%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SYO223^5 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n015.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 08:08:46 PM UTC 2025 % Result : Theorem 4.77s 4.97s % Output : Proof 4.77s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.15 % Problem : SYO223^5 : TPTP v9.2.0. Released v4.0.0. % 0.08/0.16 % Command : duper %s % 0.15/0.38 % Computer : n015.cluster.edu % 0.15/0.38 % Model : x86_64 x86_64 % 0.15/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.38 % Memory : 8042.1875MB % 0.15/0.38 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.38 % CPULimit : 300 % 0.15/0.38 % WCLimit : 300 % 0.15/0.38 % DateTime : Fri Oct 3 14:24:23 EDT 2025 % 0.15/0.39 % CPUTime : % 4.77/4.97 SZS status Theorem for theBenchmark.p % 4.77/4.97 SZS output start Proof for theBenchmark.p % 4.77/4.97 Clause #0 (by assumption #[]): Eq % 4.77/4.97 (Not % 4.77/4.97 (And (∀ (X : Iota), cUNIQUE X → ∀ (Z : Iota), Eq X Z) (cUNIQUE cS) → % 4.77/4.97 Exists fun Xan => And (Eq (Xan cP) (cLIKE cP cS)) (Eq (Xan cJ) (Exists fun X => And (cUNIQUE X) (cLIKE cJ X))))) % 4.77/4.97 True % 4.77/4.97 Clause #1 (by clausification #[0]): Eq % 4.77/4.97 (And (∀ (X : Iota), cUNIQUE X → ∀ (Z : Iota), Eq X Z) (cUNIQUE cS) → % 4.77/4.97 Exists fun Xan => And (Eq (Xan cP) (cLIKE cP cS)) (Eq (Xan cJ) (Exists fun X => And (cUNIQUE X) (cLIKE cJ X)))) % 4.77/4.97 False % 4.77/4.97 Clause #2 (by clausification #[1]): Eq (And (∀ (X : Iota), cUNIQUE X → ∀ (Z : Iota), Eq X Z) (cUNIQUE cS)) True % 4.77/4.97 Clause #3 (by clausification #[1]): Eq (Exists fun Xan => And (Eq (Xan cP) (cLIKE cP cS)) (Eq (Xan cJ) (Exists fun X => And (cUNIQUE X) (cLIKE cJ X)))) % 4.77/4.97 False % 4.77/4.97 Clause #4 (by clausification #[2]): Eq (cUNIQUE cS) True % 4.77/4.97 Clause #5 (by clausification #[2]): Eq (∀ (X : Iota), cUNIQUE X → ∀ (Z : Iota), Eq X Z) True % 4.77/4.97 Clause #6 (by clausification #[5]): ∀ (a : Iota), Eq (cUNIQUE a → ∀ (Z : Iota), Eq a Z) True % 4.77/4.97 Clause #7 (by clausification #[6]): ∀ (a : Iota), Or (Eq (cUNIQUE a) False) (Eq (∀ (Z : Iota), Eq a Z) True) % 4.77/4.97 Clause #8 (by clausification #[7]): ∀ (a a_1 : Iota), Or (Eq (cUNIQUE a) False) (Eq (Eq a a_1) True) % 4.77/4.97 Clause #9 (by clausification #[8]): ∀ (a a_1 : Iota), Or (Eq (cUNIQUE a) False) (Eq a a_1) % 4.77/4.97 Clause #10 (by superposition #[9, 4]): ∀ (a : Iota), Or (Eq cS a) (Eq False True) % 4.77/4.97 Clause #11 (by clausification #[10]): ∀ (a : Iota), Eq cS a % 4.77/4.97 Clause #12 (by superposition #[11, 4]): ∀ (a : Iota), Eq (cUNIQUE a) True % 4.77/4.97 Clause #13 (by superposition #[11, 11]): ∀ (a a_1 : Iota), Eq a a_1 % 4.77/4.97 Clause #14 (by clausification #[3]): ∀ (a : Iota → Prop), Eq (And (Eq (a cP) (cLIKE cP cS)) (Eq (a cJ) (Exists fun X => And (cUNIQUE X) (cLIKE cJ X)))) False % 4.77/4.97 Clause #15 (by clausification #[14]): ∀ (a : Iota → Prop), % 4.77/4.97 Or (Eq (Eq (a cP) (cLIKE cP cS)) False) (Eq (Eq (a cJ) (Exists fun X => And (cUNIQUE X) (cLIKE cJ X))) False) % 4.77/4.97 Clause #16 (by clausification #[15]): ∀ (a : Iota → Prop), Or (Eq (Eq (a cJ) (Exists fun X => And (cUNIQUE X) (cLIKE cJ X))) False) (Ne (a cP) (cLIKE cP cS)) % 4.77/4.97 Clause #17 (by clausification #[16]): ∀ (a : Iota → Prop), Or (Ne (a cP) (cLIKE cP cS)) (Ne (a cJ) (Exists fun X => And (cUNIQUE X) (cLIKE cJ X))) % 4.77/4.97 Clause #18 (by clausification #[17]): ∀ (a : Iota → Prop), % 4.77/4.97 Or (Ne (a cJ) (Exists fun X => And (cUNIQUE X) (cLIKE cJ X))) (Or (Eq (a cP) False) (Eq (cLIKE cP cS) False)) % 4.77/4.97 Clause #19 (by clausification #[17]): ∀ (a : Iota → Prop), % 4.77/4.97 Or (Ne (a cJ) (Exists fun X => And (cUNIQUE X) (cLIKE cJ X))) (Or (Eq (a cP) True) (Eq (cLIKE cP cS) True)) % 4.77/4.97 Clause #20 (by clausification #[18]): ∀ (a : Iota → Prop), % 4.77/4.97 Or (Eq (a cP) False) % 4.77/4.97 (Or (Eq (cLIKE cP cS) False) (Or (Eq (a cJ) False) (Eq (Exists fun X => And (cUNIQUE X) (cLIKE cJ X)) False))) % 4.77/4.97 Clause #22 (by clausification #[20]): ∀ (a : Iota → Prop) (a_1 : Iota), % 4.77/4.97 Or (Eq (a cP) False) % 4.77/4.97 (Or (Eq (cLIKE cP cS) False) (Or (Eq (a cJ) False) (Eq (And (cUNIQUE a_1) (cLIKE cJ a_1)) False))) % 4.77/4.97 Clause #23 (by clausification #[22]): ∀ (a : Iota → Prop) (a_1 : Iota), % 4.77/4.97 Or (Eq (a cP) False) % 4.77/4.97 (Or (Eq (cLIKE cP cS) False) (Or (Eq (a cJ) False) (Or (Eq (cUNIQUE a_1) False) (Eq (cLIKE cJ a_1) False)))) % 4.77/4.97 Clause #24 (by forward demodulation #[23, 12]): ∀ (a : Iota → Prop) (a_1 : Iota), % 4.77/4.97 Or (Eq (a cP) False) % 4.77/4.97 (Or (Eq (cLIKE cP cS) False) (Or (Eq (a cJ) False) (Or (Eq True False) (Eq (cLIKE cJ a_1) False)))) % 4.77/4.97 Clause #25 (by clausification #[24]): ∀ (a : Iota → Prop) (a_1 : Iota), % 4.77/4.97 Or (Eq (a cP) False) (Or (Eq (cLIKE cP cS) False) (Or (Eq (a cJ) False) (Eq (cLIKE cJ a_1) False))) % 4.77/4.97 Clause #26 (by superposition #[25, 12]): ∀ (a : Iota → Iota) (a_1 : Iota), % 4.77/4.97 Or (Eq (cLIKE cP cS) False) % 4.77/4.97 (Or (Eq ((fun x => cUNIQUE (a x)) cJ) False) (Or (Eq (cLIKE cJ a_1) False) (Eq False True))) % 4.77/4.97 Clause #65 (by clausification #[19]): ∀ (a : Iota → Prop), % 4.77/4.97 Or (Eq (a cP) True) % 4.77/4.97 (Or (Eq (cLIKE cP cS) True) (Or (Eq (a cJ) True) (Eq (Exists fun X => And (cUNIQUE X) (cLIKE cJ X)) True))) % 4.77/5.00 Clause #114 (by betaEtaReduce #[26]): ∀ (a : Iota → Iota) (a_1 : Iota), % 4.77/5.00 Or (Eq (cLIKE cP cS) False) (Or (Eq (cUNIQUE (a cJ)) False) (Or (Eq (cLIKE cJ a_1) False) (Eq False True))) % 4.77/5.00 Clause #115 (by clausification #[114]): ∀ (a : Iota → Iota) (a_1 : Iota), Or (Eq (cLIKE cP cS) False) (Or (Eq (cUNIQUE (a cJ)) False) (Eq (cLIKE cJ a_1) False)) % 4.77/5.00 Clause #304 (by clausification #[65]): ∀ (a : Iota → Prop) (a_1 : Iota), % 4.77/5.00 Or (Eq (a cP) True) % 4.77/5.00 (Or (Eq (cLIKE cP cS) True) (Or (Eq (a cJ) True) (Eq (And (cUNIQUE (skS.0 1 a_1)) (cLIKE cJ (skS.0 1 a_1))) True))) % 4.77/5.00 Clause #305 (by clausification #[304]): ∀ (a : Iota → Prop) (a_1 : Iota), % 4.77/5.00 Or (Eq (a cP) True) (Or (Eq (cLIKE cP cS) True) (Or (Eq (a cJ) True) (Eq (cLIKE cJ (skS.0 1 a_1)) True))) % 4.77/5.00 Clause #347 (by superposition #[305, 13]): ∀ (a : Iota → Prop) (a_1 : Iota), % 4.77/5.00 Or (Eq (a cP) True) (Or (Eq (cLIKE cP cS) True) (Or (Eq (a cJ) True) (Eq (cLIKE cJ a_1) True))) % 4.77/5.00 Clause #433 (by equality factoring #[347]): ∀ (a : Iota) (a_1 : Prop), % 4.77/5.00 Or (Eq (cLIKE cP cS) True) (Or (Eq (cLIKE cJ a) True) (Or (Ne True True) (Eq ((fun x => a_1) cP) True))) % 4.77/5.00 Clause #503 (by betaEtaReduce #[433]): ∀ (a : Iota) (a_1 : Prop), Or (Eq (cLIKE cP cS) True) (Or (Eq (cLIKE cJ a) True) (Or (Ne True True) (Eq a_1 True))) % 4.77/5.00 Clause #504 (by clausification #[503]): ∀ (a : Iota) (a_1 : Prop), % 4.77/5.00 Or (Eq (cLIKE cP cS) True) (Or (Eq (cLIKE cJ a) True) (Or (Eq a_1 True) (Or (Eq True False) (Eq True False)))) % 4.77/5.00 Clause #506 (by clausification #[504]): ∀ (a : Iota) (a_1 : Prop), Or (Eq (cLIKE cP cS) True) (Or (Eq (cLIKE cJ a) True) (Or (Eq a_1 True) (Eq True False))) % 4.77/5.00 Clause #507 (by clausification #[506]): ∀ (a : Iota) (a_1 : Prop), Or (Eq (cLIKE cP cS) True) (Or (Eq (cLIKE cJ a) True) (Eq a_1 True)) % 4.77/5.00 Clause #522 (by equality factoring #[507]): ∀ (a : Iota), Or (Eq (cLIKE cP cS) True) (Or (Ne True True) (Eq (cLIKE cJ a) True)) % 4.77/5.00 Clause #554 (by clausification #[522]): ∀ (a : Iota), Or (Eq (cLIKE cP cS) True) (Or (Eq (cLIKE cJ a) True) (Or (Eq True False) (Eq True False))) % 4.77/5.00 Clause #556 (by clausification #[554]): ∀ (a : Iota), Or (Eq (cLIKE cP cS) True) (Or (Eq (cLIKE cJ a) True) (Eq True False)) % 4.77/5.00 Clause #557 (by clausification #[556]): ∀ (a : Iota), Or (Eq (cLIKE cP cS) True) (Eq (cLIKE cJ a) True) % 4.77/5.00 Clause #564 (by superposition #[557, 13]): ∀ (a a_1 : Iota), Or (Eq (cLIKE cP cS) True) (Eq (cLIKE a a_1) True) % 4.77/5.00 Clause #584 (by equality factoring #[564]): Or (Ne True True) (Eq (cLIKE cP cS) True) % 4.77/5.00 Clause #603 (by clausification #[584]): Or (Eq (cLIKE cP cS) True) (Or (Eq True False) (Eq True False)) % 4.77/5.00 Clause #605 (by clausification #[603]): Or (Eq (cLIKE cP cS) True) (Eq True False) % 4.77/5.00 Clause #606 (by clausification #[605]): Eq (cLIKE cP cS) True % 4.77/5.00 Clause #610 (by backward demodulation #[606, 115]): ∀ (a : Iota → Iota) (a_1 : Iota), Or (Eq True False) (Or (Eq (cUNIQUE (a cJ)) False) (Eq (cLIKE cJ a_1) False)) % 4.77/5.00 Clause #618 (by superposition #[606, 13]): ∀ (a : Iota), Eq (cLIKE a cS) True % 4.77/5.00 Clause #623 (by superposition #[618, 13]): ∀ (a a_1 : Iota), Eq (cLIKE a a_1) True % 4.77/5.00 Clause #632 (by clausification #[610]): ∀ (a : Iota → Iota) (a_1 : Iota), Or (Eq (cUNIQUE (a cJ)) False) (Eq (cLIKE cJ a_1) False) % 4.77/5.00 Clause #633 (by superposition #[632, 12]): ∀ (a : Iota), Or (Eq (cLIKE cJ a) False) (Eq False True) % 4.77/5.00 Clause #641 (by clausification #[633]): ∀ (a : Iota), Eq (cLIKE cJ a) False % 4.77/5.00 Clause #642 (by superposition #[641, 623]): Eq False True % 4.77/5.00 Clause #644 (by clausification #[642]): False % 4.77/5.00 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------