TSTP Solution File: SYN060+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN060+1 : TPTP v8.1.0. Released v2.0.0.
% 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 23:53:26 EDT 2022
% Result : Theorem 0.14s 0.39s
% Output : Proof 0.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SYN060+1 : TPTP v8.1.0. Released v2.0.0.
% 0.11/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.34 % Computer : n021.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Mon Sep 5 01:25:01 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.34 Usage: tptp [options] [-file:]file
% 0.14/0.34 -h, -? prints this message.
% 0.14/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.34 -m, -model generate model.
% 0.14/0.34 -p, -proof generate proof.
% 0.14/0.34 -c, -core generate unsat core of named formulas.
% 0.14/0.34 -st, -statistics display statistics.
% 0.14/0.34 -t:timeout set timeout (in second).
% 0.14/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.34 -<param>:<value> configuration parameter and value.
% 0.14/0.34 -o:<output-file> file to place output in.
% 0.14/0.39 % SZS status Theorem
% 0.14/0.39 % SZS output start Proof
% 0.14/0.39 tff(big_g_type, type, (
% 0.14/0.39 big_g: $i > $o)).
% 0.14/0.39 tff(tptp_fun_X_0_type, type, (
% 0.14/0.39 tptp_fun_X_0: $i)).
% 0.14/0.39 tff(big_f_type, type, (
% 0.14/0.39 big_f: $i > $o)).
% 0.14/0.39 tff(big_h_type, type, (
% 0.14/0.39 big_h: $i > $o)).
% 0.14/0.39 tff(big_i_type, type, (
% 0.14/0.39 big_i: $i > $o)).
% 0.14/0.39 tff(1,plain,
% 0.14/0.39 ((~![X: $i] : big_i(X)) <=> (~![X: $i] : big_i(X))),
% 0.14/0.39 inference(rewrite,[status(thm)],[])).
% 0.14/0.39 tff(2,axiom,(~![X: $i] : big_i(X)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel30')).
% 0.14/0.39 tff(3,plain,
% 0.14/0.39 (~![X: $i] : big_i(X)),
% 0.14/0.39 inference(modus_ponens,[status(thm)],[2, 1])).
% 0.14/0.39 tff(4,plain,
% 0.14/0.39 (~![X: $i] : big_i(X)),
% 0.14/0.39 inference(modus_ponens,[status(thm)],[3, 1])).
% 0.14/0.39 tff(5,plain,
% 0.14/0.39 (~![X: $i] : big_i(X)),
% 0.14/0.39 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.14/0.39 tff(6,plain,
% 0.14/0.39 (~![X: $i] : big_i(X)),
% 0.14/0.39 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.14/0.39 tff(7,plain,
% 0.14/0.39 (~![X: $i] : big_i(X)),
% 0.14/0.39 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.14/0.39 tff(8,plain,
% 0.14/0.39 (~![X: $i] : big_i(X)),
% 0.14/0.39 inference(modus_ponens,[status(thm)],[7, 1])).
% 0.14/0.39 tff(9,plain,
% 0.14/0.39 (~![X: $i] : big_i(X)),
% 0.14/0.39 inference(modus_ponens,[status(thm)],[8, 1])).
% 0.14/0.39 tff(10,plain,(
% 0.14/0.39 ~big_i(X!0)),
% 0.14/0.39 inference(skolemize,[status(sab)],[9])).
% 0.14/0.39 tff(11,plain,
% 0.14/0.39 (((~big_g(X!0)) | (~big_i(X!0))) | big_i(X!0)),
% 0.14/0.39 inference(tautology,[status(thm)],[])).
% 0.14/0.39 tff(12,plain,
% 0.14/0.39 ((~big_g(X!0)) | (~big_i(X!0))),
% 0.14/0.39 inference(unit_resolution,[status(thm)],[11, 10])).
% 0.14/0.39 tff(13,plain,
% 0.14/0.39 (^[X: $i] : refl(((~((~big_g(X)) | (~big_i(X)))) | (~((~big_f(X)) | (~big_h(X))))) <=> ((~((~big_g(X)) | (~big_i(X)))) | (~((~big_f(X)) | (~big_h(X))))))),
% 0.14/0.39 inference(bind,[status(th)],[])).
% 0.14/0.39 tff(14,plain,
% 0.14/0.39 (![X: $i] : ((~((~big_g(X)) | (~big_i(X)))) | (~((~big_f(X)) | (~big_h(X))))) <=> ![X: $i] : ((~((~big_g(X)) | (~big_i(X)))) | (~((~big_f(X)) | (~big_h(X)))))),
% 0.14/0.39 inference(quant_intro,[status(thm)],[13])).
% 0.14/0.39 tff(15,plain,
% 0.14/0.39 (^[X: $i] : trans(monotonicity(rewrite((big_f(X) & big_h(X)) <=> (~((~big_f(X)) | (~big_h(X))))), (((~((~big_g(X)) | (~big_i(X)))) | (big_f(X) & big_h(X))) <=> ((~((~big_g(X)) | (~big_i(X)))) | (~((~big_f(X)) | (~big_h(X))))))), rewrite(((~((~big_g(X)) | (~big_i(X)))) | (~((~big_f(X)) | (~big_h(X))))) <=> ((~((~big_g(X)) | (~big_i(X)))) | (~((~big_f(X)) | (~big_h(X)))))), (((~((~big_g(X)) | (~big_i(X)))) | (big_f(X) & big_h(X))) <=> ((~((~big_g(X)) | (~big_i(X)))) | (~((~big_f(X)) | (~big_h(X)))))))),
% 0.14/0.39 inference(bind,[status(th)],[])).
% 0.14/0.39 tff(16,plain,
% 0.14/0.39 (![X: $i] : ((~((~big_g(X)) | (~big_i(X)))) | (big_f(X) & big_h(X))) <=> ![X: $i] : ((~((~big_g(X)) | (~big_i(X)))) | (~((~big_f(X)) | (~big_h(X)))))),
% 0.14/0.39 inference(quant_intro,[status(thm)],[15])).
% 0.14/0.39 tff(17,plain,
% 0.14/0.39 (![X: $i] : ((~((~big_g(X)) | (~big_i(X)))) | (big_f(X) & big_h(X))) <=> ![X: $i] : ((~((~big_g(X)) | (~big_i(X)))) | (big_f(X) & big_h(X)))),
% 0.14/0.39 inference(rewrite,[status(thm)],[])).
% 0.14/0.39 tff(18,plain,
% 0.14/0.39 (^[X: $i] : trans(monotonicity(rewrite((big_g(X) => (~big_i(X))) <=> ((~big_g(X)) | (~big_i(X)))), (((big_g(X) => (~big_i(X))) => (big_f(X) & big_h(X))) <=> (((~big_g(X)) | (~big_i(X))) => (big_f(X) & big_h(X))))), rewrite((((~big_g(X)) | (~big_i(X))) => (big_f(X) & big_h(X))) <=> ((~((~big_g(X)) | (~big_i(X)))) | (big_f(X) & big_h(X)))), (((big_g(X) => (~big_i(X))) => (big_f(X) & big_h(X))) <=> ((~((~big_g(X)) | (~big_i(X)))) | (big_f(X) & big_h(X)))))),
% 0.14/0.39 inference(bind,[status(th)],[])).
% 0.14/0.39 tff(19,plain,
% 0.14/0.39 (![X: $i] : ((big_g(X) => (~big_i(X))) => (big_f(X) & big_h(X))) <=> ![X: $i] : ((~((~big_g(X)) | (~big_i(X)))) | (big_f(X) & big_h(X)))),
% 0.14/0.39 inference(quant_intro,[status(thm)],[18])).
% 0.14/0.39 tff(20,axiom,(![X: $i] : ((big_g(X) => (~big_i(X))) => (big_f(X) & big_h(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel30_2')).
% 0.14/0.39 tff(21,plain,
% 0.14/0.39 (![X: $i] : ((~((~big_g(X)) | (~big_i(X)))) | (big_f(X) & big_h(X)))),
% 0.14/0.39 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.14/0.39 tff(22,plain,
% 0.14/0.39 (![X: $i] : ((~((~big_g(X)) | (~big_i(X)))) | (big_f(X) & big_h(X)))),
% 0.14/0.39 inference(modus_ponens,[status(thm)],[21, 17])).
% 0.14/0.39 tff(23,plain,(
% 0.14/0.39 ![X: $i] : ((~((~big_g(X)) | (~big_i(X)))) | (big_f(X) & big_h(X)))),
% 0.14/0.39 inference(skolemize,[status(sab)],[22])).
% 0.14/0.39 tff(24,plain,
% 0.14/0.39 (![X: $i] : ((~((~big_g(X)) | (~big_i(X)))) | (~((~big_f(X)) | (~big_h(X)))))),
% 0.14/0.39 inference(modus_ponens,[status(thm)],[23, 16])).
% 0.14/0.39 tff(25,plain,
% 0.14/0.39 (![X: $i] : ((~((~big_g(X)) | (~big_i(X)))) | (~((~big_f(X)) | (~big_h(X)))))),
% 0.14/0.39 inference(modus_ponens,[status(thm)],[24, 14])).
% 0.14/0.39 tff(26,plain,
% 0.14/0.39 (((~![X: $i] : ((~((~big_g(X)) | (~big_i(X)))) | (~((~big_f(X)) | (~big_h(X)))))) | ((~((~big_g(X!0)) | (~big_i(X!0)))) | (~((~big_f(X!0)) | (~big_h(X!0)))))) <=> ((~![X: $i] : ((~((~big_g(X)) | (~big_i(X)))) | (~((~big_f(X)) | (~big_h(X)))))) | (~((~big_g(X!0)) | (~big_i(X!0)))) | (~((~big_f(X!0)) | (~big_h(X!0)))))),
% 0.14/0.39 inference(rewrite,[status(thm)],[])).
% 0.14/0.39 tff(27,plain,
% 0.14/0.39 ((~![X: $i] : ((~((~big_g(X)) | (~big_i(X)))) | (~((~big_f(X)) | (~big_h(X)))))) | ((~((~big_g(X!0)) | (~big_i(X!0)))) | (~((~big_f(X!0)) | (~big_h(X!0)))))),
% 0.14/0.39 inference(quant_inst,[status(thm)],[])).
% 0.14/0.39 tff(28,plain,
% 0.14/0.39 ((~![X: $i] : ((~((~big_g(X)) | (~big_i(X)))) | (~((~big_f(X)) | (~big_h(X)))))) | (~((~big_g(X!0)) | (~big_i(X!0)))) | (~((~big_f(X!0)) | (~big_h(X!0))))),
% 0.14/0.39 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.14/0.39 tff(29,plain,
% 0.14/0.39 (~((~big_f(X!0)) | (~big_h(X!0)))),
% 0.14/0.39 inference(unit_resolution,[status(thm)],[28, 25, 12])).
% 0.14/0.39 tff(30,plain,
% 0.14/0.39 (((~big_f(X!0)) | (~big_h(X!0))) | big_f(X!0)),
% 0.14/0.39 inference(tautology,[status(thm)],[])).
% 0.14/0.39 tff(31,plain,
% 0.14/0.39 (big_f(X!0)),
% 0.14/0.39 inference(unit_resolution,[status(thm)],[30, 29])).
% 0.14/0.39 tff(32,plain,
% 0.14/0.39 ((big_f(X!0) | big_g(X!0)) | (~big_f(X!0))),
% 0.14/0.39 inference(tautology,[status(thm)],[])).
% 0.14/0.39 tff(33,plain,
% 0.14/0.39 (big_f(X!0) | big_g(X!0)),
% 0.14/0.39 inference(unit_resolution,[status(thm)],[32, 31])).
% 0.14/0.39 tff(34,plain,
% 0.14/0.39 (((~big_f(X!0)) | (~big_h(X!0))) | big_h(X!0)),
% 0.14/0.39 inference(tautology,[status(thm)],[])).
% 0.14/0.39 tff(35,plain,
% 0.14/0.39 (big_h(X!0)),
% 0.14/0.39 inference(unit_resolution,[status(thm)],[34, 29])).
% 0.14/0.39 tff(36,plain,
% 0.14/0.39 (^[X: $i] : refl(((~big_h(X)) | (~(big_f(X) | big_g(X)))) <=> ((~big_h(X)) | (~(big_f(X) | big_g(X)))))),
% 0.14/0.39 inference(bind,[status(th)],[])).
% 0.14/0.39 tff(37,plain,
% 0.14/0.39 (![X: $i] : ((~big_h(X)) | (~(big_f(X) | big_g(X)))) <=> ![X: $i] : ((~big_h(X)) | (~(big_f(X) | big_g(X))))),
% 0.14/0.39 inference(quant_intro,[status(thm)],[36])).
% 0.14/0.39 tff(38,plain,
% 0.14/0.39 (![X: $i] : ((~big_h(X)) | (~(big_f(X) | big_g(X)))) <=> ![X: $i] : ((~big_h(X)) | (~(big_f(X) | big_g(X))))),
% 0.14/0.39 inference(rewrite,[status(thm)],[])).
% 0.14/0.39 tff(39,plain,
% 0.14/0.39 (^[X: $i] : rewrite(((big_f(X) | big_g(X)) => (~big_h(X))) <=> ((~big_h(X)) | (~(big_f(X) | big_g(X)))))),
% 0.14/0.39 inference(bind,[status(th)],[])).
% 0.14/0.39 tff(40,plain,
% 0.14/0.39 (![X: $i] : ((big_f(X) | big_g(X)) => (~big_h(X))) <=> ![X: $i] : ((~big_h(X)) | (~(big_f(X) | big_g(X))))),
% 0.14/0.39 inference(quant_intro,[status(thm)],[39])).
% 0.14/0.39 tff(41,axiom,(![X: $i] : ((big_f(X) | big_g(X)) => (~big_h(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel30_1')).
% 0.14/0.39 tff(42,plain,
% 0.14/0.39 (![X: $i] : ((~big_h(X)) | (~(big_f(X) | big_g(X))))),
% 0.14/0.39 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.14/0.39 tff(43,plain,
% 0.14/0.39 (![X: $i] : ((~big_h(X)) | (~(big_f(X) | big_g(X))))),
% 0.14/0.39 inference(modus_ponens,[status(thm)],[42, 38])).
% 0.14/0.39 tff(44,plain,(
% 0.14/0.39 ![X: $i] : ((~big_h(X)) | (~(big_f(X) | big_g(X))))),
% 0.14/0.39 inference(skolemize,[status(sab)],[43])).
% 0.14/0.39 tff(45,plain,
% 0.14/0.39 (![X: $i] : ((~big_h(X)) | (~(big_f(X) | big_g(X))))),
% 0.14/0.39 inference(modus_ponens,[status(thm)],[44, 37])).
% 0.14/0.39 tff(46,plain,
% 0.14/0.39 (((~![X: $i] : ((~big_h(X)) | (~(big_f(X) | big_g(X))))) | ((~big_h(X!0)) | (~(big_f(X!0) | big_g(X!0))))) <=> ((~![X: $i] : ((~big_h(X)) | (~(big_f(X) | big_g(X))))) | (~big_h(X!0)) | (~(big_f(X!0) | big_g(X!0))))),
% 0.14/0.39 inference(rewrite,[status(thm)],[])).
% 0.14/0.39 tff(47,plain,
% 0.14/0.39 ((~![X: $i] : ((~big_h(X)) | (~(big_f(X) | big_g(X))))) | ((~big_h(X!0)) | (~(big_f(X!0) | big_g(X!0))))),
% 0.14/0.39 inference(quant_inst,[status(thm)],[])).
% 0.14/0.39 tff(48,plain,
% 0.14/0.39 ((~![X: $i] : ((~big_h(X)) | (~(big_f(X) | big_g(X))))) | (~big_h(X!0)) | (~(big_f(X!0) | big_g(X!0)))),
% 0.14/0.39 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.14/0.39 tff(49,plain,
% 0.14/0.39 ($false),
% 0.14/0.39 inference(unit_resolution,[status(thm)],[48, 45, 35, 33])).
% 0.14/0.39 % SZS output end Proof
%------------------------------------------------------------------------------