TSTP Solution File: SYN944+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN944+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n023.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 0.13s 0.39s
% Output : Proof 0.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SYN944+1 : TPTP v8.1.0. Released v3.1.0.
% 0.10/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n023.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 09:58:47 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(q_type, type, (
% 0.13/0.39 q: ( $i * $i ) > $o)).
% 0.13/0.39 tff(tptp_fun_C_0_type, type, (
% 0.13/0.39 tptp_fun_C_0: $i)).
% 0.13/0.39 tff(tptp_fun_B_1_type, type, (
% 0.13/0.39 tptp_fun_B_1: $i)).
% 0.13/0.39 tff(r_type, type, (
% 0.13/0.39 r: ( $i * $i ) > $o)).
% 0.13/0.39 tff(p_type, type, (
% 0.13/0.39 p: $i > $o)).
% 0.13/0.39 tff(s_type, type, (
% 0.13/0.39 s: $i > $o)).
% 0.13/0.39 tff(tptp_fun_A_2_type, type, (
% 0.13/0.39 tptp_fun_A_2: $i)).
% 0.13/0.39 tff(1,plain,
% 0.13/0.39 (^[X: $i, Y: $i] : refl(((~r(X, Y)) | q(X, Y)) <=> ((~r(X, Y)) | q(X, Y)))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(2,plain,
% 0.13/0.39 (![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y)) <=> ![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[1])).
% 0.13/0.39 tff(3,plain,
% 0.13/0.39 (((s(A!2) & s(B!1) & r(B!1, C!0) & ![X: $i] : (p(X) | (~s(X))) & ![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y))) & ![X: $i, Y: $i] : (~(p(X) & q(X, Y)))) <=> (s(A!2) & s(B!1) & r(B!1, C!0) & ![X: $i] : (p(X) | (~s(X))) & ![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y)) & ![X: $i, Y: $i] : (~(p(X) & q(X, Y))))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(4,plain,
% 0.13/0.39 ((s(A!2) & s(B!1) & r(B!1, C!0) & ![X: $i] : (p(X) | (~s(X))) & ![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y))) <=> (s(A!2) & s(B!1) & r(B!1, C!0) & ![X: $i] : (p(X) | (~s(X))) & ![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(5,plain,
% 0.13/0.39 (((s(A!2) & s(B!1) & r(B!1, C!0) & ![X: $i] : (p(X) | (~s(X))) & ![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y))) & ![X: $i, Y: $i] : (~(p(X) & q(X, Y)))) <=> ((s(A!2) & s(B!1) & r(B!1, C!0) & ![X: $i] : (p(X) | (~s(X))) & ![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y))) & ![X: $i, Y: $i] : (~(p(X) & q(X, Y))))),
% 0.13/0.39 inference(monotonicity,[status(thm)],[4])).
% 0.13/0.39 tff(6,plain,
% 0.13/0.39 (((s(A!2) & s(B!1) & r(B!1, C!0) & ![X: $i] : (p(X) | (~s(X))) & ![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y))) & ![X: $i, Y: $i] : (~(p(X) & q(X, Y)))) <=> (s(A!2) & s(B!1) & r(B!1, C!0) & ![X: $i] : (p(X) | (~s(X))) & ![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y)) & ![X: $i, Y: $i] : (~(p(X) & q(X, Y))))),
% 0.13/0.39 inference(transitivity,[status(thm)],[5, 3])).
% 0.13/0.39 tff(7,plain,
% 0.13/0.39 ((~![A: $i, B: $i, C: $i] : ((~(s(A) & s(B) & r(B, C) & ![X: $i] : (p(X) | (~s(X))) & ![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y)))) | ?[X: $i, Y: $i] : (p(X) & q(X, Y)))) <=> (~![A: $i, B: $i, C: $i] : ((~(s(A) & s(B) & r(B, C) & ![X: $i] : (p(X) | (~s(X))) & ![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y)))) | ?[X: $i, Y: $i] : (p(X) & q(X, Y))))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(8,plain,
% 0.13/0.39 ((~![A: $i, B: $i, C: $i] : (((((s(A) & s(B)) & r(B, C)) & ![X: $i] : (s(X) => p(X))) & ![X: $i, Y: $i] : (r(X, Y) => q(X, Y))) => ?[X: $i, Y: $i] : (p(X) & q(X, Y)))) <=> (~![A: $i, B: $i, C: $i] : ((~(s(A) & s(B) & r(B, C) & ![X: $i] : (p(X) | (~s(X))) & ![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y)))) | ?[X: $i, Y: $i] : (p(X) & q(X, Y))))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(9,axiom,(~![A: $i, B: $i, C: $i] : (((((s(A) & s(B)) & r(B, C)) & ![X: $i] : (s(X) => p(X))) & ![X: $i, Y: $i] : (r(X, Y) => q(X, Y))) => ?[X: $i, Y: $i] : (p(X) & q(X, Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this')).
% 0.13/0.39 tff(10,plain,
% 0.13/0.39 (~![A: $i, B: $i, C: $i] : ((~(s(A) & s(B) & r(B, C) & ![X: $i] : (p(X) | (~s(X))) & ![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y)))) | ?[X: $i, Y: $i] : (p(X) & q(X, Y)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[9, 8])).
% 0.13/0.39 tff(11,plain,
% 0.13/0.39 (~![A: $i, B: $i, C: $i] : ((~(s(A) & s(B) & r(B, C) & ![X: $i] : (p(X) | (~s(X))) & ![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y)))) | ?[X: $i, Y: $i] : (p(X) & q(X, Y)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[10, 7])).
% 0.13/0.39 tff(12,plain,
% 0.13/0.39 (~![A: $i, B: $i, C: $i] : ((~(s(A) & s(B) & r(B, C) & ![X: $i] : (p(X) | (~s(X))) & ![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y)))) | ?[X: $i, Y: $i] : (p(X) & q(X, Y)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[11, 7])).
% 0.13/0.39 tff(13,plain,
% 0.13/0.39 (~![A: $i, B: $i, C: $i] : ((~(s(A) & s(B) & r(B, C) & ![X: $i] : (p(X) | (~s(X))) & ![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y)))) | ?[X: $i, Y: $i] : (p(X) & q(X, Y)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[12, 7])).
% 0.13/0.39 tff(14,plain,
% 0.13/0.39 (~![A: $i, B: $i, C: $i] : ((~(s(A) & s(B) & r(B, C) & ![X: $i] : (p(X) | (~s(X))) & ![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y)))) | ?[X: $i, Y: $i] : (p(X) & q(X, Y)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[13, 7])).
% 0.13/0.39 tff(15,plain,
% 0.13/0.39 (~![A: $i, B: $i, C: $i] : ((~(s(A) & s(B) & r(B, C) & ![X: $i] : (p(X) | (~s(X))) & ![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y)))) | ?[X: $i, Y: $i] : (p(X) & q(X, Y)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[14, 7])).
% 0.13/0.39 tff(16,plain,
% 0.13/0.39 (~![A: $i, B: $i, C: $i] : ((~(s(A) & s(B) & r(B, C) & ![X: $i] : (p(X) | (~s(X))) & ![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y)))) | ?[X: $i, Y: $i] : (p(X) & q(X, Y)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[15, 7])).
% 0.13/0.39 tff(17,plain,
% 0.13/0.39 (s(A!2) & s(B!1) & r(B!1, C!0) & ![X: $i] : (p(X) | (~s(X))) & ![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y)) & ![X: $i, Y: $i] : (~(p(X) & q(X, Y)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[16, 6])).
% 0.13/0.39 tff(18,plain,
% 0.13/0.39 (![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y))),
% 0.13/0.39 inference(and_elim,[status(thm)],[17])).
% 0.13/0.39 tff(19,plain,
% 0.13/0.39 (![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[18, 2])).
% 0.13/0.39 tff(20,plain,
% 0.13/0.39 (r(B!1, C!0)),
% 0.13/0.39 inference(and_elim,[status(thm)],[17])).
% 0.13/0.39 tff(21,plain,
% 0.13/0.39 (((~![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y))) | ((~r(B!1, C!0)) | q(B!1, C!0))) <=> ((~![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y))) | (~r(B!1, C!0)) | q(B!1, C!0))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(22,plain,
% 0.13/0.39 ((~![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y))) | ((~r(B!1, C!0)) | q(B!1, C!0))),
% 0.13/0.39 inference(quant_inst,[status(thm)],[])).
% 0.13/0.39 tff(23,plain,
% 0.13/0.39 ((~![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y))) | (~r(B!1, C!0)) | q(B!1, C!0)),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.13/0.39 tff(24,plain,
% 0.13/0.39 (q(B!1, C!0)),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[23, 20, 19])).
% 0.13/0.39 tff(25,plain,
% 0.13/0.39 (^[X: $i] : refl((p(X) | (~s(X))) <=> (p(X) | (~s(X))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(26,plain,
% 0.13/0.39 (![X: $i] : (p(X) | (~s(X))) <=> ![X: $i] : (p(X) | (~s(X)))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[25])).
% 0.13/0.39 tff(27,plain,
% 0.13/0.39 (![X: $i] : (p(X) | (~s(X)))),
% 0.13/0.39 inference(and_elim,[status(thm)],[17])).
% 0.13/0.39 tff(28,plain,
% 0.13/0.39 (![X: $i] : (p(X) | (~s(X)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.13/0.39 tff(29,plain,
% 0.13/0.39 (s(B!1)),
% 0.13/0.39 inference(and_elim,[status(thm)],[17])).
% 0.13/0.39 tff(30,plain,
% 0.13/0.39 (((~![X: $i] : (p(X) | (~s(X)))) | (p(B!1) | (~s(B!1)))) <=> ((~![X: $i] : (p(X) | (~s(X)))) | p(B!1) | (~s(B!1)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(31,plain,
% 0.13/0.39 ((~![X: $i] : (p(X) | (~s(X)))) | (p(B!1) | (~s(B!1)))),
% 0.13/0.39 inference(quant_inst,[status(thm)],[])).
% 0.13/0.39 tff(32,plain,
% 0.13/0.39 ((~![X: $i] : (p(X) | (~s(X)))) | p(B!1) | (~s(B!1))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.13/0.39 tff(33,plain,
% 0.13/0.39 (p(B!1)),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[32, 29, 28])).
% 0.13/0.39 tff(34,plain,
% 0.13/0.39 (^[X: $i, Y: $i] : refl(((~p(X)) | (~q(X, Y))) <=> ((~p(X)) | (~q(X, Y))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(35,plain,
% 0.13/0.39 (![X: $i, Y: $i] : ((~p(X)) | (~q(X, Y))) <=> ![X: $i, Y: $i] : ((~p(X)) | (~q(X, Y)))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[34])).
% 0.13/0.39 tff(36,plain,
% 0.13/0.39 (^[X: $i, Y: $i] : trans(monotonicity(rewrite((p(X) & q(X, Y)) <=> (~((~p(X)) | (~q(X, Y))))), ((~(p(X) & q(X, Y))) <=> (~(~((~p(X)) | (~q(X, Y))))))), rewrite((~(~((~p(X)) | (~q(X, Y))))) <=> ((~p(X)) | (~q(X, Y)))), ((~(p(X) & q(X, Y))) <=> ((~p(X)) | (~q(X, Y)))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(37,plain,
% 0.13/0.39 (![X: $i, Y: $i] : (~(p(X) & q(X, Y))) <=> ![X: $i, Y: $i] : ((~p(X)) | (~q(X, Y)))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[36])).
% 0.13/0.39 tff(38,plain,
% 0.13/0.39 (![X: $i, Y: $i] : (~(p(X) & q(X, Y)))),
% 0.13/0.39 inference(and_elim,[status(thm)],[17])).
% 0.13/0.39 tff(39,plain,
% 0.13/0.39 (![X: $i, Y: $i] : ((~p(X)) | (~q(X, Y)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.13/0.39 tff(40,plain,
% 0.13/0.39 (![X: $i, Y: $i] : ((~p(X)) | (~q(X, Y)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[39, 35])).
% 0.13/0.39 tff(41,plain,
% 0.13/0.39 (((~![X: $i, Y: $i] : ((~p(X)) | (~q(X, Y)))) | ((~p(B!1)) | (~q(B!1, C!0)))) <=> ((~![X: $i, Y: $i] : ((~p(X)) | (~q(X, Y)))) | (~p(B!1)) | (~q(B!1, C!0)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(42,plain,
% 0.13/0.39 ((~![X: $i, Y: $i] : ((~p(X)) | (~q(X, Y)))) | ((~p(B!1)) | (~q(B!1, C!0)))),
% 0.13/0.39 inference(quant_inst,[status(thm)],[])).
% 0.13/0.39 tff(43,plain,
% 0.13/0.39 ((~![X: $i, Y: $i] : ((~p(X)) | (~q(X, Y)))) | (~p(B!1)) | (~q(B!1, C!0))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.13/0.39 tff(44,plain,
% 0.13/0.39 ($false),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[43, 40, 33, 24])).
% 0.13/0.39 % SZS output end Proof
%------------------------------------------------------------------------------