TSTP Solution File: SYN061+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN061+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n023.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 23:53:27 EDT 2022
% Result : Theorem 0.13s 0.35s
% Output : Proof 0.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYN061+1 : TPTP v8.1.0. Released v2.0.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n023.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 01:50:17 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.33 Usage: tptp [options] [-file:]file
% 0.13/0.33 -h, -? prints this message.
% 0.13/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.33 -m, -model generate model.
% 0.13/0.33 -p, -proof generate proof.
% 0.13/0.33 -c, -core generate unsat core of named formulas.
% 0.13/0.33 -st, -statistics display statistics.
% 0.13/0.33 -t:timeout set timeout (in second).
% 0.13/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.33 -<param>:<value> configuration parameter and value.
% 0.13/0.33 -o:<output-file> file to place output in.
% 0.13/0.35 % SZS status Theorem
% 0.13/0.35 % SZS output start Proof
% 0.13/0.35 tff(big_j_type, type, (
% 0.13/0.35 big_j: $i > $o)).
% 0.13/0.35 tff(tptp_fun_X_0_type, type, (
% 0.13/0.35 tptp_fun_X_0: $i)).
% 0.13/0.35 tff(big_i_type, type, (
% 0.13/0.35 big_i: $i > $o)).
% 0.13/0.35 tff(big_f_type, type, (
% 0.13/0.35 big_f: $i > $o)).
% 0.13/0.35 tff(big_h_type, type, (
% 0.13/0.35 big_h: $i > $o)).
% 0.13/0.35 tff(big_g_type, type, (
% 0.13/0.35 big_g: $i > $o)).
% 0.13/0.35 tff(1,plain,
% 0.13/0.35 (^[X: $i] : refl(((~big_i(X)) | (~big_j(X))) <=> ((~big_i(X)) | (~big_j(X))))),
% 0.13/0.35 inference(bind,[status(th)],[])).
% 0.13/0.35 tff(2,plain,
% 0.13/0.35 (![X: $i] : ((~big_i(X)) | (~big_j(X))) <=> ![X: $i] : ((~big_i(X)) | (~big_j(X)))),
% 0.13/0.35 inference(quant_intro,[status(thm)],[1])).
% 0.13/0.35 tff(3,plain,
% 0.13/0.35 (^[X: $i] : trans(monotonicity(rewrite((big_i(X) & big_j(X)) <=> (~((~big_i(X)) | (~big_j(X))))), ((~(big_i(X) & big_j(X))) <=> (~(~((~big_i(X)) | (~big_j(X))))))), rewrite((~(~((~big_i(X)) | (~big_j(X))))) <=> ((~big_i(X)) | (~big_j(X)))), ((~(big_i(X) & big_j(X))) <=> ((~big_i(X)) | (~big_j(X)))))),
% 0.13/0.35 inference(bind,[status(th)],[])).
% 0.13/0.35 tff(4,plain,
% 0.13/0.35 (![X: $i] : (~(big_i(X) & big_j(X))) <=> ![X: $i] : ((~big_i(X)) | (~big_j(X)))),
% 0.13/0.35 inference(quant_intro,[status(thm)],[3])).
% 0.13/0.35 tff(5,plain,
% 0.13/0.35 ((~?[X: $i] : (big_i(X) & big_j(X))) <=> (~?[X: $i] : (big_i(X) & big_j(X)))),
% 0.13/0.35 inference(rewrite,[status(thm)],[])).
% 0.13/0.35 tff(6,axiom,(~?[X: $i] : (big_i(X) & big_j(X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','pel31')).
% 0.13/0.35 tff(7,plain,
% 0.13/0.35 (~?[X: $i] : (big_i(X) & big_j(X))),
% 0.13/0.35 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.13/0.35 tff(8,plain,
% 0.13/0.35 (~?[X: $i] : (big_i(X) & big_j(X))),
% 0.13/0.35 inference(modus_ponens,[status(thm)],[7, 5])).
% 0.13/0.35 tff(9,plain,
% 0.13/0.35 (~?[X: $i] : (big_i(X) & big_j(X))),
% 0.13/0.35 inference(modus_ponens,[status(thm)],[8, 5])).
% 0.13/0.35 tff(10,plain,
% 0.13/0.35 (~?[X: $i] : (big_i(X) & big_j(X))),
% 0.13/0.35 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.13/0.35 tff(11,plain,
% 0.13/0.35 (~?[X: $i] : (big_i(X) & big_j(X))),
% 0.13/0.35 inference(modus_ponens,[status(thm)],[10, 5])).
% 0.13/0.35 tff(12,plain,
% 0.13/0.35 (~?[X: $i] : (big_i(X) & big_j(X))),
% 0.13/0.35 inference(modus_ponens,[status(thm)],[11, 5])).
% 0.13/0.35 tff(13,plain,
% 0.13/0.35 (~?[X: $i] : (big_i(X) & big_j(X))),
% 0.13/0.35 inference(modus_ponens,[status(thm)],[12, 5])).
% 0.13/0.35 tff(14,plain,
% 0.13/0.35 (^[X: $i] : refl($oeq((~(big_i(X) & big_j(X))), (~(big_i(X) & big_j(X)))))),
% 0.13/0.35 inference(bind,[status(th)],[])).
% 0.13/0.35 tff(15,plain,(
% 0.13/0.35 ![X: $i] : (~(big_i(X) & big_j(X)))),
% 0.13/0.35 inference(nnf-neg,[status(sab)],[13, 14])).
% 0.13/0.35 tff(16,plain,
% 0.13/0.35 (![X: $i] : ((~big_i(X)) | (~big_j(X)))),
% 0.13/0.35 inference(modus_ponens,[status(thm)],[15, 4])).
% 0.13/0.35 tff(17,plain,
% 0.13/0.35 (![X: $i] : ((~big_i(X)) | (~big_j(X)))),
% 0.13/0.35 inference(modus_ponens,[status(thm)],[16, 2])).
% 0.13/0.35 tff(18,plain,
% 0.13/0.35 (?[X: $i] : (big_i(X) & big_f(X)) <=> ?[X: $i] : (big_i(X) & big_f(X))),
% 0.13/0.35 inference(rewrite,[status(thm)],[])).
% 0.13/0.35 tff(19,axiom,(?[X: $i] : (big_i(X) & big_f(X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','pel31_2')).
% 0.13/0.35 tff(20,plain,
% 0.13/0.35 (?[X: $i] : (big_i(X) & big_f(X))),
% 0.13/0.35 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.13/0.35 tff(21,plain,(
% 0.13/0.35 big_i(X!0) & big_f(X!0)),
% 0.13/0.35 inference(skolemize,[status(sab)],[20])).
% 0.13/0.35 tff(22,plain,
% 0.13/0.35 (big_i(X!0)),
% 0.13/0.35 inference(and_elim,[status(thm)],[21])).
% 0.13/0.35 tff(23,plain,
% 0.13/0.35 (((~![X: $i] : ((~big_i(X)) | (~big_j(X)))) | ((~big_i(X!0)) | (~big_j(X!0)))) <=> ((~![X: $i] : ((~big_i(X)) | (~big_j(X)))) | (~big_i(X!0)) | (~big_j(X!0)))),
% 0.13/0.35 inference(rewrite,[status(thm)],[])).
% 0.13/0.35 tff(24,plain,
% 0.13/0.35 ((~![X: $i] : ((~big_i(X)) | (~big_j(X)))) | ((~big_i(X!0)) | (~big_j(X!0)))),
% 0.13/0.35 inference(quant_inst,[status(thm)],[])).
% 0.13/0.35 tff(25,plain,
% 0.13/0.35 ((~![X: $i] : ((~big_i(X)) | (~big_j(X)))) | (~big_i(X!0)) | (~big_j(X!0))),
% 0.13/0.35 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.13/0.35 tff(26,plain,
% 0.13/0.35 (~big_j(X!0)),
% 0.13/0.35 inference(unit_resolution,[status(thm)],[25, 22, 17])).
% 0.13/0.35 tff(27,plain,
% 0.13/0.35 (big_f(X!0)),
% 0.13/0.35 inference(and_elim,[status(thm)],[21])).
% 0.13/0.35 tff(28,plain,
% 0.13/0.35 (^[X: $i] : refl(((~big_f(X)) | (~(big_g(X) | big_h(X)))) <=> ((~big_f(X)) | (~(big_g(X) | big_h(X)))))),
% 0.13/0.35 inference(bind,[status(th)],[])).
% 0.13/0.35 tff(29,plain,
% 0.13/0.35 (![X: $i] : ((~big_f(X)) | (~(big_g(X) | big_h(X)))) <=> ![X: $i] : ((~big_f(X)) | (~(big_g(X) | big_h(X))))),
% 0.13/0.35 inference(quant_intro,[status(thm)],[28])).
% 0.13/0.36 tff(30,plain,
% 0.13/0.36 (^[X: $i] : trans(monotonicity(rewrite((big_f(X) & (big_g(X) | big_h(X))) <=> (~((~big_f(X)) | (~(big_g(X) | big_h(X)))))), ((~(big_f(X) & (big_g(X) | big_h(X)))) <=> (~(~((~big_f(X)) | (~(big_g(X) | big_h(X)))))))), rewrite((~(~((~big_f(X)) | (~(big_g(X) | big_h(X)))))) <=> ((~big_f(X)) | (~(big_g(X) | big_h(X))))), ((~(big_f(X) & (big_g(X) | big_h(X)))) <=> ((~big_f(X)) | (~(big_g(X) | big_h(X))))))),
% 0.13/0.36 inference(bind,[status(th)],[])).
% 0.13/0.36 tff(31,plain,
% 0.13/0.36 (![X: $i] : (~(big_f(X) & (big_g(X) | big_h(X)))) <=> ![X: $i] : ((~big_f(X)) | (~(big_g(X) | big_h(X))))),
% 0.13/0.36 inference(quant_intro,[status(thm)],[30])).
% 0.13/0.36 tff(32,plain,
% 0.13/0.36 ((~?[X: $i] : (big_f(X) & (big_g(X) | big_h(X)))) <=> (~?[X: $i] : (big_f(X) & (big_g(X) | big_h(X))))),
% 0.13/0.36 inference(rewrite,[status(thm)],[])).
% 0.13/0.36 tff(33,axiom,(~?[X: $i] : (big_f(X) & (big_g(X) | big_h(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','pel31_1')).
% 0.13/0.36 tff(34,plain,
% 0.13/0.36 (~?[X: $i] : (big_f(X) & (big_g(X) | big_h(X)))),
% 0.13/0.36 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.13/0.36 tff(35,plain,
% 0.13/0.36 (~?[X: $i] : (big_f(X) & (big_g(X) | big_h(X)))),
% 0.13/0.36 inference(modus_ponens,[status(thm)],[34, 32])).
% 0.13/0.36 tff(36,plain,
% 0.13/0.36 (~?[X: $i] : (big_f(X) & (big_g(X) | big_h(X)))),
% 0.13/0.36 inference(modus_ponens,[status(thm)],[35, 32])).
% 0.13/0.36 tff(37,plain,
% 0.13/0.36 (~?[X: $i] : (big_f(X) & (big_g(X) | big_h(X)))),
% 0.13/0.36 inference(modus_ponens,[status(thm)],[36, 32])).
% 0.13/0.36 tff(38,plain,
% 0.13/0.36 (~?[X: $i] : (big_f(X) & (big_g(X) | big_h(X)))),
% 0.13/0.36 inference(modus_ponens,[status(thm)],[37, 32])).
% 0.13/0.36 tff(39,plain,
% 0.13/0.36 (~?[X: $i] : (big_f(X) & (big_g(X) | big_h(X)))),
% 0.13/0.36 inference(modus_ponens,[status(thm)],[38, 32])).
% 0.13/0.36 tff(40,plain,
% 0.13/0.36 (~?[X: $i] : (big_f(X) & (big_g(X) | big_h(X)))),
% 0.13/0.36 inference(modus_ponens,[status(thm)],[39, 32])).
% 0.13/0.36 tff(41,plain,
% 0.13/0.36 (^[X: $i] : refl($oeq((~(big_f(X) & (big_g(X) | big_h(X)))), (~(big_f(X) & (big_g(X) | big_h(X))))))),
% 0.13/0.36 inference(bind,[status(th)],[])).
% 0.13/0.36 tff(42,plain,(
% 0.13/0.36 ![X: $i] : (~(big_f(X) & (big_g(X) | big_h(X))))),
% 0.13/0.36 inference(nnf-neg,[status(sab)],[40, 41])).
% 0.13/0.36 tff(43,plain,
% 0.13/0.36 (![X: $i] : ((~big_f(X)) | (~(big_g(X) | big_h(X))))),
% 0.13/0.36 inference(modus_ponens,[status(thm)],[42, 31])).
% 0.13/0.36 tff(44,plain,
% 0.13/0.36 (![X: $i] : ((~big_f(X)) | (~(big_g(X) | big_h(X))))),
% 0.13/0.36 inference(modus_ponens,[status(thm)],[43, 29])).
% 0.13/0.36 tff(45,plain,
% 0.13/0.36 (((~![X: $i] : ((~big_f(X)) | (~(big_g(X) | big_h(X))))) | ((~big_f(X!0)) | (~(big_g(X!0) | big_h(X!0))))) <=> ((~![X: $i] : ((~big_f(X)) | (~(big_g(X) | big_h(X))))) | (~big_f(X!0)) | (~(big_g(X!0) | big_h(X!0))))),
% 0.13/0.36 inference(rewrite,[status(thm)],[])).
% 0.13/0.36 tff(46,plain,
% 0.13/0.36 ((~![X: $i] : ((~big_f(X)) | (~(big_g(X) | big_h(X))))) | ((~big_f(X!0)) | (~(big_g(X!0) | big_h(X!0))))),
% 0.13/0.36 inference(quant_inst,[status(thm)],[])).
% 0.13/0.36 tff(47,plain,
% 0.13/0.36 ((~![X: $i] : ((~big_f(X)) | (~(big_g(X) | big_h(X))))) | (~big_f(X!0)) | (~(big_g(X!0) | big_h(X!0)))),
% 0.13/0.36 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.13/0.36 tff(48,plain,
% 0.13/0.36 (~(big_g(X!0) | big_h(X!0))),
% 0.13/0.36 inference(unit_resolution,[status(thm)],[47, 44, 27])).
% 0.13/0.36 tff(49,plain,
% 0.13/0.36 ((big_g(X!0) | big_h(X!0)) | (~big_h(X!0))),
% 0.13/0.36 inference(tautology,[status(thm)],[])).
% 0.13/0.36 tff(50,plain,
% 0.13/0.36 (~big_h(X!0)),
% 0.13/0.36 inference(unit_resolution,[status(thm)],[49, 48])).
% 0.13/0.36 tff(51,plain,
% 0.13/0.36 (^[X: $i] : refl((big_h(X) | big_j(X)) <=> (big_h(X) | big_j(X)))),
% 0.13/0.36 inference(bind,[status(th)],[])).
% 0.13/0.36 tff(52,plain,
% 0.13/0.36 (![X: $i] : (big_h(X) | big_j(X)) <=> ![X: $i] : (big_h(X) | big_j(X))),
% 0.13/0.36 inference(quant_intro,[status(thm)],[51])).
% 0.13/0.36 tff(53,plain,
% 0.13/0.36 (![X: $i] : (big_h(X) | big_j(X)) <=> ![X: $i] : (big_h(X) | big_j(X))),
% 0.13/0.36 inference(rewrite,[status(thm)],[])).
% 0.13/0.36 tff(54,plain,
% 0.13/0.36 (^[X: $i] : rewrite(((~big_h(X)) => big_j(X)) <=> (big_h(X) | big_j(X)))),
% 0.13/0.36 inference(bind,[status(th)],[])).
% 0.13/0.36 tff(55,plain,
% 0.13/0.36 (![X: $i] : ((~big_h(X)) => big_j(X)) <=> ![X: $i] : (big_h(X) | big_j(X))),
% 0.13/0.36 inference(quant_intro,[status(thm)],[54])).
% 0.13/0.36 tff(56,axiom,(![X: $i] : ((~big_h(X)) => big_j(X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','pel31_3')).
% 0.13/0.36 tff(57,plain,
% 0.13/0.36 (![X: $i] : (big_h(X) | big_j(X))),
% 0.13/0.36 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.13/0.36 tff(58,plain,
% 0.13/0.36 (![X: $i] : (big_h(X) | big_j(X))),
% 0.13/0.36 inference(modus_ponens,[status(thm)],[57, 53])).
% 0.13/0.36 tff(59,plain,(
% 0.13/0.36 ![X: $i] : (big_h(X) | big_j(X))),
% 0.13/0.36 inference(skolemize,[status(sab)],[58])).
% 0.13/0.36 tff(60,plain,
% 0.13/0.36 (![X: $i] : (big_h(X) | big_j(X))),
% 0.13/0.36 inference(modus_ponens,[status(thm)],[59, 52])).
% 0.13/0.36 tff(61,plain,
% 0.13/0.36 (((~![X: $i] : (big_h(X) | big_j(X))) | (big_h(X!0) | big_j(X!0))) <=> ((~![X: $i] : (big_h(X) | big_j(X))) | big_h(X!0) | big_j(X!0))),
% 0.13/0.36 inference(rewrite,[status(thm)],[])).
% 0.13/0.36 tff(62,plain,
% 0.13/0.36 ((~![X: $i] : (big_h(X) | big_j(X))) | (big_h(X!0) | big_j(X!0))),
% 0.13/0.36 inference(quant_inst,[status(thm)],[])).
% 0.13/0.36 tff(63,plain,
% 0.13/0.36 ((~![X: $i] : (big_h(X) | big_j(X))) | big_h(X!0) | big_j(X!0)),
% 0.13/0.36 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.13/0.36 tff(64,plain,
% 0.13/0.36 ($false),
% 0.13/0.36 inference(unit_resolution,[status(thm)],[63, 60, 50, 26])).
% 0.13/0.36 % SZS output end Proof
%------------------------------------------------------------------------------