TSTP Solution File: DAT330_1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : DAT330_1 : TPTP v8.1.0. Released v7.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 16 14:37:20 EDT 2022
% Result : Unsatisfiable 1.21s 1.00s
% Output : Proof 1.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : DAT330_1 : TPTP v8.1.0. Released v7.0.0.
% 0.06/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n002.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.34 % DateTime : Wed Aug 31 02:33:44 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 1.21/1.00 % SZS status Unsatisfiable
% 1.21/1.00 % SZS output start Proof
% 1.21/1.00 tff(member_type, type, (
% 1.21/1.00 member: ( $int * 'Set' ) > $o)).
% 1.21/1.00 tff(s0_type, type, (
% 1.21/1.00 s0: 'Set')).
% 1.21/1.00 tff(sup_type, type, (
% 1.21/1.00 sup: 'Set' > $int)).
% 1.21/1.00 tff(insert_type, type, (
% 1.21/1.00 insert: ( 'Set' * $int ) > 'Set')).
% 1.21/1.00 tff(tptp_fun__select__Array_Int_Int__Int__Int__type, type, (
% 1.21/1.00 tptp_fun__select__Array_Int_Int__Int__Int_: ( 'Array[Int,Int]' * $int ) > $int)).
% 1.21/1.00 tff(i1_type, type, (
% 1.21/1.00 i1: $int)).
% 1.21/1.00 tff(arr_type, type, (
% 1.21/1.00 arr: 'Array[Int,Int]')).
% 1.21/1.00 tff(s1_type, type, (
% 1.21/1.00 s1: 'Set')).
% 1.21/1.00 tff(g_type, type, (
% 1.21/1.00 g: $int > $int)).
% 1.21/1.00 tff(i3_type, type, (
% 1.21/1.00 i3: $int)).
% 1.21/1.00 tff(i2_type, type, (
% 1.21/1.00 i2: $int)).
% 1.21/1.00 tff(s3_type, type, (
% 1.21/1.00 s3: 'Set')).
% 1.21/1.00 tff(1,assumption,(s1 = s0), introduced(assumption)).
% 1.21/1.00 tff(2,plain,
% 1.21/1.00 (insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))) = insert(s0, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2)))),
% 1.21/1.00 inference(monotonicity,[status(thm)],[1])).
% 1.21/1.00 tff(3,plain,
% 1.21/1.00 (insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3))) = insert(insert(s0, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))),
% 1.21/1.00 inference(monotonicity,[status(thm)],[2])).
% 1.21/1.00 tff(4,plain,
% 1.21/1.00 (sup(insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))) = sup(insert(insert(s0, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3))))),
% 1.21/1.00 inference(monotonicity,[status(thm)],[3])).
% 1.21/1.00 tff(5,assumption,(~(member(sup(s0), insert(insert(s0, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))) <=> member(sup(s0), insert(s0, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2)))))), introduced(assumption)).
% 1.21/1.00 tff(6,plain,
% 1.21/1.00 (^[A__questionmark_i: $int] : refl((~$lesseq(g(A__questionmark_i), 0)) <=> (~$lesseq(g(A__questionmark_i), 0)))),
% 1.21/1.00 inference(bind,[status(th)],[])).
% 1.21/1.00 tff(7,plain,
% 1.21/1.00 (![A__questionmark_i: $int] : (~$lesseq(g(A__questionmark_i), 0)) <=> ![A__questionmark_i: $int] : (~$lesseq(g(A__questionmark_i), 0))),
% 1.21/1.00 inference(quant_intro,[status(thm)],[6])).
% 1.21/1.00 tff(8,plain,
% 1.21/1.00 (![A__questionmark_i: $int] : (~$lesseq(g(A__questionmark_i), 0)) <=> ![A__questionmark_i: $int] : (~$lesseq(g(A__questionmark_i), 0))),
% 1.21/1.00 inference(rewrite,[status(thm)],[])).
% 1.21/1.00 tff(9,plain,
% 1.21/1.00 (^[A__questionmark_i: $int] : rewrite($greater(g(A__questionmark_i), 0) <=> (~$lesseq(g(A__questionmark_i), 0)))),
% 1.21/1.00 inference(bind,[status(th)],[])).
% 1.21/1.00 tff(10,plain,
% 1.21/1.00 (![A__questionmark_i: $int] : $greater(g(A__questionmark_i), 0) <=> ![A__questionmark_i: $int] : (~$lesseq(g(A__questionmark_i), 0))),
% 1.21/1.00 inference(quant_intro,[status(thm)],[9])).
% 1.21/1.00 tff(11,axiom,(![A__questionmark_i: $int] : $greater(g(A__questionmark_i), 0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','formula_10')).
% 1.21/1.00 tff(12,plain,
% 1.21/1.00 (![A__questionmark_i: $int] : (~$lesseq(g(A__questionmark_i), 0))),
% 1.21/1.00 inference(modus_ponens,[status(thm)],[11, 10])).
% 1.21/1.00 tff(13,plain,
% 1.21/1.00 (![A__questionmark_i: $int] : (~$lesseq(g(A__questionmark_i), 0))),
% 1.21/1.00 inference(modus_ponens,[status(thm)],[12, 8])).
% 1.21/1.00 tff(14,plain,(
% 1.21/1.00 ![A__questionmark_i: $int] : (~$lesseq(g(A__questionmark_i), 0))),
% 1.21/1.00 inference(skolemize,[status(sab)],[13])).
% 1.21/1.00 tff(15,plain,
% 1.21/1.00 (![A__questionmark_i: $int] : (~$lesseq(g(A__questionmark_i), 0))),
% 1.21/1.00 inference(modus_ponens,[status(thm)],[14, 7])).
% 1.21/1.00 tff(16,plain,
% 1.21/1.00 ((~![A__questionmark_i: $int] : (~$lesseq(g(A__questionmark_i), 0))) | (~$lesseq(g(i3), 0))),
% 1.21/1.00 inference(quant_inst,[status(thm)],[])).
% 1.21/1.00 tff(17,plain,
% 1.21/1.00 (~$lesseq(g(i3), 0)),
% 1.21/1.00 inference(unit_resolution,[status(thm)],[16, 15])).
% 1.21/1.00 tff(18,plain,
% 1.21/1.00 (^[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))))),
% 1.21/1.00 inference(bind,[status(th)],[])).
% 1.21/1.00 tff(19,plain,
% 1.21/1.00 (![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)))),
% 1.21/1.00 inference(quant_intro,[status(thm)],[18])).
% 1.21/1.00 tff(20,plain,
% 1.21/1.00 (^[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)))))),
% 1.21/1.00 inference(bind,[status(th)],[])).
% 1.21/1.00 tff(21,plain,
% 1.21/1.00 (![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)))),
% 1.21/1.00 inference(quant_intro,[status(thm)],[20])).
% 1.21/1.00 tff(22,plain,
% 1.21/1.00 (![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))))),
% 1.21/1.00 inference(rewrite,[status(thm)],[])).
% 1.21/1.00 tff(23,plain,
% 1.21/1.00 (^[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))))))),
% 1.21/1.00 inference(bind,[status(th)],[])).
% 1.21/1.00 tff(24,plain,
% 1.21/1.00 (![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))))),
% 1.21/1.00 inference(quant_intro,[status(thm)],[23])).
% 1.21/1.00 tff(25,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/sandbox/benchmark/theBenchmark.p','formula_9')).
% 1.21/1.00 tff(26,plain,
% 1.21/1.00 (![A__questionmark_i: $int] : ($lesseq(A__questionmark_i, 0) | (~$lesseq(sup(s0), tptp_fun__select__Array_Int_Int__Int__Int_(arr, A__questionmark_i))))),
% 1.21/1.00 inference(modus_ponens,[status(thm)],[25, 24])).
% 1.21/1.00 tff(27,plain,
% 1.21/1.00 (![A__questionmark_i: $int] : ($lesseq(A__questionmark_i, 0) | (~$lesseq(sup(s0), tptp_fun__select__Array_Int_Int__Int__Int_(arr, A__questionmark_i))))),
% 1.21/1.00 inference(modus_ponens,[status(thm)],[26, 22])).
% 1.21/1.00 tff(28,plain,
% 1.21/1.00 (![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)))),
% 1.21/1.00 inference(modus_ponens,[status(thm)],[27, 21])).
% 1.21/1.00 tff(29,plain,(
% 1.21/1.00 ![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)))),
% 1.21/1.00 inference(skolemize,[status(sab)],[28])).
% 1.21/1.00 tff(30,plain,
% 1.21/1.00 (![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)))),
% 1.21/1.00 inference(modus_ponens,[status(thm)],[29, 19])).
% 1.21/1.00 tff(31,plain,
% 1.21/1.00 (((~![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(i3), 0) | (~$lesseq($sum(sup(s0), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))), 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)))) | $lesseq(g(i3), 0) | (~$lesseq($sum(sup(s0), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))), 0)))),
% 1.21/1.00 inference(rewrite,[status(thm)],[])).
% 1.21/1.00 tff(32,plain,
% 1.21/1.00 ((~![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(i3), 0) | (~$lesseq($sum(sup(s0), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))), 0)))),
% 1.21/1.00 inference(quant_inst,[status(thm)],[])).
% 1.21/1.00 tff(33,plain,
% 1.21/1.00 ((~![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)))) | $lesseq(g(i3), 0) | (~$lesseq($sum(sup(s0), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))), 0))),
% 1.21/1.00 inference(modus_ponens,[status(thm)],[32, 31])).
% 1.21/1.00 tff(34,plain,
% 1.21/1.00 ($lesseq(g(i3), 0) | (~$lesseq($sum(sup(s0), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))), 0))),
% 1.21/1.00 inference(unit_resolution,[status(thm)],[33, 30])).
% 1.21/1.00 tff(35,plain,
% 1.21/1.00 (~$lesseq($sum(sup(s0), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))), 0)),
% 1.21/1.00 inference(unit_resolution,[status(thm)],[34, 17])).
% 1.21/1.00 tff(36,plain,
% 1.21/1.00 ((~($sum(sup(s0), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))) = 0)) | $lesseq($sum(sup(s0), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))), 0)),
% 1.21/1.00 inference(theory_lemma,[status(thm)],[])).
% 1.21/1.00 tff(37,plain,
% 1.21/1.00 (~($sum(sup(s0), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))) = 0)),
% 1.21/1.00 inference(unit_resolution,[status(thm)],[36, 35])).
% 1.21/1.00 tff(38,plain,
% 1.21/1.00 (^[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)))),
% 1.21/1.00 inference(bind,[status(th)],[])).
% 1.21/1.00 tff(39,plain,
% 1.21/1.00 (![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))),
% 1.21/1.00 inference(quant_intro,[status(thm)],[38])).
% 1.21/1.00 tff(40,plain,
% 1.21/1.00 (^[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)))),
% 1.21/1.00 inference(bind,[status(th)],[])).
% 1.21/1.00 tff(41,plain,
% 1.21/1.00 (![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))),
% 1.21/1.00 inference(quant_intro,[status(thm)],[40])).
% 1.21/1.00 tff(42,plain,
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% 1.21/1.01 tff(108,axiom,(![A__questionmark_s: 'Set', A__questionmark_x: $int] : (member(A__questionmark_x, A__questionmark_s) => $lesseq(A__questionmark_x, sup(A__questionmark_s)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','formula_7')).
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% 1.21/1.01 tff(110,plain,
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% 1.21/1.01 inference(modus_ponens,[status(thm)],[110, 104])).
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% 1.21/1.01 inference(skolemize,[status(sab)],[111])).
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% 1.21/1.01 (![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))),
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% 1.21/1.01 inference(modus_ponens,[status(thm)],[115, 114])).
% 1.21/1.01 tff(117,plain,
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% 1.21/1.01 tff(119,plain,
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% 1.21/1.01 tff(121,assumption,(member(sup(insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))), s0)), introduced(assumption)).
% 1.21/1.01 tff(122,plain,
% 1.21/1.01 (((~![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(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))), s0)) | $greatereq($sum(sup(s0), $product(-1, sup(insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))))), 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(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))), s0)) | $greatereq($sum(sup(s0), $product(-1, sup(insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))))), 0))),
% 1.21/1.01 inference(rewrite,[status(thm)],[])).
% 1.21/1.01 tff(123,plain,
% 1.21/1.01 (((~member(sup(insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))), s0)) | $lesseq($sum(sup(insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))), $product(-1, sup(s0))), 0)) <=> ((~member(sup(insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))), s0)) | $greatereq($sum(sup(s0), $product(-1, sup(insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))))), 0))),
% 1.21/1.01 inference(rewrite,[status(thm)],[])).
% 1.21/1.01 tff(124,plain,
% 1.21/1.01 (((~![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(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))), s0)) | $lesseq($sum(sup(insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))), $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(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))), s0)) | $greatereq($sum(sup(s0), $product(-1, sup(insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))))), 0)))),
% 1.21/1.01 inference(monotonicity,[status(thm)],[123])).
% 1.21/1.01 tff(125,plain,
% 1.21/1.01 (((~![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(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))), s0)) | $lesseq($sum(sup(insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))), $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(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))), s0)) | $greatereq($sum(sup(s0), $product(-1, sup(insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))))), 0))),
% 1.21/1.01 inference(transitivity,[status(thm)],[124, 122])).
% 1.21/1.01 tff(126,plain,
% 1.21/1.01 ((~![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(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))), s0)) | $lesseq($sum(sup(insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))), $product(-1, sup(s0))), 0))),
% 1.21/1.01 inference(quant_inst,[status(thm)],[])).
% 1.21/1.01 tff(127,plain,
% 1.21/1.01 ((~![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(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))), s0)) | $greatereq($sum(sup(s0), $product(-1, sup(insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))))), 0)),
% 1.21/1.01 inference(modus_ponens,[status(thm)],[126, 125])).
% 1.21/1.01 tff(128,plain,
% 1.21/1.01 ($false),
% 1.21/1.01 inference(unit_resolution,[status(thm)],[127, 113, 120, 121])).
% 1.21/1.01 tff(129,plain,((~member(sup(insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))), s0)) | $greatereq($sum(sup(s0), $product(-1, sup(insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))))), 0)), inference(lemma,lemma(discharge,[]))).
% 1.21/1.01 tff(130,plain,
% 1.21/1.01 (~member(sup(insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))), s0)),
% 1.21/1.01 inference(unit_resolution,[status(thm)],[129, 120])).
% 1.21/1.01 tff(131,plain,
% 1.21/1.01 ($greatereq($sum(sup(s0), $product(-1, sup(insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))))), 0) | $lesseq($sum(sup(s0), $product(-1, sup(insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))))), 0)),
% 1.21/1.01 inference(theory_lemma,[status(thm)],[])).
% 1.21/1.01 tff(132,plain,
% 1.21/1.01 ($lesseq($sum(sup(s0), $product(-1, sup(insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))))), 0)),
% 1.21/1.01 inference(unit_resolution,[status(thm)],[131, 120])).
% 1.21/1.01 tff(133,plain,
% 1.21/1.01 ((~$greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2)), $product(-1, sup(insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))))), 0)) | $lesseq($sum(sup(s0), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2)))), 0) | (~$lesseq($sum(sup(s0), $product(-1, sup(insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))))), 0))),
% 1.21/1.01 inference(theory_lemma,[status(thm)],[])).
% 1.21/1.01 tff(134,plain,
% 1.21/1.01 (~$greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2)), $product(-1, sup(insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))))), 0)),
% 1.21/1.01 inference(unit_resolution,[status(thm)],[133, 132, 74])).
% 1.21/1.01 tff(135,plain,
% 1.21/1.01 ((~($sum(tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2)), $product(-1, sup(insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))))) = 0)) | $greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2)), $product(-1, sup(insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))))), 0)),
% 1.21/1.01 inference(theory_lemma,[status(thm)],[])).
% 1.21/1.01 tff(136,plain,
% 1.21/1.01 (~($sum(tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2)), $product(-1, sup(insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))))) = 0)),
% 1.21/1.01 inference(unit_resolution,[status(thm)],[135, 134])).
% 1.21/1.01 tff(137,plain,
% 1.21/1.01 (((~![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, $product(-1, A__questionmark_x)) = 0))) | ((member(sup(insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))), insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2)))) <=> member(sup(insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))), s1)) | ($sum(tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2)), $product(-1, sup(insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))))) = 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, $product(-1, A__questionmark_x)) = 0))) | (member(sup(insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))), insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2)))) <=> member(sup(insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))), s1)) | ($sum(tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2)), $product(-1, sup(insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))))) = 0))),
% 1.21/1.01 inference(rewrite,[status(thm)],[])).
% 1.21/1.01 tff(138,plain,
% 1.21/1.01 ((~![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, $product(-1, A__questionmark_x)) = 0))) | ((member(sup(insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))), insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2)))) <=> member(sup(insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))), s1)) | ($sum(tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2)), $product(-1, sup(insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))))) = 0))),
% 1.21/1.01 inference(quant_inst,[status(thm)],[])).
% 1.21/1.01 tff(139,plain,
% 1.21/1.01 ((~![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, $product(-1, A__questionmark_x)) = 0))) | (member(sup(insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))), insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2)))) <=> member(sup(insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))), s1)) | ($sum(tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2)), $product(-1, sup(insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))))) = 0)),
% 1.21/1.01 inference(modus_ponens,[status(thm)],[138, 137])).
% 1.21/1.01 tff(140,plain,
% 1.21/1.01 ((member(sup(insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))), insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2)))) <=> member(sup(insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))), s1)) | ($sum(tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2)), $product(-1, sup(insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))))) = 0)),
% 1.21/1.01 inference(unit_resolution,[status(thm)],[139, 53])).
% 1.21/1.01 tff(141,plain,
% 1.21/1.01 (member(sup(insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))), insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2)))) <=> member(sup(insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))), s1)),
% 1.21/1.01 inference(unit_resolution,[status(thm)],[140, 136])).
% 1.21/1.01 tff(142,plain,
% 1.21/1.01 ((~$greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)), $product(-1, sup(insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))))), 0)) | $lesseq($sum(sup(s0), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))), 0) | (~$lesseq($sum(sup(s0), $product(-1, sup(insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))))), 0))),
% 1.21/1.01 inference(theory_lemma,[status(thm)],[])).
% 1.21/1.01 tff(143,plain,
% 1.21/1.01 (~$greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)), $product(-1, sup(insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))))), 0)),
% 1.21/1.01 inference(unit_resolution,[status(thm)],[142, 132, 35])).
% 1.21/1.01 tff(144,plain,
% 1.21/1.01 ((~($sum(tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)), $product(-1, sup(insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))))) = 0)) | $greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)), $product(-1, sup(insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))))), 0)),
% 1.21/1.01 inference(theory_lemma,[status(thm)],[])).
% 1.21/1.01 tff(145,plain,
% 1.21/1.01 (~($sum(tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)), $product(-1, sup(insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))))) = 0)),
% 1.21/1.01 inference(unit_resolution,[status(thm)],[144, 143])).
% 1.21/1.01 tff(146,plain,
% 1.21/1.01 (((~![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, $product(-1, A__questionmark_x)) = 0))) | ((member(sup(insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))), insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))) <=> member(sup(insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))), insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))))) | ($sum(tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)), $product(-1, sup(insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))))) = 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, $product(-1, A__questionmark_x)) = 0))) | (member(sup(insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))), insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))) <=> member(sup(insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))), insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))))) | ($sum(tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)), $product(-1, sup(insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))))) = 0))),
% 1.21/1.01 inference(rewrite,[status(thm)],[])).
% 1.21/1.01 tff(147,plain,
% 1.21/1.01 ((~![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, $product(-1, A__questionmark_x)) = 0))) | ((member(sup(insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))), insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))) <=> member(sup(insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))), insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))))) | ($sum(tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)), $product(-1, sup(insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))))) = 0))),
% 1.21/1.01 inference(quant_inst,[status(thm)],[])).
% 1.21/1.01 tff(148,plain,
% 1.21/1.01 ((~![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, $product(-1, A__questionmark_x)) = 0))) | (member(sup(insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))), insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))) <=> member(sup(insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))), insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))))) | ($sum(tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)), $product(-1, sup(insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))))) = 0)),
% 1.21/1.01 inference(modus_ponens,[status(thm)],[147, 146])).
% 1.21/1.01 tff(149,plain,
% 1.21/1.01 ((member(sup(insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))), insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))) <=> member(sup(insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))), insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))))) | ($sum(tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)), $product(-1, sup(insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))))) = 0)),
% 1.21/1.01 inference(unit_resolution,[status(thm)],[148, 53])).
% 1.21/1.01 tff(150,plain,
% 1.21/1.01 (member(sup(insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))), insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))) <=> member(sup(insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))), insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))))),
% 1.21/1.01 inference(unit_resolution,[status(thm)],[149, 145])).
% 1.21/1.01 tff(151,plain,
% 1.21/1.01 ((~![A__questionmark_s: 'Set'] : member(sup(A__questionmark_s), A__questionmark_s)) | member(sup(insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))), insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3))))),
% 1.21/1.01 inference(quant_inst,[status(thm)],[])).
% 1.21/1.01 tff(152,plain,
% 1.21/1.01 (member(sup(insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))), insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3))))),
% 1.21/1.01 inference(unit_resolution,[status(thm)],[151, 90])).
% 1.21/1.01 tff(153,plain,
% 1.21/1.01 ((~(member(sup(insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))), insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))) <=> member(sup(insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))), insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2)))))) | (~member(sup(insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))), insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3))))) | member(sup(insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))), insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))))),
% 1.21/1.01 inference(tautology,[status(thm)],[])).
% 1.21/1.01 tff(154,plain,
% 1.21/1.01 ((~(member(sup(insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))), insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))) <=> member(sup(insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))), insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2)))))) | member(sup(insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))), insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))))),
% 1.21/1.01 inference(unit_resolution,[status(thm)],[153, 152])).
% 1.21/1.01 tff(155,plain,
% 1.21/1.01 (member(sup(insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))), insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))))),
% 1.21/1.01 inference(unit_resolution,[status(thm)],[154, 150])).
% 1.21/1.01 tff(156,plain,
% 1.21/1.01 ((~(member(sup(insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))), insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2)))) <=> member(sup(insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))), s1))) | (~member(sup(insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))), insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))))) | member(sup(insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))), s1)),
% 1.21/1.01 inference(tautology,[status(thm)],[])).
% 1.21/1.01 tff(157,plain,
% 1.21/1.01 ((~(member(sup(insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))), insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2)))) <=> member(sup(insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))), s1))) | member(sup(insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))), s1)),
% 1.21/1.01 inference(unit_resolution,[status(thm)],[156, 155])).
% 1.21/1.01 tff(158,plain,
% 1.21/1.01 (member(sup(insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))), s1)),
% 1.21/1.01 inference(unit_resolution,[status(thm)],[157, 141])).
% 1.21/1.01 tff(159,plain,
% 1.21/1.01 (member(sup(insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))), s1) <=> member(sup(insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))), s0)),
% 1.21/1.01 inference(monotonicity,[status(thm)],[1])).
% 1.21/1.01 tff(160,plain,
% 1.21/1.01 (member(sup(insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))), s0) <=> member(sup(insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))), s1)),
% 1.21/1.01 inference(symmetry,[status(thm)],[159])).
% 1.21/1.01 tff(161,plain,
% 1.21/1.01 ((~member(sup(insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))), s0)) <=> (~member(sup(insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))), s1))),
% 1.21/1.01 inference(monotonicity,[status(thm)],[160])).
% 1.21/1.01 tff(162,assumption,(~member(sup(insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))), s0)), introduced(assumption)).
% 1.21/1.01 tff(163,plain,
% 1.21/1.01 (~member(sup(insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))), s1)),
% 1.21/1.01 inference(modus_ponens,[status(thm)],[162, 161])).
% 1.21/1.01 tff(164,assumption,(member(sup(insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))), s1)), introduced(assumption)).
% 1.21/1.01 tff(165,plain,
% 1.21/1.01 ($false),
% 1.21/1.01 inference(unit_resolution,[status(thm)],[164, 163])).
% 1.21/1.01 tff(166,plain,((~(s1 = s0)) | (~member(sup(insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))), s1)) | member(sup(insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))), s0)), inference(lemma,lemma(discharge,[]))).
% 1.21/1.01 tff(167,plain,
% 1.21/1.01 (~(s1 = s0)),
% 1.21/1.01 inference(unit_resolution,[status(thm)],[166, 158, 130])).
% 1.21/1.01 tff(168,plain,
% 1.21/1.01 (((~$lesseq(i1, 0)) | (s1 = s0)) <=> ((~$lesseq(i1, 0)) | (s1 = s0))),
% 1.21/1.01 inference(rewrite,[status(thm)],[])).
% 1.21/1.01 tff(169,plain,
% 1.21/1.01 (($lesseq(i1, 0) => (s1 = s0)) <=> ((~$lesseq(i1, 0)) | (s1 = s0))),
% 1.21/1.01 inference(rewrite,[status(thm)],[])).
% 1.21/1.01 tff(170,plain,
% 1.21/1.01 ((~(~$lesseq(i1, 0))) <=> $lesseq(i1, 0)),
% 1.21/1.01 inference(rewrite,[status(thm)],[])).
% 1.21/1.01 tff(171,plain,
% 1.21/1.01 ($greater(i1, 0) <=> (~$lesseq(i1, 0))),
% 1.21/1.01 inference(rewrite,[status(thm)],[])).
% 1.21/1.01 tff(172,plain,
% 1.21/1.01 ((~$greater(i1, 0)) <=> (~(~$lesseq(i1, 0)))),
% 1.21/1.01 inference(monotonicity,[status(thm)],[171])).
% 1.21/1.01 tff(173,plain,
% 1.21/1.01 ((~$greater(i1, 0)) <=> $lesseq(i1, 0)),
% 1.21/1.01 inference(transitivity,[status(thm)],[172, 170])).
% 1.21/1.01 tff(174,plain,
% 1.21/1.01 (((~$greater(i1, 0)) => (s1 = s0)) <=> ($lesseq(i1, 0) => (s1 = s0))),
% 1.21/1.01 inference(monotonicity,[status(thm)],[173])).
% 1.21/1.01 tff(175,plain,
% 1.21/1.01 (((~$greater(i1, 0)) => (s1 = s0)) <=> ((~$lesseq(i1, 0)) | (s1 = s0))),
% 1.21/1.01 inference(transitivity,[status(thm)],[174, 169])).
% 1.21/1.01 tff(176,axiom,(($greater(i1, 0) => (s1 = insert(s0, tptp_fun__select__Array_Int_Int__Int__Int_(arr, i1)))) & ((~$greater(i1, 0)) => (s1 = s0))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','formula_11')).
% 1.21/1.01 tff(177,plain,
% 1.21/1.01 ((~$greater(i1, 0)) => (s1 = s0)),
% 1.21/1.01 inference(and_elim,[status(thm)],[176])).
% 1.21/1.01 tff(178,plain,
% 1.21/1.01 ((~$lesseq(i1, 0)) | (s1 = s0)),
% 1.21/1.01 inference(modus_ponens,[status(thm)],[177, 175])).
% 1.21/1.01 tff(179,plain,
% 1.21/1.01 ((~$lesseq(i1, 0)) | (s1 = s0)),
% 1.21/1.01 inference(modus_ponens,[status(thm)],[178, 168])).
% 1.21/1.01 tff(180,plain,
% 1.21/1.01 (~$lesseq(i1, 0)),
% 1.21/1.01 inference(unit_resolution,[status(thm)],[179, 167])).
% 1.21/1.01 tff(181,plain,
% 1.21/1.01 (($lesseq(i1, 0) | (s1 = insert(s0, tptp_fun__select__Array_Int_Int__Int__Int_(arr, i1)))) <=> ($lesseq(i1, 0) | (s1 = insert(s0, tptp_fun__select__Array_Int_Int__Int__Int_(arr, i1))))),
% 1.21/1.01 inference(rewrite,[status(thm)],[])).
% 1.21/1.01 tff(182,plain,
% 1.21/1.01 (((~$lesseq(i1, 0)) => (s1 = insert(s0, tptp_fun__select__Array_Int_Int__Int__Int_(arr, i1)))) <=> ($lesseq(i1, 0) | (s1 = insert(s0, tptp_fun__select__Array_Int_Int__Int__Int_(arr, i1))))),
% 1.21/1.01 inference(rewrite,[status(thm)],[])).
% 1.21/1.01 tff(183,plain,
% 1.21/1.01 (($greater(i1, 0) => (s1 = insert(s0, tptp_fun__select__Array_Int_Int__Int__Int_(arr, i1)))) <=> ((~$lesseq(i1, 0)) => (s1 = insert(s0, tptp_fun__select__Array_Int_Int__Int__Int_(arr, i1))))),
% 1.21/1.01 inference(monotonicity,[status(thm)],[171])).
% 1.21/1.01 tff(184,plain,
% 1.21/1.01 (($greater(i1, 0) => (s1 = insert(s0, tptp_fun__select__Array_Int_Int__Int__Int_(arr, i1)))) <=> ($lesseq(i1, 0) | (s1 = insert(s0, tptp_fun__select__Array_Int_Int__Int__Int_(arr, i1))))),
% 1.21/1.01 inference(transitivity,[status(thm)],[183, 182])).
% 1.21/1.01 tff(185,plain,
% 1.21/1.01 ($greater(i1, 0) => (s1 = insert(s0, tptp_fun__select__Array_Int_Int__Int__Int_(arr, i1)))),
% 1.21/1.01 inference(and_elim,[status(thm)],[176])).
% 1.21/1.01 tff(186,plain,
% 1.21/1.01 ($lesseq(i1, 0) | (s1 = insert(s0, tptp_fun__select__Array_Int_Int__Int__Int_(arr, i1)))),
% 1.21/1.01 inference(modus_ponens,[status(thm)],[185, 184])).
% 1.21/1.01 tff(187,plain,
% 1.21/1.01 ($lesseq(i1, 0) | (s1 = insert(s0, tptp_fun__select__Array_Int_Int__Int__Int_(arr, i1)))),
% 1.21/1.02 inference(modus_ponens,[status(thm)],[186, 181])).
% 1.21/1.02 tff(188,plain,
% 1.21/1.02 (s1 = insert(s0, tptp_fun__select__Array_Int_Int__Int__Int_(arr, i1))),
% 1.21/1.02 inference(unit_resolution,[status(thm)],[187, 180])).
% 1.21/1.02 tff(189,plain,
% 1.21/1.02 (insert(s0, tptp_fun__select__Array_Int_Int__Int__Int_(arr, i1)) = s1),
% 1.21/1.02 inference(symmetry,[status(thm)],[188])).
% 1.21/1.02 tff(190,plain,
% 1.21/1.02 (member(sup(insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))), insert(s0, tptp_fun__select__Array_Int_Int__Int__Int_(arr, i1))) <=> member(sup(insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))), s1)),
% 1.21/1.02 inference(monotonicity,[status(thm)],[189])).
% 1.21/1.02 tff(191,plain,
% 1.21/1.02 (member(sup(insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))), s1) <=> member(sup(insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))), insert(s0, tptp_fun__select__Array_Int_Int__Int__Int_(arr, i1)))),
% 1.21/1.02 inference(symmetry,[status(thm)],[190])).
% 1.21/1.02 tff(192,plain,
% 1.21/1.02 (member(sup(insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))), insert(s0, tptp_fun__select__Array_Int_Int__Int__Int_(arr, i1)))),
% 1.21/1.02 inference(modus_ponens,[status(thm)],[158, 191])).
% 1.21/1.02 tff(193,plain,
% 1.21/1.02 (((~![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(i1, 0) | (~$lesseq($sum(sup(s0), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, 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)))) | $lesseq(i1, 0) | (~$lesseq($sum(sup(s0), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, i1))), 0)))),
% 1.21/1.02 inference(rewrite,[status(thm)],[])).
% 1.21/1.02 tff(194,plain,
% 1.21/1.02 ((~![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(i1, 0) | (~$lesseq($sum(sup(s0), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, i1))), 0)))),
% 1.21/1.02 inference(quant_inst,[status(thm)],[])).
% 1.21/1.02 tff(195,plain,
% 1.21/1.02 ((~![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)))) | $lesseq(i1, 0) | (~$lesseq($sum(sup(s0), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, i1))), 0))),
% 1.21/1.02 inference(modus_ponens,[status(thm)],[194, 193])).
% 1.21/1.02 tff(196,plain,
% 1.21/1.02 (~$lesseq($sum(sup(s0), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, i1))), 0)),
% 1.21/1.02 inference(unit_resolution,[status(thm)],[195, 30, 180])).
% 1.21/1.02 tff(197,plain,
% 1.21/1.02 ((~$greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(arr, i1), $product(-1, sup(insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))))), 0)) | (~$lesseq($sum(sup(s0), $product(-1, sup(insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))))), 0)) | $lesseq($sum(sup(s0), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, i1))), 0)),
% 1.21/1.02 inference(theory_lemma,[status(thm)],[])).
% 1.21/1.02 tff(198,plain,
% 1.21/1.02 (~$greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(arr, i1), $product(-1, sup(insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))))), 0)),
% 1.21/1.02 inference(unit_resolution,[status(thm)],[197, 196, 132])).
% 1.21/1.02 tff(199,plain,
% 1.21/1.02 ((~($sum(tptp_fun__select__Array_Int_Int__Int__Int_(arr, i1), $product(-1, sup(insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))))) = 0)) | $greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(arr, i1), $product(-1, sup(insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))))), 0)),
% 1.21/1.02 inference(theory_lemma,[status(thm)],[])).
% 1.21/1.02 tff(200,plain,
% 1.21/1.02 (~($sum(tptp_fun__select__Array_Int_Int__Int__Int_(arr, i1), $product(-1, sup(insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))))) = 0)),
% 1.21/1.02 inference(unit_resolution,[status(thm)],[199, 198])).
% 1.21/1.02 tff(201,plain,
% 1.21/1.02 (((~![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, $product(-1, A__questionmark_x)) = 0))) | ((member(sup(insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))), insert(s0, tptp_fun__select__Array_Int_Int__Int__Int_(arr, i1))) <=> member(sup(insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))), s0)) | ($sum(tptp_fun__select__Array_Int_Int__Int__Int_(arr, i1), $product(-1, sup(insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))))) = 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, $product(-1, A__questionmark_x)) = 0))) | (member(sup(insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))), insert(s0, tptp_fun__select__Array_Int_Int__Int__Int_(arr, i1))) <=> member(sup(insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))), s0)) | ($sum(tptp_fun__select__Array_Int_Int__Int__Int_(arr, i1), $product(-1, sup(insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))))) = 0))),
% 1.21/1.02 inference(rewrite,[status(thm)],[])).
% 1.21/1.02 tff(202,plain,
% 1.21/1.02 ((~![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, $product(-1, A__questionmark_x)) = 0))) | ((member(sup(insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))), insert(s0, tptp_fun__select__Array_Int_Int__Int__Int_(arr, i1))) <=> member(sup(insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))), s0)) | ($sum(tptp_fun__select__Array_Int_Int__Int__Int_(arr, i1), $product(-1, sup(insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))))) = 0))),
% 1.21/1.02 inference(quant_inst,[status(thm)],[])).
% 1.21/1.02 tff(203,plain,
% 1.21/1.02 ((~![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, $product(-1, A__questionmark_x)) = 0))) | (member(sup(insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))), insert(s0, tptp_fun__select__Array_Int_Int__Int__Int_(arr, i1))) <=> member(sup(insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))), s0)) | ($sum(tptp_fun__select__Array_Int_Int__Int__Int_(arr, i1), $product(-1, sup(insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))))) = 0)),
% 1.21/1.02 inference(modus_ponens,[status(thm)],[202, 201])).
% 1.21/1.02 tff(204,plain,
% 1.21/1.02 ((member(sup(insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))), insert(s0, tptp_fun__select__Array_Int_Int__Int__Int_(arr, i1))) <=> member(sup(insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))), s0)) | ($sum(tptp_fun__select__Array_Int_Int__Int__Int_(arr, i1), $product(-1, sup(insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))))) = 0)),
% 1.21/1.02 inference(unit_resolution,[status(thm)],[203, 53])).
% 1.21/1.02 tff(205,plain,
% 1.21/1.02 (member(sup(insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))), insert(s0, tptp_fun__select__Array_Int_Int__Int__Int_(arr, i1))) <=> member(sup(insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))), s0)),
% 1.21/1.02 inference(unit_resolution,[status(thm)],[204, 200])).
% 1.21/1.02 tff(206,plain,
% 1.21/1.02 ((~(member(sup(insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))), insert(s0, tptp_fun__select__Array_Int_Int__Int__Int_(arr, i1))) <=> member(sup(insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))), s0))) | (~member(sup(insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))), insert(s0, tptp_fun__select__Array_Int_Int__Int__Int_(arr, i1)))) | member(sup(insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))), s0)),
% 1.21/1.02 inference(tautology,[status(thm)],[])).
% 1.21/1.02 tff(207,plain,
% 1.21/1.02 ((~(member(sup(insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))), insert(s0, tptp_fun__select__Array_Int_Int__Int__Int_(arr, i1))) <=> member(sup(insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))), s0))) | (~member(sup(insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))), insert(s0, tptp_fun__select__Array_Int_Int__Int__Int_(arr, i1))))),
% 1.21/1.02 inference(unit_resolution,[status(thm)],[206, 130])).
% 1.21/1.02 tff(208,plain,
% 1.21/1.02 (~member(sup(insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))), insert(s0, tptp_fun__select__Array_Int_Int__Int__Int_(arr, i1)))),
% 1.21/1.02 inference(unit_resolution,[status(thm)],[207, 205])).
% 1.21/1.02 tff(209,plain,
% 1.21/1.02 ($false),
% 1.21/1.02 inference(unit_resolution,[status(thm)],[208, 192])).
% 1.21/1.02 tff(210,plain,($greatereq($sum(sup(s0), $product(-1, sup(insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))))), 0)), inference(lemma,lemma(discharge,[]))).
% 1.21/1.02 tff(211,plain,
% 1.21/1.02 ((~($sum(sup(insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))), $product(-1, sup(s0))) = 0)) <=> (~($sum(sup(s0), $product(-1, sup(insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))))) = 0))),
% 1.21/1.02 inference(rewrite,[status(thm)],[])).
% 1.21/1.02 tff(212,plain,
% 1.21/1.02 ((~(sup(insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))) = sup(s0))) <=> (~($sum(sup(insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))), $product(-1, sup(s0))) = 0))),
% 1.21/1.02 inference(rewrite,[status(thm)],[])).
% 1.21/1.02 tff(213,plain,
% 1.21/1.02 ((~(sup(s3) = sup(s0))) <=> (~(sup(insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))) = sup(s0)))),
% 1.21/1.02 inference(rewrite,[status(thm)],[])).
% 1.21/1.02 tff(214,plain,
% 1.21/1.02 ((~(sup(s3) = sup(s0))) <=> (~(sup(s3) = sup(s0)))),
% 1.21/1.02 inference(rewrite,[status(thm)],[])).
% 1.21/1.02 tff(215,axiom,(~(sup(s3) = sup(s0))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','formula_15')).
% 1.21/1.02 tff(216,plain,
% 1.21/1.02 (~(sup(s3) = sup(s0))),
% 1.21/1.02 inference(modus_ponens,[status(thm)],[215, 214])).
% 1.21/1.02 tff(217,plain,
% 1.21/1.02 (~(sup(insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))) = sup(s0))),
% 1.21/1.02 inference(modus_ponens,[status(thm)],[216, 213])).
% 1.21/1.02 tff(218,plain,
% 1.21/1.02 (~($sum(sup(insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))), $product(-1, sup(s0))) = 0)),
% 1.21/1.02 inference(modus_ponens,[status(thm)],[217, 212])).
% 1.21/1.02 tff(219,plain,
% 1.21/1.02 (~($sum(sup(s0), $product(-1, sup(insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))))) = 0)),
% 1.21/1.02 inference(modus_ponens,[status(thm)],[218, 211])).
% 1.21/1.02 tff(220,plain,
% 1.21/1.02 (($sum(sup(s0), $product(-1, sup(insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))))) = 0) | (~$lesseq($sum(sup(s0), $product(-1, sup(insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))))), 0)) | (~$greatereq($sum(sup(s0), $product(-1, sup(insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))))), 0))),
% 1.21/1.02 inference(theory_lemma,[status(thm)],[])).
% 1.21/1.02 tff(221,plain,
% 1.21/1.02 ((~$lesseq($sum(sup(s0), $product(-1, sup(insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))))), 0)) | (~$greatereq($sum(sup(s0), $product(-1, sup(insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))))), 0))),
% 1.21/1.02 inference(unit_resolution,[status(thm)],[220, 219])).
% 1.21/1.02 tff(222,plain,
% 1.21/1.02 (~$lesseq($sum(sup(s0), $product(-1, sup(insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))))), 0)),
% 1.21/1.02 inference(unit_resolution,[status(thm)],[221, 210])).
% 1.21/1.02 tff(223,plain,
% 1.21/1.02 ((~$lesseq($sum(sup(s0), $product(-1, sup(insert(insert(s0, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))))), 0)) | (~$greatereq($sum(sup(insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))), $product(-1, sup(insert(insert(s0, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))))), 0)) | $lesseq($sum(sup(s0), $product(-1, sup(insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))))), 0)),
% 1.21/1.02 inference(theory_lemma,[status(thm)],[])).
% 1.21/1.02 tff(224,plain,
% 1.21/1.02 ((~$lesseq($sum(sup(s0), $product(-1, sup(insert(insert(s0, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))))), 0)) | (~$greatereq($sum(sup(insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))), $product(-1, sup(insert(insert(s0, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))))), 0))),
% 1.21/1.02 inference(unit_resolution,[status(thm)],[223, 222])).
% 1.21/1.02 tff(225,plain,
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% 1.21/1.02 inference(unit_resolution,[status(thm)],[224, 119])).
% 1.21/1.02 tff(226,plain,
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% 1.21/1.02 inference(theory_lemma,[status(thm)],[])).
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% 1.21/1.02 (~(sup(insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))) = sup(insert(insert(s0, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))))),
% 1.21/1.02 inference(unit_resolution,[status(thm)],[226, 225])).
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% 1.21/1.02 inference(unit_resolution,[status(thm)],[227, 4])).
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% 1.21/1.02 tff(230,plain,
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% 1.21/1.02 inference(unit_resolution,[status(thm)],[195, 30])).
% 1.21/1.02 tff(232,plain,
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% 1.21/1.02 ((~($sum(sup(s0), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, i1))) = 0)) | $lesseq($sum(sup(s0), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, i1))), 0)),
% 1.21/1.02 inference(theory_lemma,[status(thm)],[])).
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% 1.21/1.02 (~($sum(sup(s0), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, i1))) = 0)),
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% 1.21/1.02 inference(rewrite,[status(thm)],[])).
% 1.21/1.02 tff(264,plain,
% 1.21/1.02 (((member(sup(s0), insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))) <=> member(sup(s0), insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))))) | ($sum(tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)), $product(-1, sup(s0))) = 0)) <=> ((member(sup(s0), insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))) <=> member(sup(s0), insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))))) | ($sum(sup(s0), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))) = 0))),
% 1.21/1.03 inference(monotonicity,[status(thm)],[59])).
% 1.21/1.03 tff(265,plain,
% 1.21/1.03 (((member(sup(s0), insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))) <=> member(sup(s0), insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))))) | ($sum(tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)), $product(-1, sup(s0))) = 0)) <=> (($sum(sup(s0), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))) = 0) | (member(sup(s0), insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))) <=> member(sup(s0), insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))))))),
% 1.21/1.03 inference(transitivity,[status(thm)],[264, 263])).
% 1.21/1.03 tff(266,plain,
% 1.21/1.03 (((~![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, $product(-1, A__questionmark_x)) = 0))) | ((member(sup(s0), insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))) <=> member(sup(s0), insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))))) | ($sum(tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)), $product(-1, sup(s0))) = 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, $product(-1, A__questionmark_x)) = 0))) | (($sum(sup(s0), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))) = 0) | (member(sup(s0), insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))) <=> member(sup(s0), insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2)))))))),
% 1.21/1.03 inference(monotonicity,[status(thm)],[265])).
% 1.21/1.03 tff(267,plain,
% 1.21/1.03 (((~![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, $product(-1, A__questionmark_x)) = 0))) | ((member(sup(s0), insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))) <=> member(sup(s0), insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))))) | ($sum(tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)), $product(-1, sup(s0))) = 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, $product(-1, A__questionmark_x)) = 0))) | ($sum(sup(s0), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))) = 0) | (member(sup(s0), insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))) <=> member(sup(s0), insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))))))),
% 1.21/1.03 inference(transitivity,[status(thm)],[266, 262])).
% 1.21/1.03 tff(268,plain,
% 1.21/1.03 ((~![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, $product(-1, A__questionmark_x)) = 0))) | ((member(sup(s0), insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))) <=> member(sup(s0), insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))))) | ($sum(tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)), $product(-1, sup(s0))) = 0))),
% 1.21/1.03 inference(quant_inst,[status(thm)],[])).
% 1.21/1.03 tff(269,plain,
% 1.21/1.03 ((~![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, $product(-1, A__questionmark_x)) = 0))) | ($sum(sup(s0), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))) = 0) | (member(sup(s0), insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))) <=> member(sup(s0), insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2)))))),
% 1.21/1.03 inference(modus_ponens,[status(thm)],[268, 267])).
% 1.21/1.03 tff(270,plain,
% 1.21/1.03 ($false),
% 1.21/1.03 inference(unit_resolution,[status(thm)],[269, 53, 37, 261])).
% 1.21/1.03 tff(271,plain,(member(sup(s0), insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))) <=> member(sup(s0), insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))))), inference(lemma,lemma(discharge,[]))).
% 1.21/1.03 tff(272,plain,
% 1.21/1.03 ((~(member(sup(s0), insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))) <=> member(sup(s0), insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2)))))) | member(sup(s0), insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))) | (~member(sup(s0), insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2)))))),
% 1.21/1.03 inference(tautology,[status(thm)],[])).
% 1.21/1.03 tff(273,plain,
% 1.21/1.03 (member(sup(s0), insert(insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i3)))) | (~member(sup(s0), insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2)))))),
% 1.21/1.03 inference(unit_resolution,[status(thm)],[272, 271])).
% 1.21/1.03 tff(274,plain,
% 1.21/1.03 (~member(sup(s0), insert(s1, tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))))),
% 1.21/1.03 inference(unit_resolution,[status(thm)],[273, 260])).
% 1.21/1.03 tff(275,plain,
% 1.21/1.03 (~member(sup(s0), insert(insert(s0, tptp_fun__select__Array_Int_Int__Int__Int_(arr, i1)), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2))))),
% 1.21/1.03 inference(modus_ponens,[status(thm)],[274, 254])).
% 1.21/1.03 tff(276,plain,
% 1.21/1.03 ((~(member(sup(s0), insert(insert(s0, tptp_fun__select__Array_Int_Int__Int__Int_(arr, i1)), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2)))) <=> member(sup(s0), insert(s0, tptp_fun__select__Array_Int_Int__Int__Int_(arr, i1))))) | member(sup(s0), insert(insert(s0, tptp_fun__select__Array_Int_Int__Int__Int_(arr, i1)), tptp_fun__select__Array_Int_Int__Int__Int_(arr, g(i2)))) | (~member(sup(s0), insert(s0, tptp_fun__select__Array_Int_Int__Int__Int_(arr, i1))))),
% 1.21/1.03 inference(tautology,[status(thm)],[])).
% 1.21/1.03 tff(277,plain,
% 1.21/1.03 (~member(sup(s0), insert(s0, tptp_fun__select__Array_Int_Int__Int__Int_(arr, i1)))),
% 1.21/1.03 inference(unit_resolution,[status(thm)],[276, 275, 248])).
% 1.21/1.03 tff(278,plain,
% 1.21/1.03 ((~(member(sup(s0), insert(s0, tptp_fun__select__Array_Int_Int__Int__Int_(arr, i1))) <=> member(sup(s0), s0))) | member(sup(s0), insert(s0, tptp_fun__select__Array_Int_Int__Int__Int_(arr, i1))) | (~member(sup(s0), s0))),
% 1.21/1.03 inference(tautology,[status(thm)],[])).
% 1.21/1.03 tff(279,plain,
% 1.21/1.03 ((~(member(sup(s0), insert(s0, tptp_fun__select__Array_Int_Int__Int__Int_(arr, i1))) <=> member(sup(s0), s0))) | member(sup(s0), insert(s0, tptp_fun__select__Array_Int_Int__Int__Int_(arr, i1)))),
% 1.21/1.03 inference(unit_resolution,[status(thm)],[278, 92])).
% 1.21/1.03 tff(280,plain,
% 1.21/1.03 ($false),
% 1.21/1.03 inference(unit_resolution,[status(thm)],[279, 277, 241])).
% 1.21/1.03 % SZS output end Proof
%------------------------------------------------------------------------------