TSTP Solution File: SYN054-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN054-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n002.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 23:53:23 EDT 2022
% Result : Unsatisfiable 0.21s 0.38s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYN054-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n002.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 01:36:33 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.21/0.38 % SZS status Unsatisfiable
% 0.21/0.38 % SZS output start Proof
% 0.21/0.38 tff(big_r_type, type, (
% 0.21/0.38 big_r: $i > $o)).
% 0.21/0.38 tff(a_type, type, (
% 0.21/0.38 a: $i)).
% 0.21/0.38 tff(big_p_type, type, (
% 0.21/0.38 big_p: $i > $o)).
% 0.21/0.38 tff(big_q_type, type, (
% 0.21/0.38 big_q: $i > $o)).
% 0.21/0.38 tff(b_type, type, (
% 0.21/0.38 b: $i)).
% 0.21/0.38 tff(big_s_type, type, (
% 0.21/0.38 big_s: $i > $o)).
% 0.21/0.38 tff(1,plain,
% 0.21/0.38 (^[X: $i] : refl(((~big_q(X)) | big_s(X)) <=> ((~big_q(X)) | big_s(X)))),
% 0.21/0.38 inference(bind,[status(th)],[])).
% 0.21/0.38 tff(2,plain,
% 0.21/0.38 (![X: $i] : ((~big_q(X)) | big_s(X)) <=> ![X: $i] : ((~big_q(X)) | big_s(X))),
% 0.21/0.38 inference(quant_intro,[status(thm)],[1])).
% 0.21/0.38 tff(3,plain,
% 0.21/0.38 (![X: $i] : ((~big_q(X)) | big_s(X)) <=> ![X: $i] : ((~big_q(X)) | big_s(X))),
% 0.21/0.38 inference(rewrite,[status(thm)],[])).
% 0.21/0.38 tff(4,axiom,(![X: $i] : ((~big_q(X)) | big_s(X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_4')).
% 0.21/0.38 tff(5,plain,
% 0.21/0.38 (![X: $i] : ((~big_q(X)) | big_s(X))),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.21/0.38 tff(6,plain,(
% 0.21/0.38 ![X: $i] : ((~big_q(X)) | big_s(X))),
% 0.21/0.38 inference(skolemize,[status(sab)],[5])).
% 0.21/0.38 tff(7,plain,
% 0.21/0.38 (![X: $i] : ((~big_q(X)) | big_s(X))),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.21/0.38 tff(8,assumption,(big_q(b)), introduced(assumption)).
% 0.21/0.38 tff(9,plain,
% 0.21/0.38 (((~![X: $i] : ((~big_q(X)) | big_s(X))) | ((~big_q(b)) | big_s(b))) <=> ((~![X: $i] : ((~big_q(X)) | big_s(X))) | (~big_q(b)) | big_s(b))),
% 0.21/0.38 inference(rewrite,[status(thm)],[])).
% 0.21/0.38 tff(10,plain,
% 0.21/0.38 ((~![X: $i] : ((~big_q(X)) | big_s(X))) | ((~big_q(b)) | big_s(b))),
% 0.21/0.38 inference(quant_inst,[status(thm)],[])).
% 0.21/0.38 tff(11,plain,
% 0.21/0.38 ((~![X: $i] : ((~big_q(X)) | big_s(X))) | (~big_q(b)) | big_s(b)),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[10, 9])).
% 0.21/0.38 tff(12,plain,
% 0.21/0.38 (big_s(b)),
% 0.21/0.38 inference(unit_resolution,[status(thm)],[11, 8, 7])).
% 0.21/0.38 tff(13,plain,
% 0.21/0.38 (^[X: $i] : refl(((~big_q(X)) | (~big_s(X))) <=> ((~big_q(X)) | (~big_s(X))))),
% 0.21/0.38 inference(bind,[status(th)],[])).
% 0.21/0.38 tff(14,plain,
% 0.21/0.38 (![X: $i] : ((~big_q(X)) | (~big_s(X))) <=> ![X: $i] : ((~big_q(X)) | (~big_s(X)))),
% 0.21/0.38 inference(quant_intro,[status(thm)],[13])).
% 0.21/0.38 tff(15,plain,
% 0.21/0.38 (![X: $i] : ((~big_q(X)) | (~big_s(X))) <=> ![X: $i] : ((~big_q(X)) | (~big_s(X)))),
% 0.21/0.38 inference(rewrite,[status(thm)],[])).
% 0.21/0.38 tff(16,plain,
% 0.21/0.38 (^[X: $i] : rewrite(((~big_s(X)) | (~big_q(X))) <=> ((~big_q(X)) | (~big_s(X))))),
% 0.21/0.38 inference(bind,[status(th)],[])).
% 0.21/0.38 tff(17,plain,
% 0.21/0.38 (![X: $i] : ((~big_s(X)) | (~big_q(X))) <=> ![X: $i] : ((~big_q(X)) | (~big_s(X)))),
% 0.21/0.38 inference(quant_intro,[status(thm)],[16])).
% 0.21/0.38 tff(18,axiom,(![X: $i] : ((~big_s(X)) | (~big_q(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_1')).
% 0.21/0.38 tff(19,plain,
% 0.21/0.38 (![X: $i] : ((~big_q(X)) | (~big_s(X)))),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.21/0.38 tff(20,plain,
% 0.21/0.38 (![X: $i] : ((~big_q(X)) | (~big_s(X)))),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[19, 15])).
% 0.21/0.38 tff(21,plain,(
% 0.21/0.38 ![X: $i] : ((~big_q(X)) | (~big_s(X)))),
% 0.21/0.38 inference(skolemize,[status(sab)],[20])).
% 0.21/0.38 tff(22,plain,
% 0.21/0.38 (![X: $i] : ((~big_q(X)) | (~big_s(X)))),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[21, 14])).
% 0.21/0.38 tff(23,plain,
% 0.21/0.38 (((~![X: $i] : ((~big_q(X)) | (~big_s(X)))) | ((~big_q(b)) | (~big_s(b)))) <=> ((~![X: $i] : ((~big_q(X)) | (~big_s(X)))) | (~big_q(b)) | (~big_s(b)))),
% 0.21/0.38 inference(rewrite,[status(thm)],[])).
% 0.21/0.38 tff(24,plain,
% 0.21/0.38 ((~![X: $i] : ((~big_q(X)) | (~big_s(X)))) | ((~big_q(b)) | (~big_s(b)))),
% 0.21/0.38 inference(quant_inst,[status(thm)],[])).
% 0.21/0.38 tff(25,plain,
% 0.21/0.38 ((~![X: $i] : ((~big_q(X)) | (~big_s(X)))) | (~big_q(b)) | (~big_s(b))),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.21/0.38 tff(26,plain,
% 0.21/0.38 ($false),
% 0.21/0.38 inference(unit_resolution,[status(thm)],[25, 22, 8, 12])).
% 0.21/0.38 tff(27,plain,(~big_q(b)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.38 tff(28,plain,
% 0.21/0.38 ((big_p(a) | big_q(b)) <=> (big_p(a) | big_q(b))),
% 0.21/0.38 inference(rewrite,[status(thm)],[])).
% 0.21/0.38 tff(29,axiom,(big_p(a) | big_q(b)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_3')).
% 0.21/0.38 tff(30,plain,
% 0.21/0.38 (big_p(a) | big_q(b)),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.21/0.38 tff(31,plain,
% 0.21/0.38 (big_p(a)),
% 0.21/0.38 inference(unit_resolution,[status(thm)],[30, 27])).
% 0.21/0.39 tff(32,assumption,(big_q(a)), introduced(assumption)).
% 0.21/0.39 tff(33,plain,
% 0.21/0.39 (((~![X: $i] : ((~big_q(X)) | big_s(X))) | ((~big_q(a)) | big_s(a))) <=> ((~![X: $i] : ((~big_q(X)) | big_s(X))) | (~big_q(a)) | big_s(a))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(34,plain,
% 0.21/0.39 ((~![X: $i] : ((~big_q(X)) | big_s(X))) | ((~big_q(a)) | big_s(a))),
% 0.21/0.39 inference(quant_inst,[status(thm)],[])).
% 0.21/0.39 tff(35,plain,
% 0.21/0.39 ((~![X: $i] : ((~big_q(X)) | big_s(X))) | (~big_q(a)) | big_s(a)),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.21/0.39 tff(36,plain,
% 0.21/0.39 (big_s(a)),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[35, 7, 32])).
% 0.21/0.39 tff(37,plain,
% 0.21/0.39 (((~![X: $i] : ((~big_q(X)) | (~big_s(X)))) | ((~big_q(a)) | (~big_s(a)))) <=> ((~![X: $i] : ((~big_q(X)) | (~big_s(X)))) | (~big_q(a)) | (~big_s(a)))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(38,plain,
% 0.21/0.39 ((~![X: $i] : ((~big_q(X)) | (~big_s(X)))) | ((~big_q(a)) | (~big_s(a)))),
% 0.21/0.39 inference(quant_inst,[status(thm)],[])).
% 0.21/0.39 tff(39,plain,
% 0.21/0.39 ((~![X: $i] : ((~big_q(X)) | (~big_s(X)))) | (~big_q(a)) | (~big_s(a))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.21/0.39 tff(40,plain,
% 0.21/0.39 ($false),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[39, 22, 32, 36])).
% 0.21/0.39 tff(41,plain,(~big_q(a)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.39 tff(42,plain,
% 0.21/0.39 (^[X: $i] : refl((big_q(X) | big_r(X) | (~big_p(X))) <=> (big_q(X) | big_r(X) | (~big_p(X))))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(43,plain,
% 0.21/0.39 (![X: $i] : (big_q(X) | big_r(X) | (~big_p(X))) <=> ![X: $i] : (big_q(X) | big_r(X) | (~big_p(X)))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[42])).
% 0.21/0.39 tff(44,plain,
% 0.21/0.39 (![X: $i] : (big_q(X) | big_r(X) | (~big_p(X))) <=> ![X: $i] : (big_q(X) | big_r(X) | (~big_p(X)))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(45,plain,
% 0.21/0.39 (^[X: $i] : trans(monotonicity(rewrite(((~big_p(X)) | big_q(X)) <=> (big_q(X) | (~big_p(X)))), ((((~big_p(X)) | big_q(X)) | big_r(X)) <=> ((big_q(X) | (~big_p(X))) | big_r(X)))), rewrite(((big_q(X) | (~big_p(X))) | big_r(X)) <=> (big_q(X) | big_r(X) | (~big_p(X)))), ((((~big_p(X)) | big_q(X)) | big_r(X)) <=> (big_q(X) | big_r(X) | (~big_p(X)))))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(46,plain,
% 0.21/0.39 (![X: $i] : (((~big_p(X)) | big_q(X)) | big_r(X)) <=> ![X: $i] : (big_q(X) | big_r(X) | (~big_p(X)))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[45])).
% 0.21/0.39 tff(47,axiom,(![X: $i] : (((~big_p(X)) | big_q(X)) | big_r(X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_2')).
% 0.21/0.39 tff(48,plain,
% 0.21/0.39 (![X: $i] : (big_q(X) | big_r(X) | (~big_p(X)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.21/0.39 tff(49,plain,
% 0.21/0.39 (![X: $i] : (big_q(X) | big_r(X) | (~big_p(X)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[48, 44])).
% 0.21/0.39 tff(50,plain,(
% 0.21/0.39 ![X: $i] : (big_q(X) | big_r(X) | (~big_p(X)))),
% 0.21/0.39 inference(skolemize,[status(sab)],[49])).
% 0.21/0.39 tff(51,plain,
% 0.21/0.39 (![X: $i] : (big_q(X) | big_r(X) | (~big_p(X)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[50, 43])).
% 0.21/0.39 tff(52,plain,
% 0.21/0.39 (((~![X: $i] : (big_q(X) | big_r(X) | (~big_p(X)))) | (big_q(a) | big_r(a) | (~big_p(a)))) <=> ((~![X: $i] : (big_q(X) | big_r(X) | (~big_p(X)))) | big_q(a) | big_r(a) | (~big_p(a)))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(53,plain,
% 0.21/0.39 ((~![X: $i] : (big_q(X) | big_r(X) | (~big_p(X)))) | (big_q(a) | big_r(a) | (~big_p(a)))),
% 0.21/0.39 inference(quant_inst,[status(thm)],[])).
% 0.21/0.39 tff(54,plain,
% 0.21/0.39 ((~![X: $i] : (big_q(X) | big_r(X) | (~big_p(X)))) | big_q(a) | big_r(a) | (~big_p(a))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.21/0.39 tff(55,plain,
% 0.21/0.39 (big_r(a) | (~big_p(a))),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[54, 51, 41])).
% 0.21/0.39 tff(56,plain,
% 0.21/0.39 (big_r(a)),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[55, 31])).
% 0.21/0.39 tff(57,plain,
% 0.21/0.39 (^[X: $i] : refl(((~big_p(X)) | (~big_r(X))) <=> ((~big_p(X)) | (~big_r(X))))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(58,plain,
% 0.21/0.39 (![X: $i] : ((~big_p(X)) | (~big_r(X))) <=> ![X: $i] : ((~big_p(X)) | (~big_r(X)))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[57])).
% 0.21/0.39 tff(59,plain,
% 0.21/0.39 (![X: $i] : ((~big_p(X)) | (~big_r(X))) <=> ![X: $i] : ((~big_p(X)) | (~big_r(X)))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(60,axiom,(![X: $i] : ((~big_p(X)) | (~big_r(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_6')).
% 0.21/0.39 tff(61,plain,
% 0.21/0.39 (![X: $i] : ((~big_p(X)) | (~big_r(X)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.21/0.39 tff(62,plain,(
% 0.21/0.39 ![X: $i] : ((~big_p(X)) | (~big_r(X)))),
% 0.21/0.39 inference(skolemize,[status(sab)],[61])).
% 0.21/0.39 tff(63,plain,
% 0.21/0.39 (![X: $i] : ((~big_p(X)) | (~big_r(X)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[62, 58])).
% 0.21/0.39 tff(64,plain,
% 0.21/0.39 (((~![X: $i] : ((~big_p(X)) | (~big_r(X)))) | ((~big_p(a)) | (~big_r(a)))) <=> ((~![X: $i] : ((~big_p(X)) | (~big_r(X)))) | (~big_p(a)) | (~big_r(a)))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(65,plain,
% 0.21/0.39 ((~![X: $i] : ((~big_p(X)) | (~big_r(X)))) | ((~big_p(a)) | (~big_r(a)))),
% 0.21/0.39 inference(quant_inst,[status(thm)],[])).
% 0.21/0.39 tff(66,plain,
% 0.21/0.39 ((~![X: $i] : ((~big_p(X)) | (~big_r(X)))) | (~big_p(a)) | (~big_r(a))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.21/0.39 tff(67,plain,
% 0.21/0.39 ($false),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[66, 31, 63, 56])).
% 0.21/0.39 % SZS output end Proof
%------------------------------------------------------------------------------