TSTP Solution File: SYN733+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN733+1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n028.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 23:57:09 EDT 2022
% Result : Theorem 0.20s 0.38s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SYN733+1 : TPTP v8.1.0. Released v2.5.0.
% 0.04/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n028.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 06:59:40 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.
% 0.20/0.38 % SZS status Theorem
% 0.20/0.38 % SZS output start Proof
% 0.20/0.38 tff(q_type, type, (
% 0.20/0.38 q: $i > $o)).
% 0.20/0.38 tff(tptp_fun_Y_0_type, type, (
% 0.20/0.38 tptp_fun_Y_0: $i > $i)).
% 0.20/0.38 tff(elem_1_type, type, (
% 0.20/0.38 elem_1: $i)).
% 0.20/0.38 tff(p_type, type, (
% 0.20/0.38 p: $i > $o)).
% 0.20/0.38 tff(1,plain,
% 0.20/0.38 (^[X: $i] : refl((~((~p(X)) | (~(q(X) | q(tptp_fun_Y_0(X)))))) <=> (~((~p(X)) | (~(q(X) | q(tptp_fun_Y_0(X)))))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(2,plain,
% 0.20/0.38 (![X: $i] : (~((~p(X)) | (~(q(X) | q(tptp_fun_Y_0(X)))))) <=> ![X: $i] : (~((~p(X)) | (~(q(X) | q(tptp_fun_Y_0(X))))))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[1])).
% 0.20/0.38 tff(3,plain,
% 0.20/0.38 (^[X: $i] : rewrite((p(X) & (q(X) | q(tptp_fun_Y_0(X)))) <=> (~((~p(X)) | (~(q(X) | q(tptp_fun_Y_0(X)))))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(4,plain,
% 0.20/0.38 (![X: $i] : (p(X) & (q(X) | q(tptp_fun_Y_0(X)))) <=> ![X: $i] : (~((~p(X)) | (~(q(X) | q(tptp_fun_Y_0(X))))))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[3])).
% 0.20/0.38 tff(5,plain,
% 0.20/0.38 (^[X: $i] : rewrite((p(X) & (q(tptp_fun_Y_0(X)) | q(X))) <=> (p(X) & (q(X) | q(tptp_fun_Y_0(X)))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(6,plain,
% 0.20/0.38 (![X: $i] : (p(X) & (q(tptp_fun_Y_0(X)) | q(X))) <=> ![X: $i] : (p(X) & (q(X) | q(tptp_fun_Y_0(X))))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[5])).
% 0.20/0.38 tff(7,plain,
% 0.20/0.38 (![X: $i] : ?[Y: $i] : (p(X) & (q(Y) | q(X))) <=> ![X: $i] : ?[Y: $i] : (p(X) & (q(Y) | q(X)))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(8,plain,
% 0.20/0.38 ((~(![X: $i] : ?[Y: $i] : (p(X) & (q(Y) | q(X))) => ?[Z: $i] : (p(Z) & q(Z)))) <=> (~((~![X: $i] : ?[Y: $i] : (p(X) & (q(Y) | q(X)))) | ?[Z: $i] : (p(Z) & q(Z))))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(9,axiom,(~(![X: $i] : ?[Y: $i] : (p(X) & (q(Y) | q(X))) => ?[Z: $i] : (p(Z) & q(Z)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','y2141')).
% 0.20/0.38 tff(10,plain,
% 0.20/0.38 (~((~![X: $i] : ?[Y: $i] : (p(X) & (q(Y) | q(X)))) | ?[Z: $i] : (p(Z) & q(Z)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[9, 8])).
% 0.20/0.38 tff(11,plain,
% 0.20/0.38 (![X: $i] : ?[Y: $i] : (p(X) & (q(Y) | q(X)))),
% 0.20/0.38 inference(or_elim,[status(thm)],[10])).
% 0.20/0.38 tff(12,plain,
% 0.20/0.38 (![X: $i] : ?[Y: $i] : (p(X) & (q(Y) | q(X)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[11, 7])).
% 0.20/0.38 tff(13,plain,(
% 0.20/0.38 ![X: $i] : (p(X) & (q(tptp_fun_Y_0(X)) | q(X)))),
% 0.20/0.38 inference(skolemize,[status(sab)],[12])).
% 0.20/0.38 tff(14,plain,
% 0.20/0.38 (![X: $i] : (p(X) & (q(X) | q(tptp_fun_Y_0(X))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[13, 6])).
% 0.20/0.38 tff(15,plain,
% 0.20/0.38 (![X: $i] : (~((~p(X)) | (~(q(X) | q(tptp_fun_Y_0(X))))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[14, 4])).
% 0.20/0.38 tff(16,plain,
% 0.20/0.38 (![X: $i] : (~((~p(X)) | (~(q(X) | q(tptp_fun_Y_0(X))))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[15, 2])).
% 0.20/0.38 tff(17,plain,
% 0.20/0.38 ((~![X: $i] : (~((~p(X)) | (~(q(X) | q(tptp_fun_Y_0(X))))))) | (~((~p(tptp_fun_Y_0(elem!1))) | (~(q(tptp_fun_Y_0(elem!1)) | q(tptp_fun_Y_0(tptp_fun_Y_0(elem!1)))))))),
% 0.20/0.38 inference(quant_inst,[status(thm)],[])).
% 0.20/0.38 tff(18,plain,
% 0.20/0.38 (~((~p(tptp_fun_Y_0(elem!1))) | (~(q(tptp_fun_Y_0(elem!1)) | q(tptp_fun_Y_0(tptp_fun_Y_0(elem!1))))))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.20/0.38 tff(19,plain,
% 0.20/0.38 ((~![X: $i] : (~((~p(X)) | (~(q(X) | q(tptp_fun_Y_0(X))))))) | (~((~p(elem!1)) | (~(q(elem!1) | q(tptp_fun_Y_0(elem!1))))))),
% 0.20/0.38 inference(quant_inst,[status(thm)],[])).
% 0.20/0.38 tff(20,plain,
% 0.20/0.38 (~((~p(elem!1)) | (~(q(elem!1) | q(tptp_fun_Y_0(elem!1)))))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[19, 16])).
% 0.20/0.38 tff(21,plain,
% 0.20/0.38 (((~p(elem!1)) | (~(q(elem!1) | q(tptp_fun_Y_0(elem!1))))) | (q(elem!1) | q(tptp_fun_Y_0(elem!1)))),
% 0.20/0.38 inference(tautology,[status(thm)],[])).
% 0.20/0.38 tff(22,plain,
% 0.20/0.38 (q(elem!1) | q(tptp_fun_Y_0(elem!1))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[21, 20])).
% 0.20/0.38 tff(23,plain,
% 0.20/0.38 (((~p(elem!1)) | (~(q(elem!1) | q(tptp_fun_Y_0(elem!1))))) | p(elem!1)),
% 0.20/0.38 inference(tautology,[status(thm)],[])).
% 0.20/0.38 tff(24,plain,
% 0.20/0.38 (p(elem!1)),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[23, 20])).
% 0.20/0.38 tff(25,plain,
% 0.20/0.38 (^[Z: $i] : refl(((~p(Z)) | (~q(Z))) <=> ((~p(Z)) | (~q(Z))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(26,plain,
% 0.20/0.38 (![Z: $i] : ((~p(Z)) | (~q(Z))) <=> ![Z: $i] : ((~p(Z)) | (~q(Z)))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[25])).
% 0.20/0.39 tff(27,plain,
% 0.20/0.39 (^[Z: $i] : trans(monotonicity(rewrite((p(Z) & q(Z)) <=> (~((~p(Z)) | (~q(Z))))), ((~(p(Z) & q(Z))) <=> (~(~((~p(Z)) | (~q(Z))))))), rewrite((~(~((~p(Z)) | (~q(Z))))) <=> ((~p(Z)) | (~q(Z)))), ((~(p(Z) & q(Z))) <=> ((~p(Z)) | (~q(Z)))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(28,plain,
% 0.20/0.39 (![Z: $i] : (~(p(Z) & q(Z))) <=> ![Z: $i] : ((~p(Z)) | (~q(Z)))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[27])).
% 0.20/0.39 tff(29,plain,
% 0.20/0.39 ((~?[Z: $i] : (p(Z) & q(Z))) <=> (~?[Z: $i] : (p(Z) & q(Z)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(30,plain,
% 0.20/0.39 (~?[Z: $i] : (p(Z) & q(Z))),
% 0.20/0.39 inference(or_elim,[status(thm)],[10])).
% 0.20/0.39 tff(31,plain,
% 0.20/0.39 (~?[Z: $i] : (p(Z) & q(Z))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.20/0.39 tff(32,plain,
% 0.20/0.39 (~?[Z: $i] : (p(Z) & q(Z))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[31, 29])).
% 0.20/0.39 tff(33,plain,
% 0.20/0.39 (~?[Z: $i] : (p(Z) & q(Z))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[32, 29])).
% 0.20/0.39 tff(34,plain,
% 0.20/0.39 (~?[Z: $i] : (p(Z) & q(Z))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[33, 29])).
% 0.20/0.39 tff(35,plain,
% 0.20/0.39 (~?[Z: $i] : (p(Z) & q(Z))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[34, 29])).
% 0.20/0.39 tff(36,plain,
% 0.20/0.39 (~?[Z: $i] : (p(Z) & q(Z))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[35, 29])).
% 0.20/0.39 tff(37,plain,
% 0.20/0.39 (^[Z: $i] : refl($oeq((~(p(Z) & q(Z))), (~(p(Z) & q(Z)))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(38,plain,(
% 0.20/0.39 ![Z: $i] : (~(p(Z) & q(Z)))),
% 0.20/0.39 inference(nnf-neg,[status(sab)],[36, 37])).
% 0.20/0.39 tff(39,plain,
% 0.20/0.39 (![Z: $i] : ((~p(Z)) | (~q(Z)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[38, 28])).
% 0.20/0.39 tff(40,plain,
% 0.20/0.39 (![Z: $i] : ((~p(Z)) | (~q(Z)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[39, 26])).
% 0.20/0.39 tff(41,plain,
% 0.20/0.39 (((~![Z: $i] : ((~p(Z)) | (~q(Z)))) | ((~p(elem!1)) | (~q(elem!1)))) <=> ((~![Z: $i] : ((~p(Z)) | (~q(Z)))) | (~p(elem!1)) | (~q(elem!1)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(42,plain,
% 0.20/0.39 ((~![Z: $i] : ((~p(Z)) | (~q(Z)))) | ((~p(elem!1)) | (~q(elem!1)))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(43,plain,
% 0.20/0.39 ((~![Z: $i] : ((~p(Z)) | (~q(Z)))) | (~p(elem!1)) | (~q(elem!1))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.20/0.39 tff(44,plain,
% 0.20/0.39 (~q(elem!1)),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[43, 40, 24])).
% 0.20/0.39 tff(45,plain,
% 0.20/0.39 ((~(q(elem!1) | q(tptp_fun_Y_0(elem!1)))) | q(elem!1) | q(tptp_fun_Y_0(elem!1))),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(46,plain,
% 0.20/0.39 (q(tptp_fun_Y_0(elem!1))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[45, 44, 22])).
% 0.20/0.39 tff(47,plain,
% 0.20/0.39 (((~![Z: $i] : ((~p(Z)) | (~q(Z)))) | ((~p(tptp_fun_Y_0(elem!1))) | (~q(tptp_fun_Y_0(elem!1))))) <=> ((~![Z: $i] : ((~p(Z)) | (~q(Z)))) | (~p(tptp_fun_Y_0(elem!1))) | (~q(tptp_fun_Y_0(elem!1))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(48,plain,
% 0.20/0.39 ((~![Z: $i] : ((~p(Z)) | (~q(Z)))) | ((~p(tptp_fun_Y_0(elem!1))) | (~q(tptp_fun_Y_0(elem!1))))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(49,plain,
% 0.20/0.39 ((~![Z: $i] : ((~p(Z)) | (~q(Z)))) | (~p(tptp_fun_Y_0(elem!1))) | (~q(tptp_fun_Y_0(elem!1)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.20/0.39 tff(50,plain,
% 0.20/0.39 (~p(tptp_fun_Y_0(elem!1))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[49, 40, 46])).
% 0.20/0.39 tff(51,plain,
% 0.20/0.39 (((~p(tptp_fun_Y_0(elem!1))) | (~(q(tptp_fun_Y_0(elem!1)) | q(tptp_fun_Y_0(tptp_fun_Y_0(elem!1)))))) | p(tptp_fun_Y_0(elem!1))),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(52,plain,
% 0.20/0.39 ($false),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[51, 50, 18])).
% 0.20/0.39 % SZS output end Proof
%------------------------------------------------------------------------------