TSTP Solution File: SYN053-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN053-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n022.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 23:53:22 EDT 2022
% Result : Unsatisfiable 0.13s 0.38s
% Output : Proof 0.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SYN053-1 : TPTP v8.1.0. Released v1.0.0.
% 0.10/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n022.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
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Sep 5 01:24:54 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.
% 0.13/0.38 % SZS status Unsatisfiable
% 0.13/0.38 % SZS output start Proof
% 0.13/0.38 tff(big_f_type, type, (
% 0.13/0.38 big_f: $i > $o)).
% 0.13/0.38 tff(a_type, type, (
% 0.13/0.38 a: $i)).
% 0.13/0.38 tff(b_type, type, (
% 0.13/0.38 b: $i)).
% 0.13/0.38 tff(p_type, type, (
% 0.13/0.38 p: $o)).
% 0.13/0.38 tff(1,assumption,(~big_f(b)), introduced(assumption)).
% 0.13/0.38 tff(2,plain,
% 0.13/0.38 (^[X: $i] : refl((big_f(b) | big_f(X)) <=> (big_f(b) | big_f(X)))),
% 0.13/0.38 inference(bind,[status(th)],[])).
% 0.13/0.38 tff(3,plain,
% 0.13/0.38 (![X: $i] : (big_f(b) | big_f(X)) <=> ![X: $i] : (big_f(b) | big_f(X))),
% 0.13/0.38 inference(quant_intro,[status(thm)],[2])).
% 0.13/0.38 tff(4,plain,
% 0.13/0.38 (![X: $i] : (big_f(b) | big_f(X)) <=> ![X: $i] : (big_f(b) | big_f(X))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(5,plain,
% 0.13/0.38 (^[X: $i] : trans(monotonicity(iff_false(asserted(~p), (p <=> $false)), ((p | big_f(b) | big_f(X)) <=> ($false | big_f(b) | big_f(X)))), rewrite(($false | big_f(b) | big_f(X)) <=> (big_f(b) | big_f(X))), ((p | big_f(b) | big_f(X)) <=> (big_f(b) | big_f(X))))),
% 0.13/0.38 inference(bind,[status(th)],[])).
% 0.13/0.38 tff(6,plain,
% 0.13/0.38 (![X: $i] : (p | big_f(b) | big_f(X)) <=> ![X: $i] : (big_f(b) | big_f(X))),
% 0.13/0.38 inference(quant_intro,[status(thm)],[5])).
% 0.13/0.38 tff(7,plain,
% 0.13/0.38 (^[X: $i] : rewrite(((p | big_f(X)) | big_f(b)) <=> (p | big_f(b) | big_f(X)))),
% 0.13/0.38 inference(bind,[status(th)],[])).
% 0.13/0.38 tff(8,plain,
% 0.13/0.38 (![X: $i] : ((p | big_f(X)) | big_f(b)) <=> ![X: $i] : (p | big_f(b) | big_f(X))),
% 0.13/0.38 inference(quant_intro,[status(thm)],[7])).
% 0.13/0.38 tff(9,axiom,(![X: $i] : ((p | big_f(X)) | big_f(b))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_2')).
% 0.13/0.38 tff(10,plain,
% 0.13/0.38 (![X: $i] : (p | big_f(b) | big_f(X))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[9, 8])).
% 0.13/0.38 tff(11,plain,
% 0.13/0.38 (![X: $i] : (big_f(b) | big_f(X))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[10, 6])).
% 0.13/0.38 tff(12,plain,
% 0.13/0.38 (![X: $i] : (big_f(b) | big_f(X))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[11, 4])).
% 0.13/0.38 tff(13,plain,(
% 0.13/0.38 ![X: $i] : (big_f(b) | big_f(X))),
% 0.13/0.38 inference(skolemize,[status(sab)],[12])).
% 0.13/0.38 tff(14,plain,
% 0.13/0.38 (![X: $i] : (big_f(b) | big_f(X))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[13, 3])).
% 0.13/0.38 tff(15,plain,
% 0.13/0.38 (((~![X: $i] : (big_f(b) | big_f(X))) | big_f(b)) <=> ((~![X: $i] : (big_f(b) | big_f(X))) | big_f(b))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(16,plain,
% 0.13/0.38 ((big_f(b) | big_f(b)) <=> big_f(b)),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(17,plain,
% 0.13/0.38 (((~![X: $i] : (big_f(b) | big_f(X))) | (big_f(b) | big_f(b))) <=> ((~![X: $i] : (big_f(b) | big_f(X))) | big_f(b))),
% 0.13/0.38 inference(monotonicity,[status(thm)],[16])).
% 0.13/0.38 tff(18,plain,
% 0.13/0.38 (((~![X: $i] : (big_f(b) | big_f(X))) | (big_f(b) | big_f(b))) <=> ((~![X: $i] : (big_f(b) | big_f(X))) | big_f(b))),
% 0.13/0.38 inference(transitivity,[status(thm)],[17, 15])).
% 0.13/0.38 tff(19,plain,
% 0.13/0.38 ((~![X: $i] : (big_f(b) | big_f(X))) | (big_f(b) | big_f(b))),
% 0.13/0.38 inference(quant_inst,[status(thm)],[])).
% 0.13/0.38 tff(20,plain,
% 0.13/0.38 ((~![X: $i] : (big_f(b) | big_f(X))) | big_f(b)),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.13/0.38 tff(21,plain,
% 0.13/0.38 ($false),
% 0.13/0.38 inference(unit_resolution,[status(thm)],[20, 14, 1])).
% 0.13/0.38 tff(22,plain,(big_f(b)), inference(lemma,lemma(discharge,[]))).
% 0.13/0.38 tff(23,plain,
% 0.13/0.38 (((~big_f(a)) | (~big_f(b))) <=> ((~big_f(a)) | (~big_f(b)))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(24,axiom,((~big_f(a)) | (~big_f(b))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_5')).
% 0.13/0.38 tff(25,plain,
% 0.13/0.38 ((~big_f(a)) | (~big_f(b))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.13/0.38 tff(26,plain,
% 0.13/0.38 (~big_f(a)),
% 0.13/0.38 inference(unit_resolution,[status(thm)],[25, 22])).
% 0.13/0.38 tff(27,plain,
% 0.13/0.38 (^[Y: $i, X: $i] : refl((big_f(Y) | big_f(X)) <=> (big_f(Y) | big_f(X)))),
% 0.13/0.38 inference(bind,[status(th)],[])).
% 0.13/0.38 tff(28,plain,
% 0.13/0.38 (![Y: $i, X: $i] : (big_f(Y) | big_f(X)) <=> ![Y: $i, X: $i] : (big_f(Y) | big_f(X))),
% 0.13/0.38 inference(quant_intro,[status(thm)],[27])).
% 0.13/0.38 tff(29,plain,
% 0.13/0.38 (![Y: $i, X: $i] : (big_f(Y) | big_f(X)) <=> ![Y: $i, X: $i] : (big_f(Y) | big_f(X))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(30,plain,
% 0.13/0.38 (^[Y: $i, X: $i] : trans(monotonicity(iff_false(asserted(~p), (p <=> $false)), ((p | big_f(Y) | big_f(X)) <=> ($false | big_f(Y) | big_f(X)))), rewrite(($false | big_f(Y) | big_f(X)) <=> (big_f(Y) | big_f(X))), ((p | big_f(Y) | big_f(X)) <=> (big_f(Y) | big_f(X))))),
% 0.13/0.38 inference(bind,[status(th)],[])).
% 0.13/0.38 tff(31,plain,
% 0.13/0.38 (![Y: $i, X: $i] : (p | big_f(Y) | big_f(X)) <=> ![Y: $i, X: $i] : (big_f(Y) | big_f(X))),
% 0.13/0.38 inference(quant_intro,[status(thm)],[30])).
% 0.13/0.38 tff(32,plain,
% 0.13/0.38 (^[Y: $i, X: $i] : rewrite(((p | big_f(X)) | big_f(Y)) <=> (p | big_f(Y) | big_f(X)))),
% 0.13/0.38 inference(bind,[status(th)],[])).
% 0.13/0.38 tff(33,plain,
% 0.13/0.38 (![Y: $i, X: $i] : ((p | big_f(X)) | big_f(Y)) <=> ![Y: $i, X: $i] : (p | big_f(Y) | big_f(X))),
% 0.13/0.38 inference(quant_intro,[status(thm)],[32])).
% 0.13/0.38 tff(34,axiom,(![Y: $i, X: $i] : ((p | big_f(X)) | big_f(Y))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_1')).
% 0.13/0.38 tff(35,plain,
% 0.13/0.38 (![Y: $i, X: $i] : (p | big_f(Y) | big_f(X))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.13/0.38 tff(36,plain,
% 0.13/0.38 (![Y: $i, X: $i] : (big_f(Y) | big_f(X))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[35, 31])).
% 0.13/0.38 tff(37,plain,
% 0.13/0.38 (![Y: $i, X: $i] : (big_f(Y) | big_f(X))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[36, 29])).
% 0.13/0.38 tff(38,plain,(
% 0.13/0.38 ![Y: $i, X: $i] : (big_f(Y) | big_f(X))),
% 0.13/0.38 inference(skolemize,[status(sab)],[37])).
% 0.13/0.38 tff(39,plain,
% 0.13/0.38 (![Y: $i, X: $i] : (big_f(Y) | big_f(X))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[38, 28])).
% 0.13/0.38 tff(40,plain,
% 0.13/0.38 (((~![Y: $i, X: $i] : (big_f(Y) | big_f(X))) | big_f(a)) <=> ((~![Y: $i, X: $i] : (big_f(Y) | big_f(X))) | big_f(a))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(41,plain,
% 0.13/0.38 ((big_f(a) | big_f(a)) <=> big_f(a)),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(42,plain,
% 0.13/0.38 (((~![Y: $i, X: $i] : (big_f(Y) | big_f(X))) | (big_f(a) | big_f(a))) <=> ((~![Y: $i, X: $i] : (big_f(Y) | big_f(X))) | big_f(a))),
% 0.13/0.38 inference(monotonicity,[status(thm)],[41])).
% 0.13/0.38 tff(43,plain,
% 0.13/0.38 (((~![Y: $i, X: $i] : (big_f(Y) | big_f(X))) | (big_f(a) | big_f(a))) <=> ((~![Y: $i, X: $i] : (big_f(Y) | big_f(X))) | big_f(a))),
% 0.13/0.38 inference(transitivity,[status(thm)],[42, 40])).
% 0.13/0.38 tff(44,plain,
% 0.13/0.38 ((~![Y: $i, X: $i] : (big_f(Y) | big_f(X))) | (big_f(a) | big_f(a))),
% 0.13/0.38 inference(quant_inst,[status(thm)],[])).
% 0.13/0.38 tff(45,plain,
% 0.13/0.38 ((~![Y: $i, X: $i] : (big_f(Y) | big_f(X))) | big_f(a)),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.13/0.38 tff(46,plain,
% 0.13/0.38 ($false),
% 0.13/0.38 inference(unit_resolution,[status(thm)],[45, 39, 26])).
% 0.13/0.38 % SZS output end Proof
%------------------------------------------------------------------------------