%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : PHI023+1 : TPTP v9.0.0. Released v7.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n003.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 05:22:46 AM UTC 2025
% Result : Theorem 0.20s 0.38s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : PHI023+1 : TPTP v9.0.0. Released v7.4.0.
% 0.00/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n003.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 02:18:54 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.20/0.38 % SZS status Theorem
% 0.20/0.38 % SZS output start Proof
% 0.20/0.38 tff(absolutelyInfinite_type, type, (
% 0.20/0.38 absolutelyInfinite: $i > $o)).
% 0.20/0.38 tff(tptp_fun_X_0_type, type, (
% 0.20/0.38 tptp_fun_X_0: $i)).
% 0.20/0.38 tff(expressesInfiniteEssentiality_type, type, (
% 0.20/0.38 expressesInfiniteEssentiality: $i > $o)).
% 0.20/0.38 tff(expressesEternalEssentiality_type, type, (
% 0.20/0.38 expressesEternalEssentiality: $i > $o)).
% 0.20/0.38 tff(attributeOf_type, type, (
% 0.20/0.38 attributeOf: ( $i * $i ) > $o)).
% 0.20/0.38 tff(constInInfAttributes_type, type, (
% 0.20/0.38 constInInfAttributes: $i > $o)).
% 0.20/0.38 tff(substance_type, type, (
% 0.20/0.38 substance: $i > $o)).
% 0.20/0.38 tff(conceivedThruItself_type, type, (
% 0.20/0.38 conceivedThruItself: $i > $o)).
% 0.20/0.38 tff(inItself_type, type, (
% 0.20/0.38 inItself: $i > $o)).
% 0.20/0.38 tff(selfCaused_type, type, (
% 0.20/0.38 selfCaused: $i > $o)).
% 0.20/0.38 tff(natureConcOnlyByExistence_type, type, (
% 0.20/0.38 natureConcOnlyByExistence: $i > $o)).
% 0.20/0.38 tff(essenceInvExistence_type, type, (
% 0.20/0.38 essenceInvExistence: $i > $o)).
% 0.20/0.38 tff(hasEssence_type, type, (
% 0.20/0.38 hasEssence: $i > $o)).
% 0.20/0.38 tff(being_type, type, (
% 0.20/0.38 being: $i > $o)).
% 0.20/0.38 tff(god_type, type, (
% 0.20/0.38 god: $i > $o)).
% 0.20/0.38 tff(exists_type, type, (
% 0.20/0.38 exists: $i > $o)).
% 0.20/0.38 tff(1,plain,
% 0.20/0.38 (^[X: $i] : refl((~(((~inItself(X)) | (~conceivedThruItself(X))) <=> substance(X))) <=> (~(((~inItself(X)) | (~conceivedThruItself(X))) <=> substance(X))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(2,plain,
% 0.20/0.38 (![X: $i] : (~(((~inItself(X)) | (~conceivedThruItself(X))) <=> substance(X))) <=> ![X: $i] : (~(((~inItself(X)) | (~conceivedThruItself(X))) <=> substance(X)))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[1])).
% 0.20/0.38 tff(3,plain,
% 0.20/0.38 (^[X: $i] : trans(trans(monotonicity(rewrite((inItself(X) & conceivedThruItself(X)) <=> (~((~inItself(X)) | (~conceivedThruItself(X))))), ((substance(X) <=> (inItself(X) & conceivedThruItself(X))) <=> (substance(X) <=> (~((~inItself(X)) | (~conceivedThruItself(X))))))), rewrite((substance(X) <=> (~((~inItself(X)) | (~conceivedThruItself(X))))) <=> (~(((~inItself(X)) | (~conceivedThruItself(X))) <=> substance(X)))), ((substance(X) <=> (inItself(X) & conceivedThruItself(X))) <=> (~(((~inItself(X)) | (~conceivedThruItself(X))) <=> substance(X))))), rewrite((~(((~inItself(X)) | (~conceivedThruItself(X))) <=> substance(X))) <=> (~(((~inItself(X)) | (~conceivedThruItself(X))) <=> substance(X)))), ((substance(X) <=> (inItself(X) & conceivedThruItself(X))) <=> (~(((~inItself(X)) | (~conceivedThruItself(X))) <=> substance(X)))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(4,plain,
% 0.20/0.38 (![X: $i] : (substance(X) <=> (inItself(X) & conceivedThruItself(X))) <=> ![X: $i] : (~(((~inItself(X)) | (~conceivedThruItself(X))) <=> substance(X)))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[3])).
% 0.20/0.38 tff(5,plain,
% 0.20/0.38 (![X: $i] : (substance(X) <=> (inItself(X) & conceivedThruItself(X))) <=> ![X: $i] : (substance(X) <=> (inItself(X) & conceivedThruItself(X)))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(6,axiom,(![X: $i] : (substance(X) <=> (inItself(X) & conceivedThruItself(X)))), file('/export/starexec/sandbox2/benchmark/Axioms/PHI002+0.ax','substance')).
% 0.20/0.38 tff(7,plain,
% 0.20/0.38 (![X: $i] : (substance(X) <=> (inItself(X) & conceivedThruItself(X)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.20/0.38 tff(8,plain,(
% 0.20/0.38 ![X: $i] : (substance(X) <=> (inItself(X) & conceivedThruItself(X)))),
% 0.20/0.38 inference(skolemize,[status(sab)],[7])).
% 0.20/0.38 tff(9,plain,
% 0.20/0.38 (![X: $i] : (~(((~inItself(X)) | (~conceivedThruItself(X))) <=> substance(X)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.20/0.38 tff(10,plain,
% 0.20/0.38 (![X: $i] : (~(((~inItself(X)) | (~conceivedThruItself(X))) <=> substance(X)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.20/0.38 tff(11,plain,
% 0.20/0.38 ((~![X: $i] : (~(((~inItself(X)) | (~conceivedThruItself(X))) <=> substance(X)))) | (~(((~inItself(X!0)) | (~conceivedThruItself(X!0))) <=> substance(X!0)))),
% 0.20/0.38 inference(quant_inst,[status(thm)],[])).
% 0.20/0.38 tff(12,plain,
% 0.20/0.38 (~(((~inItself(X!0)) | (~conceivedThruItself(X!0))) <=> substance(X!0))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[11, 10])).
% 0.20/0.38 tff(13,plain,
% 0.20/0.38 (^[X: $i] : refl((~(((~essenceInvExistence(X)) | (~natureConcOnlyByExistence(X))) <=> selfCaused(X))) <=> (~(((~essenceInvExistence(X)) | (~natureConcOnlyByExistence(X))) <=> selfCaused(X))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(14,plain,
% 0.20/0.38 (![X: $i] : (~(((~essenceInvExistence(X)) | (~natureConcOnlyByExistence(X))) <=> selfCaused(X))) <=> ![X: $i] : (~(((~essenceInvExistence(X)) | (~natureConcOnlyByExistence(X))) <=> selfCaused(X)))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[13])).
% 0.20/0.38 tff(15,plain,
% 0.20/0.38 (^[X: $i] : trans(trans(monotonicity(rewrite((essenceInvExistence(X) & natureConcOnlyByExistence(X)) <=> (~((~essenceInvExistence(X)) | (~natureConcOnlyByExistence(X))))), ((selfCaused(X) <=> (essenceInvExistence(X) & natureConcOnlyByExistence(X))) <=> (selfCaused(X) <=> (~((~essenceInvExistence(X)) | (~natureConcOnlyByExistence(X))))))), rewrite((selfCaused(X) <=> (~((~essenceInvExistence(X)) | (~natureConcOnlyByExistence(X))))) <=> (~(((~essenceInvExistence(X)) | (~natureConcOnlyByExistence(X))) <=> selfCaused(X)))), ((selfCaused(X) <=> (essenceInvExistence(X) & natureConcOnlyByExistence(X))) <=> (~(((~essenceInvExistence(X)) | (~natureConcOnlyByExistence(X))) <=> selfCaused(X))))), rewrite((~(((~essenceInvExistence(X)) | (~natureConcOnlyByExistence(X))) <=> selfCaused(X))) <=> (~(((~essenceInvExistence(X)) | (~natureConcOnlyByExistence(X))) <=> selfCaused(X)))), ((selfCaused(X) <=> (essenceInvExistence(X) & natureConcOnlyByExistence(X))) <=> (~(((~essenceInvExistence(X)) | (~natureConcOnlyByExistence(X))) <=> selfCaused(X)))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(16,plain,
% 0.20/0.38 (![X: $i] : (selfCaused(X) <=> (essenceInvExistence(X) & natureConcOnlyByExistence(X))) <=> ![X: $i] : (~(((~essenceInvExistence(X)) | (~natureConcOnlyByExistence(X))) <=> selfCaused(X)))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[15])).
% 0.20/0.38 tff(17,plain,
% 0.20/0.38 (![X: $i] : (selfCaused(X) <=> (essenceInvExistence(X) & natureConcOnlyByExistence(X))) <=> ![X: $i] : (selfCaused(X) <=> (essenceInvExistence(X) & natureConcOnlyByExistence(X)))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(18,axiom,(![X: $i] : (selfCaused(X) <=> (essenceInvExistence(X) & natureConcOnlyByExistence(X)))), file('/export/starexec/sandbox2/benchmark/Axioms/PHI002+0.ax','self_caused')).
% 0.20/0.38 tff(19,plain,
% 0.20/0.38 (![X: $i] : (selfCaused(X) <=> (essenceInvExistence(X) & natureConcOnlyByExistence(X)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.20/0.38 tff(20,plain,(
% 0.20/0.38 ![X: $i] : (selfCaused(X) <=> (essenceInvExistence(X) & natureConcOnlyByExistence(X)))),
% 0.20/0.38 inference(skolemize,[status(sab)],[19])).
% 0.20/0.38 tff(21,plain,
% 0.20/0.38 (![X: $i] : (~(((~essenceInvExistence(X)) | (~natureConcOnlyByExistence(X))) <=> selfCaused(X)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[20, 16])).
% 0.20/0.38 tff(22,plain,
% 0.20/0.38 (![X: $i] : (~(((~essenceInvExistence(X)) | (~natureConcOnlyByExistence(X))) <=> selfCaused(X)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[21, 14])).
% 0.20/0.38 tff(23,plain,
% 0.20/0.38 ((~![X: $i] : (~(((~essenceInvExistence(X)) | (~natureConcOnlyByExistence(X))) <=> selfCaused(X)))) | (~(((~essenceInvExistence(X!0)) | (~natureConcOnlyByExistence(X!0))) <=> selfCaused(X!0)))),
% 0.20/0.38 inference(quant_inst,[status(thm)],[])).
% 0.20/0.38 tff(24,plain,
% 0.20/0.38 (~(((~essenceInvExistence(X!0)) | (~natureConcOnlyByExistence(X!0))) <=> selfCaused(X!0))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[23, 22])).
% 0.20/0.38 tff(25,plain,
% 0.20/0.38 (^[X: $i] : refl((~(((~being(X)) | (~absolutelyInfinite(X))) <=> god(X))) <=> (~(((~being(X)) | (~absolutelyInfinite(X))) <=> god(X))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(26,plain,
% 0.20/0.38 (![X: $i] : (~(((~being(X)) | (~absolutelyInfinite(X))) <=> god(X))) <=> ![X: $i] : (~(((~being(X)) | (~absolutelyInfinite(X))) <=> god(X)))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[25])).
% 0.20/0.38 tff(27,plain,
% 0.20/0.38 (^[X: $i] : trans(trans(monotonicity(rewrite((being(X) & absolutelyInfinite(X)) <=> (~((~being(X)) | (~absolutelyInfinite(X))))), ((god(X) <=> (being(X) & absolutelyInfinite(X))) <=> (god(X) <=> (~((~being(X)) | (~absolutelyInfinite(X))))))), rewrite((god(X) <=> (~((~being(X)) | (~absolutelyInfinite(X))))) <=> (~(((~being(X)) | (~absolutelyInfinite(X))) <=> god(X)))), ((god(X) <=> (being(X) & absolutelyInfinite(X))) <=> (~(((~being(X)) | (~absolutelyInfinite(X))) <=> god(X))))), rewrite((~(((~being(X)) | (~absolutelyInfinite(X))) <=> god(X))) <=> (~(((~being(X)) | (~absolutelyInfinite(X))) <=> god(X)))), ((god(X) <=> (being(X) & absolutelyInfinite(X))) <=> (~(((~being(X)) | (~absolutelyInfinite(X))) <=> god(X)))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(28,plain,
% 0.20/0.38 (![X: $i] : (god(X) <=> (being(X) & absolutelyInfinite(X))) <=> ![X: $i] : (~(((~being(X)) | (~absolutelyInfinite(X))) <=> god(X)))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[27])).
% 0.20/0.38 tff(29,plain,
% 0.20/0.38 (![X: $i] : (god(X) <=> (being(X) & absolutelyInfinite(X))) <=> ![X: $i] : (god(X) <=> (being(X) & absolutelyInfinite(X)))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(30,axiom,(![X: $i] : (god(X) <=> (being(X) & absolutelyInfinite(X)))), file('/export/starexec/sandbox2/benchmark/Axioms/PHI002+0.ax','god')).
% 0.20/0.38 tff(31,plain,
% 0.20/0.38 (![X: $i] : (god(X) <=> (being(X) & absolutelyInfinite(X)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.20/0.38 tff(32,plain,(
% 0.20/0.38 ![X: $i] : (god(X) <=> (being(X) & absolutelyInfinite(X)))),
% 0.20/0.38 inference(skolemize,[status(sab)],[31])).
% 0.20/0.38 tff(33,plain,
% 0.20/0.38 (![X: $i] : (~(((~being(X)) | (~absolutelyInfinite(X))) <=> god(X)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[32, 28])).
% 0.20/0.38 tff(34,plain,
% 0.20/0.38 (![X: $i] : (~(((~being(X)) | (~absolutelyInfinite(X))) <=> god(X)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[33, 26])).
% 0.20/0.38 tff(35,plain,
% 0.20/0.38 ((~![X: $i] : (~(((~being(X)) | (~absolutelyInfinite(X))) <=> god(X)))) | (~(((~being(X!0)) | (~absolutelyInfinite(X!0))) <=> god(X!0)))),
% 0.20/0.38 inference(quant_inst,[status(thm)],[])).
% 0.20/0.38 tff(36,plain,
% 0.20/0.38 (~(((~being(X!0)) | (~absolutelyInfinite(X!0))) <=> god(X!0))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[35, 34])).
% 0.20/0.38 tff(37,plain,
% 0.20/0.38 ((~![X: $i] : (exists(X) | (~god(X)))) <=> (~![X: $i] : (exists(X) | (~god(X))))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(38,plain,
% 0.20/0.38 ((~![X: $i] : (god(X) => exists(X))) <=> (~![X: $i] : (exists(X) | (~god(X))))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(39,axiom,(~![X: $i] : (god(X) => exists(X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','if_god_then_exists')).
% 0.20/0.38 tff(40,plain,
% 0.20/0.38 (~![X: $i] : (exists(X) | (~god(X)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.20/0.38 tff(41,plain,
% 0.20/0.38 (~![X: $i] : (exists(X) | (~god(X)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[40, 37])).
% 0.20/0.38 tff(42,plain,
% 0.20/0.38 (~![X: $i] : (exists(X) | (~god(X)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[41, 37])).
% 0.20/0.38 tff(43,plain,
% 0.20/0.38 (~![X: $i] : (exists(X) | (~god(X)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[42, 37])).
% 0.20/0.38 tff(44,plain,(
% 0.20/0.38 ~(exists(X!0) | (~god(X!0)))),
% 0.20/0.38 inference(skolemize,[status(sab)],[43])).
% 0.20/0.38 tff(45,plain,
% 0.20/0.38 (god(X!0)),
% 0.20/0.38 inference(or_elim,[status(thm)],[44])).
% 0.20/0.38 tff(46,plain,
% 0.20/0.38 ((((~being(X!0)) | (~absolutelyInfinite(X!0))) <=> god(X!0)) | (~((~being(X!0)) | (~absolutelyInfinite(X!0)))) | (~god(X!0))),
% 0.20/0.38 inference(tautology,[status(thm)],[])).
% 0.20/0.38 tff(47,plain,
% 0.20/0.38 ((((~being(X!0)) | (~absolutelyInfinite(X!0))) <=> god(X!0)) | (~((~being(X!0)) | (~absolutelyInfinite(X!0))))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[46, 45])).
% 0.20/0.38 tff(48,plain,
% 0.20/0.38 (~((~being(X!0)) | (~absolutelyInfinite(X!0)))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[47, 36])).
% 0.20/0.38 tff(49,plain,
% 0.20/0.38 (((~being(X!0)) | (~absolutelyInfinite(X!0))) | being(X!0)),
% 0.20/0.38 inference(tautology,[status(thm)],[])).
% 0.20/0.38 tff(50,plain,
% 0.20/0.38 (being(X!0)),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[49, 48])).
% 0.20/0.38 tff(51,plain,
% 0.20/0.38 (^[X: $i] : refl((hasEssence(X) | (~being(X))) <=> (hasEssence(X) | (~being(X))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(52,plain,
% 0.20/0.38 (![X: $i] : (hasEssence(X) | (~being(X))) <=> ![X: $i] : (hasEssence(X) | (~being(X)))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[51])).
% 0.20/0.38 tff(53,plain,
% 0.20/0.38 (![X: $i] : (hasEssence(X) | (~being(X))) <=> ![X: $i] : (hasEssence(X) | (~being(X)))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(54,plain,
% 0.20/0.38 (^[X: $i] : rewrite((being(X) => hasEssence(X)) <=> (hasEssence(X) | (~being(X))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(55,plain,
% 0.20/0.38 (![X: $i] : (being(X) => hasEssence(X)) <=> ![X: $i] : (hasEssence(X) | (~being(X)))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[54])).
% 0.20/0.39 tff(56,axiom,(![X: $i] : (being(X) => hasEssence(X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','being_has_essense')).
% 0.20/0.39 tff(57,plain,
% 0.20/0.39 (![X: $i] : (hasEssence(X) | (~being(X)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.20/0.39 tff(58,plain,
% 0.20/0.39 (![X: $i] : (hasEssence(X) | (~being(X)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[57, 53])).
% 0.20/0.39 tff(59,plain,(
% 0.20/0.39 ![X: $i] : (hasEssence(X) | (~being(X)))),
% 0.20/0.39 inference(skolemize,[status(sab)],[58])).
% 0.20/0.39 tff(60,plain,
% 0.20/0.39 (![X: $i] : (hasEssence(X) | (~being(X)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[59, 52])).
% 0.20/0.39 tff(61,plain,
% 0.20/0.39 (((~![X: $i] : (hasEssence(X) | (~being(X)))) | (hasEssence(X!0) | (~being(X!0)))) <=> ((~![X: $i] : (hasEssence(X) | (~being(X)))) | hasEssence(X!0) | (~being(X!0)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(62,plain,
% 0.20/0.39 ((~![X: $i] : (hasEssence(X) | (~being(X)))) | (hasEssence(X!0) | (~being(X!0)))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(63,plain,
% 0.20/0.39 ((~![X: $i] : (hasEssence(X) | (~being(X)))) | hasEssence(X!0) | (~being(X!0))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.20/0.39 tff(64,plain,
% 0.20/0.39 (hasEssence(X!0)),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[63, 60, 50])).
% 0.20/0.39 tff(65,plain,
% 0.20/0.39 (~exists(X!0)),
% 0.20/0.39 inference(or_elim,[status(thm)],[44])).
% 0.20/0.39 tff(66,plain,
% 0.20/0.39 (^[X: $i] : refl(((~essenceInvExistence(X)) | exists(X) | (~hasEssence(X))) <=> ((~essenceInvExistence(X)) | exists(X) | (~hasEssence(X))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(67,plain,
% 0.20/0.39 (![X: $i] : ((~essenceInvExistence(X)) | exists(X) | (~hasEssence(X))) <=> ![X: $i] : ((~essenceInvExistence(X)) | exists(X) | (~hasEssence(X)))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[66])).
% 0.20/0.39 tff(68,plain,
% 0.20/0.39 (^[X: $i] : trans(monotonicity(trans(monotonicity(rewrite((essenceInvExistence(X) & hasEssence(X)) <=> (~((~essenceInvExistence(X)) | (~hasEssence(X))))), ((~(essenceInvExistence(X) & hasEssence(X))) <=> (~(~((~essenceInvExistence(X)) | (~hasEssence(X))))))), rewrite((~(~((~essenceInvExistence(X)) | (~hasEssence(X))))) <=> ((~essenceInvExistence(X)) | (~hasEssence(X)))), ((~(essenceInvExistence(X) & hasEssence(X))) <=> ((~essenceInvExistence(X)) | (~hasEssence(X))))), ((exists(X) | (~(essenceInvExistence(X) & hasEssence(X)))) <=> (exists(X) | ((~essenceInvExistence(X)) | (~hasEssence(X)))))), rewrite((exists(X) | ((~essenceInvExistence(X)) | (~hasEssence(X)))) <=> ((~essenceInvExistence(X)) | exists(X) | (~hasEssence(X)))), ((exists(X) | (~(essenceInvExistence(X) & hasEssence(X)))) <=> ((~essenceInvExistence(X)) | exists(X) | (~hasEssence(X)))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(69,plain,
% 0.20/0.39 (![X: $i] : (exists(X) | (~(essenceInvExistence(X) & hasEssence(X)))) <=> ![X: $i] : ((~essenceInvExistence(X)) | exists(X) | (~hasEssence(X)))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[68])).
% 0.20/0.39 tff(70,plain,
% 0.20/0.39 (![X: $i] : (exists(X) | (~(essenceInvExistence(X) & hasEssence(X)))) <=> ![X: $i] : (exists(X) | (~(essenceInvExistence(X) & hasEssence(X))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(71,plain,
% 0.20/0.39 (^[X: $i] : rewrite(((essenceInvExistence(X) & hasEssence(X)) => exists(X)) <=> (exists(X) | (~(essenceInvExistence(X) & hasEssence(X)))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(72,plain,
% 0.20/0.39 (![X: $i] : ((essenceInvExistence(X) & hasEssence(X)) => exists(X)) <=> ![X: $i] : (exists(X) | (~(essenceInvExistence(X) & hasEssence(X))))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[71])).
% 0.20/0.39 tff(73,axiom,(![X: $i] : ((essenceInvExistence(X) & hasEssence(X)) => exists(X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','essence_involves_existence_exists')).
% 0.20/0.39 tff(74,plain,
% 0.20/0.39 (![X: $i] : (exists(X) | (~(essenceInvExistence(X) & hasEssence(X))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.20/0.39 tff(75,plain,
% 0.20/0.39 (![X: $i] : (exists(X) | (~(essenceInvExistence(X) & hasEssence(X))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[74, 70])).
% 0.20/0.39 tff(76,plain,(
% 0.20/0.39 ![X: $i] : (exists(X) | (~(essenceInvExistence(X) & hasEssence(X))))),
% 0.20/0.39 inference(skolemize,[status(sab)],[75])).
% 0.20/0.39 tff(77,plain,
% 0.20/0.39 (![X: $i] : ((~essenceInvExistence(X)) | exists(X) | (~hasEssence(X)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[76, 69])).
% 0.20/0.39 tff(78,plain,
% 0.20/0.39 (![X: $i] : ((~essenceInvExistence(X)) | exists(X) | (~hasEssence(X)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[77, 67])).
% 0.20/0.39 tff(79,plain,
% 0.20/0.39 (((~![X: $i] : ((~essenceInvExistence(X)) | exists(X) | (~hasEssence(X)))) | (exists(X!0) | (~essenceInvExistence(X!0)) | (~hasEssence(X!0)))) <=> ((~![X: $i] : ((~essenceInvExistence(X)) | exists(X) | (~hasEssence(X)))) | exists(X!0) | (~essenceInvExistence(X!0)) | (~hasEssence(X!0)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(80,plain,
% 0.20/0.39 (((~essenceInvExistence(X!0)) | exists(X!0) | (~hasEssence(X!0))) <=> (exists(X!0) | (~essenceInvExistence(X!0)) | (~hasEssence(X!0)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(81,plain,
% 0.20/0.39 (((~![X: $i] : ((~essenceInvExistence(X)) | exists(X) | (~hasEssence(X)))) | ((~essenceInvExistence(X!0)) | exists(X!0) | (~hasEssence(X!0)))) <=> ((~![X: $i] : ((~essenceInvExistence(X)) | exists(X) | (~hasEssence(X)))) | (exists(X!0) | (~essenceInvExistence(X!0)) | (~hasEssence(X!0))))),
% 0.20/0.39 inference(monotonicity,[status(thm)],[80])).
% 0.20/0.39 tff(82,plain,
% 0.20/0.39 (((~![X: $i] : ((~essenceInvExistence(X)) | exists(X) | (~hasEssence(X)))) | ((~essenceInvExistence(X!0)) | exists(X!0) | (~hasEssence(X!0)))) <=> ((~![X: $i] : ((~essenceInvExistence(X)) | exists(X) | (~hasEssence(X)))) | exists(X!0) | (~essenceInvExistence(X!0)) | (~hasEssence(X!0)))),
% 0.20/0.39 inference(transitivity,[status(thm)],[81, 79])).
% 0.20/0.39 tff(83,plain,
% 0.20/0.39 ((~![X: $i] : ((~essenceInvExistence(X)) | exists(X) | (~hasEssence(X)))) | ((~essenceInvExistence(X!0)) | exists(X!0) | (~hasEssence(X!0)))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(84,plain,
% 0.20/0.39 ((~![X: $i] : ((~essenceInvExistence(X)) | exists(X) | (~hasEssence(X)))) | exists(X!0) | (~essenceInvExistence(X!0)) | (~hasEssence(X!0))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.20/0.39 tff(85,plain,
% 0.20/0.39 ((~essenceInvExistence(X!0)) | (~hasEssence(X!0))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[84, 78, 65])).
% 0.20/0.39 tff(86,plain,
% 0.20/0.39 (~essenceInvExistence(X!0)),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[85, 64])).
% 0.20/0.39 tff(87,plain,
% 0.20/0.39 (((~essenceInvExistence(X!0)) | (~natureConcOnlyByExistence(X!0))) | essenceInvExistence(X!0)),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(88,plain,
% 0.20/0.39 ((~essenceInvExistence(X!0)) | (~natureConcOnlyByExistence(X!0))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[87, 86])).
% 0.20/0.39 tff(89,plain,
% 0.20/0.39 ((((~essenceInvExistence(X!0)) | (~natureConcOnlyByExistence(X!0))) <=> selfCaused(X!0)) | (~((~essenceInvExistence(X!0)) | (~natureConcOnlyByExistence(X!0)))) | (~selfCaused(X!0))),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(90,plain,
% 0.20/0.39 ((((~essenceInvExistence(X!0)) | (~natureConcOnlyByExistence(X!0))) <=> selfCaused(X!0)) | (~selfCaused(X!0))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[89, 88])).
% 0.20/0.39 tff(91,plain,
% 0.20/0.39 (~selfCaused(X!0)),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[90, 24])).
% 0.20/0.39 tff(92,plain,
% 0.20/0.39 (^[X: $i] : refl((selfCaused(X) | (~inItself(X))) <=> (selfCaused(X) | (~inItself(X))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(93,plain,
% 0.20/0.39 (![X: $i] : (selfCaused(X) | (~inItself(X))) <=> ![X: $i] : (selfCaused(X) | (~inItself(X)))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[92])).
% 0.20/0.39 tff(94,plain,
% 0.20/0.39 (![X: $i] : (selfCaused(X) | (~inItself(X))) <=> ![X: $i] : (selfCaused(X) | (~inItself(X)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(95,plain,
% 0.20/0.39 (^[X: $i] : rewrite((inItself(X) => selfCaused(X)) <=> (selfCaused(X) | (~inItself(X))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(96,plain,
% 0.20/0.39 (![X: $i] : (inItself(X) => selfCaused(X)) <=> ![X: $i] : (selfCaused(X) | (~inItself(X)))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[95])).
% 0.20/0.39 tff(97,axiom,(![X: $i] : (inItself(X) => selfCaused(X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','is_in_itself_is_self_caused')).
% 0.20/0.39 tff(98,plain,
% 0.20/0.39 (![X: $i] : (selfCaused(X) | (~inItself(X)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[97, 96])).
% 0.20/0.39 tff(99,plain,
% 0.20/0.39 (![X: $i] : (selfCaused(X) | (~inItself(X)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[98, 94])).
% 0.20/0.39 tff(100,plain,(
% 0.20/0.39 ![X: $i] : (selfCaused(X) | (~inItself(X)))),
% 0.20/0.39 inference(skolemize,[status(sab)],[99])).
% 0.20/0.39 tff(101,plain,
% 0.20/0.39 (![X: $i] : (selfCaused(X) | (~inItself(X)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[100, 93])).
% 0.20/0.39 tff(102,plain,
% 0.20/0.39 (((~![X: $i] : (selfCaused(X) | (~inItself(X)))) | (selfCaused(X!0) | (~inItself(X!0)))) <=> ((~![X: $i] : (selfCaused(X) | (~inItself(X)))) | selfCaused(X!0) | (~inItself(X!0)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(103,plain,
% 0.20/0.39 ((~![X: $i] : (selfCaused(X) | (~inItself(X)))) | (selfCaused(X!0) | (~inItself(X!0)))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(104,plain,
% 0.20/0.39 ((~![X: $i] : (selfCaused(X) | (~inItself(X)))) | selfCaused(X!0) | (~inItself(X!0))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.20/0.39 tff(105,plain,
% 0.20/0.39 (~inItself(X!0)),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[104, 101, 91])).
% 0.20/0.39 tff(106,plain,
% 0.20/0.39 (((~inItself(X!0)) | (~conceivedThruItself(X!0))) | inItself(X!0)),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(107,plain,
% 0.20/0.39 ((~inItself(X!0)) | (~conceivedThruItself(X!0))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[106, 105])).
% 0.20/0.39 tff(108,plain,
% 0.20/0.39 ((((~inItself(X!0)) | (~conceivedThruItself(X!0))) <=> substance(X!0)) | (~((~inItself(X!0)) | (~conceivedThruItself(X!0)))) | (~substance(X!0))),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(109,plain,
% 0.20/0.39 ((((~inItself(X!0)) | (~conceivedThruItself(X!0))) <=> substance(X!0)) | (~substance(X!0))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[108, 107])).
% 0.20/0.39 tff(110,plain,
% 0.20/0.39 (~substance(X!0)),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[109, 12])).
% 0.20/0.39 tff(111,plain,
% 0.20/0.39 (((~substance(X!0)) | (~constInInfAttributes(X!0)) | (~((~attributeOf(X!0, X!0)) | (~((~expressesEternalEssentiality(X!0)) | (~expressesInfiniteEssentiality(X!0))))))) | substance(X!0)),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(112,plain,
% 0.20/0.39 ((~substance(X!0)) | (~constInInfAttributes(X!0)) | (~((~attributeOf(X!0, X!0)) | (~((~expressesEternalEssentiality(X!0)) | (~expressesInfiniteEssentiality(X!0))))))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[111, 110])).
% 0.20/0.39 tff(113,plain,
% 0.20/0.39 (((~being(X!0)) | (~absolutelyInfinite(X!0))) | absolutelyInfinite(X!0)),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(114,plain,
% 0.20/0.39 (absolutelyInfinite(X!0)),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[113, 48])).
% 0.20/0.39 tff(115,plain,
% 0.20/0.39 ((((~substance(X!0)) | (~constInInfAttributes(X!0)) | (~((~attributeOf(X!0, X!0)) | (~((~expressesEternalEssentiality(X!0)) | (~expressesInfiniteEssentiality(X!0))))))) <=> absolutelyInfinite(X!0)) | (~((~substance(X!0)) | (~constInInfAttributes(X!0)) | (~((~attributeOf(X!0, X!0)) | (~((~expressesEternalEssentiality(X!0)) | (~expressesInfiniteEssentiality(X!0)))))))) | (~absolutelyInfinite(X!0))),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(116,plain,
% 0.20/0.39 (((~substance(X!0)) | (~constInInfAttributes(X!0)) | (~((~attributeOf(X!0, X!0)) | (~((~expressesEternalEssentiality(X!0)) | (~expressesInfiniteEssentiality(X!0))))))) <=> absolutelyInfinite(X!0)),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[115, 114, 112])).
% 0.20/0.39 tff(117,plain,
% 0.20/0.39 (^[X: $i, Y: $i] : refl((~(((~substance(X)) | (~constInInfAttributes(X)) | (~((~attributeOf(Y, X)) | (~((~expressesEternalEssentiality(Y)) | (~expressesInfiniteEssentiality(Y))))))) <=> absolutelyInfinite(X))) <=> (~(((~substance(X)) | (~constInInfAttributes(X)) | (~((~attributeOf(Y, X)) | (~((~expressesEternalEssentiality(Y)) | (~expressesInfiniteEssentiality(Y))))))) <=> absolutelyInfinite(X))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(118,plain,
% 0.20/0.39 (![X: $i, Y: $i] : (~(((~substance(X)) | (~constInInfAttributes(X)) | (~((~attributeOf(Y, X)) | (~((~expressesEternalEssentiality(Y)) | (~expressesInfiniteEssentiality(Y))))))) <=> absolutelyInfinite(X))) <=> ![X: $i, Y: $i] : (~(((~substance(X)) | (~constInInfAttributes(X)) | (~((~attributeOf(Y, X)) | (~((~expressesEternalEssentiality(Y)) | (~expressesInfiniteEssentiality(Y))))))) <=> absolutelyInfinite(X)))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[117])).
% 0.20/0.39 tff(119,plain,
% 0.20/0.39 (^[X: $i, Y: $i] : trans(trans(monotonicity(trans(monotonicity(rewrite(((~attributeOf(Y, X)) | (expressesEternalEssentiality(Y) & expressesInfiniteEssentiality(Y))) <=> ((~attributeOf(Y, X)) | (~((~expressesEternalEssentiality(Y)) | (~expressesInfiniteEssentiality(Y)))))), ((substance(X) & constInInfAttributes(X) & ((~attributeOf(Y, X)) | (expressesEternalEssentiality(Y) & expressesInfiniteEssentiality(Y)))) <=> (substance(X) & constInInfAttributes(X) & ((~attributeOf(Y, X)) | (~((~expressesEternalEssentiality(Y)) | (~expressesInfiniteEssentiality(Y)))))))), rewrite((substance(X) & constInInfAttributes(X) & ((~attributeOf(Y, X)) | (~((~expressesEternalEssentiality(Y)) | (~expressesInfiniteEssentiality(Y)))))) <=> (~((~substance(X)) | (~constInInfAttributes(X)) | (~((~attributeOf(Y, X)) | (~((~expressesEternalEssentiality(Y)) | (~expressesInfiniteEssentiality(Y))))))))), ((substance(X) & constInInfAttributes(X) & ((~attributeOf(Y, X)) | (expressesEternalEssentiality(Y) & expressesInfiniteEssentiality(Y)))) <=> (~((~substance(X)) | (~constInInfAttributes(X)) | (~((~attributeOf(Y, X)) | (~((~expressesEternalEssentiality(Y)) | (~expressesInfiniteEssentiality(Y)))))))))), ((absolutelyInfinite(X) <=> (substance(X) & constInInfAttributes(X) & ((~attributeOf(Y, X)) | (expressesEternalEssentiality(Y) & expressesInfiniteEssentiality(Y))))) <=> (absolutelyInfinite(X) <=> (~((~substance(X)) | (~constInInfAttributes(X)) | (~((~attributeOf(Y, X)) | (~((~expressesEternalEssentiality(Y)) | (~expressesInfiniteEssentiality(Y))))))))))), rewrite((absolutelyInfinite(X) <=> (~((~substance(X)) | (~constInInfAttributes(X)) | (~((~attributeOf(Y, X)) | (~((~expressesEternalEssentiality(Y)) | (~expressesInfiniteEssentiality(Y))))))))) <=> (~(((~substance(X)) | (~constInInfAttributes(X)) | (~((~attributeOf(Y, X)) | (~((~expressesEternalEssentiality(Y)) | (~expressesInfiniteEssentiality(Y))))))) <=> absolutelyInfinite(X)))), ((absolutelyInfinite(X) <=> (substance(X) & constInInfAttributes(X) & ((~attributeOf(Y, X)) | (expressesEternalEssentiality(Y) & expressesInfiniteEssentiality(Y))))) <=> (~(((~substance(X)) | (~constInInfAttributes(X)) | (~((~attributeOf(Y, X)) | (~((~expressesEternalEssentiality(Y)) | (~expressesInfiniteEssentiality(Y))))))) <=> absolutelyInfinite(X))))), rewrite((~(((~substance(X)) | (~constInInfAttributes(X)) | (~((~attributeOf(Y, X)) | (~((~expressesEternalEssentiality(Y)) | (~expressesInfiniteEssentiality(Y))))))) <=> absolutelyInfinite(X))) <=> (~(((~substance(X)) | (~constInInfAttributes(X)) | (~((~attributeOf(Y, X)) | (~((~expressesEternalEssentiality(Y)) | (~expressesInfiniteEssentiality(Y))))))) <=> absolutelyInfinite(X)))), ((absolutelyInfinite(X) <=> (substance(X) & constInInfAttributes(X) & ((~attributeOf(Y, X)) | (expressesEternalEssentiality(Y) & expressesInfiniteEssentiality(Y))))) <=> (~(((~substance(X)) | (~constInInfAttributes(X)) | (~((~attributeOf(Y, X)) | (~((~expressesEternalEssentiality(Y)) | (~expressesInfiniteEssentiality(Y))))))) <=> absolutelyInfinite(X)))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(120,plain,
% 0.20/0.39 (![X: $i, Y: $i] : (absolutelyInfinite(X) <=> (substance(X) & constInInfAttributes(X) & ((~attributeOf(Y, X)) | (expressesEternalEssentiality(Y) & expressesInfiniteEssentiality(Y))))) <=> ![X: $i, Y: $i] : (~(((~substance(X)) | (~constInInfAttributes(X)) | (~((~attributeOf(Y, X)) | (~((~expressesEternalEssentiality(Y)) | (~expressesInfiniteEssentiality(Y))))))) <=> absolutelyInfinite(X)))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[119])).
% 0.20/0.39 tff(121,plain,
% 0.20/0.39 (![X: $i, Y: $i] : (absolutelyInfinite(X) <=> (substance(X) & constInInfAttributes(X) & ((~attributeOf(Y, X)) | (expressesEternalEssentiality(Y) & expressesInfiniteEssentiality(Y))))) <=> ![X: $i, Y: $i] : (absolutelyInfinite(X) <=> (substance(X) & constInInfAttributes(X) & ((~attributeOf(Y, X)) | (expressesEternalEssentiality(Y) & expressesInfiniteEssentiality(Y)))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(122,plain,
% 0.20/0.39 (^[X: $i, Y: $i] : rewrite((absolutelyInfinite(X) <=> ((substance(X) & constInInfAttributes(X)) & (attributeOf(Y, X) => (expressesEternalEssentiality(Y) & expressesInfiniteEssentiality(Y))))) <=> (absolutelyInfinite(X) <=> (substance(X) & constInInfAttributes(X) & ((~attributeOf(Y, X)) | (expressesEternalEssentiality(Y) & expressesInfiniteEssentiality(Y))))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(123,plain,
% 0.20/0.39 (![X: $i, Y: $i] : (absolutelyInfinite(X) <=> ((substance(X) & constInInfAttributes(X)) & (attributeOf(Y, X) => (expressesEternalEssentiality(Y) & expressesInfiniteEssentiality(Y))))) <=> ![X: $i, Y: $i] : (absolutelyInfinite(X) <=> (substance(X) & constInInfAttributes(X) & ((~attributeOf(Y, X)) | (expressesEternalEssentiality(Y) & expressesInfiniteEssentiality(Y)))))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[122])).
% 0.20/0.39 tff(124,axiom,(![X: $i, Y: $i] : (absolutelyInfinite(X) <=> ((substance(X) & constInInfAttributes(X)) & (attributeOf(Y, X) => (expressesEternalEssentiality(Y) & expressesInfiniteEssentiality(Y)))))), file('/export/starexec/sandbox2/benchmark/Axioms/PHI002+0.ax','absolutely_infinite')).
% 0.20/0.39 tff(125,plain,
% 0.20/0.39 (![X: $i, Y: $i] : (absolutelyInfinite(X) <=> (substance(X) & constInInfAttributes(X) & ((~attributeOf(Y, X)) | (expressesEternalEssentiality(Y) & expressesInfiniteEssentiality(Y)))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[124, 123])).
% 0.20/0.39 tff(126,plain,
% 0.20/0.39 (![X: $i, Y: $i] : (absolutelyInfinite(X) <=> (substance(X) & constInInfAttributes(X) & ((~attributeOf(Y, X)) | (expressesEternalEssentiality(Y) & expressesInfiniteEssentiality(Y)))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[125, 121])).
% 0.20/0.39 tff(127,plain,(
% 0.20/0.39 ![X: $i, Y: $i] : (absolutelyInfinite(X) <=> (substance(X) & constInInfAttributes(X) & ((~attributeOf(Y, X)) | (expressesEternalEssentiality(Y) & expressesInfiniteEssentiality(Y)))))),
% 0.20/0.39 inference(skolemize,[status(sab)],[126])).
% 0.20/0.39 tff(128,plain,
% 0.20/0.39 (![X: $i, Y: $i] : (~(((~substance(X)) | (~constInInfAttributes(X)) | (~((~attributeOf(Y, X)) | (~((~expressesEternalEssentiality(Y)) | (~expressesInfiniteEssentiality(Y))))))) <=> absolutelyInfinite(X)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[127, 120])).
% 0.20/0.39 tff(129,plain,
% 0.20/0.39 (![X: $i, Y: $i] : (~(((~substance(X)) | (~constInInfAttributes(X)) | (~((~attributeOf(Y, X)) | (~((~expressesEternalEssentiality(Y)) | (~expressesInfiniteEssentiality(Y))))))) <=> absolutelyInfinite(X)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[128, 118])).
% 0.20/0.39 tff(130,plain,
% 0.20/0.39 ((~![X: $i, Y: $i] : (~(((~substance(X)) | (~constInInfAttributes(X)) | (~((~attributeOf(Y, X)) | (~((~expressesEternalEssentiality(Y)) | (~expressesInfiniteEssentiality(Y))))))) <=> absolutelyInfinite(X)))) | (~(((~substance(X!0)) | (~constInInfAttributes(X!0)) | (~((~attributeOf(X!0, X!0)) | (~((~expressesEternalEssentiality(X!0)) | (~expressesInfiniteEssentiality(X!0))))))) <=> absolutelyInfinite(X!0)))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(131,plain,
% 0.20/0.39 ($false),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[130, 129, 116])).
% 0.20/0.39 % SZS output end Proof
% 0.20/0.40 % E exiting
%------------------------------------------------------------------------------