TSTP Solution File: SET045+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET045+1 : TPTP v8.1.0. Released v2.0.0.
% 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 : Tue Sep 20 05:05:07 EDT 2022
% Result : Theorem 0.70s 0.68s
% Output : Proof 0.70s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET045+1 : TPTP v8.1.0. Released v2.0.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n028.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 : Sat Sep 3 01:55:53 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.70/0.68 % SZS status Theorem
% 0.70/0.68 % SZS output start Proof
% 0.70/0.68 tff(element_type, type, (
% 0.70/0.68 element: ( $i * $i ) > $o)).
% 0.70/0.68 tff(tptp_fun_Y_0_type, type, (
% 0.70/0.68 tptp_fun_Y_0: $i > $i)).
% 0.70/0.68 tff(tptp_fun_Z_1_type, type, (
% 0.70/0.68 tptp_fun_Z_1: $i)).
% 0.70/0.68 tff(1,plain,
% 0.70/0.68 (^[Z: $i, X: $i] : refl((element(X, tptp_fun_Y_0(Z)) <=> (~((~element(X, Z)) | element(X, X)))) <=> (element(X, tptp_fun_Y_0(Z)) <=> (~((~element(X, Z)) | element(X, X)))))),
% 0.70/0.68 inference(bind,[status(th)],[])).
% 0.70/0.68 tff(2,plain,
% 0.70/0.68 (![Z: $i, X: $i] : (element(X, tptp_fun_Y_0(Z)) <=> (~((~element(X, Z)) | element(X, X)))) <=> ![Z: $i, X: $i] : (element(X, tptp_fun_Y_0(Z)) <=> (~((~element(X, Z)) | element(X, X))))),
% 0.70/0.68 inference(quant_intro,[status(thm)],[1])).
% 0.70/0.68 tff(3,plain,
% 0.70/0.68 (^[Z: $i, X: $i] : rewrite((element(X, tptp_fun_Y_0(Z)) <=> (element(X, Z) & (~element(X, X)))) <=> (element(X, tptp_fun_Y_0(Z)) <=> (~((~element(X, Z)) | element(X, X)))))),
% 0.70/0.68 inference(bind,[status(th)],[])).
% 0.70/0.68 tff(4,plain,
% 0.70/0.68 (![Z: $i, X: $i] : (element(X, tptp_fun_Y_0(Z)) <=> (element(X, Z) & (~element(X, X)))) <=> ![Z: $i, X: $i] : (element(X, tptp_fun_Y_0(Z)) <=> (~((~element(X, Z)) | element(X, X))))),
% 0.70/0.68 inference(quant_intro,[status(thm)],[3])).
% 0.70/0.68 tff(5,plain,
% 0.70/0.68 (![Z: $i] : ![X: $i] : (element(X, tptp_fun_Y_0(Z)) <=> (element(X, Z) & (~element(X, X)))) <=> ![Z: $i, X: $i] : (element(X, tptp_fun_Y_0(Z)) <=> (element(X, Z) & (~element(X, X))))),
% 0.70/0.68 inference(pull_quant,[status(thm)],[])).
% 0.70/0.68 tff(6,plain,
% 0.70/0.68 (![Z: $i] : ?[Y: $i] : ![X: $i] : (element(X, Y) <=> (element(X, Z) & (~element(X, X)))) <=> ![Z: $i] : ?[Y: $i] : ![X: $i] : (element(X, Y) <=> (element(X, Z) & (~element(X, X))))),
% 0.70/0.68 inference(rewrite,[status(thm)],[])).
% 0.70/0.68 tff(7,axiom,(![Z: $i] : ?[Y: $i] : ![X: $i] : (element(X, Y) <=> (element(X, Z) & (~element(X, X))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel41_1')).
% 0.70/0.68 tff(8,plain,
% 0.70/0.68 (![Z: $i] : ?[Y: $i] : ![X: $i] : (element(X, Y) <=> (element(X, Z) & (~element(X, X))))),
% 0.70/0.68 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.70/0.68 tff(9,plain,(
% 0.70/0.68 ![Z: $i] : ![X: $i] : (element(X, tptp_fun_Y_0(Z)) <=> (element(X, Z) & (~element(X, X))))),
% 0.70/0.68 inference(skolemize,[status(sab)],[8])).
% 0.70/0.68 tff(10,plain,
% 0.70/0.68 (![Z: $i, X: $i] : (element(X, tptp_fun_Y_0(Z)) <=> (element(X, Z) & (~element(X, X))))),
% 0.70/0.68 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.70/0.68 tff(11,plain,
% 0.70/0.68 (![Z: $i, X: $i] : (element(X, tptp_fun_Y_0(Z)) <=> (~((~element(X, Z)) | element(X, X))))),
% 0.70/0.68 inference(modus_ponens,[status(thm)],[10, 4])).
% 0.70/0.68 tff(12,plain,
% 0.70/0.68 (![Z: $i, X: $i] : (element(X, tptp_fun_Y_0(Z)) <=> (~((~element(X, Z)) | element(X, X))))),
% 0.70/0.68 inference(modus_ponens,[status(thm)],[11, 2])).
% 0.70/0.68 tff(13,plain,
% 0.70/0.68 ((~![Z: $i, X: $i] : (element(X, tptp_fun_Y_0(Z)) <=> (~((~element(X, Z)) | element(X, X))))) | (element(tptp_fun_Y_0(tptp_fun_Y_0(Z!1)), tptp_fun_Y_0(tptp_fun_Y_0(Z!1))) <=> (~((~element(tptp_fun_Y_0(tptp_fun_Y_0(Z!1)), tptp_fun_Y_0(Z!1))) | element(tptp_fun_Y_0(tptp_fun_Y_0(Z!1)), tptp_fun_Y_0(tptp_fun_Y_0(Z!1))))))),
% 0.70/0.68 inference(quant_inst,[status(thm)],[])).
% 0.70/0.68 tff(14,plain,
% 0.70/0.68 (element(tptp_fun_Y_0(tptp_fun_Y_0(Z!1)), tptp_fun_Y_0(tptp_fun_Y_0(Z!1))) <=> (~((~element(tptp_fun_Y_0(tptp_fun_Y_0(Z!1)), tptp_fun_Y_0(Z!1))) | element(tptp_fun_Y_0(tptp_fun_Y_0(Z!1)), tptp_fun_Y_0(tptp_fun_Y_0(Z!1)))))),
% 0.70/0.68 inference(unit_resolution,[status(thm)],[13, 12])).
% 0.70/0.68 tff(15,assumption,(~element(tptp_fun_Y_0(tptp_fun_Y_0(Z!1)), tptp_fun_Y_0(tptp_fun_Y_0(Z!1)))), introduced(assumption)).
% 0.70/0.68 tff(16,plain,
% 0.70/0.68 ((~(element(tptp_fun_Y_0(tptp_fun_Y_0(Z!1)), tptp_fun_Y_0(tptp_fun_Y_0(Z!1))) <=> (~((~element(tptp_fun_Y_0(tptp_fun_Y_0(Z!1)), tptp_fun_Y_0(Z!1))) | element(tptp_fun_Y_0(tptp_fun_Y_0(Z!1)), tptp_fun_Y_0(tptp_fun_Y_0(Z!1))))))) | element(tptp_fun_Y_0(tptp_fun_Y_0(Z!1)), tptp_fun_Y_0(tptp_fun_Y_0(Z!1))) | ((~element(tptp_fun_Y_0(tptp_fun_Y_0(Z!1)), tptp_fun_Y_0(Z!1))) | element(tptp_fun_Y_0(tptp_fun_Y_0(Z!1)), tptp_fun_Y_0(tptp_fun_Y_0(Z!1))))),
% 0.70/0.68 inference(tautology,[status(thm)],[])).
% 0.70/0.68 tff(17,plain,
% 0.70/0.68 ((~element(tptp_fun_Y_0(tptp_fun_Y_0(Z!1)), tptp_fun_Y_0(Z!1))) | element(tptp_fun_Y_0(tptp_fun_Y_0(Z!1)), tptp_fun_Y_0(tptp_fun_Y_0(Z!1)))),
% 0.70/0.68 inference(unit_resolution,[status(thm)],[16, 15, 14])).
% 0.70/0.68 tff(18,plain,
% 0.70/0.68 ((~![Z: $i, X: $i] : (element(X, tptp_fun_Y_0(Z)) <=> (~((~element(X, Z)) | element(X, X))))) | (element(tptp_fun_Y_0(tptp_fun_Y_0(Z!1)), tptp_fun_Y_0(Z!1)) <=> (~((~element(tptp_fun_Y_0(tptp_fun_Y_0(Z!1)), Z!1)) | element(tptp_fun_Y_0(tptp_fun_Y_0(Z!1)), tptp_fun_Y_0(tptp_fun_Y_0(Z!1))))))),
% 0.70/0.68 inference(quant_inst,[status(thm)],[])).
% 0.70/0.68 tff(19,plain,
% 0.70/0.68 (element(tptp_fun_Y_0(tptp_fun_Y_0(Z!1)), tptp_fun_Y_0(Z!1)) <=> (~((~element(tptp_fun_Y_0(tptp_fun_Y_0(Z!1)), Z!1)) | element(tptp_fun_Y_0(tptp_fun_Y_0(Z!1)), tptp_fun_Y_0(tptp_fun_Y_0(Z!1)))))),
% 0.70/0.68 inference(unit_resolution,[status(thm)],[18, 12])).
% 0.70/0.68 tff(20,plain,
% 0.70/0.68 (^[X: $i] : refl(element(X, Z!1) <=> element(X, Z!1))),
% 0.70/0.68 inference(bind,[status(th)],[])).
% 0.70/0.68 tff(21,plain,
% 0.70/0.68 (![X: $i] : element(X, Z!1) <=> ![X: $i] : element(X, Z!1)),
% 0.70/0.68 inference(quant_intro,[status(thm)],[20])).
% 0.70/0.68 tff(22,plain,
% 0.70/0.68 (?[Z: $i] : ![X: $i] : element(X, Z) <=> ?[Z: $i] : ![X: $i] : element(X, Z)),
% 0.70/0.68 inference(rewrite,[status(thm)],[])).
% 0.70/0.68 tff(23,plain,
% 0.70/0.68 ((~(~?[Z: $i] : ![X: $i] : element(X, Z))) <=> ?[Z: $i] : ![X: $i] : element(X, Z)),
% 0.70/0.68 inference(rewrite,[status(thm)],[])).
% 0.70/0.68 tff(24,plain,
% 0.70/0.68 ((~?[Z: $i] : ![X: $i] : element(X, Z)) <=> (~?[Z: $i] : ![X: $i] : element(X, Z))),
% 0.70/0.68 inference(rewrite,[status(thm)],[])).
% 0.70/0.68 tff(25,plain,
% 0.70/0.68 ((~(~?[Z: $i] : ![X: $i] : element(X, Z))) <=> (~(~?[Z: $i] : ![X: $i] : element(X, Z)))),
% 0.70/0.68 inference(monotonicity,[status(thm)],[24])).
% 0.70/0.68 tff(26,plain,
% 0.70/0.68 ((~(~?[Z: $i] : ![X: $i] : element(X, Z))) <=> ?[Z: $i] : ![X: $i] : element(X, Z)),
% 0.70/0.68 inference(transitivity,[status(thm)],[25, 23])).
% 0.70/0.68 tff(27,axiom,(~(~?[Z: $i] : ![X: $i] : element(X, Z))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel41')).
% 0.70/0.68 tff(28,plain,
% 0.70/0.68 (?[Z: $i] : ![X: $i] : element(X, Z)),
% 0.70/0.68 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.70/0.68 tff(29,plain,
% 0.70/0.68 (?[Z: $i] : ![X: $i] : element(X, Z)),
% 0.70/0.68 inference(modus_ponens,[status(thm)],[28, 22])).
% 0.70/0.68 tff(30,plain,(
% 0.70/0.68 $oeq(![X: $i] : element(X, Z!1), ![X: $i] : element(X, Z!1))),
% 0.70/0.68 inference(transitivity,[status(sab)],[29])).
% 0.70/0.68 tff(31,plain,
% 0.70/0.68 (![X: $i] : element(X, Z!1)),
% 0.70/0.68 inference(modus_ponens,[status(thm)],[30, 21])).
% 0.70/0.68 tff(32,plain,
% 0.70/0.68 ((~![X: $i] : element(X, Z!1)) | element(tptp_fun_Y_0(tptp_fun_Y_0(Z!1)), Z!1)),
% 0.70/0.68 inference(quant_inst,[status(thm)],[])).
% 0.70/0.68 tff(33,plain,
% 0.70/0.68 (element(tptp_fun_Y_0(tptp_fun_Y_0(Z!1)), Z!1)),
% 0.70/0.68 inference(unit_resolution,[status(thm)],[32, 31])).
% 0.70/0.68 tff(34,plain,
% 0.70/0.68 ((~((~element(tptp_fun_Y_0(tptp_fun_Y_0(Z!1)), Z!1)) | element(tptp_fun_Y_0(tptp_fun_Y_0(Z!1)), tptp_fun_Y_0(tptp_fun_Y_0(Z!1))))) | (~element(tptp_fun_Y_0(tptp_fun_Y_0(Z!1)), Z!1)) | element(tptp_fun_Y_0(tptp_fun_Y_0(Z!1)), tptp_fun_Y_0(tptp_fun_Y_0(Z!1)))),
% 0.70/0.68 inference(tautology,[status(thm)],[])).
% 0.70/0.68 tff(35,plain,
% 0.70/0.68 ((~((~element(tptp_fun_Y_0(tptp_fun_Y_0(Z!1)), Z!1)) | element(tptp_fun_Y_0(tptp_fun_Y_0(Z!1)), tptp_fun_Y_0(tptp_fun_Y_0(Z!1))))) | element(tptp_fun_Y_0(tptp_fun_Y_0(Z!1)), tptp_fun_Y_0(tptp_fun_Y_0(Z!1)))),
% 0.70/0.68 inference(unit_resolution,[status(thm)],[34, 33])).
% 0.70/0.68 tff(36,plain,
% 0.70/0.68 (~((~element(tptp_fun_Y_0(tptp_fun_Y_0(Z!1)), Z!1)) | element(tptp_fun_Y_0(tptp_fun_Y_0(Z!1)), tptp_fun_Y_0(tptp_fun_Y_0(Z!1))))),
% 0.70/0.68 inference(unit_resolution,[status(thm)],[35, 15])).
% 0.70/0.68 tff(37,plain,
% 0.70/0.68 ((~(element(tptp_fun_Y_0(tptp_fun_Y_0(Z!1)), tptp_fun_Y_0(Z!1)) <=> (~((~element(tptp_fun_Y_0(tptp_fun_Y_0(Z!1)), Z!1)) | element(tptp_fun_Y_0(tptp_fun_Y_0(Z!1)), tptp_fun_Y_0(tptp_fun_Y_0(Z!1))))))) | element(tptp_fun_Y_0(tptp_fun_Y_0(Z!1)), tptp_fun_Y_0(Z!1)) | ((~element(tptp_fun_Y_0(tptp_fun_Y_0(Z!1)), Z!1)) | element(tptp_fun_Y_0(tptp_fun_Y_0(Z!1)), tptp_fun_Y_0(tptp_fun_Y_0(Z!1))))),
% 0.70/0.68 inference(tautology,[status(thm)],[])).
% 0.70/0.68 tff(38,plain,
% 0.70/0.68 (element(tptp_fun_Y_0(tptp_fun_Y_0(Z!1)), tptp_fun_Y_0(Z!1))),
% 0.70/0.68 inference(unit_resolution,[status(thm)],[37, 36, 19])).
% 0.70/0.68 tff(39,plain,
% 0.70/0.68 ((~((~element(tptp_fun_Y_0(tptp_fun_Y_0(Z!1)), tptp_fun_Y_0(Z!1))) | element(tptp_fun_Y_0(tptp_fun_Y_0(Z!1)), tptp_fun_Y_0(tptp_fun_Y_0(Z!1))))) | (~element(tptp_fun_Y_0(tptp_fun_Y_0(Z!1)), tptp_fun_Y_0(Z!1))) | element(tptp_fun_Y_0(tptp_fun_Y_0(Z!1)), tptp_fun_Y_0(tptp_fun_Y_0(Z!1)))),
% 0.70/0.68 inference(tautology,[status(thm)],[])).
% 0.70/0.68 tff(40,plain,
% 0.70/0.68 ($false),
% 0.70/0.68 inference(unit_resolution,[status(thm)],[39, 38, 17, 15])).
% 0.70/0.68 tff(41,plain,(element(tptp_fun_Y_0(tptp_fun_Y_0(Z!1)), tptp_fun_Y_0(tptp_fun_Y_0(Z!1)))), inference(lemma,lemma(discharge,[]))).
% 0.70/0.68 tff(42,plain,
% 0.70/0.68 (((~element(tptp_fun_Y_0(tptp_fun_Y_0(Z!1)), tptp_fun_Y_0(Z!1))) | element(tptp_fun_Y_0(tptp_fun_Y_0(Z!1)), tptp_fun_Y_0(tptp_fun_Y_0(Z!1)))) | (~element(tptp_fun_Y_0(tptp_fun_Y_0(Z!1)), tptp_fun_Y_0(tptp_fun_Y_0(Z!1))))),
% 0.70/0.68 inference(tautology,[status(thm)],[])).
% 0.70/0.68 tff(43,plain,
% 0.70/0.68 ((~element(tptp_fun_Y_0(tptp_fun_Y_0(Z!1)), tptp_fun_Y_0(Z!1))) | element(tptp_fun_Y_0(tptp_fun_Y_0(Z!1)), tptp_fun_Y_0(tptp_fun_Y_0(Z!1)))),
% 0.70/0.68 inference(unit_resolution,[status(thm)],[42, 41])).
% 0.70/0.68 tff(44,plain,
% 0.70/0.68 ((~(element(tptp_fun_Y_0(tptp_fun_Y_0(Z!1)), tptp_fun_Y_0(tptp_fun_Y_0(Z!1))) <=> (~((~element(tptp_fun_Y_0(tptp_fun_Y_0(Z!1)), tptp_fun_Y_0(Z!1))) | element(tptp_fun_Y_0(tptp_fun_Y_0(Z!1)), tptp_fun_Y_0(tptp_fun_Y_0(Z!1))))))) | (~element(tptp_fun_Y_0(tptp_fun_Y_0(Z!1)), tptp_fun_Y_0(tptp_fun_Y_0(Z!1)))) | (~((~element(tptp_fun_Y_0(tptp_fun_Y_0(Z!1)), tptp_fun_Y_0(Z!1))) | element(tptp_fun_Y_0(tptp_fun_Y_0(Z!1)), tptp_fun_Y_0(tptp_fun_Y_0(Z!1)))))),
% 0.70/0.68 inference(tautology,[status(thm)],[])).
% 0.70/0.68 tff(45,plain,
% 0.70/0.68 ($false),
% 0.70/0.68 inference(unit_resolution,[status(thm)],[44, 43, 41, 14])).
% 0.70/0.68 % SZS output end Proof
%------------------------------------------------------------------------------