%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SYN960+1 : TPTP v9.2.0. Released v3.1.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n008.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 08:08:19 PM UTC 2025 % Result : Theorem 3.59s 3.82s % Output : Proof 3.59s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SYN960+1 : TPTP v9.2.0. Released v3.1.0. % 0.12/0.13 % Command : duper %s % 0.13/0.34 % Computer : n008.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 15:17:53 EDT 2025 % 0.20/0.34 % CPUTime : % 3.59/3.82 SZS status Theorem for theBenchmark.p % 3.59/3.82 SZS output start Proof for theBenchmark.p % 3.59/3.82 Clause #0 (by assumption #[]): Eq (Not (Iff (Exists fun X => Exists fun Y => a X Y) (Exists fun Y => Exists fun X => a X Y))) True % 3.59/3.82 Clause #1 (by betaEtaReduce #[0]): Eq (Not (Iff (Exists fun X => Exists (a X)) (Exists fun Y => Exists fun X => a X Y))) True % 3.59/3.82 Clause #2 (by clausification #[1]): Eq (Iff (Exists fun X => Exists (a X)) (Exists fun Y => Exists fun X => a X Y)) False % 3.59/3.82 Clause #3 (by clausification #[2]): Or (Eq (Exists fun X => Exists (a X)) False) (Eq (Exists fun Y => Exists fun X => a X Y) False) % 3.59/3.82 Clause #4 (by clausification #[2]): Or (Eq (Exists fun X => Exists (a X)) True) (Eq (Exists fun Y => Exists fun X => a X Y) True) % 3.59/3.82 Clause #5 (by clausification #[3]): ∀ (a_1 : Iota), Or (Eq (Exists fun Y => Exists fun X => a X Y) False) (Eq (Exists (a a_1)) False) % 3.59/3.82 Clause #6 (by clausification #[5]): ∀ (a_1 a_2 : Iota), Or (Eq (Exists (a a_1)) False) (Eq (Exists fun X => a X a_2) False) % 3.59/3.82 Clause #7 (by clausification #[6]): ∀ (a_1 a_2 a_3 : Iota), Or (Eq (Exists fun X => a X a_1) False) (Eq (a a_2 a_3) False) % 3.59/3.82 Clause #8 (by clausification #[7]): ∀ (a_1 a_2 a_3 a_4 : Iota), Or (Eq (a a_1 a_2) False) (Eq (a a_3 a_4) False) % 3.59/3.82 Clause #9 (by clausification #[4]): ∀ (a_1 : Iota), Or (Eq (Exists fun Y => Exists fun X => a X Y) True) (Eq (Exists (a (skS.0 0 a_1))) True) % 3.59/3.82 Clause #10 (by clausification #[9]): ∀ (a_1 a_2 : Iota), Or (Eq (Exists (a (skS.0 0 a_1))) True) (Eq (Exists fun X => a X (skS.0 1 a_2)) True) % 3.59/3.82 Clause #11 (by clausification #[10]): ∀ (a_1 a_2 a_3 : Iota), Or (Eq (Exists fun X => a X (skS.0 1 a_1)) True) (Eq (a (skS.0 0 a_2) (skS.0 2 a_2 a_3)) True) % 3.59/3.82 Clause #12 (by clausification #[11]): ∀ (a_1 a_2 a_3 a_4 : Iota), % 3.59/3.82 Or (Eq (a (skS.0 0 a_1) (skS.0 2 a_1 a_2)) True) (Eq (a (skS.0 3 a_3 a_4) (skS.0 1 a_3)) True) % 3.59/3.82 Clause #14 (by superposition #[12, 8]): ∀ (a_1 a_2 a_3 a_4 : Iota), Or (Eq (a (skS.0 0 a_1) (skS.0 2 a_1 a_2)) True) (Or (Eq True False) (Eq (a a_3 a_4) False)) % 3.59/3.82 Clause #15 (by clausification #[14]): ∀ (a_1 a_2 a_3 a_4 : Iota), Or (Eq (a (skS.0 0 a_1) (skS.0 2 a_1 a_2)) True) (Eq (a a_3 a_4) False) % 3.59/3.82 Clause #17 (by superposition #[15, 12]): ∀ (a_1 a_2 a_3 a_4 : Iota), % 3.59/3.82 Or (Eq (a (skS.0 0 a_1) (skS.0 2 a_1 a_2)) True) (Or (Eq (a (skS.0 0 a_3) (skS.0 2 a_3 a_4)) True) (Eq False True)) % 3.59/3.82 Clause #21 (by clausification #[17]): ∀ (a_1 a_2 a_3 a_4 : Iota), % 3.59/3.82 Or (Eq (a (skS.0 0 a_1) (skS.0 2 a_1 a_2)) True) (Eq (a (skS.0 0 a_3) (skS.0 2 a_3 a_4)) True) % 3.59/3.82 Clause #24 (by equality factoring #[21]): ∀ (a_1 a_2 : Iota), Or (Ne True True) (Eq (a (skS.0 0 a_1) (skS.0 2 a_1 a_2)) True) % 3.59/3.82 Clause #25 (by clausification #[24]): ∀ (a_1 a_2 : Iota), Or (Eq (a (skS.0 0 a_1) (skS.0 2 a_1 a_2)) True) (Or (Eq True False) (Eq True False)) % 3.59/3.82 Clause #27 (by clausification #[25]): ∀ (a_1 a_2 : Iota), Or (Eq (a (skS.0 0 a_1) (skS.0 2 a_1 a_2)) True) (Eq True False) % 3.59/3.82 Clause #28 (by clausification #[27]): ∀ (a_1 a_2 : Iota), Eq (a (skS.0 0 a_1) (skS.0 2 a_1 a_2)) True % 3.59/3.82 Clause #29 (by superposition #[28, 8]): ∀ (a_1 a_2 : Iota), Or (Eq True False) (Eq (a a_1 a_2) False) % 3.59/3.82 Clause #31 (by clausification #[29]): ∀ (a_1 a_2 : Iota), Eq (a a_1 a_2) False % 3.59/3.82 Clause #32 (by superposition #[31, 28]): Eq False True % 3.59/3.82 Clause #33 (by clausification #[32]): False % 3.59/3.82 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------