%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : NUM686^1 : TPTP v9.2.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n014.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 07:57:03 PM UTC 2025 % Result : Theorem 4.87s 5.10s % Output : Proof 4.87s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : NUM686^1 : TPTP v9.2.0. Released v3.7.0. % 0.06/0.13 % Command : duper %s % 0.14/0.34 % Computer : n014.cluster.edu % 0.14/0.34 % Model : x86_64 x86_64 % 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.34 % Memory : 8042.1875MB % 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.34 % CPULimit : 300 % 0.14/0.34 % WCLimit : 300 % 0.14/0.34 % DateTime : Fri Oct 3 07:25:23 EDT 2025 % 0.14/0.34 % CPUTime : % 4.87/5.10 SZS status Theorem for theBenchmark.p % 4.87/5.10 SZS output start Proof for theBenchmark.p % 4.87/5.10 Clause #0 (by assumption #[]): Eq (some fun Xu => diffprop x y Xu) True % 4.87/5.10 Clause #1 (by assumption #[]): Eq (some fun Xu_0 => diffprop z u Xu_0) True % 4.87/5.10 Clause #2 (by assumption #[]): Eq % 4.87/5.10 (∀ (Xx Xy Xz : nat), % 4.87/5.10 (some fun Xv => diffprop Xy Xx Xv) → (some fun Xv => diffprop Xz Xy Xv) → some fun Xv => diffprop Xz Xx Xv) % 4.87/5.10 True % 4.87/5.10 Clause #3 (by assumption #[]): Eq (∀ (Xx Xy Xz : nat), (some fun Xu => diffprop Xx Xy Xu) → some fun Xu => diffprop (pl Xx Xz) (pl Xy Xz) Xu) True % 4.87/5.10 Clause #4 (by assumption #[]): Eq (∀ (Xx Xy : nat), Eq (pl Xx Xy) (pl Xy Xx)) True % 4.87/5.10 Clause #5 (by assumption #[]): Eq (Not (some fun Xu_0 => diffprop (pl x z) (pl y u) Xu_0)) True % 4.87/5.10 Clause #6 (by betaEtaReduce #[1]): Eq (some (diffprop z u)) True % 4.87/5.10 Clause #7 (by betaEtaReduce #[0]): Eq (some (diffprop x y)) True % 4.87/5.10 Clause #8 (by clausification #[4]): ∀ (a : nat), Eq (∀ (Xy : nat), Eq (pl a Xy) (pl Xy a)) True % 4.87/5.10 Clause #9 (by clausification #[8]): ∀ (a a_1 : nat), Eq (Eq (pl a a_1) (pl a_1 a)) True % 4.87/5.10 Clause #10 (by clausification #[9]): ∀ (a a_1 : nat), Eq (pl a a_1) (pl a_1 a) % 4.87/5.10 Clause #11 (by betaEtaReduce #[5]): Eq (Not (some (diffprop (pl x z) (pl y u)))) True % 4.87/5.10 Clause #12 (by clausification #[11]): Eq (some (diffprop (pl x z) (pl y u))) False % 4.87/5.10 Clause #13 (by forward demodulation #[12, 10]): Eq (some (diffprop (pl x z) (pl u y))) False % 4.87/5.10 Clause #14 (by forward demodulation #[13, 10]): Eq (some (diffprop (pl z x) (pl u y))) False % 4.87/5.10 Clause #15 (by betaEtaReduce #[2]): Eq (∀ (Xx Xy Xz : nat), some (diffprop Xy Xx) → some (diffprop Xz Xy) → some (diffprop Xz Xx)) True % 4.87/5.10 Clause #16 (by clausification #[15]): ∀ (a : nat), Eq (∀ (Xy Xz : nat), some (diffprop Xy a) → some (diffprop Xz Xy) → some (diffprop Xz a)) True % 4.87/5.10 Clause #17 (by clausification #[16]): ∀ (a a_1 : nat), Eq (∀ (Xz : nat), some (diffprop a a_1) → some (diffprop Xz a) → some (diffprop Xz a_1)) True % 4.87/5.10 Clause #18 (by clausification #[17]): ∀ (a a_1 a_2 : nat), Eq (some (diffprop a a_1) → some (diffprop a_2 a) → some (diffprop a_2 a_1)) True % 4.87/5.10 Clause #19 (by clausification #[18]): ∀ (a a_1 a_2 : nat), Or (Eq (some (diffprop a a_1)) False) (Eq (some (diffprop a_2 a) → some (diffprop a_2 a_1)) True) % 4.87/5.10 Clause #20 (by clausification #[19]): ∀ (a a_1 a_2 : nat), % 4.87/5.10 Or (Eq (some (diffprop a a_1)) False) (Or (Eq (some (diffprop a_2 a)) False) (Eq (some (diffprop a_2 a_1)) True)) % 4.87/5.10 Clause #23 (by betaEtaReduce #[3]): Eq (∀ (Xx Xy Xz : nat), some (diffprop Xx Xy) → some (diffprop (pl Xx Xz) (pl Xy Xz))) True % 4.87/5.10 Clause #24 (by clausification #[23]): ∀ (a : nat), Eq (∀ (Xy Xz : nat), some (diffprop a Xy) → some (diffprop (pl a Xz) (pl Xy Xz))) True % 4.87/5.10 Clause #25 (by clausification #[24]): ∀ (a a_1 : nat), Eq (∀ (Xz : nat), some (diffprop a a_1) → some (diffprop (pl a Xz) (pl a_1 Xz))) True % 4.87/5.10 Clause #26 (by clausification #[25]): ∀ (a a_1 a_2 : nat), Eq (some (diffprop a a_1) → some (diffprop (pl a a_2) (pl a_1 a_2))) True % 4.87/5.10 Clause #27 (by clausification #[26]): ∀ (a a_1 a_2 : nat), Or (Eq (some (diffprop a a_1)) False) (Eq (some (diffprop (pl a a_2) (pl a_1 a_2))) True) % 4.87/5.10 Clause #28 (by superposition #[27, 6]): ∀ (a : nat), Or (Eq (some (diffprop (pl z a) (pl u a))) True) (Eq False True) % 4.87/5.10 Clause #29 (by superposition #[27, 7]): ∀ (a : nat), Or (Eq (some (diffprop (pl x a) (pl y a))) True) (Eq False True) % 4.87/5.10 Clause #30 (by clausification #[29]): ∀ (a : nat), Eq (some (diffprop (pl x a) (pl y a))) True % 4.87/5.10 Clause #31 (by superposition #[30, 20]): ∀ (a a_1 : nat), % 4.87/5.10 Or (Eq True False) (Or (Eq (some (diffprop a (pl x a_1))) False) (Eq (some (diffprop a (pl y a_1))) True)) % 4.87/5.10 Clause #42 (by clausification #[28]): ∀ (a : nat), Eq (some (diffprop (pl z a) (pl u a))) True % 4.87/5.10 Clause #45 (by superposition #[42, 10]): ∀ (a : nat), Eq (some (diffprop (pl z a) (pl a u))) True % 4.87/5.10 Clause #61 (by clausification #[31]): ∀ (a a_1 : nat), Or (Eq (some (diffprop a (pl x a_1))) False) (Eq (some (diffprop a (pl y a_1))) True) % 4.87/5.10 Clause #64 (by superposition #[61, 45]): Or (Eq (some (diffprop (pl z x) (pl y u))) True) (Eq False True) % 4.87/5.10 Clause #68 (by clausification #[64]): Eq (some (diffprop (pl z x) (pl y u))) True % 4.87/5.10 Clause #69 (by forward demodulation #[68, 10]): Eq (some (diffprop (pl z x) (pl u y))) True % 4.87/5.10 Clause #70 (by superposition #[69, 14]): Eq True False % 4.87/5.10 Clause #73 (by clausification #[70]): False % 4.87/5.10 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------