%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU620^2 : TPTP v9.2.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n029.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 08:02:03 PM UTC 2025 % Result : Theorem 3.85s 3.99s % Output : Proof 3.85s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.13 % Problem : SEU620^2 : TPTP v9.2.0. Released v3.7.0. % 0.12/0.14 % Command : duper %s % 0.15/0.35 % Computer : n029.cluster.edu % 0.15/0.35 % Model : x86_64 x86_64 % 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.35 % Memory : 8042.1875MB % 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.35 % CPULimit : 300 % 0.15/0.35 % WCLimit : 300 % 0.15/0.35 % DateTime : Fri Oct 3 04:57:53 EDT 2025 % 0.15/0.35 % CPUTime : % 3.85/3.99 SZS status Theorem for theBenchmark.p % 3.85/3.99 SZS output start Proof for theBenchmark.p % 3.85/3.99 Clause #1 (by assumption #[]): Eq % 3.85/3.99 (Eq kpairiskpair % 3.85/3.99 (∀ (Xx Xy : Iota), % 3.85/3.99 iskpair (setadjoin (setadjoin Xx emptyset) (setadjoin (setadjoin Xx (setadjoin Xy emptyset)) emptyset)))) % 3.85/3.99 True % 3.85/3.99 Clause #2 (by assumption #[]): Eq (Eq kpair fun Xx Xy => setadjoin (setadjoin Xx emptyset) (setadjoin (setadjoin Xx (setadjoin Xy emptyset)) emptyset)) % 3.85/3.99 True % 3.85/3.99 Clause #3 (by assumption #[]): Eq (Not (kpairiskpair → ∀ (Xx Xy : Iota), iskpair (kpair Xx Xy))) True % 3.85/3.99 Clause #4 (by clausification #[3]): Eq (kpairiskpair → ∀ (Xx Xy : Iota), iskpair (kpair Xx Xy)) False % 3.85/3.99 Clause #5 (by clausification #[4]): Eq kpairiskpair True % 3.85/3.99 Clause #6 (by clausification #[4]): Eq (∀ (Xx Xy : Iota), iskpair (kpair Xx Xy)) False % 3.85/3.99 Clause #7 (by clausification #[6]): ∀ (a : Iota), Eq (Not (∀ (Xy : Iota), iskpair (kpair (skS.0 0 a) Xy))) True % 3.85/3.99 Clause #8 (by clausification #[7]): ∀ (a : Iota), Eq (∀ (Xy : Iota), iskpair (kpair (skS.0 0 a) Xy)) False % 3.85/3.99 Clause #9 (by clausification #[8]): ∀ (a a_1 : Iota), Eq (Not (iskpair (kpair (skS.0 0 a) (skS.0 1 a a_1)))) True % 3.85/3.99 Clause #10 (by clausification #[9]): ∀ (a a_1 : Iota), Eq (iskpair (kpair (skS.0 0 a) (skS.0 1 a a_1))) False % 3.85/3.99 Clause #11 (by clausification #[1]): Eq kpairiskpair % 3.85/3.99 (∀ (Xx Xy : Iota), % 3.85/3.99 iskpair (setadjoin (setadjoin Xx emptyset) (setadjoin (setadjoin Xx (setadjoin Xy emptyset)) emptyset))) % 3.85/3.99 Clause #12 (by forward demodulation #[11, 5]): Eq True % 3.85/3.99 (∀ (Xx Xy : Iota), % 3.85/3.99 iskpair (setadjoin (setadjoin Xx emptyset) (setadjoin (setadjoin Xx (setadjoin Xy emptyset)) emptyset))) % 3.85/3.99 Clause #13 (by clausification #[12]): ∀ (a : Iota), % 3.85/3.99 Eq % 3.85/3.99 (∀ (Xy : Iota), % 3.85/3.99 iskpair (setadjoin (setadjoin a emptyset) (setadjoin (setadjoin a (setadjoin Xy emptyset)) emptyset))) % 3.85/3.99 True % 3.85/3.99 Clause #14 (by clausification #[13]): ∀ (a a_1 : Iota), % 3.85/3.99 Eq (iskpair (setadjoin (setadjoin a emptyset) (setadjoin (setadjoin a (setadjoin a_1 emptyset)) emptyset))) True % 3.85/3.99 Clause #15 (by clausification #[2]): Eq kpair fun Xx Xy => setadjoin (setadjoin Xx emptyset) (setadjoin (setadjoin Xx (setadjoin Xy emptyset)) emptyset) % 3.85/3.99 Clause #16 (by argument congruence #[15]): ∀ (a : Iota), % 3.85/3.99 Eq (kpair a) % 3.85/3.99 ((fun Xx Xy => setadjoin (setadjoin Xx emptyset) (setadjoin (setadjoin Xx (setadjoin Xy emptyset)) emptyset)) a) % 3.85/3.99 Clause #18 (by betaEtaReduce #[16]): ∀ (a : Iota), % 3.85/3.99 Eq (kpair a) fun Xy => setadjoin (setadjoin a emptyset) (setadjoin (setadjoin a (setadjoin Xy emptyset)) emptyset) % 3.85/3.99 Clause #19 (by argument congruence #[18]): ∀ (a a_1 : Iota), % 3.85/3.99 Eq (kpair a a_1) % 3.85/3.99 ((fun Xy => setadjoin (setadjoin a emptyset) (setadjoin (setadjoin a (setadjoin Xy emptyset)) emptyset)) a_1) % 3.85/3.99 Clause #24 (by betaEtaReduce #[19]): ∀ (a a_1 : Iota), % 3.85/3.99 Eq (kpair a a_1) (setadjoin (setadjoin a emptyset) (setadjoin (setadjoin a (setadjoin a_1 emptyset)) emptyset)) % 3.85/3.99 Clause #25 (by backward demodulation #[24, 14]): ∀ (a a_1 : Iota), Eq (iskpair (kpair a a_1)) True % 3.85/3.99 Clause #28 (by superposition #[25, 10]): Eq True False % 3.85/3.99 Clause #31 (by clausification #[28]): False % 3.85/3.99 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------