%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEV241^5 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n021.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 08:02:59 PM UTC 2025 % Result : Theorem 3.73s 3.90s % Output : Proof 3.73s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : SEV241^5 : TPTP v9.2.0. Released v4.0.0. % 0.06/0.13 % Command : duper %s % 0.13/0.34 % Computer : n021.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 : Fri Oct 3 01:31:08 EDT 2025 % 0.13/0.34 % CPUTime : % 3.73/3.90 SZS status Theorem for theBenchmark.p % 3.73/3.90 SZS output start Proof for theBenchmark.p % 3.73/3.90 Clause #0 (by assumption #[]): Eq (Not (∀ (Xx : a), And (cU Xx) (cW Xx) → ∀ (S : a → Prop), Or (Eq S cU) (Eq S cW) → S Xx)) True % 3.73/3.90 Clause #1 (by clausification #[0]): Eq (∀ (Xx : a), And (cU Xx) (cW Xx) → ∀ (S : a → Prop), Or (Eq S cU) (Eq S cW) → S Xx) False % 3.73/3.90 Clause #2 (by clausification #[1]): ∀ (a_1 : a), % 3.73/3.90 Eq (Not (And (cU (skS.0 0 a_1)) (cW (skS.0 0 a_1)) → ∀ (S : a → Prop), Or (Eq S cU) (Eq S cW) → S (skS.0 0 a_1))) True % 3.73/3.90 Clause #3 (by clausification #[2]): ∀ (a_1 : a), % 3.73/3.90 Eq (And (cU (skS.0 0 a_1)) (cW (skS.0 0 a_1)) → ∀ (S : a → Prop), Or (Eq S cU) (Eq S cW) → S (skS.0 0 a_1)) False % 3.73/3.90 Clause #4 (by clausification #[3]): ∀ (a_1 : a), Eq (And (cU (skS.0 0 a_1)) (cW (skS.0 0 a_1))) True % 3.73/3.90 Clause #5 (by clausification #[3]): ∀ (a_1 : a), Eq (∀ (S : a → Prop), Or (Eq S cU) (Eq S cW) → S (skS.0 0 a_1)) False % 3.73/3.90 Clause #6 (by clausification #[4]): ∀ (a_1 : a), Eq (cW (skS.0 0 a_1)) True % 3.73/3.90 Clause #7 (by clausification #[4]): ∀ (a_1 : a), Eq (cU (skS.0 0 a_1)) True % 3.73/3.90 Clause #8 (by clausification #[5]): ∀ (a_1 : a) (a_2 : a → Prop), % 3.73/3.90 Eq (Not (Or (Eq (skS.0 1 a_1 a_2) cU) (Eq (skS.0 1 a_1 a_2) cW) → skS.0 1 a_1 a_2 (skS.0 0 a_1))) True % 3.73/3.90 Clause #9 (by clausification #[8]): ∀ (a_1 : a) (a_2 : a → Prop), % 3.73/3.90 Eq (Or (Eq (skS.0 1 a_1 a_2) cU) (Eq (skS.0 1 a_1 a_2) cW) → skS.0 1 a_1 a_2 (skS.0 0 a_1)) False % 3.73/3.90 Clause #10 (by clausification #[9]): ∀ (a_1 : a) (a_2 : a → Prop), Eq (Or (Eq (skS.0 1 a_1 a_2) cU) (Eq (skS.0 1 a_1 a_2) cW)) True % 3.73/3.90 Clause #11 (by clausification #[9]): ∀ (a_1 : a) (a_2 : a → Prop), Eq (skS.0 1 a_1 a_2 (skS.0 0 a_1)) False % 3.73/3.90 Clause #12 (by clausification #[10]): ∀ (a_1 : a) (a_2 : a → Prop), Or (Eq (Eq (skS.0 1 a_1 a_2) cU) True) (Eq (Eq (skS.0 1 a_1 a_2) cW) True) % 3.73/3.90 Clause #13 (by clausification #[12]): ∀ (a_1 : a) (a_2 : a → Prop), Or (Eq (Eq (skS.0 1 a_1 a_2) cW) True) (Eq (skS.0 1 a_1 a_2) cU) % 3.73/3.90 Clause #14 (by clausification #[13]): ∀ (a_1 : a) (a_2 : a → Prop), Or (Eq (skS.0 1 a_1 a_2) cU) (Eq (skS.0 1 a_1 a_2) cW) % 3.73/3.90 Clause #16 (by argument congruence #[14]): ∀ (a_1 : a) (a_2 : a → Prop) (a_3 : a), Or (Eq (skS.0 1 a_1 a_2) cU) (Eq (skS.0 1 a_1 a_2 a_3) (cW a_3)) % 3.73/3.90 Clause #19 (by superposition #[16, 11]): ∀ (a_1 : a) (a_2 : a → Prop), Or (Eq (skS.0 1 a_1 fun x => a_2 x) cU) (Eq (cW (skS.0 0 a_1)) False) % 3.73/3.90 Clause #21 (by betaEtaReduce #[19]): ∀ (a_1 : a) (a_2 : a → Prop), Or (Eq (skS.0 1 a_1 a_2) cU) (Eq (cW (skS.0 0 a_1)) False) % 3.73/3.90 Clause #22 (by forward demodulation #[21, 6]): ∀ (a_1 : a) (a_2 : a → Prop), Or (Eq (skS.0 1 a_1 a_2) cU) (Eq True False) % 3.73/3.90 Clause #23 (by clausification #[22]): ∀ (a_1 : a) (a_2 : a → Prop), Eq (skS.0 1 a_1 a_2) cU % 3.73/3.90 Clause #25 (by argument congruence #[23]): ∀ (a_1 : a) (a_2 : a → Prop) (a_3 : a), Eq (skS.0 1 a_1 a_2 a_3) (cU a_3) % 3.73/3.90 Clause #28 (by superposition #[25, 11]): ∀ (a_1 : a), Eq (cU (skS.0 0 a_1)) False % 3.73/3.90 Clause #29 (by superposition #[28, 7]): Eq False True % 3.73/3.90 Clause #30 (by clausification #[29]): False % 3.73/3.90 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------