%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU189+1 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n016.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 : Sat Jun 21 05:27:11 AM UTC 2025
% Result : Theorem 0.21s 0.38s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU189+1 : TPTP v9.0.0. Released v3.3.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n016.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 06:15:02 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.21/0.38 % SZS status Theorem
% 0.21/0.38 % SZS output start Proof
% 0.21/0.38 tff(empty_set_type, type, (
% 0.21/0.38 empty_set: $i)).
% 0.21/0.38 tff(relation_dom_type, type, (
% 0.21/0.38 relation_dom: $i > $i)).
% 0.21/0.38 tff(tptp_fun_A_5_type, type, (
% 0.21/0.38 tptp_fun_A_5: $i)).
% 0.21/0.38 tff(relation_rng_type, type, (
% 0.21/0.38 relation_rng: $i > $i)).
% 0.21/0.38 tff(relation_type, type, (
% 0.21/0.38 relation: $i > $o)).
% 0.21/0.38 tff(1,plain,
% 0.21/0.38 ((relation_dom(empty_set) = empty_set) <=> (relation_dom(empty_set) = empty_set)),
% 0.21/0.38 inference(rewrite,[status(thm)],[])).
% 0.21/0.38 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')).
% 0.21/0.38 tff(3,plain,
% 0.21/0.38 (relation_dom(empty_set) = empty_set),
% 0.21/0.38 inference(and_elim,[status(thm)],[2])).
% 0.21/0.38 tff(4,plain,
% 0.21/0.38 (relation_dom(empty_set) = empty_set),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[3, 1])).
% 0.21/0.38 tff(5,plain,
% 0.21/0.38 ((relation_rng(empty_set) = empty_set) <=> (relation_rng(empty_set) = empty_set)),
% 0.21/0.38 inference(rewrite,[status(thm)],[])).
% 0.21/0.38 tff(6,plain,
% 0.21/0.38 (relation_rng(empty_set) = empty_set),
% 0.21/0.38 inference(and_elim,[status(thm)],[2])).
% 0.21/0.38 tff(7,plain,
% 0.21/0.38 (relation_rng(empty_set) = empty_set),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.21/0.38 tff(8,assumption,(~(relation_rng(A!5) = empty_set)), introduced(assumption)).
% 0.21/0.38 tff(9,plain,
% 0.21/0.38 ((~![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))))),
% 0.21/0.38 inference(rewrite,[status(thm)],[])).
% 0.21/0.38 tff(10,plain,
% 0.21/0.38 ((~![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))))),
% 0.21/0.38 inference(rewrite,[status(thm)],[])).
% 0.21/0.38 tff(11,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')).
% 0.21/0.38 tff(12,plain,
% 0.21/0.38 (~![A: $i] : ((~relation(A)) | ((relation_dom(A) = empty_set) <=> (relation_rng(A) = empty_set)))),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.21/0.38 tff(13,plain,
% 0.21/0.38 (~![A: $i] : ((~relation(A)) | ((relation_dom(A) = empty_set) <=> (relation_rng(A) = empty_set)))),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[12, 9])).
% 0.21/0.38 tff(14,plain,
% 0.21/0.38 (~![A: $i] : ((~relation(A)) | ((relation_dom(A) = empty_set) <=> (relation_rng(A) = empty_set)))),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[13, 9])).
% 0.21/0.38 tff(15,plain,
% 0.21/0.38 (~![A: $i] : ((~relation(A)) | ((relation_dom(A) = empty_set) <=> (relation_rng(A) = empty_set)))),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[14, 9])).
% 0.21/0.38 tff(16,plain,(
% 0.21/0.38 ~((~relation(A!5)) | ((relation_dom(A!5) = empty_set) <=> (relation_rng(A!5) = empty_set)))),
% 0.21/0.38 inference(skolemize,[status(sab)],[15])).
% 0.21/0.38 tff(17,plain,
% 0.21/0.38 (~((relation_dom(A!5) = empty_set) <=> (relation_rng(A!5) = empty_set))),
% 0.21/0.38 inference(or_elim,[status(thm)],[16])).
% 0.21/0.38 tff(18,plain,
% 0.21/0.38 (((relation_dom(A!5) = empty_set) <=> (relation_rng(A!5) = empty_set)) | (relation_dom(A!5) = empty_set) | (relation_rng(A!5) = empty_set)),
% 0.21/0.38 inference(tautology,[status(thm)],[])).
% 0.21/0.38 tff(19,plain,
% 0.21/0.38 ((relation_dom(A!5) = empty_set) | (relation_rng(A!5) = empty_set)),
% 0.21/0.38 inference(unit_resolution,[status(thm)],[18, 17])).
% 0.21/0.38 tff(20,plain,
% 0.21/0.38 (relation_dom(A!5) = empty_set),
% 0.21/0.38 inference(unit_resolution,[status(thm)],[19, 8])).
% 0.21/0.38 tff(21,plain,
% 0.21/0.38 (((relation_dom(A!5) = empty_set) | (relation_rng(A!5) = empty_set)) | (~(relation_dom(A!5) = empty_set))),
% 0.21/0.38 inference(tautology,[status(thm)],[])).
% 0.21/0.38 tff(22,plain,
% 0.21/0.38 ((relation_dom(A!5) = empty_set) | (relation_rng(A!5) = empty_set)),
% 0.21/0.38 inference(unit_resolution,[status(thm)],[21, 20])).
% 0.21/0.38 tff(23,plain,
% 0.21/0.38 (^[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)))))),
% 0.21/0.38 inference(bind,[status(th)],[])).
% 0.21/0.38 tff(24,plain,
% 0.21/0.38 (![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))))),
% 0.21/0.38 inference(quant_intro,[status(thm)],[23])).
% 0.21/0.38 tff(25,plain,
% 0.21/0.38 (![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))))),
% 0.21/0.38 inference(rewrite,[status(thm)],[])).
% 0.21/0.38 tff(26,plain,
% 0.21/0.38 (^[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))))))),
% 0.21/0.38 inference(bind,[status(th)],[])).
% 0.21/0.38 tff(27,plain,
% 0.21/0.38 (![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))))),
% 0.21/0.38 inference(quant_intro,[status(thm)],[26])).
% 0.21/0.38 tff(28,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')).
% 0.21/0.38 tff(29,plain,
% 0.21/0.38 (![A: $i] : ((A = empty_set) | (~relation(A)) | (~((relation_dom(A) = empty_set) | (relation_rng(A) = empty_set))))),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.21/0.38 tff(30,plain,
% 0.21/0.38 (![A: $i] : ((A = empty_set) | (~relation(A)) | (~((relation_dom(A) = empty_set) | (relation_rng(A) = empty_set))))),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[29, 25])).
% 0.21/0.38 tff(31,plain,(
% 0.21/0.38 ![A: $i] : ((A = empty_set) | (~relation(A)) | (~((relation_dom(A) = empty_set) | (relation_rng(A) = empty_set))))),
% 0.21/0.38 inference(skolemize,[status(sab)],[30])).
% 0.21/0.38 tff(32,plain,
% 0.21/0.38 (![A: $i] : ((A = empty_set) | (~relation(A)) | (~((relation_dom(A) = empty_set) | (relation_rng(A) = empty_set))))),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[31, 24])).
% 0.21/0.38 tff(33,plain,
% 0.21/0.38 (relation(A!5)),
% 0.21/0.38 inference(or_elim,[status(thm)],[16])).
% 0.21/0.38 tff(34,plain,
% 0.21/0.38 (((~![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))))),
% 0.21/0.38 inference(rewrite,[status(thm)],[])).
% 0.21/0.38 tff(35,plain,
% 0.21/0.38 (((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))))),
% 0.21/0.38 inference(rewrite,[status(thm)],[])).
% 0.21/0.38 tff(36,plain,
% 0.21/0.38 (((~![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)))))),
% 0.21/0.38 inference(monotonicity,[status(thm)],[35])).
% 0.21/0.38 tff(37,plain,
% 0.21/0.38 (((~![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))))),
% 0.21/0.38 inference(transitivity,[status(thm)],[36, 34])).
% 0.21/0.38 tff(38,plain,
% 0.21/0.38 ((~![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))))),
% 0.21/0.38 inference(quant_inst,[status(thm)],[])).
% 0.21/0.38 tff(39,plain,
% 0.21/0.38 ((~![A: $i] : ((A = empty_set) | (~relation(A)) | (~((relation_dom(A) = empty_set) | (relation_rng(A) = empty_set))))) | (~relation(A!5)) | (A!5 = empty_set) | (~((relation_dom(A!5) = empty_set) | (relation_rng(A!5) = empty_set)))),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.21/0.38 tff(40,plain,
% 0.21/0.38 ((A!5 = empty_set) | (~((relation_dom(A!5) = empty_set) | (relation_rng(A!5) = empty_set)))),
% 0.21/0.38 inference(unit_resolution,[status(thm)],[39, 33, 32])).
% 0.21/0.38 tff(41,plain,
% 0.21/0.38 (A!5 = empty_set),
% 0.21/0.38 inference(unit_resolution,[status(thm)],[40, 22])).
% 0.21/0.38 tff(42,plain,
% 0.21/0.38 (relation_rng(A!5) = relation_rng(empty_set)),
% 0.21/0.38 inference(monotonicity,[status(thm)],[41])).
% 0.21/0.38 tff(43,plain,
% 0.21/0.38 (relation_rng(A!5) = empty_set),
% 0.21/0.38 inference(transitivity,[status(thm)],[42, 7])).
% 0.21/0.38 tff(44,plain,
% 0.21/0.38 ($false),
% 0.21/0.38 inference(unit_resolution,[status(thm)],[8, 43])).
% 0.21/0.38 tff(45,plain,(relation_rng(A!5) = empty_set), inference(lemma,lemma(discharge,[]))).
% 0.21/0.38 tff(46,plain,
% 0.21/0.38 (((relation_dom(A!5) = empty_set) | (relation_rng(A!5) = empty_set)) | (~(relation_rng(A!5) = empty_set))),
% 0.21/0.38 inference(tautology,[status(thm)],[])).
% 0.21/0.38 tff(47,plain,
% 0.21/0.38 ((relation_dom(A!5) = empty_set) | (relation_rng(A!5) = empty_set)),
% 0.21/0.38 inference(unit_resolution,[status(thm)],[46, 45])).
% 0.21/0.38 tff(48,plain,
% 0.21/0.38 (A!5 = empty_set),
% 0.21/0.38 inference(unit_resolution,[status(thm)],[40, 47])).
% 0.21/0.38 tff(49,plain,
% 0.21/0.38 (relation_dom(A!5) = relation_dom(empty_set)),
% 0.21/0.38 inference(monotonicity,[status(thm)],[48])).
% 0.21/0.38 tff(50,plain,
% 0.21/0.38 (relation_dom(A!5) = empty_set),
% 0.21/0.38 inference(transitivity,[status(thm)],[49, 4])).
% 0.21/0.38 tff(51,plain,
% 0.21/0.38 (((relation_dom(A!5) = empty_set) <=> (relation_rng(A!5) = empty_set)) | (~(relation_dom(A!5) = empty_set)) | (~(relation_rng(A!5) = empty_set))),
% 0.21/0.38 inference(tautology,[status(thm)],[])).
% 0.21/0.38 tff(52,plain,
% 0.21/0.38 ((~(relation_dom(A!5) = empty_set)) | (~(relation_rng(A!5) = empty_set))),
% 0.21/0.38 inference(unit_resolution,[status(thm)],[51, 17])).
% 0.21/0.38 tff(53,plain,
% 0.21/0.38 (~(relation_dom(A!5) = empty_set)),
% 0.21/0.38 inference(unit_resolution,[status(thm)],[52, 45])).
% 0.21/0.38 tff(54,plain,
% 0.21/0.38 ($false),
% 0.21/0.38 inference(unit_resolution,[status(thm)],[53, 50])).
% 0.21/0.38 % SZS output end Proof
% 0.21/0.39 % E exiting
%------------------------------------------------------------------------------