%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : PHI023+1 : TPTP v9.2.0. Released v7.4.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n009.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 : Fri Oct 3 07:57:57 PM UTC 2025 % Result : Theorem 3.81s 3.96s % Output : Proof 3.81s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.11 % Problem : PHI023+1 : TPTP v9.2.0. Released v7.4.0. % 0.03/0.13 % Command : duper %s % 0.12/0.34 % Computer : n009.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 Oct 3 09:08:53 EDT 2025 % 0.12/0.34 % CPUTime : % 3.81/3.96 SZS status Theorem for theBenchmark.p % 3.81/3.96 SZS output start Proof for theBenchmark.p % 3.81/3.96 Clause #0 (by assumption #[]): Eq (∀ (X : Iota), Iff (selfCaused X) (And (essenceInvExistence X) (natureConcOnlyByExistence X))) True % 3.81/3.96 Clause #2 (by assumption #[]): Eq (∀ (X : Iota), Iff (substance X) (And (inItself X) (conceivedThruItself X))) True % 3.81/3.96 Clause #5 (by assumption #[]): Eq (∀ (X : Iota), Iff (god X) (And (being X) (absolutelyInfinite X))) True % 3.81/3.96 Clause #6 (by assumption #[]): Eq % 3.81/3.96 (∀ (X Y : Iota), % 3.81/3.96 Iff (absolutelyInfinite X) % 3.81/3.96 (And (And (substance X) (constInInfAttributes X)) % 3.81/3.96 (attributeOf Y X → And (expressesEternalEssentiality Y) (expressesInfiniteEssentiality Y)))) % 3.81/3.96 True % 3.81/3.96 Clause #17 (by assumption #[]): Eq (∀ (X : Iota), inItself X → selfCaused X) True % 3.81/3.96 Clause #18 (by assumption #[]): Eq (∀ (X : Iota), being X → hasEssence X) True % 3.81/3.96 Clause #19 (by assumption #[]): Eq (∀ (X : Iota), And (essenceInvExistence X) (hasEssence X) → exists X) True % 3.81/3.96 Clause #20 (by assumption #[]): Eq (Not (∀ (X : Iota), god X → exists X)) True % 3.81/3.96 Clause #21 (by clausification #[19]): ∀ (a : Iota), Eq (And (essenceInvExistence a) (hasEssence a) → exists a) True % 3.81/3.96 Clause #22 (by clausification #[21]): ∀ (a : Iota), Or (Eq (And (essenceInvExistence a) (hasEssence a)) False) (Eq (exists a) True) % 3.81/3.96 Clause #23 (by clausification #[22]): ∀ (a : Iota), Or (Eq (exists a) True) (Or (Eq (essenceInvExistence a) False) (Eq (hasEssence a) False)) % 3.81/3.96 Clause #24 (by clausification #[17]): ∀ (a : Iota), Eq (inItself a → selfCaused a) True % 3.81/3.96 Clause #25 (by clausification #[24]): ∀ (a : Iota), Or (Eq (inItself a) False) (Eq (selfCaused a) True) % 3.81/3.96 Clause #26 (by clausification #[18]): ∀ (a : Iota), Eq (being a → hasEssence a) True % 3.81/3.96 Clause #27 (by clausification #[26]): ∀ (a : Iota), Or (Eq (being a) False) (Eq (hasEssence a) True) % 3.81/3.96 Clause #28 (by clausification #[20]): Eq (∀ (X : Iota), god X → exists X) False % 3.81/3.96 Clause #29 (by clausification #[28]): ∀ (a : Iota), Eq (Not (god (skS.0 0 a) → exists (skS.0 0 a))) True % 3.81/3.96 Clause #30 (by clausification #[29]): ∀ (a : Iota), Eq (god (skS.0 0 a) → exists (skS.0 0 a)) False % 3.81/3.96 Clause #31 (by clausification #[30]): ∀ (a : Iota), Eq (god (skS.0 0 a)) True % 3.81/3.96 Clause #32 (by clausification #[30]): ∀ (a : Iota), Eq (exists (skS.0 0 a)) False % 3.81/3.96 Clause #36 (by clausification #[0]): ∀ (a : Iota), Eq (Iff (selfCaused a) (And (essenceInvExistence a) (natureConcOnlyByExistence a))) True % 3.81/3.96 Clause #38 (by clausification #[36]): ∀ (a : Iota), Or (Eq (selfCaused a) False) (Eq (And (essenceInvExistence a) (natureConcOnlyByExistence a)) True) % 3.81/3.96 Clause #56 (by clausification #[38]): ∀ (a : Iota), Or (Eq (selfCaused a) False) (Eq (essenceInvExistence a) True) % 3.81/3.96 Clause #57 (by clausification #[5]): ∀ (a : Iota), Eq (Iff (god a) (And (being a) (absolutelyInfinite a))) True % 3.81/3.96 Clause #59 (by clausification #[57]): ∀ (a : Iota), Or (Eq (god a) False) (Eq (And (being a) (absolutelyInfinite a)) True) % 3.81/3.96 Clause #61 (by clausification #[2]): ∀ (a : Iota), Eq (Iff (substance a) (And (inItself a) (conceivedThruItself a))) True % 3.81/3.96 Clause #63 (by clausification #[61]): ∀ (a : Iota), Or (Eq (substance a) False) (Eq (And (inItself a) (conceivedThruItself a)) True) % 3.81/3.96 Clause #66 (by clausification #[63]): ∀ (a : Iota), Or (Eq (substance a) False) (Eq (inItself a) True) % 3.81/3.96 Clause #67 (by clausification #[59]): ∀ (a : Iota), Or (Eq (god a) False) (Eq (absolutelyInfinite a) True) % 3.81/3.96 Clause #68 (by clausification #[59]): ∀ (a : Iota), Or (Eq (god a) False) (Eq (being a) True) % 3.81/3.96 Clause #69 (by superposition #[67, 31]): ∀ (a : Iota), Or (Eq (absolutelyInfinite (skS.0 0 a)) True) (Eq False True) % 3.81/3.96 Clause #70 (by superposition #[68, 31]): ∀ (a : Iota), Or (Eq (being (skS.0 0 a)) True) (Eq False True) % 3.81/3.96 Clause #71 (by clausification #[70]): ∀ (a : Iota), Eq (being (skS.0 0 a)) True % 3.81/3.96 Clause #72 (by superposition #[71, 27]): ∀ (a : Iota), Or (Eq True False) (Eq (hasEssence (skS.0 0 a)) True) % 3.81/3.96 Clause #83 (by clausification #[72]): ∀ (a : Iota), Eq (hasEssence (skS.0 0 a)) True % 3.81/3.96 Clause #84 (by clausification #[69]): ∀ (a : Iota), Eq (absolutelyInfinite (skS.0 0 a)) True % 3.81/3.98 Clause #87 (by clausification #[6]): ∀ (a : Iota), % 3.81/3.98 Eq % 3.81/3.98 (∀ (Y : Iota), % 3.81/3.98 Iff (absolutelyInfinite a) % 3.81/3.98 (And (And (substance a) (constInInfAttributes a)) % 3.81/3.98 (attributeOf Y a → And (expressesEternalEssentiality Y) (expressesInfiniteEssentiality Y)))) % 3.81/3.98 True % 3.81/3.98 Clause #88 (by clausification #[87]): ∀ (a a_1 : Iota), % 3.81/3.98 Eq % 3.81/3.98 (Iff (absolutelyInfinite a) % 3.81/3.98 (And (And (substance a) (constInInfAttributes a)) % 3.81/3.98 (attributeOf a_1 a → And (expressesEternalEssentiality a_1) (expressesInfiniteEssentiality a_1)))) % 3.81/3.98 True % 3.81/3.98 Clause #90 (by clausification #[88]): ∀ (a a_1 : Iota), % 3.81/3.98 Or (Eq (absolutelyInfinite a) False) % 3.81/3.98 (Eq % 3.81/3.98 (And (And (substance a) (constInInfAttributes a)) % 3.81/3.98 (attributeOf a_1 a → And (expressesEternalEssentiality a_1) (expressesInfiniteEssentiality a_1))) % 3.81/3.98 True) % 3.81/3.98 Clause #146 (by clausification #[90]): ∀ (a : Iota), Or (Eq (absolutelyInfinite a) False) (Eq (And (substance a) (constInInfAttributes a)) True) % 3.81/3.98 Clause #152 (by clausification #[146]): ∀ (a : Iota), Or (Eq (absolutelyInfinite a) False) (Eq (substance a) True) % 3.81/3.98 Clause #154 (by superposition #[152, 84]): ∀ (a : Iota), Or (Eq (substance (skS.0 0 a)) True) (Eq False True) % 3.81/3.98 Clause #163 (by clausification #[154]): ∀ (a : Iota), Eq (substance (skS.0 0 a)) True % 3.81/3.98 Clause #165 (by superposition #[163, 66]): ∀ (a : Iota), Or (Eq True False) (Eq (inItself (skS.0 0 a)) True) % 3.81/3.98 Clause #168 (by clausification #[165]): ∀ (a : Iota), Eq (inItself (skS.0 0 a)) True % 3.81/3.98 Clause #169 (by superposition #[168, 25]): ∀ (a : Iota), Or (Eq True False) (Eq (selfCaused (skS.0 0 a)) True) % 3.81/3.98 Clause #171 (by clausification #[169]): ∀ (a : Iota), Eq (selfCaused (skS.0 0 a)) True % 3.81/3.98 Clause #173 (by superposition #[171, 56]): ∀ (a : Iota), Or (Eq True False) (Eq (essenceInvExistence (skS.0 0 a)) True) % 3.81/3.98 Clause #176 (by clausification #[173]): ∀ (a : Iota), Eq (essenceInvExistence (skS.0 0 a)) True % 3.81/3.98 Clause #177 (by superposition #[176, 23]): ∀ (a : Iota), Or (Eq (exists (skS.0 0 a)) True) (Or (Eq True False) (Eq (hasEssence (skS.0 0 a)) False)) % 3.81/3.98 Clause #203 (by clausification #[177]): ∀ (a : Iota), Or (Eq (exists (skS.0 0 a)) True) (Eq (hasEssence (skS.0 0 a)) False) % 3.81/3.98 Clause #204 (by forward demodulation #[203, 32]): ∀ (a : Iota), Or (Eq False True) (Eq (hasEssence (skS.0 0 a)) False) % 3.81/3.98 Clause #205 (by clausification #[204]): ∀ (a : Iota), Eq (hasEssence (skS.0 0 a)) False % 3.81/3.98 Clause #206 (by superposition #[205, 83]): Eq False True % 3.81/3.98 Clause #210 (by clausification #[206]): False % 3.81/3.98 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------