TSTP Solution File: SYN317+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN317+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n026.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 23:54:40 EDT 2022
% Result : Theorem 0.19s 0.37s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.11 % Problem : SYN317+1 : TPTP v8.1.0. Released v2.0.0.
% 0.02/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.11/0.32 % Computer : n026.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Mon Sep 5 02:44:40 EDT 2022
% 0.11/0.32 % CPUTime :
% 0.11/0.32 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.11/0.32 Usage: tptp [options] [-file:]file
% 0.11/0.32 -h, -? prints this message.
% 0.11/0.32 -smt2 print SMT-LIB2 benchmark.
% 0.11/0.32 -m, -model generate model.
% 0.11/0.32 -p, -proof generate proof.
% 0.11/0.32 -c, -core generate unsat core of named formulas.
% 0.11/0.32 -st, -statistics display statistics.
% 0.11/0.32 -t:timeout set timeout (in second).
% 0.11/0.32 -smt2status display status in smt2 format instead of SZS.
% 0.11/0.32 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.11/0.32 -<param>:<value> configuration parameter and value.
% 0.11/0.32 -o:<output-file> file to place output in.
% 0.19/0.37 % SZS status Theorem
% 0.19/0.37 % SZS output start Proof
% 0.19/0.37 tff(big_f_type, type, (
% 0.19/0.37 big_f: $i > $o)).
% 0.19/0.37 tff(tptp_fun_X_2_type, type, (
% 0.19/0.37 tptp_fun_X_2: $i)).
% 0.19/0.37 tff(big_g_type, type, (
% 0.19/0.37 big_g: $i > $o)).
% 0.19/0.37 tff(tptp_fun_X_0_type, type, (
% 0.19/0.37 tptp_fun_X_0: $i)).
% 0.19/0.37 tff(tptp_fun_Y_1_type, type, (
% 0.19/0.37 tptp_fun_Y_1: $i)).
% 0.19/0.37 tff(1,assumption,(~big_g(X!0)), introduced(assumption)).
% 0.19/0.37 tff(2,assumption,(![X: $i, Y: $i] : (~(big_g(Y) | (~big_f(X))))), introduced(assumption)).
% 0.19/0.37 tff(3,plain,
% 0.19/0.37 ((~![X: $i, Y: $i] : (~(big_g(Y) | (~big_f(X))))) | (~(big_g(X!2) | (~big_f(X!2))))),
% 0.19/0.37 inference(quant_inst,[status(thm)],[])).
% 0.19/0.37 tff(4,plain,
% 0.19/0.37 (~(big_g(X!2) | (~big_f(X!2)))),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[3, 2])).
% 0.19/0.37 tff(5,plain,
% 0.19/0.37 ((big_g(X!2) | (~big_f(X!2))) | big_f(X!2)),
% 0.19/0.37 inference(tautology,[status(thm)],[])).
% 0.19/0.37 tff(6,plain,
% 0.19/0.37 (big_f(X!2)),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[5, 4])).
% 0.19/0.37 tff(7,assumption,(big_g(X!2) | (~big_f(X!0))), introduced(assumption)).
% 0.19/0.37 tff(8,plain,
% 0.19/0.37 ((~![X: $i, Y: $i] : (~(big_g(Y) | (~big_f(X))))) | (~(big_g(X!2) | (~big_f(X!0))))),
% 0.19/0.37 inference(quant_inst,[status(thm)],[])).
% 0.19/0.37 tff(9,plain,
% 0.19/0.37 ($false),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[8, 2, 7])).
% 0.19/0.37 tff(10,plain,((~(big_g(X!2) | (~big_f(X!0)))) | (~![X: $i, Y: $i] : (~(big_g(Y) | (~big_f(X)))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.37 tff(11,plain,
% 0.19/0.37 (~(big_g(X!2) | (~big_f(X!0)))),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[10, 2])).
% 0.19/0.37 tff(12,plain,
% 0.19/0.37 ((big_g(X!2) | (~big_f(X!0))) | big_f(X!0)),
% 0.19/0.37 inference(tautology,[status(thm)],[])).
% 0.19/0.37 tff(13,plain,
% 0.19/0.37 (big_f(X!0)),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[12, 11])).
% 0.19/0.37 tff(14,plain,
% 0.19/0.37 ((((big_g(X!0) | (~big_f(X!0))) | (big_g(Y!1) | (~big_f(X!2)))) & (![X: $i] : (~(big_g(X) | (~big_f(X)))) | ![X: $i, Y: $i] : (~(big_g(Y) | (~big_f(X)))))) <=> ((big_g(X!0) | (~big_f(X!0)) | big_g(Y!1) | (~big_f(X!2))) & (![X: $i] : (~(big_g(X) | (~big_f(X)))) | ![X: $i, Y: $i] : (~(big_g(Y) | (~big_f(X))))))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(15,plain,
% 0.19/0.37 (((~?[X: $i] : (big_g(X) | (~big_f(X)))) <=> ?[X: $i, Y: $i] : (big_g(Y) | (~big_f(X)))) <=> ((~?[X: $i] : (big_g(X) | (~big_f(X)))) <=> ?[X: $i, Y: $i] : (big_g(Y) | (~big_f(X))))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(16,plain,
% 0.19/0.37 ((~(?[X: $i] : (big_g(X) | (~big_f(X))) <=> ?[X: $i, Y: $i] : (big_g(Y) | (~big_f(X))))) <=> ((~?[X: $i] : (big_g(X) | (~big_f(X)))) <=> ?[X: $i, Y: $i] : (big_g(Y) | (~big_f(X))))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(17,plain,
% 0.19/0.37 ((?[X: $i] : (big_f(X) => big_g(X)) <=> ?[X: $i, Y: $i] : (big_f(X) => big_g(Y))) <=> (?[X: $i] : (big_g(X) | (~big_f(X))) <=> ?[X: $i, Y: $i] : (big_g(Y) | (~big_f(X))))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(18,plain,
% 0.19/0.37 ((~(?[X: $i] : (big_f(X) => big_g(X)) <=> ?[X: $i, Y: $i] : (big_f(X) => big_g(Y)))) <=> (~(?[X: $i] : (big_g(X) | (~big_f(X))) <=> ?[X: $i, Y: $i] : (big_g(Y) | (~big_f(X)))))),
% 0.19/0.37 inference(monotonicity,[status(thm)],[17])).
% 0.19/0.37 tff(19,plain,
% 0.19/0.37 ((~(?[X: $i] : (big_f(X) => big_g(X)) <=> ?[X: $i, Y: $i] : (big_f(X) => big_g(Y)))) <=> ((~?[X: $i] : (big_g(X) | (~big_f(X)))) <=> ?[X: $i, Y: $i] : (big_g(Y) | (~big_f(X))))),
% 0.19/0.37 inference(transitivity,[status(thm)],[18, 16])).
% 0.19/0.37 tff(20,axiom,(~(?[X: $i] : (big_f(X) => big_g(X)) <=> ?[X: $i, Y: $i] : (big_f(X) => big_g(Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','church_46_2_3')).
% 0.19/0.37 tff(21,plain,
% 0.19/0.37 ((~?[X: $i] : (big_g(X) | (~big_f(X)))) <=> ?[X: $i, Y: $i] : (big_g(Y) | (~big_f(X)))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.19/0.37 tff(22,plain,
% 0.19/0.37 ((~?[X: $i] : (big_g(X) | (~big_f(X)))) <=> ?[X: $i, Y: $i] : (big_g(Y) | (~big_f(X)))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[21, 15])).
% 0.19/0.37 tff(23,plain,
% 0.19/0.37 ((~?[X: $i] : (big_g(X) | (~big_f(X)))) <=> ?[X: $i, Y: $i] : (big_g(Y) | (~big_f(X)))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[22, 15])).
% 0.19/0.37 tff(24,plain,
% 0.19/0.37 ((~?[X: $i] : (big_g(X) | (~big_f(X)))) <=> ?[X: $i, Y: $i] : (big_g(Y) | (~big_f(X)))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[23, 15])).
% 0.19/0.37 tff(25,plain,
% 0.19/0.37 ((~?[X: $i] : (big_g(X) | (~big_f(X)))) <=> ?[X: $i, Y: $i] : (big_g(Y) | (~big_f(X)))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[24, 15])).
% 0.19/0.37 tff(26,plain,
% 0.19/0.37 ((~?[X: $i] : (big_g(X) | (~big_f(X)))) <=> ?[X: $i, Y: $i] : (big_g(Y) | (~big_f(X)))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[25, 15])).
% 0.19/0.37 tff(27,plain,
% 0.19/0.37 ((~?[X: $i] : (big_g(X) | (~big_f(X)))) <=> ?[X: $i, Y: $i] : (big_g(Y) | (~big_f(X)))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[26, 15])).
% 0.19/0.37 tff(28,plain,(
% 0.19/0.37 ((big_g(X!0) | (~big_f(X!0))) | (big_g(Y!1) | (~big_f(X!2)))) & (![X: $i] : (~(big_g(X) | (~big_f(X)))) | ![X: $i, Y: $i] : (~(big_g(Y) | (~big_f(X)))))),
% 0.19/0.37 inference(skolemize,[status(sab)],[27])).
% 0.19/0.37 tff(29,plain,
% 0.19/0.37 ((big_g(X!0) | (~big_f(X!0)) | big_g(Y!1) | (~big_f(X!2))) & (![X: $i] : (~(big_g(X) | (~big_f(X)))) | ![X: $i, Y: $i] : (~(big_g(Y) | (~big_f(X)))))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[28, 14])).
% 0.19/0.37 tff(30,plain,
% 0.19/0.37 (big_g(X!0) | (~big_f(X!0)) | big_g(Y!1) | (~big_f(X!2))),
% 0.19/0.37 inference(and_elim,[status(thm)],[29])).
% 0.19/0.37 tff(31,plain,
% 0.19/0.37 (big_g(Y!1)),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[30, 13, 1, 6])).
% 0.19/0.37 tff(32,plain,
% 0.19/0.37 ((big_g(Y!1) | (~big_f(X!2))) | (~big_g(Y!1))),
% 0.19/0.37 inference(tautology,[status(thm)],[])).
% 0.19/0.37 tff(33,plain,
% 0.19/0.37 (big_g(Y!1) | (~big_f(X!2))),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[32, 31])).
% 0.19/0.37 tff(34,plain,
% 0.19/0.37 ((~![X: $i, Y: $i] : (~(big_g(Y) | (~big_f(X))))) | (~(big_g(Y!1) | (~big_f(X!2))))),
% 0.19/0.37 inference(quant_inst,[status(thm)],[])).
% 0.19/0.37 tff(35,plain,
% 0.19/0.37 ($false),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[34, 2, 33])).
% 0.19/0.37 tff(36,plain,((~![X: $i, Y: $i] : (~(big_g(Y) | (~big_f(X))))) | big_g(X!0)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.37 tff(37,plain,
% 0.19/0.37 (~![X: $i, Y: $i] : (~(big_g(Y) | (~big_f(X))))),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[36, 1])).
% 0.19/0.37 tff(38,plain,
% 0.19/0.37 ((![X: $i] : (~(big_g(X) | (~big_f(X)))) | ![X: $i, Y: $i] : (~(big_g(Y) | (~big_f(X))))) <=> (![X: $i] : (~(big_g(X) | (~big_f(X)))) | ![X: $i, Y: $i] : (~(big_g(Y) | (~big_f(X)))))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(39,plain,
% 0.19/0.37 (![X: $i] : (~(big_g(X) | (~big_f(X)))) | ![X: $i, Y: $i] : (~(big_g(Y) | (~big_f(X))))),
% 0.19/0.37 inference(and_elim,[status(thm)],[29])).
% 0.19/0.37 tff(40,plain,
% 0.19/0.37 (![X: $i] : (~(big_g(X) | (~big_f(X)))) | ![X: $i, Y: $i] : (~(big_g(Y) | (~big_f(X))))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.19/0.37 tff(41,plain,
% 0.19/0.37 (![X: $i] : (~(big_g(X) | (~big_f(X))))),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[40, 37])).
% 0.19/0.37 tff(42,assumption,(big_g(X!0) | (~big_f(X!0))), introduced(assumption)).
% 0.19/0.37 tff(43,assumption,(![X: $i] : (~(big_g(X) | (~big_f(X))))), introduced(assumption)).
% 0.19/0.37 tff(44,plain,
% 0.19/0.37 ((~![X: $i] : (~(big_g(X) | (~big_f(X))))) | (~(big_g(X!0) | (~big_f(X!0))))),
% 0.19/0.37 inference(quant_inst,[status(thm)],[])).
% 0.19/0.37 tff(45,plain,
% 0.19/0.37 ($false),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[44, 43, 42])).
% 0.19/0.37 tff(46,plain,((~(big_g(X!0) | (~big_f(X!0)))) | (~![X: $i] : (~(big_g(X) | (~big_f(X)))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.37 tff(47,plain,
% 0.19/0.37 (~(big_g(X!0) | (~big_f(X!0)))),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[46, 41])).
% 0.19/0.37 tff(48,plain,
% 0.19/0.37 ((big_g(X!0) | (~big_f(X!0))) | big_f(X!0)),
% 0.19/0.37 inference(tautology,[status(thm)],[])).
% 0.19/0.37 tff(49,plain,
% 0.19/0.37 (big_f(X!0)),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[48, 47])).
% 0.19/0.37 tff(50,assumption,(big_g(X!2) | (~big_f(X!2))), introduced(assumption)).
% 0.19/0.37 tff(51,plain,
% 0.19/0.37 ((~![X: $i] : (~(big_g(X) | (~big_f(X))))) | (~(big_g(X!2) | (~big_f(X!2))))),
% 0.19/0.37 inference(quant_inst,[status(thm)],[])).
% 0.19/0.37 tff(52,plain,
% 0.19/0.37 ($false),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[51, 43, 50])).
% 0.19/0.37 tff(53,plain,((~(big_g(X!2) | (~big_f(X!2)))) | (~![X: $i] : (~(big_g(X) | (~big_f(X)))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.37 tff(54,plain,
% 0.19/0.37 (~(big_g(X!2) | (~big_f(X!2)))),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[53, 41])).
% 0.19/0.37 tff(55,plain,
% 0.19/0.37 (big_f(X!2)),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[5, 54])).
% 0.19/0.37 tff(56,plain,
% 0.19/0.37 (big_g(Y!1)),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[30, 55, 1, 49])).
% 0.19/0.37 tff(57,plain,
% 0.19/0.37 ((big_g(Y!1) | (~big_f(Y!1))) | (~big_g(Y!1))),
% 0.19/0.37 inference(tautology,[status(thm)],[])).
% 0.19/0.37 tff(58,plain,
% 0.19/0.37 (big_g(Y!1) | (~big_f(Y!1))),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[57, 56])).
% 0.19/0.37 tff(59,plain,
% 0.19/0.37 ((~![X: $i] : (~(big_g(X) | (~big_f(X))))) | (~(big_g(Y!1) | (~big_f(Y!1))))),
% 0.19/0.37 inference(quant_inst,[status(thm)],[])).
% 0.19/0.37 tff(60,plain,
% 0.19/0.37 ($false),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[59, 41, 58])).
% 0.19/0.37 tff(61,plain,(big_g(X!0)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.37 tff(62,plain,
% 0.19/0.37 ((big_g(X!0) | (~big_f(X!2))) | (~big_g(X!0))),
% 0.19/0.37 inference(tautology,[status(thm)],[])).
% 0.19/0.37 tff(63,plain,
% 0.19/0.37 (big_g(X!0) | (~big_f(X!2))),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[62, 61])).
% 0.19/0.37 tff(64,plain,
% 0.19/0.37 ((big_g(X!0) | (~big_f(X!0))) | (~big_g(X!0))),
% 0.19/0.37 inference(tautology,[status(thm)],[])).
% 0.19/0.37 tff(65,plain,
% 0.19/0.37 (big_g(X!0) | (~big_f(X!0))),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[64, 61])).
% 0.19/0.37 tff(66,plain,
% 0.19/0.37 (~![X: $i] : (~(big_g(X) | (~big_f(X))))),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[46, 65])).
% 0.19/0.37 tff(67,plain,
% 0.19/0.37 (![X: $i, Y: $i] : (~(big_g(Y) | (~big_f(X))))),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[40, 66])).
% 0.19/0.37 tff(68,plain,
% 0.19/0.37 ((~![X: $i, Y: $i] : (~(big_g(Y) | (~big_f(X))))) | (~(big_g(X!0) | (~big_f(X!2))))),
% 0.19/0.37 inference(quant_inst,[status(thm)],[])).
% 0.19/0.37 tff(69,plain,
% 0.19/0.37 ($false),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[68, 67, 63])).
% 0.19/0.37 % SZS output end Proof
%------------------------------------------------------------------------------