TSTP Solution File: SYN362+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN362+1 : TPTP v8.1.0. Released v2.0.0.
% 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 23:54:59 EDT 2022
% Result : Theorem 0.13s 0.37s
% Output : Proof 0.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYN362+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 : n022.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 02:56:09 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.
% 0.13/0.37 % SZS status Theorem
% 0.13/0.37 % SZS output start Proof
% 0.13/0.37 tff(big_p_type, type, (
% 0.13/0.37 big_p: $i > $o)).
% 0.13/0.37 tff(tptp_fun_W_0_type, type, (
% 0.13/0.37 tptp_fun_W_0: $i > $i)).
% 0.13/0.37 tff(tptp_fun_Z_1_type, type, (
% 0.13/0.37 tptp_fun_Z_1: $i)).
% 0.13/0.37 tff(big_r_type, type, (
% 0.13/0.37 big_r: ( $i * $i ) > $o)).
% 0.13/0.37 tff(1,plain,
% 0.13/0.37 (![Y: $i] : ?[W: $i] : big_r(Y, W) <=> ![Y: $i] : ?[W: $i] : big_r(Y, W)),
% 0.13/0.37 inference(rewrite,[status(thm)],[])).
% 0.13/0.37 tff(2,plain,
% 0.13/0.37 ((~((![Y: $i] : ?[W: $i] : big_r(Y, W) & ?[Z: $i] : ![X: $i] : (big_p(X) => (~big_r(Z, X)))) => ?[X: $i] : (~big_p(X)))) <=> (~((~(![Y: $i] : ?[W: $i] : big_r(Y, W) & ?[Z: $i] : ![X: $i] : ((~big_p(X)) | (~big_r(Z, X))))) | ?[X: $i] : (~big_p(X))))),
% 0.13/0.37 inference(rewrite,[status(thm)],[])).
% 0.13/0.37 tff(3,axiom,(~((![Y: $i] : ?[W: $i] : big_r(Y, W) & ?[Z: $i] : ![X: $i] : (big_p(X) => (~big_r(Z, X)))) => ?[X: $i] : (~big_p(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','x2113')).
% 0.13/0.37 tff(4,plain,
% 0.13/0.37 (~((~(![Y: $i] : ?[W: $i] : big_r(Y, W) & ?[Z: $i] : ![X: $i] : ((~big_p(X)) | (~big_r(Z, X))))) | ?[X: $i] : (~big_p(X)))),
% 0.13/0.37 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.13/0.37 tff(5,plain,
% 0.13/0.37 (![Y: $i] : ?[W: $i] : big_r(Y, W) & ?[Z: $i] : ![X: $i] : ((~big_p(X)) | (~big_r(Z, X)))),
% 0.13/0.37 inference(or_elim,[status(thm)],[4])).
% 0.13/0.37 tff(6,plain,
% 0.13/0.37 (![Y: $i] : ?[W: $i] : big_r(Y, W)),
% 0.13/0.37 inference(and_elim,[status(thm)],[5])).
% 0.13/0.37 tff(7,plain,
% 0.13/0.37 (![Y: $i] : ?[W: $i] : big_r(Y, W)),
% 0.13/0.37 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.13/0.37 tff(8,plain,(
% 0.13/0.37 ![Y: $i] : big_r(Y, tptp_fun_W_0(Y))),
% 0.13/0.37 inference(skolemize,[status(sab)],[7])).
% 0.13/0.37 tff(9,plain,
% 0.13/0.37 ((~![Y: $i] : big_r(Y, tptp_fun_W_0(Y))) | big_r(Z!1, tptp_fun_W_0(Z!1))),
% 0.13/0.37 inference(quant_inst,[status(thm)],[])).
% 0.13/0.37 tff(10,plain,
% 0.13/0.37 (big_r(Z!1, tptp_fun_W_0(Z!1))),
% 0.13/0.37 inference(unit_resolution,[status(thm)],[9, 8])).
% 0.13/0.37 tff(11,plain,
% 0.13/0.37 (^[X: $i] : refl(((~big_p(X)) | (~big_r(Z!1, X))) <=> ((~big_p(X)) | (~big_r(Z!1, X))))),
% 0.13/0.37 inference(bind,[status(th)],[])).
% 0.13/0.37 tff(12,plain,
% 0.13/0.37 (![X: $i] : ((~big_p(X)) | (~big_r(Z!1, X))) <=> ![X: $i] : ((~big_p(X)) | (~big_r(Z!1, X)))),
% 0.13/0.37 inference(quant_intro,[status(thm)],[11])).
% 0.13/0.37 tff(13,plain,
% 0.13/0.37 (?[Z: $i] : ![X: $i] : ((~big_p(X)) | (~big_r(Z, X))) <=> ?[Z: $i] : ![X: $i] : ((~big_p(X)) | (~big_r(Z, X)))),
% 0.13/0.37 inference(rewrite,[status(thm)],[])).
% 0.13/0.37 tff(14,plain,
% 0.13/0.37 (?[Z: $i] : ![X: $i] : ((~big_p(X)) | (~big_r(Z, X)))),
% 0.13/0.37 inference(and_elim,[status(thm)],[5])).
% 0.13/0.37 tff(15,plain,
% 0.13/0.37 (?[Z: $i] : ![X: $i] : ((~big_p(X)) | (~big_r(Z, X)))),
% 0.13/0.37 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.13/0.37 tff(16,plain,(
% 0.13/0.37 $oeq(![X: $i] : ((~big_p(X)) | (~big_r(Z!1, X))), ![X: $i] : ((~big_p(X)) | (~big_r(Z!1, X))))),
% 0.13/0.37 inference(transitivity,[status(sab)],[15])).
% 0.13/0.37 tff(17,plain,
% 0.13/0.37 (![X: $i] : ((~big_p(X)) | (~big_r(Z!1, X)))),
% 0.13/0.37 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.13/0.37 tff(18,plain,
% 0.13/0.37 (((~![X: $i] : ((~big_p(X)) | (~big_r(Z!1, X)))) | ((~big_p(tptp_fun_W_0(Z!1))) | (~big_r(Z!1, tptp_fun_W_0(Z!1))))) <=> ((~![X: $i] : ((~big_p(X)) | (~big_r(Z!1, X)))) | (~big_p(tptp_fun_W_0(Z!1))) | (~big_r(Z!1, tptp_fun_W_0(Z!1))))),
% 0.13/0.37 inference(rewrite,[status(thm)],[])).
% 0.13/0.37 tff(19,plain,
% 0.13/0.37 ((~![X: $i] : ((~big_p(X)) | (~big_r(Z!1, X)))) | ((~big_p(tptp_fun_W_0(Z!1))) | (~big_r(Z!1, tptp_fun_W_0(Z!1))))),
% 0.13/0.37 inference(quant_inst,[status(thm)],[])).
% 0.13/0.37 tff(20,plain,
% 0.13/0.37 ((~![X: $i] : ((~big_p(X)) | (~big_r(Z!1, X)))) | (~big_p(tptp_fun_W_0(Z!1))) | (~big_r(Z!1, tptp_fun_W_0(Z!1)))),
% 0.13/0.37 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.13/0.37 tff(21,plain,
% 0.13/0.37 (~big_p(tptp_fun_W_0(Z!1))),
% 0.13/0.37 inference(unit_resolution,[status(thm)],[20, 17, 10])).
% 0.13/0.37 tff(22,plain,
% 0.13/0.37 (^[X: $i] : refl(big_p(X) <=> big_p(X))),
% 0.13/0.37 inference(bind,[status(th)],[])).
% 0.13/0.37 tff(23,plain,
% 0.13/0.37 (![X: $i] : big_p(X) <=> ![X: $i] : big_p(X)),
% 0.13/0.37 inference(quant_intro,[status(thm)],[22])).
% 0.13/0.37 tff(24,plain,
% 0.13/0.37 (^[X: $i] : rewrite((~(~big_p(X))) <=> big_p(X))),
% 0.13/0.37 inference(bind,[status(th)],[])).
% 0.13/0.37 tff(25,plain,
% 0.13/0.37 (![X: $i] : (~(~big_p(X))) <=> ![X: $i] : big_p(X)),
% 0.13/0.37 inference(quant_intro,[status(thm)],[24])).
% 0.13/0.37 tff(26,plain,
% 0.13/0.37 ((~?[X: $i] : (~big_p(X))) <=> (~?[X: $i] : (~big_p(X)))),
% 0.13/0.37 inference(rewrite,[status(thm)],[])).
% 0.13/0.37 tff(27,plain,
% 0.13/0.37 (~?[X: $i] : (~big_p(X))),
% 0.13/0.37 inference(or_elim,[status(thm)],[4])).
% 0.13/0.37 tff(28,plain,
% 0.13/0.37 (~?[X: $i] : (~big_p(X))),
% 0.13/0.37 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.13/0.37 tff(29,plain,
% 0.13/0.37 (~?[X: $i] : (~big_p(X))),
% 0.13/0.37 inference(modus_ponens,[status(thm)],[28, 26])).
% 0.13/0.37 tff(30,plain,
% 0.13/0.37 (~?[X: $i] : (~big_p(X))),
% 0.13/0.37 inference(modus_ponens,[status(thm)],[29, 26])).
% 0.13/0.37 tff(31,plain,
% 0.13/0.37 (~?[X: $i] : (~big_p(X))),
% 0.13/0.37 inference(modus_ponens,[status(thm)],[30, 26])).
% 0.13/0.37 tff(32,plain,
% 0.13/0.37 (~?[X: $i] : (~big_p(X))),
% 0.13/0.37 inference(modus_ponens,[status(thm)],[31, 26])).
% 0.13/0.37 tff(33,plain,
% 0.13/0.37 (~?[X: $i] : (~big_p(X))),
% 0.13/0.37 inference(modus_ponens,[status(thm)],[32, 26])).
% 0.13/0.37 tff(34,plain,
% 0.13/0.37 (^[X: $i] : refl($oeq((~(~big_p(X))), (~(~big_p(X)))))),
% 0.13/0.37 inference(bind,[status(th)],[])).
% 0.13/0.37 tff(35,plain,(
% 0.13/0.37 ![X: $i] : (~(~big_p(X)))),
% 0.13/0.37 inference(nnf-neg,[status(sab)],[33, 34])).
% 0.13/0.37 tff(36,plain,
% 0.13/0.37 (![X: $i] : big_p(X)),
% 0.13/0.37 inference(modus_ponens,[status(thm)],[35, 25])).
% 0.13/0.37 tff(37,plain,
% 0.13/0.37 (![X: $i] : big_p(X)),
% 0.13/0.37 inference(modus_ponens,[status(thm)],[36, 23])).
% 0.13/0.37 tff(38,plain,
% 0.13/0.37 ((~![X: $i] : big_p(X)) | big_p(tptp_fun_W_0(Z!1))),
% 0.13/0.37 inference(quant_inst,[status(thm)],[])).
% 0.13/0.37 tff(39,plain,
% 0.13/0.37 ($false),
% 0.13/0.37 inference(unit_resolution,[status(thm)],[38, 37, 21])).
% 0.13/0.37 % SZS output end Proof
%------------------------------------------------------------------------------