TSTP Solution File: SYN407+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN407+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n020.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 23:55:11 EDT 2022
% Result : Theorem 0.14s 0.40s
% Output : Proof 0.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SYN407+1 : TPTP v8.1.0. Released v2.0.0.
% 0.11/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.35 % Computer : n020.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Mon Sep 5 03:12:44 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.35 Usage: tptp [options] [-file:]file
% 0.14/0.35 -h, -? prints this message.
% 0.14/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.35 -m, -model generate model.
% 0.14/0.35 -p, -proof generate proof.
% 0.14/0.35 -c, -core generate unsat core of named formulas.
% 0.14/0.35 -st, -statistics display statistics.
% 0.14/0.35 -t:timeout set timeout (in second).
% 0.14/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.35 -<param>:<value> configuration parameter and value.
% 0.14/0.35 -o:<output-file> file to place output in.
% 0.14/0.40 % SZS status Theorem
% 0.14/0.40 % SZS output start Proof
% 0.14/0.40 tff(h_type, type, (
% 0.14/0.40 h: $i > $o)).
% 0.14/0.40 tff(tptp_fun_Y_0_type, type, (
% 0.14/0.40 tptp_fun_Y_0: $i)).
% 0.14/0.40 tff(f_type, type, (
% 0.14/0.40 f: $i > $o)).
% 0.14/0.40 tff(g_type, type, (
% 0.14/0.40 g: $i > $o)).
% 0.14/0.40 tff(1,plain,
% 0.14/0.40 ((~![Y: $i] : (g(Y) | (~f(Y)))) <=> (~![Y: $i] : (g(Y) | (~f(Y))))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(2,plain,
% 0.14/0.40 ((~(![X: $i] : (f(X) => (g(X) | h(X))) => (![Y: $i] : (f(Y) => g(Y)) | ?[Z: $i] : (f(Z) & h(Z))))) <=> (~(?[Z: $i] : (f(Z) & h(Z)) | ![Y: $i] : (g(Y) | (~f(Y))) | (~![X: $i] : (h(X) | g(X) | (~f(X))))))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(3,axiom,(~(![X: $i] : (f(X) => (g(X) | h(X))) => (![Y: $i] : (f(Y) => g(Y)) | ?[Z: $i] : (f(Z) & h(Z))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','kalish241')).
% 0.14/0.40 tff(4,plain,
% 0.14/0.40 (~(?[Z: $i] : (f(Z) & h(Z)) | ![Y: $i] : (g(Y) | (~f(Y))) | (~![X: $i] : (h(X) | g(X) | (~f(X)))))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.14/0.40 tff(5,plain,
% 0.14/0.40 (~![Y: $i] : (g(Y) | (~f(Y)))),
% 0.14/0.40 inference(or_elim,[status(thm)],[4])).
% 0.14/0.40 tff(6,plain,
% 0.14/0.40 (~![Y: $i] : (g(Y) | (~f(Y)))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.14/0.40 tff(7,plain,
% 0.14/0.40 (~![Y: $i] : (g(Y) | (~f(Y)))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.14/0.40 tff(8,plain,
% 0.14/0.40 (~![Y: $i] : (g(Y) | (~f(Y)))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[7, 1])).
% 0.14/0.40 tff(9,plain,
% 0.14/0.40 (~![Y: $i] : (g(Y) | (~f(Y)))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[8, 1])).
% 0.14/0.40 tff(10,plain,
% 0.14/0.40 (~![Y: $i] : (g(Y) | (~f(Y)))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[9, 1])).
% 0.14/0.40 tff(11,plain,
% 0.14/0.40 (~![Y: $i] : (g(Y) | (~f(Y)))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[10, 1])).
% 0.14/0.40 tff(12,plain,(
% 0.14/0.40 ~(g(Y!0) | (~f(Y!0)))),
% 0.14/0.40 inference(skolemize,[status(sab)],[11])).
% 0.14/0.40 tff(13,plain,
% 0.14/0.40 (f(Y!0)),
% 0.14/0.40 inference(or_elim,[status(thm)],[12])).
% 0.14/0.40 tff(14,plain,
% 0.14/0.40 (^[Z: $i] : refl(((~f(Z)) | (~h(Z))) <=> ((~f(Z)) | (~h(Z))))),
% 0.14/0.40 inference(bind,[status(th)],[])).
% 0.14/0.40 tff(15,plain,
% 0.14/0.40 (![Z: $i] : ((~f(Z)) | (~h(Z))) <=> ![Z: $i] : ((~f(Z)) | (~h(Z)))),
% 0.14/0.40 inference(quant_intro,[status(thm)],[14])).
% 0.14/0.40 tff(16,plain,
% 0.14/0.40 (^[Z: $i] : trans(monotonicity(rewrite((f(Z) & h(Z)) <=> (~((~f(Z)) | (~h(Z))))), ((~(f(Z) & h(Z))) <=> (~(~((~f(Z)) | (~h(Z))))))), rewrite((~(~((~f(Z)) | (~h(Z))))) <=> ((~f(Z)) | (~h(Z)))), ((~(f(Z) & h(Z))) <=> ((~f(Z)) | (~h(Z)))))),
% 0.14/0.40 inference(bind,[status(th)],[])).
% 0.14/0.40 tff(17,plain,
% 0.14/0.40 (![Z: $i] : (~(f(Z) & h(Z))) <=> ![Z: $i] : ((~f(Z)) | (~h(Z)))),
% 0.14/0.40 inference(quant_intro,[status(thm)],[16])).
% 0.14/0.40 tff(18,plain,
% 0.14/0.40 ((~?[Z: $i] : (f(Z) & h(Z))) <=> (~?[Z: $i] : (f(Z) & h(Z)))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(19,plain,
% 0.14/0.40 (~?[Z: $i] : (f(Z) & h(Z))),
% 0.14/0.40 inference(or_elim,[status(thm)],[4])).
% 0.14/0.40 tff(20,plain,
% 0.14/0.40 (~?[Z: $i] : (f(Z) & h(Z))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.14/0.40 tff(21,plain,
% 0.14/0.40 (~?[Z: $i] : (f(Z) & h(Z))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[20, 18])).
% 0.14/0.40 tff(22,plain,
% 0.14/0.40 (~?[Z: $i] : (f(Z) & h(Z))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[21, 18])).
% 0.14/0.40 tff(23,plain,
% 0.14/0.40 (~?[Z: $i] : (f(Z) & h(Z))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[22, 18])).
% 0.14/0.40 tff(24,plain,
% 0.14/0.40 (~?[Z: $i] : (f(Z) & h(Z))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[23, 18])).
% 0.14/0.40 tff(25,plain,
% 0.14/0.40 (~?[Z: $i] : (f(Z) & h(Z))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[24, 18])).
% 0.14/0.40 tff(26,plain,
% 0.14/0.40 (^[Z: $i] : refl($oeq((~(f(Z) & h(Z))), (~(f(Z) & h(Z)))))),
% 0.14/0.40 inference(bind,[status(th)],[])).
% 0.14/0.40 tff(27,plain,(
% 0.14/0.40 ![Z: $i] : (~(f(Z) & h(Z)))),
% 0.14/0.40 inference(nnf-neg,[status(sab)],[25, 26])).
% 0.14/0.40 tff(28,plain,
% 0.14/0.40 (![Z: $i] : ((~f(Z)) | (~h(Z)))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[27, 17])).
% 0.14/0.40 tff(29,plain,
% 0.14/0.40 (![Z: $i] : ((~f(Z)) | (~h(Z)))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[28, 15])).
% 0.14/0.40 tff(30,plain,
% 0.14/0.40 (((~![Z: $i] : ((~f(Z)) | (~h(Z)))) | ((~f(Y!0)) | (~h(Y!0)))) <=> ((~![Z: $i] : ((~f(Z)) | (~h(Z)))) | (~f(Y!0)) | (~h(Y!0)))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(31,plain,
% 0.14/0.40 ((~![Z: $i] : ((~f(Z)) | (~h(Z)))) | ((~f(Y!0)) | (~h(Y!0)))),
% 0.14/0.40 inference(quant_inst,[status(thm)],[])).
% 0.14/0.40 tff(32,plain,
% 0.14/0.40 ((~![Z: $i] : ((~f(Z)) | (~h(Z)))) | (~f(Y!0)) | (~h(Y!0))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.14/0.40 tff(33,plain,
% 0.14/0.40 (~h(Y!0)),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[32, 29, 13])).
% 0.14/0.40 tff(34,plain,
% 0.14/0.40 (^[X: $i] : refl((h(X) | g(X) | (~f(X))) <=> (h(X) | g(X) | (~f(X))))),
% 0.14/0.40 inference(bind,[status(th)],[])).
% 0.14/0.40 tff(35,plain,
% 0.14/0.40 (![X: $i] : (h(X) | g(X) | (~f(X))) <=> ![X: $i] : (h(X) | g(X) | (~f(X)))),
% 0.14/0.40 inference(quant_intro,[status(thm)],[34])).
% 0.14/0.40 tff(36,plain,
% 0.14/0.40 (![X: $i] : (h(X) | g(X) | (~f(X))) <=> ![X: $i] : (h(X) | g(X) | (~f(X)))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(37,plain,
% 0.14/0.40 (![X: $i] : (h(X) | g(X) | (~f(X)))),
% 0.14/0.40 inference(or_elim,[status(thm)],[4])).
% 0.14/0.40 tff(38,plain,
% 0.14/0.40 (![X: $i] : (h(X) | g(X) | (~f(X)))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.14/0.40 tff(39,plain,(
% 0.14/0.40 ![X: $i] : (h(X) | g(X) | (~f(X)))),
% 0.14/0.40 inference(skolemize,[status(sab)],[38])).
% 0.14/0.40 tff(40,plain,
% 0.14/0.40 (![X: $i] : (h(X) | g(X) | (~f(X)))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[39, 35])).
% 0.14/0.40 tff(41,plain,
% 0.14/0.40 (~g(Y!0)),
% 0.14/0.40 inference(or_elim,[status(thm)],[12])).
% 0.14/0.40 tff(42,plain,
% 0.14/0.40 (((~![X: $i] : (h(X) | g(X) | (~f(X)))) | (g(Y!0) | (~f(Y!0)) | h(Y!0))) <=> ((~![X: $i] : (h(X) | g(X) | (~f(X)))) | g(Y!0) | (~f(Y!0)) | h(Y!0))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(43,plain,
% 0.14/0.40 ((h(Y!0) | g(Y!0) | (~f(Y!0))) <=> (g(Y!0) | (~f(Y!0)) | h(Y!0))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(44,plain,
% 0.14/0.40 (((~![X: $i] : (h(X) | g(X) | (~f(X)))) | (h(Y!0) | g(Y!0) | (~f(Y!0)))) <=> ((~![X: $i] : (h(X) | g(X) | (~f(X)))) | (g(Y!0) | (~f(Y!0)) | h(Y!0)))),
% 0.14/0.40 inference(monotonicity,[status(thm)],[43])).
% 0.14/0.40 tff(45,plain,
% 0.14/0.40 (((~![X: $i] : (h(X) | g(X) | (~f(X)))) | (h(Y!0) | g(Y!0) | (~f(Y!0)))) <=> ((~![X: $i] : (h(X) | g(X) | (~f(X)))) | g(Y!0) | (~f(Y!0)) | h(Y!0))),
% 0.14/0.40 inference(transitivity,[status(thm)],[44, 42])).
% 0.14/0.40 tff(46,plain,
% 0.14/0.40 ((~![X: $i] : (h(X) | g(X) | (~f(X)))) | (h(Y!0) | g(Y!0) | (~f(Y!0)))),
% 0.14/0.40 inference(quant_inst,[status(thm)],[])).
% 0.14/0.40 tff(47,plain,
% 0.14/0.40 ((~![X: $i] : (h(X) | g(X) | (~f(X)))) | g(Y!0) | (~f(Y!0)) | h(Y!0)),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.14/0.40 tff(48,plain,
% 0.14/0.40 ($false),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[47, 41, 13, 40, 33])).
% 0.14/0.40 % SZS output end Proof
%------------------------------------------------------------------------------