%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU769^2 : TPTP v9.2.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n013.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 08:02:24 PM UTC 2025 % Result : Theorem 7.81s 8.00s % Output : Proof 7.81s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SEU769^2 : TPTP v9.2.0. Released v3.7.0. % 0.07/0.13 % Command : duper %s % 0.14/0.34 % Computer : n013.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 06:40:53 EDT 2025 % 0.14/0.35 % CPUTime : % 7.81/8.00 SZS status Theorem for theBenchmark.p % 7.81/8.00 SZS output start Proof for theBenchmark.p % 7.81/8.00 Clause #0 (by assumption #[]): Eq (Eq dsetconstrER (∀ (A : Iota) (Xphi : Iota → Prop) (Xx : Iota), in Xx (dsetconstr A fun Xy => Xphi Xy) → Xphi Xx)) % 7.81/8.00 True % 7.81/8.00 Clause #3 (by assumption #[]): Eq (Eq breln1Set fun A => dsetconstr (powerset (cartprod A A)) fun R => breln1 A R) True % 7.81/8.00 Clause #4 (by assumption #[]): Eq (Not (dsetconstrER → ∀ (A R : Iota), in R (breln1Set A) → breln1 A R)) True % 7.81/8.00 Clause #5 (by clausification #[4]): Eq (dsetconstrER → ∀ (A R : Iota), in R (breln1Set A) → breln1 A R) False % 7.81/8.00 Clause #6 (by clausification #[5]): Eq dsetconstrER True % 7.81/8.00 Clause #7 (by clausification #[5]): Eq (∀ (A R : Iota), in R (breln1Set A) → breln1 A R) False % 7.81/8.00 Clause #8 (by clausification #[7]): ∀ (a : Iota), Eq (Not (∀ (R : Iota), in R (breln1Set (skS.0 0 a)) → breln1 (skS.0 0 a) R)) True % 7.81/8.00 Clause #9 (by clausification #[8]): ∀ (a : Iota), Eq (∀ (R : Iota), in R (breln1Set (skS.0 0 a)) → breln1 (skS.0 0 a) R) False % 7.81/8.00 Clause #10 (by clausification #[9]): ∀ (a a_1 : Iota), Eq (Not (in (skS.0 1 a a_1) (breln1Set (skS.0 0 a)) → breln1 (skS.0 0 a) (skS.0 1 a a_1))) True % 7.81/8.00 Clause #11 (by clausification #[10]): ∀ (a a_1 : Iota), Eq (in (skS.0 1 a a_1) (breln1Set (skS.0 0 a)) → breln1 (skS.0 0 a) (skS.0 1 a a_1)) False % 7.81/8.00 Clause #12 (by clausification #[11]): ∀ (a a_1 : Iota), Eq (in (skS.0 1 a a_1) (breln1Set (skS.0 0 a))) True % 7.81/8.00 Clause #13 (by clausification #[11]): ∀ (a a_1 : Iota), Eq (breln1 (skS.0 0 a) (skS.0 1 a a_1)) False % 7.81/8.00 Clause #14 (by betaEtaReduce #[0]): Eq (Eq dsetconstrER (∀ (A : Iota) (Xphi : Iota → Prop) (Xx : Iota), in Xx (dsetconstr A Xphi) → Xphi Xx)) True % 7.81/8.00 Clause #15 (by clausification #[14]): Eq dsetconstrER (∀ (A : Iota) (Xphi : Iota → Prop) (Xx : Iota), in Xx (dsetconstr A Xphi) → Xphi Xx) % 7.81/8.00 Clause #16 (by forward demodulation #[15, 6]): Eq True (∀ (A : Iota) (Xphi : Iota → Prop) (Xx : Iota), in Xx (dsetconstr A Xphi) → Xphi Xx) % 7.81/8.00 Clause #17 (by clausification #[16]): ∀ (a : Iota), Eq (∀ (Xphi : Iota → Prop) (Xx : Iota), in Xx (dsetconstr a Xphi) → Xphi Xx) True % 7.81/8.00 Clause #18 (by clausification #[17]): ∀ (a : Iota) (a_1 : Iota → Prop), Eq (∀ (Xx : Iota), in Xx (dsetconstr a a_1) → a_1 Xx) True % 7.81/8.00 Clause #19 (by clausification #[18]): ∀ (a a_1 : Iota) (a_2 : Iota → Prop), Eq (in a (dsetconstr a_1 a_2) → a_2 a) True % 7.81/8.00 Clause #20 (by clausification #[19]): ∀ (a a_1 : Iota) (a_2 : Iota → Prop), Or (Eq (in a (dsetconstr a_1 a_2)) False) (Eq (a_2 a) True) % 7.81/8.00 Clause #58 (by betaEtaReduce #[3]): Eq (Eq breln1Set fun A => dsetconstr (powerset (cartprod A A)) (breln1 A)) True % 7.81/8.00 Clause #59 (by clausification #[58]): Eq breln1Set fun A => dsetconstr (powerset (cartprod A A)) (breln1 A) % 7.81/8.00 Clause #60 (by argument congruence #[59]): ∀ (a : Iota), Eq (breln1Set a) ((fun A => dsetconstr (powerset (cartprod A A)) (breln1 A)) a) % 7.81/8.00 Clause #65 (by betaEtaReduce #[60]): ∀ (a : Iota), Eq (breln1Set a) (dsetconstr (powerset (cartprod a a)) (breln1 a)) % 7.81/8.00 Clause #66 (by superposition #[65, 20]): ∀ (a a_1 : Iota), Or (Eq (in a (breln1Set a_1)) False) (Eq (breln1 a_1 a) True) % 7.81/8.00 Clause #74 (by superposition #[66, 12]): ∀ (a a_1 : Iota), Or (Eq (breln1 (skS.0 0 a) (skS.0 1 a a_1)) True) (Eq False True) % 7.81/8.00 Clause #1136 (by clausification #[74]): ∀ (a a_1 : Iota), Eq (breln1 (skS.0 0 a) (skS.0 1 a a_1)) True % 7.81/8.00 Clause #1137 (by superposition #[1136, 13]): Eq True False % 7.81/8.00 Clause #1155 (by clausification #[1137]): False % 7.81/8.00 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------