TSTP Solution File: SYN947+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN947+1 : TPTP v8.1.0. Released v3.1.0.
% 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 : Fri Sep 30 00:01:21 EDT 2022
% Result : Theorem 0.14s 0.40s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SYN947+1 : TPTP v8.1.0. Released v3.1.0.
% 0.07/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.35 % Computer : n027.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Mon Sep 5 09:57:37 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.35 Usage: tptp [options] [-file:]file
% 0.14/0.35 -h, -? prints this message.
% 0.14/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.35 -m, -model generate model.
% 0.14/0.35 -p, -proof generate proof.
% 0.14/0.35 -c, -core generate unsat core of named formulas.
% 0.14/0.35 -st, -statistics display statistics.
% 0.14/0.35 -t:timeout set timeout (in second).
% 0.14/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.35 -<param>:<value> configuration parameter and value.
% 0.14/0.35 -o:<output-file> file to place output in.
% 0.14/0.40 % SZS status Theorem
% 0.14/0.40 % SZS output start Proof
% 0.14/0.40 tff(q_type, type, (
% 0.14/0.40 q: $i > $o)).
% 0.14/0.40 tff(tptp_fun_Y_0_type, type, (
% 0.14/0.40 tptp_fun_Y_0: $i > $i)).
% 0.14/0.40 tff(tptp_fun_Y_1_type, type, (
% 0.14/0.40 tptp_fun_Y_1: $i > $i)).
% 0.14/0.40 tff(elem_2_type, type, (
% 0.14/0.40 elem_2: $i)).
% 0.14/0.40 tff(p_type, type, (
% 0.14/0.40 p: $i > $o)).
% 0.14/0.40 tff(r_type, type, (
% 0.14/0.40 r: $i > $o)).
% 0.14/0.40 tff(1,plain,
% 0.14/0.40 (^[Z: $i] : refl((~(p(tptp_fun_Y_1(Z)) | r(Z))) <=> (~(p(tptp_fun_Y_1(Z)) | r(Z))))),
% 0.14/0.40 inference(bind,[status(th)],[])).
% 0.14/0.40 tff(2,plain,
% 0.14/0.40 (![Z: $i] : (~(p(tptp_fun_Y_1(Z)) | r(Z))) <=> ![Z: $i] : (~(p(tptp_fun_Y_1(Z)) | r(Z)))),
% 0.14/0.40 inference(quant_intro,[status(thm)],[1])).
% 0.14/0.40 tff(3,plain,
% 0.14/0.40 ((~?[Z: $i] : ![Y: $i] : (p(Y) | r(Z))) <=> (~?[Z: $i] : ![Y: $i] : (p(Y) | r(Z)))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(4,plain,
% 0.14/0.40 ((~(![X: $i] : ?[Y: $i] : (p(X) & q(Y)) => ?[Z: $i] : ![Y: $i] : (p(Y) | r(Z)))) <=> (~((~![X: $i] : ?[Y: $i] : (p(X) & q(Y))) | ?[Z: $i] : ![Y: $i] : (p(Y) | r(Z))))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(5,axiom,(~(![X: $i] : ?[Y: $i] : (p(X) & q(Y)) => ?[Z: $i] : ![Y: $i] : (p(Y) | r(Z)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this')).
% 0.14/0.40 tff(6,plain,
% 0.14/0.40 (~((~![X: $i] : ?[Y: $i] : (p(X) & q(Y))) | ?[Z: $i] : ![Y: $i] : (p(Y) | r(Z)))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.14/0.40 tff(7,plain,
% 0.14/0.40 (~?[Z: $i] : ![Y: $i] : (p(Y) | r(Z))),
% 0.14/0.40 inference(or_elim,[status(thm)],[6])).
% 0.14/0.40 tff(8,plain,
% 0.14/0.40 (~?[Z: $i] : ![Y: $i] : (p(Y) | r(Z))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.14/0.40 tff(9,plain,
% 0.14/0.40 (~?[Z: $i] : ![Y: $i] : (p(Y) | r(Z))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[8, 3])).
% 0.14/0.40 tff(10,plain,
% 0.14/0.40 (~?[Z: $i] : ![Y: $i] : (p(Y) | r(Z))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[9, 3])).
% 0.14/0.40 tff(11,plain,
% 0.14/0.40 (~?[Z: $i] : ![Y: $i] : (p(Y) | r(Z))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[10, 3])).
% 0.14/0.40 tff(12,plain,
% 0.14/0.40 (~?[Z: $i] : ![Y: $i] : (p(Y) | r(Z))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[11, 3])).
% 0.14/0.40 tff(13,plain,
% 0.14/0.40 (~?[Z: $i] : ![Y: $i] : (p(Y) | r(Z))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[12, 3])).
% 0.14/0.40 tff(14,plain,
% 0.14/0.40 (^[Z: $i] : sk($oeq((~![Y: $i] : (p(Y) | r(Z))), (~(p(tptp_fun_Y_1(Z)) | r(Z)))))),
% 0.14/0.40 inference(bind,[status(th)],[])).
% 0.14/0.40 tff(15,plain,(
% 0.14/0.40 ![Z: $i] : (~(p(tptp_fun_Y_1(Z)) | r(Z)))),
% 0.14/0.40 inference(nnf-neg,[status(sab)],[13, 14])).
% 0.14/0.40 tff(16,plain,
% 0.14/0.40 (![Z: $i] : (~(p(tptp_fun_Y_1(Z)) | r(Z)))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[15, 2])).
% 0.14/0.40 tff(17,plain,
% 0.14/0.40 (((~![Z: $i] : (~(p(tptp_fun_Y_1(Z)) | r(Z)))) | (~(r(elem!2) | p(tptp_fun_Y_1(elem!2))))) <=> ((~![Z: $i] : (~(p(tptp_fun_Y_1(Z)) | r(Z)))) | (~(r(elem!2) | p(tptp_fun_Y_1(elem!2)))))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(18,plain,
% 0.14/0.40 ((~(p(tptp_fun_Y_1(elem!2)) | r(elem!2))) <=> (~(r(elem!2) | p(tptp_fun_Y_1(elem!2))))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(19,plain,
% 0.14/0.40 (((~![Z: $i] : (~(p(tptp_fun_Y_1(Z)) | r(Z)))) | (~(p(tptp_fun_Y_1(elem!2)) | r(elem!2)))) <=> ((~![Z: $i] : (~(p(tptp_fun_Y_1(Z)) | r(Z)))) | (~(r(elem!2) | p(tptp_fun_Y_1(elem!2)))))),
% 0.14/0.40 inference(monotonicity,[status(thm)],[18])).
% 0.14/0.40 tff(20,plain,
% 0.14/0.40 (((~![Z: $i] : (~(p(tptp_fun_Y_1(Z)) | r(Z)))) | (~(p(tptp_fun_Y_1(elem!2)) | r(elem!2)))) <=> ((~![Z: $i] : (~(p(tptp_fun_Y_1(Z)) | r(Z)))) | (~(r(elem!2) | p(tptp_fun_Y_1(elem!2)))))),
% 0.14/0.40 inference(transitivity,[status(thm)],[19, 17])).
% 0.14/0.40 tff(21,plain,
% 0.14/0.40 ((~![Z: $i] : (~(p(tptp_fun_Y_1(Z)) | r(Z)))) | (~(p(tptp_fun_Y_1(elem!2)) | r(elem!2)))),
% 0.14/0.40 inference(quant_inst,[status(thm)],[])).
% 0.14/0.40 tff(22,plain,
% 0.14/0.40 ((~![Z: $i] : (~(p(tptp_fun_Y_1(Z)) | r(Z)))) | (~(r(elem!2) | p(tptp_fun_Y_1(elem!2))))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.14/0.40 tff(23,plain,
% 0.14/0.40 (~(r(elem!2) | p(tptp_fun_Y_1(elem!2)))),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[22, 16])).
% 0.14/0.40 tff(24,plain,
% 0.14/0.40 ((r(elem!2) | p(tptp_fun_Y_1(elem!2))) | (~p(tptp_fun_Y_1(elem!2)))),
% 0.14/0.40 inference(tautology,[status(thm)],[])).
% 0.14/0.40 tff(25,plain,
% 0.14/0.40 (~p(tptp_fun_Y_1(elem!2))),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[24, 23])).
% 0.14/0.40 tff(26,plain,
% 0.14/0.40 (((~p(tptp_fun_Y_1(elem!2))) | (~q(tptp_fun_Y_0(tptp_fun_Y_1(elem!2))))) | p(tptp_fun_Y_1(elem!2))),
% 0.21/0.40 inference(tautology,[status(thm)],[])).
% 0.21/0.40 tff(27,plain,
% 0.21/0.40 ((~p(tptp_fun_Y_1(elem!2))) | (~q(tptp_fun_Y_0(tptp_fun_Y_1(elem!2))))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[26, 25])).
% 0.21/0.40 tff(28,plain,
% 0.21/0.40 (^[X: $i] : refl((~((~p(X)) | (~q(tptp_fun_Y_0(X))))) <=> (~((~p(X)) | (~q(tptp_fun_Y_0(X))))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(29,plain,
% 0.21/0.40 (![X: $i] : (~((~p(X)) | (~q(tptp_fun_Y_0(X))))) <=> ![X: $i] : (~((~p(X)) | (~q(tptp_fun_Y_0(X)))))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[28])).
% 0.21/0.40 tff(30,plain,
% 0.21/0.40 (^[X: $i] : rewrite((p(X) & q(tptp_fun_Y_0(X))) <=> (~((~p(X)) | (~q(tptp_fun_Y_0(X))))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(31,plain,
% 0.21/0.40 (![X: $i] : (p(X) & q(tptp_fun_Y_0(X))) <=> ![X: $i] : (~((~p(X)) | (~q(tptp_fun_Y_0(X)))))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[30])).
% 0.21/0.40 tff(32,plain,
% 0.21/0.40 (![X: $i] : ?[Y: $i] : (p(X) & q(Y)) <=> ![X: $i] : ?[Y: $i] : (p(X) & q(Y))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(33,plain,
% 0.21/0.40 (![X: $i] : ?[Y: $i] : (p(X) & q(Y))),
% 0.21/0.40 inference(or_elim,[status(thm)],[6])).
% 0.21/0.40 tff(34,plain,
% 0.21/0.40 (![X: $i] : ?[Y: $i] : (p(X) & q(Y))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.21/0.40 tff(35,plain,(
% 0.21/0.40 ![X: $i] : (p(X) & q(tptp_fun_Y_0(X)))),
% 0.21/0.40 inference(skolemize,[status(sab)],[34])).
% 0.21/0.40 tff(36,plain,
% 0.21/0.40 (![X: $i] : (~((~p(X)) | (~q(tptp_fun_Y_0(X)))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[35, 31])).
% 0.21/0.40 tff(37,plain,
% 0.21/0.40 (![X: $i] : (~((~p(X)) | (~q(tptp_fun_Y_0(X)))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[36, 29])).
% 0.21/0.40 tff(38,plain,
% 0.21/0.40 ((~![X: $i] : (~((~p(X)) | (~q(tptp_fun_Y_0(X)))))) | (~((~p(tptp_fun_Y_1(elem!2))) | (~q(tptp_fun_Y_0(tptp_fun_Y_1(elem!2))))))),
% 0.21/0.40 inference(quant_inst,[status(thm)],[])).
% 0.21/0.40 tff(39,plain,
% 0.21/0.40 ($false),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[38, 37, 27])).
% 0.21/0.40 % SZS output end Proof
%------------------------------------------------------------------------------