TSTP Solution File: SWV041+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWV041+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n027.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 29 15:09:44 EDT 2022
% Result : Theorem 0.20s 0.47s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWV041+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% 0.12/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n027.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sun Sep 4 01:25:51 EDT 2022
% 0.12/0.35 % CPUTime :
% 0.12/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.35 Usage: tptp [options] [-file:]file
% 0.12/0.35 -h, -? prints this message.
% 0.12/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.35 -m, -model generate model.
% 0.12/0.35 -p, -proof generate proof.
% 0.12/0.35 -c, -core generate unsat core of named formulas.
% 0.12/0.35 -st, -statistics display statistics.
% 0.12/0.35 -t:timeout set timeout (in second).
% 0.12/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.35 -<param>:<value> configuration parameter and value.
% 0.12/0.35 -o:<output-file> file to place output in.
% 0.20/0.47 % SZS status Theorem
% 0.20/0.47 % SZS output start Proof
% 0.20/0.47 tff(gt_type, type, (
% 0.20/0.47 gt: ( $i * $i ) > $o)).
% 0.20/0.47 tff(succ_type, type, (
% 0.20/0.47 succ: $i > $i)).
% 0.20/0.47 tff(tptp_minus_1_type, type, (
% 0.20/0.47 tptp_minus_1: $i)).
% 0.20/0.47 tff(leq_type, type, (
% 0.20/0.47 leq: ( $i * $i ) > $o)).
% 0.20/0.47 tff(minus_type, type, (
% 0.20/0.47 minus: ( $i * $i ) > $i)).
% 0.20/0.47 tff(pred_type, type, (
% 0.20/0.47 pred: $i > $i)).
% 0.20/0.47 tff(n1_type, type, (
% 0.20/0.47 n1: $i)).
% 0.20/0.47 tff(tptp_fun_B_14_type, type, (
% 0.20/0.47 tptp_fun_B_14: $i)).
% 0.20/0.47 tff(init_type, type, (
% 0.20/0.47 init: $i)).
% 0.20/0.47 tff(a_select3_type, type, (
% 0.20/0.47 a_select3: ( $i * $i * $i ) > $i)).
% 0.20/0.47 tff(tptp_fun_A_13_type, type, (
% 0.20/0.47 tptp_fun_A_13: $i)).
% 0.20/0.47 tff(tptp_const_array2_type, type, (
% 0.20/0.47 tptp_const_array2: ( $i * $i * $i ) > $i)).
% 0.20/0.47 tff(uninit_type, type, (
% 0.20/0.47 uninit: $i)).
% 0.20/0.47 tff(dim_type, type, (
% 0.20/0.47 dim: ( $i * $i ) > $i)).
% 0.20/0.47 tff(n2_type, type, (
% 0.20/0.47 n2: $i)).
% 0.20/0.47 tff(n0_type, type, (
% 0.20/0.47 n0: $i)).
% 0.20/0.47 tff(n3_type, type, (
% 0.20/0.47 n3: $i)).
% 0.20/0.47 tff(geq_type, type, (
% 0.20/0.47 geq: ( $i * $i ) > $o)).
% 0.20/0.47 tff(n410_type, type, (
% 0.20/0.47 n410: $i)).
% 0.20/0.47 tff(n330_type, type, (
% 0.20/0.47 n330: $i)).
% 0.20/0.47 tff(1,plain,
% 0.20/0.47 (^[X: $i, Y: $i] : refl((leq(X, Y) <=> gt(succ(Y), X)) <=> (leq(X, Y) <=> gt(succ(Y), X)))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(2,plain,
% 0.20/0.47 (![X: $i, Y: $i] : (leq(X, Y) <=> gt(succ(Y), X)) <=> ![X: $i, Y: $i] : (leq(X, Y) <=> gt(succ(Y), X))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[1])).
% 0.20/0.47 tff(3,plain,
% 0.20/0.47 (![X: $i, Y: $i] : (leq(X, Y) <=> gt(succ(Y), X)) <=> ![X: $i, Y: $i] : (leq(X, Y) <=> gt(succ(Y), X))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(4,axiom,(![X: $i, Y: $i] : (leq(X, Y) <=> gt(succ(Y), X))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV003+0.ax','leq_succ_gt_equiv')).
% 0.20/0.47 tff(5,plain,
% 0.20/0.47 (![X: $i, Y: $i] : (leq(X, Y) <=> gt(succ(Y), X))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.20/0.47 tff(6,plain,(
% 0.20/0.47 ![X: $i, Y: $i] : (leq(X, Y) <=> gt(succ(Y), X))),
% 0.20/0.47 inference(skolemize,[status(sab)],[5])).
% 0.20/0.47 tff(7,plain,
% 0.20/0.47 (![X: $i, Y: $i] : (leq(X, Y) <=> gt(succ(Y), X))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.20/0.47 tff(8,plain,
% 0.20/0.47 ((~![X: $i, Y: $i] : (leq(X, Y) <=> gt(succ(Y), X))) | (leq(succ(tptp_minus_1), tptp_minus_1) <=> gt(succ(tptp_minus_1), succ(tptp_minus_1)))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(9,plain,
% 0.20/0.47 (leq(succ(tptp_minus_1), tptp_minus_1) <=> gt(succ(tptp_minus_1), succ(tptp_minus_1))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.20/0.47 tff(10,plain,
% 0.20/0.47 (^[X: $i] : refl((minus(X, succ(succ(tptp_minus_1))) = pred(X)) <=> (minus(X, succ(succ(tptp_minus_1))) = pred(X)))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(11,plain,
% 0.20/0.47 (![X: $i] : (minus(X, succ(succ(tptp_minus_1))) = pred(X)) <=> ![X: $i] : (minus(X, succ(succ(tptp_minus_1))) = pred(X))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[10])).
% 0.20/0.47 tff(12,plain,
% 0.20/0.47 (^[X: $i] : rewrite((minus(X, n1) = pred(X)) <=> (minus(X, succ(succ(tptp_minus_1))) = pred(X)))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(13,plain,
% 0.20/0.47 (![X: $i] : (minus(X, n1) = pred(X)) <=> ![X: $i] : (minus(X, succ(succ(tptp_minus_1))) = pred(X))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[12])).
% 0.20/0.47 tff(14,plain,
% 0.20/0.47 (![X: $i] : (minus(X, n1) = pred(X)) <=> ![X: $i] : (minus(X, n1) = pred(X))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(15,axiom,(![X: $i] : (minus(X, n1) = pred(X))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV003+0.ax','pred_minus_1')).
% 0.20/0.47 tff(16,plain,
% 0.20/0.47 (![X: $i] : (minus(X, n1) = pred(X))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.20/0.47 tff(17,plain,
% 0.20/0.47 (![X: $i] : (minus(X, succ(succ(tptp_minus_1))) = pred(X))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[16, 13])).
% 0.20/0.47 tff(18,plain,(
% 0.20/0.47 ![X: $i] : (minus(X, succ(succ(tptp_minus_1))) = pred(X))),
% 0.20/0.47 inference(skolemize,[status(sab)],[17])).
% 0.20/0.47 tff(19,plain,
% 0.20/0.47 (![X: $i] : (minus(X, succ(succ(tptp_minus_1))) = pred(X))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[18, 11])).
% 0.20/0.47 tff(20,plain,
% 0.20/0.47 ((~![X: $i] : (minus(X, succ(succ(tptp_minus_1))) = pred(X))) | (minus(succ(tptp_minus_1), succ(succ(tptp_minus_1))) = pred(succ(tptp_minus_1)))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(21,plain,
% 0.20/0.47 (minus(succ(tptp_minus_1), succ(succ(tptp_minus_1))) = pred(succ(tptp_minus_1))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[20, 19])).
% 0.20/0.47 tff(22,plain,
% 0.20/0.47 (pred(succ(tptp_minus_1)) = minus(succ(tptp_minus_1), succ(succ(tptp_minus_1)))),
% 0.20/0.47 inference(symmetry,[status(thm)],[21])).
% 0.20/0.47 tff(23,plain,
% 0.20/0.47 (![X: $i] : (pred(succ(X)) = X) <=> ![X: $i] : (pred(succ(X)) = X)),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(24,plain,
% 0.20/0.47 (![X: $i] : (pred(succ(X)) = X) <=> ![X: $i] : (pred(succ(X)) = X)),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(25,axiom,(![X: $i] : (pred(succ(X)) = X)), file('/export/starexec/sandbox2/benchmark/Axioms/SWV003+0.ax','pred_succ')).
% 0.20/0.47 tff(26,plain,
% 0.20/0.47 (![X: $i] : (pred(succ(X)) = X)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.20/0.47 tff(27,plain,(
% 0.20/0.47 ![X: $i] : (pred(succ(X)) = X)),
% 0.20/0.47 inference(skolemize,[status(sab)],[26])).
% 0.20/0.47 tff(28,plain,
% 0.20/0.47 (![X: $i] : (pred(succ(X)) = X)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[27, 23])).
% 0.20/0.47 tff(29,plain,
% 0.20/0.47 ((~![X: $i] : (pred(succ(X)) = X)) | (pred(succ(tptp_minus_1)) = tptp_minus_1)),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(30,plain,
% 0.20/0.47 (pred(succ(tptp_minus_1)) = tptp_minus_1),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[29, 28])).
% 0.20/0.47 tff(31,plain,
% 0.20/0.47 (tptp_minus_1 = pred(succ(tptp_minus_1))),
% 0.20/0.47 inference(symmetry,[status(thm)],[30])).
% 0.20/0.47 tff(32,plain,
% 0.20/0.47 (tptp_minus_1 = minus(succ(tptp_minus_1), succ(succ(tptp_minus_1)))),
% 0.20/0.47 inference(transitivity,[status(thm)],[31, 22])).
% 0.20/0.47 tff(33,plain,
% 0.20/0.47 (leq(succ(tptp_minus_1), tptp_minus_1) <=> leq(succ(tptp_minus_1), minus(succ(tptp_minus_1), succ(succ(tptp_minus_1))))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[32])).
% 0.20/0.47 tff(34,plain,
% 0.20/0.47 (leq(succ(tptp_minus_1), minus(succ(tptp_minus_1), succ(succ(tptp_minus_1)))) <=> leq(succ(tptp_minus_1), tptp_minus_1)),
% 0.20/0.47 inference(symmetry,[status(thm)],[33])).
% 0.20/0.47 tff(35,plain,
% 0.20/0.47 (((leq(succ(tptp_minus_1), A!13) & leq(A!13, succ(succ(succ(tptp_minus_1))))) & (~((~(leq(succ(tptp_minus_1), B!14) & leq(B!14, minus(succ(tptp_minus_1), succ(succ(tptp_minus_1)))))) | (a_select3(tptp_const_array2(dim(succ(tptp_minus_1), succ(succ(succ(succ(tptp_minus_1))))), dim(succ(tptp_minus_1), succ(succ(succ(tptp_minus_1)))), uninit), B!14, A!13) = init)))) <=> (leq(succ(tptp_minus_1), A!13) & leq(A!13, succ(succ(succ(tptp_minus_1)))) & (~((~(leq(succ(tptp_minus_1), B!14) & leq(B!14, minus(succ(tptp_minus_1), succ(succ(tptp_minus_1)))))) | (a_select3(tptp_const_array2(dim(succ(tptp_minus_1), succ(succ(succ(succ(tptp_minus_1))))), dim(succ(tptp_minus_1), succ(succ(succ(tptp_minus_1)))), uninit), B!14, A!13) = init))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(36,plain,
% 0.20/0.47 ((~(~(leq(succ(tptp_minus_1), A!13) & leq(A!13, succ(succ(succ(tptp_minus_1))))))) <=> (leq(succ(tptp_minus_1), A!13) & leq(A!13, succ(succ(succ(tptp_minus_1)))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(37,plain,
% 0.20/0.47 (((~(~(leq(succ(tptp_minus_1), A!13) & leq(A!13, succ(succ(succ(tptp_minus_1))))))) & (~((~(leq(succ(tptp_minus_1), B!14) & leq(B!14, minus(succ(tptp_minus_1), succ(succ(tptp_minus_1)))))) | (a_select3(tptp_const_array2(dim(succ(tptp_minus_1), succ(succ(succ(succ(tptp_minus_1))))), dim(succ(tptp_minus_1), succ(succ(succ(tptp_minus_1)))), uninit), B!14, A!13) = init)))) <=> ((leq(succ(tptp_minus_1), A!13) & leq(A!13, succ(succ(succ(tptp_minus_1))))) & (~((~(leq(succ(tptp_minus_1), B!14) & leq(B!14, minus(succ(tptp_minus_1), succ(succ(tptp_minus_1)))))) | (a_select3(tptp_const_array2(dim(succ(tptp_minus_1), succ(succ(succ(succ(tptp_minus_1))))), dim(succ(tptp_minus_1), succ(succ(succ(tptp_minus_1)))), uninit), B!14, A!13) = init))))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[36])).
% 0.20/0.47 tff(38,plain,
% 0.20/0.47 (((~(~(leq(succ(tptp_minus_1), A!13) & leq(A!13, succ(succ(succ(tptp_minus_1))))))) & (~((~(leq(succ(tptp_minus_1), B!14) & leq(B!14, minus(succ(tptp_minus_1), succ(succ(tptp_minus_1)))))) | (a_select3(tptp_const_array2(dim(succ(tptp_minus_1), succ(succ(succ(succ(tptp_minus_1))))), dim(succ(tptp_minus_1), succ(succ(succ(tptp_minus_1)))), uninit), B!14, A!13) = init)))) <=> (leq(succ(tptp_minus_1), A!13) & leq(A!13, succ(succ(succ(tptp_minus_1)))) & (~((~(leq(succ(tptp_minus_1), B!14) & leq(B!14, minus(succ(tptp_minus_1), succ(succ(tptp_minus_1)))))) | (a_select3(tptp_const_array2(dim(succ(tptp_minus_1), succ(succ(succ(succ(tptp_minus_1))))), dim(succ(tptp_minus_1), succ(succ(succ(tptp_minus_1)))), uninit), B!14, A!13) = init))))),
% 0.20/0.48 inference(transitivity,[status(thm)],[37, 35])).
% 0.20/0.48 tff(39,plain,
% 0.20/0.48 ((~![A: $i] : ((~(leq(succ(tptp_minus_1), A) & leq(A, succ(succ(succ(tptp_minus_1)))))) | ![B: $i] : ((~(leq(succ(tptp_minus_1), B) & leq(B, minus(succ(tptp_minus_1), succ(succ(tptp_minus_1)))))) | (a_select3(tptp_const_array2(dim(succ(tptp_minus_1), succ(succ(succ(succ(tptp_minus_1))))), dim(succ(tptp_minus_1), succ(succ(succ(tptp_minus_1)))), uninit), B, A) = init)))) <=> (~![A: $i] : ((~(leq(succ(tptp_minus_1), A) & leq(A, succ(succ(succ(tptp_minus_1)))))) | ![B: $i] : ((~(leq(succ(tptp_minus_1), B) & leq(B, minus(succ(tptp_minus_1), succ(succ(tptp_minus_1)))))) | (a_select3(tptp_const_array2(dim(succ(tptp_minus_1), succ(succ(succ(succ(tptp_minus_1))))), dim(succ(tptp_minus_1), succ(succ(succ(tptp_minus_1)))), uninit), B, A) = init))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(40,plain,
% 0.20/0.48 ((~![A: $i] : ((~(leq(n0, A) & leq(A, n2))) | ![B: $i] : ((~(leq(n0, B) & leq(B, minus(n0, n1)))) | (a_select3(tptp_const_array2(dim(n0, n3), dim(n0, n2), uninit), B, A) = init)))) <=> (~![A: $i] : ((~(leq(succ(tptp_minus_1), A) & leq(A, succ(succ(succ(tptp_minus_1)))))) | ![B: $i] : ((~(leq(succ(tptp_minus_1), B) & leq(B, minus(succ(tptp_minus_1), succ(succ(tptp_minus_1)))))) | (a_select3(tptp_const_array2(dim(succ(tptp_minus_1), succ(succ(succ(succ(tptp_minus_1))))), dim(succ(tptp_minus_1), succ(succ(succ(tptp_minus_1)))), uninit), B, A) = init))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(41,plain,
% 0.20/0.48 ((~![A: $i] : ((~(leq(n0, A) & leq(A, n2))) | ![B: $i] : ((~(leq(n0, B) & leq(B, minus(n0, n1)))) | (a_select3(tptp_const_array2(dim(n0, n3), dim(n0, n2), uninit), B, A) = init)))) <=> (~![A: $i] : ((~(leq(n0, A) & leq(A, n2))) | ![B: $i] : ((~(leq(n0, B) & leq(B, minus(n0, n1)))) | (a_select3(tptp_const_array2(dim(n0, n3), dim(n0, n2), uninit), B, A) = init))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(42,plain,
% 0.20/0.48 ((~((geq(minus(n330, n1), n0) & geq(minus(n410, n1), n0)) => ![A: $i] : ((leq(n0, A) & leq(A, n2)) => ![B: $i] : ((leq(n0, B) & leq(B, minus(n0, n1))) => (a_select3(tptp_const_array2(dim(n0, n3), dim(n0, n2), uninit), B, A) = init))))) <=> (~((~(geq(minus(n330, n1), n0) & geq(minus(n410, n1), n0))) | ![A: $i] : ((~(leq(n0, A) & leq(A, n2))) | ![B: $i] : ((~(leq(n0, B) & leq(B, minus(n0, n1)))) | (a_select3(tptp_const_array2(dim(n0, n3), dim(n0, n2), uninit), B, A) = init)))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(43,axiom,(~((geq(minus(n330, n1), n0) & geq(minus(n410, n1), n0)) => ![A: $i] : ((leq(n0, A) & leq(A, n2)) => ![B: $i] : ((leq(n0, B) & leq(B, minus(n0, n1))) => (a_select3(tptp_const_array2(dim(n0, n3), dim(n0, n2), uninit), B, A) = init))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','gauss_init_0077')).
% 0.20/0.48 tff(44,plain,
% 0.20/0.48 (~((~(geq(minus(n330, n1), n0) & geq(minus(n410, n1), n0))) | ![A: $i] : ((~(leq(n0, A) & leq(A, n2))) | ![B: $i] : ((~(leq(n0, B) & leq(B, minus(n0, n1)))) | (a_select3(tptp_const_array2(dim(n0, n3), dim(n0, n2), uninit), B, A) = init))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.20/0.48 tff(45,plain,
% 0.20/0.48 (~![A: $i] : ((~(leq(n0, A) & leq(A, n2))) | ![B: $i] : ((~(leq(n0, B) & leq(B, minus(n0, n1)))) | (a_select3(tptp_const_array2(dim(n0, n3), dim(n0, n2), uninit), B, A) = init)))),
% 0.20/0.48 inference(or_elim,[status(thm)],[44])).
% 0.20/0.48 tff(46,plain,
% 0.20/0.48 (~![A: $i] : ((~(leq(n0, A) & leq(A, n2))) | ![B: $i] : ((~(leq(n0, B) & leq(B, minus(n0, n1)))) | (a_select3(tptp_const_array2(dim(n0, n3), dim(n0, n2), uninit), B, A) = init)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[45, 41])).
% 0.20/0.48 tff(47,plain,
% 0.20/0.48 (~![A: $i] : ((~(leq(n0, A) & leq(A, n2))) | ![B: $i] : ((~(leq(n0, B) & leq(B, minus(n0, n1)))) | (a_select3(tptp_const_array2(dim(n0, n3), dim(n0, n2), uninit), B, A) = init)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[46, 41])).
% 0.20/0.48 tff(48,plain,
% 0.20/0.48 (~![A: $i] : ((~(leq(n0, A) & leq(A, n2))) | ![B: $i] : ((~(leq(n0, B) & leq(B, minus(n0, n1)))) | (a_select3(tptp_const_array2(dim(n0, n3), dim(n0, n2), uninit), B, A) = init)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[47, 41])).
% 0.20/0.48 tff(49,plain,
% 0.20/0.48 (~![A: $i] : ((~(leq(succ(tptp_minus_1), A) & leq(A, succ(succ(succ(tptp_minus_1)))))) | ![B: $i] : ((~(leq(succ(tptp_minus_1), B) & leq(B, minus(succ(tptp_minus_1), succ(succ(tptp_minus_1)))))) | (a_select3(tptp_const_array2(dim(succ(tptp_minus_1), succ(succ(succ(succ(tptp_minus_1))))), dim(succ(tptp_minus_1), succ(succ(succ(tptp_minus_1)))), uninit), B, A) = init)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[48, 40])).
% 0.20/0.48 tff(50,plain,
% 0.20/0.48 (~![A: $i] : ((~(leq(succ(tptp_minus_1), A) & leq(A, succ(succ(succ(tptp_minus_1)))))) | ![B: $i] : ((~(leq(succ(tptp_minus_1), B) & leq(B, minus(succ(tptp_minus_1), succ(succ(tptp_minus_1)))))) | (a_select3(tptp_const_array2(dim(succ(tptp_minus_1), succ(succ(succ(succ(tptp_minus_1))))), dim(succ(tptp_minus_1), succ(succ(succ(tptp_minus_1)))), uninit), B, A) = init)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[49, 39])).
% 0.20/0.48 tff(51,plain,
% 0.20/0.48 (~![A: $i] : ((~(leq(succ(tptp_minus_1), A) & leq(A, succ(succ(succ(tptp_minus_1)))))) | ![B: $i] : ((~(leq(succ(tptp_minus_1), B) & leq(B, minus(succ(tptp_minus_1), succ(succ(tptp_minus_1)))))) | (a_select3(tptp_const_array2(dim(succ(tptp_minus_1), succ(succ(succ(succ(tptp_minus_1))))), dim(succ(tptp_minus_1), succ(succ(succ(tptp_minus_1)))), uninit), B, A) = init)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[50, 39])).
% 0.20/0.48 tff(52,plain,
% 0.20/0.48 (~![A: $i] : ((~(leq(succ(tptp_minus_1), A) & leq(A, succ(succ(succ(tptp_minus_1)))))) | ![B: $i] : ((~(leq(succ(tptp_minus_1), B) & leq(B, minus(succ(tptp_minus_1), succ(succ(tptp_minus_1)))))) | (a_select3(tptp_const_array2(dim(succ(tptp_minus_1), succ(succ(succ(succ(tptp_minus_1))))), dim(succ(tptp_minus_1), succ(succ(succ(tptp_minus_1)))), uninit), B, A) = init)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[51, 39])).
% 0.20/0.48 tff(53,plain,
% 0.20/0.48 (leq(succ(tptp_minus_1), A!13) & leq(A!13, succ(succ(succ(tptp_minus_1)))) & (~((~(leq(succ(tptp_minus_1), B!14) & leq(B!14, minus(succ(tptp_minus_1), succ(succ(tptp_minus_1)))))) | (a_select3(tptp_const_array2(dim(succ(tptp_minus_1), succ(succ(succ(succ(tptp_minus_1))))), dim(succ(tptp_minus_1), succ(succ(succ(tptp_minus_1)))), uninit), B!14, A!13) = init)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[52, 38])).
% 0.20/0.48 tff(54,plain,
% 0.20/0.48 (~((~(leq(succ(tptp_minus_1), B!14) & leq(B!14, minus(succ(tptp_minus_1), succ(succ(tptp_minus_1)))))) | (a_select3(tptp_const_array2(dim(succ(tptp_minus_1), succ(succ(succ(succ(tptp_minus_1))))), dim(succ(tptp_minus_1), succ(succ(succ(tptp_minus_1)))), uninit), B!14, A!13) = init))),
% 0.20/0.48 inference(and_elim,[status(thm)],[53])).
% 0.20/0.48 tff(55,plain,
% 0.20/0.48 (leq(succ(tptp_minus_1), B!14) & leq(B!14, minus(succ(tptp_minus_1), succ(succ(tptp_minus_1))))),
% 0.20/0.48 inference(or_elim,[status(thm)],[54])).
% 0.20/0.48 tff(56,plain,
% 0.20/0.48 (leq(B!14, minus(succ(tptp_minus_1), succ(succ(tptp_minus_1))))),
% 0.20/0.48 inference(and_elim,[status(thm)],[55])).
% 0.20/0.48 tff(57,plain,
% 0.20/0.48 (leq(succ(tptp_minus_1), B!14)),
% 0.20/0.48 inference(and_elim,[status(thm)],[55])).
% 0.20/0.48 tff(58,plain,
% 0.20/0.48 (![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(59,plain,
% 0.20/0.48 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(trans(monotonicity(rewrite((leq(X, Y) & leq(Y, Z)) <=> (~((~leq(Y, Z)) | (~leq(X, Y))))), ((~(leq(X, Y) & leq(Y, Z))) <=> (~(~((~leq(Y, Z)) | (~leq(X, Y))))))), rewrite((~(~((~leq(Y, Z)) | (~leq(X, Y))))) <=> ((~leq(Y, Z)) | (~leq(X, Y)))), ((~(leq(X, Y) & leq(Y, Z))) <=> ((~leq(Y, Z)) | (~leq(X, Y))))), (((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z)) <=> (((~leq(Y, Z)) | (~leq(X, Y))) | leq(X, Z)))), rewrite((((~leq(Y, Z)) | (~leq(X, Y))) | leq(X, Z)) <=> (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))), (((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z)) <=> (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(60,plain,
% 0.20/0.48 (![X: $i, Y: $i, Z: $i] : ((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z)) <=> ![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[59])).
% 0.20/0.48 tff(61,plain,
% 0.20/0.48 (![X: $i, Y: $i, Z: $i] : ((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z)) <=> ![X: $i, Y: $i, Z: $i] : ((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(62,plain,
% 0.20/0.48 (^[X: $i, Y: $i, Z: $i] : rewrite(((leq(X, Y) & leq(Y, Z)) => leq(X, Z)) <=> ((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z)))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(63,plain,
% 0.20/0.48 (![X: $i, Y: $i, Z: $i] : ((leq(X, Y) & leq(Y, Z)) => leq(X, Z)) <=> ![X: $i, Y: $i, Z: $i] : ((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[62])).
% 0.20/0.48 tff(64,axiom,(![X: $i, Y: $i, Z: $i] : ((leq(X, Y) & leq(Y, Z)) => leq(X, Z))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV003+0.ax','transitivity_leq')).
% 0.20/0.48 tff(65,plain,
% 0.20/0.48 (![X: $i, Y: $i, Z: $i] : ((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.20/0.48 tff(66,plain,
% 0.20/0.48 (![X: $i, Y: $i, Z: $i] : ((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[65, 61])).
% 0.20/0.48 tff(67,plain,(
% 0.20/0.48 ![X: $i, Y: $i, Z: $i] : ((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z))),
% 0.20/0.48 inference(skolemize,[status(sab)],[66])).
% 0.20/0.48 tff(68,plain,
% 0.20/0.48 (![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[67, 60])).
% 0.20/0.48 tff(69,plain,
% 0.20/0.48 (![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[68, 58])).
% 0.20/0.48 tff(70,plain,
% 0.20/0.48 (((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | ((~leq(succ(tptp_minus_1), B!14)) | leq(succ(tptp_minus_1), minus(succ(tptp_minus_1), succ(succ(tptp_minus_1)))) | (~leq(B!14, minus(succ(tptp_minus_1), succ(succ(tptp_minus_1))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | (~leq(succ(tptp_minus_1), B!14)) | leq(succ(tptp_minus_1), minus(succ(tptp_minus_1), succ(succ(tptp_minus_1)))) | (~leq(B!14, minus(succ(tptp_minus_1), succ(succ(tptp_minus_1))))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(71,plain,
% 0.20/0.48 ((leq(succ(tptp_minus_1), minus(succ(tptp_minus_1), succ(succ(tptp_minus_1)))) | (~leq(B!14, minus(succ(tptp_minus_1), succ(succ(tptp_minus_1))))) | (~leq(succ(tptp_minus_1), B!14))) <=> ((~leq(succ(tptp_minus_1), B!14)) | leq(succ(tptp_minus_1), minus(succ(tptp_minus_1), succ(succ(tptp_minus_1)))) | (~leq(B!14, minus(succ(tptp_minus_1), succ(succ(tptp_minus_1))))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(72,plain,
% 0.20/0.48 (((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | (leq(succ(tptp_minus_1), minus(succ(tptp_minus_1), succ(succ(tptp_minus_1)))) | (~leq(B!14, minus(succ(tptp_minus_1), succ(succ(tptp_minus_1))))) | (~leq(succ(tptp_minus_1), B!14)))) <=> ((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | ((~leq(succ(tptp_minus_1), B!14)) | leq(succ(tptp_minus_1), minus(succ(tptp_minus_1), succ(succ(tptp_minus_1)))) | (~leq(B!14, minus(succ(tptp_minus_1), succ(succ(tptp_minus_1)))))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[71])).
% 0.20/0.48 tff(73,plain,
% 0.20/0.48 (((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | (leq(succ(tptp_minus_1), minus(succ(tptp_minus_1), succ(succ(tptp_minus_1)))) | (~leq(B!14, minus(succ(tptp_minus_1), succ(succ(tptp_minus_1))))) | (~leq(succ(tptp_minus_1), B!14)))) <=> ((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | (~leq(succ(tptp_minus_1), B!14)) | leq(succ(tptp_minus_1), minus(succ(tptp_minus_1), succ(succ(tptp_minus_1)))) | (~leq(B!14, minus(succ(tptp_minus_1), succ(succ(tptp_minus_1))))))),
% 0.20/0.48 inference(transitivity,[status(thm)],[72, 70])).
% 0.20/0.48 tff(74,plain,
% 0.20/0.48 ((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | (leq(succ(tptp_minus_1), minus(succ(tptp_minus_1), succ(succ(tptp_minus_1)))) | (~leq(B!14, minus(succ(tptp_minus_1), succ(succ(tptp_minus_1))))) | (~leq(succ(tptp_minus_1), B!14)))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(75,plain,
% 0.20/0.49 ((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | (~leq(succ(tptp_minus_1), B!14)) | leq(succ(tptp_minus_1), minus(succ(tptp_minus_1), succ(succ(tptp_minus_1)))) | (~leq(B!14, minus(succ(tptp_minus_1), succ(succ(tptp_minus_1)))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.20/0.49 tff(76,plain,
% 0.20/0.49 (leq(succ(tptp_minus_1), minus(succ(tptp_minus_1), succ(succ(tptp_minus_1))))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[75, 69, 57, 56])).
% 0.20/0.49 tff(77,plain,
% 0.20/0.49 (leq(succ(tptp_minus_1), tptp_minus_1)),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[76, 34])).
% 0.20/0.49 tff(78,plain,
% 0.20/0.49 (^[X: $i] : refl((~gt(X, X)) <=> (~gt(X, X)))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(79,plain,
% 0.20/0.49 (![X: $i] : (~gt(X, X)) <=> ![X: $i] : (~gt(X, X))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[78])).
% 0.20/0.49 tff(80,plain,
% 0.20/0.49 (![X: $i] : (~gt(X, X)) <=> ![X: $i] : (~gt(X, X))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(81,axiom,(![X: $i] : (~gt(X, X))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV003+0.ax','irreflexivity_gt')).
% 0.20/0.49 tff(82,plain,
% 0.20/0.49 (![X: $i] : (~gt(X, X))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[81, 80])).
% 0.20/0.49 tff(83,plain,(
% 0.20/0.49 ![X: $i] : (~gt(X, X))),
% 0.20/0.49 inference(skolemize,[status(sab)],[82])).
% 0.20/0.49 tff(84,plain,
% 0.20/0.49 (![X: $i] : (~gt(X, X))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[83, 79])).
% 0.20/0.49 tff(85,plain,
% 0.20/0.49 ((~![X: $i] : (~gt(X, X))) | (~gt(succ(tptp_minus_1), succ(tptp_minus_1)))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(86,plain,
% 0.20/0.49 (~gt(succ(tptp_minus_1), succ(tptp_minus_1))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[85, 84])).
% 0.20/0.49 tff(87,plain,
% 0.20/0.49 ((~(leq(succ(tptp_minus_1), tptp_minus_1) <=> gt(succ(tptp_minus_1), succ(tptp_minus_1)))) | (~leq(succ(tptp_minus_1), tptp_minus_1)) | gt(succ(tptp_minus_1), succ(tptp_minus_1))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(88,plain,
% 0.20/0.49 ($false),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[87, 86, 77, 9])).
% 0.20/0.49 % SZS output end Proof
%------------------------------------------------------------------------------