TSTP Solution File: SYN293-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN293-1 : TPTP v8.1.0. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n021.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 23:54:33 EDT 2022
% Result : Unsatisfiable 0.74s 0.73s
% Output : Proof 0.74s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYN293-1 : TPTP v8.1.0. Released v1.1.0.
% 0.03/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n021.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
% 0.12/0.33 % DateTime : Mon Sep 5 02:19:16 EDT 2022
% 0.12/0.33 % 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.
% 0.74/0.73 % SZS status Unsatisfiable
% 0.74/0.73 % SZS output start Proof
% 0.74/0.73 tff(q0_type, type, (
% 0.74/0.73 q0: ( $i * $i ) > $o)).
% 0.74/0.73 tff(d_type, type, (
% 0.74/0.73 d: $i)).
% 0.74/0.73 tff(a_type, type, (
% 0.74/0.73 a: $i)).
% 0.74/0.73 tff(p0_type, type, (
% 0.74/0.73 p0: ( $i * $i ) > $o)).
% 0.74/0.73 tff(b_type, type, (
% 0.74/0.73 b: $i)).
% 0.74/0.73 tff(q1_type, type, (
% 0.74/0.73 q1: ( $i * $i * $i ) > $o)).
% 0.74/0.73 tff(k1_type, type, (
% 0.74/0.73 k1: $i > $o)).
% 0.74/0.73 tff(n0_type, type, (
% 0.74/0.73 n0: ( $i * $i ) > $o)).
% 0.74/0.73 tff(c_type, type, (
% 0.74/0.73 c: $i)).
% 0.74/0.73 tff(1,plain,
% 0.74/0.73 (^[X: $i] : refl(q0(X, d) <=> q0(X, d))),
% 0.74/0.73 inference(bind,[status(th)],[])).
% 0.74/0.73 tff(2,plain,
% 0.74/0.73 (![X: $i] : q0(X, d) <=> ![X: $i] : q0(X, d)),
% 0.74/0.73 inference(quant_intro,[status(thm)],[1])).
% 0.74/0.73 tff(3,plain,
% 0.74/0.73 (![X: $i] : q0(X, d) <=> ![X: $i] : q0(X, d)),
% 0.74/0.73 inference(rewrite,[status(thm)],[])).
% 0.74/0.73 tff(4,axiom,(![X: $i] : q0(X, d)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_17')).
% 0.74/0.73 tff(5,plain,
% 0.74/0.73 (![X: $i] : q0(X, d)),
% 0.74/0.73 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.74/0.73 tff(6,plain,(
% 0.74/0.73 ![X: $i] : q0(X, d)),
% 0.74/0.73 inference(skolemize,[status(sab)],[5])).
% 0.74/0.73 tff(7,plain,
% 0.74/0.73 (![X: $i] : q0(X, d)),
% 0.74/0.73 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.74/0.73 tff(8,plain,
% 0.74/0.73 ((~![X: $i] : q0(X, d)) | q0(a, d)),
% 0.74/0.73 inference(quant_inst,[status(thm)],[])).
% 0.74/0.73 tff(9,plain,
% 0.74/0.73 (q0(a, d)),
% 0.74/0.73 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.74/0.73 tff(10,assumption,(~p0(b, b)), introduced(assumption)).
% 0.74/0.73 tff(11,plain,
% 0.74/0.73 (^[X: $i] : refl(p0(b, X) <=> p0(b, X))),
% 0.74/0.73 inference(bind,[status(th)],[])).
% 0.74/0.73 tff(12,plain,
% 0.74/0.73 (![X: $i] : p0(b, X) <=> ![X: $i] : p0(b, X)),
% 0.74/0.73 inference(quant_intro,[status(thm)],[11])).
% 0.74/0.73 tff(13,plain,
% 0.74/0.73 (![X: $i] : p0(b, X) <=> ![X: $i] : p0(b, X)),
% 0.74/0.73 inference(rewrite,[status(thm)],[])).
% 0.74/0.73 tff(14,axiom,(![X: $i] : p0(b, X)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_14')).
% 0.74/0.73 tff(15,plain,
% 0.74/0.73 (![X: $i] : p0(b, X)),
% 0.74/0.73 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.74/0.73 tff(16,plain,(
% 0.74/0.73 ![X: $i] : p0(b, X)),
% 0.74/0.73 inference(skolemize,[status(sab)],[15])).
% 0.74/0.73 tff(17,plain,
% 0.74/0.73 (![X: $i] : p0(b, X)),
% 0.74/0.73 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.74/0.73 tff(18,plain,
% 0.74/0.73 ((~![X: $i] : p0(b, X)) | p0(b, b)),
% 0.74/0.73 inference(quant_inst,[status(thm)],[])).
% 0.74/0.73 tff(19,plain,
% 0.74/0.73 ($false),
% 0.74/0.73 inference(unit_resolution,[status(thm)],[18, 17, 10])).
% 0.74/0.73 tff(20,plain,(p0(b, b)), inference(lemma,lemma(discharge,[]))).
% 0.74/0.73 tff(21,plain,
% 0.74/0.73 ((~q1(d, d, a)) <=> (~q1(d, d, a))),
% 0.74/0.73 inference(rewrite,[status(thm)],[])).
% 0.74/0.73 tff(22,axiom,(~q1(d, d, a)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this')).
% 0.74/0.73 tff(23,plain,
% 0.74/0.73 (~q1(d, d, a)),
% 0.74/0.73 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.74/0.73 tff(24,plain,
% 0.74/0.73 (^[I: $i, J: $i] : refl((k1(I) | (~n0(J, I))) <=> (k1(I) | (~n0(J, I))))),
% 0.74/0.73 inference(bind,[status(th)],[])).
% 0.74/0.73 tff(25,plain,
% 0.74/0.73 (![I: $i, J: $i] : (k1(I) | (~n0(J, I))) <=> ![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 0.74/0.73 inference(quant_intro,[status(thm)],[24])).
% 0.74/0.73 tff(26,plain,
% 0.74/0.73 (![I: $i, J: $i] : (k1(I) | (~n0(J, I))) <=> ![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 0.74/0.73 inference(rewrite,[status(thm)],[])).
% 0.74/0.73 tff(27,axiom,(![I: $i, J: $i] : (k1(I) | (~n0(J, I)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_001')).
% 0.74/0.73 tff(28,plain,
% 0.74/0.73 (![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 0.74/0.73 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.74/0.73 tff(29,plain,(
% 0.74/0.73 ![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 0.74/0.73 inference(skolemize,[status(sab)],[28])).
% 0.74/0.73 tff(30,plain,
% 0.74/0.73 (![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 0.74/0.73 inference(modus_ponens,[status(thm)],[29, 25])).
% 0.74/0.73 tff(31,plain,
% 0.74/0.73 (n0(c, d) <=> n0(c, d)),
% 0.74/0.73 inference(rewrite,[status(thm)],[])).
% 0.74/0.73 tff(32,axiom,(n0(c, d)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_34')).
% 0.74/0.73 tff(33,plain,
% 0.74/0.73 (n0(c, d)),
% 0.74/0.73 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.74/0.73 tff(34,plain,
% 0.74/0.73 (((~![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)))),
% 0.74/0.73 inference(rewrite,[status(thm)],[])).
% 0.74/0.73 tff(35,plain,
% 0.74/0.73 ((~![I: $i, J: $i] : (k1(I) | (~n0(J, I)))) | (k1(d) | (~n0(c, d)))),
% 0.74/0.73 inference(quant_inst,[status(thm)],[])).
% 0.74/0.73 tff(36,plain,
% 0.74/0.73 ((~![I: $i, J: $i] : (k1(I) | (~n0(J, I)))) | k1(d) | (~n0(c, d))),
% 0.74/0.73 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.74/0.73 tff(37,plain,
% 0.74/0.73 (k1(d)),
% 0.74/0.73 inference(unit_resolution,[status(thm)],[36, 33, 30])).
% 0.74/0.73 tff(38,plain,
% 0.74/0.73 (^[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)))),
% 0.74/0.73 inference(bind,[status(th)],[])).
% 0.74/0.73 tff(39,plain,
% 0.74/0.73 (![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))),
% 0.74/0.73 inference(quant_intro,[status(thm)],[38])).
% 0.74/0.73 tff(40,plain,
% 0.74/0.73 (![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))),
% 0.74/0.73 inference(rewrite,[status(thm)],[])).
% 0.74/0.73 tff(41,plain,
% 0.74/0.73 (^[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))))),
% 0.74/0.73 inference(bind,[status(th)],[])).
% 0.74/0.73 tff(42,plain,
% 0.74/0.73 (![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))),
% 0.74/0.73 inference(quant_intro,[status(thm)],[41])).
% 0.74/0.73 tff(43,axiom,(![E: $i, F: $i, G: $i] : (((q1(E, E, F) | (~p0(G, G))) | (~q0(F, E))) | (~k1(E)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_109')).
% 0.74/0.73 tff(44,plain,
% 0.74/0.73 (![E: $i, F: $i, G: $i] : ((~p0(G, G)) | (~k1(E)) | (~q0(F, E)) | q1(E, E, F))),
% 0.74/0.73 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.74/0.73 tff(45,plain,
% 0.74/0.73 (![E: $i, F: $i, G: $i] : ((~p0(G, G)) | (~k1(E)) | (~q0(F, E)) | q1(E, E, F))),
% 0.74/0.73 inference(modus_ponens,[status(thm)],[44, 40])).
% 0.74/0.73 tff(46,plain,(
% 0.74/0.73 ![E: $i, F: $i, G: $i] : ((~p0(G, G)) | (~k1(E)) | (~q0(F, E)) | q1(E, E, F))),
% 0.74/0.73 inference(skolemize,[status(sab)],[45])).
% 0.74/0.73 tff(47,plain,
% 0.74/0.73 (![E: $i, F: $i, G: $i] : ((~p0(G, G)) | (~k1(E)) | (~q0(F, E)) | q1(E, E, F))),
% 0.74/0.73 inference(modus_ponens,[status(thm)],[46, 39])).
% 0.74/0.73 tff(48,plain,
% 0.74/0.73 (((~![E: $i, F: $i, G: $i] : ((~p0(G, G)) | (~k1(E)) | (~q0(F, E)) | q1(E, E, F))) | ((~k1(d)) | q1(d, d, a) | (~p0(b, b)) | (~q0(a, d)))) <=> ((~![E: $i, F: $i, G: $i] : ((~p0(G, G)) | (~k1(E)) | (~q0(F, E)) | q1(E, E, F))) | (~k1(d)) | q1(d, d, a) | (~p0(b, b)) | (~q0(a, d)))),
% 0.74/0.73 inference(rewrite,[status(thm)],[])).
% 0.74/0.73 tff(49,plain,
% 0.74/0.73 (((~p0(b, b)) | (~k1(d)) | (~q0(a, d)) | q1(d, d, a)) <=> ((~k1(d)) | q1(d, d, a) | (~p0(b, b)) | (~q0(a, d)))),
% 0.74/0.73 inference(rewrite,[status(thm)],[])).
% 0.74/0.73 tff(50,plain,
% 0.74/0.73 (((~![E: $i, F: $i, G: $i] : ((~p0(G, G)) | (~k1(E)) | (~q0(F, E)) | q1(E, E, F))) | ((~p0(b, b)) | (~k1(d)) | (~q0(a, d)) | q1(d, d, a))) <=> ((~![E: $i, F: $i, G: $i] : ((~p0(G, G)) | (~k1(E)) | (~q0(F, E)) | q1(E, E, F))) | ((~k1(d)) | q1(d, d, a) | (~p0(b, b)) | (~q0(a, d))))),
% 0.74/0.73 inference(monotonicity,[status(thm)],[49])).
% 0.74/0.73 tff(51,plain,
% 0.74/0.73 (((~![E: $i, F: $i, G: $i] : ((~p0(G, G)) | (~k1(E)) | (~q0(F, E)) | q1(E, E, F))) | ((~p0(b, b)) | (~k1(d)) | (~q0(a, d)) | q1(d, d, a))) <=> ((~![E: $i, F: $i, G: $i] : ((~p0(G, G)) | (~k1(E)) | (~q0(F, E)) | q1(E, E, F))) | (~k1(d)) | q1(d, d, a) | (~p0(b, b)) | (~q0(a, d)))),
% 0.74/0.73 inference(transitivity,[status(thm)],[50, 48])).
% 0.74/0.73 tff(52,plain,
% 0.74/0.73 ((~![E: $i, F: $i, G: $i] : ((~p0(G, G)) | (~k1(E)) | (~q0(F, E)) | q1(E, E, F))) | ((~p0(b, b)) | (~k1(d)) | (~q0(a, d)) | q1(d, d, a))),
% 0.74/0.73 inference(quant_inst,[status(thm)],[])).
% 0.74/0.74 tff(53,plain,
% 0.74/0.74 ((~![E: $i, F: $i, G: $i] : ((~p0(G, G)) | (~k1(E)) | (~q0(F, E)) | q1(E, E, F))) | (~k1(d)) | q1(d, d, a) | (~p0(b, b)) | (~q0(a, d))),
% 0.74/0.74 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.74/0.74 tff(54,plain,
% 0.74/0.74 ($false),
% 0.74/0.74 inference(unit_resolution,[status(thm)],[53, 47, 37, 23, 20, 9])).
% 0.74/0.74 % SZS output end Proof
%------------------------------------------------------------------------------