%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : NUM721^1 : TPTP v9.2.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n005.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 07:57:10 PM UTC 2025 % Result : Theorem 3.91s 4.09s % Output : Proof 3.91s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.12 % Problem : NUM721^1 : TPTP v9.2.0. Released v3.7.0. % 0.08/0.14 % Command : duper %s % 0.13/0.35 % Computer : n005.cluster.edu % 0.13/0.35 % Model : x86_64 x86_64 % 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.35 % Memory : 8042.1875MB % 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 300 % 0.13/0.35 % DateTime : Fri Oct 3 08:31:08 EDT 2025 % 0.13/0.35 % CPUTime : % 3.91/4.09 SZS status Theorem for theBenchmark.p % 3.91/4.09 SZS output start Proof for theBenchmark.p % 3.91/4.09 Clause #0 (by assumption #[]): Eq (some fun Xv => diffprop y x Xv) True % 3.91/4.09 Clause #1 (by assumption #[]): Eq (some fun Xv => diffprop u z Xv) True % 3.91/4.09 Clause #2 (by assumption #[]): Eq % 3.91/4.09 (∀ (Xx Xy Xz Xu : nat), % 3.91/4.09 (some fun Xu => diffprop Xx Xy Xu) → % 3.91/4.09 (some fun Xu_0 => diffprop Xz Xu Xu_0) → some fun Xu_0 => diffprop (ts Xx Xz) (ts Xy Xu) Xu_0) % 3.91/4.09 True % 3.91/4.09 Clause #3 (by assumption #[]): Eq (Not (some fun Xv => diffprop (ts y u) (ts x z) Xv)) True % 3.91/4.09 Clause #4 (by betaEtaReduce #[1]): Eq (some (diffprop u z)) True % 3.91/4.09 Clause #5 (by betaEtaReduce #[0]): Eq (some (diffprop y x)) True % 3.91/4.09 Clause #6 (by betaEtaReduce #[3]): Eq (Not (some (diffprop (ts y u) (ts x z)))) True % 3.91/4.09 Clause #7 (by clausification #[6]): Eq (some (diffprop (ts y u) (ts x z))) False % 3.91/4.09 Clause #8 (by betaEtaReduce #[2]): Eq (∀ (Xx Xy Xz Xu : nat), some (diffprop Xx Xy) → some (diffprop Xz Xu) → some (diffprop (ts Xx Xz) (ts Xy Xu))) True % 3.91/4.09 Clause #9 (by clausification #[8]): ∀ (a : nat), % 3.91/4.09 Eq (∀ (Xy Xz Xu : nat), some (diffprop a Xy) → some (diffprop Xz Xu) → some (diffprop (ts a Xz) (ts Xy Xu))) True % 3.91/4.09 Clause #10 (by clausification #[9]): ∀ (a a_1 : nat), % 3.91/4.09 Eq (∀ (Xz Xu : nat), some (diffprop a a_1) → some (diffprop Xz Xu) → some (diffprop (ts a Xz) (ts a_1 Xu))) True % 3.91/4.09 Clause #11 (by clausification #[10]): ∀ (a a_1 a_2 : nat), % 3.91/4.09 Eq (∀ (Xu : nat), some (diffprop a a_1) → some (diffprop a_2 Xu) → some (diffprop (ts a a_2) (ts a_1 Xu))) True % 3.91/4.09 Clause #12 (by clausification #[11]): ∀ (a a_1 a_2 a_3 : nat), % 3.91/4.09 Eq (some (diffprop a a_1) → some (diffprop a_2 a_3) → some (diffprop (ts a a_2) (ts a_1 a_3))) True % 3.91/4.09 Clause #13 (by clausification #[12]): ∀ (a a_1 a_2 a_3 : nat), % 3.91/4.09 Or (Eq (some (diffprop a a_1)) False) (Eq (some (diffprop a_2 a_3) → some (diffprop (ts a a_2) (ts a_1 a_3))) True) % 3.91/4.09 Clause #14 (by clausification #[13]): ∀ (a a_1 a_2 a_3 : nat), % 3.91/4.09 Or (Eq (some (diffprop a a_1)) False) % 3.91/4.09 (Or (Eq (some (diffprop a_2 a_3)) False) (Eq (some (diffprop (ts a a_2) (ts a_1 a_3))) True)) % 3.91/4.09 Clause #16 (by superposition #[14, 5]): ∀ (a a_1 : nat), % 3.91/4.09 Or (Eq (some (diffprop a a_1)) False) (Or (Eq (some (diffprop (ts y a) (ts x a_1))) True) (Eq False True)) % 3.91/4.09 Clause #17 (by clausification #[16]): ∀ (a a_1 : nat), Or (Eq (some (diffprop a a_1)) False) (Eq (some (diffprop (ts y a) (ts x a_1))) True) % 3.91/4.09 Clause #18 (by superposition #[17, 4]): Or (Eq (some (diffprop (ts y u) (ts x z))) True) (Eq False True) % 3.91/4.09 Clause #27 (by clausification #[18]): Eq (some (diffprop (ts y u) (ts x z))) True % 3.91/4.09 Clause #28 (by superposition #[27, 7]): Eq True False % 3.91/4.09 Clause #32 (by clausification #[28]): False % 3.91/4.09 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------