TSTP Solution File: SYN064+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN064+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n027.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 23:53:28 EDT 2022
% Result : Theorem 0.13s 0.40s
% Output : Proof 0.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SYN064+1 : TPTP v8.1.0. Released v2.0.0.
% 0.12/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35 % Computer : n027.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon Sep 5 01:45:37 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.13/0.40 % SZS status Theorem
% 0.13/0.40 % SZS output start Proof
% 0.13/0.40 tff(big_p_type, type, (
% 0.13/0.40 big_p: ( $i * $i ) > $o)).
% 0.13/0.40 tff(tptp_fun_W_0_type, type, (
% 0.13/0.40 tptp_fun_W_0: $i)).
% 0.13/0.40 tff(tptp_fun_Z_1_type, type, (
% 0.13/0.40 tptp_fun_Z_1: $i)).
% 0.13/0.40 tff(1,plain,
% 0.13/0.40 (((~![X: $i, Y: $i] : (~((~big_p(X, Y)) | big_p(Z!1, W!0)))) | $false) <=> (~![X: $i, Y: $i] : (~((~big_p(X, Y)) | big_p(Z!1, W!0))))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(2,plain,
% 0.13/0.40 ((~$true) <=> $false),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(3,plain,
% 0.13/0.40 (((~big_p(Z!1, W!0)) | big_p(Z!1, W!0)) <=> $true),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(4,plain,
% 0.13/0.40 ((~((~big_p(Z!1, W!0)) | big_p(Z!1, W!0))) <=> (~$true)),
% 0.13/0.40 inference(monotonicity,[status(thm)],[3])).
% 0.13/0.40 tff(5,plain,
% 0.13/0.40 ((~((~big_p(Z!1, W!0)) | big_p(Z!1, W!0))) <=> $false),
% 0.13/0.40 inference(transitivity,[status(thm)],[4, 2])).
% 0.13/0.40 tff(6,plain,
% 0.13/0.40 (((~![X: $i, Y: $i] : (~((~big_p(X, Y)) | big_p(Z!1, W!0)))) | (~((~big_p(Z!1, W!0)) | big_p(Z!1, W!0)))) <=> ((~![X: $i, Y: $i] : (~((~big_p(X, Y)) | big_p(Z!1, W!0)))) | $false)),
% 0.13/0.40 inference(monotonicity,[status(thm)],[5])).
% 0.13/0.40 tff(7,plain,
% 0.13/0.40 (((~![X: $i, Y: $i] : (~((~big_p(X, Y)) | big_p(Z!1, W!0)))) | (~((~big_p(Z!1, W!0)) | big_p(Z!1, W!0)))) <=> (~![X: $i, Y: $i] : (~((~big_p(X, Y)) | big_p(Z!1, W!0))))),
% 0.13/0.40 inference(transitivity,[status(thm)],[6, 1])).
% 0.13/0.40 tff(8,plain,
% 0.13/0.40 ((~![X: $i, Y: $i] : (~((~big_p(X, Y)) | big_p(Z!1, W!0)))) | (~((~big_p(Z!1, W!0)) | big_p(Z!1, W!0)))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(9,plain,
% 0.13/0.40 (~![X: $i, Y: $i] : (~((~big_p(X, Y)) | big_p(Z!1, W!0)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.13/0.40 tff(10,plain,
% 0.13/0.40 (^[X: $i, Y: $i] : refl((~((~big_p(X, Y)) | big_p(Z!1, W!0))) <=> (~((~big_p(X, Y)) | big_p(Z!1, W!0))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(11,plain,
% 0.13/0.40 (![X: $i, Y: $i] : (~((~big_p(X, Y)) | big_p(Z!1, W!0))) <=> ![X: $i, Y: $i] : (~((~big_p(X, Y)) | big_p(Z!1, W!0)))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[10])).
% 0.13/0.40 tff(12,plain,
% 0.13/0.40 (^[X: $i, Y: $i] : rewrite((big_p(X, Y) & (~big_p(Z!1, W!0))) <=> (~((~big_p(X, Y)) | big_p(Z!1, W!0))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(13,plain,
% 0.13/0.40 (![X: $i, Y: $i] : (big_p(X, Y) & (~big_p(Z!1, W!0))) <=> ![X: $i, Y: $i] : (~((~big_p(X, Y)) | big_p(Z!1, W!0)))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[12])).
% 0.13/0.40 tff(14,plain,
% 0.13/0.40 (^[X: $i, Y: $i] : rewrite(((~(~big_p(X, Y))) & (~big_p(Z!1, W!0))) <=> (big_p(X, Y) & (~big_p(Z!1, W!0))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(15,plain,
% 0.13/0.40 (![X: $i, Y: $i] : ((~(~big_p(X, Y))) & (~big_p(Z!1, W!0))) <=> ![X: $i, Y: $i] : (big_p(X, Y) & (~big_p(Z!1, W!0)))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[14])).
% 0.13/0.40 tff(16,plain,
% 0.13/0.40 ((~?[X: $i, Y: $i] : ((~big_p(X, Y)) | ![Z: $i, W: $i] : big_p(Z, W))) <=> (~?[X: $i, Y: $i] : ((~big_p(X, Y)) | ![Z: $i, W: $i] : big_p(Z, W)))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(17,plain,
% 0.13/0.40 ((~?[X: $i, Y: $i] : (big_p(X, Y) => ![Z: $i, W: $i] : big_p(Z, W))) <=> (~?[X: $i, Y: $i] : ((~big_p(X, Y)) | ![Z: $i, W: $i] : big_p(Z, W)))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(18,axiom,(~?[X: $i, Y: $i] : (big_p(X, Y) => ![Z: $i, W: $i] : big_p(Z, W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel35')).
% 0.13/0.40 tff(19,plain,
% 0.13/0.40 (~?[X: $i, Y: $i] : ((~big_p(X, Y)) | ![Z: $i, W: $i] : big_p(Z, W))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.13/0.40 tff(20,plain,
% 0.13/0.40 (~?[X: $i, Y: $i] : ((~big_p(X, Y)) | ![Z: $i, W: $i] : big_p(Z, W))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[19, 16])).
% 0.13/0.40 tff(21,plain,
% 0.13/0.40 (~?[X: $i, Y: $i] : ((~big_p(X, Y)) | ![Z: $i, W: $i] : big_p(Z, W))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[20, 16])).
% 0.13/0.40 tff(22,plain,
% 0.13/0.40 (~?[X: $i, Y: $i] : ((~big_p(X, Y)) | ![Z: $i, W: $i] : big_p(Z, W))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[21, 16])).
% 0.13/0.40 tff(23,plain,
% 0.13/0.40 (~?[X: $i, Y: $i] : ((~big_p(X, Y)) | ![Z: $i, W: $i] : big_p(Z, W))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[22, 16])).
% 0.13/0.40 tff(24,plain,
% 0.13/0.40 (~?[X: $i, Y: $i] : ((~big_p(X, Y)) | ![Z: $i, W: $i] : big_p(Z, W))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[23, 16])).
% 0.13/0.40 tff(25,plain,
% 0.13/0.40 (~?[X: $i, Y: $i] : ((~big_p(X, Y)) | ![Z: $i, W: $i] : big_p(Z, W))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[24, 16])).
% 0.13/0.40 tff(26,plain,
% 0.13/0.40 (^[X: $i, Y: $i] : nnf_neg(refl($oeq((~(~big_p(X, Y))), (~(~big_p(X, Y))))), sk($oeq((~![Z: $i, W: $i] : big_p(Z, W)), (~big_p(Z!1, W!0)))), $oeq((~((~big_p(X, Y)) | ![Z: $i, W: $i] : big_p(Z, W))), ((~(~big_p(X, Y))) & (~big_p(Z!1, W!0)))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(27,plain,(
% 0.13/0.40 ![X: $i, Y: $i] : ((~(~big_p(X, Y))) & (~big_p(Z!1, W!0)))),
% 0.13/0.40 inference(nnf-neg,[status(sab)],[25, 26])).
% 0.13/0.40 tff(28,plain,
% 0.13/0.40 (![X: $i, Y: $i] : (big_p(X, Y) & (~big_p(Z!1, W!0)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[27, 15])).
% 0.13/0.40 tff(29,plain,
% 0.13/0.40 (![X: $i, Y: $i] : (~((~big_p(X, Y)) | big_p(Z!1, W!0)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[28, 13])).
% 0.13/0.40 tff(30,plain,
% 0.13/0.40 (![X: $i, Y: $i] : (~((~big_p(X, Y)) | big_p(Z!1, W!0)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[29, 11])).
% 0.13/0.40 tff(31,plain,
% 0.13/0.40 ($false),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[30, 9])).
% 0.13/0.40 % SZS output end Proof
%------------------------------------------------------------------------------