TSTP Solution File: SYN081+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN081+1 : TPTP v8.1.0. Released v2.0.0.
% 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 23:53:39 EDT 2022
% Result : Theorem 0.21s 0.39s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SYN081+1 : TPTP v8.1.0. Released v2.0.0.
% 0.06/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n002.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Mon Sep 5 01:52:48 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.21/0.39 % SZS status Theorem
% 0.21/0.39 % SZS output start Proof
% 0.21/0.39 tff(big_f_type, type, (
% 0.21/0.39 big_f: $i > $o)).
% 0.21/0.39 tff(f_type, type, (
% 0.21/0.39 f: $i > $i)).
% 0.21/0.39 tff(elem_0_type, type, (
% 0.21/0.39 elem_0: $i)).
% 0.21/0.39 tff(1,assumption,(big_f(f(elem!0))), introduced(assumption)).
% 0.21/0.39 tff(2,plain,
% 0.21/0.39 (^[X: $i] : refl((big_f(f(X)) | (~big_f(X))) <=> (big_f(f(X)) | (~big_f(X))))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(3,plain,
% 0.21/0.39 (![X: $i] : (big_f(f(X)) | (~big_f(X))) <=> ![X: $i] : (big_f(f(X)) | (~big_f(X)))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[2])).
% 0.21/0.39 tff(4,plain,
% 0.21/0.39 (^[X: $i] : trans(monotonicity(rewrite((big_f(X) & (~big_f(f(X)))) <=> (~(big_f(f(X)) | (~big_f(X))))), ((~(big_f(X) & (~big_f(f(X))))) <=> (~(~(big_f(f(X)) | (~big_f(X))))))), rewrite((~(~(big_f(f(X)) | (~big_f(X))))) <=> (big_f(f(X)) | (~big_f(X)))), ((~(big_f(X) & (~big_f(f(X))))) <=> (big_f(f(X)) | (~big_f(X)))))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(5,plain,
% 0.21/0.39 (![X: $i] : (~(big_f(X) & (~big_f(f(X))))) <=> ![X: $i] : (big_f(f(X)) | (~big_f(X)))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[4])).
% 0.21/0.39 tff(6,plain,
% 0.21/0.39 ((~?[X: $i] : (big_f(X) & (~big_f(f(X))))) <=> (~?[X: $i] : (big_f(X) & (~big_f(f(X)))))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(7,axiom,(~?[X: $i] : (big_f(X) & (~big_f(f(X))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','pel59')).
% 0.21/0.39 tff(8,plain,
% 0.21/0.39 (~?[X: $i] : (big_f(X) & (~big_f(f(X))))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.21/0.39 tff(9,plain,
% 0.21/0.39 (~?[X: $i] : (big_f(X) & (~big_f(f(X))))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[8, 6])).
% 0.21/0.39 tff(10,plain,
% 0.21/0.39 (~?[X: $i] : (big_f(X) & (~big_f(f(X))))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[9, 6])).
% 0.21/0.39 tff(11,plain,
% 0.21/0.39 (~?[X: $i] : (big_f(X) & (~big_f(f(X))))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[10, 6])).
% 0.21/0.39 tff(12,plain,
% 0.21/0.39 (~?[X: $i] : (big_f(X) & (~big_f(f(X))))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[11, 6])).
% 0.21/0.39 tff(13,plain,
% 0.21/0.39 (~?[X: $i] : (big_f(X) & (~big_f(f(X))))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[12, 6])).
% 0.21/0.39 tff(14,plain,
% 0.21/0.39 (~?[X: $i] : (big_f(X) & (~big_f(f(X))))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[13, 6])).
% 0.21/0.39 tff(15,plain,
% 0.21/0.39 (^[X: $i] : refl($oeq((~(big_f(X) & (~big_f(f(X))))), (~(big_f(X) & (~big_f(f(X)))))))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(16,plain,(
% 0.21/0.39 ![X: $i] : (~(big_f(X) & (~big_f(f(X)))))),
% 0.21/0.39 inference(nnf-neg,[status(sab)],[14, 15])).
% 0.21/0.39 tff(17,plain,
% 0.21/0.39 (![X: $i] : (big_f(f(X)) | (~big_f(X)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[16, 5])).
% 0.21/0.39 tff(18,plain,
% 0.21/0.39 (![X: $i] : (big_f(f(X)) | (~big_f(X)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[17, 3])).
% 0.21/0.39 tff(19,plain,
% 0.21/0.39 (((~![X: $i] : (big_f(f(X)) | (~big_f(X)))) | (big_f(f(f(elem!0))) | (~big_f(f(elem!0))))) <=> ((~![X: $i] : (big_f(f(X)) | (~big_f(X)))) | big_f(f(f(elem!0))) | (~big_f(f(elem!0))))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(20,plain,
% 0.21/0.39 ((~![X: $i] : (big_f(f(X)) | (~big_f(X)))) | (big_f(f(f(elem!0))) | (~big_f(f(elem!0))))),
% 0.21/0.39 inference(quant_inst,[status(thm)],[])).
% 0.21/0.39 tff(21,plain,
% 0.21/0.39 ((~![X: $i] : (big_f(f(X)) | (~big_f(X)))) | big_f(f(f(elem!0))) | (~big_f(f(elem!0)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.21/0.39 tff(22,plain,
% 0.21/0.39 (big_f(f(f(elem!0))) | (~big_f(f(elem!0)))),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[21, 18])).
% 0.21/0.39 tff(23,plain,
% 0.21/0.39 (big_f(f(f(elem!0)))),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[22, 1])).
% 0.21/0.39 tff(24,assumption,(~(big_f(f(elem!0)) <=> (~big_f(f(f(elem!0)))))), introduced(assumption)).
% 0.21/0.39 tff(25,plain,
% 0.21/0.39 (^[X: $i] : refl((big_f(X) <=> (~big_f(f(X)))) <=> (big_f(X) <=> (~big_f(f(X)))))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(26,plain,
% 0.21/0.39 (![X: $i] : (big_f(X) <=> (~big_f(f(X)))) <=> ![X: $i] : (big_f(X) <=> (~big_f(f(X))))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[25])).
% 0.21/0.39 tff(27,plain,
% 0.21/0.39 (![X: $i] : (big_f(X) <=> (~big_f(f(X)))) <=> ![X: $i] : (big_f(X) <=> (~big_f(f(X))))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(28,axiom,(![X: $i] : (big_f(X) <=> (~big_f(f(X))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','pel59_1')).
% 0.21/0.39 tff(29,plain,
% 0.21/0.39 (![X: $i] : (big_f(X) <=> (~big_f(f(X))))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.21/0.40 tff(30,plain,(
% 0.21/0.40 ![X: $i] : (big_f(X) <=> (~big_f(f(X))))),
% 0.21/0.40 inference(skolemize,[status(sab)],[29])).
% 0.21/0.40 tff(31,plain,
% 0.21/0.40 (![X: $i] : (big_f(X) <=> (~big_f(f(X))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[30, 26])).
% 0.21/0.40 tff(32,plain,
% 0.21/0.40 ((~![X: $i] : (big_f(X) <=> (~big_f(f(X))))) | (big_f(f(elem!0)) <=> (~big_f(f(f(elem!0)))))),
% 0.21/0.40 inference(quant_inst,[status(thm)],[])).
% 0.21/0.40 tff(33,plain,
% 0.21/0.40 ($false),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[32, 31, 24])).
% 0.21/0.40 tff(34,plain,(big_f(f(elem!0)) <=> (~big_f(f(f(elem!0))))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.40 tff(35,plain,
% 0.21/0.40 ((~(big_f(f(elem!0)) <=> (~big_f(f(f(elem!0)))))) | (~big_f(f(elem!0))) | (~big_f(f(f(elem!0))))),
% 0.21/0.40 inference(tautology,[status(thm)],[])).
% 0.21/0.40 tff(36,plain,
% 0.21/0.40 ((~big_f(f(elem!0))) | (~big_f(f(f(elem!0))))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[35, 34])).
% 0.21/0.40 tff(37,plain,
% 0.21/0.40 ($false),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[36, 23, 1])).
% 0.21/0.40 tff(38,plain,(~big_f(f(elem!0))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.40 tff(39,plain,
% 0.21/0.40 ((~![X: $i] : (big_f(X) <=> (~big_f(f(X))))) | (big_f(elem!0) <=> (~big_f(f(elem!0))))),
% 0.21/0.40 inference(quant_inst,[status(thm)],[])).
% 0.21/0.40 tff(40,plain,
% 0.21/0.40 (big_f(elem!0) <=> (~big_f(f(elem!0)))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[39, 31])).
% 0.21/0.40 tff(41,plain,
% 0.21/0.40 ((~(big_f(elem!0) <=> (~big_f(f(elem!0))))) | big_f(elem!0) | big_f(f(elem!0))),
% 0.21/0.40 inference(tautology,[status(thm)],[])).
% 0.21/0.40 tff(42,plain,
% 0.21/0.40 (big_f(elem!0) | big_f(f(elem!0))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[41, 40])).
% 0.21/0.40 tff(43,plain,
% 0.21/0.40 (big_f(elem!0)),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[42, 38])).
% 0.21/0.40 tff(44,plain,
% 0.21/0.40 (((~![X: $i] : (big_f(f(X)) | (~big_f(X)))) | (big_f(f(elem!0)) | (~big_f(elem!0)))) <=> ((~![X: $i] : (big_f(f(X)) | (~big_f(X)))) | big_f(f(elem!0)) | (~big_f(elem!0)))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(45,plain,
% 0.21/0.40 ((~![X: $i] : (big_f(f(X)) | (~big_f(X)))) | (big_f(f(elem!0)) | (~big_f(elem!0)))),
% 0.21/0.40 inference(quant_inst,[status(thm)],[])).
% 0.21/0.40 tff(46,plain,
% 0.21/0.40 ((~![X: $i] : (big_f(f(X)) | (~big_f(X)))) | big_f(f(elem!0)) | (~big_f(elem!0))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.21/0.40 tff(47,plain,
% 0.21/0.40 (big_f(f(elem!0)) | (~big_f(elem!0))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[46, 18])).
% 0.21/0.40 tff(48,plain,
% 0.21/0.40 ($false),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[47, 43, 38])).
% 0.21/0.40 % SZS output end Proof
%------------------------------------------------------------------------------