TSTP Solution File: SYN942+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN942+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n018.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 : Fri Sep 30 00:01:20 EDT 2022
% Result : Theorem 0.13s 0.39s
% Output : Proof 0.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SYN942+1 : TPTP v8.1.0. Released v3.1.0.
% 0.12/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n018.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Sep 5 09:41:31 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.13/0.39 % SZS status Theorem
% 0.13/0.39 % SZS output start Proof
% 0.13/0.39 tff(c_type, type, (
% 0.13/0.39 c: $i > $o)).
% 0.13/0.39 tff(tptp_fun_X_0_type, type, (
% 0.13/0.39 tptp_fun_X_0: $i)).
% 0.13/0.39 tff(a_type, type, (
% 0.13/0.39 a: $i > $o)).
% 0.13/0.39 tff(b_type, type, (
% 0.13/0.39 b: $i > $o)).
% 0.13/0.39 tff(1,plain,
% 0.13/0.39 ((~![X: $i] : (b(X) | (~a(X)))) <=> (~![X: $i] : (b(X) | (~a(X))))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(2,plain,
% 0.13/0.39 ((~((![X: $i] : (a(X) => (b(X) | c(X))) & (~![X: $i] : (a(X) => b(X)))) => ?[X: $i] : (a(X) & c(X)))) <=> (~((~(![X: $i] : (c(X) | b(X) | (~a(X))) & (~![X: $i] : (b(X) | (~a(X)))))) | ?[X: $i] : (a(X) & c(X))))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(3,axiom,(~((![X: $i] : (a(X) => (b(X) | c(X))) & (~![X: $i] : (a(X) => b(X)))) => ?[X: $i] : (a(X) & c(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this')).
% 0.13/0.39 tff(4,plain,
% 0.13/0.39 (~((~(![X: $i] : (c(X) | b(X) | (~a(X))) & (~![X: $i] : (b(X) | (~a(X)))))) | ?[X: $i] : (a(X) & c(X)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.13/0.39 tff(5,plain,
% 0.13/0.39 (![X: $i] : (c(X) | b(X) | (~a(X))) & (~![X: $i] : (b(X) | (~a(X))))),
% 0.13/0.39 inference(or_elim,[status(thm)],[4])).
% 0.13/0.39 tff(6,plain,
% 0.13/0.39 (~![X: $i] : (b(X) | (~a(X)))),
% 0.13/0.39 inference(and_elim,[status(thm)],[5])).
% 0.13/0.39 tff(7,plain,
% 0.13/0.39 (~![X: $i] : (b(X) | (~a(X)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.13/0.39 tff(8,plain,
% 0.13/0.39 (~![X: $i] : (b(X) | (~a(X)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[7, 1])).
% 0.13/0.39 tff(9,plain,
% 0.13/0.39 (~![X: $i] : (b(X) | (~a(X)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[8, 1])).
% 0.13/0.39 tff(10,plain,
% 0.13/0.39 (~![X: $i] : (b(X) | (~a(X)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[9, 1])).
% 0.13/0.39 tff(11,plain,
% 0.13/0.39 (~![X: $i] : (b(X) | (~a(X)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[10, 1])).
% 0.13/0.39 tff(12,plain,
% 0.13/0.39 (~![X: $i] : (b(X) | (~a(X)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[11, 1])).
% 0.13/0.39 tff(13,plain,(
% 0.13/0.39 ~(b(X!0) | (~a(X!0)))),
% 0.13/0.39 inference(skolemize,[status(sab)],[12])).
% 0.13/0.39 tff(14,plain,
% 0.13/0.39 (a(X!0)),
% 0.13/0.39 inference(or_elim,[status(thm)],[13])).
% 0.13/0.39 tff(15,plain,
% 0.13/0.39 (~b(X!0)),
% 0.13/0.39 inference(or_elim,[status(thm)],[13])).
% 0.13/0.39 tff(16,plain,
% 0.13/0.39 (^[X: $i] : refl((c(X) | b(X) | (~a(X))) <=> (c(X) | b(X) | (~a(X))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(17,plain,
% 0.13/0.39 (![X: $i] : (c(X) | b(X) | (~a(X))) <=> ![X: $i] : (c(X) | b(X) | (~a(X)))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[16])).
% 0.13/0.39 tff(18,plain,
% 0.13/0.39 (![X: $i] : (c(X) | b(X) | (~a(X))) <=> ![X: $i] : (c(X) | b(X) | (~a(X)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(19,plain,
% 0.13/0.39 (![X: $i] : (c(X) | b(X) | (~a(X)))),
% 0.13/0.39 inference(and_elim,[status(thm)],[5])).
% 0.13/0.39 tff(20,plain,
% 0.13/0.39 (![X: $i] : (c(X) | b(X) | (~a(X)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.13/0.39 tff(21,plain,(
% 0.13/0.39 ![X: $i] : (c(X) | b(X) | (~a(X)))),
% 0.13/0.39 inference(skolemize,[status(sab)],[20])).
% 0.13/0.39 tff(22,plain,
% 0.13/0.39 (![X: $i] : (c(X) | b(X) | (~a(X)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[21, 17])).
% 0.13/0.39 tff(23,plain,
% 0.13/0.39 (((~![X: $i] : (c(X) | b(X) | (~a(X)))) | (b(X!0) | (~a(X!0)) | c(X!0))) <=> ((~![X: $i] : (c(X) | b(X) | (~a(X)))) | b(X!0) | (~a(X!0)) | c(X!0))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(24,plain,
% 0.13/0.39 ((c(X!0) | b(X!0) | (~a(X!0))) <=> (b(X!0) | (~a(X!0)) | c(X!0))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(25,plain,
% 0.13/0.39 (((~![X: $i] : (c(X) | b(X) | (~a(X)))) | (c(X!0) | b(X!0) | (~a(X!0)))) <=> ((~![X: $i] : (c(X) | b(X) | (~a(X)))) | (b(X!0) | (~a(X!0)) | c(X!0)))),
% 0.13/0.39 inference(monotonicity,[status(thm)],[24])).
% 0.13/0.39 tff(26,plain,
% 0.13/0.39 (((~![X: $i] : (c(X) | b(X) | (~a(X)))) | (c(X!0) | b(X!0) | (~a(X!0)))) <=> ((~![X: $i] : (c(X) | b(X) | (~a(X)))) | b(X!0) | (~a(X!0)) | c(X!0))),
% 0.13/0.39 inference(transitivity,[status(thm)],[25, 23])).
% 0.13/0.39 tff(27,plain,
% 0.13/0.39 ((~![X: $i] : (c(X) | b(X) | (~a(X)))) | (c(X!0) | b(X!0) | (~a(X!0)))),
% 0.13/0.39 inference(quant_inst,[status(thm)],[])).
% 0.13/0.39 tff(28,plain,
% 0.13/0.39 ((~![X: $i] : (c(X) | b(X) | (~a(X)))) | b(X!0) | (~a(X!0)) | c(X!0)),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.13/0.39 tff(29,plain,
% 0.13/0.39 (c(X!0)),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[28, 22, 15, 14])).
% 0.13/0.39 tff(30,plain,
% 0.13/0.39 (^[X: $i] : refl(((~a(X)) | (~c(X))) <=> ((~a(X)) | (~c(X))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(31,plain,
% 0.13/0.39 (![X: $i] : ((~a(X)) | (~c(X))) <=> ![X: $i] : ((~a(X)) | (~c(X)))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[30])).
% 0.13/0.39 tff(32,plain,
% 0.13/0.39 (^[X: $i] : trans(monotonicity(rewrite((a(X) & c(X)) <=> (~((~a(X)) | (~c(X))))), ((~(a(X) & c(X))) <=> (~(~((~a(X)) | (~c(X))))))), rewrite((~(~((~a(X)) | (~c(X))))) <=> ((~a(X)) | (~c(X)))), ((~(a(X) & c(X))) <=> ((~a(X)) | (~c(X)))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(33,plain,
% 0.13/0.39 (![X: $i] : (~(a(X) & c(X))) <=> ![X: $i] : ((~a(X)) | (~c(X)))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[32])).
% 0.13/0.39 tff(34,plain,
% 0.13/0.39 ((~?[X: $i] : (a(X) & c(X))) <=> (~?[X: $i] : (a(X) & c(X)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(35,plain,
% 0.13/0.39 (~?[X: $i] : (a(X) & c(X))),
% 0.13/0.39 inference(or_elim,[status(thm)],[4])).
% 0.13/0.39 tff(36,plain,
% 0.13/0.39 (~?[X: $i] : (a(X) & c(X))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.13/0.39 tff(37,plain,
% 0.13/0.39 (~?[X: $i] : (a(X) & c(X))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[36, 34])).
% 0.13/0.39 tff(38,plain,
% 0.13/0.39 (~?[X: $i] : (a(X) & c(X))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[37, 34])).
% 0.13/0.39 tff(39,plain,
% 0.13/0.39 (~?[X: $i] : (a(X) & c(X))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[38, 34])).
% 0.13/0.39 tff(40,plain,
% 0.13/0.39 (~?[X: $i] : (a(X) & c(X))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[39, 34])).
% 0.13/0.39 tff(41,plain,
% 0.13/0.39 (~?[X: $i] : (a(X) & c(X))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[40, 34])).
% 0.13/0.39 tff(42,plain,
% 0.13/0.39 (^[X: $i] : refl($oeq((~(a(X) & c(X))), (~(a(X) & c(X)))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(43,plain,(
% 0.13/0.39 ![X: $i] : (~(a(X) & c(X)))),
% 0.13/0.39 inference(nnf-neg,[status(sab)],[41, 42])).
% 0.13/0.39 tff(44,plain,
% 0.13/0.39 (![X: $i] : ((~a(X)) | (~c(X)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[43, 33])).
% 0.13/0.39 tff(45,plain,
% 0.13/0.39 (![X: $i] : ((~a(X)) | (~c(X)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[44, 31])).
% 0.13/0.39 tff(46,plain,
% 0.13/0.39 (((~![X: $i] : ((~a(X)) | (~c(X)))) | ((~a(X!0)) | (~c(X!0)))) <=> ((~![X: $i] : ((~a(X)) | (~c(X)))) | (~a(X!0)) | (~c(X!0)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(47,plain,
% 0.13/0.39 ((~![X: $i] : ((~a(X)) | (~c(X)))) | ((~a(X!0)) | (~c(X!0)))),
% 0.13/0.39 inference(quant_inst,[status(thm)],[])).
% 0.13/0.39 tff(48,plain,
% 0.13/0.39 ((~![X: $i] : ((~a(X)) | (~c(X)))) | (~a(X!0)) | (~c(X!0))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.13/0.39 tff(49,plain,
% 0.13/0.39 ($false),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[48, 14, 45, 29])).
% 0.13/0.39 % SZS output end Proof
%------------------------------------------------------------------------------