TSTP Solution File: SWV189+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWV189+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n025.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 15:10:18 EDT 2022
% Result : Theorem 0.14s 0.37s
% Output : Proof 0.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.09 % Problem : SWV189+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% 0.08/0.09 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.09/0.29 % Computer : n025.cluster.edu
% 0.09/0.29 % Model : x86_64 x86_64
% 0.09/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29 % Memory : 8042.1875MB
% 0.09/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29 % CPULimit : 300
% 0.09/0.29 % WCLimit : 300
% 0.09/0.29 % DateTime : Sun Sep 4 01:50:20 EDT 2022
% 0.09/0.29 % CPUTime :
% 0.09/0.30 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.09/0.30 Usage: tptp [options] [-file:]file
% 0.09/0.30 -h, -? prints this message.
% 0.09/0.30 -smt2 print SMT-LIB2 benchmark.
% 0.09/0.30 -m, -model generate model.
% 0.09/0.30 -p, -proof generate proof.
% 0.09/0.30 -c, -core generate unsat core of named formulas.
% 0.09/0.30 -st, -statistics display statistics.
% 0.09/0.30 -t:timeout set timeout (in second).
% 0.09/0.30 -smt2status display status in smt2 format instead of SZS.
% 0.09/0.30 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.09/0.30 -<param>:<value> configuration parameter and value.
% 0.09/0.30 -o:<output-file> file to place output in.
% 0.14/0.37 % SZS status Theorem
% 0.14/0.37 % SZS output start Proof
% 0.14/0.37 tff(gt_type, type, (
% 0.14/0.37 gt: ( $i * $i ) > $o)).
% 0.14/0.37 tff(succ_type, type, (
% 0.14/0.37 succ: $i > $i)).
% 0.14/0.37 tff(tptp_minus_1_type, type, (
% 0.14/0.37 tptp_minus_1: $i)).
% 0.14/0.37 tff(leq_type, type, (
% 0.14/0.37 leq: ( $i * $i ) > $o)).
% 0.14/0.37 tff(tptp_fun_B_13_type, type, (
% 0.14/0.37 tptp_fun_B_13: $i)).
% 0.14/0.37 tff(init_type, type, (
% 0.14/0.37 init: $i)).
% 0.14/0.37 tff(a_select3_type, type, (
% 0.14/0.37 a_select3: ( $i * $i * $i ) > $i)).
% 0.14/0.37 tff(tptp_fun_C_14_type, type, (
% 0.14/0.37 tptp_fun_C_14: $i)).
% 0.14/0.37 tff(q_init_type, type, (
% 0.14/0.37 q_init: $i)).
% 0.14/0.37 tff(n4_type, type, (
% 0.14/0.37 n4: $i)).
% 0.14/0.37 tff(n0_type, type, (
% 0.14/0.37 n0: $i)).
% 0.14/0.37 tff(center_init_type, type, (
% 0.14/0.37 center_init: $i)).
% 0.14/0.37 tff(1,plain,
% 0.14/0.37 (^[X: $i, Y: $i] : refl((leq(X, Y) <=> gt(succ(Y), X)) <=> (leq(X, Y) <=> gt(succ(Y), X)))),
% 0.14/0.37 inference(bind,[status(th)],[])).
% 0.14/0.37 tff(2,plain,
% 0.14/0.37 (![X: $i, Y: $i] : (leq(X, Y) <=> gt(succ(Y), X)) <=> ![X: $i, Y: $i] : (leq(X, Y) <=> gt(succ(Y), X))),
% 0.14/0.37 inference(quant_intro,[status(thm)],[1])).
% 0.14/0.37 tff(3,plain,
% 0.14/0.37 (![X: $i, Y: $i] : (leq(X, Y) <=> gt(succ(Y), X)) <=> ![X: $i, Y: $i] : (leq(X, Y) <=> gt(succ(Y), X))),
% 0.14/0.37 inference(rewrite,[status(thm)],[])).
% 0.14/0.37 tff(4,axiom,(![X: $i, Y: $i] : (leq(X, Y) <=> gt(succ(Y), X))), file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax','leq_succ_gt_equiv')).
% 0.14/0.37 tff(5,plain,
% 0.14/0.37 (![X: $i, Y: $i] : (leq(X, Y) <=> gt(succ(Y), X))),
% 0.14/0.37 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.14/0.37 tff(6,plain,(
% 0.14/0.37 ![X: $i, Y: $i] : (leq(X, Y) <=> gt(succ(Y), X))),
% 0.14/0.37 inference(skolemize,[status(sab)],[5])).
% 0.14/0.37 tff(7,plain,
% 0.14/0.37 (![X: $i, Y: $i] : (leq(X, Y) <=> gt(succ(Y), X))),
% 0.14/0.37 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.14/0.37 tff(8,plain,
% 0.14/0.37 ((~![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)))),
% 0.14/0.37 inference(quant_inst,[status(thm)],[])).
% 0.14/0.37 tff(9,plain,
% 0.14/0.37 (leq(succ(tptp_minus_1), tptp_minus_1) <=> gt(succ(tptp_minus_1), succ(tptp_minus_1))),
% 0.14/0.37 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.14/0.37 tff(10,plain,
% 0.14/0.37 (((leq(succ(tptp_minus_1), B!13) & leq(B!13, tptp_minus_1)) & (~((~(leq(succ(tptp_minus_1), C!14) & leq(C!14, succ(succ(succ(succ(succ(tptp_minus_1)))))))) | (a_select3(q_init, B!13, C!14) = init)))) <=> (leq(succ(tptp_minus_1), B!13) & leq(B!13, tptp_minus_1) & (~((~(leq(succ(tptp_minus_1), C!14) & leq(C!14, succ(succ(succ(succ(succ(tptp_minus_1)))))))) | (a_select3(q_init, B!13, C!14) = init))))),
% 0.14/0.37 inference(rewrite,[status(thm)],[])).
% 0.14/0.37 tff(11,plain,
% 0.14/0.37 ((~(~(leq(succ(tptp_minus_1), B!13) & leq(B!13, tptp_minus_1)))) <=> (leq(succ(tptp_minus_1), B!13) & leq(B!13, tptp_minus_1))),
% 0.14/0.37 inference(rewrite,[status(thm)],[])).
% 0.14/0.37 tff(12,plain,
% 0.14/0.37 (((~(~(leq(succ(tptp_minus_1), B!13) & leq(B!13, tptp_minus_1)))) & (~((~(leq(succ(tptp_minus_1), C!14) & leq(C!14, succ(succ(succ(succ(succ(tptp_minus_1)))))))) | (a_select3(q_init, B!13, C!14) = init)))) <=> ((leq(succ(tptp_minus_1), B!13) & leq(B!13, tptp_minus_1)) & (~((~(leq(succ(tptp_minus_1), C!14) & leq(C!14, succ(succ(succ(succ(succ(tptp_minus_1)))))))) | (a_select3(q_init, B!13, C!14) = init))))),
% 0.14/0.37 inference(monotonicity,[status(thm)],[11])).
% 0.14/0.37 tff(13,plain,
% 0.14/0.37 (((~(~(leq(succ(tptp_minus_1), B!13) & leq(B!13, tptp_minus_1)))) & (~((~(leq(succ(tptp_minus_1), C!14) & leq(C!14, succ(succ(succ(succ(succ(tptp_minus_1)))))))) | (a_select3(q_init, B!13, C!14) = init)))) <=> (leq(succ(tptp_minus_1), B!13) & leq(B!13, tptp_minus_1) & (~((~(leq(succ(tptp_minus_1), C!14) & leq(C!14, succ(succ(succ(succ(succ(tptp_minus_1)))))))) | (a_select3(q_init, B!13, C!14) = init))))),
% 0.14/0.37 inference(transitivity,[status(thm)],[12, 10])).
% 0.14/0.37 tff(14,plain,
% 0.14/0.37 ((~![B: $i] : ((~(leq(succ(tptp_minus_1), B) & leq(B, tptp_minus_1))) | ![C: $i] : ((~(leq(succ(tptp_minus_1), C) & leq(C, succ(succ(succ(succ(succ(tptp_minus_1)))))))) | (a_select3(q_init, B, C) = init)))) <=> (~![B: $i] : ((~(leq(succ(tptp_minus_1), B) & leq(B, tptp_minus_1))) | ![C: $i] : ((~(leq(succ(tptp_minus_1), C) & leq(C, succ(succ(succ(succ(succ(tptp_minus_1)))))))) | (a_select3(q_init, B, C) = init))))),
% 0.14/0.37 inference(rewrite,[status(thm)],[])).
% 0.14/0.37 tff(15,plain,
% 0.14/0.37 ((~![B: $i] : ((~(leq(n0, B) & leq(B, tptp_minus_1))) | ![C: $i] : ((~(leq(n0, C) & leq(C, n4))) | (a_select3(q_init, B, C) = init)))) <=> (~![B: $i] : ((~(leq(succ(tptp_minus_1), B) & leq(B, tptp_minus_1))) | ![C: $i] : ((~(leq(succ(tptp_minus_1), C) & leq(C, succ(succ(succ(succ(succ(tptp_minus_1)))))))) | (a_select3(q_init, B, C) = init))))),
% 0.14/0.38 inference(rewrite,[status(thm)],[])).
% 0.14/0.38 tff(16,plain,
% 0.14/0.38 ((~![B: $i] : ((~(leq(n0, B) & leq(B, tptp_minus_1))) | ![C: $i] : ((~(leq(n0, C) & leq(C, n4))) | (a_select3(q_init, B, C) = init)))) <=> (~![B: $i] : ((~(leq(n0, B) & leq(B, tptp_minus_1))) | ![C: $i] : ((~(leq(n0, C) & leq(C, n4))) | (a_select3(q_init, B, C) = init))))),
% 0.14/0.38 inference(rewrite,[status(thm)],[])).
% 0.14/0.38 tff(17,plain,
% 0.14/0.38 ((~(![A: $i] : ((leq(n0, A) & leq(A, n4)) => (a_select3(center_init, A, n0) = init)) => ![B: $i] : ((leq(n0, B) & leq(B, tptp_minus_1)) => ![C: $i] : ((leq(n0, C) & leq(C, n4)) => (a_select3(q_init, B, C) = init))))) <=> (~((~![A: $i] : ((~(leq(n0, A) & leq(A, n4))) | (a_select3(center_init, A, n0) = init))) | ![B: $i] : ((~(leq(n0, B) & leq(B, tptp_minus_1))) | ![C: $i] : ((~(leq(n0, C) & leq(C, n4))) | (a_select3(q_init, B, C) = init)))))),
% 0.14/0.38 inference(rewrite,[status(thm)],[])).
% 0.14/0.38 tff(18,axiom,(~(![A: $i] : ((leq(n0, A) & leq(A, n4)) => (a_select3(center_init, A, n0) = init)) => ![B: $i] : ((leq(n0, B) & leq(B, tptp_minus_1)) => ![C: $i] : ((leq(n0, C) & leq(C, n4)) => (a_select3(q_init, B, C) = init))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cl5_nebula_init_0121')).
% 0.14/0.38 tff(19,plain,
% 0.14/0.38 (~((~![A: $i] : ((~(leq(n0, A) & leq(A, n4))) | (a_select3(center_init, A, n0) = init))) | ![B: $i] : ((~(leq(n0, B) & leq(B, tptp_minus_1))) | ![C: $i] : ((~(leq(n0, C) & leq(C, n4))) | (a_select3(q_init, B, C) = init))))),
% 0.14/0.38 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.14/0.38 tff(20,plain,
% 0.14/0.38 (~![B: $i] : ((~(leq(n0, B) & leq(B, tptp_minus_1))) | ![C: $i] : ((~(leq(n0, C) & leq(C, n4))) | (a_select3(q_init, B, C) = init)))),
% 0.14/0.38 inference(or_elim,[status(thm)],[19])).
% 0.14/0.38 tff(21,plain,
% 0.14/0.38 (~![B: $i] : ((~(leq(n0, B) & leq(B, tptp_minus_1))) | ![C: $i] : ((~(leq(n0, C) & leq(C, n4))) | (a_select3(q_init, B, C) = init)))),
% 0.14/0.38 inference(modus_ponens,[status(thm)],[20, 16])).
% 0.14/0.38 tff(22,plain,
% 0.14/0.38 (~![B: $i] : ((~(leq(n0, B) & leq(B, tptp_minus_1))) | ![C: $i] : ((~(leq(n0, C) & leq(C, n4))) | (a_select3(q_init, B, C) = init)))),
% 0.14/0.38 inference(modus_ponens,[status(thm)],[21, 16])).
% 0.14/0.38 tff(23,plain,
% 0.14/0.38 (~![B: $i] : ((~(leq(n0, B) & leq(B, tptp_minus_1))) | ![C: $i] : ((~(leq(n0, C) & leq(C, n4))) | (a_select3(q_init, B, C) = init)))),
% 0.14/0.38 inference(modus_ponens,[status(thm)],[22, 16])).
% 0.14/0.38 tff(24,plain,
% 0.14/0.38 (~![B: $i] : ((~(leq(succ(tptp_minus_1), B) & leq(B, tptp_minus_1))) | ![C: $i] : ((~(leq(succ(tptp_minus_1), C) & leq(C, succ(succ(succ(succ(succ(tptp_minus_1)))))))) | (a_select3(q_init, B, C) = init)))),
% 0.14/0.38 inference(modus_ponens,[status(thm)],[23, 15])).
% 0.14/0.38 tff(25,plain,
% 0.14/0.38 (~![B: $i] : ((~(leq(succ(tptp_minus_1), B) & leq(B, tptp_minus_1))) | ![C: $i] : ((~(leq(succ(tptp_minus_1), C) & leq(C, succ(succ(succ(succ(succ(tptp_minus_1)))))))) | (a_select3(q_init, B, C) = init)))),
% 0.14/0.38 inference(modus_ponens,[status(thm)],[24, 14])).
% 0.14/0.38 tff(26,plain,
% 0.14/0.38 (~![B: $i] : ((~(leq(succ(tptp_minus_1), B) & leq(B, tptp_minus_1))) | ![C: $i] : ((~(leq(succ(tptp_minus_1), C) & leq(C, succ(succ(succ(succ(succ(tptp_minus_1)))))))) | (a_select3(q_init, B, C) = init)))),
% 0.14/0.38 inference(modus_ponens,[status(thm)],[25, 14])).
% 0.14/0.38 tff(27,plain,
% 0.14/0.38 (~![B: $i] : ((~(leq(succ(tptp_minus_1), B) & leq(B, tptp_minus_1))) | ![C: $i] : ((~(leq(succ(tptp_minus_1), C) & leq(C, succ(succ(succ(succ(succ(tptp_minus_1)))))))) | (a_select3(q_init, B, C) = init)))),
% 0.14/0.38 inference(modus_ponens,[status(thm)],[26, 14])).
% 0.14/0.38 tff(28,plain,
% 0.14/0.38 (leq(succ(tptp_minus_1), B!13) & leq(B!13, tptp_minus_1) & (~((~(leq(succ(tptp_minus_1), C!14) & leq(C!14, succ(succ(succ(succ(succ(tptp_minus_1)))))))) | (a_select3(q_init, B!13, C!14) = init)))),
% 0.14/0.38 inference(modus_ponens,[status(thm)],[27, 13])).
% 0.14/0.38 tff(29,plain,
% 0.14/0.38 (leq(B!13, tptp_minus_1)),
% 0.14/0.38 inference(and_elim,[status(thm)],[28])).
% 0.14/0.38 tff(30,plain,
% 0.14/0.38 (leq(succ(tptp_minus_1), B!13)),
% 0.14/0.38 inference(and_elim,[status(thm)],[28])).
% 0.14/0.38 tff(31,plain,
% 0.14/0.38 (![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)))),
% 0.14/0.38 inference(rewrite,[status(thm)],[])).
% 0.14/0.38 tff(32,plain,
% 0.14/0.38 (^[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)))))),
% 0.14/0.38 inference(bind,[status(th)],[])).
% 0.14/0.38 tff(33,plain,
% 0.14/0.38 (![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)))),
% 0.14/0.38 inference(quant_intro,[status(thm)],[32])).
% 0.14/0.38 tff(34,plain,
% 0.14/0.38 (![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))),
% 0.14/0.38 inference(rewrite,[status(thm)],[])).
% 0.14/0.38 tff(35,plain,
% 0.14/0.38 (^[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)))),
% 0.14/0.38 inference(bind,[status(th)],[])).
% 0.14/0.38 tff(36,plain,
% 0.14/0.38 (![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))),
% 0.14/0.38 inference(quant_intro,[status(thm)],[35])).
% 0.14/0.38 tff(37,axiom,(![X: $i, Y: $i, Z: $i] : ((leq(X, Y) & leq(Y, Z)) => leq(X, Z))), file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax','transitivity_leq')).
% 0.14/0.38 tff(38,plain,
% 0.14/0.38 (![X: $i, Y: $i, Z: $i] : ((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z))),
% 0.14/0.38 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.14/0.38 tff(39,plain,
% 0.14/0.38 (![X: $i, Y: $i, Z: $i] : ((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z))),
% 0.14/0.38 inference(modus_ponens,[status(thm)],[38, 34])).
% 0.14/0.38 tff(40,plain,(
% 0.14/0.38 ![X: $i, Y: $i, Z: $i] : ((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z))),
% 0.14/0.38 inference(skolemize,[status(sab)],[39])).
% 0.14/0.38 tff(41,plain,
% 0.14/0.38 (![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))),
% 0.14/0.38 inference(modus_ponens,[status(thm)],[40, 33])).
% 0.14/0.38 tff(42,plain,
% 0.14/0.38 (![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))),
% 0.14/0.38 inference(modus_ponens,[status(thm)],[41, 31])).
% 0.14/0.38 tff(43,plain,
% 0.14/0.38 (((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | ((~leq(succ(tptp_minus_1), B!13)) | leq(succ(tptp_minus_1), tptp_minus_1) | (~leq(B!13, tptp_minus_1)))) <=> ((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | (~leq(succ(tptp_minus_1), B!13)) | leq(succ(tptp_minus_1), tptp_minus_1) | (~leq(B!13, tptp_minus_1)))),
% 0.14/0.38 inference(rewrite,[status(thm)],[])).
% 0.14/0.38 tff(44,plain,
% 0.14/0.38 ((leq(succ(tptp_minus_1), tptp_minus_1) | (~leq(B!13, tptp_minus_1)) | (~leq(succ(tptp_minus_1), B!13))) <=> ((~leq(succ(tptp_minus_1), B!13)) | leq(succ(tptp_minus_1), tptp_minus_1) | (~leq(B!13, tptp_minus_1)))),
% 0.14/0.38 inference(rewrite,[status(thm)],[])).
% 0.14/0.38 tff(45,plain,
% 0.14/0.38 (((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | (leq(succ(tptp_minus_1), tptp_minus_1) | (~leq(B!13, tptp_minus_1)) | (~leq(succ(tptp_minus_1), B!13)))) <=> ((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | ((~leq(succ(tptp_minus_1), B!13)) | leq(succ(tptp_minus_1), tptp_minus_1) | (~leq(B!13, tptp_minus_1))))),
% 0.14/0.38 inference(monotonicity,[status(thm)],[44])).
% 0.14/0.38 tff(46,plain,
% 0.14/0.38 (((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | (leq(succ(tptp_minus_1), tptp_minus_1) | (~leq(B!13, tptp_minus_1)) | (~leq(succ(tptp_minus_1), B!13)))) <=> ((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | (~leq(succ(tptp_minus_1), B!13)) | leq(succ(tptp_minus_1), tptp_minus_1) | (~leq(B!13, tptp_minus_1)))),
% 0.14/0.38 inference(transitivity,[status(thm)],[45, 43])).
% 0.14/0.38 tff(47,plain,
% 0.14/0.38 ((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | (leq(succ(tptp_minus_1), tptp_minus_1) | (~leq(B!13, tptp_minus_1)) | (~leq(succ(tptp_minus_1), B!13)))),
% 0.14/0.38 inference(quant_inst,[status(thm)],[])).
% 0.14/0.38 tff(48,plain,
% 0.14/0.38 ((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | (~leq(succ(tptp_minus_1), B!13)) | leq(succ(tptp_minus_1), tptp_minus_1) | (~leq(B!13, tptp_minus_1))),
% 0.14/0.38 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.14/0.38 tff(49,plain,
% 0.14/0.38 (leq(succ(tptp_minus_1), tptp_minus_1)),
% 0.14/0.38 inference(unit_resolution,[status(thm)],[48, 42, 30, 29])).
% 0.14/0.38 tff(50,plain,
% 0.14/0.38 ((~(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))),
% 0.14/0.38 inference(tautology,[status(thm)],[])).
% 0.14/0.38 tff(51,plain,
% 0.14/0.38 ((~(leq(succ(tptp_minus_1), tptp_minus_1) <=> gt(succ(tptp_minus_1), succ(tptp_minus_1)))) | gt(succ(tptp_minus_1), succ(tptp_minus_1))),
% 0.14/0.38 inference(unit_resolution,[status(thm)],[50, 49])).
% 0.14/0.38 tff(52,plain,
% 0.14/0.38 (gt(succ(tptp_minus_1), succ(tptp_minus_1))),
% 0.14/0.38 inference(unit_resolution,[status(thm)],[51, 9])).
% 0.14/0.38 tff(53,plain,
% 0.14/0.38 (^[X: $i] : refl((~gt(X, X)) <=> (~gt(X, X)))),
% 0.14/0.38 inference(bind,[status(th)],[])).
% 0.14/0.38 tff(54,plain,
% 0.14/0.38 (![X: $i] : (~gt(X, X)) <=> ![X: $i] : (~gt(X, X))),
% 0.14/0.38 inference(quant_intro,[status(thm)],[53])).
% 0.14/0.38 tff(55,plain,
% 0.14/0.38 (![X: $i] : (~gt(X, X)) <=> ![X: $i] : (~gt(X, X))),
% 0.14/0.38 inference(rewrite,[status(thm)],[])).
% 0.14/0.38 tff(56,axiom,(![X: $i] : (~gt(X, X))), file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax','irreflexivity_gt')).
% 0.14/0.38 tff(57,plain,
% 0.14/0.38 (![X: $i] : (~gt(X, X))),
% 0.14/0.38 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.14/0.38 tff(58,plain,(
% 0.14/0.38 ![X: $i] : (~gt(X, X))),
% 0.14/0.38 inference(skolemize,[status(sab)],[57])).
% 0.14/0.38 tff(59,plain,
% 0.14/0.38 (![X: $i] : (~gt(X, X))),
% 0.14/0.38 inference(modus_ponens,[status(thm)],[58, 54])).
% 0.14/0.38 tff(60,plain,
% 0.14/0.38 ((~![X: $i] : (~gt(X, X))) | (~gt(succ(tptp_minus_1), succ(tptp_minus_1)))),
% 0.14/0.39 inference(quant_inst,[status(thm)],[])).
% 0.14/0.39 tff(61,plain,
% 0.14/0.39 ($false),
% 0.14/0.39 inference(unit_resolution,[status(thm)],[60, 59, 52])).
% 0.14/0.39 % SZS output end Proof
%------------------------------------------------------------------------------