TSTP Solution File: DAT332_1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : DAT332_1 : TPTP v8.1.0. Released v7.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n024.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 14:37:21 EDT 2022
% Result : Unsatisfiable 0.20s 0.41s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : DAT332_1 : TPTP v8.1.0. Released v7.0.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.35 % Computer : n024.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Wed Aug 31 02:25:04 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.35 Usage: tptp [options] [-file:]file
% 0.14/0.35 -h, -? prints this message.
% 0.14/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.35 -m, -model generate model.
% 0.14/0.35 -p, -proof generate proof.
% 0.14/0.35 -c, -core generate unsat core of named formulas.
% 0.14/0.35 -st, -statistics display statistics.
% 0.14/0.35 -t:timeout set timeout (in second).
% 0.14/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.35 -<param>:<value> configuration parameter and value.
% 0.14/0.35 -o:<output-file> file to place output in.
% 0.20/0.41 % SZS status Unsatisfiable
% 0.20/0.41 % SZS output start Proof
% 0.20/0.41 tff(member_type, type, (
% 0.20/0.41 member: ( $int * 'Set' ) > $o)).
% 0.20/0.41 tff(insert_type, type, (
% 0.20/0.41 insert: ( 'Set' * $int ) > 'Set')).
% 0.20/0.41 tff(tptp_fun__select__Array_Int_Int__Int__Int__type, type, (
% 0.20/0.41 tptp_fun__select__Array_Int_Int__Int__Int_: ( 'Array[Int,Int]' * $int ) > $int)).
% 0.20/0.41 tff(g_type, type, (
% 0.20/0.41 g: $int > $int)).
% 0.20/0.41 tff(i1_type, type, (
% 0.20/0.41 i1: $int)).
% 0.20/0.41 tff(arr_type, type, (
% 0.20/0.41 arr: 'Array[Int,Int]')).
% 0.20/0.41 tff(s0_type, type, (
% 0.20/0.41 s0: 'Set')).
% 0.20/0.41 tff(sup_type, type, (
% 0.20/0.41 sup: 'Set' > $int)).
% 0.20/0.41 tff(s1_type, type, (
% 0.20/0.41 s1: 'Set')).
% 0.20/0.41 tff(1,plain,
% 0.20/0.41 (^[A__questionmark_i: $int] : refl((~$lesseq(g(A__questionmark_i), 0)) <=> (~$lesseq(g(A__questionmark_i), 0)))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(2,plain,
% 0.20/0.41 (![A__questionmark_i: $int] : (~$lesseq(g(A__questionmark_i), 0)) <=> ![A__questionmark_i: $int] : (~$lesseq(g(A__questionmark_i), 0))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[1])).
% 0.20/0.41 tff(3,plain,
% 0.20/0.41 (![A__questionmark_i: $int] : (~$lesseq(g(A__questionmark_i), 0)) <=> ![A__questionmark_i: $int] : (~$lesseq(g(A__questionmark_i), 0))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(4,plain,
% 0.20/0.41 (^[A__questionmark_i: $int] : rewrite($greater(g(A__questionmark_i), 0) <=> (~$lesseq(g(A__questionmark_i), 0)))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(5,plain,
% 0.20/0.41 (![A__questionmark_i: $int] : $greater(g(A__questionmark_i), 0) <=> ![A__questionmark_i: $int] : (~$lesseq(g(A__questionmark_i), 0))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[4])).
% 0.20/0.41 tff(6,axiom,(![A__questionmark_i: $int] : $greater(g(A__questionmark_i), 0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','formula_10')).
% 0.20/0.41 tff(7,plain,
% 0.20/0.41 (![A__questionmark_i: $int] : (~$lesseq(g(A__questionmark_i), 0))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.20/0.41 tff(8,plain,
% 0.20/0.41 (![A__questionmark_i: $int] : (~$lesseq(g(A__questionmark_i), 0))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.20/0.41 tff(9,plain,(
% 0.20/0.41 ![A__questionmark_i: $int] : (~$lesseq(g(A__questionmark_i), 0))),
% 0.20/0.41 inference(skolemize,[status(sab)],[8])).
% 0.20/0.41 tff(10,plain,
% 0.20/0.41 (![A__questionmark_i: $int] : (~$lesseq(g(A__questionmark_i), 0))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.20/0.41 tff(11,plain,
% 0.20/0.41 ((~![A__questionmark_i: $int] : (~$lesseq(g(A__questionmark_i), 0))) | (~$lesseq(g(i1), 0))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(12,plain,
% 0.20/0.41 (~$lesseq(g(i1), 0)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[11, 10])).
% 0.20/0.41 tff(13,plain,
% 0.20/0.41 (^[A__questionmark_i: $int] : refl(($lesseq(A__questionmark_i, 0) | (~$lesseq($sum(sup(s0), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, A__questionmark_i))), 0))) <=> ($lesseq(A__questionmark_i, 0) | (~$lesseq($sum(sup(s0), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, A__questionmark_i))), 0))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(14,plain,
% 0.20/0.41 (![A__questionmark_i: $int] : ($lesseq(A__questionmark_i, 0) | (~$lesseq($sum(sup(s0), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, A__questionmark_i))), 0))) <=> ![A__questionmark_i: $int] : ($lesseq(A__questionmark_i, 0) | (~$lesseq($sum(sup(s0), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, A__questionmark_i))), 0)))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[13])).
% 0.20/0.41 tff(15,plain,
% 0.20/0.41 (^[A__questionmark_i: $int] : trans(monotonicity(rewrite((~$lesseq(sup(s0), tptp_fun__select__Array_Int_Int__Int__Int_(arr, A__questionmark_i))) <=> (~$lesseq($sum(sup(s0), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, A__questionmark_i))), 0))), (($lesseq(A__questionmark_i, 0) | (~$lesseq(sup(s0), tptp_fun__select__Array_Int_Int__Int__Int_(arr, A__questionmark_i)))) <=> ($lesseq(A__questionmark_i, 0) | (~$lesseq($sum(sup(s0), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, A__questionmark_i))), 0))))), rewrite(($lesseq(A__questionmark_i, 0) | (~$lesseq($sum(sup(s0), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, A__questionmark_i))), 0))) <=> ($lesseq(A__questionmark_i, 0) | (~$lesseq($sum(sup(s0), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, A__questionmark_i))), 0)))), (($lesseq(A__questionmark_i, 0) | (~$lesseq(sup(s0), tptp_fun__select__Array_Int_Int__Int__Int_(arr, A__questionmark_i)))) <=> ($lesseq(A__questionmark_i, 0) | (~$lesseq($sum(sup(s0), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, A__questionmark_i))), 0)))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(16,plain,
% 0.20/0.42 (![A__questionmark_i: $int] : ($lesseq(A__questionmark_i, 0) | (~$lesseq(sup(s0), tptp_fun__select__Array_Int_Int__Int__Int_(arr, A__questionmark_i)))) <=> ![A__questionmark_i: $int] : ($lesseq(A__questionmark_i, 0) | (~$lesseq($sum(sup(s0), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, A__questionmark_i))), 0)))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[15])).
% 0.20/0.42 tff(17,plain,
% 0.20/0.42 (![A__questionmark_i: $int] : ($lesseq(A__questionmark_i, 0) | (~$lesseq(sup(s0), tptp_fun__select__Array_Int_Int__Int__Int_(arr, A__questionmark_i)))) <=> ![A__questionmark_i: $int] : ($lesseq(A__questionmark_i, 0) | (~$lesseq(sup(s0), tptp_fun__select__Array_Int_Int__Int__Int_(arr, A__questionmark_i))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(18,plain,
% 0.20/0.42 (^[A__questionmark_i: $int] : trans(monotonicity(rewrite($greater(A__questionmark_i, 0) <=> (~$lesseq(A__questionmark_i, 0))), rewrite($less(tptp_fun__select__Array_Int_Int__Int__Int_(arr, A__questionmark_i), sup(s0)) <=> (~$lesseq(sup(s0), tptp_fun__select__Array_Int_Int__Int__Int_(arr, A__questionmark_i)))), (($greater(A__questionmark_i, 0) => $less(tptp_fun__select__Array_Int_Int__Int__Int_(arr, A__questionmark_i), sup(s0))) <=> ((~$lesseq(A__questionmark_i, 0)) => (~$lesseq(sup(s0), tptp_fun__select__Array_Int_Int__Int__Int_(arr, A__questionmark_i)))))), rewrite(((~$lesseq(A__questionmark_i, 0)) => (~$lesseq(sup(s0), tptp_fun__select__Array_Int_Int__Int__Int_(arr, A__questionmark_i)))) <=> ($lesseq(A__questionmark_i, 0) | (~$lesseq(sup(s0), tptp_fun__select__Array_Int_Int__Int__Int_(arr, A__questionmark_i))))), (($greater(A__questionmark_i, 0) => $less(tptp_fun__select__Array_Int_Int__Int__Int_(arr, A__questionmark_i), sup(s0))) <=> ($lesseq(A__questionmark_i, 0) | (~$lesseq(sup(s0), tptp_fun__select__Array_Int_Int__Int__Int_(arr, A__questionmark_i))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(19,plain,
% 0.20/0.42 (![A__questionmark_i: $int] : ($greater(A__questionmark_i, 0) => $less(tptp_fun__select__Array_Int_Int__Int__Int_(arr, A__questionmark_i), sup(s0))) <=> ![A__questionmark_i: $int] : ($lesseq(A__questionmark_i, 0) | (~$lesseq(sup(s0), tptp_fun__select__Array_Int_Int__Int__Int_(arr, A__questionmark_i))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[18])).
% 0.20/0.42 tff(20,axiom,(![A__questionmark_i: $int] : ($greater(A__questionmark_i, 0) => $less(tptp_fun__select__Array_Int_Int__Int__Int_(arr, A__questionmark_i), sup(s0)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','formula_9')).
% 0.20/0.42 tff(21,plain,
% 0.20/0.42 (![A__questionmark_i: $int] : ($lesseq(A__questionmark_i, 0) | (~$lesseq(sup(s0), tptp_fun__select__Array_Int_Int__Int__Int_(arr, A__questionmark_i))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.20/0.42 tff(22,plain,
% 0.20/0.42 (![A__questionmark_i: $int] : ($lesseq(A__questionmark_i, 0) | (~$lesseq(sup(s0), tptp_fun__select__Array_Int_Int__Int__Int_(arr, A__questionmark_i))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[21, 17])).
% 0.20/0.42 tff(23,plain,
% 0.20/0.42 (![A__questionmark_i: $int] : ($lesseq(A__questionmark_i, 0) | (~$lesseq($sum(sup(s0), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, A__questionmark_i))), 0)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[22, 16])).
% 0.20/0.42 tff(24,plain,(
% 0.20/0.42 ![A__questionmark_i: $int] : ($lesseq(A__questionmark_i, 0) | (~$lesseq($sum(sup(s0), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, A__questionmark_i))), 0)))),
% 0.20/0.42 inference(skolemize,[status(sab)],[23])).
% 0.20/0.42 tff(25,plain,
% 0.20/0.42 (![A__questionmark_i: $int] : ($lesseq(A__questionmark_i, 0) | (~$lesseq($sum(sup(s0), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, A__questionmark_i))), 0)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[24, 14])).
% 0.20/0.42 tff(26,plain,
% 0.20/0.42 (((~![A__questionmark_i: $int] : ($lesseq(A__questionmark_i, 0) | (~$lesseq($sum(sup(s0), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, A__questionmark_i))), 0)))) | ($lesseq(g(i1), 0) | (~$lesseq($sum(sup(s0), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i1)))), 0)))) <=> ((~![A__questionmark_i: $int] : ($lesseq(A__questionmark_i, 0) | (~$lesseq($sum(sup(s0), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, A__questionmark_i))), 0)))) | $lesseq(g(i1), 0) | (~$lesseq($sum(sup(s0), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i1)))), 0)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(27,plain,
% 0.20/0.42 ((~![A__questionmark_i: $int] : ($lesseq(A__questionmark_i, 0) | (~$lesseq($sum(sup(s0), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, A__questionmark_i))), 0)))) | ($lesseq(g(i1), 0) | (~$lesseq($sum(sup(s0), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i1)))), 0)))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(28,plain,
% 0.20/0.42 ((~![A__questionmark_i: $int] : ($lesseq(A__questionmark_i, 0) | (~$lesseq($sum(sup(s0), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, A__questionmark_i))), 0)))) | $lesseq(g(i1), 0) | (~$lesseq($sum(sup(s0), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i1)))), 0))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.20/0.42 tff(29,plain,
% 0.20/0.42 ($lesseq(g(i1), 0) | (~$lesseq($sum(sup(s0), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i1)))), 0))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[28, 25])).
% 0.20/0.42 tff(30,plain,
% 0.20/0.42 (~$lesseq($sum(sup(s0), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i1)))), 0)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[29, 12])).
% 0.20/0.42 tff(31,plain,
% 0.20/0.42 ((~($sum(sup(s0), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i1)))) = 0)) | $lesseq($sum(sup(s0), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i1)))), 0)),
% 0.20/0.42 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.42 tff(32,plain,
% 0.20/0.42 (~($sum(sup(s0), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i1)))) = 0)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[31, 30])).
% 0.20/0.42 tff(33,plain,
% 0.20/0.42 (^[A__questionmark_x: $int, A__questionmark_y: $int, A__questionmark_s: 'Set'] : refl(((member(A__questionmark_x, insert(A__questionmark_s, A__questionmark_y)) <=> member(A__questionmark_x, A__questionmark_s)) | ($sum(A__questionmark_y, $product(-1, A__questionmark_x)) = 0)) <=> ((member(A__questionmark_x, insert(A__questionmark_s, A__questionmark_y)) <=> member(A__questionmark_x, A__questionmark_s)) | ($sum(A__questionmark_y, $product(-1, A__questionmark_x)) = 0)))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(34,plain,
% 0.20/0.42 (![A__questionmark_x: $int, A__questionmark_y: $int, A__questionmark_s: 'Set'] : ((member(A__questionmark_x, insert(A__questionmark_s, A__questionmark_y)) <=> member(A__questionmark_x, A__questionmark_s)) | ($sum(A__questionmark_y, $product(-1, A__questionmark_x)) = 0)) <=> ![A__questionmark_x: $int, A__questionmark_y: $int, A__questionmark_s: 'Set'] : ((member(A__questionmark_x, insert(A__questionmark_s, A__questionmark_y)) <=> member(A__questionmark_x, A__questionmark_s)) | ($sum(A__questionmark_y, $product(-1, A__questionmark_x)) = 0))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[33])).
% 0.20/0.42 tff(35,plain,
% 0.20/0.42 (^[A__questionmark_x: $int, A__questionmark_y: $int, A__questionmark_s: 'Set'] : rewrite(((member(A__questionmark_x, insert(A__questionmark_s, A__questionmark_y)) <=> member(A__questionmark_x, A__questionmark_s)) | ($sum(A__questionmark_x, $product(-1, A__questionmark_y)) = 0)) <=> ((member(A__questionmark_x, insert(A__questionmark_s, A__questionmark_y)) <=> member(A__questionmark_x, A__questionmark_s)) | ($sum(A__questionmark_y, $product(-1, A__questionmark_x)) = 0)))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(36,plain,
% 0.20/0.42 (![A__questionmark_x: $int, A__questionmark_y: $int, A__questionmark_s: 'Set'] : ((member(A__questionmark_x, insert(A__questionmark_s, A__questionmark_y)) <=> member(A__questionmark_x, A__questionmark_s)) | ($sum(A__questionmark_x, $product(-1, A__questionmark_y)) = 0)) <=> ![A__questionmark_x: $int, A__questionmark_y: $int, A__questionmark_s: 'Set'] : ((member(A__questionmark_x, insert(A__questionmark_s, A__questionmark_y)) <=> member(A__questionmark_x, A__questionmark_s)) | ($sum(A__questionmark_y, $product(-1, A__questionmark_x)) = 0))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[35])).
% 0.20/0.42 tff(37,plain,
% 0.20/0.42 (^[A__questionmark_x: $int, A__questionmark_y: $int, A__questionmark_s: 'Set'] : trans(monotonicity(rewrite((A__questionmark_x = A__questionmark_y) <=> ($sum(A__questionmark_x, $product(-1, A__questionmark_y)) = 0)), (((A__questionmark_x = A__questionmark_y) | (member(A__questionmark_x, insert(A__questionmark_s, A__questionmark_y)) <=> member(A__questionmark_x, A__questionmark_s))) <=> (($sum(A__questionmark_x, $product(-1, A__questionmark_y)) = 0) | (member(A__questionmark_x, insert(A__questionmark_s, A__questionmark_y)) <=> member(A__questionmark_x, A__questionmark_s))))), rewrite((($sum(A__questionmark_x, $product(-1, A__questionmark_y)) = 0) | (member(A__questionmark_x, insert(A__questionmark_s, A__questionmark_y)) <=> member(A__questionmark_x, A__questionmark_s))) <=> ((member(A__questionmark_x, insert(A__questionmark_s, A__questionmark_y)) <=> member(A__questionmark_x, A__questionmark_s)) | ($sum(A__questionmark_x, $product(-1, A__questionmark_y)) = 0))), (((A__questionmark_x = A__questionmark_y) | (member(A__questionmark_x, insert(A__questionmark_s, A__questionmark_y)) <=> member(A__questionmark_x, A__questionmark_s))) <=> ((member(A__questionmark_x, insert(A__questionmark_s, A__questionmark_y)) <=> member(A__questionmark_x, A__questionmark_s)) | ($sum(A__questionmark_x, $product(-1, A__questionmark_y)) = 0))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(38,plain,
% 0.20/0.42 (![A__questionmark_x: $int, A__questionmark_y: $int, A__questionmark_s: 'Set'] : ((A__questionmark_x = A__questionmark_y) | (member(A__questionmark_x, insert(A__questionmark_s, A__questionmark_y)) <=> member(A__questionmark_x, A__questionmark_s))) <=> ![A__questionmark_x: $int, A__questionmark_y: $int, A__questionmark_s: 'Set'] : ((member(A__questionmark_x, insert(A__questionmark_s, A__questionmark_y)) <=> member(A__questionmark_x, A__questionmark_s)) | ($sum(A__questionmark_x, $product(-1, A__questionmark_y)) = 0))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[37])).
% 0.20/0.42 tff(39,plain,
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% 0.20/0.43 inference(tautology,[status(thm)],[])).
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% 0.20/0.43 inference(unit_resolution,[status(thm)],[82, 81])).
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% 0.20/0.43 inference(modus_ponens,[status(thm)],[94, 88])).
% 0.20/0.43 tff(96,plain,(
% 0.20/0.43 ![A__questionmark_s: 'Set', A__questionmark_x: $int] : ((~member(A__questionmark_x, A__questionmark_s)) | $lesseq($sum(A__questionmark_x, $product(-1, sup(A__questionmark_s))), 0))),
% 0.20/0.43 inference(skolemize,[status(sab)],[95])).
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% 0.20/0.43 (((~member(sup(insert(s0, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i1)))), s0)) | $lesseq($sum(sup(insert(s0, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i1)))), $product(-1, sup(s0))), 0)) <=> ((~member(sup(insert(s0, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i1)))), s0)) | $greatereq($sum(sup(s0), $product(-1, sup(insert(s0, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i1)))))), 0))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(100,plain,
% 0.20/0.43 (((~![A__questionmark_s: 'Set', A__questionmark_x: $int] : ((~member(A__questionmark_x, A__questionmark_s)) | $lesseq($sum(A__questionmark_x, $product(-1, sup(A__questionmark_s))), 0))) | ((~member(sup(insert(s0, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i1)))), s0)) | $lesseq($sum(sup(insert(s0, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i1)))), $product(-1, sup(s0))), 0))) <=> ((~![A__questionmark_s: 'Set', A__questionmark_x: $int] : ((~member(A__questionmark_x, A__questionmark_s)) | $lesseq($sum(A__questionmark_x, $product(-1, sup(A__questionmark_s))), 0))) | ((~member(sup(insert(s0, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i1)))), s0)) | $greatereq($sum(sup(s0), $product(-1, sup(insert(s0, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i1)))))), 0)))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[99])).
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% 0.20/0.43 inference(modus_ponens,[status(thm)],[102, 101])).
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% 0.20/0.43 ($false),
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% 0.20/0.43 ((~(sup(s1) = sup(s0))) <=> (~(sup(s1) = sup(s0)))),
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% 0.20/0.43 (~(sup(insert(s0, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i1)))) = sup(s0))),
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% 0.20/0.43 (~($sum(sup(s0), $product(-1, sup(insert(s0, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i1)))))) = 0)),
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% 0.20/0.43 ((~![A__questionmark_s: 'Set', A__questionmark_x: $int] : ((~member(A__questionmark_x, A__questionmark_s)) | $lesseq($sum(A__questionmark_x, $product(-1, sup(A__questionmark_s))), 0))) | ((~member(sup(s0), insert(s0, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i1))))) | $lesseq($sum(sup(s0), $product(-1, sup(insert(s0, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i1)))))), 0))),
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% 0.20/0.43 ((~![A__questionmark_s: 'Set', A__questionmark_x: $int] : ((~member(A__questionmark_x, A__questionmark_s)) | $lesseq($sum(A__questionmark_x, $product(-1, sup(A__questionmark_s))), 0))) | (~member(sup(s0), insert(s0, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i1))))) | $lesseq($sum(sup(s0), $product(-1, sup(insert(s0, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i1)))))), 0)),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[119, 118])).
% 0.20/0.43 tff(121,plain,
% 0.20/0.43 ($false),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[120, 97, 117, 67])).
% 0.20/0.43 % SZS output end Proof
%------------------------------------------------------------------------------