%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SYN361^5 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n019.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 08:07:30 PM UTC 2025 % Result : Theorem 3.71s 3.86s % Output : Proof 3.71s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SYN361^5 : TPTP v9.2.0. Released v4.0.0. % 0.03/0.13 % Command : duper %s % 0.13/0.34 % Computer : n019.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 : Thu Oct 2 15:46:23 EDT 2025 % 0.13/0.34 % CPUTime : % 3.71/3.86 SZS status Theorem for theBenchmark.p % 3.71/3.86 SZS output start Proof for theBenchmark.p % 3.71/3.86 Clause #0 (by assumption #[]): Eq % 3.71/3.86 (Not % 3.71/3.86 (And (And (Exists fun Xv => ∀ (Xx : Iota), cP Xx Xv) (∀ (Xx : Iota), cS Xx → Exists fun Xy => cQ Xy Xx)) % 3.71/3.86 (∀ (Xx Xy : Iota), cP Xx Xy → Not (cQ Xx Xy)) → % 3.71/3.86 Exists fun Xu => Not (cS Xu))) % 3.71/3.86 True % 3.71/3.86 Clause #1 (by clausification #[0]): Eq % 3.71/3.86 (And (And (Exists fun Xv => ∀ (Xx : Iota), cP Xx Xv) (∀ (Xx : Iota), cS Xx → Exists fun Xy => cQ Xy Xx)) % 3.71/3.86 (∀ (Xx Xy : Iota), cP Xx Xy → Not (cQ Xx Xy)) → % 3.71/3.86 Exists fun Xu => Not (cS Xu)) % 3.71/3.86 False % 3.71/3.86 Clause #2 (by clausification #[1]): Eq % 3.71/3.86 (And (And (Exists fun Xv => ∀ (Xx : Iota), cP Xx Xv) (∀ (Xx : Iota), cS Xx → Exists fun Xy => cQ Xy Xx)) % 3.71/3.86 (∀ (Xx Xy : Iota), cP Xx Xy → Not (cQ Xx Xy))) % 3.71/3.86 True % 3.71/3.86 Clause #3 (by clausification #[1]): Eq (Exists fun Xu => Not (cS Xu)) False % 3.71/3.86 Clause #4 (by clausification #[2]): Eq (∀ (Xx Xy : Iota), cP Xx Xy → Not (cQ Xx Xy)) True % 3.71/3.86 Clause #5 (by clausification #[2]): Eq (And (Exists fun Xv => ∀ (Xx : Iota), cP Xx Xv) (∀ (Xx : Iota), cS Xx → Exists fun Xy => cQ Xy Xx)) True % 3.71/3.86 Clause #6 (by clausification #[4]): ∀ (a : Iota), Eq (∀ (Xy : Iota), cP a Xy → Not (cQ a Xy)) True % 3.71/3.86 Clause #7 (by clausification #[6]): ∀ (a a_1 : Iota), Eq (cP a a_1 → Not (cQ a a_1)) True % 3.71/3.86 Clause #8 (by clausification #[7]): ∀ (a a_1 : Iota), Or (Eq (cP a a_1) False) (Eq (Not (cQ a a_1)) True) % 3.71/3.86 Clause #9 (by clausification #[8]): ∀ (a a_1 : Iota), Or (Eq (cP a a_1) False) (Eq (cQ a a_1) False) % 3.71/3.86 Clause #10 (by clausification #[3]): ∀ (a : Iota), Eq (Not (cS a)) False % 3.71/3.86 Clause #11 (by clausification #[10]): ∀ (a : Iota), Eq (cS a) True % 3.71/3.86 Clause #12 (by clausification #[5]): Eq (∀ (Xx : Iota), cS Xx → Exists fun Xy => cQ Xy Xx) True % 3.71/3.86 Clause #13 (by clausification #[5]): Eq (Exists fun Xv => ∀ (Xx : Iota), cP Xx Xv) True % 3.71/3.86 Clause #14 (by clausification #[12]): ∀ (a : Iota), Eq (cS a → Exists fun Xy => cQ Xy a) True % 3.71/3.86 Clause #15 (by clausification #[14]): ∀ (a : Iota), Or (Eq (cS a) False) (Eq (Exists fun Xy => cQ Xy a) True) % 3.71/3.86 Clause #16 (by clausification #[15]): ∀ (a a_1 : Iota), Or (Eq (cS a) False) (Eq (cQ (skS.0 0 a a_1) a) True) % 3.71/3.86 Clause #17 (by forward demodulation #[16, 11]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (cQ (skS.0 0 a a_1) a) True) % 3.71/3.86 Clause #18 (by clausification #[17]): ∀ (a a_1 : Iota), Eq (cQ (skS.0 0 a a_1) a) True % 3.71/3.86 Clause #19 (by clausification #[13]): ∀ (a : Iota), Eq (∀ (Xx : Iota), cP Xx (skS.0 1 a)) True % 3.71/3.86 Clause #20 (by clausification #[19]): ∀ (a a_1 : Iota), Eq (cP a (skS.0 1 a_1)) True % 3.71/3.86 Clause #21 (by superposition #[20, 9]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (cQ a (skS.0 1 a_1)) False) % 3.71/3.86 Clause #22 (by clausification #[21]): ∀ (a a_1 : Iota), Eq (cQ a (skS.0 1 a_1)) False % 3.71/3.86 Clause #23 (by superposition #[22, 18]): Eq False True % 3.71/3.86 Clause #24 (by clausification #[23]): False % 3.71/3.86 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------