%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU667^2 : TPTP v9.2.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n011.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 08:02:10 PM UTC 2025 % Result : Theorem 3.68s 3.84s % Output : Proof 3.68s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.13 % Problem : SEU667^2 : TPTP v9.2.0. Released v3.7.0. % 0.08/0.14 % Command : duper %s % 0.15/0.36 % Computer : n011.cluster.edu % 0.15/0.36 % Model : x86_64 x86_64 % 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.36 % Memory : 8042.1875MB % 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.36 % CPULimit : 300 % 0.15/0.36 % WCLimit : 300 % 0.15/0.36 % DateTime : Fri Oct 3 05:30:38 EDT 2025 % 0.15/0.36 % CPUTime : % 3.68/3.84 SZS status Theorem for theBenchmark.p % 3.68/3.84 SZS output start Proof for theBenchmark.p % 3.68/3.84 Clause #0 (by assumption #[]): Eq (Eq breln fun A B C => subset C (cartprod A B)) True % 3.68/3.84 Clause #2 (by assumption #[]): Eq % 3.68/3.84 (Eq dpsetconstrSub % 3.68/3.84 (∀ (A B : Iota) (Xphi : Iota → Iota → Prop), subset (dpsetconstr A B fun Xx Xy => Xphi Xx Xy) (cartprod A B))) % 3.68/3.84 True % 3.68/3.84 Clause #3 (by assumption #[]): Eq % 3.68/3.84 (Not % 3.68/3.84 (dpsetconstrSub → ∀ (A B : Iota) (Xphi : Iota → Iota → Prop), breln A B (dpsetconstr A B fun Xx Xy => Xphi Xx Xy))) % 3.68/3.84 True % 3.68/3.84 Clause #4 (by clausification #[0]): Eq breln fun A B C => subset C (cartprod A B) % 3.68/3.84 Clause #5 (by argument congruence #[4]): ∀ (a : Iota), Eq (breln a) ((fun A B C => subset C (cartprod A B)) a) % 3.68/3.84 Clause #8 (by betaEtaReduce #[5]): ∀ (a : Iota), Eq (breln a) fun B C => subset C (cartprod a B) % 3.68/3.84 Clause #9 (by argument congruence #[8]): ∀ (a a_1 : Iota), Eq (breln a a_1) ((fun B C => subset C (cartprod a B)) a_1) % 3.68/3.84 Clause #16 (by betaEtaReduce #[9]): ∀ (a a_1 : Iota), Eq (breln a a_1) fun C => subset C (cartprod a a_1) % 3.68/3.84 Clause #17 (by argument congruence #[16]): ∀ (a a_1 a_2 : Iota), Eq (breln a a_1 a_2) ((fun C => subset C (cartprod a a_1)) a_2) % 3.68/3.84 Clause #29 (by betaEtaReduce #[17]): ∀ (a a_1 a_2 : Iota), Eq (breln a a_1 a_2) (subset a_2 (cartprod a a_1)) % 3.68/3.84 Clause #43 (by betaEtaReduce #[2]): Eq (Eq dpsetconstrSub (∀ (A B : Iota) (Xphi : Iota → Iota → Prop), subset (dpsetconstr A B Xphi) (cartprod A B))) True % 3.68/3.84 Clause #44 (by clausification #[43]): Eq dpsetconstrSub (∀ (A B : Iota) (Xphi : Iota → Iota → Prop), subset (dpsetconstr A B Xphi) (cartprod A B)) % 3.68/3.84 Clause #59 (by betaEtaReduce #[3]): Eq (Not (dpsetconstrSub → ∀ (A B : Iota) (Xphi : Iota → Iota → Prop), breln A B (dpsetconstr A B Xphi))) True % 3.68/3.84 Clause #60 (by clausification #[59]): Eq (dpsetconstrSub → ∀ (A B : Iota) (Xphi : Iota → Iota → Prop), breln A B (dpsetconstr A B Xphi)) False % 3.68/3.84 Clause #61 (by clausification #[60]): Eq dpsetconstrSub True % 3.68/3.84 Clause #62 (by clausification #[60]): Eq (∀ (A B : Iota) (Xphi : Iota → Iota → Prop), breln A B (dpsetconstr A B Xphi)) False % 3.68/3.84 Clause #63 (by backward demodulation #[61, 44]): Eq True (∀ (A B : Iota) (Xphi : Iota → Iota → Prop), subset (dpsetconstr A B Xphi) (cartprod A B)) % 3.68/3.84 Clause #88 (by clausification #[62]): ∀ (a : Iota), % 3.68/3.84 Eq (Not (∀ (B : Iota) (Xphi : Iota → Iota → Prop), breln (skS.0 0 a) B (dpsetconstr (skS.0 0 a) B Xphi))) True % 3.68/3.84 Clause #89 (by clausification #[88]): ∀ (a : Iota), Eq (∀ (B : Iota) (Xphi : Iota → Iota → Prop), breln (skS.0 0 a) B (dpsetconstr (skS.0 0 a) B Xphi)) False % 3.68/3.84 Clause #90 (by clausification #[89]): ∀ (a a_1 : Iota), % 3.68/3.84 Eq % 3.68/3.84 (Not % 3.68/3.84 (∀ (Xphi : Iota → Iota → Prop), breln (skS.0 0 a) (skS.0 1 a a_1) (dpsetconstr (skS.0 0 a) (skS.0 1 a a_1) Xphi))) % 3.68/3.84 True % 3.68/3.84 Clause #91 (by clausification #[90]): ∀ (a a_1 : Iota), % 3.68/3.84 Eq (∀ (Xphi : Iota → Iota → Prop), breln (skS.0 0 a) (skS.0 1 a a_1) (dpsetconstr (skS.0 0 a) (skS.0 1 a a_1) Xphi)) % 3.68/3.84 False % 3.68/3.84 Clause #92 (by clausification #[91]): ∀ (a a_1 : Iota) (a_2 : Iota → Iota → Prop), % 3.68/3.84 Eq (Not (breln (skS.0 0 a) (skS.0 1 a a_1) (dpsetconstr (skS.0 0 a) (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)))) True % 3.68/3.84 Clause #93 (by clausification #[92]): ∀ (a a_1 : Iota) (a_2 : Iota → Iota → Prop), % 3.68/3.84 Eq (breln (skS.0 0 a) (skS.0 1 a a_1) (dpsetconstr (skS.0 0 a) (skS.0 1 a a_1) (skS.0 2 a a_1 a_2))) False % 3.68/3.84 Clause #95 (by clausification #[63]): ∀ (a : Iota), Eq (∀ (B : Iota) (Xphi : Iota → Iota → Prop), subset (dpsetconstr a B Xphi) (cartprod a B)) True % 3.68/3.84 Clause #96 (by clausification #[95]): ∀ (a a_1 : Iota), Eq (∀ (Xphi : Iota → Iota → Prop), subset (dpsetconstr a a_1 Xphi) (cartprod a a_1)) True % 3.68/3.84 Clause #97 (by clausification #[96]): ∀ (a a_1 : Iota) (a_2 : Iota → Iota → Prop), Eq (subset (dpsetconstr a a_1 a_2) (cartprod a a_1)) True % 3.68/3.84 Clause #98 (by superposition #[97, 29]): ∀ (a a_1 : Iota) (a_2 : Iota → Iota → Prop), Eq (breln a a_1 (dpsetconstr a a_1 a_2)) True % 3.68/3.84 Clause #106 (by superposition #[98, 93]): Eq True False % 3.68/3.84 Clause #110 (by clausification #[106]): False % 3.68/3.84 SZS output end Proof for theBenchmark.p 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