TSTP Solution File: DAT076_1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : DAT076_1 : 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 : Fri Sep 16 14:36:38 EDT 2022
% Result : Theorem 0.21s 0.43s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : DAT076_1 : TPTP v8.1.0. Released v6.1.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n016.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Aug 31 02:11:47 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.21/0.43 % SZS status Theorem
% 0.21/0.43 % SZS output start Proof
% 0.21/0.43 tff(read_type, type, (
% 0.21/0.43 read: ( array * $int ) > $int)).
% 0.21/0.43 tff(tptp_fun_I_7_type, type, (
% 0.21/0.43 tptp_fun_I_7: ( $int * array * array ) > $int)).
% 0.21/0.43 tff(elem_8_type, type, (
% 0.21/0.43 elem_8: array)).
% 0.21/0.43 tff(rev_type, type, (
% 0.21/0.43 rev: ( array * $int ) > array)).
% 0.21/0.43 tff(sorted_type, type, (
% 0.21/0.43 sorted: ( array * $int ) > $o)).
% 0.21/0.43 tff(tptp_fun_I_3_type, type, (
% 0.21/0.43 tptp_fun_I_3: ( $int * array ) > $int)).
% 0.21/0.43 tff(tptp_fun_J_2_type, type, (
% 0.21/0.43 tptp_fun_J_2: ( $int * array ) > $int)).
% 0.21/0.43 tff(1,assumption,(rev(elem!8, 1) = elem!8), introduced(assumption)).
% 0.21/0.43 tff(2,plain,
% 0.21/0.43 (sorted(rev(elem!8, 1), 1) <=> sorted(elem!8, 1)),
% 0.21/0.43 inference(monotonicity,[status(thm)],[1])).
% 0.21/0.43 tff(3,plain,
% 0.21/0.43 (sorted(elem!8, 1) <=> sorted(rev(elem!8, 1), 1)),
% 0.21/0.43 inference(symmetry,[status(thm)],[2])).
% 0.21/0.43 tff(4,assumption,(~($lesseq($sum(read(elem!8, tptp_fun_I_3(1, elem!8)), $product(-1, read(elem!8, tptp_fun_J_2(1, elem!8)))), 0) | $greatereq(tptp_fun_I_3(1, elem!8), 1) | $lesseq($sum(tptp_fun_J_2(1, elem!8), $product(-1, tptp_fun_I_3(1, elem!8))), 0) | $greatereq(tptp_fun_J_2(1, elem!8), 1) | (~$greatereq(tptp_fun_I_3(1, elem!8), 0)))), introduced(assumption)).
% 0.21/0.43 tff(5,plain,
% 0.21/0.43 (($lesseq($sum(read(elem!8, tptp_fun_I_3(1, elem!8)), $product(-1, read(elem!8, tptp_fun_J_2(1, elem!8)))), 0) | $greatereq(tptp_fun_I_3(1, elem!8), 1) | $lesseq($sum(tptp_fun_J_2(1, elem!8), $product(-1, tptp_fun_I_3(1, elem!8))), 0) | $greatereq(tptp_fun_J_2(1, elem!8), 1) | (~$greatereq(tptp_fun_I_3(1, elem!8), 0))) | (~$lesseq($sum(tptp_fun_J_2(1, elem!8), $product(-1, tptp_fun_I_3(1, elem!8))), 0))),
% 0.21/0.43 inference(tautology,[status(thm)],[])).
% 0.21/0.43 tff(6,plain,
% 0.21/0.43 (~$lesseq($sum(tptp_fun_J_2(1, elem!8), $product(-1, tptp_fun_I_3(1, elem!8))), 0)),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[5, 4])).
% 0.21/0.43 tff(7,plain,
% 0.21/0.43 (($lesseq($sum(read(elem!8, tptp_fun_I_3(1, elem!8)), $product(-1, read(elem!8, tptp_fun_J_2(1, elem!8)))), 0) | $greatereq(tptp_fun_I_3(1, elem!8), 1) | $lesseq($sum(tptp_fun_J_2(1, elem!8), $product(-1, tptp_fun_I_3(1, elem!8))), 0) | $greatereq(tptp_fun_J_2(1, elem!8), 1) | (~$greatereq(tptp_fun_I_3(1, elem!8), 0))) | $greatereq(tptp_fun_I_3(1, elem!8), 0)),
% 0.21/0.43 inference(tautology,[status(thm)],[])).
% 0.21/0.43 tff(8,plain,
% 0.21/0.43 ($greatereq(tptp_fun_I_3(1, elem!8), 0)),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[7, 4])).
% 0.21/0.43 tff(9,plain,
% 0.21/0.43 (($lesseq($sum(read(elem!8, tptp_fun_I_3(1, elem!8)), $product(-1, read(elem!8, tptp_fun_J_2(1, elem!8)))), 0) | $greatereq(tptp_fun_I_3(1, elem!8), 1) | $lesseq($sum(tptp_fun_J_2(1, elem!8), $product(-1, tptp_fun_I_3(1, elem!8))), 0) | $greatereq(tptp_fun_J_2(1, elem!8), 1) | (~$greatereq(tptp_fun_I_3(1, elem!8), 0))) | (~$greatereq(tptp_fun_J_2(1, elem!8), 1))),
% 0.21/0.43 inference(tautology,[status(thm)],[])).
% 0.21/0.43 tff(10,plain,
% 0.21/0.43 (~$greatereq(tptp_fun_J_2(1, elem!8), 1)),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[9, 4])).
% 0.21/0.43 tff(11,plain,
% 0.21/0.43 ($false),
% 0.21/0.43 inference(theory_lemma,[status(thm)],[10, 8, 6])).
% 0.21/0.43 tff(12,plain,($lesseq($sum(read(elem!8, tptp_fun_I_3(1, elem!8)), $product(-1, read(elem!8, tptp_fun_J_2(1, elem!8)))), 0) | $greatereq(tptp_fun_I_3(1, elem!8), 1) | $lesseq($sum(tptp_fun_J_2(1, elem!8), $product(-1, tptp_fun_I_3(1, elem!8))), 0) | $greatereq(tptp_fun_J_2(1, elem!8), 1) | (~$greatereq(tptp_fun_I_3(1, elem!8), 0))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.43 tff(13,plain,
% 0.21/0.43 (^[A: array, N: $int] : refl((~((~((~sorted(A, N)) | ![I: $int, J: $int] : ($greatereq($sum(J, $product(-1, N)), 0) | $greatereq($sum(I, $product(-1, J)), 0) | $greatereq($sum(I, $product(-1, N)), 0) | $lesseq($sum(read(A, I), $product(-1, read(A, J))), 0) | (~$greatereq(I, 0))))) | (~(sorted(A, N) | (~($lesseq($sum(read(A, tptp_fun_I_3(N, A)), $product(-1, read(A, tptp_fun_J_2(N, A)))), 0) | $lesseq($sum(N, $product(-1, tptp_fun_I_3(N, A))), 0) | $lesseq($sum(tptp_fun_J_2(N, A), $product(-1, tptp_fun_I_3(N, A))), 0) | $lesseq($sum(N, $product(-1, tptp_fun_J_2(N, A))), 0) | (~$greatereq(tptp_fun_I_3(N, A), 0)))))))) <=> (~((~((~sorted(A, N)) | ![I: $int, J: $int] : ($greatereq($sum(J, $product(-1, N)), 0) | $greatereq($sum(I, $product(-1, J)), 0) | $greatereq($sum(I, $product(-1, N)), 0) | $lesseq($sum(read(A, I), $product(-1, read(A, J))), 0) | (~$greatereq(I, 0))))) | (~(sorted(A, N) | (~($lesseq($sum(read(A, tptp_fun_I_3(N, A)), $product(-1, read(A, tptp_fun_J_2(N, A)))), 0) | $lesseq($sum(N, $product(-1, tptp_fun_I_3(N, A))), 0) | $lesseq($sum(tptp_fun_J_2(N, A), $product(-1, tptp_fun_I_3(N, A))), 0) | $lesseq($sum(N, $product(-1, tptp_fun_J_2(N, A))), 0) | (~$greatereq(tptp_fun_I_3(N, A), 0)))))))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(14,plain,
% 0.21/0.43 (![A: array, N: $int] : (~((~((~sorted(A, N)) | ![I: $int, J: $int] : ($greatereq($sum(J, $product(-1, N)), 0) | $greatereq($sum(I, $product(-1, J)), 0) | $greatereq($sum(I, $product(-1, N)), 0) | $lesseq($sum(read(A, I), $product(-1, read(A, J))), 0) | (~$greatereq(I, 0))))) | (~(sorted(A, N) | (~($lesseq($sum(read(A, tptp_fun_I_3(N, A)), $product(-1, read(A, tptp_fun_J_2(N, A)))), 0) | $lesseq($sum(N, $product(-1, tptp_fun_I_3(N, A))), 0) | $lesseq($sum(tptp_fun_J_2(N, A), $product(-1, tptp_fun_I_3(N, A))), 0) | $lesseq($sum(N, $product(-1, tptp_fun_J_2(N, A))), 0) | (~$greatereq(tptp_fun_I_3(N, A), 0)))))))) <=> ![A: array, N: $int] : (~((~((~sorted(A, N)) | ![I: $int, J: $int] : ($greatereq($sum(J, $product(-1, N)), 0) | $greatereq($sum(I, $product(-1, J)), 0) | $greatereq($sum(I, $product(-1, N)), 0) | $lesseq($sum(read(A, I), $product(-1, read(A, J))), 0) | (~$greatereq(I, 0))))) | (~(sorted(A, N) | (~($lesseq($sum(read(A, tptp_fun_I_3(N, A)), $product(-1, read(A, tptp_fun_J_2(N, A)))), 0) | $lesseq($sum(N, $product(-1, tptp_fun_I_3(N, A))), 0) | $lesseq($sum(tptp_fun_J_2(N, A), $product(-1, tptp_fun_I_3(N, A))), 0) | $lesseq($sum(N, $product(-1, tptp_fun_J_2(N, A))), 0) | (~$greatereq(tptp_fun_I_3(N, A), 0))))))))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[13])).
% 0.21/0.43 tff(15,plain,
% 0.21/0.43 (^[A: array, N: $int] : rewrite((~((~((~sorted(A, N)) | ![I: $int, J: $int] : ($greatereq($sum(J, $product(-1, N)), 0) | $greatereq($sum(I, $product(-1, J)), 0) | $greatereq($sum(I, $product(-1, N)), 0) | $lesseq($sum(read(A, I), $product(-1, read(A, J))), 0) | (~$greatereq(I, 0))))) | (~(sorted(A, N) | (~($lesseq($sum(read(A, tptp_fun_I_3(N, A)), $product(-1, read(A, tptp_fun_J_2(N, A)))), 0) | $lesseq($sum(N, $product(-1, tptp_fun_I_3(N, A))), 0) | $lesseq($sum(tptp_fun_J_2(N, A), $product(-1, tptp_fun_I_3(N, A))), 0) | $lesseq($sum(N, $product(-1, tptp_fun_J_2(N, A))), 0) | (~$greatereq(tptp_fun_I_3(N, A), 0)))))))) <=> (~((~((~sorted(A, N)) | ![I: $int, J: $int] : ($greatereq($sum(J, $product(-1, N)), 0) | $greatereq($sum(I, $product(-1, J)), 0) | $greatereq($sum(I, $product(-1, N)), 0) | $lesseq($sum(read(A, I), $product(-1, read(A, J))), 0) | (~$greatereq(I, 0))))) | (~(sorted(A, N) | (~($lesseq($sum(read(A, tptp_fun_I_3(N, A)), $product(-1, read(A, tptp_fun_J_2(N, A)))), 0) | $lesseq($sum(N, $product(-1, tptp_fun_I_3(N, A))), 0) | $lesseq($sum(tptp_fun_J_2(N, A), $product(-1, tptp_fun_I_3(N, A))), 0) | $lesseq($sum(N, $product(-1, tptp_fun_J_2(N, A))), 0) | (~$greatereq(tptp_fun_I_3(N, A), 0)))))))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(16,plain,
% 0.21/0.43 (![A: array, N: $int] : (~((~((~sorted(A, N)) | ![I: $int, J: $int] : ($greatereq($sum(J, $product(-1, N)), 0) | $greatereq($sum(I, $product(-1, J)), 0) | $greatereq($sum(I, $product(-1, N)), 0) | $lesseq($sum(read(A, I), $product(-1, read(A, J))), 0) | (~$greatereq(I, 0))))) | (~(sorted(A, N) | (~($lesseq($sum(read(A, tptp_fun_I_3(N, A)), $product(-1, read(A, tptp_fun_J_2(N, A)))), 0) | $lesseq($sum(N, $product(-1, tptp_fun_I_3(N, A))), 0) | $lesseq($sum(tptp_fun_J_2(N, A), $product(-1, tptp_fun_I_3(N, A))), 0) | $lesseq($sum(N, $product(-1, tptp_fun_J_2(N, A))), 0) | (~$greatereq(tptp_fun_I_3(N, A), 0)))))))) <=> ![A: array, N: $int] : (~((~((~sorted(A, N)) | ![I: $int, J: $int] : ($greatereq($sum(J, $product(-1, N)), 0) | $greatereq($sum(I, $product(-1, J)), 0) | $greatereq($sum(I, $product(-1, N)), 0) | $lesseq($sum(read(A, I), $product(-1, read(A, J))), 0) | (~$greatereq(I, 0))))) | (~(sorted(A, N) | (~($lesseq($sum(read(A, tptp_fun_I_3(N, A)), $product(-1, read(A, tptp_fun_J_2(N, A)))), 0) | $lesseq($sum(N, $product(-1, tptp_fun_I_3(N, A))), 0) | $lesseq($sum(tptp_fun_J_2(N, A), $product(-1, tptp_fun_I_3(N, A))), 0) | $lesseq($sum(N, $product(-1, tptp_fun_J_2(N, A))), 0) | (~$greatereq(tptp_fun_I_3(N, A), 0))))))))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[15])).
% 0.21/0.43 tff(17,plain,
% 0.21/0.43 (![A: array, N: $int] : (~((~((~sorted(A, N)) | ![I: $int, J: $int] : ($greatereq($sum(J, $product(-1, N)), 0) | $greatereq($sum(I, $product(-1, J)), 0) | $greatereq($sum(I, $product(-1, N)), 0) | $lesseq($sum(read(A, I), $product(-1, read(A, J))), 0) | (~$greatereq(I, 0))))) | (~(sorted(A, N) | (~($lesseq($sum(read(A, tptp_fun_I_3(N, A)), $product(-1, read(A, tptp_fun_J_2(N, A)))), 0) | $lesseq($sum(N, $product(-1, tptp_fun_I_3(N, A))), 0) | $lesseq($sum(tptp_fun_J_2(N, A), $product(-1, tptp_fun_I_3(N, A))), 0) | $lesseq($sum(N, $product(-1, tptp_fun_J_2(N, A))), 0) | (~$greatereq(tptp_fun_I_3(N, A), 0)))))))) <=> ![A: array, N: $int] : (~((~((~sorted(A, N)) | ![I: $int, J: $int] : ($greatereq($sum(J, $product(-1, N)), 0) | $greatereq($sum(I, $product(-1, J)), 0) | $greatereq($sum(I, $product(-1, N)), 0) | $lesseq($sum(read(A, I), $product(-1, read(A, J))), 0) | (~$greatereq(I, 0))))) | (~(sorted(A, N) | (~($lesseq($sum(read(A, tptp_fun_I_3(N, A)), $product(-1, read(A, tptp_fun_J_2(N, A)))), 0) | $lesseq($sum(N, $product(-1, tptp_fun_I_3(N, A))), 0) | $lesseq($sum(tptp_fun_J_2(N, A), $product(-1, tptp_fun_I_3(N, A))), 0) | $lesseq($sum(N, $product(-1, tptp_fun_J_2(N, A))), 0) | (~$greatereq(tptp_fun_I_3(N, A), 0))))))))),
% 0.21/0.43 inference(transitivity,[status(thm)],[16, 14])).
% 0.21/0.43 tff(18,plain,
% 0.21/0.43 (^[A: array, N: $int] : trans(monotonicity(rewrite(((~sorted(A, N)) | ![I: $int, J: $int] : ((~($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, N)), 0)) & (~$greatereq($sum(I, $product(-1, J)), 0)) & (~$greatereq($sum(J, $product(-1, N)), 0)))) | $lesseq($sum(read(A, I), $product(-1, read(A, J))), 0))) <=> ((~sorted(A, N)) | ![I: $int, J: $int] : ($greatereq($sum(J, $product(-1, N)), 0) | $greatereq($sum(I, $product(-1, J)), 0) | $greatereq($sum(I, $product(-1, N)), 0) | $lesseq($sum(read(A, I), $product(-1, read(A, J))), 0) | (~$greatereq(I, 0))))), trans(monotonicity(rewrite((~((~($greatereq(tptp_fun_I_3(N, A), 0) & (~$lesseq($sum(N, $product(-1, tptp_fun_I_3(N, A))), 0)) & (~$lesseq($sum(tptp_fun_J_2(N, A), $product(-1, tptp_fun_I_3(N, A))), 0)) & (~$lesseq($sum(N, $product(-1, tptp_fun_J_2(N, A))), 0)))) | $lesseq($sum(read(A, tptp_fun_I_3(N, A)), $product(-1, read(A, tptp_fun_J_2(N, A)))), 0))) <=> (~($lesseq($sum(read(A, tptp_fun_I_3(N, A)), $product(-1, read(A, tptp_fun_J_2(N, A)))), 0) | $lesseq($sum(N, $product(-1, tptp_fun_I_3(N, A))), 0) | $lesseq($sum(tptp_fun_J_2(N, A), $product(-1, tptp_fun_I_3(N, A))), 0) | $lesseq($sum(N, $product(-1, tptp_fun_J_2(N, A))), 0) | (~$greatereq(tptp_fun_I_3(N, A), 0))))), ((sorted(A, N) | (~((~($greatereq(tptp_fun_I_3(N, A), 0) & (~$lesseq($sum(N, $product(-1, tptp_fun_I_3(N, A))), 0)) & (~$lesseq($sum(tptp_fun_J_2(N, A), $product(-1, tptp_fun_I_3(N, A))), 0)) & (~$lesseq($sum(N, $product(-1, tptp_fun_J_2(N, A))), 0)))) | $lesseq($sum(read(A, tptp_fun_I_3(N, A)), $product(-1, read(A, tptp_fun_J_2(N, A)))), 0)))) <=> (sorted(A, N) | (~($lesseq($sum(read(A, tptp_fun_I_3(N, A)), $product(-1, read(A, tptp_fun_J_2(N, A)))), 0) | $lesseq($sum(N, $product(-1, tptp_fun_I_3(N, A))), 0) | $lesseq($sum(tptp_fun_J_2(N, A), $product(-1, tptp_fun_I_3(N, A))), 0) | $lesseq($sum(N, $product(-1, tptp_fun_J_2(N, A))), 0) | (~$greatereq(tptp_fun_I_3(N, A), 0))))))), rewrite((sorted(A, N) | (~($lesseq($sum(read(A, tptp_fun_I_3(N, A)), $product(-1, read(A, tptp_fun_J_2(N, A)))), 0) | $lesseq($sum(N, $product(-1, tptp_fun_I_3(N, A))), 0) | $lesseq($sum(tptp_fun_J_2(N, A), $product(-1, tptp_fun_I_3(N, A))), 0) | $lesseq($sum(N, $product(-1, tptp_fun_J_2(N, A))), 0) | (~$greatereq(tptp_fun_I_3(N, A), 0))))) <=> (sorted(A, N) | (~($lesseq($sum(read(A, tptp_fun_I_3(N, A)), $product(-1, read(A, tptp_fun_J_2(N, A)))), 0) | $lesseq($sum(N, $product(-1, tptp_fun_I_3(N, A))), 0) | $lesseq($sum(tptp_fun_J_2(N, A), $product(-1, tptp_fun_I_3(N, A))), 0) | $lesseq($sum(N, $product(-1, tptp_fun_J_2(N, A))), 0) | (~$greatereq(tptp_fun_I_3(N, A), 0)))))), ((sorted(A, N) | (~((~($greatereq(tptp_fun_I_3(N, A), 0) & (~$lesseq($sum(N, $product(-1, tptp_fun_I_3(N, A))), 0)) & (~$lesseq($sum(tptp_fun_J_2(N, A), $product(-1, tptp_fun_I_3(N, A))), 0)) & (~$lesseq($sum(N, $product(-1, tptp_fun_J_2(N, A))), 0)))) | $lesseq($sum(read(A, tptp_fun_I_3(N, A)), $product(-1, read(A, tptp_fun_J_2(N, A)))), 0)))) <=> (sorted(A, N) | (~($lesseq($sum(read(A, tptp_fun_I_3(N, A)), $product(-1, read(A, tptp_fun_J_2(N, A)))), 0) | $lesseq($sum(N, $product(-1, tptp_fun_I_3(N, A))), 0) | $lesseq($sum(tptp_fun_J_2(N, A), $product(-1, tptp_fun_I_3(N, A))), 0) | $lesseq($sum(N, $product(-1, tptp_fun_J_2(N, A))), 0) | (~$greatereq(tptp_fun_I_3(N, A), 0))))))), ((((~sorted(A, N)) | ![I: $int, J: $int] : ((~($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, N)), 0)) & (~$greatereq($sum(I, $product(-1, J)), 0)) & (~$greatereq($sum(J, $product(-1, N)), 0)))) | $lesseq($sum(read(A, I), $product(-1, read(A, J))), 0))) & (sorted(A, N) | (~((~($greatereq(tptp_fun_I_3(N, A), 0) & (~$lesseq($sum(N, $product(-1, tptp_fun_I_3(N, A))), 0)) & (~$lesseq($sum(tptp_fun_J_2(N, A), $product(-1, tptp_fun_I_3(N, A))), 0)) & (~$lesseq($sum(N, $product(-1, tptp_fun_J_2(N, A))), 0)))) | $lesseq($sum(read(A, tptp_fun_I_3(N, A)), $product(-1, read(A, tptp_fun_J_2(N, A)))), 0))))) <=> (((~sorted(A, N)) | ![I: $int, J: $int] : ($greatereq($sum(J, $product(-1, N)), 0) | $greatereq($sum(I, $product(-1, J)), 0) | $greatereq($sum(I, $product(-1, N)), 0) | $lesseq($sum(read(A, I), $product(-1, read(A, J))), 0) | (~$greatereq(I, 0)))) & (sorted(A, N) | (~($lesseq($sum(read(A, tptp_fun_I_3(N, A)), $product(-1, read(A, tptp_fun_J_2(N, A)))), 0) | $lesseq($sum(N, $product(-1, tptp_fun_I_3(N, A))), 0) | $lesseq($sum(tptp_fun_J_2(N, A), $product(-1, tptp_fun_I_3(N, A))), 0) | $lesseq($sum(N, $product(-1, tptp_fun_J_2(N, A))), 0) | (~$greatereq(tptp_fun_I_3(N, A), 0)))))))), rewrite((((~sorted(A, N)) | ![I: $int, J: $int] : ($greatereq($sum(J, $product(-1, N)), 0) | $greatereq($sum(I, $product(-1, J)), 0) | $greatereq($sum(I, $product(-1, N)), 0) | $lesseq($sum(read(A, I), $product(-1, read(A, J))), 0) | (~$greatereq(I, 0)))) & (sorted(A, N) | (~($lesseq($sum(read(A, tptp_fun_I_3(N, A)), $product(-1, read(A, tptp_fun_J_2(N, A)))), 0) | $lesseq($sum(N, $product(-1, tptp_fun_I_3(N, A))), 0) | $lesseq($sum(tptp_fun_J_2(N, A), $product(-1, tptp_fun_I_3(N, A))), 0) | $lesseq($sum(N, $product(-1, tptp_fun_J_2(N, A))), 0) | (~$greatereq(tptp_fun_I_3(N, A), 0)))))) <=> (~((~((~sorted(A, N)) | ![I: $int, J: $int] : ($greatereq($sum(J, $product(-1, N)), 0) | $greatereq($sum(I, $product(-1, J)), 0) | $greatereq($sum(I, $product(-1, N)), 0) | $lesseq($sum(read(A, I), $product(-1, read(A, J))), 0) | (~$greatereq(I, 0))))) | (~(sorted(A, N) | (~($lesseq($sum(read(A, tptp_fun_I_3(N, A)), $product(-1, read(A, tptp_fun_J_2(N, A)))), 0) | $lesseq($sum(N, $product(-1, tptp_fun_I_3(N, A))), 0) | $lesseq($sum(tptp_fun_J_2(N, A), $product(-1, tptp_fun_I_3(N, A))), 0) | $lesseq($sum(N, $product(-1, tptp_fun_J_2(N, A))), 0) | (~$greatereq(tptp_fun_I_3(N, A), 0))))))))), ((((~sorted(A, N)) | ![I: $int, J: $int] : ((~($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, N)), 0)) & (~$greatereq($sum(I, $product(-1, J)), 0)) & (~$greatereq($sum(J, $product(-1, N)), 0)))) | $lesseq($sum(read(A, I), $product(-1, read(A, J))), 0))) & (sorted(A, N) | (~((~($greatereq(tptp_fun_I_3(N, A), 0) & (~$lesseq($sum(N, $product(-1, tptp_fun_I_3(N, A))), 0)) & (~$lesseq($sum(tptp_fun_J_2(N, A), $product(-1, tptp_fun_I_3(N, A))), 0)) & (~$lesseq($sum(N, $product(-1, tptp_fun_J_2(N, A))), 0)))) | $lesseq($sum(read(A, tptp_fun_I_3(N, A)), $product(-1, read(A, tptp_fun_J_2(N, A)))), 0))))) <=> (~((~((~sorted(A, N)) | ![I: $int, J: $int] : ($greatereq($sum(J, $product(-1, N)), 0) | $greatereq($sum(I, $product(-1, J)), 0) | $greatereq($sum(I, $product(-1, N)), 0) | $lesseq($sum(read(A, I), $product(-1, read(A, J))), 0) | (~$greatereq(I, 0))))) | (~(sorted(A, N) | (~($lesseq($sum(read(A, tptp_fun_I_3(N, A)), $product(-1, read(A, tptp_fun_J_2(N, A)))), 0) | $lesseq($sum(N, $product(-1, tptp_fun_I_3(N, A))), 0) | $lesseq($sum(tptp_fun_J_2(N, A), $product(-1, tptp_fun_I_3(N, A))), 0) | $lesseq($sum(N, $product(-1, tptp_fun_J_2(N, A))), 0) | (~$greatereq(tptp_fun_I_3(N, A), 0))))))))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(19,plain,
% 0.21/0.43 (![A: array, N: $int] : (((~sorted(A, N)) | ![I: $int, J: $int] : ((~($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, N)), 0)) & (~$greatereq($sum(I, $product(-1, J)), 0)) & (~$greatereq($sum(J, $product(-1, N)), 0)))) | $lesseq($sum(read(A, I), $product(-1, read(A, J))), 0))) & (sorted(A, N) | (~((~($greatereq(tptp_fun_I_3(N, A), 0) & (~$lesseq($sum(N, $product(-1, tptp_fun_I_3(N, A))), 0)) & (~$lesseq($sum(tptp_fun_J_2(N, A), $product(-1, tptp_fun_I_3(N, A))), 0)) & (~$lesseq($sum(N, $product(-1, tptp_fun_J_2(N, A))), 0)))) | $lesseq($sum(read(A, tptp_fun_I_3(N, A)), $product(-1, read(A, tptp_fun_J_2(N, A)))), 0))))) <=> ![A: array, N: $int] : (~((~((~sorted(A, N)) | ![I: $int, J: $int] : ($greatereq($sum(J, $product(-1, N)), 0) | $greatereq($sum(I, $product(-1, J)), 0) | $greatereq($sum(I, $product(-1, N)), 0) | $lesseq($sum(read(A, I), $product(-1, read(A, J))), 0) | (~$greatereq(I, 0))))) | (~(sorted(A, N) | (~($lesseq($sum(read(A, tptp_fun_I_3(N, A)), $product(-1, read(A, tptp_fun_J_2(N, A)))), 0) | $lesseq($sum(N, $product(-1, tptp_fun_I_3(N, A))), 0) | $lesseq($sum(tptp_fun_J_2(N, A), $product(-1, tptp_fun_I_3(N, A))), 0) | $lesseq($sum(N, $product(-1, tptp_fun_J_2(N, A))), 0) | (~$greatereq(tptp_fun_I_3(N, A), 0))))))))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[18])).
% 0.21/0.43 tff(20,plain,
% 0.21/0.43 (^[A: array, N: $int] : rewrite((((~sorted(A, N)) | ![I: $int, J: $int] : ((~($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, N)), 0)) & (~$greatereq($sum(I, $product(-1, J)), 0)) & (~$greatereq($sum(J, $product(-1, N)), 0)))) | $lesseq($sum(read(A, I), $product(-1, read(A, J))), 0))) & (sorted(A, N) | (~((~($greatereq(tptp_fun_I_3(N, A), 0) & (~$greatereq($sum(tptp_fun_I_3(N, A), $product(-1, N)), 0)) & (~$greatereq($sum(tptp_fun_I_3(N, A), $product(-1, tptp_fun_J_2(N, A))), 0)) & (~$greatereq($sum(tptp_fun_J_2(N, A), $product(-1, N)), 0)))) | $lesseq($sum(read(A, tptp_fun_I_3(N, A)), $product(-1, read(A, tptp_fun_J_2(N, A)))), 0))))) <=> (((~sorted(A, N)) | ![I: $int, J: $int] : ((~($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, N)), 0)) & (~$greatereq($sum(I, $product(-1, J)), 0)) & (~$greatereq($sum(J, $product(-1, N)), 0)))) | $lesseq($sum(read(A, I), $product(-1, read(A, J))), 0))) & (sorted(A, N) | (~((~($greatereq(tptp_fun_I_3(N, A), 0) & (~$lesseq($sum(N, $product(-1, tptp_fun_I_3(N, A))), 0)) & (~$lesseq($sum(tptp_fun_J_2(N, A), $product(-1, tptp_fun_I_3(N, A))), 0)) & (~$lesseq($sum(N, $product(-1, tptp_fun_J_2(N, A))), 0)))) | $lesseq($sum(read(A, tptp_fun_I_3(N, A)), $product(-1, read(A, tptp_fun_J_2(N, A)))), 0))))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(21,plain,
% 0.21/0.43 (![A: array, N: $int] : (((~sorted(A, N)) | ![I: $int, J: $int] : ((~($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, N)), 0)) & (~$greatereq($sum(I, $product(-1, J)), 0)) & (~$greatereq($sum(J, $product(-1, N)), 0)))) | $lesseq($sum(read(A, I), $product(-1, read(A, J))), 0))) & (sorted(A, N) | (~((~($greatereq(tptp_fun_I_3(N, A), 0) & (~$greatereq($sum(tptp_fun_I_3(N, A), $product(-1, N)), 0)) & (~$greatereq($sum(tptp_fun_I_3(N, A), $product(-1, tptp_fun_J_2(N, A))), 0)) & (~$greatereq($sum(tptp_fun_J_2(N, A), $product(-1, N)), 0)))) | $lesseq($sum(read(A, tptp_fun_I_3(N, A)), $product(-1, read(A, tptp_fun_J_2(N, A)))), 0))))) <=> ![A: array, N: $int] : (((~sorted(A, N)) | ![I: $int, J: $int] : ((~($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, N)), 0)) & (~$greatereq($sum(I, $product(-1, J)), 0)) & (~$greatereq($sum(J, $product(-1, N)), 0)))) | $lesseq($sum(read(A, I), $product(-1, read(A, J))), 0))) & (sorted(A, N) | (~((~($greatereq(tptp_fun_I_3(N, A), 0) & (~$lesseq($sum(N, $product(-1, tptp_fun_I_3(N, A))), 0)) & (~$lesseq($sum(tptp_fun_J_2(N, A), $product(-1, tptp_fun_I_3(N, A))), 0)) & (~$lesseq($sum(N, $product(-1, tptp_fun_J_2(N, A))), 0)))) | $lesseq($sum(read(A, tptp_fun_I_3(N, A)), $product(-1, read(A, tptp_fun_J_2(N, A)))), 0)))))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[20])).
% 0.21/0.43 tff(22,plain,
% 0.21/0.43 (^[A: array, N: $int] : rewrite((sorted(A, N) <=> ![I: $int, J: $int] : ((~($greatereq(I, 0) & (~$lesseq($sum(N, $product(-1, I)), 0)) & (~$lesseq($sum(J, $product(-1, I)), 0)) & (~$lesseq($sum(N, $product(-1, J)), 0)))) | $lesseq($sum(read(A, I), $product(-1, read(A, J))), 0))) <=> (sorted(A, N) <=> ![I: $int, J: $int] : ((~($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, N)), 0)) & (~$greatereq($sum(I, $product(-1, J)), 0)) & (~$greatereq($sum(J, $product(-1, N)), 0)))) | $lesseq($sum(read(A, I), $product(-1, read(A, J))), 0))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(23,plain,
% 0.21/0.43 (![A: array, N: $int] : (sorted(A, N) <=> ![I: $int, J: $int] : ((~($greatereq(I, 0) & (~$lesseq($sum(N, $product(-1, I)), 0)) & (~$lesseq($sum(J, $product(-1, I)), 0)) & (~$lesseq($sum(N, $product(-1, J)), 0)))) | $lesseq($sum(read(A, I), $product(-1, read(A, J))), 0))) <=> ![A: array, N: $int] : (sorted(A, N) <=> ![I: $int, J: $int] : ((~($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, N)), 0)) & (~$greatereq($sum(I, $product(-1, J)), 0)) & (~$greatereq($sum(J, $product(-1, N)), 0)))) | $lesseq($sum(read(A, I), $product(-1, read(A, J))), 0)))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[22])).
% 0.21/0.43 tff(24,plain,
% 0.21/0.43 (^[A: array, N: $int] : rewrite((sorted(A, N) <=> ![I: $int, J: $int] : ((~($lesseq(0, I) & (~$lesseq(N, I)) & (~$lesseq(J, I)) & (~$lesseq(N, J)))) | $lesseq(read(A, I), read(A, J)))) <=> (sorted(A, N) <=> ![I: $int, J: $int] : ((~($greatereq(I, 0) & (~$lesseq($sum(N, $product(-1, I)), 0)) & (~$lesseq($sum(J, $product(-1, I)), 0)) & (~$lesseq($sum(N, $product(-1, J)), 0)))) | $lesseq($sum(read(A, I), $product(-1, read(A, J))), 0))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(25,plain,
% 0.21/0.43 (![A: array, N: $int] : (sorted(A, N) <=> ![I: $int, J: $int] : ((~($lesseq(0, I) & (~$lesseq(N, I)) & (~$lesseq(J, I)) & (~$lesseq(N, J)))) | $lesseq(read(A, I), read(A, J)))) <=> ![A: array, N: $int] : (sorted(A, N) <=> ![I: $int, J: $int] : ((~($greatereq(I, 0) & (~$lesseq($sum(N, $product(-1, I)), 0)) & (~$lesseq($sum(J, $product(-1, I)), 0)) & (~$lesseq($sum(N, $product(-1, J)), 0)))) | $lesseq($sum(read(A, I), $product(-1, read(A, J))), 0)))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[24])).
% 0.21/0.43 tff(26,plain,
% 0.21/0.43 (![A: array, N: $int] : (sorted(A, N) <=> ![I: $int, J: $int] : ((~($lesseq(0, I) & (~$lesseq(N, I)) & (~$lesseq(J, I)) & (~$lesseq(N, J)))) | $lesseq(read(A, I), read(A, J)))) <=> ![A: array, N: $int] : (sorted(A, N) <=> ![I: $int, J: $int] : ((~($lesseq(0, I) & (~$lesseq(N, I)) & (~$lesseq(J, I)) & (~$lesseq(N, J)))) | $lesseq(read(A, I), read(A, J))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(27,plain,
% 0.21/0.43 (^[A: array, N: $int] : rewrite((sorted(A, N) <=> ![I: $int, J: $int] : (((($lesseq(0, I) & $less(I, N)) & $less(I, J)) & $less(J, N)) => $lesseq(read(A, I), read(A, J)))) <=> (sorted(A, N) <=> ![I: $int, J: $int] : ((~($lesseq(0, I) & (~$lesseq(N, I)) & (~$lesseq(J, I)) & (~$lesseq(N, J)))) | $lesseq(read(A, I), read(A, J)))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(28,plain,
% 0.21/0.43 (![A: array, N: $int] : (sorted(A, N) <=> ![I: $int, J: $int] : (((($lesseq(0, I) & $less(I, N)) & $less(I, J)) & $less(J, N)) => $lesseq(read(A, I), read(A, J)))) <=> ![A: array, N: $int] : (sorted(A, N) <=> ![I: $int, J: $int] : ((~($lesseq(0, I) & (~$lesseq(N, I)) & (~$lesseq(J, I)) & (~$lesseq(N, J)))) | $lesseq(read(A, I), read(A, J))))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[27])).
% 0.21/0.43 tff(29,axiom,(![A: array, N: $int] : (sorted(A, N) <=> ![I: $int, J: $int] : (((($lesseq(0, I) & $less(I, N)) & $less(I, J)) & $less(J, N)) => $lesseq(read(A, I), read(A, J))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','sorted1')).
% 0.21/0.43 tff(30,plain,
% 0.21/0.43 (![A: array, N: $int] : (sorted(A, N) <=> ![I: $int, J: $int] : ((~($lesseq(0, I) & (~$lesseq(N, I)) & (~$lesseq(J, I)) & (~$lesseq(N, J)))) | $lesseq(read(A, I), read(A, J))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.21/0.44 tff(31,plain,
% 0.21/0.44 (![A: array, N: $int] : (sorted(A, N) <=> ![I: $int, J: $int] : ((~($lesseq(0, I) & (~$lesseq(N, I)) & (~$lesseq(J, I)) & (~$lesseq(N, J)))) | $lesseq(read(A, I), read(A, J))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[30, 26])).
% 0.21/0.44 tff(32,plain,
% 0.21/0.44 (![A: array, N: $int] : (sorted(A, N) <=> ![I: $int, J: $int] : ((~($greatereq(I, 0) & (~$lesseq($sum(N, $product(-1, I)), 0)) & (~$lesseq($sum(J, $product(-1, I)), 0)) & (~$lesseq($sum(N, $product(-1, J)), 0)))) | $lesseq($sum(read(A, I), $product(-1, read(A, J))), 0)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[31, 25])).
% 0.21/0.44 tff(33,plain,
% 0.21/0.44 (![A: array, N: $int] : (sorted(A, N) <=> ![I: $int, J: $int] : ((~($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, N)), 0)) & (~$greatereq($sum(I, $product(-1, J)), 0)) & (~$greatereq($sum(J, $product(-1, N)), 0)))) | $lesseq($sum(read(A, I), $product(-1, read(A, J))), 0)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[32, 23])).
% 0.21/0.44 tff(34,plain,(
% 0.21/0.44 ![A: array, N: $int] : (((~sorted(A, N)) | ![I: $int, J: $int] : ((~($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, N)), 0)) & (~$greatereq($sum(I, $product(-1, J)), 0)) & (~$greatereq($sum(J, $product(-1, N)), 0)))) | $lesseq($sum(read(A, I), $product(-1, read(A, J))), 0))) & (sorted(A, N) | (~((~($greatereq(tptp_fun_I_3(N, A), 0) & (~$greatereq($sum(tptp_fun_I_3(N, A), $product(-1, N)), 0)) & (~$greatereq($sum(tptp_fun_I_3(N, A), $product(-1, tptp_fun_J_2(N, A))), 0)) & (~$greatereq($sum(tptp_fun_J_2(N, A), $product(-1, N)), 0)))) | $lesseq($sum(read(A, tptp_fun_I_3(N, A)), $product(-1, read(A, tptp_fun_J_2(N, A)))), 0)))))),
% 0.21/0.44 inference(skolemize,[status(sab)],[33])).
% 0.21/0.44 tff(35,plain,
% 0.21/0.44 (![A: array, N: $int] : (((~sorted(A, N)) | ![I: $int, J: $int] : ((~($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, N)), 0)) & (~$greatereq($sum(I, $product(-1, J)), 0)) & (~$greatereq($sum(J, $product(-1, N)), 0)))) | $lesseq($sum(read(A, I), $product(-1, read(A, J))), 0))) & (sorted(A, N) | (~((~($greatereq(tptp_fun_I_3(N, A), 0) & (~$lesseq($sum(N, $product(-1, tptp_fun_I_3(N, A))), 0)) & (~$lesseq($sum(tptp_fun_J_2(N, A), $product(-1, tptp_fun_I_3(N, A))), 0)) & (~$lesseq($sum(N, $product(-1, tptp_fun_J_2(N, A))), 0)))) | $lesseq($sum(read(A, tptp_fun_I_3(N, A)), $product(-1, read(A, tptp_fun_J_2(N, A)))), 0)))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[34, 21])).
% 0.21/0.44 tff(36,plain,
% 0.21/0.44 (![A: array, N: $int] : (~((~((~sorted(A, N)) | ![I: $int, J: $int] : ($greatereq($sum(J, $product(-1, N)), 0) | $greatereq($sum(I, $product(-1, J)), 0) | $greatereq($sum(I, $product(-1, N)), 0) | $lesseq($sum(read(A, I), $product(-1, read(A, J))), 0) | (~$greatereq(I, 0))))) | (~(sorted(A, N) | (~($lesseq($sum(read(A, tptp_fun_I_3(N, A)), $product(-1, read(A, tptp_fun_J_2(N, A)))), 0) | $lesseq($sum(N, $product(-1, tptp_fun_I_3(N, A))), 0) | $lesseq($sum(tptp_fun_J_2(N, A), $product(-1, tptp_fun_I_3(N, A))), 0) | $lesseq($sum(N, $product(-1, tptp_fun_J_2(N, A))), 0) | (~$greatereq(tptp_fun_I_3(N, A), 0))))))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[35, 19])).
% 0.21/0.44 tff(37,plain,
% 0.21/0.44 (![A: array, N: $int] : (~((~((~sorted(A, N)) | ![I: $int, J: $int] : ($greatereq($sum(J, $product(-1, N)), 0) | $greatereq($sum(I, $product(-1, J)), 0) | $greatereq($sum(I, $product(-1, N)), 0) | $lesseq($sum(read(A, I), $product(-1, read(A, J))), 0) | (~$greatereq(I, 0))))) | (~(sorted(A, N) | (~($lesseq($sum(read(A, tptp_fun_I_3(N, A)), $product(-1, read(A, tptp_fun_J_2(N, A)))), 0) | $lesseq($sum(N, $product(-1, tptp_fun_I_3(N, A))), 0) | $lesseq($sum(tptp_fun_J_2(N, A), $product(-1, tptp_fun_I_3(N, A))), 0) | $lesseq($sum(N, $product(-1, tptp_fun_J_2(N, A))), 0) | (~$greatereq(tptp_fun_I_3(N, A), 0))))))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[36, 17])).
% 0.21/0.44 tff(38,plain,
% 0.21/0.44 (((~![A: array, N: $int] : (~((~((~sorted(A, N)) | ![I: $int, J: $int] : ($greatereq($sum(J, $product(-1, N)), 0) | $greatereq($sum(I, $product(-1, J)), 0) | $greatereq($sum(I, $product(-1, N)), 0) | $lesseq($sum(read(A, I), $product(-1, read(A, J))), 0) | (~$greatereq(I, 0))))) | (~(sorted(A, N) | (~($lesseq($sum(read(A, tptp_fun_I_3(N, A)), $product(-1, read(A, tptp_fun_J_2(N, A)))), 0) | $lesseq($sum(N, $product(-1, tptp_fun_I_3(N, A))), 0) | $lesseq($sum(tptp_fun_J_2(N, A), $product(-1, tptp_fun_I_3(N, A))), 0) | $lesseq($sum(N, $product(-1, tptp_fun_J_2(N, A))), 0) | (~$greatereq(tptp_fun_I_3(N, A), 0))))))))) | (~((~((~sorted(elem!8, 1)) | ![I: $int, J: $int] : ($greatereq($sum(I, $product(-1, J)), 0) | (~$greatereq(I, 0)) | $greatereq(J, 1) | $lesseq($sum(read(elem!8, I), $product(-1, read(elem!8, J))), 0) | $greatereq(I, 1)))) | (~(sorted(elem!8, 1) | (~($lesseq($sum(read(elem!8, tptp_fun_I_3(1, elem!8)), $product(-1, read(elem!8, tptp_fun_J_2(1, elem!8)))), 0) | $greatereq(tptp_fun_I_3(1, elem!8), 1) | $lesseq($sum(tptp_fun_J_2(1, elem!8), $product(-1, tptp_fun_I_3(1, elem!8))), 0) | $greatereq(tptp_fun_J_2(1, elem!8), 1) | (~$greatereq(tptp_fun_I_3(1, elem!8), 0))))))))) <=> ((~![A: array, N: $int] : (~((~((~sorted(A, N)) | ![I: $int, J: $int] : ($greatereq($sum(J, $product(-1, N)), 0) | $greatereq($sum(I, $product(-1, J)), 0) | $greatereq($sum(I, $product(-1, N)), 0) | $lesseq($sum(read(A, I), $product(-1, read(A, J))), 0) | (~$greatereq(I, 0))))) | (~(sorted(A, N) | (~($lesseq($sum(read(A, tptp_fun_I_3(N, A)), $product(-1, read(A, tptp_fun_J_2(N, A)))), 0) | $lesseq($sum(N, $product(-1, tptp_fun_I_3(N, A))), 0) | $lesseq($sum(tptp_fun_J_2(N, A), $product(-1, tptp_fun_I_3(N, A))), 0) | $lesseq($sum(N, $product(-1, tptp_fun_J_2(N, A))), 0) | (~$greatereq(tptp_fun_I_3(N, A), 0))))))))) | (~((~((~sorted(elem!8, 1)) | ![I: $int, J: $int] : ($greatereq($sum(I, $product(-1, J)), 0) | (~$greatereq(I, 0)) | $greatereq(J, 1) | $lesseq($sum(read(elem!8, I), $product(-1, read(elem!8, J))), 0) | $greatereq(I, 1)))) | (~(sorted(elem!8, 1) | (~($lesseq($sum(read(elem!8, tptp_fun_I_3(1, elem!8)), $product(-1, read(elem!8, tptp_fun_J_2(1, elem!8)))), 0) | $greatereq(tptp_fun_I_3(1, elem!8), 1) | $lesseq($sum(tptp_fun_J_2(1, elem!8), $product(-1, tptp_fun_I_3(1, elem!8))), 0) | $greatereq(tptp_fun_J_2(1, elem!8), 1) | (~$greatereq(tptp_fun_I_3(1, elem!8), 0)))))))))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(39,plain,
% 0.21/0.44 ((~((~((~sorted(elem!8, $sum($sum(-1, $product(-1, -1)), $product(-1, -1)))) | ![I: $int, J: $int] : ($greatereq($sum(J, $product(-1, $sum($sum(-1, $product(-1, -1)), $product(-1, -1)))), 0) | $greatereq($sum(I, $product(-1, J)), 0) | $greatereq($sum(I, $product(-1, $sum($sum(-1, $product(-1, -1)), $product(-1, -1)))), 0) | $lesseq($sum(read(elem!8, I), $product(-1, read(elem!8, J))), 0) | (~$greatereq(I, 0))))) | (~(sorted(elem!8, $sum($sum(-1, $product(-1, -1)), $product(-1, -1))) | (~($lesseq($sum(read(elem!8, tptp_fun_I_3($sum($sum(-1, $product(-1, -1)), $product(-1, -1)), elem!8)), $product(-1, read(elem!8, tptp_fun_J_2($sum($sum(-1, $product(-1, -1)), $product(-1, -1)), elem!8)))), 0) | $lesseq($sum($sum($sum(-1, $product(-1, -1)), $product(-1, -1)), $product(-1, tptp_fun_I_3($sum($sum(-1, $product(-1, -1)), $product(-1, -1)), elem!8))), 0) | $lesseq($sum(tptp_fun_J_2($sum($sum(-1, $product(-1, -1)), $product(-1, -1)), elem!8), $product(-1, tptp_fun_I_3($sum($sum(-1, $product(-1, -1)), $product(-1, -1)), elem!8))), 0) | $lesseq($sum($sum($sum(-1, $product(-1, -1)), $product(-1, -1)), $product(-1, tptp_fun_J_2($sum($sum(-1, $product(-1, -1)), $product(-1, -1)), elem!8))), 0) | (~$greatereq(tptp_fun_I_3($sum($sum(-1, $product(-1, -1)), $product(-1, -1)), elem!8), 0)))))))) <=> (~((~((~sorted(elem!8, 1)) | ![I: $int, J: $int] : ($greatereq($sum(I, $product(-1, J)), 0) | (~$greatereq(I, 0)) | $greatereq(J, 1) | $lesseq($sum(read(elem!8, I), $product(-1, read(elem!8, J))), 0) | $greatereq(I, 1)))) | (~(sorted(elem!8, 1) | (~($lesseq($sum(read(elem!8, tptp_fun_I_3(1, elem!8)), $product(-1, read(elem!8, tptp_fun_J_2(1, elem!8)))), 0) | $greatereq(tptp_fun_I_3(1, elem!8), 1) | $lesseq($sum(tptp_fun_J_2(1, elem!8), $product(-1, tptp_fun_I_3(1, elem!8))), 0) | $greatereq(tptp_fun_J_2(1, elem!8), 1) | (~$greatereq(tptp_fun_I_3(1, elem!8), 0))))))))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(40,plain,
% 0.21/0.44 (((~![A: array, N: $int] : (~((~((~sorted(A, N)) | ![I: $int, J: $int] : ($greatereq($sum(J, $product(-1, N)), 0) | $greatereq($sum(I, $product(-1, J)), 0) | $greatereq($sum(I, $product(-1, N)), 0) | $lesseq($sum(read(A, I), $product(-1, read(A, J))), 0) | (~$greatereq(I, 0))))) | (~(sorted(A, N) | (~($lesseq($sum(read(A, tptp_fun_I_3(N, A)), $product(-1, read(A, tptp_fun_J_2(N, A)))), 0) | $lesseq($sum(N, $product(-1, tptp_fun_I_3(N, A))), 0) | $lesseq($sum(tptp_fun_J_2(N, A), $product(-1, tptp_fun_I_3(N, A))), 0) | $lesseq($sum(N, $product(-1, tptp_fun_J_2(N, A))), 0) | (~$greatereq(tptp_fun_I_3(N, A), 0))))))))) | (~((~((~sorted(elem!8, $sum($sum(-1, $product(-1, -1)), $product(-1, -1)))) | ![I: $int, J: $int] : ($greatereq($sum(J, $product(-1, $sum($sum(-1, $product(-1, -1)), $product(-1, -1)))), 0) | $greatereq($sum(I, $product(-1, J)), 0) | $greatereq($sum(I, $product(-1, $sum($sum(-1, $product(-1, -1)), $product(-1, -1)))), 0) | $lesseq($sum(read(elem!8, I), $product(-1, read(elem!8, J))), 0) | (~$greatereq(I, 0))))) | (~(sorted(elem!8, $sum($sum(-1, $product(-1, -1)), $product(-1, -1))) | (~($lesseq($sum(read(elem!8, tptp_fun_I_3($sum($sum(-1, $product(-1, -1)), $product(-1, -1)), elem!8)), $product(-1, read(elem!8, tptp_fun_J_2($sum($sum(-1, $product(-1, -1)), $product(-1, -1)), elem!8)))), 0) | $lesseq($sum($sum($sum(-1, $product(-1, -1)), $product(-1, -1)), $product(-1, tptp_fun_I_3($sum($sum(-1, $product(-1, -1)), $product(-1, -1)), elem!8))), 0) | $lesseq($sum(tptp_fun_J_2($sum($sum(-1, $product(-1, -1)), $product(-1, -1)), elem!8), $product(-1, tptp_fun_I_3($sum($sum(-1, $product(-1, -1)), $product(-1, -1)), elem!8))), 0) | $lesseq($sum($sum($sum(-1, $product(-1, -1)), $product(-1, -1)), $product(-1, tptp_fun_J_2($sum($sum(-1, $product(-1, -1)), $product(-1, -1)), elem!8))), 0) | (~$greatereq(tptp_fun_I_3($sum($sum(-1, $product(-1, -1)), $product(-1, -1)), elem!8), 0))))))))) <=> ((~![A: array, N: $int] : (~((~((~sorted(A, N)) | ![I: $int, J: $int] : ($greatereq($sum(J, $product(-1, N)), 0) | $greatereq($sum(I, $product(-1, J)), 0) | $greatereq($sum(I, $product(-1, N)), 0) | $lesseq($sum(read(A, I), $product(-1, read(A, J))), 0) | (~$greatereq(I, 0))))) | (~(sorted(A, N) | (~($lesseq($sum(read(A, tptp_fun_I_3(N, A)), $product(-1, read(A, tptp_fun_J_2(N, A)))), 0) | $lesseq($sum(N, $product(-1, tptp_fun_I_3(N, A))), 0) | $lesseq($sum(tptp_fun_J_2(N, A), $product(-1, tptp_fun_I_3(N, A))), 0) | $lesseq($sum(N, $product(-1, tptp_fun_J_2(N, A))), 0) | (~$greatereq(tptp_fun_I_3(N, A), 0))))))))) | (~((~((~sorted(elem!8, 1)) | ![I: $int, J: $int] : ($greatereq($sum(I, $product(-1, J)), 0) | (~$greatereq(I, 0)) | $greatereq(J, 1) | $lesseq($sum(read(elem!8, I), $product(-1, read(elem!8, J))), 0) | $greatereq(I, 1)))) | (~(sorted(elem!8, 1) | (~($lesseq($sum(read(elem!8, tptp_fun_I_3(1, elem!8)), $product(-1, read(elem!8, tptp_fun_J_2(1, elem!8)))), 0) | $greatereq(tptp_fun_I_3(1, elem!8), 1) | $lesseq($sum(tptp_fun_J_2(1, elem!8), $product(-1, tptp_fun_I_3(1, elem!8))), 0) | $greatereq(tptp_fun_J_2(1, elem!8), 1) | (~$greatereq(tptp_fun_I_3(1, elem!8), 0)))))))))),
% 0.21/0.44 inference(monotonicity,[status(thm)],[39])).
% 0.21/0.44 tff(41,plain,
% 0.21/0.44 (((~![A: array, N: $int] : (~((~((~sorted(A, N)) | ![I: $int, J: $int] : ($greatereq($sum(J, $product(-1, N)), 0) | $greatereq($sum(I, $product(-1, J)), 0) | $greatereq($sum(I, $product(-1, N)), 0) | $lesseq($sum(read(A, I), $product(-1, read(A, J))), 0) | (~$greatereq(I, 0))))) | (~(sorted(A, N) | (~($lesseq($sum(read(A, tptp_fun_I_3(N, A)), $product(-1, read(A, tptp_fun_J_2(N, A)))), 0) | $lesseq($sum(N, $product(-1, tptp_fun_I_3(N, A))), 0) | $lesseq($sum(tptp_fun_J_2(N, A), $product(-1, tptp_fun_I_3(N, A))), 0) | $lesseq($sum(N, $product(-1, tptp_fun_J_2(N, A))), 0) | (~$greatereq(tptp_fun_I_3(N, A), 0))))))))) | (~((~((~sorted(elem!8, $sum($sum(-1, $product(-1, -1)), $product(-1, -1)))) | ![I: $int, J: $int] : ($greatereq($sum(J, $product(-1, $sum($sum(-1, $product(-1, -1)), $product(-1, -1)))), 0) | $greatereq($sum(I, $product(-1, J)), 0) | $greatereq($sum(I, $product(-1, $sum($sum(-1, $product(-1, -1)), $product(-1, -1)))), 0) | $lesseq($sum(read(elem!8, I), $product(-1, read(elem!8, J))), 0) | (~$greatereq(I, 0))))) | (~(sorted(elem!8, $sum($sum(-1, $product(-1, -1)), $product(-1, -1))) | (~($lesseq($sum(read(elem!8, tptp_fun_I_3($sum($sum(-1, $product(-1, -1)), $product(-1, -1)), elem!8)), $product(-1, read(elem!8, tptp_fun_J_2($sum($sum(-1, $product(-1, -1)), $product(-1, -1)), elem!8)))), 0) | $lesseq($sum($sum($sum(-1, $product(-1, -1)), $product(-1, -1)), $product(-1, tptp_fun_I_3($sum($sum(-1, $product(-1, -1)), $product(-1, -1)), elem!8))), 0) | $lesseq($sum(tptp_fun_J_2($sum($sum(-1, $product(-1, -1)), $product(-1, -1)), elem!8), $product(-1, tptp_fun_I_3($sum($sum(-1, $product(-1, -1)), $product(-1, -1)), elem!8))), 0) | $lesseq($sum($sum($sum(-1, $product(-1, -1)), $product(-1, -1)), $product(-1, tptp_fun_J_2($sum($sum(-1, $product(-1, -1)), $product(-1, -1)), elem!8))), 0) | (~$greatereq(tptp_fun_I_3($sum($sum(-1, $product(-1, -1)), $product(-1, -1)), elem!8), 0))))))))) <=> ((~![A: array, N: $int] : (~((~((~sorted(A, N)) | ![I: $int, J: $int] : ($greatereq($sum(J, $product(-1, N)), 0) | $greatereq($sum(I, $product(-1, J)), 0) | $greatereq($sum(I, $product(-1, N)), 0) | $lesseq($sum(read(A, I), $product(-1, read(A, J))), 0) | (~$greatereq(I, 0))))) | (~(sorted(A, N) | (~($lesseq($sum(read(A, tptp_fun_I_3(N, A)), $product(-1, read(A, tptp_fun_J_2(N, A)))), 0) | $lesseq($sum(N, $product(-1, tptp_fun_I_3(N, A))), 0) | $lesseq($sum(tptp_fun_J_2(N, A), $product(-1, tptp_fun_I_3(N, A))), 0) | $lesseq($sum(N, $product(-1, tptp_fun_J_2(N, A))), 0) | (~$greatereq(tptp_fun_I_3(N, A), 0))))))))) | (~((~((~sorted(elem!8, 1)) | ![I: $int, J: $int] : ($greatereq($sum(I, $product(-1, J)), 0) | (~$greatereq(I, 0)) | $greatereq(J, 1) | $lesseq($sum(read(elem!8, I), $product(-1, read(elem!8, J))), 0) | $greatereq(I, 1)))) | (~(sorted(elem!8, 1) | (~($lesseq($sum(read(elem!8, tptp_fun_I_3(1, elem!8)), $product(-1, read(elem!8, tptp_fun_J_2(1, elem!8)))), 0) | $greatereq(tptp_fun_I_3(1, elem!8), 1) | $lesseq($sum(tptp_fun_J_2(1, elem!8), $product(-1, tptp_fun_I_3(1, elem!8))), 0) | $greatereq(tptp_fun_J_2(1, elem!8), 1) | (~$greatereq(tptp_fun_I_3(1, elem!8), 0)))))))))),
% 0.21/0.44 inference(transitivity,[status(thm)],[40, 38])).
% 0.21/0.44 tff(42,plain,
% 0.21/0.44 ((~![A: array, N: $int] : (~((~((~sorted(A, N)) | ![I: $int, J: $int] : ($greatereq($sum(J, $product(-1, N)), 0) | $greatereq($sum(I, $product(-1, J)), 0) | $greatereq($sum(I, $product(-1, N)), 0) | $lesseq($sum(read(A, I), $product(-1, read(A, J))), 0) | (~$greatereq(I, 0))))) | (~(sorted(A, N) | (~($lesseq($sum(read(A, tptp_fun_I_3(N, A)), $product(-1, read(A, tptp_fun_J_2(N, A)))), 0) | $lesseq($sum(N, $product(-1, tptp_fun_I_3(N, A))), 0) | $lesseq($sum(tptp_fun_J_2(N, A), $product(-1, tptp_fun_I_3(N, A))), 0) | $lesseq($sum(N, $product(-1, tptp_fun_J_2(N, A))), 0) | (~$greatereq(tptp_fun_I_3(N, A), 0))))))))) | (~((~((~sorted(elem!8, $sum($sum(-1, $product(-1, -1)), $product(-1, -1)))) | ![I: $int, J: $int] : ($greatereq($sum(J, $product(-1, $sum($sum(-1, $product(-1, -1)), $product(-1, -1)))), 0) | $greatereq($sum(I, $product(-1, J)), 0) | $greatereq($sum(I, $product(-1, $sum($sum(-1, $product(-1, -1)), $product(-1, -1)))), 0) | $lesseq($sum(read(elem!8, I), $product(-1, read(elem!8, J))), 0) | (~$greatereq(I, 0))))) | (~(sorted(elem!8, $sum($sum(-1, $product(-1, -1)), $product(-1, -1))) | (~($lesseq($sum(read(elem!8, tptp_fun_I_3($sum($sum(-1, $product(-1, -1)), $product(-1, -1)), elem!8)), $product(-1, read(elem!8, tptp_fun_J_2($sum($sum(-1, $product(-1, -1)), $product(-1, -1)), elem!8)))), 0) | $lesseq($sum($sum($sum(-1, $product(-1, -1)), $product(-1, -1)), $product(-1, tptp_fun_I_3($sum($sum(-1, $product(-1, -1)), $product(-1, -1)), elem!8))), 0) | $lesseq($sum(tptp_fun_J_2($sum($sum(-1, $product(-1, -1)), $product(-1, -1)), elem!8), $product(-1, tptp_fun_I_3($sum($sum(-1, $product(-1, -1)), $product(-1, -1)), elem!8))), 0) | $lesseq($sum($sum($sum(-1, $product(-1, -1)), $product(-1, -1)), $product(-1, tptp_fun_J_2($sum($sum(-1, $product(-1, -1)), $product(-1, -1)), elem!8))), 0) | (~$greatereq(tptp_fun_I_3($sum($sum(-1, $product(-1, -1)), $product(-1, -1)), elem!8), 0))))))))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(43,plain,
% 0.21/0.44 ((~![A: array, N: $int] : (~((~((~sorted(A, N)) | ![I: $int, J: $int] : ($greatereq($sum(J, $product(-1, N)), 0) | $greatereq($sum(I, $product(-1, J)), 0) | $greatereq($sum(I, $product(-1, N)), 0) | $lesseq($sum(read(A, I), $product(-1, read(A, J))), 0) | (~$greatereq(I, 0))))) | (~(sorted(A, N) | (~($lesseq($sum(read(A, tptp_fun_I_3(N, A)), $product(-1, read(A, tptp_fun_J_2(N, A)))), 0) | $lesseq($sum(N, $product(-1, tptp_fun_I_3(N, A))), 0) | $lesseq($sum(tptp_fun_J_2(N, A), $product(-1, tptp_fun_I_3(N, A))), 0) | $lesseq($sum(N, $product(-1, tptp_fun_J_2(N, A))), 0) | (~$greatereq(tptp_fun_I_3(N, A), 0))))))))) | (~((~((~sorted(elem!8, 1)) | ![I: $int, J: $int] : ($greatereq($sum(I, $product(-1, J)), 0) | (~$greatereq(I, 0)) | $greatereq(J, 1) | $lesseq($sum(read(elem!8, I), $product(-1, read(elem!8, J))), 0) | $greatereq(I, 1)))) | (~(sorted(elem!8, 1) | (~($lesseq($sum(read(elem!8, tptp_fun_I_3(1, elem!8)), $product(-1, read(elem!8, tptp_fun_J_2(1, elem!8)))), 0) | $greatereq(tptp_fun_I_3(1, elem!8), 1) | $lesseq($sum(tptp_fun_J_2(1, elem!8), $product(-1, tptp_fun_I_3(1, elem!8))), 0) | $greatereq(tptp_fun_J_2(1, elem!8), 1) | (~$greatereq(tptp_fun_I_3(1, elem!8), 0))))))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.21/0.44 tff(44,plain,
% 0.21/0.44 (~((~((~sorted(elem!8, 1)) | ![I: $int, J: $int] : ($greatereq($sum(I, $product(-1, J)), 0) | (~$greatereq(I, 0)) | $greatereq(J, 1) | $lesseq($sum(read(elem!8, I), $product(-1, read(elem!8, J))), 0) | $greatereq(I, 1)))) | (~(sorted(elem!8, 1) | (~($lesseq($sum(read(elem!8, tptp_fun_I_3(1, elem!8)), $product(-1, read(elem!8, tptp_fun_J_2(1, elem!8)))), 0) | $greatereq(tptp_fun_I_3(1, elem!8), 1) | $lesseq($sum(tptp_fun_J_2(1, elem!8), $product(-1, tptp_fun_I_3(1, elem!8))), 0) | $greatereq(tptp_fun_J_2(1, elem!8), 1) | (~$greatereq(tptp_fun_I_3(1, elem!8), 0)))))))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[43, 37])).
% 0.21/0.44 tff(45,plain,
% 0.21/0.44 (((~((~sorted(elem!8, 1)) | ![I: $int, J: $int] : ($greatereq($sum(I, $product(-1, J)), 0) | (~$greatereq(I, 0)) | $greatereq(J, 1) | $lesseq($sum(read(elem!8, I), $product(-1, read(elem!8, J))), 0) | $greatereq(I, 1)))) | (~(sorted(elem!8, 1) | (~($lesseq($sum(read(elem!8, tptp_fun_I_3(1, elem!8)), $product(-1, read(elem!8, tptp_fun_J_2(1, elem!8)))), 0) | $greatereq(tptp_fun_I_3(1, elem!8), 1) | $lesseq($sum(tptp_fun_J_2(1, elem!8), $product(-1, tptp_fun_I_3(1, elem!8))), 0) | $greatereq(tptp_fun_J_2(1, elem!8), 1) | (~$greatereq(tptp_fun_I_3(1, elem!8), 0))))))) | (sorted(elem!8, 1) | (~($lesseq($sum(read(elem!8, tptp_fun_I_3(1, elem!8)), $product(-1, read(elem!8, tptp_fun_J_2(1, elem!8)))), 0) | $greatereq(tptp_fun_I_3(1, elem!8), 1) | $lesseq($sum(tptp_fun_J_2(1, elem!8), $product(-1, tptp_fun_I_3(1, elem!8))), 0) | $greatereq(tptp_fun_J_2(1, elem!8), 1) | (~$greatereq(tptp_fun_I_3(1, elem!8), 0)))))),
% 0.21/0.44 inference(tautology,[status(thm)],[])).
% 0.21/0.44 tff(46,plain,
% 0.21/0.44 (sorted(elem!8, 1) | (~($lesseq($sum(read(elem!8, tptp_fun_I_3(1, elem!8)), $product(-1, read(elem!8, tptp_fun_J_2(1, elem!8)))), 0) | $greatereq(tptp_fun_I_3(1, elem!8), 1) | $lesseq($sum(tptp_fun_J_2(1, elem!8), $product(-1, tptp_fun_I_3(1, elem!8))), 0) | $greatereq(tptp_fun_J_2(1, elem!8), 1) | (~$greatereq(tptp_fun_I_3(1, elem!8), 0))))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[45, 44])).
% 0.21/0.44 tff(47,plain,
% 0.21/0.44 ((~(sorted(elem!8, 1) | (~($lesseq($sum(read(elem!8, tptp_fun_I_3(1, elem!8)), $product(-1, read(elem!8, tptp_fun_J_2(1, elem!8)))), 0) | $greatereq(tptp_fun_I_3(1, elem!8), 1) | $lesseq($sum(tptp_fun_J_2(1, elem!8), $product(-1, tptp_fun_I_3(1, elem!8))), 0) | $greatereq(tptp_fun_J_2(1, elem!8), 1) | (~$greatereq(tptp_fun_I_3(1, elem!8), 0)))))) | sorted(elem!8, 1) | (~($lesseq($sum(read(elem!8, tptp_fun_I_3(1, elem!8)), $product(-1, read(elem!8, tptp_fun_J_2(1, elem!8)))), 0) | $greatereq(tptp_fun_I_3(1, elem!8), 1) | $lesseq($sum(tptp_fun_J_2(1, elem!8), $product(-1, tptp_fun_I_3(1, elem!8))), 0) | $greatereq(tptp_fun_J_2(1, elem!8), 1) | (~$greatereq(tptp_fun_I_3(1, elem!8), 0))))),
% 0.21/0.45 inference(tautology,[status(thm)],[])).
% 0.21/0.45 tff(48,plain,
% 0.21/0.45 (sorted(elem!8, 1) | (~($lesseq($sum(read(elem!8, tptp_fun_I_3(1, elem!8)), $product(-1, read(elem!8, tptp_fun_J_2(1, elem!8)))), 0) | $greatereq(tptp_fun_I_3(1, elem!8), 1) | $lesseq($sum(tptp_fun_J_2(1, elem!8), $product(-1, tptp_fun_I_3(1, elem!8))), 0) | $greatereq(tptp_fun_J_2(1, elem!8), 1) | (~$greatereq(tptp_fun_I_3(1, elem!8), 0))))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[47, 46])).
% 0.21/0.45 tff(49,plain,
% 0.21/0.45 (sorted(elem!8, 1)),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[48, 12])).
% 0.21/0.45 tff(50,plain,
% 0.21/0.45 (sorted(rev(elem!8, 1), 1)),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[49, 3])).
% 0.21/0.45 tff(51,plain,
% 0.21/0.45 (^[A: array, N: $int] : refl(((~sorted(A, N)) | (~sorted(rev(A, N), N))) <=> ((~sorted(A, N)) | (~sorted(rev(A, N), N))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(52,plain,
% 0.21/0.45 (![A: array, N: $int] : ((~sorted(A, N)) | (~sorted(rev(A, N), N))) <=> ![A: array, N: $int] : ((~sorted(A, N)) | (~sorted(rev(A, N), N)))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[51])).
% 0.21/0.45 tff(53,plain,
% 0.21/0.45 (![A: array, N: $int] : ((~sorted(A, N)) | (~sorted(rev(A, N), N))) <=> ![A: array, N: $int] : ((~sorted(A, N)) | (~sorted(rev(A, N), N)))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(54,plain,
% 0.21/0.45 ((~(~![A: array, N: $int] : ((~sorted(A, N)) | (~sorted(rev(A, N), N))))) <=> ![A: array, N: $int] : ((~sorted(A, N)) | (~sorted(rev(A, N), N)))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(55,plain,
% 0.21/0.45 ((~![A: array, N: $int] : (sorted(A, N) => (~sorted(rev(A, N), N)))) <=> (~![A: array, N: $int] : ((~sorted(A, N)) | (~sorted(rev(A, N), N))))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(56,plain,
% 0.21/0.45 ((~(~![A: array, N: $int] : (sorted(A, N) => (~sorted(rev(A, N), N))))) <=> (~(~![A: array, N: $int] : ((~sorted(A, N)) | (~sorted(rev(A, N), N)))))),
% 0.21/0.45 inference(monotonicity,[status(thm)],[55])).
% 0.21/0.45 tff(57,plain,
% 0.21/0.45 ((~(~![A: array, N: $int] : (sorted(A, N) => (~sorted(rev(A, N), N))))) <=> ![A: array, N: $int] : ((~sorted(A, N)) | (~sorted(rev(A, N), N)))),
% 0.21/0.45 inference(transitivity,[status(thm)],[56, 54])).
% 0.21/0.45 tff(58,axiom,(~(~![A: array, N: $int] : (sorted(A, N) => (~sorted(rev(A, N), N))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','c4')).
% 0.21/0.45 tff(59,plain,
% 0.21/0.45 (![A: array, N: $int] : ((~sorted(A, N)) | (~sorted(rev(A, N), N)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.21/0.45 tff(60,plain,
% 0.21/0.45 (![A: array, N: $int] : ((~sorted(A, N)) | (~sorted(rev(A, N), N)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[59, 53])).
% 0.21/0.45 tff(61,plain,(
% 0.21/0.45 ![A: array, N: $int] : ((~sorted(A, N)) | (~sorted(rev(A, N), N)))),
% 0.21/0.45 inference(skolemize,[status(sab)],[60])).
% 0.21/0.45 tff(62,plain,
% 0.21/0.45 (![A: array, N: $int] : ((~sorted(A, N)) | (~sorted(rev(A, N), N)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[61, 52])).
% 0.21/0.45 tff(63,plain,
% 0.21/0.45 (((~![A: array, N: $int] : ((~sorted(A, N)) | (~sorted(rev(A, N), N)))) | ((~sorted(elem!8, 1)) | (~sorted(rev(elem!8, 1), 1)))) <=> ((~![A: array, N: $int] : ((~sorted(A, N)) | (~sorted(rev(A, N), N)))) | (~sorted(elem!8, 1)) | (~sorted(rev(elem!8, 1), 1)))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(64,plain,
% 0.21/0.45 ((~![A: array, N: $int] : ((~sorted(A, N)) | (~sorted(rev(A, N), N)))) | ((~sorted(elem!8, 1)) | (~sorted(rev(elem!8, 1), 1)))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(65,plain,
% 0.21/0.45 ((~![A: array, N: $int] : ((~sorted(A, N)) | (~sorted(rev(A, N), N)))) | (~sorted(elem!8, 1)) | (~sorted(rev(elem!8, 1), 1))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.21/0.45 tff(66,plain,
% 0.21/0.45 (~sorted(rev(elem!8, 1), 1)),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[65, 62, 49])).
% 0.21/0.45 tff(67,plain,
% 0.21/0.45 ($false),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[66, 50])).
% 0.21/0.45 tff(68,plain,(~(rev(elem!8, 1) = elem!8)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.45 tff(69,plain,
% 0.21/0.45 (^[A: array, B: array, N: $int] : rewrite(((~(($greatereq(tptp_fun_I_7(N, B, A), 0) & (~$lesseq($sum(N, $product(-1, tptp_fun_I_7(N, B, A))), 0)) & ($sum(read(B, tptp_fun_I_7(N, B, A)), $product(-1, read(A, $sum(-1, $sum(N, $product(-1, tptp_fun_I_7(N, B, A))))))) = 0)) | (((~$greatereq(tptp_fun_I_7(N, B, A), 0)) | $lesseq($sum(N, $product(-1, tptp_fun_I_7(N, B, A))), 0)) & ($sum(read(B, tptp_fun_I_7(N, B, A)), $product(-1, read(A, tptp_fun_I_7(N, B, A)))) = 0)))) | (rev(A, N) = B)) <=> ((~((~($lesseq($sum(N, $product(-1, tptp_fun_I_7(N, B, A))), 0) | (~$greatereq(tptp_fun_I_7(N, B, A), 0)) | (~($sum(read(B, tptp_fun_I_7(N, B, A)), $product(-1, read(A, $sum(-1, $sum(N, $product(-1, tptp_fun_I_7(N, B, A))))))) = 0)))) | (~((~((~$greatereq(tptp_fun_I_7(N, B, A), 0)) | $lesseq($sum(N, $product(-1, tptp_fun_I_7(N, B, A))), 0))) | (~($sum(read(B, tptp_fun_I_7(N, B, A)), $product(-1, read(A, tptp_fun_I_7(N, B, A)))) = 0)))))) | (rev(A, N) = B)))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(70,plain,
% 0.21/0.45 (![A: array, B: array, N: $int] : ((~(($greatereq(tptp_fun_I_7(N, B, A), 0) & (~$lesseq($sum(N, $product(-1, tptp_fun_I_7(N, B, A))), 0)) & ($sum(read(B, tptp_fun_I_7(N, B, A)), $product(-1, read(A, $sum(-1, $sum(N, $product(-1, tptp_fun_I_7(N, B, A))))))) = 0)) | (((~$greatereq(tptp_fun_I_7(N, B, A), 0)) | $lesseq($sum(N, $product(-1, tptp_fun_I_7(N, B, A))), 0)) & ($sum(read(B, tptp_fun_I_7(N, B, A)), $product(-1, read(A, tptp_fun_I_7(N, B, A)))) = 0)))) | (rev(A, N) = B)) <=> ![A: array, B: array, N: $int] : ((~((~($lesseq($sum(N, $product(-1, tptp_fun_I_7(N, B, A))), 0) | (~$greatereq(tptp_fun_I_7(N, B, A), 0)) | (~($sum(read(B, tptp_fun_I_7(N, B, A)), $product(-1, read(A, $sum(-1, $sum(N, $product(-1, tptp_fun_I_7(N, B, A))))))) = 0)))) | (~((~((~$greatereq(tptp_fun_I_7(N, B, A), 0)) | $lesseq($sum(N, $product(-1, tptp_fun_I_7(N, B, A))), 0))) | (~($sum(read(B, tptp_fun_I_7(N, B, A)), $product(-1, read(A, tptp_fun_I_7(N, B, A)))) = 0)))))) | (rev(A, N) = B))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[69])).
% 0.21/0.45 tff(71,plain,
% 0.21/0.45 (^[A: array, B: array, N: $int] : rewrite(((~![I: $int] : (($greatereq(I, 0) & (~$lesseq($sum(N, $product(-1, I)), 0)) & ($sum(read(B, I), $product(-1, read(A, $sum(-1, $sum(N, $product(-1, I)))))) = 0)) | (((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N)), 0)) & ($sum(read(B, I), $product(-1, read(A, I))) = 0)))) | (rev(A, N) = B)) <=> ((~![I: $int] : (($greatereq(I, 0) & (~$lesseq($sum(N, $product(-1, I)), 0)) & ($sum(read(B, I), $product(-1, read(A, $sum(-1, $sum(N, $product(-1, I)))))) = 0)) | (((~$greatereq(I, 0)) | $lesseq($sum(N, $product(-1, I)), 0)) & ($sum(read(B, I), $product(-1, read(A, I))) = 0)))) | (rev(A, N) = B)))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(72,plain,
% 0.21/0.45 (![A: array, B: array, N: $int] : ((~![I: $int] : (($greatereq(I, 0) & (~$lesseq($sum(N, $product(-1, I)), 0)) & ($sum(read(B, I), $product(-1, read(A, $sum(-1, $sum(N, $product(-1, I)))))) = 0)) | (((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N)), 0)) & ($sum(read(B, I), $product(-1, read(A, I))) = 0)))) | (rev(A, N) = B)) <=> ![A: array, B: array, N: $int] : ((~![I: $int] : (($greatereq(I, 0) & (~$lesseq($sum(N, $product(-1, I)), 0)) & ($sum(read(B, I), $product(-1, read(A, $sum(-1, $sum(N, $product(-1, I)))))) = 0)) | (((~$greatereq(I, 0)) | $lesseq($sum(N, $product(-1, I)), 0)) & ($sum(read(B, I), $product(-1, read(A, I))) = 0)))) | (rev(A, N) = B))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[71])).
% 0.21/0.45 tff(73,plain,
% 0.21/0.45 (^[A: array, B: array, N: $int] : rewrite(((~![I: $int] : (($greatereq(I, 0) & (~$lesseq(N, I)) & (read(B, I) = read(A, $sum(-1, $sum(N, $product(-1, I)))))) | (((~$lesseq(0, I)) | $greatereq(I, N)) & (read(B, I) = read(A, I))))) | (rev(A, N) = B)) <=> ((~![I: $int] : (($greatereq(I, 0) & (~$lesseq($sum(N, $product(-1, I)), 0)) & ($sum(read(B, I), $product(-1, read(A, $sum(-1, $sum(N, $product(-1, I)))))) = 0)) | (((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N)), 0)) & ($sum(read(B, I), $product(-1, read(A, I))) = 0)))) | (rev(A, N) = B)))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(74,plain,
% 0.21/0.45 (![A: array, B: array, N: $int] : ((~![I: $int] : (($greatereq(I, 0) & (~$lesseq(N, I)) & (read(B, I) = read(A, $sum(-1, $sum(N, $product(-1, I)))))) | (((~$lesseq(0, I)) | $greatereq(I, N)) & (read(B, I) = read(A, I))))) | (rev(A, N) = B)) <=> ![A: array, B: array, N: $int] : ((~![I: $int] : (($greatereq(I, 0) & (~$lesseq($sum(N, $product(-1, I)), 0)) & ($sum(read(B, I), $product(-1, read(A, $sum(-1, $sum(N, $product(-1, I)))))) = 0)) | (((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N)), 0)) & ($sum(read(B, I), $product(-1, read(A, I))) = 0)))) | (rev(A, N) = B))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[73])).
% 0.21/0.45 tff(75,plain,
% 0.21/0.45 (![A: array, B: array, N: $int] : ((~![I: $int] : (($greatereq(I, 0) & (~$lesseq(N, I)) & (read(B, I) = read(A, $sum(-1, $sum(N, $product(-1, I)))))) | (((~$lesseq(0, I)) | $greatereq(I, N)) & (read(B, I) = read(A, I))))) | (rev(A, N) = B)) <=> ![A: array, B: array, N: $int] : ((~![I: $int] : (($greatereq(I, 0) & (~$lesseq(N, I)) & (read(B, I) = read(A, $sum(-1, $sum(N, $product(-1, I)))))) | (((~$lesseq(0, I)) | $greatereq(I, N)) & (read(B, I) = read(A, I))))) | (rev(A, N) = B))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(76,plain,
% 0.21/0.45 (^[A: array, B: array, N: $int] : trans(monotonicity(quant_intro(proof_bind(^[I: $int] : trans(monotonicity(trans(monotonicity(rewrite(($greatereq(I, 0) & $greater(N, I)) <=> ($greatereq(I, 0) & (~$lesseq(N, I)))), rewrite((read(B, I) = read(A, $difference(N, $sum(I, 1)))) <=> (read(B, I) = read(A, $sum(-1, $sum(N, $product(-1, I)))))), ((($greatereq(I, 0) & $greater(N, I)) & (read(B, I) = read(A, $difference(N, $sum(I, 1))))) <=> (($greatereq(I, 0) & (~$lesseq(N, I))) & (read(B, I) = read(A, $sum(-1, $sum(N, $product(-1, I)))))))), rewrite((($greatereq(I, 0) & (~$lesseq(N, I))) & (read(B, I) = read(A, $sum(-1, $sum(N, $product(-1, I)))))) <=> ($greatereq(I, 0) & (~$lesseq(N, I)) & (read(B, I) = read(A, $sum(-1, $sum(N, $product(-1, I))))))), ((($greatereq(I, 0) & $greater(N, I)) & (read(B, I) = read(A, $difference(N, $sum(I, 1))))) <=> ($greatereq(I, 0) & (~$lesseq(N, I)) & (read(B, I) = read(A, $sum(-1, $sum(N, $product(-1, I)))))))), rewrite((($greater(0, I) | $greatereq(I, N)) & (read(B, I) = read(A, I))) <=> (((~$lesseq(0, I)) | $greatereq(I, N)) & (read(B, I) = read(A, I)))), (((($greatereq(I, 0) & $greater(N, I)) & (read(B, I) = read(A, $difference(N, $sum(I, 1))))) | (($greater(0, I) | $greatereq(I, N)) & (read(B, I) = read(A, I)))) <=> (($greatereq(I, 0) & (~$lesseq(N, I)) & (read(B, I) = read(A, $sum(-1, $sum(N, $product(-1, I)))))) | (((~$lesseq(0, I)) | $greatereq(I, N)) & (read(B, I) = read(A, I)))))), rewrite((($greatereq(I, 0) & (~$lesseq(N, I)) & (read(B, I) = read(A, $sum(-1, $sum(N, $product(-1, I)))))) | (((~$lesseq(0, I)) | $greatereq(I, N)) & (read(B, I) = read(A, I)))) <=> (($greatereq(I, 0) & (~$lesseq(N, I)) & (read(B, I) = read(A, $sum(-1, $sum(N, $product(-1, I)))))) | (((~$lesseq(0, I)) | $greatereq(I, N)) & (read(B, I) = read(A, I))))), (((($greatereq(I, 0) & $greater(N, I)) & (read(B, I) = read(A, $difference(N, $sum(I, 1))))) | (($greater(0, I) | $greatereq(I, N)) & (read(B, I) = read(A, I)))) <=> (($greatereq(I, 0) & (~$lesseq(N, I)) & (read(B, I) = read(A, $sum(-1, $sum(N, $product(-1, I)))))) | (((~$lesseq(0, I)) | $greatereq(I, N)) & (read(B, I) = read(A, I))))))), (![I: $int] : ((($greatereq(I, 0) & $greater(N, I)) & (read(B, I) = read(A, $difference(N, $sum(I, 1))))) | (($greater(0, I) | $greatereq(I, N)) & (read(B, I) = read(A, I)))) <=> ![I: $int] : (($greatereq(I, 0) & (~$lesseq(N, I)) & (read(B, I) = read(A, $sum(-1, $sum(N, $product(-1, I)))))) | (((~$lesseq(0, I)) | $greatereq(I, N)) & (read(B, I) = read(A, I)))))), ((![I: $int] : ((($greatereq(I, 0) & $greater(N, I)) & (read(B, I) = read(A, $difference(N, $sum(I, 1))))) | (($greater(0, I) | $greatereq(I, N)) & (read(B, I) = read(A, I)))) => (rev(A, N) = B)) <=> (![I: $int] : (($greatereq(I, 0) & (~$lesseq(N, I)) & (read(B, I) = read(A, $sum(-1, $sum(N, $product(-1, I)))))) | (((~$lesseq(0, I)) | $greatereq(I, N)) & (read(B, I) = read(A, I)))) => (rev(A, N) = B)))), rewrite((![I: $int] : (($greatereq(I, 0) & (~$lesseq(N, I)) & (read(B, I) = read(A, $sum(-1, $sum(N, $product(-1, I)))))) | (((~$lesseq(0, I)) | $greatereq(I, N)) & (read(B, I) = read(A, I)))) => (rev(A, N) = B)) <=> ((~![I: $int] : (($greatereq(I, 0) & (~$lesseq(N, I)) & (read(B, I) = read(A, $sum(-1, $sum(N, $product(-1, I)))))) | (((~$lesseq(0, I)) | $greatereq(I, N)) & (read(B, I) = read(A, I))))) | (rev(A, N) = B))), ((![I: $int] : ((($greatereq(I, 0) & $greater(N, I)) & (read(B, I) = read(A, $difference(N, $sum(I, 1))))) | (($greater(0, I) | $greatereq(I, N)) & (read(B, I) = read(A, I)))) => (rev(A, N) = B)) <=> ((~![I: $int] : (($greatereq(I, 0) & (~$lesseq(N, I)) & (read(B, I) = read(A, $sum(-1, $sum(N, $product(-1, I)))))) | (((~$lesseq(0, I)) | $greatereq(I, N)) & (read(B, I) = read(A, I))))) | (rev(A, N) = B))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(77,plain,
% 0.21/0.45 (![A: array, B: array, N: $int] : (![I: $int] : ((($greatereq(I, 0) & $greater(N, I)) & (read(B, I) = read(A, $difference(N, $sum(I, 1))))) | (($greater(0, I) | $greatereq(I, N)) & (read(B, I) = read(A, I)))) => (rev(A, N) = B)) <=> ![A: array, B: array, N: $int] : ((~![I: $int] : (($greatereq(I, 0) & (~$lesseq(N, I)) & (read(B, I) = read(A, $sum(-1, $sum(N, $product(-1, I)))))) | (((~$lesseq(0, I)) | $greatereq(I, N)) & (read(B, I) = read(A, I))))) | (rev(A, N) = B))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[76])).
% 0.21/0.45 tff(78,axiom,(![A: array, B: array, N: $int] : (![I: $int] : ((($greatereq(I, 0) & $greater(N, I)) & (read(B, I) = read(A, $difference(N, $sum(I, 1))))) | (($greater(0, I) | $greatereq(I, N)) & (read(B, I) = read(A, I)))) => (rev(A, N) = B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','rev_n1_proper')).
% 0.21/0.45 tff(79,plain,
% 0.21/0.45 (![A: array, B: array, N: $int] : ((~![I: $int] : (($greatereq(I, 0) & (~$lesseq(N, I)) & (read(B, I) = read(A, $sum(-1, $sum(N, $product(-1, I)))))) | (((~$lesseq(0, I)) | $greatereq(I, N)) & (read(B, I) = read(A, I))))) | (rev(A, N) = B))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.21/0.45 tff(80,plain,
% 0.21/0.45 (![A: array, B: array, N: $int] : ((~![I: $int] : (($greatereq(I, 0) & (~$lesseq(N, I)) & (read(B, I) = read(A, $sum(-1, $sum(N, $product(-1, I)))))) | (((~$lesseq(0, I)) | $greatereq(I, N)) & (read(B, I) = read(A, I))))) | (rev(A, N) = B))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[79, 75])).
% 0.21/0.45 tff(81,plain,
% 0.21/0.45 (![A: array, B: array, N: $int] : ((~![I: $int] : (($greatereq(I, 0) & (~$lesseq($sum(N, $product(-1, I)), 0)) & ($sum(read(B, I), $product(-1, read(A, $sum(-1, $sum(N, $product(-1, I)))))) = 0)) | (((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N)), 0)) & ($sum(read(B, I), $product(-1, read(A, I))) = 0)))) | (rev(A, N) = B))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[80, 74])).
% 0.21/0.45 tff(82,plain,
% 0.21/0.45 (![A: array, B: array, N: $int] : ((~![I: $int] : (($greatereq(I, 0) & (~$lesseq($sum(N, $product(-1, I)), 0)) & ($sum(read(B, I), $product(-1, read(A, $sum(-1, $sum(N, $product(-1, I)))))) = 0)) | (((~$greatereq(I, 0)) | $lesseq($sum(N, $product(-1, I)), 0)) & ($sum(read(B, I), $product(-1, read(A, I))) = 0)))) | (rev(A, N) = B))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[81, 72])).
% 0.21/0.45 tff(83,plain,(
% 0.21/0.45 ![A: array, B: array, N: $int] : ((~(($greatereq(tptp_fun_I_7(N, B, A), 0) & (~$lesseq($sum(N, $product(-1, tptp_fun_I_7(N, B, A))), 0)) & ($sum(read(B, tptp_fun_I_7(N, B, A)), $product(-1, read(A, $sum(-1, $sum(N, $product(-1, tptp_fun_I_7(N, B, A))))))) = 0)) | (((~$greatereq(tptp_fun_I_7(N, B, A), 0)) | $lesseq($sum(N, $product(-1, tptp_fun_I_7(N, B, A))), 0)) & ($sum(read(B, tptp_fun_I_7(N, B, A)), $product(-1, read(A, tptp_fun_I_7(N, B, A)))) = 0)))) | (rev(A, N) = B))),
% 0.21/0.45 inference(skolemize,[status(sab)],[82])).
% 0.21/0.45 tff(84,plain,
% 0.21/0.45 (![A: array, B: array, N: $int] : ((~((~($lesseq($sum(N, $product(-1, tptp_fun_I_7(N, B, A))), 0) | (~$greatereq(tptp_fun_I_7(N, B, A), 0)) | (~($sum(read(B, tptp_fun_I_7(N, B, A)), $product(-1, read(A, $sum(-1, $sum(N, $product(-1, tptp_fun_I_7(N, B, A))))))) = 0)))) | (~((~((~$greatereq(tptp_fun_I_7(N, B, A), 0)) | $lesseq($sum(N, $product(-1, tptp_fun_I_7(N, B, A))), 0))) | (~($sum(read(B, tptp_fun_I_7(N, B, A)), $product(-1, read(A, tptp_fun_I_7(N, B, A)))) = 0)))))) | (rev(A, N) = B))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[83, 70])).
% 0.21/0.45 tff(85,plain,
% 0.21/0.45 (((~![A: array, B: array, N: $int] : ((~((~($lesseq($sum(N, $product(-1, tptp_fun_I_7(N, B, A))), 0) | (~$greatereq(tptp_fun_I_7(N, B, A), 0)) | (~($sum(read(B, tptp_fun_I_7(N, B, A)), $product(-1, read(A, $sum(-1, $sum(N, $product(-1, tptp_fun_I_7(N, B, A))))))) = 0)))) | (~((~((~$greatereq(tptp_fun_I_7(N, B, A), 0)) | $lesseq($sum(N, $product(-1, tptp_fun_I_7(N, B, A))), 0))) | (~($sum(read(B, tptp_fun_I_7(N, B, A)), $product(-1, read(A, tptp_fun_I_7(N, B, A)))) = 0)))))) | (rev(A, N) = B))) | ((~($greatereq(tptp_fun_I_7(1, elem!8, elem!8), 1) | (~$greatereq(tptp_fun_I_7(1, elem!8, elem!8), 0)) | (~($greatereq(tptp_fun_I_7(1, elem!8, elem!8), 1) | (~$greatereq(tptp_fun_I_7(1, elem!8, elem!8), 0)) | (~($sum(read(elem!8, tptp_fun_I_7(1, elem!8, elem!8)), $product(-1, read(elem!8, $product(-1, tptp_fun_I_7(1, elem!8, elem!8))))) = 0)))))) | (rev(elem!8, 1) = elem!8))) <=> ((~![A: array, B: array, N: $int] : ((~((~($lesseq($sum(N, $product(-1, tptp_fun_I_7(N, B, A))), 0) | (~$greatereq(tptp_fun_I_7(N, B, A), 0)) | (~($sum(read(B, tptp_fun_I_7(N, B, A)), $product(-1, read(A, $sum(-1, $sum(N, $product(-1, tptp_fun_I_7(N, B, A))))))) = 0)))) | (~((~((~$greatereq(tptp_fun_I_7(N, B, A), 0)) | $lesseq($sum(N, $product(-1, tptp_fun_I_7(N, B, A))), 0))) | (~($sum(read(B, tptp_fun_I_7(N, B, A)), $product(-1, read(A, tptp_fun_I_7(N, B, A)))) = 0)))))) | (rev(A, N) = B))) | (~($greatereq(tptp_fun_I_7(1, elem!8, elem!8), 1) | (~$greatereq(tptp_fun_I_7(1, elem!8, elem!8), 0)) | (~($greatereq(tptp_fun_I_7(1, elem!8, elem!8), 1) | (~$greatereq(tptp_fun_I_7(1, elem!8, elem!8), 0)) | (~($sum(read(elem!8, tptp_fun_I_7(1, elem!8, elem!8)), $product(-1, read(elem!8, $product(-1, tptp_fun_I_7(1, elem!8, elem!8))))) = 0)))))) | (rev(elem!8, 1) = elem!8))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(86,plain,
% 0.21/0.45 (((~((~($lesseq($sum($sum($sum(-1, $product(-1, -1)), $product(-1, -1)), $product(-1, tptp_fun_I_7($sum($sum(-1, $product(-1, -1)), $product(-1, -1)), elem!8, elem!8))), 0) | (~$greatereq(tptp_fun_I_7($sum($sum(-1, $product(-1, -1)), $product(-1, -1)), elem!8, elem!8), 0)) | (~($sum(read(elem!8, tptp_fun_I_7($sum($sum(-1, $product(-1, -1)), $product(-1, -1)), elem!8, elem!8)), $product(-1, read(elem!8, $sum(-1, $sum($sum($sum(-1, $product(-1, -1)), $product(-1, -1)), $product(-1, tptp_fun_I_7($sum($sum(-1, $product(-1, -1)), $product(-1, -1)), elem!8, elem!8))))))) = 0)))) | (~((~((~$greatereq(tptp_fun_I_7($sum($sum(-1, $product(-1, -1)), $product(-1, -1)), elem!8, elem!8), 0)) | $lesseq($sum($sum($sum(-1, $product(-1, -1)), $product(-1, -1)), $product(-1, tptp_fun_I_7($sum($sum(-1, $product(-1, -1)), $product(-1, -1)), elem!8, elem!8))), 0))) | (~($sum(read(elem!8, tptp_fun_I_7($sum($sum(-1, $product(-1, -1)), $product(-1, -1)), elem!8, elem!8)), $product(-1, read(elem!8, tptp_fun_I_7($sum($sum(-1, $product(-1, -1)), $product(-1, -1)), elem!8, elem!8)))) = 0)))))) | (rev(elem!8, $sum($sum(-1, $product(-1, -1)), $product(-1, -1))) = elem!8)) <=> ((~($greatereq(tptp_fun_I_7(1, elem!8, elem!8), 1) | (~$greatereq(tptp_fun_I_7(1, elem!8, elem!8), 0)) | (~($greatereq(tptp_fun_I_7(1, elem!8, elem!8), 1) | (~$greatereq(tptp_fun_I_7(1, elem!8, elem!8), 0)) | (~($sum(read(elem!8, tptp_fun_I_7(1, elem!8, elem!8)), $product(-1, read(elem!8, $product(-1, tptp_fun_I_7(1, elem!8, elem!8))))) = 0)))))) | (rev(elem!8, 1) = elem!8))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(87,plain,
% 0.21/0.45 (((~![A: array, B: array, N: $int] : ((~((~($lesseq($sum(N, $product(-1, tptp_fun_I_7(N, B, A))), 0) | (~$greatereq(tptp_fun_I_7(N, B, A), 0)) | (~($sum(read(B, tptp_fun_I_7(N, B, A)), $product(-1, read(A, $sum(-1, $sum(N, $product(-1, tptp_fun_I_7(N, B, A))))))) = 0)))) | (~((~((~$greatereq(tptp_fun_I_7(N, B, A), 0)) | $lesseq($sum(N, $product(-1, tptp_fun_I_7(N, B, A))), 0))) | (~($sum(read(B, tptp_fun_I_7(N, B, A)), $product(-1, read(A, tptp_fun_I_7(N, B, A)))) = 0)))))) | (rev(A, N) = B))) | ((~((~($lesseq($sum($sum($sum(-1, $product(-1, -1)), $product(-1, -1)), $product(-1, tptp_fun_I_7($sum($sum(-1, $product(-1, -1)), $product(-1, -1)), elem!8, elem!8))), 0) | (~$greatereq(tptp_fun_I_7($sum($sum(-1, $product(-1, -1)), $product(-1, -1)), elem!8, elem!8), 0)) | (~($sum(read(elem!8, tptp_fun_I_7($sum($sum(-1, $product(-1, -1)), $product(-1, -1)), elem!8, elem!8)), $product(-1, read(elem!8, $sum(-1, $sum($sum($sum(-1, $product(-1, -1)), $product(-1, -1)), $product(-1, tptp_fun_I_7($sum($sum(-1, $product(-1, -1)), $product(-1, -1)), elem!8, elem!8))))))) = 0)))) | (~((~((~$greatereq(tptp_fun_I_7($sum($sum(-1, $product(-1, -1)), $product(-1, -1)), elem!8, elem!8), 0)) | $lesseq($sum($sum($sum(-1, $product(-1, -1)), $product(-1, -1)), $product(-1, tptp_fun_I_7($sum($sum(-1, $product(-1, -1)), $product(-1, -1)), elem!8, elem!8))), 0))) | (~($sum(read(elem!8, tptp_fun_I_7($sum($sum(-1, $product(-1, -1)), $product(-1, -1)), elem!8, elem!8)), $product(-1, read(elem!8, tptp_fun_I_7($sum($sum(-1, $product(-1, -1)), $product(-1, -1)), elem!8, elem!8)))) = 0)))))) | (rev(elem!8, $sum($sum(-1, $product(-1, -1)), $product(-1, -1))) = elem!8))) <=> ((~![A: array, B: array, N: $int] : ((~((~($lesseq($sum(N, $product(-1, tptp_fun_I_7(N, B, A))), 0) | (~$greatereq(tptp_fun_I_7(N, B, A), 0)) | (~($sum(read(B, tptp_fun_I_7(N, B, A)), $product(-1, read(A, $sum(-1, $sum(N, $product(-1, tptp_fun_I_7(N, B, A))))))) = 0)))) | (~((~((~$greatereq(tptp_fun_I_7(N, B, A), 0)) | $lesseq($sum(N, $product(-1, tptp_fun_I_7(N, B, A))), 0))) | (~($sum(read(B, tptp_fun_I_7(N, B, A)), $product(-1, read(A, tptp_fun_I_7(N, B, A)))) = 0)))))) | (rev(A, N) = B))) | ((~($greatereq(tptp_fun_I_7(1, elem!8, elem!8), 1) | (~$greatereq(tptp_fun_I_7(1, elem!8, elem!8), 0)) | (~($greatereq(tptp_fun_I_7(1, elem!8, elem!8), 1) | (~$greatereq(tptp_fun_I_7(1, elem!8, elem!8), 0)) | (~($sum(read(elem!8, tptp_fun_I_7(1, elem!8, elem!8)), $product(-1, read(elem!8, $product(-1, tptp_fun_I_7(1, elem!8, elem!8))))) = 0)))))) | (rev(elem!8, 1) = elem!8)))),
% 0.21/0.45 inference(monotonicity,[status(thm)],[86])).
% 0.21/0.45 tff(88,plain,
% 0.21/0.45 (((~![A: array, B: array, N: $int] : ((~((~($lesseq($sum(N, $product(-1, tptp_fun_I_7(N, B, A))), 0) | (~$greatereq(tptp_fun_I_7(N, B, A), 0)) | (~($sum(read(B, tptp_fun_I_7(N, B, A)), $product(-1, read(A, $sum(-1, $sum(N, $product(-1, tptp_fun_I_7(N, B, A))))))) = 0)))) | (~((~((~$greatereq(tptp_fun_I_7(N, B, A), 0)) | $lesseq($sum(N, $product(-1, tptp_fun_I_7(N, B, A))), 0))) | (~($sum(read(B, tptp_fun_I_7(N, B, A)), $product(-1, read(A, tptp_fun_I_7(N, B, A)))) = 0)))))) | (rev(A, N) = B))) | ((~((~($lesseq($sum($sum($sum(-1, $product(-1, -1)), $product(-1, -1)), $product(-1, tptp_fun_I_7($sum($sum(-1, $product(-1, -1)), $product(-1, -1)), elem!8, elem!8))), 0) | (~$greatereq(tptp_fun_I_7($sum($sum(-1, $product(-1, -1)), $product(-1, -1)), elem!8, elem!8), 0)) | (~($sum(read(elem!8, tptp_fun_I_7($sum($sum(-1, $product(-1, -1)), $product(-1, -1)), elem!8, elem!8)), $product(-1, read(elem!8, $sum(-1, $sum($sum($sum(-1, $product(-1, -1)), $product(-1, -1)), $product(-1, tptp_fun_I_7($sum($sum(-1, $product(-1, -1)), $product(-1, -1)), elem!8, elem!8))))))) = 0)))) | (~((~((~$greatereq(tptp_fun_I_7($sum($sum(-1, $product(-1, -1)), $product(-1, -1)), elem!8, elem!8), 0)) | $lesseq($sum($sum($sum(-1, $product(-1, -1)), $product(-1, -1)), $product(-1, tptp_fun_I_7($sum($sum(-1, $product(-1, -1)), $product(-1, -1)), elem!8, elem!8))), 0))) | (~($sum(read(elem!8, tptp_fun_I_7($sum($sum(-1, $product(-1, -1)), $product(-1, -1)), elem!8, elem!8)), $product(-1, read(elem!8, tptp_fun_I_7($sum($sum(-1, $product(-1, -1)), $product(-1, -1)), elem!8, elem!8)))) = 0)))))) | (rev(elem!8, $sum($sum(-1, $product(-1, -1)), $product(-1, -1))) = elem!8))) <=> ((~![A: array, B: array, N: $int] : ((~((~($lesseq($sum(N, $product(-1, tptp_fun_I_7(N, B, A))), 0) | (~$greatereq(tptp_fun_I_7(N, B, A), 0)) | (~($sum(read(B, tptp_fun_I_7(N, B, A)), $product(-1, read(A, $sum(-1, $sum(N, $product(-1, tptp_fun_I_7(N, B, A))))))) = 0)))) | (~((~((~$greatereq(tptp_fun_I_7(N, B, A), 0)) | $lesseq($sum(N, $product(-1, tptp_fun_I_7(N, B, A))), 0))) | (~($sum(read(B, tptp_fun_I_7(N, B, A)), $product(-1, read(A, tptp_fun_I_7(N, B, A)))) = 0)))))) | (rev(A, N) = B))) | (~($greatereq(tptp_fun_I_7(1, elem!8, elem!8), 1) | (~$greatereq(tptp_fun_I_7(1, elem!8, elem!8), 0)) | (~($greatereq(tptp_fun_I_7(1, elem!8, elem!8), 1) | (~$greatereq(tptp_fun_I_7(1, elem!8, elem!8), 0)) | (~($sum(read(elem!8, tptp_fun_I_7(1, elem!8, elem!8)), $product(-1, read(elem!8, $product(-1, tptp_fun_I_7(1, elem!8, elem!8))))) = 0)))))) | (rev(elem!8, 1) = elem!8))),
% 0.21/0.46 inference(transitivity,[status(thm)],[87, 85])).
% 0.21/0.46 tff(89,plain,
% 0.21/0.46 ((~![A: array, B: array, N: $int] : ((~((~($lesseq($sum(N, $product(-1, tptp_fun_I_7(N, B, A))), 0) | (~$greatereq(tptp_fun_I_7(N, B, A), 0)) | (~($sum(read(B, tptp_fun_I_7(N, B, A)), $product(-1, read(A, $sum(-1, $sum(N, $product(-1, tptp_fun_I_7(N, B, A))))))) = 0)))) | (~((~((~$greatereq(tptp_fun_I_7(N, B, A), 0)) | $lesseq($sum(N, $product(-1, tptp_fun_I_7(N, B, A))), 0))) | (~($sum(read(B, tptp_fun_I_7(N, B, A)), $product(-1, read(A, tptp_fun_I_7(N, B, A)))) = 0)))))) | (rev(A, N) = B))) | ((~((~($lesseq($sum($sum($sum(-1, $product(-1, -1)), $product(-1, -1)), $product(-1, tptp_fun_I_7($sum($sum(-1, $product(-1, -1)), $product(-1, -1)), elem!8, elem!8))), 0) | (~$greatereq(tptp_fun_I_7($sum($sum(-1, $product(-1, -1)), $product(-1, -1)), elem!8, elem!8), 0)) | (~($sum(read(elem!8, tptp_fun_I_7($sum($sum(-1, $product(-1, -1)), $product(-1, -1)), elem!8, elem!8)), $product(-1, read(elem!8, $sum(-1, $sum($sum($sum(-1, $product(-1, -1)), $product(-1, -1)), $product(-1, tptp_fun_I_7($sum($sum(-1, $product(-1, -1)), $product(-1, -1)), elem!8, elem!8))))))) = 0)))) | (~((~((~$greatereq(tptp_fun_I_7($sum($sum(-1, $product(-1, -1)), $product(-1, -1)), elem!8, elem!8), 0)) | $lesseq($sum($sum($sum(-1, $product(-1, -1)), $product(-1, -1)), $product(-1, tptp_fun_I_7($sum($sum(-1, $product(-1, -1)), $product(-1, -1)), elem!8, elem!8))), 0))) | (~($sum(read(elem!8, tptp_fun_I_7($sum($sum(-1, $product(-1, -1)), $product(-1, -1)), elem!8, elem!8)), $product(-1, read(elem!8, tptp_fun_I_7($sum($sum(-1, $product(-1, -1)), $product(-1, -1)), elem!8, elem!8)))) = 0)))))) | (rev(elem!8, $sum($sum(-1, $product(-1, -1)), $product(-1, -1))) = elem!8))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(90,plain,
% 0.21/0.46 ((~![A: array, B: array, N: $int] : ((~((~($lesseq($sum(N, $product(-1, tptp_fun_I_7(N, B, A))), 0) | (~$greatereq(tptp_fun_I_7(N, B, A), 0)) | (~($sum(read(B, tptp_fun_I_7(N, B, A)), $product(-1, read(A, $sum(-1, $sum(N, $product(-1, tptp_fun_I_7(N, B, A))))))) = 0)))) | (~((~((~$greatereq(tptp_fun_I_7(N, B, A), 0)) | $lesseq($sum(N, $product(-1, tptp_fun_I_7(N, B, A))), 0))) | (~($sum(read(B, tptp_fun_I_7(N, B, A)), $product(-1, read(A, tptp_fun_I_7(N, B, A)))) = 0)))))) | (rev(A, N) = B))) | (~($greatereq(tptp_fun_I_7(1, elem!8, elem!8), 1) | (~$greatereq(tptp_fun_I_7(1, elem!8, elem!8), 0)) | (~($greatereq(tptp_fun_I_7(1, elem!8, elem!8), 1) | (~$greatereq(tptp_fun_I_7(1, elem!8, elem!8), 0)) | (~($sum(read(elem!8, tptp_fun_I_7(1, elem!8, elem!8)), $product(-1, read(elem!8, $product(-1, tptp_fun_I_7(1, elem!8, elem!8))))) = 0)))))) | (rev(elem!8, 1) = elem!8)),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[89, 88])).
% 0.21/0.46 tff(91,plain,
% 0.21/0.46 ((~($greatereq(tptp_fun_I_7(1, elem!8, elem!8), 1) | (~$greatereq(tptp_fun_I_7(1, elem!8, elem!8), 0)) | (~($greatereq(tptp_fun_I_7(1, elem!8, elem!8), 1) | (~$greatereq(tptp_fun_I_7(1, elem!8, elem!8), 0)) | (~($sum(read(elem!8, tptp_fun_I_7(1, elem!8, elem!8)), $product(-1, read(elem!8, $product(-1, tptp_fun_I_7(1, elem!8, elem!8))))) = 0)))))) | (rev(elem!8, 1) = elem!8)),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[90, 84])).
% 0.21/0.46 tff(92,plain,
% 0.21/0.46 (~($greatereq(tptp_fun_I_7(1, elem!8, elem!8), 1) | (~$greatereq(tptp_fun_I_7(1, elem!8, elem!8), 0)) | (~($greatereq(tptp_fun_I_7(1, elem!8, elem!8), 1) | (~$greatereq(tptp_fun_I_7(1, elem!8, elem!8), 0)) | (~($sum(read(elem!8, tptp_fun_I_7(1, elem!8, elem!8)), $product(-1, read(elem!8, $product(-1, tptp_fun_I_7(1, elem!8, elem!8))))) = 0)))))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[91, 68])).
% 0.21/0.46 tff(93,plain,
% 0.21/0.46 (($greatereq(tptp_fun_I_7(1, elem!8, elem!8), 1) | (~$greatereq(tptp_fun_I_7(1, elem!8, elem!8), 0)) | (~($greatereq(tptp_fun_I_7(1, elem!8, elem!8), 1) | (~$greatereq(tptp_fun_I_7(1, elem!8, elem!8), 0)) | (~($sum(read(elem!8, tptp_fun_I_7(1, elem!8, elem!8)), $product(-1, read(elem!8, $product(-1, tptp_fun_I_7(1, elem!8, elem!8))))) = 0))))) | ($greatereq(tptp_fun_I_7(1, elem!8, elem!8), 1) | (~$greatereq(tptp_fun_I_7(1, elem!8, elem!8), 0)) | (~($sum(read(elem!8, tptp_fun_I_7(1, elem!8, elem!8)), $product(-1, read(elem!8, $product(-1, tptp_fun_I_7(1, elem!8, elem!8))))) = 0)))),
% 0.21/0.46 inference(tautology,[status(thm)],[])).
% 0.21/0.46 tff(94,plain,
% 0.21/0.46 ($greatereq(tptp_fun_I_7(1, elem!8, elem!8), 1) | (~$greatereq(tptp_fun_I_7(1, elem!8, elem!8), 0)) | (~($sum(read(elem!8, tptp_fun_I_7(1, elem!8, elem!8)), $product(-1, read(elem!8, $product(-1, tptp_fun_I_7(1, elem!8, elem!8))))) = 0))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[93, 92])).
% 0.21/0.46 tff(95,plain,
% 0.21/0.46 (($greatereq(tptp_fun_I_7(1, elem!8, elem!8), 1) | (~$greatereq(tptp_fun_I_7(1, elem!8, elem!8), 0)) | (~($greatereq(tptp_fun_I_7(1, elem!8, elem!8), 1) | (~$greatereq(tptp_fun_I_7(1, elem!8, elem!8), 0)) | (~($sum(read(elem!8, tptp_fun_I_7(1, elem!8, elem!8)), $product(-1, read(elem!8, $product(-1, tptp_fun_I_7(1, elem!8, elem!8))))) = 0))))) | (~$greatereq(tptp_fun_I_7(1, elem!8, elem!8), 1))),
% 0.21/0.46 inference(tautology,[status(thm)],[])).
% 0.21/0.46 tff(96,plain,
% 0.21/0.46 (~$greatereq(tptp_fun_I_7(1, elem!8, elem!8), 1)),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[95, 92])).
% 0.21/0.46 tff(97,plain,
% 0.21/0.46 (($greatereq(tptp_fun_I_7(1, elem!8, elem!8), 1) | (~$greatereq(tptp_fun_I_7(1, elem!8, elem!8), 0)) | (~($greatereq(tptp_fun_I_7(1, elem!8, elem!8), 1) | (~$greatereq(tptp_fun_I_7(1, elem!8, elem!8), 0)) | (~($sum(read(elem!8, tptp_fun_I_7(1, elem!8, elem!8)), $product(-1, read(elem!8, $product(-1, tptp_fun_I_7(1, elem!8, elem!8))))) = 0))))) | $greatereq(tptp_fun_I_7(1, elem!8, elem!8), 0)),
% 0.21/0.46 inference(tautology,[status(thm)],[])).
% 0.21/0.46 tff(98,plain,
% 0.21/0.46 ($greatereq(tptp_fun_I_7(1, elem!8, elem!8), 0)),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[97, 92])).
% 0.21/0.46 tff(99,plain,
% 0.21/0.46 ((~($greatereq(tptp_fun_I_7(1, elem!8, elem!8), 1) | (~$greatereq(tptp_fun_I_7(1, elem!8, elem!8), 0)) | (~($sum(read(elem!8, tptp_fun_I_7(1, elem!8, elem!8)), $product(-1, read(elem!8, $product(-1, tptp_fun_I_7(1, elem!8, elem!8))))) = 0)))) | $greatereq(tptp_fun_I_7(1, elem!8, elem!8), 1) | (~$greatereq(tptp_fun_I_7(1, elem!8, elem!8), 0)) | (~($sum(read(elem!8, tptp_fun_I_7(1, elem!8, elem!8)), $product(-1, read(elem!8, $product(-1, tptp_fun_I_7(1, elem!8, elem!8))))) = 0))),
% 0.21/0.46 inference(tautology,[status(thm)],[])).
% 0.21/0.46 tff(100,plain,
% 0.21/0.46 (~($sum(read(elem!8, tptp_fun_I_7(1, elem!8, elem!8)), $product(-1, read(elem!8, $product(-1, tptp_fun_I_7(1, elem!8, elem!8))))) = 0)),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[99, 98, 96, 94])).
% 0.21/0.46 tff(101,plain,
% 0.21/0.46 (tptp_fun_I_7(1, elem!8, elem!8) = 0),
% 0.21/0.46 inference(theory_lemma,[status(thm)],[98, 96])).
% 0.21/0.46 tff(102,plain,
% 0.21/0.46 (0 = tptp_fun_I_7(1, elem!8, elem!8)),
% 0.21/0.46 inference(symmetry,[status(thm)],[101])).
% 0.21/0.46 tff(103,plain,
% 0.21/0.46 ($product(-1, tptp_fun_I_7(1, elem!8, elem!8)) = 0),
% 0.21/0.46 inference(theory_lemma,[status(thm)],[98, 96])).
% 0.21/0.46 tff(104,plain,
% 0.21/0.46 ($product(-1, tptp_fun_I_7(1, elem!8, elem!8)) = tptp_fun_I_7(1, elem!8, elem!8)),
% 0.21/0.46 inference(transitivity,[status(thm)],[103, 102])).
% 0.21/0.46 tff(105,plain,
% 0.21/0.46 (read(elem!8, $product(-1, tptp_fun_I_7(1, elem!8, elem!8))) = read(elem!8, tptp_fun_I_7(1, elem!8, elem!8))),
% 0.21/0.46 inference(monotonicity,[status(thm)],[104])).
% 0.21/0.46 tff(106,plain,
% 0.21/0.46 (read(elem!8, tptp_fun_I_7(1, elem!8, elem!8)) = read(elem!8, $product(-1, tptp_fun_I_7(1, elem!8, elem!8)))),
% 0.21/0.46 inference(symmetry,[status(thm)],[105])).
% 0.21/0.46 tff(107,plain,
% 0.21/0.46 ((~(read(elem!8, tptp_fun_I_7(1, elem!8, elem!8)) = read(elem!8, $product(-1, tptp_fun_I_7(1, elem!8, elem!8))))) | $lesseq($sum(read(elem!8, tptp_fun_I_7(1, elem!8, elem!8)), $product(-1, read(elem!8, $product(-1, tptp_fun_I_7(1, elem!8, elem!8))))), 0)),
% 0.21/0.46 inference(theory_lemma,[status(thm)],[])).
% 0.21/0.46 tff(108,plain,
% 0.21/0.46 ($lesseq($sum(read(elem!8, tptp_fun_I_7(1, elem!8, elem!8)), $product(-1, read(elem!8, $product(-1, tptp_fun_I_7(1, elem!8, elem!8))))), 0)),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[107, 106])).
% 0.21/0.46 tff(109,plain,
% 0.21/0.46 ((~(read(elem!8, tptp_fun_I_7(1, elem!8, elem!8)) = read(elem!8, $product(-1, tptp_fun_I_7(1, elem!8, elem!8))))) | $greatereq($sum(read(elem!8, tptp_fun_I_7(1, elem!8, elem!8)), $product(-1, read(elem!8, $product(-1, tptp_fun_I_7(1, elem!8, elem!8))))), 0)),
% 0.21/0.46 inference(theory_lemma,[status(thm)],[])).
% 0.21/0.46 tff(110,plain,
% 0.21/0.46 ($greatereq($sum(read(elem!8, tptp_fun_I_7(1, elem!8, elem!8)), $product(-1, read(elem!8, $product(-1, tptp_fun_I_7(1, elem!8, elem!8))))), 0)),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[109, 106])).
% 0.21/0.46 tff(111,plain,
% 0.21/0.46 (($sum(read(elem!8, tptp_fun_I_7(1, elem!8, elem!8)), $product(-1, read(elem!8, $product(-1, tptp_fun_I_7(1, elem!8, elem!8))))) = 0) | (~$lesseq($sum(read(elem!8, tptp_fun_I_7(1, elem!8, elem!8)), $product(-1, read(elem!8, $product(-1, tptp_fun_I_7(1, elem!8, elem!8))))), 0)) | (~$greatereq($sum(read(elem!8, tptp_fun_I_7(1, elem!8, elem!8)), $product(-1, read(elem!8, $product(-1, tptp_fun_I_7(1, elem!8, elem!8))))), 0))),
% 0.21/0.46 inference(theory_lemma,[status(thm)],[])).
% 0.21/0.46 tff(112,plain,
% 0.21/0.46 ($false),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[111, 110, 108, 100])).
% 0.21/0.46 % SZS output end Proof
%------------------------------------------------------------------------------