum(N, 1), 1)))) & ((~(V2 = $uminus(1))) => (appear_twice1(tb2t1(mk_array1(int, A, t2tb2(A1))), V2, $sum($sum(N, 1), 1)) & (~(V2 = V1))))) & ![V: $int] : (($lesseq(0, V) & $less(V, N)) => (((tb2t3(get(bool, int, t2tb4(Deja_vu), t2tb(V))) = true1) & ?[J: $int] : (($lesseq(0, J) & $less(J, $sum($sum(N, 1), 1))) & (tb2t(get(int, int, t2tb2(A1), t2tb(J))) = V))) | ((~(tb2t3(get(bool, int, t2tb4(Deja_vu), t2tb(V))) = true1)) & ![J: $int] : (($lesseq(0, J) & $less(J, $sum($sum(N, 1), 1))) => (~(tb2t(get(int, int, t2tb2(A1), t2tb(J))) = V))))))) & ((V1 = $uminus(1)) => ![V: $int] : (($lesseq(0, V) & $less(V, N)) => (~appear_twice1(tb2t1(mk_array1(int, A, t2tb2(A1))), V, $sum($sum(N, 1), 1)))))) & ((V2 = $uminus(1)) => ![V: $int] : (($lesseq(0, V) & $less(V, N)) => ((~(V = V1)) => (~appear_twice1(tb2t1(mk_array1(int, A, t2tb2(A1))), V, $sum($sum(N, 1), 1))))))) => appear_twice1(tb2t1(mk_array1(int, A, t2tb2(A1))), V1, $sum(N, 2)))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','wP_parameter_two_equal_elements')).
% 0.22/0.49 tff(58,plain,
% 0.22/0.49 (~![A: $int, A1: map_int_int, N: $int] : ((~$lesseq(0, N)) | (~$lesseq(-1, N)) | ![V2: $int, V1: $int, Deja_vu: map_int_bool] : ((~(((~(V1 = -1)) | (V2 = -1)) & ((V1 = -1) | appear_twice1(tb2t1(mk_array1(int, A, t2tb2(A1))), V1, $sum(2, N))) & ((V2 = -1) | (appear_twice1(tb2t1(mk_array1(int, A, t2tb2(A1))), V2, $sum(2, N)) & (~(V2 = V1)))) & ![V: $int] : ((~($lesseq(0, V) & (~$lesseq(N, V)))) | ((~(tb2t3(get(bool, int, t2tb4(Deja_vu), t2tb(V))) = true1)) & ![J: $int] : ((~(tb2t(get(int, int, t2tb2(A1), t2tb(J))) = V)) | (~($lesseq(0, J) & (~$lesseq(N, $sum(-2, J))))))) | ((tb2t3(get(bool, int, t2tb4(Deja_vu), t2tb(V))) = true1) & ?[J: $int] : ($lesseq(0, J) & (~$lesseq(N, $sum(-2, J))) & (tb2t(get(int, int, t2tb2(A1), t2tb(J))) = V)))) & ((~(V1 = -1)) | ![V: $int] : ((~($lesseq(0, V) & (~$lesseq(N, V)))) | (~appear_twice1(tb2t1(mk_array1(int, A, t2tb2(A1))), V, $sum(2, N))))) & ((~(V2 = -1)) | ![V: $int] : ((V = V1) | (~($lesseq(0, V) & (~$lesseq(N, V)))) | (~appear_twice1(tb2t1(mk_array1(int, A, t2tb2(A1))), V, $sum(2, N))))))) | appear_twice1(tb2t1(mk_array1(int, A, t2tb2(A1))), V1, $sum(2, N))) | (~($lesseq(0, A) & (A = $sum(2, N)) & $lesseq(2, N) & ![I: $int] : ((~($lesseq(0, I) & (~$lesseq(A, I)))) | ($lesseq(0, tb2t(get(int, int, t2tb2(A1), t2tb(I)))) & (~$lesseq(N, tb2t(get(int, int, t2tb2(A1), t2tb(I))))))) & ?[V1: $int] : (appear_twice1(tb2t1(mk_array1(int, A, t2tb2(A1))), V1, $sum(2, N)) & ?[V2: $int] : (appear_twice1(tb2t1(mk_array1(int, A, t2tb2(A1))), V2, $sum(2, N)) & (~(V2 = V1)))))))),
% 0.22/0.50 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.22/0.50 tff(59,plain,
% 0.22/0.50 (~![A: $int, A1: map_int_int, N: $int] : ((~$lesseq(0, N)) | (~$lesseq(-1, N)) | ![V2: $int, V1: $int, Deja_vu: map_int_bool] : ((~(((~(V1 = -1)) | (V2 = -1)) & ((V1 = -1) | appear_twice1(tb2t1(mk_array1(int, A, t2tb2(A1))), V1, $sum(2, N))) & ((V2 = -1) | (appear_twice1(tb2t1(mk_array1(int, A, t2tb2(A1))), V2, $sum(2, N)) & (~(V2 = V1)))) & ![V: $int] : ((~($lesseq(0, V) & (~$lesseq(N, V)))) | ((~(tb2t3(get(bool, int, t2tb4(Deja_vu), t2tb(V))) = true1)) & ![J: $int] : ((~(tb2t(get(int, int, t2tb2(A1), t2tb(J))) = V)) | (~($lesseq(0, J) & (~$lesseq(N, $sum(-2, J))))))) | ((tb2t3(get(bool, int, t2tb4(Deja_vu), t2tb(V))) = true1) & ?[J: $int] : ($lesseq(0, J) & (~$lesseq(N, $sum(-2, J))) & (tb2t(get(int, int, t2tb2(A1), t2tb(J))) = V)))) & ((~(V1 = -1)) | ![V: $int] : ((~($lesseq(0, V) & (~$lesseq(N, V)))) | (~appear_twice1(tb2t1(mk_array1(int, A, t2tb2(A1))), V, $sum(2, N))))) & ((~(V2 = -1)) | ![V: $int] : ((V = V1) | (~($lesseq(0, V) & (~$lesseq(N, V)))) | (~appear_twice1(tb2t1(mk_array1(int, A, t2tb2(A1))), V, $sum(2, N))))))) | appear_twice1(tb2t1(mk_array1(int, A, t2tb2(A1))), V1, $sum(2, N))) | (~($lesseq(0, A) & (A = $sum(2, N)) & $lesseq(2, N) & ![I: $int] : ((~($lesseq(0, I) & (~$lesseq(A, I)))) | ($lesseq(0, tb2t(get(int, int, t2tb2(A1), t2tb(I)))) & (~$lesseq(N, tb2t(get(int, int, t2tb2(A1), t2tb(I))))))) & ?[V1: $int] : (appear_twice1(tb2t1(mk_array1(int, A, t2tb2(A1))), V1, $sum(2, N)) & ?[V2: $int] : (appear_twice1(tb2t1(mk_array1(int, A, t2tb2(A1))), V2, $sum(2, N)) & (~(V2 = V1)))))))),
% 0.22/0.50 inference(modus_ponens,[status(thm)],[58, 55])).
% 0.22/0.50 tff(60,plain,
% 0.22/0.50 (~![A: $int, A1: map_int_int, N: $int] : ((~$lesseq(0, N)) | (~$lesseq(-1, N)) | ![V2: $int, V1: $int, Deja_vu: map_int_bool] : ((~(((~(V1 = -1)) | (V2 = -1)) & ((V1 = -1) | appear_twice1(tb2t1(mk_array1(int, A, t2tb2(A1))), V1, $sum(2, N))) & ((V2 = -1) | (appear_twice1(tb2t1(mk_array1(int, A, t2tb2(A1))), V2, $sum(2, N)) & (~(V2 = V1)))) & ![V: $int] : ((~($lesseq(0, V) & (~$lesseq(N, V)))) | ((~(tb2t3(get(bool, int, t2tb4(Deja_vu), t2tb(V))) = true1)) & ![J: $int] : ((~(tb2t(get(int, int, t2tb2(A1), t2tb(J))) = V)) | (~($lesseq(0, J) & (~$lesseq(N, $sum(-2, J))))))) | ((tb2t3(get(bool, int, t2tb4(Deja_vu), t2tb(V))) = true1) & ?[J: $int] : ($lesseq(0, J) & (~$lesseq(N, $sum(-2, J))) & (tb2t(get(int, int, t2tb2(A1), t2tb(J))) = V)))) & ((~(V1 = -1)) | ![V: $int] : ((~($lesseq(0, V) & (~$lesseq(N, V)))) | (~appear_twice1(tb2t1(mk_array1(int, A, t2tb2(A1))), V, $sum(2, N))))) & ((~(V2 = -1)) | ![V: $int] : ((V = V1) | (~($lesseq(0, V) & (~$lesseq(N, V)))) | (~appear_twice1(tb2t1(mk_array1(int, A, t2tb2(A1))), V, $sum(2, N))))))) | appear_twice1(tb2t1(mk_array1(int, A, t2tb2(A1))), V1, $sum(2, N))) | (~($lesseq(0, A) & (A = $sum(2, N)) & $lesseq(2, N) & ![I: $int] : ((~($lesseq(0, I) & (~$lesseq(A, I)))) | ($lesseq(0, tb2t(get(int, int, t2tb2(A1), t2tb(I)))) & (~$lesseq(N, tb2t(get(int, int, t2tb2(A1), t2tb(I))))))) & ?[V1: $int] : (appear_twice1(tb2t1(mk_array1(int, A, t2tb2(A1))), V1, $sum(2, N)) & ?[V2: $int] : (appear_twice1(tb2t1(mk_array1(int, A, t2tb2(A1))), V2, $sum(2, N)) & (~(V2 = V1)))))))),
% 0.22/0.50 inference(modus_ponens,[status(thm)],[59, 55])).
% 0.22/0.50 tff(61,plain,
% 0.22/0.50 (~![A: $int, A1: map_int_int, N: $int] : ((~$lesseq(0, N)) | (~$lesseq(-1, N)) | ![V2: $int, V1: $int, Deja_vu: map_int_bool] : ((~(((~(V1 = -1)) | (V2 = -1)) & ((V1 = -1) | appear_twice1(tb2t1(mk_array1(int, A, t2tb2(A1))), V1, $sum(2, N))) & ((V2 = -1) | (appear_twice1(tb2t1(mk_array1(int, A, t2tb2(A1))), V2, $sum(2, N)) & (~(V2 = V1)))) & ![V: $int] : ((~($lesseq(0, V) & (~$lesseq(N, V)))) | ((~(tb2t3(get(bool, int, t2tb4(Deja_vu), t2tb(V))) = true1)) & ![J: $int] : ((~(tb2t(get(int, int, t2tb2(A1), t2tb(J))) = V)) | (~($lesseq(0, J) & (~$lesseq(N, $sum(-2, J))))))) | ((tb2t3(get(bool, int, t2tb4(Deja_vu), t2tb(V))) = true1) & ?[J: $int] : ($lesseq(0, J) & (~$lesseq(N, $sum(-2, J))) & (tb2t(get(int, int, t2tb2(A1), t2tb(J))) = V)))) & ((~(V1 = -1)) | ![V: $int] : ((~($lesseq(0, V) & (~$lesseq(N, V)))) | (~appear_twice1(tb2t1(mk_array1(int, A, t2tb2(A1))), V, $sum(2, N))))) & ((~(V2 = -1)) | ![V: $int] : ((V = V1) | (~($lesseq(0, V) & (~$lesseq(N, V)))) | (~appear_twice1(tb2t1(mk_array1(int, A, t2tb2(A1))), V, $sum(2, N))))))) | appear_twice1(tb2t1(mk_array1(int, A, t2tb2(A1))), V1, $sum(2, N))) | (~($lesseq(0, A) & (A = $sum(2, N)) & $lesseq(2, N) & ![I: $int] : ((~($lesseq(0, I) & (~$lesseq(A, I)))) | ($lesseq(0, tb2t(get(int, int, t2tb2(A1), t2tb(I)))) & (~$lesseq(N, tb2t(get(int, int, t2tb2(A1), t2tb(I))))))) & ?[V1: $int] : (appear_twice1(tb2t1(mk_array1(int, A, t2tb2(A1))), V1, $sum(2, N)) & ?[V2: $int] : (appear_twice1(tb2t1(mk_array1(int, A, t2tb2(A1))), V2, $sum(2, N)) & (~(V2 = V1)))))))),
% 0.22/0.50 inference(modus_ponens,[status(thm)],[60, 55])).
% 0.22/0.50 tff(62,plain,
% 0.22/0.50 (~![A: $int, A1: map_int_int, N: $int] : ((~$greatereq(N, 0)) | (~$greatereq(N, -1)) | (~($greatereq(A, 0) & ($sum(A, $product(-1, N)) = 2) & $greatereq(N, 2) & ![I: $int] : ((~($greatereq(I, 0) & (~$lesseq($sum(A, $product(-1, I)), 0)))) | ($greatereq(tb2t(get(int, int, t2tb2(A1), t2tb(I))), 0) & (~$lesseq($sum(N, $product(-1, tb2t(get(int, int, t2tb2(A1), t2tb(I))))), 0)))) & ?[V1: $int] : (appear_twice1(tb2t1(mk_array1(int, A, t2tb2(A1))), V1, $sum(2, N)) & ?[V2: $int] : (appear_twice1(tb2t1(mk_array1(int, A, t2tb2(A1))), V2, $sum(2, N)) & (~($sum(V2, $product(-1, V1)) = 0)))))) | ![V2: $int, V1: $int, Deja_vu: map_int_bool] : ((~(((~(V1 = -1)) | (V2 = -1)) & ((V1 = -1) | appear_twice1(tb2t1(mk_array1(int, A, t2tb2(A1))), V1, $sum(2, N))) & ((V2 = -1) | (appear_twice1(tb2t1(mk_array1(int, A, t2tb2(A1))), V2, $sum(2, N)) & (~($sum(V2, $product(-1, V1)) = 0)))) & ![V: $int] : ((~($greatereq(V, 0) & (~$lesseq($sum(N, $product(-1, V)), 0)))) | ((~(tb2t3(get(bool, int, t2tb4(Deja_vu), t2tb(V))) = true1)) & ![J: $int] : ((~($sum(tb2t(get(int, int, t2tb2(A1), t2tb(J))), $product(-1, V)) = 0)) | (~($greatereq(J, 0) & (~$lesseq($sum(N, $product(-1, J)), -2)))))) | ((tb2t3(get(bool, int, t2tb4(Deja_vu), t2tb(V))) = true1) & ?[J: $int] : ($greatereq(J, 0) & (~$lesseq($sum(N, $product(-1, J)), -2)) & ($sum(tb2t(get(int, int, t2tb2(A1), t2tb(J))), $product(-1, V)) = 0)))) & ((~(V1 = -1)) | ![V: $int] : ((~appear_twice1(tb2t1(mk_array1(int, A, t2tb2(A1))), V, $sum(2, N))) | (~($greatereq(V, 0) & (~$lesseq($sum(N, $product(-1, V)), 0)))))) & ((~(V2 = -1)) | ![V: $int] : ((~appear_twice1(tb2t1(mk_array1(int, A, t2tb2(A1))), V, $sum(2, N))) | (~($greatereq(V, 0) & (~$lesseq($sum(N, $product(-1, V)), 0)))) | ($sum(V, $product(-1, V1)) = 0))))) | appear_twice1(tb2t1(mk_array1(int, A, t2tb2(A1))), V1, $sum(2, N))))),
% 0.22/0.50 inference(modus_ponens,[status(thm)],[61, 54])).
% 0.22/0.50 tff(63,plain,
% 0.22/0.50 (~![A: $int, A1: map_int_int, N: $int] : ((~$greatereq(N, 0)) | (~$greatereq(N, -1)) | (~($greatereq(A, 0) & ($sum(A, $product(-1, N)) = 2) & $greatereq(N, 2) & ![I: $int] : ((~($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, A)), 0)))) | ($greatereq(tb2t(get(int, int, t2tb2(A1), t2tb(I))), 0) & (~$lesseq($sum(N, $product(-1, tb2t(get(int, int, t2tb2(A1), t2tb(I))))), 0)))) & ?[V1: $int] : (appear_twice1(tb2t1(mk_array1(int, A, t2tb2(A1))), V1, $sum(2, N)) & ?[V2: $int] : (appear_twice1(tb2t1(mk_array1(int, A, t2tb2(A1))), V2, $sum(2, N)) & (~($sum(V1, $product(-1, V2)) = 0)))))) | ![V2: $int, V1: $int, Deja_vu: map_int_bool] : ((~(((~(V1 = -1)) | (V2 = -1)) & ((V1 = -1) | appear_twice1(tb2t1(mk_array1(int, A, t2tb2(A1))), V1, $sum(2, N))) & ((V2 = -1) | (appear_twice1(tb2t1(mk_array1(int, A, t2tb2(A1))), V2, $sum(2, N)) & (~($sum(V2, $product(-1, V1)) = 0)))) & ![V: $int] : ((~($greatereq(V, 0) & (~$greatereq($sum(V, $product(-1, N)), 0)))) | ((tb2t3(get(bool, int, t2tb4(Deja_vu), t2tb(V))) = true1) & ?[J: $int] : ($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, N)), 2)) & ($sum(V, $product(-1, tb2t(get(int, int, t2tb2(A1), t2tb(J))))) = 0))) | ((~(tb2t3(get(bool, int, t2tb4(Deja_vu), t2tb(V))) = true1)) & ![J: $int] : ((~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, N)), 2)))) | (~($sum(V, $product(-1, tb2t(get(int, int, t2tb2(A1), t2tb(J))))) = 0))))) & ((~(V1 = -1)) | ![V: $int] : ((~appear_twice1(tb2t1(mk_array1(int, A, t2tb2(A1))), V, $sum(2, N))) | (~($greatereq(V, 0) & (~$greatereq($sum(V, $product(-1, N)), 0)))))) & ((~(V2 = -1)) | ![V: $int] : ((~appear_twice1(tb2t1(mk_array1(int, A, t2tb2(A1))), V, $sum(2, N))) | (~($greatereq(V, 0) & (~$greatereq($sum(V, $product(-1, N)), 0)))) | ($sum(V1, $product(-1, V)) = 0))))) | appear_twice1(tb2t1(mk_array1(int, A, t2tb2(A1))), V1, $sum(2, N))))),
% 0.22/0.50 inference(modus_ponens,[status(thm)],[62, 53])).
% 0.22/0.50 tff(64,plain,
% 0.22/0.50 (~![A: $int, A1: map_int_int, N: $int] : ((~$greatereq(N, 0)) | (~$greatereq(N, -1)) | (~($greatereq(A, 0) & ($sum(A, $product(-1, N)) = 2) & $greatereq(N, 2) & ![I: $int] : ((~($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, A)), 0)))) | ($greatereq(tb2t(get(int, int, t2tb2(A1), t2tb(I))), 0) & (~$lesseq($sum(N, $product(-1, tb2t(get(int, int, t2tb2(A1), t2tb(I))))), 0)))) & ?[V1: $int] : (appear_twice1(tb2t1(mk_array1(int, A, t2tb2(A1))), V1, $sum(2, N)) & ?[V2: $int] : (appear_twice1(tb2t1(mk_array1(int, A, t2tb2(A1))), V2, $sum(2, N)) & (~($sum(V1, $product(-1, V2)) = 0)))))) | ![V2: $int, V1: $int, Deja_vu: map_int_bool] : ((~(((~(V1 = -1)) | (V2 = -1)) & ((V1 = -1) | appear_twice1(tb2t1(mk_array1(int, A, t2tb2(A1))), V1, $sum(2, N))) & ((V2 = -1) | (appear_twice1(tb2t1(mk_array1(int, A, t2tb2(A1))), V2, $sum(2, N)) & (~($sum(V2, $product(-1, V1)) = 0)))) & ![V: $int] : ((~($greatereq(V, 0) & (~$greatereq($sum(V, $product(-1, N)), 0)))) | ((tb2t3(get(bool, int, t2tb4(Deja_vu), t2tb(V))) = true1) & ?[J: $int] : ($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, N)), 2)) & ($sum(V, $product(-1, tb2t(get(int, int, t2tb2(A1), t2tb(J))))) = 0))) | ((~(tb2t3(get(bool, int, t2tb4(Deja_vu), t2tb(V))) = true1)) & ![J: $int] : ((~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, N)), 2)))) | (~($sum(V, $product(-1, tb2t(get(int, int, t2tb2(A1), t2tb(J))))) = 0))))) & ((~(V1 = -1)) | ![V: $int] : ((~appear_twice1(tb2t1(mk_array1(int, A, t2tb2(A1))), V, $sum(2, N))) | (~($greatereq(V, 0) & (~$greatereq($sum(V, $product(-1, N)), 0)))))) & ((~(V2 = -1)) | ![V: $int] : ((~appear_twice1(tb2t1(mk_array1(int, A, t2tb2(A1))), V, $sum(2, N))) | (~($greatereq(V, 0) & (~$greatereq($sum(V, $product(-1, N)), 0)))) | ($sum(V1, $product(-1, V)) = 0))))) | appear_twice1(tb2t1(mk_array1(int, A, t2tb2(A1))), V1, $sum(2, N))))),
% 0.22/0.50 inference(modus_ponens,[status(thm)],[63, 52])).
% 0.22/0.50 tff(65,plain,
% 0.22/0.50 (~![A: $int, A1: map_int_int, N: $int] : ((~$greatereq(N, 0)) | (~$greatereq(N, -1)) | (~($greatereq(A, 0) & ($sum(A, $product(-1, N)) = 2) & $greatereq(N, 2) & ![I: $int] : ((~($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, A)), 0)))) | ($greatereq(tb2t(get(int, int, t2tb2(A1), t2tb(I))), 0) & (~$lesseq($sum(N, $product(-1, tb2t(get(int, int, t2tb2(A1), t2tb(I))))), 0)))) & ?[V1: $int] : (appear_twice1(tb2t1(mk_array1(int, A, t2tb2(A1))), V1, $sum(2, N)) & ?[V2: $int] : (appear_twice1(tb2t1(mk_array1(int, A, t2tb2(A1))), V2, $sum(2, N)) & (~($sum(V1, $product(-1, V2)) = 0)))))) | ![V2: $int, V1: $int, Deja_vu: map_int_bool] : ((~(((~(V1 = -1)) | (V2 = -1)) & ((V1 = -1) | appear_twice1(tb2t1(mk_array1(int, A, t2tb2(A1))), V1, $sum(2, N))) & ((V2 = -1) | (appear_twice1(tb2t1(mk_array1(int, A, t2tb2(A1))), V2, $sum(2, N)) & (~($sum(V2, $product(-1, V1)) = 0)))) & ![V: $int] : ((~($greatereq(V, 0) & (~$greatereq($sum(V, $product(-1, N)), 0)))) | ((tb2t3(get(bool, int, t2tb4(Deja_vu), t2tb(V))) = true1) & ?[J: $int] : ($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, N)), 2)) & ($sum(V, $product(-1, tb2t(get(int, int, t2tb2(A1), t2tb(J))))) = 0))) | ((~(tb2t3(get(bool, int, t2tb4(Deja_vu), t2tb(V))) = true1)) & ![J: $int] : ((~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, N)), 2)))) | (~($sum(V, $product(-1, tb2t(get(int, int, t2tb2(A1), t2tb(J))))) = 0))))) & ((~(V1 = -1)) | ![V: $int] : ((~appear_twice1(tb2t1(mk_array1(int, A, t2tb2(A1))), V, $sum(2, N))) | (~($greatereq(V, 0) & (~$greatereq($sum(V, $product(-1, N)), 0)))))) & ((~(V2 = -1)) | ![V: $int] : ((~appear_twice1(tb2t1(mk_array1(int, A, t2tb2(A1))), V, $sum(2, N))) | (~($greatereq(V, 0) & (~$greatereq($sum(V, $product(-1, N)), 0)))) | ($sum(V1, $product(-1, V)) = 0))))) | appear_twice1(tb2t1(mk_array1(int, A, t2tb2(A1))), V1, $sum(2, N))))),
% 0.22/0.50 inference(modus_ponens,[status(thm)],[64, 52])).
% 0.22/0.50 tff(66,plain,
% 0.22/0.50 ($greatereq(N!2, 0) & $greatereq(N!2, -1) & $greatereq(A!4, 0) & ($sum(N!2, $product(-1, A!4)) = -2) & $greatereq(N!2, 2) & ![I: $int] : ((~($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, A!4)), 0)))) | ($greatereq(tb2t(get(int, int, t2tb2(A1!3), t2tb(I))), 0) & (~$lesseq($sum(N!2, $product(-1, tb2t(get(int, int, t2tb2(A1!3), t2tb(I))))), 0)))) & appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V1!5, $sum(2, N!2)) & appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V2!6, $sum(2, N!2)) & (~($sum(V1!5, $product(-1, V2!6)) = 0)) & ((~(V1!8 = -1)) | (V2!9 = -1)) & ((V1!8 = -1) | appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V1!8, $sum(2, N!2))) & ((V2!9 = -1) | (appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V2!9, $sum(2, N!2)) & (~($sum(V1!8, $product(-1, V2!9)) = 0)))) & ![V: $int] : ((~($greatereq(V, 0) & (~$greatereq($sum(V, $product(-1, N!2)), 0)))) | ((~(tb2t3(get(bool, int, t2tb4(Deja_vu!7), t2tb(V))) = true1)) & ![J: $int] : ((~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, N!2)), 2)))) | (~($sum(V, $product(-1, tb2t(get(int, int, t2tb2(A1!3), t2tb(J))))) = 0)))) | ((tb2t3(get(bool, int, t2tb4(Deja_vu!7), t2tb(V))) = true1) & $greatereq(tptp_fun_J_10(V), 0) & (~$lesseq($sum(N!2, $product(-1, tptp_fun_J_10(V))), -2)) & ($sum(V, $product(-1, tb2t(get(int, int, t2tb2(A1!3), t2tb(tptp_fun_J_10(V)))))) = 0))) & ((~(V1!8 = -1)) | ![V: $int] : ((~appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V, $sum(2, N!2))) | (~($greatereq(V, 0) & (~$greatereq($sum(V, $product(-1, N!2)), 0)))))) & ((~(V2!9 = -1)) | ![V: $int] : ((~appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V, $sum(2, N!2))) | (~($greatereq(V, 0) & (~$greatereq($sum(V, $product(-1, N!2)), 0)))) | ($sum(V, $product(-1, V1!8)) = 0))) & (~appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V1!8, $sum(2, N!2)))),
% 0.22/0.50 inference(modus_ponens,[status(thm)],[65, 51])).
% 0.22/0.50 tff(67,plain,
% 0.22/0.50 (appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V2!6, $sum(2, N!2))),
% 0.22/0.50 inference(and_elim,[status(thm)],[66])).
% 0.22/0.50 tff(68,plain,
% 0.22/0.50 ((~((~appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V2!6, $sum(2, N!2))) | (~(($sum(tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), $product(-1, tptp_fun_J_1($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))) = 0) | (~$greatereq(tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), 0)) | (~($sum(V2!6, $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))))) = 0)) | (~$greatereq(tptp_fun_J_1($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), 0)) | (~($sum(V2!6, $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), tptp_fun_J_1($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))))) = 0)) | $lesseq($sum(N!2, $product(-1, tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))), -2) | $lesseq($sum(N!2, $product(-1, tptp_fun_J_1($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))), -2))))) | (~appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V2!6, $sum(2, N!2))) | (~(($sum(tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), $product(-1, tptp_fun_J_1($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))) = 0) | (~$greatereq(tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), 0)) | (~($sum(V2!6, $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))))) = 0)) | (~$greatereq(tptp_fun_J_1($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), 0)) | (~($sum(V2!6, $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), tptp_fun_J_1($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))))) = 0)) | $lesseq($sum(N!2, $product(-1, tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))), -2) | $lesseq($sum(N!2, $product(-1, tptp_fun_J_1($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))), -2)))),
% 0.22/0.50 inference(tautology,[status(thm)],[])).
% 0.22/0.50 tff(69,plain,
% 0.22/0.50 ((~((~appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V2!6, $sum(2, N!2))) | (~(($sum(tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), $product(-1, tptp_fun_J_1($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))) = 0) | (~$greatereq(tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), 0)) | (~($sum(V2!6, $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))))) = 0)) | (~$greatereq(tptp_fun_J_1($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), 0)) | (~($sum(V2!6, $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), tptp_fun_J_1($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))))) = 0)) | $lesseq($sum(N!2, $product(-1, tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))), -2) | $lesseq($sum(N!2, $product(-1, tptp_fun_J_1($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))), -2))))) | (~(($sum(tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), $product(-1, tptp_fun_J_1($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))) = 0) | (~$greatereq(tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), 0)) | (~($sum(V2!6, $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))))) = 0)) | (~$greatereq(tptp_fun_J_1($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), 0)) | (~($sum(V2!6, $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), tptp_fun_J_1($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))))) = 0)) | $lesseq($sum(N!2, $product(-1, tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))), -2) | $lesseq($sum(N!2, $product(-1, tptp_fun_J_1($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))), -2)))),
% 0.22/0.50 inference(unit_resolution,[status(thm)],[68, 67])).
% 0.22/0.50 tff(70,plain,
% 0.22/0.50 (~(($sum(tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), $product(-1, tptp_fun_J_1($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))) = 0) | (~$greatereq(tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), 0)) | (~($sum(V2!6, $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))))) = 0)) | (~$greatereq(tptp_fun_J_1($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), 0)) | (~($sum(V2!6, $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), tptp_fun_J_1($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))))) = 0)) | $lesseq($sum(N!2, $product(-1, tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))), -2) | $lesseq($sum(N!2, $product(-1, tptp_fun_J_1($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))), -2))),
% 0.22/0.50 inference(unit_resolution,[status(thm)],[69, 34])).
% 0.22/0.50 tff(71,plain,
% 0.22/0.50 ((($sum(tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), $product(-1, tptp_fun_J_1($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))) = 0) | (~$greatereq(tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), 0)) | (~($sum(V2!6, $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))))) = 0)) | (~$greatereq(tptp_fun_J_1($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), 0)) | (~($sum(V2!6, $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), tptp_fun_J_1($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))))) = 0)) | $lesseq($sum(N!2, $product(-1, tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))), -2) | $lesseq($sum(N!2, $product(-1, tptp_fun_J_1($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))), -2)) | (~$lesseq($sum(N!2, $product(-1, tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))), -2))),
% 0.22/0.50 inference(tautology,[status(thm)],[])).
% 0.22/0.50 tff(72,plain,
% 0.22/0.50 (~$lesseq($sum(N!2, $product(-1, tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))), -2)),
% 0.22/0.50 inference(unit_resolution,[status(thm)],[71, 70])).
% 0.22/0.50 tff(73,plain,
% 0.22/0.50 ($sum(N!2, $product(-1, A!4)) = -2),
% 0.22/0.50 inference(and_elim,[status(thm)],[66])).
% 0.22/0.50 tff(74,plain,
% 0.22/0.50 ((~($sum(N!2, $product(-1, A!4)) = -2)) | $lesseq($sum(N!2, $product(-1, A!4)), -2)),
% 0.22/0.50 inference(theory_lemma,[status(thm)],[])).
% 0.22/0.50 tff(75,plain,
% 0.22/0.50 ($lesseq($sum(N!2, $product(-1, A!4)), -2)),
% 0.22/0.50 inference(unit_resolution,[status(thm)],[74, 73])).
% 0.22/0.50 tff(76,assumption,(~((~$greatereq(tb2t(get(int, int, t2tb2(A1!3), t2tb(tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3))))))), 0)) | $lesseq($sum(N!2, $product(-1, tb2t(get(int, int, t2tb2(A1!3), t2tb(tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3))))))))), 0))), introduced(assumption)).
% 0.22/0.50 tff(77,plain,
% 0.22/0.50 (((~$greatereq(tb2t(get(int, int, t2tb2(A1!3), t2tb(tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3))))))), 0)) | $lesseq($sum(N!2, $product(-1, tb2t(get(int, int, t2tb2(A1!3), t2tb(tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3))))))))), 0)) | (~$lesseq($sum(N!2, $product(-1, tb2t(get(int, int, t2tb2(A1!3), t2tb(tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3))))))))), 0))),
% 0.22/0.50 inference(tautology,[status(thm)],[])).
% 0.22/0.50 tff(78,plain,
% 0.22/0.50 (~$lesseq($sum(N!2, $product(-1, tb2t(get(int, int, t2tb2(A1!3), t2tb(tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3))))))))), 0)),
% 0.22/0.50 inference(unit_resolution,[status(thm)],[77, 76])).
% 0.22/0.50 tff(79,plain,
% 0.22/0.50 ((($sum(tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), $product(-1, tptp_fun_J_1($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))) = 0) | (~$greatereq(tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), 0)) | (~($sum(V2!6, $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))))) = 0)) | (~$greatereq(tptp_fun_J_1($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), 0)) | (~($sum(V2!6, $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), tptp_fun_J_1($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))))) = 0)) | $lesseq($sum(N!2, $product(-1, tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))), -2) | $lesseq($sum(N!2, $product(-1, tptp_fun_J_1($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))), -2)) | ($sum(V2!6, $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))))) = 0)),
% 0.22/0.51 inference(tautology,[status(thm)],[])).
% 0.22/0.51 tff(80,plain,
% 0.22/0.51 ($sum(V2!6, $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))))) = 0),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[79, 70])).
% 0.22/0.51 tff(81,plain,
% 0.22/0.51 ((~($sum(V2!6, $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))))) = 0)) | $lesseq($sum(V2!6, $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))))), 0)),
% 0.22/0.51 inference(theory_lemma,[status(thm)],[])).
% 0.22/0.51 tff(82,plain,
% 0.22/0.51 ($lesseq($sum(V2!6, $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))))), 0)),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[81, 80])).
% 0.22/0.51 tff(83,plain,
% 0.22/0.51 ((~($sum(V2!6, $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))))) = 0)) | $greatereq($sum(V2!6, $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))))), 0)),
% 0.22/0.51 inference(theory_lemma,[status(thm)],[])).
% 0.22/0.51 tff(84,plain,
% 0.22/0.51 ($greatereq($sum(V2!6, $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))))), 0)),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[83, 80])).
% 0.22/0.51 tff(85,plain,
% 0.22/0.51 (![J: uni] : (t2tb1(tb2t1(J)) = J) <=> ![J: uni] : (t2tb1(tb2t1(J)) = J)),
% 0.22/0.51 inference(rewrite,[status(thm)],[])).
% 0.22/0.51 tff(86,plain,
% 0.22/0.51 (![J: uni] : (t2tb1(tb2t1(J)) = J) <=> ![J: uni] : (t2tb1(tb2t1(J)) = J)),
% 0.22/0.51 inference(rewrite,[status(thm)],[])).
% 0.22/0.51 tff(87,axiom,(![J: uni] : (t2tb1(tb2t1(J)) = J)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bridgeR1')).
% 0.22/0.51 tff(88,plain,
% 0.22/0.51 (![J: uni] : (t2tb1(tb2t1(J)) = J)),
% 0.22/0.51 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.22/0.51 tff(89,plain,(
% 0.22/0.51 ![J: uni] : (t2tb1(tb2t1(J)) = J)),
% 0.22/0.51 inference(skolemize,[status(sab)],[88])).
% 0.22/0.51 tff(90,plain,
% 0.22/0.51 (![J: uni] : (t2tb1(tb2t1(J)) = J)),
% 0.22/0.51 inference(modus_ponens,[status(thm)],[89, 85])).
% 0.22/0.51 tff(91,plain,
% 0.22/0.51 ((~![J: uni] : (t2tb1(tb2t1(J)) = J)) | (t2tb1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))) = mk_array1(int, A!4, t2tb2(A1!3)))),
% 0.22/0.51 inference(quant_inst,[status(thm)],[])).
% 0.22/0.51 tff(92,plain,
% 0.22/0.51 (t2tb1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))) = mk_array1(int, A!4, t2tb2(A1!3))),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[91, 90])).
% 0.22/0.51 tff(93,plain,
% 0.22/0.51 (mk_array1(int, A!4, t2tb2(A1!3)) = t2tb1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))))),
% 0.22/0.51 inference(symmetry,[status(thm)],[92])).
% 0.22/0.51 tff(94,plain,
% 0.22/0.51 (get2(int, mk_array1(int, A!4, t2tb2(A1!3)), tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3))))) = get2(int, t2tb1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))),
% 0.22/0.51 inference(monotonicity,[status(thm)],[93])).
% 0.22/0.51 tff(95,plain,
% 0.22/0.51 (^[A: ty, A1: uni, I: $int] : refl((get2(A, A1, I) = get(A, int, elts(A, A1), t2tb(I))) <=> (get2(A, A1, I) = get(A, int, elts(A, A1), t2tb(I))))),
% 0.22/0.51 inference(bind,[status(th)],[])).
% 0.22/0.51 tff(96,plain,
% 0.22/0.51 (![A: ty, A1: uni, I: $int] : (get2(A, A1, I) = get(A, int, elts(A, A1), t2tb(I))) <=> ![A: ty, A1: uni, I: $int] : (get2(A, A1, I) = get(A, int, elts(A, A1), t2tb(I)))),
% 0.22/0.51 inference(quant_intro,[status(thm)],[95])).
% 0.22/0.51 tff(97,plain,
% 0.22/0.51 (![A: ty, A1: uni, I: $int] : (get2(A, A1, I) = get(A, int, elts(A, A1), t2tb(I))) <=> ![A: ty, A1: uni, I: $int] : (get2(A, A1, I) = get(A, int, elts(A, A1), t2tb(I)))),
% 0.22/0.51 inference(rewrite,[status(thm)],[])).
% 0.22/0.51 tff(98,axiom,(![A: ty, A1: uni, I: $int] : (get2(A, A1, I) = get(A, int, elts(A, A1), t2tb(I)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','get_def')).
% 0.22/0.51 tff(99,plain,
% 0.22/0.51 (![A: ty, A1: uni, I: $int] : (get2(A, A1, I) = get(A, int, elts(A, A1), t2tb(I)))),
% 0.22/0.51 inference(modus_ponens,[status(thm)],[98, 97])).
% 0.22/0.51 tff(100,plain,(
% 0.22/0.51 ![A: ty, A1: uni, I: $int] : (get2(A, A1, I) = get(A, int, elts(A, A1), t2tb(I)))),
% 0.22/0.51 inference(skolemize,[status(sab)],[99])).
% 0.22/0.51 tff(101,plain,
% 0.22/0.51 (![A: ty, A1: uni, I: $int] : (get2(A, A1, I) = get(A, int, elts(A, A1), t2tb(I)))),
% 0.22/0.51 inference(modus_ponens,[status(thm)],[100, 96])).
% 0.22/0.51 tff(102,plain,
% 0.22/0.51 ((~![A: ty, A1: uni, I: $int] : (get2(A, A1, I) = get(A, int, elts(A, A1), t2tb(I)))) | (get2(int, mk_array1(int, A!4, t2tb2(A1!3)), tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3))))) = get(int, int, elts(int, mk_array1(int, A!4, t2tb2(A1!3))), t2tb(tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))))),
% 0.22/0.51 inference(quant_inst,[status(thm)],[])).
% 0.22/0.51 tff(103,plain,
% 0.22/0.51 (get2(int, mk_array1(int, A!4, t2tb2(A1!3)), tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3))))) = get(int, int, elts(int, mk_array1(int, A!4, t2tb2(A1!3))), t2tb(tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3))))))),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[102, 101])).
% 0.22/0.51 tff(104,plain,
% 0.22/0.51 (get(int, int, elts(int, mk_array1(int, A!4, t2tb2(A1!3))), t2tb(tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))) = get2(int, mk_array1(int, A!4, t2tb2(A1!3)), tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))),
% 0.22/0.51 inference(symmetry,[status(thm)],[103])).
% 0.22/0.51 tff(105,plain,
% 0.22/0.51 (^[X: map_int_int] : refl(sort1(map(int, int), t2tb2(X)) <=> sort1(map(int, int), t2tb2(X)))),
% 0.22/0.51 inference(bind,[status(th)],[])).
% 0.22/0.51 tff(106,plain,
% 0.22/0.51 (![X: map_int_int] : sort1(map(int, int), t2tb2(X)) <=> ![X: map_int_int] : sort1(map(int, int), t2tb2(X))),
% 0.22/0.51 inference(quant_intro,[status(thm)],[105])).
% 0.22/0.51 tff(107,plain,
% 0.22/0.51 (![X: map_int_int] : sort1(map(int, int), t2tb2(X)) <=> ![X: map_int_int] : sort1(map(int, int), t2tb2(X))),
% 0.22/0.51 inference(rewrite,[status(thm)],[])).
% 0.22/0.51 tff(108,axiom,(![X: map_int_int] : sort1(map(int, int), t2tb2(X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t2tb_sort2')).
% 0.22/0.51 tff(109,plain,
% 0.22/0.51 (![X: map_int_int] : sort1(map(int, int), t2tb2(X))),
% 0.22/0.51 inference(modus_ponens,[status(thm)],[108, 107])).
% 0.22/0.51 tff(110,plain,(
% 0.22/0.51 ![X: map_int_int] : sort1(map(int, int), t2tb2(X))),
% 0.22/0.51 inference(skolemize,[status(sab)],[109])).
% 0.22/0.51 tff(111,plain,
% 0.22/0.51 (![X: map_int_int] : sort1(map(int, int), t2tb2(X))),
% 0.22/0.51 inference(modus_ponens,[status(thm)],[110, 106])).
% 0.22/0.51 tff(112,plain,
% 0.22/0.51 ((~![X: map_int_int] : sort1(map(int, int), t2tb2(X))) | sort1(map(int, int), t2tb2(A1!3))),
% 0.22/0.51 inference(quant_inst,[status(thm)],[])).
% 0.22/0.51 tff(113,plain,
% 0.22/0.51 (sort1(map(int, int), t2tb2(A1!3))),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[112, 111])).
% 0.22/0.51 tff(114,plain,
% 0.22/0.51 (^[A: ty, U: $int, U1: uni] : refl(((~sort1(map(int, A), U1)) | (elts(A, mk_array1(A, U, U1)) = U1)) <=> ((~sort1(map(int, A), U1)) | (elts(A, mk_array1(A, U, U1)) = U1)))),
% 0.22/0.51 inference(bind,[status(th)],[])).
% 0.22/0.51 tff(115,plain,
% 0.22/0.51 (![A: ty, U: $int, U1: uni] : ((~sort1(map(int, A), U1)) | (elts(A, mk_array1(A, U, U1)) = U1)) <=> ![A: ty, U: $int, U1: uni] : ((~sort1(map(int, A), U1)) | (elts(A, mk_array1(A, U, U1)) = U1))),
% 0.22/0.51 inference(quant_intro,[status(thm)],[114])).
% 0.22/0.51 tff(116,plain,
% 0.22/0.51 (![A: ty, U: $int, U1: uni] : ((~sort1(map(int, A), U1)) | (elts(A, mk_array1(A, U, U1)) = U1)) <=> ![A: ty, U: $int, U1: uni] : ((~sort1(map(int, A), U1)) | (elts(A, mk_array1(A, U, U1)) = U1))),
% 0.22/0.51 inference(rewrite,[status(thm)],[])).
% 0.22/0.51 tff(117,plain,
% 0.22/0.51 (^[A: ty, U: $int, U1: uni] : rewrite((sort1(map(int, A), U1) => (elts(A, mk_array1(A, U, U1)) = U1)) <=> ((~sort1(map(int, A), U1)) | (elts(A, mk_array1(A, U, U1)) = U1)))),
% 0.22/0.51 inference(bind,[status(th)],[])).
% 0.22/0.51 tff(118,plain,
% 0.22/0.51 (![A: ty, U: $int, U1: uni] : (sort1(map(int, A), U1) => (elts(A, mk_array1(A, U, U1)) = U1)) <=> ![A: ty, U: $int, U1: uni] : ((~sort1(map(int, A), U1)) | (elts(A, mk_array1(A, U, U1)) = U1))),
% 0.22/0.51 inference(quant_intro,[status(thm)],[117])).
% 0.22/0.51 tff(119,axiom,(![A: ty, U: $int, U1: uni] : (sort1(map(int, A), U1) => (elts(A, mk_array1(A, U, U1)) = U1))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','elts_def1')).
% 0.22/0.51 tff(120,plain,
% 0.22/0.51 (![A: ty, U: $int, U1: uni] : ((~sort1(map(int, A), U1)) | (elts(A, mk_array1(A, U, U1)) = U1))),
% 0.22/0.51 inference(modus_ponens,[status(thm)],[119, 118])).
% 0.22/0.51 tff(121,plain,
% 0.22/0.51 (![A: ty, U: $int, U1: uni] : ((~sort1(map(int, A), U1)) | (elts(A, mk_array1(A, U, U1)) = U1))),
% 0.22/0.51 inference(modus_ponens,[status(thm)],[120, 116])).
% 0.22/0.51 tff(122,plain,(
% 0.22/0.51 ![A: ty, U: $int, U1: uni] : ((~sort1(map(int, A), U1)) | (elts(A, mk_array1(A, U, U1)) = U1))),
% 0.22/0.51 inference(skolemize,[status(sab)],[121])).
% 0.22/0.51 tff(123,plain,
% 0.22/0.51 (![A: ty, U: $int, U1: uni] : ((~sort1(map(int, A), U1)) | (elts(A, mk_array1(A, U, U1)) = U1))),
% 0.22/0.51 inference(modus_ponens,[status(thm)],[122, 115])).
% 0.22/0.51 tff(124,plain,
% 0.22/0.51 (((~![A: ty, U: $int, U1: uni] : ((~sort1(map(int, A), U1)) | (elts(A, mk_array1(A, U, U1)) = U1))) | ((~sort1(map(int, int), t2tb2(A1!3))) | (elts(int, mk_array1(int, A!4, t2tb2(A1!3))) = t2tb2(A1!3)))) <=> ((~![A: ty, U: $int, U1: uni] : ((~sort1(map(int, A), U1)) | (elts(A, mk_array1(A, U, U1)) = U1))) | (~sort1(map(int, int), t2tb2(A1!3))) | (elts(int, mk_array1(int, A!4, t2tb2(A1!3))) = t2tb2(A1!3)))),
% 0.22/0.51 inference(rewrite,[status(thm)],[])).
% 0.22/0.51 tff(125,plain,
% 0.22/0.51 ((~![A: ty, U: $int, U1: uni] : ((~sort1(map(int, A), U1)) | (elts(A, mk_array1(A, U, U1)) = U1))) | ((~sort1(map(int, int), t2tb2(A1!3))) | (elts(int, mk_array1(int, A!4, t2tb2(A1!3))) = t2tb2(A1!3)))),
% 0.22/0.51 inference(quant_inst,[status(thm)],[])).
% 0.22/0.51 tff(126,plain,
% 0.22/0.51 ((~![A: ty, U: $int, U1: uni] : ((~sort1(map(int, A), U1)) | (elts(A, mk_array1(A, U, U1)) = U1))) | (~sort1(map(int, int), t2tb2(A1!3))) | (elts(int, mk_array1(int, A!4, t2tb2(A1!3))) = t2tb2(A1!3))),
% 0.22/0.51 inference(modus_ponens,[status(thm)],[125, 124])).
% 0.22/0.51 tff(127,plain,
% 0.22/0.51 ((~sort1(map(int, int), t2tb2(A1!3))) | (elts(int, mk_array1(int, A!4, t2tb2(A1!3))) = t2tb2(A1!3))),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[126, 123])).
% 0.22/0.51 tff(128,plain,
% 0.22/0.51 (elts(int, mk_array1(int, A!4, t2tb2(A1!3))) = t2tb2(A1!3)),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[127, 113])).
% 0.22/0.51 tff(129,plain,
% 0.22/0.51 (t2tb2(A1!3) = elts(int, mk_array1(int, A!4, t2tb2(A1!3)))),
% 0.22/0.51 inference(symmetry,[status(thm)],[128])).
% 0.22/0.51 tff(130,plain,
% 0.22/0.51 (get(int, int, t2tb2(A1!3), t2tb(tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))) = get(int, int, elts(int, mk_array1(int, A!4, t2tb2(A1!3))), t2tb(tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3))))))),
% 0.22/0.51 inference(monotonicity,[status(thm)],[129])).
% 0.22/0.51 tff(131,plain,
% 0.22/0.51 (get(int, int, t2tb2(A1!3), t2tb(tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))) = get2(int, t2tb1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))),
% 0.22/0.51 inference(transitivity,[status(thm)],[130, 104, 94])).
% 0.22/0.51 tff(132,plain,
% 0.22/0.51 (tb2t(get(int, int, t2tb2(A1!3), t2tb(tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3))))))) = tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3))))))),
% 0.22/0.51 inference(monotonicity,[status(thm)],[131])).
% 0.22/0.51 tff(133,plain,
% 0.22/0.51 (tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))) = tb2t(get(int, int, t2tb2(A1!3), t2tb(tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))))),
% 0.22/0.51 inference(symmetry,[status(thm)],[132])).
% 0.22/0.51 tff(134,plain,
% 0.22/0.51 ((~(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))) = tb2t(get(int, int, t2tb2(A1!3), t2tb(tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3))))))))) | $greatereq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))), $product(-1, tb2t(get(int, int, t2tb2(A1!3), t2tb(tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3))))))))), 0)),
% 0.22/0.51 inference(theory_lemma,[status(thm)],[])).
% 0.22/0.51 tff(135,plain,
% 0.22/0.51 ($greatereq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))), $product(-1, tb2t(get(int, int, t2tb2(A1!3), t2tb(tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3))))))))), 0)),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[134, 133])).
% 0.22/0.51 tff(136,plain,
% 0.22/0.51 (((~$greatereq(tb2t(get(int, int, t2tb2(A1!3), t2tb(tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3))))))), 0)) | $lesseq($sum(N!2, $product(-1, tb2t(get(int, int, t2tb2(A1!3), t2tb(tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3))))))))), 0)) | $greatereq(tb2t(get(int, int, t2tb2(A1!3), t2tb(tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3))))))), 0)),
% 0.22/0.51 inference(tautology,[status(thm)],[])).
% 0.22/0.51 tff(137,plain,
% 0.22/0.51 ($greatereq(tb2t(get(int, int, t2tb2(A1!3), t2tb(tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3))))))), 0)),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[136, 76])).
% 0.22/0.51 tff(138,plain,
% 0.22/0.51 ((~$lesseq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))), -1)) | (~$greatereq(tb2t(get(int, int, t2tb2(A1!3), t2tb(tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3))))))), 0)) | (~$greatereq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))), $product(-1, tb2t(get(int, int, t2tb2(A1!3), t2tb(tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3))))))))), 0))),
% 0.22/0.51 inference(theory_lemma,[status(thm)],[])).
% 0.22/0.51 tff(139,plain,
% 0.22/0.51 (~$lesseq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))), -1)),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[138, 137, 135])).
% 0.22/0.51 tff(140,plain,
% 0.22/0.51 ($greatereq(V2!6, 0) | $lesseq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))), -1) | (~$greatereq($sum(V2!6, $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))))), 0))),
% 0.22/0.51 inference(theory_lemma,[status(thm)],[])).
% 0.22/0.51 tff(141,plain,
% 0.22/0.51 ($greatereq(V2!6, 0)),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[140, 139, 84])).
% 0.22/0.51 tff(142,plain,
% 0.22/0.51 (~appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V1!8, $sum(2, N!2))),
% 0.22/0.51 inference(and_elim,[status(thm)],[66])).
% 0.22/0.51 tff(143,plain,
% 0.22/0.51 ((V1!8 = -1) | appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V1!8, $sum(2, N!2))),
% 0.22/0.51 inference(and_elim,[status(thm)],[66])).
% 0.22/0.51 tff(144,plain,
% 0.22/0.51 (V1!8 = -1),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[143, 142])).
% 0.22/0.51 tff(145,plain,
% 0.22/0.51 (((~(V1!8 = -1)) | ![V: $int] : ((~$greatereq(V, 0)) | $greatereq($sum(V, $product(-1, N!2)), 0) | (~appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V, $sum(2, N!2))))) <=> ((~(V1!8 = -1)) | ![V: $int] : ((~$greatereq(V, 0)) | $greatereq($sum(V, $product(-1, N!2)), 0) | (~appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V, $sum(2, N!2)))))),
% 0.22/0.51 inference(rewrite,[status(thm)],[])).
% 0.22/0.51 tff(146,plain,
% 0.22/0.51 (((~(V1!8 = -1)) | ![V: $int] : ((~appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V, $sum(2, N!2))) | (~($greatereq(V, 0) & (~$greatereq($sum(V, $product(-1, N!2)), 0)))))) <=> ((~(V1!8 = -1)) | ![V: $int] : ((~$greatereq(V, 0)) | $greatereq($sum(V, $product(-1, N!2)), 0) | (~appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V, $sum(2, N!2)))))),
% 0.22/0.51 inference(rewrite,[status(thm)],[])).
% 0.22/0.51 tff(147,plain,
% 0.22/0.51 ((~(V1!8 = -1)) | ![V: $int] : ((~appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V, $sum(2, N!2))) | (~($greatereq(V, 0) & (~$greatereq($sum(V, $product(-1, N!2)), 0)))))),
% 0.22/0.51 inference(and_elim,[status(thm)],[66])).
% 0.22/0.51 tff(148,plain,
% 0.22/0.51 ((~(V1!8 = -1)) | ![V: $int] : ((~$greatereq(V, 0)) | $greatereq($sum(V, $product(-1, N!2)), 0) | (~appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V, $sum(2, N!2))))),
% 0.22/0.51 inference(modus_ponens,[status(thm)],[147, 146])).
% 0.22/0.51 tff(149,plain,
% 0.22/0.51 ((~(V1!8 = -1)) | ![V: $int] : ((~$greatereq(V, 0)) | $greatereq($sum(V, $product(-1, N!2)), 0) | (~appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V, $sum(2, N!2))))),
% 0.22/0.51 inference(modus_ponens,[status(thm)],[148, 145])).
% 0.22/0.51 tff(150,plain,
% 0.22/0.51 (![V: $int] : ((~$greatereq(V, 0)) | $greatereq($sum(V, $product(-1, N!2)), 0) | (~appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V, $sum(2, N!2))))),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[149, 144])).
% 0.22/0.51 tff(151,plain,
% 0.22/0.51 (((~![V: $int] : ((~$greatereq(V, 0)) | $greatereq($sum(V, $product(-1, N!2)), 0) | (~appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V, $sum(2, N!2))))) | ((~$greatereq(V2!6, 0)) | (~appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V2!6, $sum(2, N!2))) | $lesseq($sum(N!2, $product(-1, V2!6)), 0))) <=> ((~![V: $int] : ((~$greatereq(V, 0)) | $greatereq($sum(V, $product(-1, N!2)), 0) | (~appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V, $sum(2, N!2))))) | (~$greatereq(V2!6, 0)) | (~appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V2!6, $sum(2, N!2))) | $lesseq($sum(N!2, $product(-1, V2!6)), 0))),
% 0.22/0.51 inference(rewrite,[status(thm)],[])).
% 0.22/0.51 tff(152,plain,
% 0.22/0.51 (((~$greatereq(V2!6, 0)) | $lesseq($sum(N!2, $product(-1, V2!6)), 0) | (~appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V2!6, $sum(2, N!2)))) <=> ((~$greatereq(V2!6, 0)) | (~appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V2!6, $sum(2, N!2))) | $lesseq($sum(N!2, $product(-1, V2!6)), 0))),
% 0.22/0.51 inference(rewrite,[status(thm)],[])).
% 0.22/0.51 tff(153,plain,
% 0.22/0.51 ($greatereq($sum($product(-1, N!2), V2!6), 0) <=> $lesseq($sum(N!2, $product(-1, V2!6)), 0)),
% 0.22/0.51 inference(rewrite,[status(thm)],[])).
% 0.22/0.51 tff(154,plain,
% 0.22/0.51 ($sum(V2!6, $product(-1, N!2)) = $sum($product(-1, N!2), V2!6)),
% 0.22/0.51 inference(rewrite,[status(thm)],[])).
% 0.22/0.51 tff(155,plain,
% 0.22/0.51 ($greatereq($sum(V2!6, $product(-1, N!2)), 0) <=> $greatereq($sum($product(-1, N!2), V2!6), 0)),
% 0.22/0.51 inference(monotonicity,[status(thm)],[154])).
% 0.22/0.51 tff(156,plain,
% 0.22/0.51 ($greatereq($sum(V2!6, $product(-1, N!2)), 0) <=> $lesseq($sum(N!2, $product(-1, V2!6)), 0)),
% 0.22/0.51 inference(transitivity,[status(thm)],[155, 153])).
% 0.22/0.51 tff(157,plain,
% 0.22/0.51 (((~$greatereq(V2!6, 0)) | $greatereq($sum(V2!6, $product(-1, N!2)), 0) | (~appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V2!6, $sum(2, N!2)))) <=> ((~$greatereq(V2!6, 0)) | $lesseq($sum(N!2, $product(-1, V2!6)), 0) | (~appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V2!6, $sum(2, N!2))))),
% 0.22/0.51 inference(monotonicity,[status(thm)],[156])).
% 0.22/0.51 tff(158,plain,
% 0.22/0.51 (((~$greatereq(V2!6, 0)) | $greatereq($sum(V2!6, $product(-1, N!2)), 0) | (~appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V2!6, $sum(2, N!2)))) <=> ((~$greatereq(V2!6, 0)) | (~appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V2!6, $sum(2, N!2))) | $lesseq($sum(N!2, $product(-1, V2!6)), 0))),
% 0.22/0.51 inference(transitivity,[status(thm)],[157, 152])).
% 0.22/0.51 tff(159,plain,
% 0.22/0.51 (((~![V: $int] : ((~$greatereq(V, 0)) | $greatereq($sum(V, $product(-1, N!2)), 0) | (~appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V, $sum(2, N!2))))) | ((~$greatereq(V2!6, 0)) | $greatereq($sum(V2!6, $product(-1, N!2)), 0) | (~appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V2!6, $sum(2, N!2))))) <=> ((~![V: $int] : ((~$greatereq(V, 0)) | $greatereq($sum(V, $product(-1, N!2)), 0) | (~appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V, $sum(2, N!2))))) | ((~$greatereq(V2!6, 0)) | (~appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V2!6, $sum(2, N!2))) | $lesseq($sum(N!2, $product(-1, V2!6)), 0)))),
% 0.22/0.52 inference(monotonicity,[status(thm)],[158])).
% 0.22/0.52 tff(160,plain,
% 0.22/0.52 (((~![V: $int] : ((~$greatereq(V, 0)) | $greatereq($sum(V, $product(-1, N!2)), 0) | (~appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V, $sum(2, N!2))))) | ((~$greatereq(V2!6, 0)) | $greatereq($sum(V2!6, $product(-1, N!2)), 0) | (~appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V2!6, $sum(2, N!2))))) <=> ((~![V: $int] : ((~$greatereq(V, 0)) | $greatereq($sum(V, $product(-1, N!2)), 0) | (~appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V, $sum(2, N!2))))) | (~$greatereq(V2!6, 0)) | (~appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V2!6, $sum(2, N!2))) | $lesseq($sum(N!2, $product(-1, V2!6)), 0))),
% 0.22/0.52 inference(transitivity,[status(thm)],[159, 151])).
% 0.22/0.52 tff(161,plain,
% 0.22/0.52 ((~![V: $int] : ((~$greatereq(V, 0)) | $greatereq($sum(V, $product(-1, N!2)), 0) | (~appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V, $sum(2, N!2))))) | ((~$greatereq(V2!6, 0)) | $greatereq($sum(V2!6, $product(-1, N!2)), 0) | (~appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V2!6, $sum(2, N!2))))),
% 0.22/0.52 inference(quant_inst,[status(thm)],[])).
% 0.22/0.52 tff(162,plain,
% 0.22/0.52 ((~![V: $int] : ((~$greatereq(V, 0)) | $greatereq($sum(V, $product(-1, N!2)), 0) | (~appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V, $sum(2, N!2))))) | (~$greatereq(V2!6, 0)) | (~appear_twice1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3))), V2!6, $sum(2, N!2))) | $lesseq($sum(N!2, $product(-1, V2!6)), 0)),
% 0.22/0.52 inference(modus_ponens,[status(thm)],[161, 160])).
% 0.22/0.52 tff(163,plain,
% 0.22/0.52 ((~$greatereq(V2!6, 0)) | $lesseq($sum(N!2, $product(-1, V2!6)), 0)),
% 0.22/0.52 inference(unit_resolution,[status(thm)],[162, 67, 150])).
% 0.22/0.52 tff(164,plain,
% 0.22/0.52 ($lesseq($sum(N!2, $product(-1, V2!6)), 0)),
% 0.22/0.52 inference(unit_resolution,[status(thm)],[163, 141])).
% 0.22/0.52 tff(165,plain,
% 0.22/0.52 ((~(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))) = tb2t(get(int, int, t2tb2(A1!3), t2tb(tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3))))))))) | $lesseq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))), $product(-1, tb2t(get(int, int, t2tb2(A1!3), t2tb(tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3))))))))), 0)),
% 0.22/0.52 inference(theory_lemma,[status(thm)],[])).
% 0.22/0.52 tff(166,plain,
% 0.22/0.52 ($lesseq($sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))), $product(-1, tb2t(get(int, int, t2tb2(A1!3), t2tb(tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3))))))))), 0)),
% 0.22/0.52 inference(unit_resolution,[status(thm)],[165, 133])).
% 0.22/0.52 tff(167,plain,
% 0.22/0.52 ($false),
% 0.22/0.52 inference(theory_lemma,[status(thm)],[166, 164, 82, 78])).
% 0.22/0.52 tff(168,plain,((~$greatereq(tb2t(get(int, int, t2tb2(A1!3), t2tb(tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3))))))), 0)) | $lesseq($sum(N!2, $product(-1, tb2t(get(int, int, t2tb2(A1!3), t2tb(tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3))))))))), 0)), inference(lemma,lemma(discharge,[]))).
% 0.22/0.52 tff(169,plain,
% 0.22/0.52 ((($sum(tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), $product(-1, tptp_fun_J_1($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))) = 0) | (~$greatereq(tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), 0)) | (~($sum(V2!6, $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))))) = 0)) | (~$greatereq(tptp_fun_J_1($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), 0)) | (~($sum(V2!6, $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), tptp_fun_J_1($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))))) = 0)) | $lesseq($sum(N!2, $product(-1, tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))), -2) | $lesseq($sum(N!2, $product(-1, tptp_fun_J_1($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))), -2)) | $greatereq(tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), 0)),
% 0.22/0.52 inference(tautology,[status(thm)],[])).
% 0.22/0.52 tff(170,plain,
% 0.22/0.52 ($greatereq(tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), 0)),
% 0.22/0.52 inference(unit_resolution,[status(thm)],[169, 70])).
% 0.22/0.52 tff(171,plain,
% 0.22/0.52 (^[I: $int] : refl(((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, A!4)), 0) | (~((~$greatereq(tb2t(get(int, int, t2tb2(A1!3), t2tb(I))), 0)) | $lesseq($sum(N!2, $product(-1, tb2t(get(int, int, t2tb2(A1!3), t2tb(I))))), 0)))) <=> ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, A!4)), 0) | (~((~$greatereq(tb2t(get(int, int, t2tb2(A1!3), t2tb(I))), 0)) | $lesseq($sum(N!2, $product(-1, tb2t(get(int, int, t2tb2(A1!3), t2tb(I))))), 0)))))),
% 0.22/0.52 inference(bind,[status(th)],[])).
% 0.22/0.52 tff(172,plain,
% 0.22/0.52 (![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, A!4)), 0) | (~((~$greatereq(tb2t(get(int, int, t2tb2(A1!3), t2tb(I))), 0)) | $lesseq($sum(N!2, $product(-1, tb2t(get(int, int, t2tb2(A1!3), t2tb(I))))), 0)))) <=> ![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, A!4)), 0) | (~((~$greatereq(tb2t(get(int, int, t2tb2(A1!3), t2tb(I))), 0)) | $lesseq($sum(N!2, $product(-1, tb2t(get(int, int, t2tb2(A1!3), t2tb(I))))), 0))))),
% 0.22/0.52 inference(quant_intro,[status(thm)],[171])).
% 0.22/0.52 tff(173,plain,
% 0.22/0.52 (^[I: $int] : trans(monotonicity(trans(monotonicity(rewrite(($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, A!4)), 0))) <=> (~((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, A!4)), 0)))), ((~($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, A!4)), 0)))) <=> (~(~((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, A!4)), 0)))))), rewrite((~(~((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, A!4)), 0)))) <=> ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, A!4)), 0))), ((~($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, A!4)), 0)))) <=> ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, A!4)), 0)))), rewrite(($greatereq(tb2t(get(int, int, t2tb2(A1!3), t2tb(I))), 0) & (~$lesseq($sum(N!2, $product(-1, tb2t(get(int, int, t2tb2(A1!3), t2tb(I))))), 0))) <=> (~((~$greatereq(tb2t(get(int, int, t2tb2(A1!3), t2tb(I))), 0)) | $lesseq($sum(N!2, $product(-1, tb2t(get(int, int, t2tb2(A1!3), t2tb(I))))), 0)))), (((~($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, A!4)), 0)))) | ($greatereq(tb2t(get(int, int, t2tb2(A1!3), t2tb(I))), 0) & (~$lesseq($sum(N!2, $product(-1, tb2t(get(int, int, t2tb2(A1!3), t2tb(I))))), 0)))) <=> (((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, A!4)), 0)) | (~((~$greatereq(tb2t(get(int, int, t2tb2(A1!3), t2tb(I))), 0)) | $lesseq($sum(N!2, $product(-1, tb2t(get(int, int, t2tb2(A1!3), t2tb(I))))), 0)))))), rewrite((((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, A!4)), 0)) | (~((~$greatereq(tb2t(get(int, int, t2tb2(A1!3), t2tb(I))), 0)) | $lesseq($sum(N!2, $product(-1, tb2t(get(int, int, t2tb2(A1!3), t2tb(I))))), 0)))) <=> ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, A!4)), 0) | (~((~$greatereq(tb2t(get(int, int, t2tb2(A1!3), t2tb(I))), 0)) | $lesseq($sum(N!2, $product(-1, tb2t(get(int, int, t2tb2(A1!3), t2tb(I))))), 0))))), (((~($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, A!4)), 0)))) | ($greatereq(tb2t(get(int, int, t2tb2(A1!3), t2tb(I))), 0) & (~$lesseq($sum(N!2, $product(-1, tb2t(get(int, int, t2tb2(A1!3), t2tb(I))))), 0)))) <=> ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, A!4)), 0) | (~((~$greatereq(tb2t(get(int, int, t2tb2(A1!3), t2tb(I))), 0)) | $lesseq($sum(N!2, $product(-1, tb2t(get(int, int, t2tb2(A1!3), t2tb(I))))), 0))))))),
% 0.22/0.52 inference(bind,[status(th)],[])).
% 0.22/0.52 tff(174,plain,
% 0.22/0.52 (![I: $int] : ((~($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, A!4)), 0)))) | ($greatereq(tb2t(get(int, int, t2tb2(A1!3), t2tb(I))), 0) & (~$lesseq($sum(N!2, $product(-1, tb2t(get(int, int, t2tb2(A1!3), t2tb(I))))), 0)))) <=> ![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, A!4)), 0) | (~((~$greatereq(tb2t(get(int, int, t2tb2(A1!3), t2tb(I))), 0)) | $lesseq($sum(N!2, $product(-1, tb2t(get(int, int, t2tb2(A1!3), t2tb(I))))), 0))))),
% 0.22/0.52 inference(quant_intro,[status(thm)],[173])).
% 0.22/0.52 tff(175,plain,
% 0.22/0.52 (![I: $int] : ((~($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, A!4)), 0)))) | ($greatereq(tb2t(get(int, int, t2tb2(A1!3), t2tb(I))), 0) & (~$lesseq($sum(N!2, $product(-1, tb2t(get(int, int, t2tb2(A1!3), t2tb(I))))), 0))))),
% 0.22/0.52 inference(and_elim,[status(thm)],[66])).
% 0.22/0.52 tff(176,plain,
% 0.22/0.52 (![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, A!4)), 0) | (~((~$greatereq(tb2t(get(int, int, t2tb2(A1!3), t2tb(I))), 0)) | $lesseq($sum(N!2, $product(-1, tb2t(get(int, int, t2tb2(A1!3), t2tb(I))))), 0))))),
% 0.22/0.52 inference(modus_ponens,[status(thm)],[175, 174])).
% 0.22/0.52 tff(177,plain,
% 0.22/0.52 (![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, A!4)), 0) | (~((~$greatereq(tb2t(get(int, int, t2tb2(A1!3), t2tb(I))), 0)) | $lesseq($sum(N!2, $product(-1, tb2t(get(int, int, t2tb2(A1!3), t2tb(I))))), 0))))),
% 0.22/0.52 inference(modus_ponens,[status(thm)],[176, 172])).
% 0.22/0.52 tff(178,plain,
% 0.22/0.52 (((~![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, A!4)), 0) | (~((~$greatereq(tb2t(get(int, int, t2tb2(A1!3), t2tb(I))), 0)) | $lesseq($sum(N!2, $product(-1, tb2t(get(int, int, t2tb2(A1!3), t2tb(I))))), 0))))) | ((~$greatereq(tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), 0)) | (~((~$greatereq(tb2t(get(int, int, t2tb2(A1!3), t2tb(tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3))))))), 0)) | $lesseq($sum(N!2, $product(-1, tb2t(get(int, int, t2tb2(A1!3), t2tb(tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3))))))))), 0))) | $lesseq($sum(A!4, $product(-1, tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))), 0))) <=> ((~![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, A!4)), 0) | (~((~$greatereq(tb2t(get(int, int, t2tb2(A1!3), t2tb(I))), 0)) | $lesseq($sum(N!2, $product(-1, tb2t(get(int, int, t2tb2(A1!3), t2tb(I))))), 0))))) | (~$greatereq(tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), 0)) | (~((~$greatereq(tb2t(get(int, int, t2tb2(A1!3), t2tb(tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3))))))), 0)) | $lesseq($sum(N!2, $product(-1, tb2t(get(int, int, t2tb2(A1!3), t2tb(tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3))))))))), 0))) | $lesseq($sum(A!4, $product(-1, tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))), 0))),
% 0.22/0.52 inference(rewrite,[status(thm)],[])).
% 0.22/0.52 tff(179,plain,
% 0.22/0.52 (((~$greatereq(tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), 0)) | $lesseq($sum(A!4, $product(-1, tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))), 0) | (~((~$greatereq(tb2t(get(int, int, t2tb2(A1!3), t2tb(tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3))))))), 0)) | $lesseq($sum(N!2, $product(-1, tb2t(get(int, int, t2tb2(A1!3), t2tb(tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3))))))))), 0)))) <=> ((~$greatereq(tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), 0)) | (~((~$greatereq(tb2t(get(int, int, t2tb2(A1!3), t2tb(tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3))))))), 0)) | $lesseq($sum(N!2, $product(-1, tb2t(get(int, int, t2tb2(A1!3), t2tb(tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3))))))))), 0))) | $lesseq($sum(A!4, $product(-1, tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))), 0))),
% 0.22/0.52 inference(rewrite,[status(thm)],[])).
% 0.22/0.52 tff(180,plain,
% 0.22/0.52 ($greatereq($sum($product(-1, A!4), tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3))))), 0) <=> $lesseq($sum(A!4, $product(-1, tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))), 0)),
% 0.22/0.52 inference(rewrite,[status(thm)],[])).
% 0.22/0.52 tff(181,plain,
% 0.22/0.52 ($sum(tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), $product(-1, A!4)) = $sum($product(-1, A!4), tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))),
% 0.22/0.52 inference(rewrite,[status(thm)],[])).
% 0.22/0.52 tff(182,plain,
% 0.22/0.52 ($greatereq($sum(tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), $product(-1, A!4)), 0) <=> $greatereq($sum($product(-1, A!4), tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3))))), 0)),
% 0.22/0.52 inference(monotonicity,[status(thm)],[181])).
% 0.22/0.52 tff(183,plain,
% 0.22/0.52 ($greatereq($sum(tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), $product(-1, A!4)), 0) <=> $lesseq($sum(A!4, $product(-1, tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))), 0)),
% 0.22/0.52 inference(transitivity,[status(thm)],[182, 180])).
% 0.22/0.52 tff(184,plain,
% 0.22/0.52 (((~$greatereq(tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), 0)) | $greatereq($sum(tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), $product(-1, A!4)), 0) | (~((~$greatereq(tb2t(get(int, int, t2tb2(A1!3), t2tb(tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3))))))), 0)) | $lesseq($sum(N!2, $product(-1, tb2t(get(int, int, t2tb2(A1!3), t2tb(tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3))))))))), 0)))) <=> ((~$greatereq(tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), 0)) | $lesseq($sum(A!4, $product(-1, tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))), 0) | (~((~$greatereq(tb2t(get(int, int, t2tb2(A1!3), t2tb(tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3))))))), 0)) | $lesseq($sum(N!2, $product(-1, tb2t(get(int, int, t2tb2(A1!3), t2tb(tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3))))))))), 0))))),
% 0.22/0.52 inference(monotonicity,[status(thm)],[183])).
% 0.22/0.52 tff(185,plain,
% 0.22/0.52 (((~$greatereq(tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), 0)) | $greatereq($sum(tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), $product(-1, A!4)), 0) | (~((~$greatereq(tb2t(get(int, int, t2tb2(A1!3), t2tb(tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3))))))), 0)) | $lesseq($sum(N!2, $product(-1, tb2t(get(int, int, t2tb2(A1!3), t2tb(tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3))))))))), 0)))) <=> ((~$greatereq(tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), 0)) | (~((~$greatereq(tb2t(get(int, int, t2tb2(A1!3), t2tb(tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3))))))), 0)) | $lesseq($sum(N!2, $product(-1, tb2t(get(int, int, t2tb2(A1!3), t2tb(tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3))))))))), 0))) | $lesseq($sum(A!4, $product(-1, tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))), 0))),
% 0.22/0.52 inference(transitivity,[status(thm)],[184, 179])).
% 0.22/0.52 tff(186,plain,
% 0.22/0.52 (((~![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, A!4)), 0) | (~((~$greatereq(tb2t(get(int, int, t2tb2(A1!3), t2tb(I))), 0)) | $lesseq($sum(N!2, $product(-1, tb2t(get(int, int, t2tb2(A1!3), t2tb(I))))), 0))))) | ((~$greatereq(tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), 0)) | $greatereq($sum(tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), $product(-1, A!4)), 0) | (~((~$greatereq(tb2t(get(int, int, t2tb2(A1!3), t2tb(tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3))))))), 0)) | $lesseq($sum(N!2, $product(-1, tb2t(get(int, int, t2tb2(A1!3), t2tb(tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3))))))))), 0))))) <=> ((~![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, A!4)), 0) | (~((~$greatereq(tb2t(get(int, int, t2tb2(A1!3), t2tb(I))), 0)) | $lesseq($sum(N!2, $product(-1, tb2t(get(int, int, t2tb2(A1!3), t2tb(I))))), 0))))) | ((~$greatereq(tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), 0)) | (~((~$greatereq(tb2t(get(int, int, t2tb2(A1!3), t2tb(tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3))))))), 0)) | $lesseq($sum(N!2, $product(-1, tb2t(get(int, int, t2tb2(A1!3), t2tb(tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3))))))))), 0))) | $lesseq($sum(A!4, $product(-1, tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))), 0)))),
% 0.22/0.53 inference(monotonicity,[status(thm)],[185])).
% 0.22/0.53 tff(187,plain,
% 0.22/0.53 (((~![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, A!4)), 0) | (~((~$greatereq(tb2t(get(int, int, t2tb2(A1!3), t2tb(I))), 0)) | $lesseq($sum(N!2, $product(-1, tb2t(get(int, int, t2tb2(A1!3), t2tb(I))))), 0))))) | ((~$greatereq(tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), 0)) | $greatereq($sum(tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), $product(-1, A!4)), 0) | (~((~$greatereq(tb2t(get(int, int, t2tb2(A1!3), t2tb(tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3))))))), 0)) | $lesseq($sum(N!2, $product(-1, tb2t(get(int, int, t2tb2(A1!3), t2tb(tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3))))))))), 0))))) <=> ((~![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, A!4)), 0) | (~((~$greatereq(tb2t(get(int, int, t2tb2(A1!3), t2tb(I))), 0)) | $lesseq($sum(N!2, $product(-1, tb2t(get(int, int, t2tb2(A1!3), t2tb(I))))), 0))))) | (~$greatereq(tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), 0)) | (~((~$greatereq(tb2t(get(int, int, t2tb2(A1!3), t2tb(tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3))))))), 0)) | $lesseq($sum(N!2, $product(-1, tb2t(get(int, int, t2tb2(A1!3), t2tb(tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3))))))))), 0))) | $lesseq($sum(A!4, $product(-1, tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))), 0))),
% 0.22/0.53 inference(transitivity,[status(thm)],[186, 178])).
% 0.22/0.53 tff(188,plain,
% 0.22/0.53 ((~![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, A!4)), 0) | (~((~$greatereq(tb2t(get(int, int, t2tb2(A1!3), t2tb(I))), 0)) | $lesseq($sum(N!2, $product(-1, tb2t(get(int, int, t2tb2(A1!3), t2tb(I))))), 0))))) | ((~$greatereq(tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), 0)) | $greatereq($sum(tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), $product(-1, A!4)), 0) | (~((~$greatereq(tb2t(get(int, int, t2tb2(A1!3), t2tb(tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3))))))), 0)) | $lesseq($sum(N!2, $product(-1, tb2t(get(int, int, t2tb2(A1!3), t2tb(tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3))))))))), 0))))),
% 0.22/0.53 inference(quant_inst,[status(thm)],[])).
% 0.22/0.53 tff(189,plain,
% 0.22/0.53 ((~![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, A!4)), 0) | (~((~$greatereq(tb2t(get(int, int, t2tb2(A1!3), t2tb(I))), 0)) | $lesseq($sum(N!2, $product(-1, tb2t(get(int, int, t2tb2(A1!3), t2tb(I))))), 0))))) | (~$greatereq(tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))), 0)) | (~((~$greatereq(tb2t(get(int, int, t2tb2(A1!3), t2tb(tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3))))))), 0)) | $lesseq($sum(N!2, $product(-1, tb2t(get(int, int, t2tb2(A1!3), t2tb(tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3))))))))), 0))) | $lesseq($sum(A!4, $product(-1, tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))), 0)),
% 0.22/0.53 inference(modus_ponens,[status(thm)],[188, 187])).
% 0.22/0.53 tff(190,plain,
% 0.22/0.53 ((~((~$greatereq(tb2t(get(int, int, t2tb2(A1!3), t2tb(tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3))))))), 0)) | $lesseq($sum(N!2, $product(-1, tb2t(get(int, int, t2tb2(A1!3), t2tb(tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3))))))))), 0))) | $lesseq($sum(A!4, $product(-1, tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))), 0)),
% 0.22/0.53 inference(unit_resolution,[status(thm)],[189, 177, 170])).
% 0.22/0.53 tff(191,plain,
% 0.22/0.53 ($lesseq($sum(A!4, $product(-1, tptp_fun_I_0($sum(2, N!2), V2!6, tb2t1(mk_array1(int, A!4, t2tb2(A1!3)))))), 0)),
% 0.22/0.53 inference(unit_resolution,[status(thm)],[190, 168])).
% 0.22/0.53 tff(192,plain,
% 0.22/0.53 ($false),
% 0.22/0.53 inference(theory_lemma,[status(thm)],[191, 75, 72])).
% 0.22/0.53 % SZS output end Proof
%------------------------------------------------------------------------------