TSTP Solution File: SWW620_2 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWW620_2 : TPTP v8.1.0. Released v6.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n001.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 20:59:28 EDT 2022
% Result : Theorem 0.21s 0.47s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SWW620_2 : TPTP v8.1.0. Released v6.1.0.
% 0.07/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35 % Computer : n001.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sun Sep 4 20:44:13 EDT 2022
% 0.13/0.36 % CPUTime :
% 0.13/0.36 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.36 Usage: tptp [options] [-file:]file
% 0.13/0.36 -h, -? prints this message.
% 0.13/0.36 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.36 -m, -model generate model.
% 0.13/0.36 -p, -proof generate proof.
% 0.13/0.36 -c, -core generate unsat core of named formulas.
% 0.13/0.36 -st, -statistics display statistics.
% 0.13/0.36 -t:timeout set timeout (in second).
% 0.13/0.36 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.36 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.36 -<param>:<value> configuration parameter and value.
% 0.13/0.36 -o:<output-file> file to place output in.
% 0.21/0.47 % SZS status Theorem
% 0.21/0.47 % SZS output start Proof
% 0.21/0.47 tff(tptp_fun_I1_1_type, type, (
% 0.21/0.47 tptp_fun_I1_1: ( $int * $int * array_elt3 ) > $int)).
% 0.21/0.47 tff(tb2t10_type, type, (
% 0.21/0.47 tb2t10: uni > array_elt3)).
% 0.21/0.47 tff(mk_array1_type, type, (
% 0.21/0.47 mk_array1: ( ty * $int * uni ) > uni)).
% 0.21/0.47 tff(t2tb12_type, type, (
% 0.21/0.47 t2tb12: map_int_elt3 > uni)).
% 0.21/0.47 tff(tptp_fun_A1_12_type, type, (
% 0.21/0.47 tptp_fun_A1_12: map_int_elt3)).
% 0.21/0.47 tff(tptp_fun_A_13_type, type, (
% 0.21/0.47 tptp_fun_A_13: $int)).
% 0.21/0.47 tff(elt7_type, type, (
% 0.21/0.47 elt7: ty)).
% 0.21/0.47 tff(tptp_fun_Lo_11_type, type, (
% 0.21/0.47 tptp_fun_Lo_11: $int)).
% 0.21/0.47 tff(tptp_fun_I2_0_type, type, (
% 0.21/0.47 tptp_fun_I2_0: ( $int * $int * array_elt3 ) > $int)).
% 0.21/0.47 tff(le4_type, type, (
% 0.21/0.47 le4: ( elt6 * elt6 ) > $o)).
% 0.21/0.47 tff(tb2t11_type, type, (
% 0.21/0.47 tb2t11: uni > elt6)).
% 0.21/0.47 tff(get2_type, type, (
% 0.21/0.47 get2: ( ty * uni * $int ) > uni)).
% 0.21/0.47 tff(t2tb10_type, type, (
% 0.21/0.47 t2tb10: array_elt3 > uni)).
% 0.21/0.47 tff(sorted_sub4_type, type, (
% 0.21/0.47 sorted_sub4: ( array_elt3 * $int * $int ) > $o)).
% 0.21/0.47 tff(1,plain,
% 0.21/0.47 (^[A: array_elt3, L: $int, U: $int] : refl((~((~((~sorted_sub4(A, L, U)) | ![I1: $int, I2: $int] : (le4(tb2t11(get2(elt7, t2tb10(A), I1)), tb2t11(get2(elt7, t2tb10(A), I2))) | $lesseq($sum(U, $product(-1, I2)), 0) | (~$lesseq($sum(I1, $product(-1, I2)), 0)) | (~$greatereq($sum(I1, $product(-1, L)), 0))))) | (~(sorted_sub4(A, L, U) | (~($lesseq($sum(U, $product(-1, tptp_fun_I2_0(U, L, A))), 0) | le4(tb2t11(get2(elt7, t2tb10(A), tptp_fun_I1_1(U, L, A))), tb2t11(get2(elt7, t2tb10(A), tptp_fun_I2_0(U, L, A)))) | (~$lesseq($sum(L, $product(-1, tptp_fun_I1_1(U, L, A))), 0)) | (~$greatereq($sum(tptp_fun_I2_0(U, L, A), $product(-1, tptp_fun_I1_1(U, L, A))), 0)))))))) <=> (~((~((~sorted_sub4(A, L, U)) | ![I1: $int, I2: $int] : (le4(tb2t11(get2(elt7, t2tb10(A), I1)), tb2t11(get2(elt7, t2tb10(A), I2))) | $lesseq($sum(U, $product(-1, I2)), 0) | (~$lesseq($sum(I1, $product(-1, I2)), 0)) | (~$greatereq($sum(I1, $product(-1, L)), 0))))) | (~(sorted_sub4(A, L, U) | (~($lesseq($sum(U, $product(-1, tptp_fun_I2_0(U, L, A))), 0) | le4(tb2t11(get2(elt7, t2tb10(A), tptp_fun_I1_1(U, L, A))), tb2t11(get2(elt7, t2tb10(A), tptp_fun_I2_0(U, L, A)))) | (~$lesseq($sum(L, $product(-1, tptp_fun_I1_1(U, L, A))), 0)) | (~$greatereq($sum(tptp_fun_I2_0(U, L, A), $product(-1, tptp_fun_I1_1(U, L, A))), 0)))))))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(2,plain,
% 0.21/0.47 (![A: array_elt3, L: $int, U: $int] : (~((~((~sorted_sub4(A, L, U)) | ![I1: $int, I2: $int] : (le4(tb2t11(get2(elt7, t2tb10(A), I1)), tb2t11(get2(elt7, t2tb10(A), I2))) | $lesseq($sum(U, $product(-1, I2)), 0) | (~$lesseq($sum(I1, $product(-1, I2)), 0)) | (~$greatereq($sum(I1, $product(-1, L)), 0))))) | (~(sorted_sub4(A, L, U) | (~($lesseq($sum(U, $product(-1, tptp_fun_I2_0(U, L, A))), 0) | le4(tb2t11(get2(elt7, t2tb10(A), tptp_fun_I1_1(U, L, A))), tb2t11(get2(elt7, t2tb10(A), tptp_fun_I2_0(U, L, A)))) | (~$lesseq($sum(L, $product(-1, tptp_fun_I1_1(U, L, A))), 0)) | (~$greatereq($sum(tptp_fun_I2_0(U, L, A), $product(-1, tptp_fun_I1_1(U, L, A))), 0)))))))) <=> ![A: array_elt3, L: $int, U: $int] : (~((~((~sorted_sub4(A, L, U)) | ![I1: $int, I2: $int] : (le4(tb2t11(get2(elt7, t2tb10(A), I1)), tb2t11(get2(elt7, t2tb10(A), I2))) | $lesseq($sum(U, $product(-1, I2)), 0) | (~$lesseq($sum(I1, $product(-1, I2)), 0)) | (~$greatereq($sum(I1, $product(-1, L)), 0))))) | (~(sorted_sub4(A, L, U) | (~($lesseq($sum(U, $product(-1, tptp_fun_I2_0(U, L, A))), 0) | le4(tb2t11(get2(elt7, t2tb10(A), tptp_fun_I1_1(U, L, A))), tb2t11(get2(elt7, t2tb10(A), tptp_fun_I2_0(U, L, A)))) | (~$lesseq($sum(L, $product(-1, tptp_fun_I1_1(U, L, A))), 0)) | (~$greatereq($sum(tptp_fun_I2_0(U, L, A), $product(-1, tptp_fun_I1_1(U, L, A))), 0))))))))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[1])).
% 0.21/0.47 tff(3,plain,
% 0.21/0.47 (^[A: array_elt3, L: $int, U: $int] : rewrite((~((~((~sorted_sub4(A, L, U)) | ![I1: $int, I2: $int] : (le4(tb2t11(get2(elt7, t2tb10(A), I1)), tb2t11(get2(elt7, t2tb10(A), I2))) | $lesseq($sum(U, $product(-1, I2)), 0) | (~$lesseq($sum(I1, $product(-1, I2)), 0)) | (~$greatereq($sum(I1, $product(-1, L)), 0))))) | (~(sorted_sub4(A, L, U) | (~($lesseq($sum(U, $product(-1, tptp_fun_I2_0(U, L, A))), 0) | le4(tb2t11(get2(elt7, t2tb10(A), tptp_fun_I1_1(U, L, A))), tb2t11(get2(elt7, t2tb10(A), tptp_fun_I2_0(U, L, A)))) | (~$lesseq($sum(L, $product(-1, tptp_fun_I1_1(U, L, A))), 0)) | (~$greatereq($sum(tptp_fun_I2_0(U, L, A), $product(-1, tptp_fun_I1_1(U, L, A))), 0)))))))) <=> (~((~((~sorted_sub4(A, L, U)) | ![I1: $int, I2: $int] : (le4(tb2t11(get2(elt7, t2tb10(A), I1)), tb2t11(get2(elt7, t2tb10(A), I2))) | $lesseq($sum(U, $product(-1, I2)), 0) | (~$lesseq($sum(I1, $product(-1, I2)), 0)) | (~$greatereq($sum(I1, $product(-1, L)), 0))))) | (~(sorted_sub4(A, L, U) | (~($lesseq($sum(U, $product(-1, tptp_fun_I2_0(U, L, A))), 0) | le4(tb2t11(get2(elt7, t2tb10(A), tptp_fun_I1_1(U, L, A))), tb2t11(get2(elt7, t2tb10(A), tptp_fun_I2_0(U, L, A)))) | (~$lesseq($sum(L, $product(-1, tptp_fun_I1_1(U, L, A))), 0)) | (~$greatereq($sum(tptp_fun_I2_0(U, L, A), $product(-1, tptp_fun_I1_1(U, L, A))), 0)))))))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(4,plain,
% 0.21/0.47 (![A: array_elt3, L: $int, U: $int] : (~((~((~sorted_sub4(A, L, U)) | ![I1: $int, I2: $int] : (le4(tb2t11(get2(elt7, t2tb10(A), I1)), tb2t11(get2(elt7, t2tb10(A), I2))) | $lesseq($sum(U, $product(-1, I2)), 0) | (~$lesseq($sum(I1, $product(-1, I2)), 0)) | (~$greatereq($sum(I1, $product(-1, L)), 0))))) | (~(sorted_sub4(A, L, U) | (~($lesseq($sum(U, $product(-1, tptp_fun_I2_0(U, L, A))), 0) | le4(tb2t11(get2(elt7, t2tb10(A), tptp_fun_I1_1(U, L, A))), tb2t11(get2(elt7, t2tb10(A), tptp_fun_I2_0(U, L, A)))) | (~$lesseq($sum(L, $product(-1, tptp_fun_I1_1(U, L, A))), 0)) | (~$greatereq($sum(tptp_fun_I2_0(U, L, A), $product(-1, tptp_fun_I1_1(U, L, A))), 0)))))))) <=> ![A: array_elt3, L: $int, U: $int] : (~((~((~sorted_sub4(A, L, U)) | ![I1: $int, I2: $int] : (le4(tb2t11(get2(elt7, t2tb10(A), I1)), tb2t11(get2(elt7, t2tb10(A), I2))) | $lesseq($sum(U, $product(-1, I2)), 0) | (~$lesseq($sum(I1, $product(-1, I2)), 0)) | (~$greatereq($sum(I1, $product(-1, L)), 0))))) | (~(sorted_sub4(A, L, U) | (~($lesseq($sum(U, $product(-1, tptp_fun_I2_0(U, L, A))), 0) | le4(tb2t11(get2(elt7, t2tb10(A), tptp_fun_I1_1(U, L, A))), tb2t11(get2(elt7, t2tb10(A), tptp_fun_I2_0(U, L, A)))) | (~$lesseq($sum(L, $product(-1, tptp_fun_I1_1(U, L, A))), 0)) | (~$greatereq($sum(tptp_fun_I2_0(U, L, A), $product(-1, tptp_fun_I1_1(U, L, A))), 0))))))))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[3])).
% 0.21/0.47 tff(5,plain,
% 0.21/0.47 (![A: array_elt3, L: $int, U: $int] : (~((~((~sorted_sub4(A, L, U)) | ![I1: $int, I2: $int] : (le4(tb2t11(get2(elt7, t2tb10(A), I1)), tb2t11(get2(elt7, t2tb10(A), I2))) | $lesseq($sum(U, $product(-1, I2)), 0) | (~$lesseq($sum(I1, $product(-1, I2)), 0)) | (~$greatereq($sum(I1, $product(-1, L)), 0))))) | (~(sorted_sub4(A, L, U) | (~($lesseq($sum(U, $product(-1, tptp_fun_I2_0(U, L, A))), 0) | le4(tb2t11(get2(elt7, t2tb10(A), tptp_fun_I1_1(U, L, A))), tb2t11(get2(elt7, t2tb10(A), tptp_fun_I2_0(U, L, A)))) | (~$lesseq($sum(L, $product(-1, tptp_fun_I1_1(U, L, A))), 0)) | (~$greatereq($sum(tptp_fun_I2_0(U, L, A), $product(-1, tptp_fun_I1_1(U, L, A))), 0)))))))) <=> ![A: array_elt3, L: $int, U: $int] : (~((~((~sorted_sub4(A, L, U)) | ![I1: $int, I2: $int] : (le4(tb2t11(get2(elt7, t2tb10(A), I1)), tb2t11(get2(elt7, t2tb10(A), I2))) | $lesseq($sum(U, $product(-1, I2)), 0) | (~$lesseq($sum(I1, $product(-1, I2)), 0)) | (~$greatereq($sum(I1, $product(-1, L)), 0))))) | (~(sorted_sub4(A, L, U) | (~($lesseq($sum(U, $product(-1, tptp_fun_I2_0(U, L, A))), 0) | le4(tb2t11(get2(elt7, t2tb10(A), tptp_fun_I1_1(U, L, A))), tb2t11(get2(elt7, t2tb10(A), tptp_fun_I2_0(U, L, A)))) | (~$lesseq($sum(L, $product(-1, tptp_fun_I1_1(U, L, A))), 0)) | (~$greatereq($sum(tptp_fun_I2_0(U, L, A), $product(-1, tptp_fun_I1_1(U, L, A))), 0))))))))),
% 0.21/0.47 inference(transitivity,[status(thm)],[4, 2])).
% 0.21/0.47 tff(6,plain,
% 0.21/0.47 (^[A: array_elt3, L: $int, U: $int] : trans(monotonicity(rewrite(((~sorted_sub4(A, L, U)) | ![I1: $int, I2: $int] : ((~($greatereq($sum(I1, $product(-1, L)), 0) & $lesseq($sum(I1, $product(-1, I2)), 0) & (~$lesseq($sum(U, $product(-1, I2)), 0)))) | le4(tb2t11(get2(elt7, t2tb10(A), I1)), tb2t11(get2(elt7, t2tb10(A), I2))))) <=> ((~sorted_sub4(A, L, U)) | ![I1: $int, I2: $int] : (le4(tb2t11(get2(elt7, t2tb10(A), I1)), tb2t11(get2(elt7, t2tb10(A), I2))) | $lesseq($sum(U, $product(-1, I2)), 0) | (~$lesseq($sum(I1, $product(-1, I2)), 0)) | (~$greatereq($sum(I1, $product(-1, L)), 0))))), trans(monotonicity(rewrite((~((~($lesseq($sum(L, $product(-1, tptp_fun_I1_1(U, L, A))), 0) & $greatereq($sum(tptp_fun_I2_0(U, L, A), $product(-1, tptp_fun_I1_1(U, L, A))), 0) & (~$lesseq($sum(U, $product(-1, tptp_fun_I2_0(U, L, A))), 0)))) | le4(tb2t11(get2(elt7, t2tb10(A), tptp_fun_I1_1(U, L, A))), tb2t11(get2(elt7, t2tb10(A), tptp_fun_I2_0(U, L, A)))))) <=> (~($lesseq($sum(U, $product(-1, tptp_fun_I2_0(U, L, A))), 0) | le4(tb2t11(get2(elt7, t2tb10(A), tptp_fun_I1_1(U, L, A))), tb2t11(get2(elt7, t2tb10(A), tptp_fun_I2_0(U, L, A)))) | (~$lesseq($sum(L, $product(-1, tptp_fun_I1_1(U, L, A))), 0)) | (~$greatereq($sum(tptp_fun_I2_0(U, L, A), $product(-1, tptp_fun_I1_1(U, L, A))), 0))))), ((sorted_sub4(A, L, U) | (~((~($lesseq($sum(L, $product(-1, tptp_fun_I1_1(U, L, A))), 0) & $greatereq($sum(tptp_fun_I2_0(U, L, A), $product(-1, tptp_fun_I1_1(U, L, A))), 0) & (~$lesseq($sum(U, $product(-1, tptp_fun_I2_0(U, L, A))), 0)))) | le4(tb2t11(get2(elt7, t2tb10(A), tptp_fun_I1_1(U, L, A))), tb2t11(get2(elt7, t2tb10(A), tptp_fun_I2_0(U, L, A))))))) <=> (sorted_sub4(A, L, U) | (~($lesseq($sum(U, $product(-1, tptp_fun_I2_0(U, L, A))), 0) | le4(tb2t11(get2(elt7, t2tb10(A), tptp_fun_I1_1(U, L, A))), tb2t11(get2(elt7, t2tb10(A), tptp_fun_I2_0(U, L, A)))) | (~$lesseq($sum(L, $product(-1, tptp_fun_I1_1(U, L, A))), 0)) | (~$greatereq($sum(tptp_fun_I2_0(U, L, A), $product(-1, tptp_fun_I1_1(U, L, A))), 0))))))), rewrite((sorted_sub4(A, L, U) | (~($lesseq($sum(U, $product(-1, tptp_fun_I2_0(U, L, A))), 0) | le4(tb2t11(get2(elt7, t2tb10(A), tptp_fun_I1_1(U, L, A))), tb2t11(get2(elt7, t2tb10(A), tptp_fun_I2_0(U, L, A)))) | (~$lesseq($sum(L, $product(-1, tptp_fun_I1_1(U, L, A))), 0)) | (~$greatereq($sum(tptp_fun_I2_0(U, L, A), $product(-1, tptp_fun_I1_1(U, L, A))), 0))))) <=> (sorted_sub4(A, L, U) | (~($lesseq($sum(U, $product(-1, tptp_fun_I2_0(U, L, A))), 0) | le4(tb2t11(get2(elt7, t2tb10(A), tptp_fun_I1_1(U, L, A))), tb2t11(get2(elt7, t2tb10(A), tptp_fun_I2_0(U, L, A)))) | (~$lesseq($sum(L, $product(-1, tptp_fun_I1_1(U, L, A))), 0)) | (~$greatereq($sum(tptp_fun_I2_0(U, L, A), $product(-1, tptp_fun_I1_1(U, L, A))), 0)))))), ((sorted_sub4(A, L, U) | (~((~($lesseq($sum(L, $product(-1, tptp_fun_I1_1(U, L, A))), 0) & $greatereq($sum(tptp_fun_I2_0(U, L, A), $product(-1, tptp_fun_I1_1(U, L, A))), 0) & (~$lesseq($sum(U, $product(-1, tptp_fun_I2_0(U, L, A))), 0)))) | le4(tb2t11(get2(elt7, t2tb10(A), tptp_fun_I1_1(U, L, A))), tb2t11(get2(elt7, t2tb10(A), tptp_fun_I2_0(U, L, A))))))) <=> (sorted_sub4(A, L, U) | (~($lesseq($sum(U, $product(-1, tptp_fun_I2_0(U, L, A))), 0) | le4(tb2t11(get2(elt7, t2tb10(A), tptp_fun_I1_1(U, L, A))), tb2t11(get2(elt7, t2tb10(A), tptp_fun_I2_0(U, L, A)))) | (~$lesseq($sum(L, $product(-1, tptp_fun_I1_1(U, L, A))), 0)) | (~$greatereq($sum(tptp_fun_I2_0(U, L, A), $product(-1, tptp_fun_I1_1(U, L, A))), 0))))))), ((((~sorted_sub4(A, L, U)) | ![I1: $int, I2: $int] : ((~($greatereq($sum(I1, $product(-1, L)), 0) & $lesseq($sum(I1, $product(-1, I2)), 0) & (~$lesseq($sum(U, $product(-1, I2)), 0)))) | le4(tb2t11(get2(elt7, t2tb10(A), I1)), tb2t11(get2(elt7, t2tb10(A), I2))))) & (sorted_sub4(A, L, U) | (~((~($lesseq($sum(L, $product(-1, tptp_fun_I1_1(U, L, A))), 0) & $greatereq($sum(tptp_fun_I2_0(U, L, A), $product(-1, tptp_fun_I1_1(U, L, A))), 0) & (~$lesseq($sum(U, $product(-1, tptp_fun_I2_0(U, L, A))), 0)))) | le4(tb2t11(get2(elt7, t2tb10(A), tptp_fun_I1_1(U, L, A))), tb2t11(get2(elt7, t2tb10(A), tptp_fun_I2_0(U, L, A)))))))) <=> (((~sorted_sub4(A, L, U)) | ![I1: $int, I2: $int] : (le4(tb2t11(get2(elt7, t2tb10(A), I1)), tb2t11(get2(elt7, t2tb10(A), I2))) | $lesseq($sum(U, $product(-1, I2)), 0) | (~$lesseq($sum(I1, $product(-1, I2)), 0)) | (~$greatereq($sum(I1, $product(-1, L)), 0)))) & (sorted_sub4(A, L, U) | (~($lesseq($sum(U, $product(-1, tptp_fun_I2_0(U, L, A))), 0) | le4(tb2t11(get2(elt7, t2tb10(A), tptp_fun_I1_1(U, L, A))), tb2t11(get2(elt7, t2tb10(A), tptp_fun_I2_0(U, L, A)))) | (~$lesseq($sum(L, $product(-1, tptp_fun_I1_1(U, L, A))), 0)) | (~$greatereq($sum(tptp_fun_I2_0(U, L, A), $product(-1, tptp_fun_I1_1(U, L, A))), 0)))))))), rewrite((((~sorted_sub4(A, L, U)) | ![I1: $int, I2: $int] : (le4(tb2t11(get2(elt7, t2tb10(A), I1)), tb2t11(get2(elt7, t2tb10(A), I2))) | $lesseq($sum(U, $product(-1, I2)), 0) | (~$lesseq($sum(I1, $product(-1, I2)), 0)) | (~$greatereq($sum(I1, $product(-1, L)), 0)))) & (sorted_sub4(A, L, U) | (~($lesseq($sum(U, $product(-1, tptp_fun_I2_0(U, L, A))), 0) | le4(tb2t11(get2(elt7, t2tb10(A), tptp_fun_I1_1(U, L, A))), tb2t11(get2(elt7, t2tb10(A), tptp_fun_I2_0(U, L, A)))) | (~$lesseq($sum(L, $product(-1, tptp_fun_I1_1(U, L, A))), 0)) | (~$greatereq($sum(tptp_fun_I2_0(U, L, A), $product(-1, tptp_fun_I1_1(U, L, A))), 0)))))) <=> (~((~((~sorted_sub4(A, L, U)) | ![I1: $int, I2: $int] : (le4(tb2t11(get2(elt7, t2tb10(A), I1)), tb2t11(get2(elt7, t2tb10(A), I2))) | $lesseq($sum(U, $product(-1, I2)), 0) | (~$lesseq($sum(I1, $product(-1, I2)), 0)) | (~$greatereq($sum(I1, $product(-1, L)), 0))))) | (~(sorted_sub4(A, L, U) | (~($lesseq($sum(U, $product(-1, tptp_fun_I2_0(U, L, A))), 0) | le4(tb2t11(get2(elt7, t2tb10(A), tptp_fun_I1_1(U, L, A))), tb2t11(get2(elt7, t2tb10(A), tptp_fun_I2_0(U, L, A)))) | (~$lesseq($sum(L, $product(-1, tptp_fun_I1_1(U, L, A))), 0)) | (~$greatereq($sum(tptp_fun_I2_0(U, L, A), $product(-1, tptp_fun_I1_1(U, L, A))), 0))))))))), ((((~sorted_sub4(A, L, U)) | ![I1: $int, I2: $int] : ((~($greatereq($sum(I1, $product(-1, L)), 0) & $lesseq($sum(I1, $product(-1, I2)), 0) & (~$lesseq($sum(U, $product(-1, I2)), 0)))) | le4(tb2t11(get2(elt7, t2tb10(A), I1)), tb2t11(get2(elt7, t2tb10(A), I2))))) & (sorted_sub4(A, L, U) | (~((~($lesseq($sum(L, $product(-1, tptp_fun_I1_1(U, L, A))), 0) & $greatereq($sum(tptp_fun_I2_0(U, L, A), $product(-1, tptp_fun_I1_1(U, L, A))), 0) & (~$lesseq($sum(U, $product(-1, tptp_fun_I2_0(U, L, A))), 0)))) | le4(tb2t11(get2(elt7, t2tb10(A), tptp_fun_I1_1(U, L, A))), tb2t11(get2(elt7, t2tb10(A), tptp_fun_I2_0(U, L, A)))))))) <=> (~((~((~sorted_sub4(A, L, U)) | ![I1: $int, I2: $int] : (le4(tb2t11(get2(elt7, t2tb10(A), I1)), tb2t11(get2(elt7, t2tb10(A), I2))) | $lesseq($sum(U, $product(-1, I2)), 0) | (~$lesseq($sum(I1, $product(-1, I2)), 0)) | (~$greatereq($sum(I1, $product(-1, L)), 0))))) | (~(sorted_sub4(A, L, U) | (~($lesseq($sum(U, $product(-1, tptp_fun_I2_0(U, L, A))), 0) | le4(tb2t11(get2(elt7, t2tb10(A), tptp_fun_I1_1(U, L, A))), tb2t11(get2(elt7, t2tb10(A), tptp_fun_I2_0(U, L, A)))) | (~$lesseq($sum(L, $product(-1, tptp_fun_I1_1(U, L, A))), 0)) | (~$greatereq($sum(tptp_fun_I2_0(U, L, A), $product(-1, tptp_fun_I1_1(U, L, A))), 0))))))))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(7,plain,
% 0.21/0.47 (![A: array_elt3, L: $int, U: $int] : (((~sorted_sub4(A, L, U)) | ![I1: $int, I2: $int] : ((~($greatereq($sum(I1, $product(-1, L)), 0) & $lesseq($sum(I1, $product(-1, I2)), 0) & (~$lesseq($sum(U, $product(-1, I2)), 0)))) | le4(tb2t11(get2(elt7, t2tb10(A), I1)), tb2t11(get2(elt7, t2tb10(A), I2))))) & (sorted_sub4(A, L, U) | (~((~($lesseq($sum(L, $product(-1, tptp_fun_I1_1(U, L, A))), 0) & $greatereq($sum(tptp_fun_I2_0(U, L, A), $product(-1, tptp_fun_I1_1(U, L, A))), 0) & (~$lesseq($sum(U, $product(-1, tptp_fun_I2_0(U, L, A))), 0)))) | le4(tb2t11(get2(elt7, t2tb10(A), tptp_fun_I1_1(U, L, A))), tb2t11(get2(elt7, t2tb10(A), tptp_fun_I2_0(U, L, A)))))))) <=> ![A: array_elt3, L: $int, U: $int] : (~((~((~sorted_sub4(A, L, U)) | ![I1: $int, I2: $int] : (le4(tb2t11(get2(elt7, t2tb10(A), I1)), tb2t11(get2(elt7, t2tb10(A), I2))) | $lesseq($sum(U, $product(-1, I2)), 0) | (~$lesseq($sum(I1, $product(-1, I2)), 0)) | (~$greatereq($sum(I1, $product(-1, L)), 0))))) | (~(sorted_sub4(A, L, U) | (~($lesseq($sum(U, $product(-1, tptp_fun_I2_0(U, L, A))), 0) | le4(tb2t11(get2(elt7, t2tb10(A), tptp_fun_I1_1(U, L, A))), tb2t11(get2(elt7, t2tb10(A), tptp_fun_I2_0(U, L, A)))) | (~$lesseq($sum(L, $product(-1, tptp_fun_I1_1(U, L, A))), 0)) | (~$greatereq($sum(tptp_fun_I2_0(U, L, A), $product(-1, tptp_fun_I1_1(U, L, A))), 0))))))))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[6])).
% 0.21/0.47 tff(8,plain,
% 0.21/0.47 (^[A: array_elt3, L: $int, U: $int] : rewrite((((~sorted_sub4(A, L, U)) | ![I1: $int, I2: $int] : ((~($greatereq($sum(I1, $product(-1, L)), 0) & $lesseq($sum(I1, $product(-1, I2)), 0) & (~$lesseq($sum(U, $product(-1, I2)), 0)))) | le4(tb2t11(get2(elt7, t2tb10(A), I1)), tb2t11(get2(elt7, t2tb10(A), I2))))) & (sorted_sub4(A, L, U) | (~((~($greatereq($sum(tptp_fun_I1_1(U, L, A), $product(-1, L)), 0) & $lesseq($sum(tptp_fun_I1_1(U, L, A), $product(-1, tptp_fun_I2_0(U, L, A))), 0) & (~$lesseq($sum(U, $product(-1, tptp_fun_I2_0(U, L, A))), 0)))) | le4(tb2t11(get2(elt7, t2tb10(A), tptp_fun_I1_1(U, L, A))), tb2t11(get2(elt7, t2tb10(A), tptp_fun_I2_0(U, L, A)))))))) <=> (((~sorted_sub4(A, L, U)) | ![I1: $int, I2: $int] : ((~($greatereq($sum(I1, $product(-1, L)), 0) & $lesseq($sum(I1, $product(-1, I2)), 0) & (~$lesseq($sum(U, $product(-1, I2)), 0)))) | le4(tb2t11(get2(elt7, t2tb10(A), I1)), tb2t11(get2(elt7, t2tb10(A), I2))))) & (sorted_sub4(A, L, U) | (~((~($lesseq($sum(L, $product(-1, tptp_fun_I1_1(U, L, A))), 0) & $greatereq($sum(tptp_fun_I2_0(U, L, A), $product(-1, tptp_fun_I1_1(U, L, A))), 0) & (~$lesseq($sum(U, $product(-1, tptp_fun_I2_0(U, L, A))), 0)))) | le4(tb2t11(get2(elt7, t2tb10(A), tptp_fun_I1_1(U, L, A))), tb2t11(get2(elt7, t2tb10(A), tptp_fun_I2_0(U, L, A)))))))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(9,plain,
% 0.21/0.47 (![A: array_elt3, L: $int, U: $int] : (((~sorted_sub4(A, L, U)) | ![I1: $int, I2: $int] : ((~($greatereq($sum(I1, $product(-1, L)), 0) & $lesseq($sum(I1, $product(-1, I2)), 0) & (~$lesseq($sum(U, $product(-1, I2)), 0)))) | le4(tb2t11(get2(elt7, t2tb10(A), I1)), tb2t11(get2(elt7, t2tb10(A), I2))))) & (sorted_sub4(A, L, U) | (~((~($greatereq($sum(tptp_fun_I1_1(U, L, A), $product(-1, L)), 0) & $lesseq($sum(tptp_fun_I1_1(U, L, A), $product(-1, tptp_fun_I2_0(U, L, A))), 0) & (~$lesseq($sum(U, $product(-1, tptp_fun_I2_0(U, L, A))), 0)))) | le4(tb2t11(get2(elt7, t2tb10(A), tptp_fun_I1_1(U, L, A))), tb2t11(get2(elt7, t2tb10(A), tptp_fun_I2_0(U, L, A)))))))) <=> ![A: array_elt3, L: $int, U: $int] : (((~sorted_sub4(A, L, U)) | ![I1: $int, I2: $int] : ((~($greatereq($sum(I1, $product(-1, L)), 0) & $lesseq($sum(I1, $product(-1, I2)), 0) & (~$lesseq($sum(U, $product(-1, I2)), 0)))) | le4(tb2t11(get2(elt7, t2tb10(A), I1)), tb2t11(get2(elt7, t2tb10(A), I2))))) & (sorted_sub4(A, L, U) | (~((~($lesseq($sum(L, $product(-1, tptp_fun_I1_1(U, L, A))), 0) & $greatereq($sum(tptp_fun_I2_0(U, L, A), $product(-1, tptp_fun_I1_1(U, L, A))), 0) & (~$lesseq($sum(U, $product(-1, tptp_fun_I2_0(U, L, A))), 0)))) | le4(tb2t11(get2(elt7, t2tb10(A), tptp_fun_I1_1(U, L, A))), tb2t11(get2(elt7, t2tb10(A), tptp_fun_I2_0(U, L, A))))))))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[8])).
% 0.21/0.47 tff(10,plain,
% 0.21/0.47 (^[A: array_elt3, L: $int, U: $int] : rewrite((sorted_sub4(A, L, U) <=> ![I1: $int, I2: $int] : ((~($lesseq($sum(L, $product(-1, I1)), 0) & $lesseq($sum(I1, $product(-1, I2)), 0) & (~$lesseq($sum(U, $product(-1, I2)), 0)))) | le4(tb2t11(get2(elt7, t2tb10(A), I1)), tb2t11(get2(elt7, t2tb10(A), I2))))) <=> (sorted_sub4(A, L, U) <=> ![I1: $int, I2: $int] : ((~($greatereq($sum(I1, $product(-1, L)), 0) & $lesseq($sum(I1, $product(-1, I2)), 0) & (~$lesseq($sum(U, $product(-1, I2)), 0)))) | le4(tb2t11(get2(elt7, t2tb10(A), I1)), tb2t11(get2(elt7, t2tb10(A), I2))))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(11,plain,
% 0.21/0.47 (![A: array_elt3, L: $int, U: $int] : (sorted_sub4(A, L, U) <=> ![I1: $int, I2: $int] : ((~($lesseq($sum(L, $product(-1, I1)), 0) & $lesseq($sum(I1, $product(-1, I2)), 0) & (~$lesseq($sum(U, $product(-1, I2)), 0)))) | le4(tb2t11(get2(elt7, t2tb10(A), I1)), tb2t11(get2(elt7, t2tb10(A), I2))))) <=> ![A: array_elt3, L: $int, U: $int] : (sorted_sub4(A, L, U) <=> ![I1: $int, I2: $int] : ((~($greatereq($sum(I1, $product(-1, L)), 0) & $lesseq($sum(I1, $product(-1, I2)), 0) & (~$lesseq($sum(U, $product(-1, I2)), 0)))) | le4(tb2t11(get2(elt7, t2tb10(A), I1)), tb2t11(get2(elt7, t2tb10(A), I2)))))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[10])).
% 0.21/0.48 tff(12,plain,
% 0.21/0.48 (^[A: array_elt3, L: $int, U: $int] : rewrite((sorted_sub4(A, L, U) <=> ![I1: $int, I2: $int] : ((~($lesseq(L, I1) & $lesseq(I1, I2) & (~$lesseq(U, I2)))) | le4(tb2t11(get2(elt7, t2tb10(A), I1)), tb2t11(get2(elt7, t2tb10(A), I2))))) <=> (sorted_sub4(A, L, U) <=> ![I1: $int, I2: $int] : ((~($lesseq($sum(L, $product(-1, I1)), 0) & $lesseq($sum(I1, $product(-1, I2)), 0) & (~$lesseq($sum(U, $product(-1, I2)), 0)))) | le4(tb2t11(get2(elt7, t2tb10(A), I1)), tb2t11(get2(elt7, t2tb10(A), I2))))))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(13,plain,
% 0.21/0.48 (![A: array_elt3, L: $int, U: $int] : (sorted_sub4(A, L, U) <=> ![I1: $int, I2: $int] : ((~($lesseq(L, I1) & $lesseq(I1, I2) & (~$lesseq(U, I2)))) | le4(tb2t11(get2(elt7, t2tb10(A), I1)), tb2t11(get2(elt7, t2tb10(A), I2))))) <=> ![A: array_elt3, L: $int, U: $int] : (sorted_sub4(A, L, U) <=> ![I1: $int, I2: $int] : ((~($lesseq($sum(L, $product(-1, I1)), 0) & $lesseq($sum(I1, $product(-1, I2)), 0) & (~$lesseq($sum(U, $product(-1, I2)), 0)))) | le4(tb2t11(get2(elt7, t2tb10(A), I1)), tb2t11(get2(elt7, t2tb10(A), I2)))))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[12])).
% 0.21/0.48 tff(14,plain,
% 0.21/0.48 (![A: array_elt3, L: $int, U: $int] : (sorted_sub4(A, L, U) <=> ![I1: $int, I2: $int] : ((~($lesseq(L, I1) & $lesseq(I1, I2) & (~$lesseq(U, I2)))) | le4(tb2t11(get2(elt7, t2tb10(A), I1)), tb2t11(get2(elt7, t2tb10(A), I2))))) <=> ![A: array_elt3, L: $int, U: $int] : (sorted_sub4(A, L, U) <=> ![I1: $int, I2: $int] : ((~($lesseq(L, I1) & $lesseq(I1, I2) & (~$lesseq(U, I2)))) | le4(tb2t11(get2(elt7, t2tb10(A), I1)), tb2t11(get2(elt7, t2tb10(A), I2)))))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(15,plain,
% 0.21/0.48 (^[A: array_elt3, L: $int, U: $int] : rewrite((sorted_sub4(A, L, U) <=> ![I1: $int, I2: $int] : ((($lesseq(L, I1) & $lesseq(I1, I2)) & $less(I2, U)) => le4(tb2t11(get2(elt7, t2tb10(A), I1)), tb2t11(get2(elt7, t2tb10(A), I2))))) <=> (sorted_sub4(A, L, U) <=> ![I1: $int, I2: $int] : ((~($lesseq(L, I1) & $lesseq(I1, I2) & (~$lesseq(U, I2)))) | le4(tb2t11(get2(elt7, t2tb10(A), I1)), tb2t11(get2(elt7, t2tb10(A), I2))))))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(16,plain,
% 0.21/0.48 (![A: array_elt3, L: $int, U: $int] : (sorted_sub4(A, L, U) <=> ![I1: $int, I2: $int] : ((($lesseq(L, I1) & $lesseq(I1, I2)) & $less(I2, U)) => le4(tb2t11(get2(elt7, t2tb10(A), I1)), tb2t11(get2(elt7, t2tb10(A), I2))))) <=> ![A: array_elt3, L: $int, U: $int] : (sorted_sub4(A, L, U) <=> ![I1: $int, I2: $int] : ((~($lesseq(L, I1) & $lesseq(I1, I2) & (~$lesseq(U, I2)))) | le4(tb2t11(get2(elt7, t2tb10(A), I1)), tb2t11(get2(elt7, t2tb10(A), I2)))))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[15])).
% 0.21/0.48 tff(17,axiom,(![A: array_elt3, L: $int, U: $int] : (sorted_sub4(A, L, U) <=> ![I1: $int, I2: $int] : ((($lesseq(L, I1) & $lesseq(I1, I2)) & $less(I2, U)) => le4(tb2t11(get2(elt7, t2tb10(A), I1)), tb2t11(get2(elt7, t2tb10(A), I2)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','sorted_sub_def3')).
% 0.21/0.48 tff(18,plain,
% 0.21/0.48 (![A: array_elt3, L: $int, U: $int] : (sorted_sub4(A, L, U) <=> ![I1: $int, I2: $int] : ((~($lesseq(L, I1) & $lesseq(I1, I2) & (~$lesseq(U, I2)))) | le4(tb2t11(get2(elt7, t2tb10(A), I1)), tb2t11(get2(elt7, t2tb10(A), I2)))))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.21/0.48 tff(19,plain,
% 0.21/0.48 (![A: array_elt3, L: $int, U: $int] : (sorted_sub4(A, L, U) <=> ![I1: $int, I2: $int] : ((~($lesseq(L, I1) & $lesseq(I1, I2) & (~$lesseq(U, I2)))) | le4(tb2t11(get2(elt7, t2tb10(A), I1)), tb2t11(get2(elt7, t2tb10(A), I2)))))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.21/0.48 tff(20,plain,
% 0.21/0.48 (![A: array_elt3, L: $int, U: $int] : (sorted_sub4(A, L, U) <=> ![I1: $int, I2: $int] : ((~($lesseq($sum(L, $product(-1, I1)), 0) & $lesseq($sum(I1, $product(-1, I2)), 0) & (~$lesseq($sum(U, $product(-1, I2)), 0)))) | le4(tb2t11(get2(elt7, t2tb10(A), I1)), tb2t11(get2(elt7, t2tb10(A), I2)))))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[19, 13])).
% 0.21/0.48 tff(21,plain,
% 0.21/0.48 (![A: array_elt3, L: $int, U: $int] : (sorted_sub4(A, L, U) <=> ![I1: $int, I2: $int] : ((~($greatereq($sum(I1, $product(-1, L)), 0) & $lesseq($sum(I1, $product(-1, I2)), 0) & (~$lesseq($sum(U, $product(-1, I2)), 0)))) | le4(tb2t11(get2(elt7, t2tb10(A), I1)), tb2t11(get2(elt7, t2tb10(A), I2)))))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[20, 11])).
% 0.21/0.48 tff(22,plain,(
% 0.21/0.48 ![A: array_elt3, L: $int, U: $int] : (((~sorted_sub4(A, L, U)) | ![I1: $int, I2: $int] : ((~($greatereq($sum(I1, $product(-1, L)), 0) & $lesseq($sum(I1, $product(-1, I2)), 0) & (~$lesseq($sum(U, $product(-1, I2)), 0)))) | le4(tb2t11(get2(elt7, t2tb10(A), I1)), tb2t11(get2(elt7, t2tb10(A), I2))))) & (sorted_sub4(A, L, U) | (~((~($greatereq($sum(tptp_fun_I1_1(U, L, A), $product(-1, L)), 0) & $lesseq($sum(tptp_fun_I1_1(U, L, A), $product(-1, tptp_fun_I2_0(U, L, A))), 0) & (~$lesseq($sum(U, $product(-1, tptp_fun_I2_0(U, L, A))), 0)))) | le4(tb2t11(get2(elt7, t2tb10(A), tptp_fun_I1_1(U, L, A))), tb2t11(get2(elt7, t2tb10(A), tptp_fun_I2_0(U, L, A))))))))),
% 0.21/0.48 inference(skolemize,[status(sab)],[21])).
% 0.21/0.48 tff(23,plain,
% 0.21/0.48 (![A: array_elt3, L: $int, U: $int] : (((~sorted_sub4(A, L, U)) | ![I1: $int, I2: $int] : ((~($greatereq($sum(I1, $product(-1, L)), 0) & $lesseq($sum(I1, $product(-1, I2)), 0) & (~$lesseq($sum(U, $product(-1, I2)), 0)))) | le4(tb2t11(get2(elt7, t2tb10(A), I1)), tb2t11(get2(elt7, t2tb10(A), I2))))) & (sorted_sub4(A, L, U) | (~((~($lesseq($sum(L, $product(-1, tptp_fun_I1_1(U, L, A))), 0) & $greatereq($sum(tptp_fun_I2_0(U, L, A), $product(-1, tptp_fun_I1_1(U, L, A))), 0) & (~$lesseq($sum(U, $product(-1, tptp_fun_I2_0(U, L, A))), 0)))) | le4(tb2t11(get2(elt7, t2tb10(A), tptp_fun_I1_1(U, L, A))), tb2t11(get2(elt7, t2tb10(A), tptp_fun_I2_0(U, L, A))))))))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[22, 9])).
% 0.21/0.48 tff(24,plain,
% 0.21/0.48 (![A: array_elt3, L: $int, U: $int] : (~((~((~sorted_sub4(A, L, U)) | ![I1: $int, I2: $int] : (le4(tb2t11(get2(elt7, t2tb10(A), I1)), tb2t11(get2(elt7, t2tb10(A), I2))) | $lesseq($sum(U, $product(-1, I2)), 0) | (~$lesseq($sum(I1, $product(-1, I2)), 0)) | (~$greatereq($sum(I1, $product(-1, L)), 0))))) | (~(sorted_sub4(A, L, U) | (~($lesseq($sum(U, $product(-1, tptp_fun_I2_0(U, L, A))), 0) | le4(tb2t11(get2(elt7, t2tb10(A), tptp_fun_I1_1(U, L, A))), tb2t11(get2(elt7, t2tb10(A), tptp_fun_I2_0(U, L, A)))) | (~$lesseq($sum(L, $product(-1, tptp_fun_I1_1(U, L, A))), 0)) | (~$greatereq($sum(tptp_fun_I2_0(U, L, A), $product(-1, tptp_fun_I1_1(U, L, A))), 0))))))))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[23, 7])).
% 0.21/0.48 tff(25,plain,
% 0.21/0.48 (![A: array_elt3, L: $int, U: $int] : (~((~((~sorted_sub4(A, L, U)) | ![I1: $int, I2: $int] : (le4(tb2t11(get2(elt7, t2tb10(A), I1)), tb2t11(get2(elt7, t2tb10(A), I2))) | $lesseq($sum(U, $product(-1, I2)), 0) | (~$lesseq($sum(I1, $product(-1, I2)), 0)) | (~$greatereq($sum(I1, $product(-1, L)), 0))))) | (~(sorted_sub4(A, L, U) | (~($lesseq($sum(U, $product(-1, tptp_fun_I2_0(U, L, A))), 0) | le4(tb2t11(get2(elt7, t2tb10(A), tptp_fun_I1_1(U, L, A))), tb2t11(get2(elt7, t2tb10(A), tptp_fun_I2_0(U, L, A)))) | (~$lesseq($sum(L, $product(-1, tptp_fun_I1_1(U, L, A))), 0)) | (~$greatereq($sum(tptp_fun_I2_0(U, L, A), $product(-1, tptp_fun_I1_1(U, L, A))), 0))))))))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[24, 5])).
% 0.21/0.48 tff(26,plain,
% 0.21/0.48 (((~![A: array_elt3, L: $int, U: $int] : (~((~((~sorted_sub4(A, L, U)) | ![I1: $int, I2: $int] : (le4(tb2t11(get2(elt7, t2tb10(A), I1)), tb2t11(get2(elt7, t2tb10(A), I2))) | $lesseq($sum(U, $product(-1, I2)), 0) | (~$lesseq($sum(I1, $product(-1, I2)), 0)) | (~$greatereq($sum(I1, $product(-1, L)), 0))))) | (~(sorted_sub4(A, L, U) | (~($lesseq($sum(U, $product(-1, tptp_fun_I2_0(U, L, A))), 0) | le4(tb2t11(get2(elt7, t2tb10(A), tptp_fun_I1_1(U, L, A))), tb2t11(get2(elt7, t2tb10(A), tptp_fun_I2_0(U, L, A)))) | (~$lesseq($sum(L, $product(-1, tptp_fun_I1_1(U, L, A))), 0)) | (~$greatereq($sum(tptp_fun_I2_0(U, L, A), $product(-1, tptp_fun_I1_1(U, L, A))), 0))))))))) | (~((~((~sorted_sub4(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12))), Lo!11, $sum(1, Lo!11))) | ![I1: $int, I2: $int] : ((~$lesseq($sum(I1, $product(-1, I2)), 0)) | le4(tb2t11(get2(elt7, t2tb10(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), I1)), tb2t11(get2(elt7, t2tb10(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), I2))) | (~$greatereq($sum(I1, $product(-1, Lo!11)), 0)) | $greatereq($sum(I2, $product(-1, Lo!11)), 1)))) | (~(sorted_sub4(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12))), Lo!11, $sum(1, Lo!11)) | (~(le4(tb2t11(get2(elt7, t2tb10(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), tptp_fun_I1_1($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))), tb2t11(get2(elt7, t2tb10(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), tptp_fun_I2_0($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12))))))) | (~$lesseq($sum(Lo!11, $product(-1, tptp_fun_I1_1($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))), 0)) | (~$greatereq($sum(tptp_fun_I2_0($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), $product(-1, tptp_fun_I1_1($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))), 0)) | $lesseq($sum(Lo!11, $product(-1, tptp_fun_I2_0($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))), -1)))))))) <=> ((~![A: array_elt3, L: $int, U: $int] : (~((~((~sorted_sub4(A, L, U)) | ![I1: $int, I2: $int] : (le4(tb2t11(get2(elt7, t2tb10(A), I1)), tb2t11(get2(elt7, t2tb10(A), I2))) | $lesseq($sum(U, $product(-1, I2)), 0) | (~$lesseq($sum(I1, $product(-1, I2)), 0)) | (~$greatereq($sum(I1, $product(-1, L)), 0))))) | (~(sorted_sub4(A, L, U) | (~($lesseq($sum(U, $product(-1, tptp_fun_I2_0(U, L, A))), 0) | le4(tb2t11(get2(elt7, t2tb10(A), tptp_fun_I1_1(U, L, A))), tb2t11(get2(elt7, t2tb10(A), tptp_fun_I2_0(U, L, A)))) | (~$lesseq($sum(L, $product(-1, tptp_fun_I1_1(U, L, A))), 0)) | (~$greatereq($sum(tptp_fun_I2_0(U, L, A), $product(-1, tptp_fun_I1_1(U, L, A))), 0))))))))) | (~((~((~sorted_sub4(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12))), Lo!11, $sum(1, Lo!11))) | ![I1: $int, I2: $int] : ((~$lesseq($sum(I1, $product(-1, I2)), 0)) | le4(tb2t11(get2(elt7, t2tb10(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), I1)), tb2t11(get2(elt7, t2tb10(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), I2))) | (~$greatereq($sum(I1, $product(-1, Lo!11)), 0)) | $greatereq($sum(I2, $product(-1, Lo!11)), 1)))) | (~(sorted_sub4(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12))), Lo!11, $sum(1, Lo!11)) | (~(le4(tb2t11(get2(elt7, t2tb10(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), tptp_fun_I1_1($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))), tb2t11(get2(elt7, t2tb10(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), tptp_fun_I2_0($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12))))))) | (~$lesseq($sum(Lo!11, $product(-1, tptp_fun_I1_1($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))), 0)) | (~$greatereq($sum(tptp_fun_I2_0($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), $product(-1, tptp_fun_I1_1($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))), 0)) | $lesseq($sum(Lo!11, $product(-1, tptp_fun_I2_0($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))), -1))))))))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(27,plain,
% 0.21/0.48 ((~((~((~sorted_sub4(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12))), Lo!11, $sum(1, Lo!11))) | ![I1: $int, I2: $int] : (le4(tb2t11(get2(elt7, t2tb10(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), I1)), tb2t11(get2(elt7, t2tb10(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), I2))) | $lesseq($sum($sum(1, Lo!11), $product(-1, I2)), 0) | (~$lesseq($sum(I1, $product(-1, I2)), 0)) | (~$greatereq($sum(I1, $product(-1, Lo!11)), 0))))) | (~(sorted_sub4(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12))), Lo!11, $sum(1, Lo!11)) | (~($lesseq($sum($sum(1, Lo!11), $product(-1, tptp_fun_I2_0($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))), 0) | le4(tb2t11(get2(elt7, t2tb10(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), tptp_fun_I1_1($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))), tb2t11(get2(elt7, t2tb10(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), tptp_fun_I2_0($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12))))))) | (~$lesseq($sum(Lo!11, $product(-1, tptp_fun_I1_1($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))), 0)) | (~$greatereq($sum(tptp_fun_I2_0($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), $product(-1, tptp_fun_I1_1($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))), 0)))))))) <=> (~((~((~sorted_sub4(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12))), Lo!11, $sum(1, Lo!11))) | ![I1: $int, I2: $int] : ((~$lesseq($sum(I1, $product(-1, I2)), 0)) | le4(tb2t11(get2(elt7, t2tb10(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), I1)), tb2t11(get2(elt7, t2tb10(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), I2))) | (~$greatereq($sum(I1, $product(-1, Lo!11)), 0)) | $greatereq($sum(I2, $product(-1, Lo!11)), 1)))) | (~(sorted_sub4(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12))), Lo!11, $sum(1, Lo!11)) | (~(le4(tb2t11(get2(elt7, t2tb10(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), tptp_fun_I1_1($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))), tb2t11(get2(elt7, t2tb10(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), tptp_fun_I2_0($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12))))))) | (~$lesseq($sum(Lo!11, $product(-1, tptp_fun_I1_1($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))), 0)) | (~$greatereq($sum(tptp_fun_I2_0($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), $product(-1, tptp_fun_I1_1($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))), 0)) | $lesseq($sum(Lo!11, $product(-1, tptp_fun_I2_0($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))), -1)))))))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(28,plain,
% 0.21/0.48 (((~![A: array_elt3, L: $int, U: $int] : (~((~((~sorted_sub4(A, L, U)) | ![I1: $int, I2: $int] : (le4(tb2t11(get2(elt7, t2tb10(A), I1)), tb2t11(get2(elt7, t2tb10(A), I2))) | $lesseq($sum(U, $product(-1, I2)), 0) | (~$lesseq($sum(I1, $product(-1, I2)), 0)) | (~$greatereq($sum(I1, $product(-1, L)), 0))))) | (~(sorted_sub4(A, L, U) | (~($lesseq($sum(U, $product(-1, tptp_fun_I2_0(U, L, A))), 0) | le4(tb2t11(get2(elt7, t2tb10(A), tptp_fun_I1_1(U, L, A))), tb2t11(get2(elt7, t2tb10(A), tptp_fun_I2_0(U, L, A)))) | (~$lesseq($sum(L, $product(-1, tptp_fun_I1_1(U, L, A))), 0)) | (~$greatereq($sum(tptp_fun_I2_0(U, L, A), $product(-1, tptp_fun_I1_1(U, L, A))), 0))))))))) | (~((~((~sorted_sub4(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12))), Lo!11, $sum(1, Lo!11))) | ![I1: $int, I2: $int] : (le4(tb2t11(get2(elt7, t2tb10(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), I1)), tb2t11(get2(elt7, t2tb10(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), I2))) | $lesseq($sum($sum(1, Lo!11), $product(-1, I2)), 0) | (~$lesseq($sum(I1, $product(-1, I2)), 0)) | (~$greatereq($sum(I1, $product(-1, Lo!11)), 0))))) | (~(sorted_sub4(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12))), Lo!11, $sum(1, Lo!11)) | (~($lesseq($sum($sum(1, Lo!11), $product(-1, tptp_fun_I2_0($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))), 0) | le4(tb2t11(get2(elt7, t2tb10(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), tptp_fun_I1_1($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))), tb2t11(get2(elt7, t2tb10(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), tptp_fun_I2_0($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12))))))) | (~$lesseq($sum(Lo!11, $product(-1, tptp_fun_I1_1($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))), 0)) | (~$greatereq($sum(tptp_fun_I2_0($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), $product(-1, tptp_fun_I1_1($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))), 0))))))))) <=> ((~![A: array_elt3, L: $int, U: $int] : (~((~((~sorted_sub4(A, L, U)) | ![I1: $int, I2: $int] : (le4(tb2t11(get2(elt7, t2tb10(A), I1)), tb2t11(get2(elt7, t2tb10(A), I2))) | $lesseq($sum(U, $product(-1, I2)), 0) | (~$lesseq($sum(I1, $product(-1, I2)), 0)) | (~$greatereq($sum(I1, $product(-1, L)), 0))))) | (~(sorted_sub4(A, L, U) | (~($lesseq($sum(U, $product(-1, tptp_fun_I2_0(U, L, A))), 0) | le4(tb2t11(get2(elt7, t2tb10(A), tptp_fun_I1_1(U, L, A))), tb2t11(get2(elt7, t2tb10(A), tptp_fun_I2_0(U, L, A)))) | (~$lesseq($sum(L, $product(-1, tptp_fun_I1_1(U, L, A))), 0)) | (~$greatereq($sum(tptp_fun_I2_0(U, L, A), $product(-1, tptp_fun_I1_1(U, L, A))), 0))))))))) | (~((~((~sorted_sub4(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12))), Lo!11, $sum(1, Lo!11))) | ![I1: $int, I2: $int] : ((~$lesseq($sum(I1, $product(-1, I2)), 0)) | le4(tb2t11(get2(elt7, t2tb10(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), I1)), tb2t11(get2(elt7, t2tb10(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), I2))) | (~$greatereq($sum(I1, $product(-1, Lo!11)), 0)) | $greatereq($sum(I2, $product(-1, Lo!11)), 1)))) | (~(sorted_sub4(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12))), Lo!11, $sum(1, Lo!11)) | (~(le4(tb2t11(get2(elt7, t2tb10(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), tptp_fun_I1_1($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))), tb2t11(get2(elt7, t2tb10(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), tptp_fun_I2_0($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12))))))) | (~$lesseq($sum(Lo!11, $product(-1, tptp_fun_I1_1($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))), 0)) | (~$greatereq($sum(tptp_fun_I2_0($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), $product(-1, tptp_fun_I1_1($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))), 0)) | $lesseq($sum(Lo!11, $product(-1, tptp_fun_I2_0($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))), -1))))))))),
% 0.21/0.49 inference(monotonicity,[status(thm)],[27])).
% 0.21/0.49 tff(29,plain,
% 0.21/0.49 (((~![A: array_elt3, L: $int, U: $int] : (~((~((~sorted_sub4(A, L, U)) | ![I1: $int, I2: $int] : (le4(tb2t11(get2(elt7, t2tb10(A), I1)), tb2t11(get2(elt7, t2tb10(A), I2))) | $lesseq($sum(U, $product(-1, I2)), 0) | (~$lesseq($sum(I1, $product(-1, I2)), 0)) | (~$greatereq($sum(I1, $product(-1, L)), 0))))) | (~(sorted_sub4(A, L, U) | (~($lesseq($sum(U, $product(-1, tptp_fun_I2_0(U, L, A))), 0) | le4(tb2t11(get2(elt7, t2tb10(A), tptp_fun_I1_1(U, L, A))), tb2t11(get2(elt7, t2tb10(A), tptp_fun_I2_0(U, L, A)))) | (~$lesseq($sum(L, $product(-1, tptp_fun_I1_1(U, L, A))), 0)) | (~$greatereq($sum(tptp_fun_I2_0(U, L, A), $product(-1, tptp_fun_I1_1(U, L, A))), 0))))))))) | (~((~((~sorted_sub4(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12))), Lo!11, $sum(1, Lo!11))) | ![I1: $int, I2: $int] : (le4(tb2t11(get2(elt7, t2tb10(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), I1)), tb2t11(get2(elt7, t2tb10(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), I2))) | $lesseq($sum($sum(1, Lo!11), $product(-1, I2)), 0) | (~$lesseq($sum(I1, $product(-1, I2)), 0)) | (~$greatereq($sum(I1, $product(-1, Lo!11)), 0))))) | (~(sorted_sub4(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12))), Lo!11, $sum(1, Lo!11)) | (~($lesseq($sum($sum(1, Lo!11), $product(-1, tptp_fun_I2_0($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))), 0) | le4(tb2t11(get2(elt7, t2tb10(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), tptp_fun_I1_1($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))), tb2t11(get2(elt7, t2tb10(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), tptp_fun_I2_0($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12))))))) | (~$lesseq($sum(Lo!11, $product(-1, tptp_fun_I1_1($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))), 0)) | (~$greatereq($sum(tptp_fun_I2_0($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), $product(-1, tptp_fun_I1_1($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))), 0))))))))) <=> ((~![A: array_elt3, L: $int, U: $int] : (~((~((~sorted_sub4(A, L, U)) | ![I1: $int, I2: $int] : (le4(tb2t11(get2(elt7, t2tb10(A), I1)), tb2t11(get2(elt7, t2tb10(A), I2))) | $lesseq($sum(U, $product(-1, I2)), 0) | (~$lesseq($sum(I1, $product(-1, I2)), 0)) | (~$greatereq($sum(I1, $product(-1, L)), 0))))) | (~(sorted_sub4(A, L, U) | (~($lesseq($sum(U, $product(-1, tptp_fun_I2_0(U, L, A))), 0) | le4(tb2t11(get2(elt7, t2tb10(A), tptp_fun_I1_1(U, L, A))), tb2t11(get2(elt7, t2tb10(A), tptp_fun_I2_0(U, L, A)))) | (~$lesseq($sum(L, $product(-1, tptp_fun_I1_1(U, L, A))), 0)) | (~$greatereq($sum(tptp_fun_I2_0(U, L, A), $product(-1, tptp_fun_I1_1(U, L, A))), 0))))))))) | (~((~((~sorted_sub4(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12))), Lo!11, $sum(1, Lo!11))) | ![I1: $int, I2: $int] : ((~$lesseq($sum(I1, $product(-1, I2)), 0)) | le4(tb2t11(get2(elt7, t2tb10(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), I1)), tb2t11(get2(elt7, t2tb10(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), I2))) | (~$greatereq($sum(I1, $product(-1, Lo!11)), 0)) | $greatereq($sum(I2, $product(-1, Lo!11)), 1)))) | (~(sorted_sub4(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12))), Lo!11, $sum(1, Lo!11)) | (~(le4(tb2t11(get2(elt7, t2tb10(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), tptp_fun_I1_1($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))), tb2t11(get2(elt7, t2tb10(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), tptp_fun_I2_0($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12))))))) | (~$lesseq($sum(Lo!11, $product(-1, tptp_fun_I1_1($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))), 0)) | (~$greatereq($sum(tptp_fun_I2_0($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), $product(-1, tptp_fun_I1_1($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))), 0)) | $lesseq($sum(Lo!11, $product(-1, tptp_fun_I2_0($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))), -1))))))))),
% 0.21/0.49 inference(transitivity,[status(thm)],[28, 26])).
% 0.21/0.49 tff(30,plain,
% 0.21/0.49 ((~![A: array_elt3, L: $int, U: $int] : (~((~((~sorted_sub4(A, L, U)) | ![I1: $int, I2: $int] : (le4(tb2t11(get2(elt7, t2tb10(A), I1)), tb2t11(get2(elt7, t2tb10(A), I2))) | $lesseq($sum(U, $product(-1, I2)), 0) | (~$lesseq($sum(I1, $product(-1, I2)), 0)) | (~$greatereq($sum(I1, $product(-1, L)), 0))))) | (~(sorted_sub4(A, L, U) | (~($lesseq($sum(U, $product(-1, tptp_fun_I2_0(U, L, A))), 0) | le4(tb2t11(get2(elt7, t2tb10(A), tptp_fun_I1_1(U, L, A))), tb2t11(get2(elt7, t2tb10(A), tptp_fun_I2_0(U, L, A)))) | (~$lesseq($sum(L, $product(-1, tptp_fun_I1_1(U, L, A))), 0)) | (~$greatereq($sum(tptp_fun_I2_0(U, L, A), $product(-1, tptp_fun_I1_1(U, L, A))), 0))))))))) | (~((~((~sorted_sub4(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12))), Lo!11, $sum(1, Lo!11))) | ![I1: $int, I2: $int] : (le4(tb2t11(get2(elt7, t2tb10(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), I1)), tb2t11(get2(elt7, t2tb10(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), I2))) | $lesseq($sum($sum(1, Lo!11), $product(-1, I2)), 0) | (~$lesseq($sum(I1, $product(-1, I2)), 0)) | (~$greatereq($sum(I1, $product(-1, Lo!11)), 0))))) | (~(sorted_sub4(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12))), Lo!11, $sum(1, Lo!11)) | (~($lesseq($sum($sum(1, Lo!11), $product(-1, tptp_fun_I2_0($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))), 0) | le4(tb2t11(get2(elt7, t2tb10(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), tptp_fun_I1_1($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))), tb2t11(get2(elt7, t2tb10(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), tptp_fun_I2_0($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12))))))) | (~$lesseq($sum(Lo!11, $product(-1, tptp_fun_I1_1($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))), 0)) | (~$greatereq($sum(tptp_fun_I2_0($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), $product(-1, tptp_fun_I1_1($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))), 0))))))))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(31,plain,
% 0.21/0.49 ((~![A: array_elt3, L: $int, U: $int] : (~((~((~sorted_sub4(A, L, U)) | ![I1: $int, I2: $int] : (le4(tb2t11(get2(elt7, t2tb10(A), I1)), tb2t11(get2(elt7, t2tb10(A), I2))) | $lesseq($sum(U, $product(-1, I2)), 0) | (~$lesseq($sum(I1, $product(-1, I2)), 0)) | (~$greatereq($sum(I1, $product(-1, L)), 0))))) | (~(sorted_sub4(A, L, U) | (~($lesseq($sum(U, $product(-1, tptp_fun_I2_0(U, L, A))), 0) | le4(tb2t11(get2(elt7, t2tb10(A), tptp_fun_I1_1(U, L, A))), tb2t11(get2(elt7, t2tb10(A), tptp_fun_I2_0(U, L, A)))) | (~$lesseq($sum(L, $product(-1, tptp_fun_I1_1(U, L, A))), 0)) | (~$greatereq($sum(tptp_fun_I2_0(U, L, A), $product(-1, tptp_fun_I1_1(U, L, A))), 0))))))))) | (~((~((~sorted_sub4(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12))), Lo!11, $sum(1, Lo!11))) | ![I1: $int, I2: $int] : ((~$lesseq($sum(I1, $product(-1, I2)), 0)) | le4(tb2t11(get2(elt7, t2tb10(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), I1)), tb2t11(get2(elt7, t2tb10(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), I2))) | (~$greatereq($sum(I1, $product(-1, Lo!11)), 0)) | $greatereq($sum(I2, $product(-1, Lo!11)), 1)))) | (~(sorted_sub4(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12))), Lo!11, $sum(1, Lo!11)) | (~(le4(tb2t11(get2(elt7, t2tb10(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), tptp_fun_I1_1($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))), tb2t11(get2(elt7, t2tb10(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), tptp_fun_I2_0($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12))))))) | (~$lesseq($sum(Lo!11, $product(-1, tptp_fun_I1_1($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))), 0)) | (~$greatereq($sum(tptp_fun_I2_0($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), $product(-1, tptp_fun_I1_1($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))), 0)) | $lesseq($sum(Lo!11, $product(-1, tptp_fun_I2_0($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))), -1)))))))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.21/0.49 tff(32,plain,
% 0.21/0.49 (~((~((~sorted_sub4(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12))), Lo!11, $sum(1, Lo!11))) | ![I1: $int, I2: $int] : ((~$lesseq($sum(I1, $product(-1, I2)), 0)) | le4(tb2t11(get2(elt7, t2tb10(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), I1)), tb2t11(get2(elt7, t2tb10(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), I2))) | (~$greatereq($sum(I1, $product(-1, Lo!11)), 0)) | $greatereq($sum(I2, $product(-1, Lo!11)), 1)))) | (~(sorted_sub4(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12))), Lo!11, $sum(1, Lo!11)) | (~(le4(tb2t11(get2(elt7, t2tb10(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), tptp_fun_I1_1($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))), tb2t11(get2(elt7, t2tb10(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), tptp_fun_I2_0($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12))))))) | (~$lesseq($sum(Lo!11, $product(-1, tptp_fun_I1_1($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))), 0)) | (~$greatereq($sum(tptp_fun_I2_0($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), $product(-1, tptp_fun_I1_1($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))), 0)) | $lesseq($sum(Lo!11, $product(-1, tptp_fun_I2_0($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))), -1))))))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[31, 25])).
% 0.21/0.49 tff(33,plain,
% 0.21/0.49 (((~((~sorted_sub4(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12))), Lo!11, $sum(1, Lo!11))) | ![I1: $int, I2: $int] : ((~$lesseq($sum(I1, $product(-1, I2)), 0)) | le4(tb2t11(get2(elt7, t2tb10(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), I1)), tb2t11(get2(elt7, t2tb10(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), I2))) | (~$greatereq($sum(I1, $product(-1, Lo!11)), 0)) | $greatereq($sum(I2, $product(-1, Lo!11)), 1)))) | (~(sorted_sub4(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12))), Lo!11, $sum(1, Lo!11)) | (~(le4(tb2t11(get2(elt7, t2tb10(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), tptp_fun_I1_1($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))), tb2t11(get2(elt7, t2tb10(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), tptp_fun_I2_0($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12))))))) | (~$lesseq($sum(Lo!11, $product(-1, tptp_fun_I1_1($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))), 0)) | (~$greatereq($sum(tptp_fun_I2_0($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), $product(-1, tptp_fun_I1_1($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))), 0)) | $lesseq($sum(Lo!11, $product(-1, tptp_fun_I2_0($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))), -1)))))) | (sorted_sub4(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12))), Lo!11, $sum(1, Lo!11)) | (~(le4(tb2t11(get2(elt7, t2tb10(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), tptp_fun_I1_1($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))), tb2t11(get2(elt7, t2tb10(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), tptp_fun_I2_0($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12))))))) | (~$lesseq($sum(Lo!11, $product(-1, tptp_fun_I1_1($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))), 0)) | (~$greatereq($sum(tptp_fun_I2_0($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), $product(-1, tptp_fun_I1_1($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))), 0)) | $lesseq($sum(Lo!11, $product(-1, tptp_fun_I2_0($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))), -1))))),
% 0.21/0.49 inference(tautology,[status(thm)],[])).
% 0.21/0.49 tff(34,plain,
% 0.21/0.49 (sorted_sub4(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12))), Lo!11, $sum(1, Lo!11)) | (~(le4(tb2t11(get2(elt7, t2tb10(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), tptp_fun_I1_1($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))), tb2t11(get2(elt7, t2tb10(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), tptp_fun_I2_0($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12))))))) | (~$lesseq($sum(Lo!11, $product(-1, tptp_fun_I1_1($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))), 0)) | (~$greatereq($sum(tptp_fun_I2_0($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), $product(-1, tptp_fun_I1_1($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))), 0)) | $lesseq($sum(Lo!11, $product(-1, tptp_fun_I2_0($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))), -1)))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[33, 32])).
% 0.21/0.49 tff(35,plain,
% 0.21/0.49 ((~((~($greatereq(A!13, 0) & $greatereq(Lo!11, 0) & (~$lesseq($sum(A!13, $product(-1, Lo!11)), 0)))) | sorted_sub4(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12))), Lo!11, $sum(1, Lo!11)))) <=> (~((~($greatereq(A!13, 0) & $greatereq(Lo!11, 0) & (~$greatereq($sum(Lo!11, $product(-1, A!13)), 0)))) | sorted_sub4(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12))), Lo!11, $sum(1, Lo!11))))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(36,plain,
% 0.21/0.49 ((~![A: $int, A1: map_int_elt3, Lo: $int] : ((~($greatereq(A, 0) & $greatereq(Lo, 0) & (~$lesseq($sum(A, $product(-1, Lo)), 0)))) | sorted_sub4(tb2t10(mk_array1(elt7, A, t2tb12(A1))), Lo, $sum(1, Lo)))) <=> (~![A: $int, A1: map_int_elt3, Lo: $int] : ((~($greatereq(A, 0) & $greatereq(Lo, 0) & (~$lesseq($sum(A, $product(-1, Lo)), 0)))) | sorted_sub4(tb2t10(mk_array1(elt7, A, t2tb12(A1))), Lo, $sum(1, Lo))))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(37,plain,
% 0.21/0.49 ((~![A: $int, A1: map_int_elt3, Lo: $int] : ((~($lesseq(0, A) & $lesseq(0, Lo) & (~$lesseq(A, Lo)))) | sorted_sub4(tb2t10(mk_array1(elt7, A, t2tb12(A1))), Lo, $sum(1, Lo)))) <=> (~![A: $int, A1: map_int_elt3, Lo: $int] : ((~($greatereq(A, 0) & $greatereq(Lo, 0) & (~$lesseq($sum(A, $product(-1, Lo)), 0)))) | sorted_sub4(tb2t10(mk_array1(elt7, A, t2tb12(A1))), Lo, $sum(1, Lo))))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(38,plain,
% 0.21/0.49 ((~![A: $int, A1: map_int_elt3, Lo: $int] : ((~($lesseq(0, A) & $lesseq(0, Lo) & (~$lesseq(A, Lo)))) | sorted_sub4(tb2t10(mk_array1(elt7, A, t2tb12(A1))), Lo, $sum(1, Lo)))) <=> (~![A: $int, A1: map_int_elt3, Lo: $int] : ((~($lesseq(0, A) & $lesseq(0, Lo) & (~$lesseq(A, Lo)))) | sorted_sub4(tb2t10(mk_array1(elt7, A, t2tb12(A1))), Lo, $sum(1, Lo))))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(39,plain,
% 0.21/0.49 ((~![A: $int, A1: map_int_elt3, Lo: $int] : ((($lesseq(0, A) & $lesseq(0, Lo)) & $less(Lo, A)) => sorted_sub4(tb2t10(mk_array1(elt7, A, t2tb12(A1))), Lo, $sum(Lo, 1)))) <=> (~![A: $int, A1: map_int_elt3, Lo: $int] : ((~($lesseq(0, A) & $lesseq(0, Lo) & (~$lesseq(A, Lo)))) | sorted_sub4(tb2t10(mk_array1(elt7, A, t2tb12(A1))), Lo, $sum(1, Lo))))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(40,axiom,(~![A: $int, A1: map_int_elt3, Lo: $int] : ((($lesseq(0, A) & $lesseq(0, Lo)) & $less(Lo, A)) => sorted_sub4(tb2t10(mk_array1(elt7, A, t2tb12(A1))), Lo, $sum(Lo, 1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','wP_parameter_find_run')).
% 0.21/0.50 tff(41,plain,
% 0.21/0.50 (~![A: $int, A1: map_int_elt3, Lo: $int] : ((~($lesseq(0, A) & $lesseq(0, Lo) & (~$lesseq(A, Lo)))) | sorted_sub4(tb2t10(mk_array1(elt7, A, t2tb12(A1))), Lo, $sum(1, Lo)))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.21/0.50 tff(42,plain,
% 0.21/0.50 (~![A: $int, A1: map_int_elt3, Lo: $int] : ((~($lesseq(0, A) & $lesseq(0, Lo) & (~$lesseq(A, Lo)))) | sorted_sub4(tb2t10(mk_array1(elt7, A, t2tb12(A1))), Lo, $sum(1, Lo)))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[41, 38])).
% 0.21/0.50 tff(43,plain,
% 0.21/0.50 (~![A: $int, A1: map_int_elt3, Lo: $int] : ((~($lesseq(0, A) & $lesseq(0, Lo) & (~$lesseq(A, Lo)))) | sorted_sub4(tb2t10(mk_array1(elt7, A, t2tb12(A1))), Lo, $sum(1, Lo)))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[42, 38])).
% 0.21/0.50 tff(44,plain,
% 0.21/0.50 (~![A: $int, A1: map_int_elt3, Lo: $int] : ((~($lesseq(0, A) & $lesseq(0, Lo) & (~$lesseq(A, Lo)))) | sorted_sub4(tb2t10(mk_array1(elt7, A, t2tb12(A1))), Lo, $sum(1, Lo)))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[43, 38])).
% 0.21/0.50 tff(45,plain,
% 0.21/0.50 (~![A: $int, A1: map_int_elt3, Lo: $int] : ((~($greatereq(A, 0) & $greatereq(Lo, 0) & (~$lesseq($sum(A, $product(-1, Lo)), 0)))) | sorted_sub4(tb2t10(mk_array1(elt7, A, t2tb12(A1))), Lo, $sum(1, Lo)))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[44, 37])).
% 0.21/0.50 tff(46,plain,
% 0.21/0.50 (~![A: $int, A1: map_int_elt3, Lo: $int] : ((~($greatereq(A, 0) & $greatereq(Lo, 0) & (~$lesseq($sum(A, $product(-1, Lo)), 0)))) | sorted_sub4(tb2t10(mk_array1(elt7, A, t2tb12(A1))), Lo, $sum(1, Lo)))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[45, 36])).
% 0.21/0.50 tff(47,plain,
% 0.21/0.50 (~![A: $int, A1: map_int_elt3, Lo: $int] : ((~($greatereq(A, 0) & $greatereq(Lo, 0) & (~$lesseq($sum(A, $product(-1, Lo)), 0)))) | sorted_sub4(tb2t10(mk_array1(elt7, A, t2tb12(A1))), Lo, $sum(1, Lo)))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[46, 36])).
% 0.21/0.50 tff(48,plain,(
% 0.21/0.50 ~((~($greatereq(A!13, 0) & $greatereq(Lo!11, 0) & (~$lesseq($sum(A!13, $product(-1, Lo!11)), 0)))) | sorted_sub4(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12))), Lo!11, $sum(1, Lo!11)))),
% 0.21/0.50 inference(skolemize,[status(sab)],[47])).
% 0.21/0.50 tff(49,plain,
% 0.21/0.50 (~((~($greatereq(A!13, 0) & $greatereq(Lo!11, 0) & (~$greatereq($sum(Lo!11, $product(-1, A!13)), 0)))) | sorted_sub4(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12))), Lo!11, $sum(1, Lo!11)))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[48, 35])).
% 0.21/0.50 tff(50,plain,
% 0.21/0.50 (~sorted_sub4(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12))), Lo!11, $sum(1, Lo!11))),
% 0.21/0.50 inference(or_elim,[status(thm)],[49])).
% 0.21/0.50 tff(51,plain,
% 0.21/0.50 ((~(sorted_sub4(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12))), Lo!11, $sum(1, Lo!11)) | (~(le4(tb2t11(get2(elt7, t2tb10(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), tptp_fun_I1_1($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))), tb2t11(get2(elt7, t2tb10(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), tptp_fun_I2_0($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12))))))) | (~$lesseq($sum(Lo!11, $product(-1, tptp_fun_I1_1($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))), 0)) | (~$greatereq($sum(tptp_fun_I2_0($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), $product(-1, tptp_fun_I1_1($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))), 0)) | $lesseq($sum(Lo!11, $product(-1, tptp_fun_I2_0($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))), -1))))) | sorted_sub4(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12))), Lo!11, $sum(1, Lo!11)) | (~(le4(tb2t11(get2(elt7, t2tb10(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), tptp_fun_I1_1($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))), tb2t11(get2(elt7, t2tb10(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), tptp_fun_I2_0($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12))))))) | (~$lesseq($sum(Lo!11, $product(-1, tptp_fun_I1_1($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))), 0)) | (~$greatereq($sum(tptp_fun_I2_0($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), $product(-1, tptp_fun_I1_1($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))), 0)) | $lesseq($sum(Lo!11, $product(-1, tptp_fun_I2_0($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))), -1)))),
% 0.21/0.50 inference(tautology,[status(thm)],[])).
% 0.21/0.50 tff(52,plain,
% 0.21/0.50 ((~(sorted_sub4(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12))), Lo!11, $sum(1, Lo!11)) | (~(le4(tb2t11(get2(elt7, t2tb10(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), tptp_fun_I1_1($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))), tb2t11(get2(elt7, t2tb10(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), tptp_fun_I2_0($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12))))))) | (~$lesseq($sum(Lo!11, $product(-1, tptp_fun_I1_1($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))), 0)) | (~$greatereq($sum(tptp_fun_I2_0($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), $product(-1, tptp_fun_I1_1($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))), 0)) | $lesseq($sum(Lo!11, $product(-1, tptp_fun_I2_0($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))), -1))))) | (~(le4(tb2t11(get2(elt7, t2tb10(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), tptp_fun_I1_1($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))), tb2t11(get2(elt7, t2tb10(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), tptp_fun_I2_0($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12))))))) | (~$lesseq($sum(Lo!11, $product(-1, tptp_fun_I1_1($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))), 0)) | (~$greatereq($sum(tptp_fun_I2_0($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), $product(-1, tptp_fun_I1_1($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))), 0)) | $lesseq($sum(Lo!11, $product(-1, tptp_fun_I2_0($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))), -1)))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[51, 50])).
% 0.21/0.50 tff(53,plain,
% 0.21/0.50 (~(le4(tb2t11(get2(elt7, t2tb10(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), tptp_fun_I1_1($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))), tb2t11(get2(elt7, t2tb10(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), tptp_fun_I2_0($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12))))))) | (~$lesseq($sum(Lo!11, $product(-1, tptp_fun_I1_1($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))), 0)) | (~$greatereq($sum(tptp_fun_I2_0($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), $product(-1, tptp_fun_I1_1($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))), 0)) | $lesseq($sum(Lo!11, $product(-1, tptp_fun_I2_0($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))), -1))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[52, 34])).
% 0.21/0.50 tff(54,plain,
% 0.21/0.50 ((le4(tb2t11(get2(elt7, t2tb10(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), tptp_fun_I1_1($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))), tb2t11(get2(elt7, t2tb10(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), tptp_fun_I2_0($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12))))))) | (~$lesseq($sum(Lo!11, $product(-1, tptp_fun_I1_1($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))), 0)) | (~$greatereq($sum(tptp_fun_I2_0($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), $product(-1, tptp_fun_I1_1($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))), 0)) | $lesseq($sum(Lo!11, $product(-1, tptp_fun_I2_0($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))), -1)) | $lesseq($sum(Lo!11, $product(-1, tptp_fun_I1_1($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))), 0)),
% 0.21/0.50 inference(tautology,[status(thm)],[])).
% 0.21/0.50 tff(55,plain,
% 0.21/0.50 ($lesseq($sum(Lo!11, $product(-1, tptp_fun_I1_1($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))), 0)),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[54, 53])).
% 0.21/0.50 tff(56,assumption,(~$lesseq($sum(Lo!11, $product(-1, tptp_fun_I2_0($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))), 0)), introduced(assumption)).
% 0.21/0.50 tff(57,plain,
% 0.21/0.50 ((le4(tb2t11(get2(elt7, t2tb10(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), tptp_fun_I1_1($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))), tb2t11(get2(elt7, t2tb10(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), tptp_fun_I2_0($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12))))))) | (~$lesseq($sum(Lo!11, $product(-1, tptp_fun_I1_1($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))), 0)) | (~$greatereq($sum(tptp_fun_I2_0($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), $product(-1, tptp_fun_I1_1($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))), 0)) | $lesseq($sum(Lo!11, $product(-1, tptp_fun_I2_0($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))), -1)) | $greatereq($sum(tptp_fun_I2_0($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), $product(-1, tptp_fun_I1_1($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))), 0)),
% 0.21/0.50 inference(tautology,[status(thm)],[])).
% 0.21/0.50 tff(58,plain,
% 0.21/0.50 ($greatereq($sum(tptp_fun_I2_0($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), $product(-1, tptp_fun_I1_1($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))), 0)),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[57, 53])).
% 0.21/0.50 tff(59,plain,
% 0.21/0.50 ($false),
% 0.21/0.50 inference(theory_lemma,[status(thm)],[58, 56, 55])).
% 0.21/0.50 tff(60,plain,($lesseq($sum(Lo!11, $product(-1, tptp_fun_I2_0($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))), 0)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.50 tff(61,plain,
% 0.21/0.50 ((le4(tb2t11(get2(elt7, t2tb10(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), tptp_fun_I1_1($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))), tb2t11(get2(elt7, t2tb10(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), tptp_fun_I2_0($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12))))))) | (~$lesseq($sum(Lo!11, $product(-1, tptp_fun_I1_1($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))), 0)) | (~$greatereq($sum(tptp_fun_I2_0($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), $product(-1, tptp_fun_I1_1($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))), 0)) | $lesseq($sum(Lo!11, $product(-1, tptp_fun_I2_0($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))), -1)) | (~$lesseq($sum(Lo!11, $product(-1, tptp_fun_I2_0($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))), -1))),
% 0.21/0.50 inference(tautology,[status(thm)],[])).
% 0.21/0.50 tff(62,plain,
% 0.21/0.50 (~$lesseq($sum(Lo!11, $product(-1, tptp_fun_I2_0($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))), -1)),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[61, 53])).
% 0.21/0.50 tff(63,plain,
% 0.21/0.50 ($greatereq($sum(Lo!11, $product(-1, tptp_fun_I2_0($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))), 0) | $lesseq($sum(Lo!11, $product(-1, tptp_fun_I2_0($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))), -1)),
% 0.21/0.50 inference(theory_lemma,[status(thm)],[])).
% 0.21/0.50 tff(64,plain,
% 0.21/0.50 ($greatereq($sum(Lo!11, $product(-1, tptp_fun_I2_0($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))), 0)),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[63, 62])).
% 0.21/0.50 tff(65,plain,
% 0.21/0.50 ((Lo!11 = tptp_fun_I2_0($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12))))) | (~$lesseq($sum(Lo!11, $product(-1, tptp_fun_I2_0($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))), 0)) | (~$greatereq($sum(Lo!11, $product(-1, tptp_fun_I2_0($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))), 0))),
% 0.21/0.50 inference(theory_lemma,[status(thm)],[])).
% 0.21/0.50 tff(66,plain,
% 0.21/0.50 ((Lo!11 = tptp_fun_I2_0($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12))))) | (~$lesseq($sum(Lo!11, $product(-1, tptp_fun_I2_0($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))), 0))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[65, 64])).
% 0.21/0.50 tff(67,plain,
% 0.21/0.50 (Lo!11 = tptp_fun_I2_0($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12))))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[66, 60])).
% 0.21/0.50 tff(68,assumption,(Lo!11 = tptp_fun_I1_1($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12))))), introduced(assumption)).
% 0.21/0.50 tff(69,assumption,(Lo!11 = tptp_fun_I2_0($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12))))), introduced(assumption)).
% 0.21/0.50 tff(70,plain,
% 0.21/0.50 (tptp_fun_I2_0($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))) = Lo!11),
% 0.21/0.50 inference(symmetry,[status(thm)],[69])).
% 0.21/0.50 tff(71,plain,
% 0.21/0.50 (tptp_fun_I2_0($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))) = tptp_fun_I1_1($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12))))),
% 0.21/0.50 inference(transitivity,[status(thm)],[70, 68])).
% 0.21/0.50 tff(72,plain,
% 0.21/0.50 (get2(elt7, t2tb10(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), tptp_fun_I2_0($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12))))) = get2(elt7, t2tb10(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), tptp_fun_I1_1($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))),
% 0.21/0.50 inference(monotonicity,[status(thm)],[71])).
% 0.21/0.50 tff(73,plain,
% 0.21/0.50 (tb2t11(get2(elt7, t2tb10(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), tptp_fun_I2_0($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))) = tb2t11(get2(elt7, t2tb10(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), tptp_fun_I1_1($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12))))))),
% 0.21/0.50 inference(monotonicity,[status(thm)],[72])).
% 0.21/0.50 tff(74,plain,
% 0.21/0.50 (tb2t11(get2(elt7, t2tb10(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), tptp_fun_I1_1($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))) = tb2t11(get2(elt7, t2tb10(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), tptp_fun_I2_0($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12))))))),
% 0.21/0.50 inference(symmetry,[status(thm)],[73])).
% 0.21/0.50 tff(75,plain,
% 0.21/0.50 (le4(tb2t11(get2(elt7, t2tb10(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), tptp_fun_I2_0($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))), tb2t11(get2(elt7, t2tb10(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), tptp_fun_I1_1($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12))))))) <=> le4(tb2t11(get2(elt7, t2tb10(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), tptp_fun_I1_1($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))), tb2t11(get2(elt7, t2tb10(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), tptp_fun_I2_0($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))))),
% 0.21/0.50 inference(monotonicity,[status(thm)],[73, 74])).
% 0.21/0.50 tff(76,plain,
% 0.21/0.50 (le4(tb2t11(get2(elt7, t2tb10(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), tptp_fun_I1_1($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))), tb2t11(get2(elt7, t2tb10(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), tptp_fun_I2_0($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12))))))) <=> le4(tb2t11(get2(elt7, t2tb10(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), tptp_fun_I2_0($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))), tb2t11(get2(elt7, t2tb10(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), tptp_fun_I1_1($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))))),
% 0.21/0.50 inference(symmetry,[status(thm)],[75])).
% 0.21/0.50 tff(77,plain,
% 0.21/0.50 ((~le4(tb2t11(get2(elt7, t2tb10(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), tptp_fun_I1_1($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))), tb2t11(get2(elt7, t2tb10(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), tptp_fun_I2_0($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))))) <=> (~le4(tb2t11(get2(elt7, t2tb10(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), tptp_fun_I2_0($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))), tb2t11(get2(elt7, t2tb10(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), tptp_fun_I1_1($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12))))))))),
% 0.21/0.50 inference(monotonicity,[status(thm)],[76])).
% 0.21/0.50 tff(78,plain,
% 0.21/0.50 ((le4(tb2t11(get2(elt7, t2tb10(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), tptp_fun_I1_1($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))), tb2t11(get2(elt7, t2tb10(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), tptp_fun_I2_0($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12))))))) | (~$lesseq($sum(Lo!11, $product(-1, tptp_fun_I1_1($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))), 0)) | (~$greatereq($sum(tptp_fun_I2_0($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), $product(-1, tptp_fun_I1_1($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))), 0)) | $lesseq($sum(Lo!11, $product(-1, tptp_fun_I2_0($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))), -1)) | (~le4(tb2t11(get2(elt7, t2tb10(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), tptp_fun_I1_1($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))), tb2t11(get2(elt7, t2tb10(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), tptp_fun_I2_0($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12))))))))),
% 0.21/0.50 inference(tautology,[status(thm)],[])).
% 0.21/0.50 tff(79,plain,
% 0.21/0.50 (~le4(tb2t11(get2(elt7, t2tb10(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), tptp_fun_I1_1($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))), tb2t11(get2(elt7, t2tb10(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), tptp_fun_I2_0($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[78, 53])).
% 0.21/0.50 tff(80,plain,
% 0.21/0.50 (~le4(tb2t11(get2(elt7, t2tb10(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), tptp_fun_I2_0($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))), tb2t11(get2(elt7, t2tb10(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), tptp_fun_I1_1($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[79, 77])).
% 0.21/0.50 tff(81,plain,
% 0.21/0.50 (^[X: elt6, Y: elt6] : refl((le4(Y, X) | le4(X, Y)) <=> (le4(Y, X) | le4(X, Y)))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(82,plain,
% 0.21/0.50 (![X: elt6, Y: elt6] : (le4(Y, X) | le4(X, Y)) <=> ![X: elt6, Y: elt6] : (le4(Y, X) | le4(X, Y))),
% 0.21/0.50 inference(quant_intro,[status(thm)],[81])).
% 0.21/0.50 tff(83,plain,
% 0.21/0.50 (![X: elt6, Y: elt6] : (le4(Y, X) | le4(X, Y)) <=> ![X: elt6, Y: elt6] : (le4(Y, X) | le4(X, Y))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(84,plain,
% 0.21/0.50 (^[X: elt6, Y: elt6] : rewrite((le4(X, Y) | le4(Y, X)) <=> (le4(Y, X) | le4(X, Y)))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(85,plain,
% 0.21/0.50 (![X: elt6, Y: elt6] : (le4(X, Y) | le4(Y, X)) <=> ![X: elt6, Y: elt6] : (le4(Y, X) | le4(X, Y))),
% 0.21/0.50 inference(quant_intro,[status(thm)],[84])).
% 0.21/0.50 tff(86,axiom,(![X: elt6, Y: elt6] : (le4(X, Y) | le4(Y, X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','total4')).
% 0.21/0.50 tff(87,plain,
% 0.21/0.50 (![X: elt6, Y: elt6] : (le4(Y, X) | le4(X, Y))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.21/0.50 tff(88,plain,
% 0.21/0.50 (![X: elt6, Y: elt6] : (le4(Y, X) | le4(X, Y))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[87, 83])).
% 0.21/0.50 tff(89,plain,(
% 0.21/0.50 ![X: elt6, Y: elt6] : (le4(Y, X) | le4(X, Y))),
% 0.21/0.50 inference(skolemize,[status(sab)],[88])).
% 0.21/0.50 tff(90,plain,
% 0.21/0.50 (![X: elt6, Y: elt6] : (le4(Y, X) | le4(X, Y))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[89, 82])).
% 0.21/0.50 tff(91,plain,
% 0.21/0.50 (((~![X: elt6, Y: elt6] : (le4(Y, X) | le4(X, Y))) | (le4(tb2t11(get2(elt7, t2tb10(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), tptp_fun_I1_1($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))), tb2t11(get2(elt7, t2tb10(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), tptp_fun_I2_0($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12))))))) | le4(tb2t11(get2(elt7, t2tb10(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), tptp_fun_I2_0($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))), tb2t11(get2(elt7, t2tb10(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), tptp_fun_I1_1($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12))))))))) <=> ((~![X: elt6, Y: elt6] : (le4(Y, X) | le4(X, Y))) | le4(tb2t11(get2(elt7, t2tb10(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), tptp_fun_I1_1($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))), tb2t11(get2(elt7, t2tb10(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), tptp_fun_I2_0($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12))))))) | le4(tb2t11(get2(elt7, t2tb10(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), tptp_fun_I2_0($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))), tb2t11(get2(elt7, t2tb10(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), tptp_fun_I1_1($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12))))))))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(92,plain,
% 0.21/0.51 ((le4(tb2t11(get2(elt7, t2tb10(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), tptp_fun_I2_0($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))), tb2t11(get2(elt7, t2tb10(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), tptp_fun_I1_1($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12))))))) | le4(tb2t11(get2(elt7, t2tb10(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), tptp_fun_I1_1($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))), tb2t11(get2(elt7, t2tb10(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), tptp_fun_I2_0($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))))) <=> (le4(tb2t11(get2(elt7, t2tb10(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), tptp_fun_I1_1($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))), tb2t11(get2(elt7, t2tb10(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), tptp_fun_I2_0($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12))))))) | le4(tb2t11(get2(elt7, t2tb10(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), tptp_fun_I2_0($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))), tb2t11(get2(elt7, t2tb10(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), tptp_fun_I1_1($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12))))))))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(93,plain,
% 0.21/0.51 (((~![X: elt6, Y: elt6] : (le4(Y, X) | le4(X, Y))) | (le4(tb2t11(get2(elt7, t2tb10(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), tptp_fun_I2_0($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))), tb2t11(get2(elt7, t2tb10(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), tptp_fun_I1_1($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12))))))) | le4(tb2t11(get2(elt7, t2tb10(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), tptp_fun_I1_1($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))), tb2t11(get2(elt7, t2tb10(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), tptp_fun_I2_0($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12))))))))) <=> ((~![X: elt6, Y: elt6] : (le4(Y, X) | le4(X, Y))) | (le4(tb2t11(get2(elt7, t2tb10(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), tptp_fun_I1_1($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))), tb2t11(get2(elt7, t2tb10(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), tptp_fun_I2_0($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12))))))) | le4(tb2t11(get2(elt7, t2tb10(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), tptp_fun_I2_0($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))), tb2t11(get2(elt7, t2tb10(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), tptp_fun_I1_1($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))))))),
% 0.21/0.51 inference(monotonicity,[status(thm)],[92])).
% 0.21/0.51 tff(94,plain,
% 0.21/0.51 (((~![X: elt6, Y: elt6] : (le4(Y, X) | le4(X, Y))) | (le4(tb2t11(get2(elt7, t2tb10(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), tptp_fun_I2_0($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))), tb2t11(get2(elt7, t2tb10(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), tptp_fun_I1_1($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12))))))) | le4(tb2t11(get2(elt7, t2tb10(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), tptp_fun_I1_1($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))), tb2t11(get2(elt7, t2tb10(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), tptp_fun_I2_0($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12))))))))) <=> ((~![X: elt6, Y: elt6] : (le4(Y, X) | le4(X, Y))) | le4(tb2t11(get2(elt7, t2tb10(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), tptp_fun_I1_1($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))), tb2t11(get2(elt7, t2tb10(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), tptp_fun_I2_0($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12))))))) | le4(tb2t11(get2(elt7, t2tb10(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), tptp_fun_I2_0($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))), tb2t11(get2(elt7, t2tb10(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), tptp_fun_I1_1($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12))))))))),
% 0.21/0.51 inference(transitivity,[status(thm)],[93, 91])).
% 0.21/0.51 tff(95,plain,
% 0.21/0.51 ((~![X: elt6, Y: elt6] : (le4(Y, X) | le4(X, Y))) | (le4(tb2t11(get2(elt7, t2tb10(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), tptp_fun_I2_0($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))), tb2t11(get2(elt7, t2tb10(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), tptp_fun_I1_1($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12))))))) | le4(tb2t11(get2(elt7, t2tb10(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), tptp_fun_I1_1($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))), tb2t11(get2(elt7, t2tb10(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), tptp_fun_I2_0($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12))))))))),
% 0.21/0.51 inference(quant_inst,[status(thm)],[])).
% 0.21/0.51 tff(96,plain,
% 0.21/0.51 ((~![X: elt6, Y: elt6] : (le4(Y, X) | le4(X, Y))) | le4(tb2t11(get2(elt7, t2tb10(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), tptp_fun_I1_1($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))), tb2t11(get2(elt7, t2tb10(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), tptp_fun_I2_0($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12))))))) | le4(tb2t11(get2(elt7, t2tb10(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), tptp_fun_I2_0($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))), tb2t11(get2(elt7, t2tb10(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), tptp_fun_I1_1($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.21/0.51 tff(97,plain,
% 0.21/0.51 (le4(tb2t11(get2(elt7, t2tb10(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), tptp_fun_I2_0($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))), tb2t11(get2(elt7, t2tb10(tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))), tptp_fun_I1_1($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[96, 90, 79])).
% 0.21/0.51 tff(98,plain,
% 0.21/0.51 ($false),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[97, 80])).
% 0.21/0.51 tff(99,plain,((~(Lo!11 = tptp_fun_I2_0($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))) | (~(Lo!11 = tptp_fun_I1_1($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12))))))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.51 tff(100,plain,
% 0.21/0.51 (~(Lo!11 = tptp_fun_I1_1($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[99, 67])).
% 0.21/0.51 tff(101,plain,
% 0.21/0.51 ((Lo!11 = tptp_fun_I1_1($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12))))) | (~$lesseq($sum(Lo!11, $product(-1, tptp_fun_I1_1($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))), 0)) | (~$greatereq($sum(Lo!11, $product(-1, tptp_fun_I1_1($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))), 0))),
% 0.21/0.51 inference(theory_lemma,[status(thm)],[])).
% 0.21/0.51 tff(102,plain,
% 0.21/0.51 ((Lo!11 = tptp_fun_I1_1($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12))))) | (~$greatereq($sum(Lo!11, $product(-1, tptp_fun_I1_1($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))), 0))),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[101, 55])).
% 0.21/0.52 tff(103,plain,
% 0.21/0.52 (~$greatereq($sum(Lo!11, $product(-1, tptp_fun_I1_1($sum(1, Lo!11), Lo!11, tb2t10(mk_array1(elt7, A!13, t2tb12(A1!12)))))), 0)),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[102, 100])).
% 0.21/0.52 tff(104,plain,
% 0.21/0.52 ($false),
% 0.21/0.52 inference(theory_lemma,[status(thm)],[58, 62, 103])).
% 0.21/0.52 % SZS output end Proof
%------------------------------------------------------------------------------