TSTP Solution File: SEU189+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SEU189+1 : TPTP v8.1.0. Released v3.3.0.
% 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 : Tue Sep 20 07:28:04 EDT 2022
% Result : Theorem 0.15s 0.35s
% Output : Proof 0.15s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.09 % Problem : SEU189+1 : TPTP v8.1.0. Released v3.3.0.
% 0.02/0.10 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.09/0.30 % Computer : n026.cluster.edu
% 0.09/0.30 % Model : x86_64 x86_64
% 0.09/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30 % Memory : 8042.1875MB
% 0.09/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30 % CPULimit : 300
% 0.09/0.30 % WCLimit : 300
% 0.09/0.30 % DateTime : Sat Sep 3 10:21:08 EDT 2022
% 0.09/0.30 % CPUTime :
% 0.09/0.31 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.09/0.31 Usage: tptp [options] [-file:]file
% 0.09/0.31 -h, -? prints this message.
% 0.09/0.31 -smt2 print SMT-LIB2 benchmark.
% 0.09/0.31 -m, -model generate model.
% 0.09/0.31 -p, -proof generate proof.
% 0.09/0.31 -c, -core generate unsat core of named formulas.
% 0.09/0.31 -st, -statistics display statistics.
% 0.09/0.31 -t:timeout set timeout (in second).
% 0.09/0.31 -smt2status display status in smt2 format instead of SZS.
% 0.09/0.31 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.09/0.31 -<param>:<value> configuration parameter and value.
% 0.09/0.31 -o:<output-file> file to place output in.
% 0.15/0.35 % SZS status Theorem
% 0.15/0.35 % SZS output start Proof
% 0.15/0.35 tff(empty_set_type, type, (
% 0.15/0.35 empty_set: $i)).
% 0.15/0.35 tff(relation_dom_type, type, (
% 0.15/0.35 relation_dom: $i > $i)).
% 0.15/0.35 tff(tptp_fun_A_5_type, type, (
% 0.15/0.35 tptp_fun_A_5: $i)).
% 0.15/0.35 tff(relation_rng_type, type, (
% 0.15/0.35 relation_rng: $i > $i)).
% 0.15/0.35 tff(relation_type, type, (
% 0.15/0.35 relation: $i > $o)).
% 0.15/0.35 tff(1,plain,
% 0.15/0.35 ((relation_dom(empty_set) = empty_set) <=> (relation_dom(empty_set) = empty_set)),
% 0.15/0.35 inference(rewrite,[status(thm)],[])).
% 0.15/0.35 tff(2,axiom,((relation_dom(empty_set) = empty_set) & (relation_rng(empty_set) = empty_set)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t60_relat_1')).
% 0.15/0.35 tff(3,plain,
% 0.15/0.35 (relation_dom(empty_set) = empty_set),
% 0.15/0.35 inference(and_elim,[status(thm)],[2])).
% 0.15/0.35 tff(4,plain,
% 0.15/0.35 (relation_dom(empty_set) = empty_set),
% 0.15/0.35 inference(modus_ponens,[status(thm)],[3, 1])).
% 0.15/0.35 tff(5,plain,
% 0.15/0.35 ((relation_rng(empty_set) = empty_set) <=> (relation_rng(empty_set) = empty_set)),
% 0.15/0.35 inference(rewrite,[status(thm)],[])).
% 0.15/0.35 tff(6,plain,
% 0.15/0.35 (relation_rng(empty_set) = empty_set),
% 0.15/0.35 inference(and_elim,[status(thm)],[2])).
% 0.15/0.35 tff(7,plain,
% 0.15/0.35 (relation_rng(empty_set) = empty_set),
% 0.15/0.35 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.15/0.35 tff(8,assumption,(~(relation_rng(A!5) = empty_set)), introduced(assumption)).
% 0.15/0.35 tff(9,plain,
% 0.15/0.35 ((~((relation_dom(A!5) = empty_set) <=> (relation_rng(A!5) = empty_set))) <=> ((~(relation_dom(A!5) = empty_set)) <=> (relation_rng(A!5) = empty_set))),
% 0.15/0.35 inference(rewrite,[status(thm)],[])).
% 0.15/0.35 tff(10,plain,
% 0.15/0.35 ((~![A: $i] : ((~relation(A)) | ((relation_dom(A) = empty_set) <=> (relation_rng(A) = empty_set)))) <=> (~![A: $i] : ((~relation(A)) | ((relation_dom(A) = empty_set) <=> (relation_rng(A) = empty_set))))),
% 0.15/0.35 inference(rewrite,[status(thm)],[])).
% 0.15/0.35 tff(11,plain,
% 0.15/0.35 ((~![A: $i] : (relation(A) => ((relation_dom(A) = empty_set) <=> (relation_rng(A) = empty_set)))) <=> (~![A: $i] : ((~relation(A)) | ((relation_dom(A) = empty_set) <=> (relation_rng(A) = empty_set))))),
% 0.15/0.35 inference(rewrite,[status(thm)],[])).
% 0.15/0.35 tff(12,axiom,(~![A: $i] : (relation(A) => ((relation_dom(A) = empty_set) <=> (relation_rng(A) = empty_set)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t65_relat_1')).
% 0.15/0.35 tff(13,plain,
% 0.15/0.35 (~![A: $i] : ((~relation(A)) | ((relation_dom(A) = empty_set) <=> (relation_rng(A) = empty_set)))),
% 0.15/0.35 inference(modus_ponens,[status(thm)],[12, 11])).
% 0.15/0.35 tff(14,plain,
% 0.15/0.35 (~![A: $i] : ((~relation(A)) | ((relation_dom(A) = empty_set) <=> (relation_rng(A) = empty_set)))),
% 0.15/0.35 inference(modus_ponens,[status(thm)],[13, 10])).
% 0.15/0.35 tff(15,plain,
% 0.15/0.35 (~![A: $i] : ((~relation(A)) | ((relation_dom(A) = empty_set) <=> (relation_rng(A) = empty_set)))),
% 0.15/0.35 inference(modus_ponens,[status(thm)],[14, 10])).
% 0.15/0.35 tff(16,plain,
% 0.15/0.35 (~![A: $i] : ((~relation(A)) | ((relation_dom(A) = empty_set) <=> (relation_rng(A) = empty_set)))),
% 0.15/0.35 inference(modus_ponens,[status(thm)],[15, 10])).
% 0.15/0.35 tff(17,plain,
% 0.15/0.35 (~![A: $i] : ((~relation(A)) | ((relation_dom(A) = empty_set) <=> (relation_rng(A) = empty_set)))),
% 0.15/0.35 inference(modus_ponens,[status(thm)],[16, 10])).
% 0.15/0.35 tff(18,plain,
% 0.15/0.35 (~![A: $i] : ((~relation(A)) | ((relation_dom(A) = empty_set) <=> (relation_rng(A) = empty_set)))),
% 0.15/0.35 inference(modus_ponens,[status(thm)],[17, 10])).
% 0.15/0.35 tff(19,plain,
% 0.15/0.35 (~![A: $i] : ((~relation(A)) | ((relation_dom(A) = empty_set) <=> (relation_rng(A) = empty_set)))),
% 0.15/0.35 inference(modus_ponens,[status(thm)],[18, 10])).
% 0.15/0.35 tff(20,plain,(
% 0.15/0.35 ~((~relation(A!5)) | ((relation_dom(A!5) = empty_set) <=> (relation_rng(A!5) = empty_set)))),
% 0.15/0.35 inference(skolemize,[status(sab)],[19])).
% 0.15/0.35 tff(21,plain,
% 0.15/0.35 (~((relation_dom(A!5) = empty_set) <=> (relation_rng(A!5) = empty_set))),
% 0.15/0.35 inference(or_elim,[status(thm)],[20])).
% 0.15/0.35 tff(22,plain,
% 0.15/0.35 ((~(relation_dom(A!5) = empty_set)) <=> (relation_rng(A!5) = empty_set)),
% 0.15/0.35 inference(modus_ponens,[status(thm)],[21, 9])).
% 0.15/0.35 tff(23,plain,
% 0.15/0.35 ((relation_dom(A!5) = empty_set) | (relation_rng(A!5) = empty_set) | (~((~(relation_dom(A!5) = empty_set)) <=> (relation_rng(A!5) = empty_set)))),
% 0.15/0.35 inference(tautology,[status(thm)],[])).
% 0.15/0.35 tff(24,plain,
% 0.15/0.35 ((relation_dom(A!5) = empty_set) | (relation_rng(A!5) = empty_set)),
% 0.15/0.35 inference(unit_resolution,[status(thm)],[23, 22])).
% 0.15/0.35 tff(25,plain,
% 0.15/0.35 (relation_dom(A!5) = empty_set),
% 0.15/0.35 inference(unit_resolution,[status(thm)],[24, 8])).
% 0.15/0.35 tff(26,plain,
% 0.15/0.35 (((relation_dom(A!5) = empty_set) | (relation_rng(A!5) = empty_set)) | (~(relation_dom(A!5) = empty_set))),
% 0.15/0.35 inference(tautology,[status(thm)],[])).
% 0.15/0.35 tff(27,plain,
% 0.15/0.35 ((relation_dom(A!5) = empty_set) | (relation_rng(A!5) = empty_set)),
% 0.15/0.35 inference(unit_resolution,[status(thm)],[26, 25])).
% 0.15/0.35 tff(28,plain,
% 0.15/0.35 (^[A: $i] : refl(((A = empty_set) | (~relation(A)) | (~((relation_dom(A) = empty_set) | (relation_rng(A) = empty_set)))) <=> ((A = empty_set) | (~relation(A)) | (~((relation_dom(A) = empty_set) | (relation_rng(A) = empty_set)))))),
% 0.15/0.35 inference(bind,[status(th)],[])).
% 0.15/0.35 tff(29,plain,
% 0.15/0.35 (![A: $i] : ((A = empty_set) | (~relation(A)) | (~((relation_dom(A) = empty_set) | (relation_rng(A) = empty_set)))) <=> ![A: $i] : ((A = empty_set) | (~relation(A)) | (~((relation_dom(A) = empty_set) | (relation_rng(A) = empty_set))))),
% 0.15/0.35 inference(quant_intro,[status(thm)],[28])).
% 0.15/0.35 tff(30,plain,
% 0.15/0.35 (![A: $i] : ((A = empty_set) | (~relation(A)) | (~((relation_dom(A) = empty_set) | (relation_rng(A) = empty_set)))) <=> ![A: $i] : ((A = empty_set) | (~relation(A)) | (~((relation_dom(A) = empty_set) | (relation_rng(A) = empty_set))))),
% 0.15/0.35 inference(rewrite,[status(thm)],[])).
% 0.15/0.35 tff(31,plain,
% 0.15/0.35 (^[A: $i] : trans(monotonicity(rewrite((((relation_dom(A) = empty_set) | (relation_rng(A) = empty_set)) => (A = empty_set)) <=> ((~((relation_dom(A) = empty_set) | (relation_rng(A) = empty_set))) | (A = empty_set))), ((relation(A) => (((relation_dom(A) = empty_set) | (relation_rng(A) = empty_set)) => (A = empty_set))) <=> (relation(A) => ((~((relation_dom(A) = empty_set) | (relation_rng(A) = empty_set))) | (A = empty_set))))), rewrite((relation(A) => ((~((relation_dom(A) = empty_set) | (relation_rng(A) = empty_set))) | (A = empty_set))) <=> ((A = empty_set) | (~relation(A)) | (~((relation_dom(A) = empty_set) | (relation_rng(A) = empty_set))))), ((relation(A) => (((relation_dom(A) = empty_set) | (relation_rng(A) = empty_set)) => (A = empty_set))) <=> ((A = empty_set) | (~relation(A)) | (~((relation_dom(A) = empty_set) | (relation_rng(A) = empty_set))))))),
% 0.15/0.35 inference(bind,[status(th)],[])).
% 0.15/0.35 tff(32,plain,
% 0.15/0.35 (![A: $i] : (relation(A) => (((relation_dom(A) = empty_set) | (relation_rng(A) = empty_set)) => (A = empty_set))) <=> ![A: $i] : ((A = empty_set) | (~relation(A)) | (~((relation_dom(A) = empty_set) | (relation_rng(A) = empty_set))))),
% 0.15/0.35 inference(quant_intro,[status(thm)],[31])).
% 0.15/0.35 tff(33,axiom,(![A: $i] : (relation(A) => (((relation_dom(A) = empty_set) | (relation_rng(A) = empty_set)) => (A = empty_set)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t64_relat_1')).
% 0.15/0.35 tff(34,plain,
% 0.15/0.35 (![A: $i] : ((A = empty_set) | (~relation(A)) | (~((relation_dom(A) = empty_set) | (relation_rng(A) = empty_set))))),
% 0.15/0.35 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.15/0.35 tff(35,plain,
% 0.15/0.35 (![A: $i] : ((A = empty_set) | (~relation(A)) | (~((relation_dom(A) = empty_set) | (relation_rng(A) = empty_set))))),
% 0.15/0.35 inference(modus_ponens,[status(thm)],[34, 30])).
% 0.15/0.35 tff(36,plain,(
% 0.15/0.35 ![A: $i] : ((A = empty_set) | (~relation(A)) | (~((relation_dom(A) = empty_set) | (relation_rng(A) = empty_set))))),
% 0.15/0.35 inference(skolemize,[status(sab)],[35])).
% 0.15/0.35 tff(37,plain,
% 0.15/0.35 (![A: $i] : ((A = empty_set) | (~relation(A)) | (~((relation_dom(A) = empty_set) | (relation_rng(A) = empty_set))))),
% 0.15/0.35 inference(modus_ponens,[status(thm)],[36, 29])).
% 0.15/0.35 tff(38,plain,
% 0.15/0.35 (relation(A!5)),
% 0.15/0.35 inference(or_elim,[status(thm)],[20])).
% 0.15/0.35 tff(39,plain,
% 0.15/0.35 (((~![A: $i] : ((A = empty_set) | (~relation(A)) | (~((relation_dom(A) = empty_set) | (relation_rng(A) = empty_set))))) | ((~relation(A!5)) | (A!5 = empty_set) | (~((relation_dom(A!5) = empty_set) | (relation_rng(A!5) = empty_set))))) <=> ((~![A: $i] : ((A = empty_set) | (~relation(A)) | (~((relation_dom(A) = empty_set) | (relation_rng(A) = empty_set))))) | (~relation(A!5)) | (A!5 = empty_set) | (~((relation_dom(A!5) = empty_set) | (relation_rng(A!5) = empty_set))))),
% 0.15/0.36 inference(rewrite,[status(thm)],[])).
% 0.15/0.36 tff(40,plain,
% 0.15/0.36 (((A!5 = empty_set) | (~relation(A!5)) | (~((relation_dom(A!5) = empty_set) | (relation_rng(A!5) = empty_set)))) <=> ((~relation(A!5)) | (A!5 = empty_set) | (~((relation_dom(A!5) = empty_set) | (relation_rng(A!5) = empty_set))))),
% 0.15/0.36 inference(rewrite,[status(thm)],[])).
% 0.15/0.36 tff(41,plain,
% 0.15/0.36 (((~![A: $i] : ((A = empty_set) | (~relation(A)) | (~((relation_dom(A) = empty_set) | (relation_rng(A) = empty_set))))) | ((A!5 = empty_set) | (~relation(A!5)) | (~((relation_dom(A!5) = empty_set) | (relation_rng(A!5) = empty_set))))) <=> ((~![A: $i] : ((A = empty_set) | (~relation(A)) | (~((relation_dom(A) = empty_set) | (relation_rng(A) = empty_set))))) | ((~relation(A!5)) | (A!5 = empty_set) | (~((relation_dom(A!5) = empty_set) | (relation_rng(A!5) = empty_set)))))),
% 0.15/0.36 inference(monotonicity,[status(thm)],[40])).
% 0.15/0.36 tff(42,plain,
% 0.15/0.36 (((~![A: $i] : ((A = empty_set) | (~relation(A)) | (~((relation_dom(A) = empty_set) | (relation_rng(A) = empty_set))))) | ((A!5 = empty_set) | (~relation(A!5)) | (~((relation_dom(A!5) = empty_set) | (relation_rng(A!5) = empty_set))))) <=> ((~![A: $i] : ((A = empty_set) | (~relation(A)) | (~((relation_dom(A) = empty_set) | (relation_rng(A) = empty_set))))) | (~relation(A!5)) | (A!5 = empty_set) | (~((relation_dom(A!5) = empty_set) | (relation_rng(A!5) = empty_set))))),
% 0.15/0.36 inference(transitivity,[status(thm)],[41, 39])).
% 0.15/0.36 tff(43,plain,
% 0.15/0.36 ((~![A: $i] : ((A = empty_set) | (~relation(A)) | (~((relation_dom(A) = empty_set) | (relation_rng(A) = empty_set))))) | ((A!5 = empty_set) | (~relation(A!5)) | (~((relation_dom(A!5) = empty_set) | (relation_rng(A!5) = empty_set))))),
% 0.15/0.36 inference(quant_inst,[status(thm)],[])).
% 0.15/0.36 tff(44,plain,
% 0.15/0.36 ((~![A: $i] : ((A = empty_set) | (~relation(A)) | (~((relation_dom(A) = empty_set) | (relation_rng(A) = empty_set))))) | (~relation(A!5)) | (A!5 = empty_set) | (~((relation_dom(A!5) = empty_set) | (relation_rng(A!5) = empty_set)))),
% 0.15/0.36 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.15/0.36 tff(45,plain,
% 0.15/0.36 ((A!5 = empty_set) | (~((relation_dom(A!5) = empty_set) | (relation_rng(A!5) = empty_set)))),
% 0.15/0.36 inference(unit_resolution,[status(thm)],[44, 38, 37])).
% 0.15/0.36 tff(46,plain,
% 0.15/0.36 (A!5 = empty_set),
% 0.15/0.36 inference(unit_resolution,[status(thm)],[45, 27])).
% 0.15/0.36 tff(47,plain,
% 0.15/0.36 (relation_rng(A!5) = relation_rng(empty_set)),
% 0.15/0.36 inference(monotonicity,[status(thm)],[46])).
% 0.15/0.36 tff(48,plain,
% 0.15/0.36 (relation_rng(A!5) = empty_set),
% 0.15/0.36 inference(transitivity,[status(thm)],[47, 7])).
% 0.15/0.36 tff(49,plain,
% 0.15/0.36 ($false),
% 0.15/0.36 inference(unit_resolution,[status(thm)],[8, 48])).
% 0.15/0.36 tff(50,plain,(relation_rng(A!5) = empty_set), inference(lemma,lemma(discharge,[]))).
% 0.15/0.36 tff(51,plain,
% 0.15/0.36 (((relation_dom(A!5) = empty_set) | (relation_rng(A!5) = empty_set)) | (~(relation_rng(A!5) = empty_set))),
% 0.15/0.36 inference(tautology,[status(thm)],[])).
% 0.15/0.36 tff(52,plain,
% 0.15/0.36 ((relation_dom(A!5) = empty_set) | (relation_rng(A!5) = empty_set)),
% 0.15/0.36 inference(unit_resolution,[status(thm)],[51, 50])).
% 0.15/0.36 tff(53,plain,
% 0.15/0.36 (A!5 = empty_set),
% 0.15/0.36 inference(unit_resolution,[status(thm)],[45, 52])).
% 0.15/0.36 tff(54,plain,
% 0.15/0.36 (relation_dom(A!5) = relation_dom(empty_set)),
% 0.15/0.36 inference(monotonicity,[status(thm)],[53])).
% 0.15/0.36 tff(55,plain,
% 0.15/0.36 (relation_dom(A!5) = empty_set),
% 0.15/0.36 inference(transitivity,[status(thm)],[54, 4])).
% 0.15/0.36 tff(56,plain,
% 0.15/0.36 ((~(relation_dom(A!5) = empty_set)) | (~(relation_rng(A!5) = empty_set)) | (~((~(relation_dom(A!5) = empty_set)) <=> (relation_rng(A!5) = empty_set)))),
% 0.15/0.36 inference(tautology,[status(thm)],[])).
% 0.15/0.36 tff(57,plain,
% 0.15/0.36 ((~(relation_dom(A!5) = empty_set)) | (~(relation_rng(A!5) = empty_set))),
% 0.15/0.36 inference(unit_resolution,[status(thm)],[56, 22])).
% 0.15/0.36 tff(58,plain,
% 0.15/0.36 (~(relation_dom(A!5) = empty_set)),
% 0.15/0.36 inference(unit_resolution,[status(thm)],[57, 50])).
% 0.15/0.36 tff(59,plain,
% 0.15/0.36 ($false),
% 0.15/0.36 inference(unit_resolution,[status(thm)],[58, 55])).
% 0.15/0.36 % SZS output end Proof
%------------------------------------------------------------------------------