TSTP Solution File: SYN380+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN380+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 23:55:04 EDT 2022
% Result : Theorem 0.13s 0.39s
% Output : Proof 0.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYN380+1 : TPTP v8.1.0. Released v2.0.0.
% 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 03:11:33 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.
% 0.13/0.39 % SZS status Theorem
% 0.13/0.39 % SZS output start Proof
% 0.13/0.39 tff(big_r_type, type, (
% 0.13/0.39 big_r: ( $i * $i ) > $o)).
% 0.13/0.39 tff(tptp_fun_Z_0_type, type, (
% 0.13/0.39 tptp_fun_Z_0: $i)).
% 0.13/0.39 tff(big_q_type, type, (
% 0.13/0.39 big_q: ( $i * $i ) > $o)).
% 0.13/0.39 tff(1,assumption,(big_r(Z!0, Z!0)), introduced(assumption)).
% 0.13/0.39 tff(2,plain,
% 0.13/0.39 (^[W: $i] : refl((~big_r(W, W)) <=> (~big_r(W, W)))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(3,plain,
% 0.13/0.39 (![W: $i] : (~big_r(W, W)) <=> ![W: $i] : (~big_r(W, W))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[2])).
% 0.13/0.39 tff(4,plain,
% 0.13/0.39 (![W: $i] : (~big_r(W, W)) <=> ![W: $i] : (~big_r(W, W))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(5,plain,
% 0.13/0.39 ((~(![W: $i] : (~big_r(W, W)) => ?[X: $i, Y: $i] : ((~big_r(X, Y)) & (big_q(Y, X) => ![Z: $i] : big_q(Z, Z))))) <=> (~((~![W: $i] : (~big_r(W, W))) | ?[X: $i, Y: $i] : ((~big_r(X, Y)) & ((~big_q(Y, X)) | ![Z: $i] : big_q(Z, Z)))))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(6,axiom,(~(![W: $i] : (~big_r(W, W)) => ?[X: $i, Y: $i] : ((~big_r(X, Y)) & (big_q(Y, X) => ![Z: $i] : big_q(Z, Z))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','x2132')).
% 0.13/0.39 tff(7,plain,
% 0.13/0.39 (~((~![W: $i] : (~big_r(W, W))) | ?[X: $i, Y: $i] : ((~big_r(X, Y)) & ((~big_q(Y, X)) | ![Z: $i] : big_q(Z, Z))))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.13/0.39 tff(8,plain,
% 0.13/0.39 (![W: $i] : (~big_r(W, W))),
% 0.13/0.39 inference(or_elim,[status(thm)],[7])).
% 0.13/0.39 tff(9,plain,
% 0.13/0.39 (![W: $i] : (~big_r(W, W))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.13/0.39 tff(10,plain,(
% 0.13/0.39 ![W: $i] : (~big_r(W, W))),
% 0.13/0.39 inference(skolemize,[status(sab)],[9])).
% 0.13/0.39 tff(11,plain,
% 0.13/0.39 (![W: $i] : (~big_r(W, W))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[10, 3])).
% 0.13/0.39 tff(12,plain,
% 0.13/0.39 ((~![W: $i] : (~big_r(W, W))) | (~big_r(Z!0, Z!0))),
% 0.13/0.39 inference(quant_inst,[status(thm)],[])).
% 0.13/0.39 tff(13,plain,
% 0.13/0.39 ($false),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[12, 11, 1])).
% 0.13/0.39 tff(14,plain,(~big_r(Z!0, Z!0)), inference(lemma,lemma(discharge,[]))).
% 0.13/0.39 tff(15,plain,
% 0.13/0.39 (^[X: $i, Y: $i] : refl((big_r(X, Y) | (~((~big_q(Y, X)) | big_q(Z!0, Z!0)))) <=> (big_r(X, Y) | (~((~big_q(Y, X)) | big_q(Z!0, Z!0)))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(16,plain,
% 0.13/0.39 (![X: $i, Y: $i] : (big_r(X, Y) | (~((~big_q(Y, X)) | big_q(Z!0, Z!0)))) <=> ![X: $i, Y: $i] : (big_r(X, Y) | (~((~big_q(Y, X)) | big_q(Z!0, Z!0))))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[15])).
% 0.13/0.39 tff(17,plain,
% 0.13/0.39 (^[X: $i, Y: $i] : trans(monotonicity(rewrite((big_q(Y, X) & (~big_q(Z!0, Z!0))) <=> (~((~big_q(Y, X)) | big_q(Z!0, Z!0)))), ((big_r(X, Y) | (big_q(Y, X) & (~big_q(Z!0, Z!0)))) <=> (big_r(X, Y) | (~((~big_q(Y, X)) | big_q(Z!0, Z!0)))))), rewrite((big_r(X, Y) | (~((~big_q(Y, X)) | big_q(Z!0, Z!0)))) <=> (big_r(X, Y) | (~((~big_q(Y, X)) | big_q(Z!0, Z!0))))), ((big_r(X, Y) | (big_q(Y, X) & (~big_q(Z!0, Z!0)))) <=> (big_r(X, Y) | (~((~big_q(Y, X)) | big_q(Z!0, Z!0))))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(18,plain,
% 0.13/0.39 (![X: $i, Y: $i] : (big_r(X, Y) | (big_q(Y, X) & (~big_q(Z!0, Z!0)))) <=> ![X: $i, Y: $i] : (big_r(X, Y) | (~((~big_q(Y, X)) | big_q(Z!0, Z!0))))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[17])).
% 0.13/0.39 tff(19,plain,
% 0.13/0.39 (^[X: $i, Y: $i] : rewrite(((~(~big_r(X, Y))) | ((~(~big_q(Y, X))) & (~big_q(Z!0, Z!0)))) <=> (big_r(X, Y) | (big_q(Y, X) & (~big_q(Z!0, Z!0)))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(20,plain,
% 0.13/0.39 (![X: $i, Y: $i] : ((~(~big_r(X, Y))) | ((~(~big_q(Y, X))) & (~big_q(Z!0, Z!0)))) <=> ![X: $i, Y: $i] : (big_r(X, Y) | (big_q(Y, X) & (~big_q(Z!0, Z!0))))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[19])).
% 0.13/0.39 tff(21,plain,
% 0.13/0.39 ((~?[X: $i, Y: $i] : ((~big_r(X, Y)) & ((~big_q(Y, X)) | ![Z: $i] : big_q(Z, Z)))) <=> (~?[X: $i, Y: $i] : ((~big_r(X, Y)) & ((~big_q(Y, X)) | ![Z: $i] : big_q(Z, Z))))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(22,plain,
% 0.13/0.39 (~?[X: $i, Y: $i] : ((~big_r(X, Y)) & ((~big_q(Y, X)) | ![Z: $i] : big_q(Z, Z)))),
% 0.13/0.39 inference(or_elim,[status(thm)],[7])).
% 0.13/0.39 tff(23,plain,
% 0.13/0.39 (~?[X: $i, Y: $i] : ((~big_r(X, Y)) & ((~big_q(Y, X)) | ![Z: $i] : big_q(Z, Z)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.13/0.39 tff(24,plain,
% 0.13/0.39 (~?[X: $i, Y: $i] : ((~big_r(X, Y)) & ((~big_q(Y, X)) | ![Z: $i] : big_q(Z, Z)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[23, 21])).
% 0.13/0.39 tff(25,plain,
% 0.13/0.39 (~?[X: $i, Y: $i] : ((~big_r(X, Y)) & ((~big_q(Y, X)) | ![Z: $i] : big_q(Z, Z)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[24, 21])).
% 0.13/0.39 tff(26,plain,
% 0.13/0.39 (~?[X: $i, Y: $i] : ((~big_r(X, Y)) & ((~big_q(Y, X)) | ![Z: $i] : big_q(Z, Z)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[25, 21])).
% 0.13/0.39 tff(27,plain,
% 0.13/0.39 (~?[X: $i, Y: $i] : ((~big_r(X, Y)) & ((~big_q(Y, X)) | ![Z: $i] : big_q(Z, Z)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[26, 21])).
% 0.13/0.39 tff(28,plain,
% 0.13/0.39 (~?[X: $i, Y: $i] : ((~big_r(X, Y)) & ((~big_q(Y, X)) | ![Z: $i] : big_q(Z, Z)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[27, 21])).
% 0.13/0.39 tff(29,plain,
% 0.13/0.39 (^[X: $i, Y: $i] : nnf_neg(refl($oeq((~(~big_r(X, Y))), (~(~big_r(X, Y))))), nnf_neg(refl($oeq((~(~big_q(Y, X))), (~(~big_q(Y, X))))), sk($oeq((~![Z: $i] : big_q(Z, Z)), (~big_q(Z!0, Z!0)))), $oeq((~((~big_q(Y, X)) | ![Z: $i] : big_q(Z, Z))), ((~(~big_q(Y, X))) & (~big_q(Z!0, Z!0))))), $oeq((~((~big_r(X, Y)) & ((~big_q(Y, X)) | ![Z: $i] : big_q(Z, Z)))), ((~(~big_r(X, Y))) | ((~(~big_q(Y, X))) & (~big_q(Z!0, Z!0))))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(30,plain,(
% 0.13/0.39 ![X: $i, Y: $i] : ((~(~big_r(X, Y))) | ((~(~big_q(Y, X))) & (~big_q(Z!0, Z!0))))),
% 0.13/0.39 inference(nnf-neg,[status(sab)],[28, 29])).
% 0.13/0.39 tff(31,plain,
% 0.13/0.39 (![X: $i, Y: $i] : (big_r(X, Y) | (big_q(Y, X) & (~big_q(Z!0, Z!0))))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[30, 20])).
% 0.13/0.39 tff(32,plain,
% 0.13/0.39 (![X: $i, Y: $i] : (big_r(X, Y) | (~((~big_q(Y, X)) | big_q(Z!0, Z!0))))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[31, 18])).
% 0.13/0.39 tff(33,plain,
% 0.13/0.39 (![X: $i, Y: $i] : (big_r(X, Y) | (~((~big_q(Y, X)) | big_q(Z!0, Z!0))))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[32, 16])).
% 0.13/0.39 tff(34,plain,
% 0.13/0.39 (((~![X: $i, Y: $i] : (big_r(X, Y) | (~((~big_q(Y, X)) | big_q(Z!0, Z!0))))) | big_r(Z!0, Z!0)) <=> ((~![X: $i, Y: $i] : (big_r(X, Y) | (~((~big_q(Y, X)) | big_q(Z!0, Z!0))))) | big_r(Z!0, Z!0))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(35,plain,
% 0.13/0.39 ((big_r(Z!0, Z!0) | $false) <=> big_r(Z!0, Z!0)),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(36,plain,
% 0.13/0.39 ((~$true) <=> $false),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(37,plain,
% 0.13/0.39 (((~big_q(Z!0, Z!0)) | big_q(Z!0, Z!0)) <=> $true),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(38,plain,
% 0.13/0.39 ((~((~big_q(Z!0, Z!0)) | big_q(Z!0, Z!0))) <=> (~$true)),
% 0.13/0.39 inference(monotonicity,[status(thm)],[37])).
% 0.13/0.39 tff(39,plain,
% 0.13/0.39 ((~((~big_q(Z!0, Z!0)) | big_q(Z!0, Z!0))) <=> $false),
% 0.13/0.39 inference(transitivity,[status(thm)],[38, 36])).
% 0.13/0.39 tff(40,plain,
% 0.13/0.39 ((big_r(Z!0, Z!0) | (~((~big_q(Z!0, Z!0)) | big_q(Z!0, Z!0)))) <=> (big_r(Z!0, Z!0) | $false)),
% 0.13/0.39 inference(monotonicity,[status(thm)],[39])).
% 0.13/0.39 tff(41,plain,
% 0.13/0.39 ((big_r(Z!0, Z!0) | (~((~big_q(Z!0, Z!0)) | big_q(Z!0, Z!0)))) <=> big_r(Z!0, Z!0)),
% 0.13/0.39 inference(transitivity,[status(thm)],[40, 35])).
% 0.13/0.39 tff(42,plain,
% 0.13/0.39 (((~![X: $i, Y: $i] : (big_r(X, Y) | (~((~big_q(Y, X)) | big_q(Z!0, Z!0))))) | (big_r(Z!0, Z!0) | (~((~big_q(Z!0, Z!0)) | big_q(Z!0, Z!0))))) <=> ((~![X: $i, Y: $i] : (big_r(X, Y) | (~((~big_q(Y, X)) | big_q(Z!0, Z!0))))) | big_r(Z!0, Z!0))),
% 0.13/0.39 inference(monotonicity,[status(thm)],[41])).
% 0.13/0.39 tff(43,plain,
% 0.13/0.39 (((~![X: $i, Y: $i] : (big_r(X, Y) | (~((~big_q(Y, X)) | big_q(Z!0, Z!0))))) | (big_r(Z!0, Z!0) | (~((~big_q(Z!0, Z!0)) | big_q(Z!0, Z!0))))) <=> ((~![X: $i, Y: $i] : (big_r(X, Y) | (~((~big_q(Y, X)) | big_q(Z!0, Z!0))))) | big_r(Z!0, Z!0))),
% 0.13/0.39 inference(transitivity,[status(thm)],[42, 34])).
% 0.13/0.39 tff(44,plain,
% 0.13/0.39 ((~![X: $i, Y: $i] : (big_r(X, Y) | (~((~big_q(Y, X)) | big_q(Z!0, Z!0))))) | (big_r(Z!0, Z!0) | (~((~big_q(Z!0, Z!0)) | big_q(Z!0, Z!0))))),
% 0.13/0.39 inference(quant_inst,[status(thm)],[])).
% 0.13/0.39 tff(45,plain,
% 0.13/0.39 ((~![X: $i, Y: $i] : (big_r(X, Y) | (~((~big_q(Y, X)) | big_q(Z!0, Z!0))))) | big_r(Z!0, Z!0)),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.13/0.39 tff(46,plain,
% 0.13/0.39 ($false),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[45, 33, 14])).
% 0.13/0.39 % SZS output end Proof
%------------------------------------------------------------------------------