TSTP Solution File: SYN399+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN399+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n019.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 23:55:10 EDT 2022
% Result : Theorem 0.20s 0.39s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYN399+1 : TPTP v8.1.0. Released v2.0.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n019.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 03:11:35 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.
% 0.20/0.39 % SZS status Theorem
% 0.20/0.39 % SZS output start Proof
% 0.20/0.39 tff(f_type, type, (
% 0.20/0.39 f: $i > $o)).
% 0.20/0.39 tff(tptp_fun_Y_0_type, type, (
% 0.20/0.39 tptp_fun_Y_0: $i)).
% 0.20/0.39 tff(p_type, type, (
% 0.20/0.39 p: $o)).
% 0.20/0.39 tff(1,assumption,(~f(Y!0)), introduced(assumption)).
% 0.20/0.39 tff(2,plain,
% 0.20/0.39 (^[X: $i] : refl((~((~((~f(X)) | (~f(Y!0)))) | (~(f(X) | ![Y: $i] : f(Y))))) <=> (~((~((~f(X)) | (~f(Y!0)))) | (~(f(X) | ![Y: $i] : f(Y))))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(3,plain,
% 0.20/0.39 (![X: $i] : (~((~((~f(X)) | (~f(Y!0)))) | (~(f(X) | ![Y: $i] : f(Y))))) <=> ![X: $i] : (~((~((~f(X)) | (~f(Y!0)))) | (~(f(X) | ![Y: $i] : f(Y)))))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[2])).
% 0.20/0.39 tff(4,plain,
% 0.20/0.39 (^[X: $i] : rewrite((~((~((~f(X)) | (~f(Y!0)))) | (~(f(X) | ![Y: $i] : f(Y))))) <=> (~((~((~f(X)) | (~f(Y!0)))) | (~(f(X) | ![Y: $i] : f(Y))))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(5,plain,
% 0.20/0.39 (![X: $i] : (~((~((~f(X)) | (~f(Y!0)))) | (~(f(X) | ![Y: $i] : f(Y))))) <=> ![X: $i] : (~((~((~f(X)) | (~f(Y!0)))) | (~(f(X) | ![Y: $i] : f(Y)))))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[4])).
% 0.20/0.39 tff(6,plain,
% 0.20/0.39 (![X: $i] : (~((~((~f(X)) | (~f(Y!0)))) | (~(f(X) | ![Y: $i] : f(Y))))) <=> ![X: $i] : (~((~((~f(X)) | (~f(Y!0)))) | (~(f(X) | ![Y: $i] : f(Y)))))),
% 0.20/0.39 inference(transitivity,[status(thm)],[5, 3])).
% 0.20/0.39 tff(7,plain,
% 0.20/0.39 (^[X: $i] : trans(monotonicity(rewrite(((~f(X)) | (~f(Y!0))) <=> ((~f(X)) | (~f(Y!0)))), rewrite((f(X) | ![Y: $i] : f(Y)) <=> (f(X) | ![Y: $i] : f(Y))), ((((~f(X)) | (~f(Y!0))) & (f(X) | ![Y: $i] : f(Y))) <=> (((~f(X)) | (~f(Y!0))) & (f(X) | ![Y: $i] : f(Y))))), rewrite((((~f(X)) | (~f(Y!0))) & (f(X) | ![Y: $i] : f(Y))) <=> (~((~((~f(X)) | (~f(Y!0)))) | (~(f(X) | ![Y: $i] : f(Y)))))), ((((~f(X)) | (~f(Y!0))) & (f(X) | ![Y: $i] : f(Y))) <=> (~((~((~f(X)) | (~f(Y!0)))) | (~(f(X) | ![Y: $i] : f(Y)))))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(8,plain,
% 0.20/0.39 (![X: $i] : (((~f(X)) | (~f(Y!0))) & (f(X) | ![Y: $i] : f(Y))) <=> ![X: $i] : (~((~((~f(X)) | (~f(Y!0)))) | (~(f(X) | ![Y: $i] : f(Y)))))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[7])).
% 0.20/0.39 tff(9,plain,
% 0.20/0.39 (^[X: $i] : rewrite((f(X) <=> p) <=> (f(X) <=> (~![Y: $i] : f(Y))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(10,plain,
% 0.20/0.39 (![X: $i] : (f(X) <=> p) <=> ![X: $i] : (f(X) <=> (~![Y: $i] : f(Y)))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[9])).
% 0.20/0.39 tff(11,plain,
% 0.20/0.39 (![X: $i] : (f(X) <=> p) <=> ![X: $i] : (f(X) <=> p)),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(12,plain,
% 0.20/0.39 ((~(![X: $i] : (f(X) <=> p) => (![Y: $i] : f(Y) <=> p))) <=> (~((~![X: $i] : (f(X) <=> p)) | (![Y: $i] : f(Y) <=> p)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(13,axiom,(~(![X: $i] : (f(X) <=> p) => (![Y: $i] : f(Y) <=> p))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','kalish223')).
% 0.20/0.39 tff(14,plain,
% 0.20/0.39 (~((~![X: $i] : (f(X) <=> p)) | (![Y: $i] : f(Y) <=> p))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.20/0.39 tff(15,plain,
% 0.20/0.39 (![X: $i] : (f(X) <=> p)),
% 0.20/0.39 inference(or_elim,[status(thm)],[14])).
% 0.20/0.39 tff(16,plain,
% 0.20/0.39 (![X: $i] : (f(X) <=> p)),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[15, 11])).
% 0.20/0.39 tff(17,plain,
% 0.20/0.39 (![X: $i] : (f(X) <=> (~![Y: $i] : f(Y)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[16, 10])).
% 0.20/0.39 tff(18,plain,(
% 0.20/0.39 ![X: $i] : (((~f(X)) | (~f(Y!0))) & (f(X) | ![Y: $i] : f(Y)))),
% 0.20/0.39 inference(skolemize,[status(sab)],[17])).
% 0.20/0.39 tff(19,plain,
% 0.20/0.39 (![X: $i] : (~((~((~f(X)) | (~f(Y!0)))) | (~(f(X) | ![Y: $i] : f(Y)))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[18, 8])).
% 0.20/0.39 tff(20,plain,
% 0.20/0.39 (![X: $i] : (~((~((~f(X)) | (~f(Y!0)))) | (~(f(X) | ![Y: $i] : f(Y)))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[19, 6])).
% 0.20/0.39 tff(21,plain,
% 0.20/0.39 (((~![X: $i] : (~((~((~f(X)) | (~f(Y!0)))) | (~(f(X) | ![Y: $i] : f(Y)))))) | (~(f(Y!0) | (~(f(Y!0) | ![Y: $i] : f(Y)))))) <=> ((~![X: $i] : (~((~((~f(X)) | (~f(Y!0)))) | (~(f(X) | ![Y: $i] : f(Y)))))) | (~(f(Y!0) | (~(f(Y!0) | ![Y: $i] : f(Y))))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(22,plain,
% 0.20/0.39 ((~((~((~f(Y!0)) | (~f(Y!0)))) | (~(f(Y!0) | ![Y: $i] : f(Y))))) <=> (~(f(Y!0) | (~(f(Y!0) | ![Y: $i] : f(Y)))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(23,plain,
% 0.20/0.39 (((~![X: $i] : (~((~((~f(X)) | (~f(Y!0)))) | (~(f(X) | ![Y: $i] : f(Y)))))) | (~((~((~f(Y!0)) | (~f(Y!0)))) | (~(f(Y!0) | ![Y: $i] : f(Y)))))) <=> ((~![X: $i] : (~((~((~f(X)) | (~f(Y!0)))) | (~(f(X) | ![Y: $i] : f(Y)))))) | (~(f(Y!0) | (~(f(Y!0) | ![Y: $i] : f(Y))))))),
% 0.20/0.39 inference(monotonicity,[status(thm)],[22])).
% 0.20/0.39 tff(24,plain,
% 0.20/0.39 (((~![X: $i] : (~((~((~f(X)) | (~f(Y!0)))) | (~(f(X) | ![Y: $i] : f(Y)))))) | (~((~((~f(Y!0)) | (~f(Y!0)))) | (~(f(Y!0) | ![Y: $i] : f(Y)))))) <=> ((~![X: $i] : (~((~((~f(X)) | (~f(Y!0)))) | (~(f(X) | ![Y: $i] : f(Y)))))) | (~(f(Y!0) | (~(f(Y!0) | ![Y: $i] : f(Y))))))),
% 0.20/0.39 inference(transitivity,[status(thm)],[23, 21])).
% 0.20/0.39 tff(25,plain,
% 0.20/0.39 ((~![X: $i] : (~((~((~f(X)) | (~f(Y!0)))) | (~(f(X) | ![Y: $i] : f(Y)))))) | (~((~((~f(Y!0)) | (~f(Y!0)))) | (~(f(Y!0) | ![Y: $i] : f(Y)))))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(26,plain,
% 0.20/0.39 ((~![X: $i] : (~((~((~f(X)) | (~f(Y!0)))) | (~(f(X) | ![Y: $i] : f(Y)))))) | (~(f(Y!0) | (~(f(Y!0) | ![Y: $i] : f(Y)))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.20/0.39 tff(27,plain,
% 0.20/0.39 (~(f(Y!0) | (~(f(Y!0) | ![Y: $i] : f(Y))))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[26, 20])).
% 0.20/0.39 tff(28,plain,
% 0.20/0.39 ((f(Y!0) | (~(f(Y!0) | ![Y: $i] : f(Y)))) | (f(Y!0) | ![Y: $i] : f(Y))),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(29,plain,
% 0.20/0.39 (f(Y!0) | ![Y: $i] : f(Y)),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[28, 27])).
% 0.20/0.39 tff(30,plain,
% 0.20/0.39 ((~(f(Y!0) | ![Y: $i] : f(Y))) | f(Y!0) | ![Y: $i] : f(Y)),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(31,plain,
% 0.20/0.39 ((~(f(Y!0) | ![Y: $i] : f(Y))) | ![Y: $i] : f(Y)),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[30, 1])).
% 0.20/0.39 tff(32,plain,
% 0.20/0.39 (![Y: $i] : f(Y)),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[31, 29])).
% 0.20/0.39 tff(33,plain,
% 0.20/0.39 ((~![Y: $i] : f(Y)) | f(Y!0)),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(34,plain,
% 0.20/0.39 ($false),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[33, 32, 1])).
% 0.20/0.39 tff(35,plain,(f(Y!0)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.39 tff(36,plain,
% 0.20/0.39 ((f(Y!0) | (~(f(Y!0) | ![Y: $i] : f(Y)))) | (~f(Y!0))),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(37,plain,
% 0.20/0.39 (f(Y!0) | (~(f(Y!0) | ![Y: $i] : f(Y)))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[36, 35])).
% 0.20/0.39 tff(38,plain,
% 0.20/0.39 ($false),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[26, 20, 37])).
% 0.20/0.39 % SZS output end Proof
%------------------------------------------------------------------------------