TSTP Solution File: SYN294-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN294-1 : TPTP v8.1.0. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n005.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 23:54:34 EDT 2022
% Result : Unsatisfiable 0.20s 0.50s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYN294-1 : TPTP v8.1.0. Released v1.1.0.
% 0.07/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n005.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Mon Sep 5 02:22:33 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.20/0.50 % SZS status Unsatisfiable
% 0.20/0.50 % SZS output start Proof
% 0.20/0.50 tff(p0_type, type, (
% 0.20/0.50 p0: ( $i * $i ) > $o)).
% 0.20/0.50 tff(b_type, type, (
% 0.20/0.50 b: $i)).
% 0.20/0.50 tff(q1_type, type, (
% 0.20/0.50 q1: ( $i * $i * $i ) > $o)).
% 0.20/0.50 tff(c_type, type, (
% 0.20/0.50 c: $i)).
% 0.20/0.50 tff(d_type, type, (
% 0.20/0.50 d: $i)).
% 0.20/0.50 tff(k1_type, type, (
% 0.20/0.50 k1: $i > $o)).
% 0.20/0.50 tff(n0_type, type, (
% 0.20/0.50 n0: ( $i * $i ) > $o)).
% 0.20/0.50 tff(q0_type, type, (
% 0.20/0.50 q0: ( $i * $i ) > $o)).
% 0.20/0.50 tff(1,assumption,(~p0(b, b)), introduced(assumption)).
% 0.20/0.50 tff(2,plain,
% 0.20/0.50 (^[X: $i] : refl(p0(b, X) <=> p0(b, X))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(3,plain,
% 0.20/0.50 (![X: $i] : p0(b, X) <=> ![X: $i] : p0(b, X)),
% 0.20/0.50 inference(quant_intro,[status(thm)],[2])).
% 0.20/0.50 tff(4,plain,
% 0.20/0.50 (![X: $i] : p0(b, X) <=> ![X: $i] : p0(b, X)),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(5,axiom,(![X: $i] : p0(b, X)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_14')).
% 0.20/0.50 tff(6,plain,
% 0.20/0.50 (![X: $i] : p0(b, X)),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.20/0.50 tff(7,plain,(
% 0.20/0.50 ![X: $i] : p0(b, X)),
% 0.20/0.50 inference(skolemize,[status(sab)],[6])).
% 0.20/0.50 tff(8,plain,
% 0.20/0.50 (![X: $i] : p0(b, X)),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.20/0.50 tff(9,plain,
% 0.20/0.50 ((~![X: $i] : p0(b, X)) | p0(b, b)),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(10,plain,
% 0.20/0.50 ($false),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.20/0.50 tff(11,plain,(p0(b, b)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.50 tff(12,plain,
% 0.20/0.50 ((~q1(d, d, c)) <=> (~q1(d, d, c))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(13,axiom,(~q1(d, d, c)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this')).
% 0.20/0.50 tff(14,plain,
% 0.20/0.50 (~q1(d, d, c)),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.20/0.50 tff(15,plain,
% 0.20/0.50 (^[I: $i, J: $i] : refl((k1(I) | (~n0(J, I))) <=> (k1(I) | (~n0(J, I))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(16,plain,
% 0.20/0.50 (![I: $i, J: $i] : (k1(I) | (~n0(J, I))) <=> ![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[15])).
% 0.20/0.50 tff(17,plain,
% 0.20/0.50 (![I: $i, J: $i] : (k1(I) | (~n0(J, I))) <=> ![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(18,axiom,(![I: $i, J: $i] : (k1(I) | (~n0(J, I)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_001')).
% 0.20/0.50 tff(19,plain,
% 0.20/0.50 (![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.20/0.50 tff(20,plain,(
% 0.20/0.50 ![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 0.20/0.50 inference(skolemize,[status(sab)],[19])).
% 0.20/0.50 tff(21,plain,
% 0.20/0.50 (![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[20, 16])).
% 0.20/0.50 tff(22,plain,
% 0.20/0.50 (n0(c, d) <=> n0(c, d)),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(23,axiom,(n0(c, d)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_34')).
% 0.20/0.50 tff(24,plain,
% 0.20/0.50 (n0(c, d)),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.20/0.50 tff(25,plain,
% 0.20/0.50 (((~![I: $i, J: $i] : (k1(I) | (~n0(J, I)))) | (k1(d) | (~n0(c, d)))) <=> ((~![I: $i, J: $i] : (k1(I) | (~n0(J, I)))) | k1(d) | (~n0(c, d)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(26,plain,
% 0.20/0.50 ((~![I: $i, J: $i] : (k1(I) | (~n0(J, I)))) | (k1(d) | (~n0(c, d)))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(27,plain,
% 0.20/0.50 ((~![I: $i, J: $i] : (k1(I) | (~n0(J, I)))) | k1(d) | (~n0(c, d))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.20/0.50 tff(28,plain,
% 0.20/0.50 (k1(d)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[27, 24, 21])).
% 0.20/0.50 tff(29,plain,
% 0.20/0.50 (^[E: $i, F: $i, G: $i] : refl(((~p0(G, G)) | (~k1(E)) | (~q0(F, E)) | q1(E, E, F)) <=> ((~p0(G, G)) | (~k1(E)) | (~q0(F, E)) | q1(E, E, F)))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(30,plain,
% 0.20/0.50 (![E: $i, F: $i, G: $i] : ((~p0(G, G)) | (~k1(E)) | (~q0(F, E)) | q1(E, E, F)) <=> ![E: $i, F: $i, G: $i] : ((~p0(G, G)) | (~k1(E)) | (~q0(F, E)) | q1(E, E, F))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[29])).
% 0.20/0.50 tff(31,plain,
% 0.20/0.50 (![E: $i, F: $i, G: $i] : ((~p0(G, G)) | (~k1(E)) | (~q0(F, E)) | q1(E, E, F)) <=> ![E: $i, F: $i, G: $i] : ((~p0(G, G)) | (~k1(E)) | (~q0(F, E)) | q1(E, E, F))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(32,plain,
% 0.20/0.50 (^[E: $i, F: $i, G: $i] : trans(monotonicity(trans(monotonicity(rewrite((q1(E, E, F) | (~p0(G, G))) <=> ((~p0(G, G)) | q1(E, E, F))), (((q1(E, E, F) | (~p0(G, G))) | (~q0(F, E))) <=> (((~p0(G, G)) | q1(E, E, F)) | (~q0(F, E))))), rewrite((((~p0(G, G)) | q1(E, E, F)) | (~q0(F, E))) <=> ((~p0(G, G)) | (~q0(F, E)) | q1(E, E, F))), (((q1(E, E, F) | (~p0(G, G))) | (~q0(F, E))) <=> ((~p0(G, G)) | (~q0(F, E)) | q1(E, E, F)))), ((((q1(E, E, F) | (~p0(G, G))) | (~q0(F, E))) | (~k1(E))) <=> (((~p0(G, G)) | (~q0(F, E)) | q1(E, E, F)) | (~k1(E))))), rewrite((((~p0(G, G)) | (~q0(F, E)) | q1(E, E, F)) | (~k1(E))) <=> ((~p0(G, G)) | (~k1(E)) | (~q0(F, E)) | q1(E, E, F))), ((((q1(E, E, F) | (~p0(G, G))) | (~q0(F, E))) | (~k1(E))) <=> ((~p0(G, G)) | (~k1(E)) | (~q0(F, E)) | q1(E, E, F))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(33,plain,
% 0.20/0.51 (![E: $i, F: $i, G: $i] : (((q1(E, E, F) | (~p0(G, G))) | (~q0(F, E))) | (~k1(E))) <=> ![E: $i, F: $i, G: $i] : ((~p0(G, G)) | (~k1(E)) | (~q0(F, E)) | q1(E, E, F))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[32])).
% 0.20/0.51 tff(34,axiom,(![E: $i, F: $i, G: $i] : (((q1(E, E, F) | (~p0(G, G))) | (~q0(F, E))) | (~k1(E)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_109')).
% 0.20/0.51 tff(35,plain,
% 0.20/0.51 (![E: $i, F: $i, G: $i] : ((~p0(G, G)) | (~k1(E)) | (~q0(F, E)) | q1(E, E, F))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.20/0.51 tff(36,plain,
% 0.20/0.51 (![E: $i, F: $i, G: $i] : ((~p0(G, G)) | (~k1(E)) | (~q0(F, E)) | q1(E, E, F))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[35, 31])).
% 0.20/0.51 tff(37,plain,(
% 0.20/0.51 ![E: $i, F: $i, G: $i] : ((~p0(G, G)) | (~k1(E)) | (~q0(F, E)) | q1(E, E, F))),
% 0.20/0.51 inference(skolemize,[status(sab)],[36])).
% 0.20/0.51 tff(38,plain,
% 0.20/0.51 (![E: $i, F: $i, G: $i] : ((~p0(G, G)) | (~k1(E)) | (~q0(F, E)) | q1(E, E, F))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[37, 30])).
% 0.20/0.51 tff(39,assumption,(~q0(c, d)), introduced(assumption)).
% 0.20/0.51 tff(40,plain,
% 0.20/0.51 (^[X: $i] : refl(q0(X, d) <=> q0(X, d))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(41,plain,
% 0.20/0.51 (![X: $i] : q0(X, d) <=> ![X: $i] : q0(X, d)),
% 0.20/0.51 inference(quant_intro,[status(thm)],[40])).
% 0.20/0.51 tff(42,plain,
% 0.20/0.51 (![X: $i] : q0(X, d) <=> ![X: $i] : q0(X, d)),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(43,axiom,(![X: $i] : q0(X, d)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_17')).
% 0.20/0.51 tff(44,plain,
% 0.20/0.51 (![X: $i] : q0(X, d)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.20/0.51 tff(45,plain,(
% 0.20/0.51 ![X: $i] : q0(X, d)),
% 0.20/0.51 inference(skolemize,[status(sab)],[44])).
% 0.20/0.51 tff(46,plain,
% 0.20/0.51 (![X: $i] : q0(X, d)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[45, 41])).
% 0.20/0.51 tff(47,plain,
% 0.20/0.51 ((~![X: $i] : q0(X, d)) | q0(c, d)),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(48,plain,
% 0.20/0.51 ($false),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[47, 46, 39])).
% 0.20/0.51 tff(49,plain,(q0(c, d)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.51 tff(50,plain,
% 0.20/0.51 (((~![E: $i, F: $i, G: $i] : ((~p0(G, G)) | (~k1(E)) | (~q0(F, E)) | q1(E, E, F))) | ((~q0(c, d)) | q1(d, d, c) | (~k1(d)) | (~p0(b, b)))) <=> ((~![E: $i, F: $i, G: $i] : ((~p0(G, G)) | (~k1(E)) | (~q0(F, E)) | q1(E, E, F))) | (~q0(c, d)) | q1(d, d, c) | (~k1(d)) | (~p0(b, b)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(51,plain,
% 0.20/0.51 (((~p0(b, b)) | (~k1(d)) | (~q0(c, d)) | q1(d, d, c)) <=> ((~q0(c, d)) | q1(d, d, c) | (~k1(d)) | (~p0(b, b)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(52,plain,
% 0.20/0.51 (((~![E: $i, F: $i, G: $i] : ((~p0(G, G)) | (~k1(E)) | (~q0(F, E)) | q1(E, E, F))) | ((~p0(b, b)) | (~k1(d)) | (~q0(c, d)) | q1(d, d, c))) <=> ((~![E: $i, F: $i, G: $i] : ((~p0(G, G)) | (~k1(E)) | (~q0(F, E)) | q1(E, E, F))) | ((~q0(c, d)) | q1(d, d, c) | (~k1(d)) | (~p0(b, b))))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[51])).
% 0.20/0.51 tff(53,plain,
% 0.20/0.51 (((~![E: $i, F: $i, G: $i] : ((~p0(G, G)) | (~k1(E)) | (~q0(F, E)) | q1(E, E, F))) | ((~p0(b, b)) | (~k1(d)) | (~q0(c, d)) | q1(d, d, c))) <=> ((~![E: $i, F: $i, G: $i] : ((~p0(G, G)) | (~k1(E)) | (~q0(F, E)) | q1(E, E, F))) | (~q0(c, d)) | q1(d, d, c) | (~k1(d)) | (~p0(b, b)))),
% 0.20/0.51 inference(transitivity,[status(thm)],[52, 50])).
% 0.20/0.51 tff(54,plain,
% 0.20/0.51 ((~![E: $i, F: $i, G: $i] : ((~p0(G, G)) | (~k1(E)) | (~q0(F, E)) | q1(E, E, F))) | ((~p0(b, b)) | (~k1(d)) | (~q0(c, d)) | q1(d, d, c))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(55,plain,
% 0.20/0.52 ((~![E: $i, F: $i, G: $i] : ((~p0(G, G)) | (~k1(E)) | (~q0(F, E)) | q1(E, E, F))) | (~q0(c, d)) | q1(d, d, c) | (~k1(d)) | (~p0(b, b))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.20/0.52 tff(56,plain,
% 0.20/0.52 ($false),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[55, 49, 38, 28, 14, 11])).
% 0.20/0.52 % SZS output end Proof
%------------------------------------------------------------------------------