%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEV197^5 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n026.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 08:02:56 PM UTC 2025 % Result : Theorem 4.56s 4.73s % Output : Proof 4.56s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SEV197^5 : TPTP v9.2.0. Released v4.0.0. % 0.07/0.13 % Command : duper %s % 0.13/0.35 % Computer : n026.cluster.edu % 0.13/0.35 % Model : x86_64 x86_64 % 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.35 % Memory : 8042.1875MB % 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 300 % 0.13/0.35 % DateTime : Fri Oct 3 01:24:23 EDT 2025 % 0.13/0.35 % CPUTime : % 4.56/4.73 SZS status Theorem for theBenchmark.p % 4.56/4.73 SZS output start Proof for theBenchmark.p % 4.56/4.73 Clause #0 (by assumption #[]): Eq % 4.56/4.73 (Not % 4.56/4.73 (And % 4.56/4.73 (And (∀ (Xx Xy : iS), Ne (cP Xx Xy) c0) % 4.56/4.73 (∀ (Xx Xy Xu Xv : iS), Eq (cP Xx Xu) (cP Xy Xv) → And (Eq Xx Xy) (Eq Xu Xv))) % 4.56/4.73 (∀ (X : iS → Prop), And (X c0) (∀ (Xx Xy : iS), And (X Xx) (X Xy) → X (cP Xx Xy)) → ∀ (Xx : iS), X Xx) → % 4.56/4.73 And (∀ (Xx Xy Xu Xv : iS), Eq (cP Xx Xu) (cP Xy Xv) → And (Eq Xx Xy) (Eq Xu Xv)) % 4.56/4.73 (∀ (Xx Xy : iS), Ne (cP Xx Xy) c0))) % 4.56/4.73 True % 4.56/4.73 Clause #1 (by clausification #[0]): Eq % 4.56/4.73 (And % 4.56/4.73 (And (∀ (Xx Xy : iS), Ne (cP Xx Xy) c0) % 4.56/4.73 (∀ (Xx Xy Xu Xv : iS), Eq (cP Xx Xu) (cP Xy Xv) → And (Eq Xx Xy) (Eq Xu Xv))) % 4.56/4.73 (∀ (X : iS → Prop), And (X c0) (∀ (Xx Xy : iS), And (X Xx) (X Xy) → X (cP Xx Xy)) → ∀ (Xx : iS), X Xx) → % 4.56/4.73 And (∀ (Xx Xy Xu Xv : iS), Eq (cP Xx Xu) (cP Xy Xv) → And (Eq Xx Xy) (Eq Xu Xv)) (∀ (Xx Xy : iS), Ne (cP Xx Xy) c0)) % 4.56/4.73 False % 4.56/4.73 Clause #2 (by clausification #[1]): Eq % 4.56/4.73 (And % 4.56/4.73 (And (∀ (Xx Xy : iS), Ne (cP Xx Xy) c0) % 4.56/4.73 (∀ (Xx Xy Xu Xv : iS), Eq (cP Xx Xu) (cP Xy Xv) → And (Eq Xx Xy) (Eq Xu Xv))) % 4.56/4.73 (∀ (X : iS → Prop), And (X c0) (∀ (Xx Xy : iS), And (X Xx) (X Xy) → X (cP Xx Xy)) → ∀ (Xx : iS), X Xx)) % 4.56/4.73 True % 4.56/4.73 Clause #3 (by clausification #[1]): Eq (And (∀ (Xx Xy Xu Xv : iS), Eq (cP Xx Xu) (cP Xy Xv) → And (Eq Xx Xy) (Eq Xu Xv)) (∀ (Xx Xy : iS), Ne (cP Xx Xy) c0)) % 4.56/4.73 False % 4.56/4.73 Clause #5 (by clausification #[2]): Eq (And (∀ (Xx Xy : iS), Ne (cP Xx Xy) c0) (∀ (Xx Xy Xu Xv : iS), Eq (cP Xx Xu) (cP Xy Xv) → And (Eq Xx Xy) (Eq Xu Xv))) % 4.56/4.73 True % 4.56/4.73 Clause #46 (by clausification #[3]): Or (Eq (∀ (Xx Xy Xu Xv : iS), Eq (cP Xx Xu) (cP Xy Xv) → And (Eq Xx Xy) (Eq Xu Xv)) False) % 4.56/4.73 (Eq (∀ (Xx Xy : iS), Ne (cP Xx Xy) c0) False) % 4.56/4.73 Clause #47 (by clausification #[46]): ∀ (a : iS), % 4.56/4.73 Or (Eq (∀ (Xx Xy : iS), Ne (cP Xx Xy) c0) False) % 4.56/4.73 (Eq (Not (∀ (Xy Xu Xv : iS), Eq (cP (skS.0 2 a) Xu) (cP Xy Xv) → And (Eq (skS.0 2 a) Xy) (Eq Xu Xv))) True) % 4.56/4.73 Clause #48 (by clausification #[47]): ∀ (a a_1 : iS), % 4.56/4.73 Or (Eq (Not (∀ (Xy Xu Xv : iS), Eq (cP (skS.0 2 a) Xu) (cP Xy Xv) → And (Eq (skS.0 2 a) Xy) (Eq Xu Xv))) True) % 4.56/4.73 (Eq (Not (∀ (Xy : iS), Ne (cP (skS.0 3 a_1) Xy) c0)) True) % 4.56/4.73 Clause #49 (by clausification #[48]): ∀ (a a_1 : iS), % 4.56/4.73 Or (Eq (Not (∀ (Xy : iS), Ne (cP (skS.0 3 a) Xy) c0)) True) % 4.56/4.73 (Eq (∀ (Xy Xu Xv : iS), Eq (cP (skS.0 2 a_1) Xu) (cP Xy Xv) → And (Eq (skS.0 2 a_1) Xy) (Eq Xu Xv)) False) % 4.56/4.73 Clause #50 (by clausification #[49]): ∀ (a a_1 : iS), % 4.56/4.73 Or (Eq (∀ (Xy Xu Xv : iS), Eq (cP (skS.0 2 a) Xu) (cP Xy Xv) → And (Eq (skS.0 2 a) Xy) (Eq Xu Xv)) False) % 4.56/4.73 (Eq (∀ (Xy : iS), Ne (cP (skS.0 3 a_1) Xy) c0) False) % 4.56/4.73 Clause #51 (by clausification #[50]): ∀ (a a_1 a_2 : iS), % 4.56/4.73 Or (Eq (∀ (Xy : iS), Ne (cP (skS.0 3 a) Xy) c0) False) % 4.56/4.73 (Eq % 4.56/4.73 (Not % 4.56/4.73 (∀ (Xu Xv : iS), % 4.56/4.73 Eq (cP (skS.0 2 a_1) Xu) (cP (skS.0 4 a_1 a_2) Xv) → And (Eq (skS.0 2 a_1) (skS.0 4 a_1 a_2)) (Eq Xu Xv))) % 4.56/4.73 True) % 4.56/4.73 Clause #52 (by clausification #[51]): ∀ (a a_1 a_2 a_3 : iS), % 4.56/4.73 Or % 4.56/4.73 (Eq % 4.56/4.73 (Not % 4.56/4.73 (∀ (Xu Xv : iS), % 4.56/4.73 Eq (cP (skS.0 2 a) Xu) (cP (skS.0 4 a a_1) Xv) → And (Eq (skS.0 2 a) (skS.0 4 a a_1)) (Eq Xu Xv))) % 4.56/4.73 True) % 4.56/4.73 (Eq (Not (Ne (cP (skS.0 3 a_2) (skS.0 5 a_2 a_3)) c0)) True) % 4.56/4.73 Clause #53 (by clausification #[52]): ∀ (a a_1 a_2 a_3 : iS), % 4.56/4.73 Or (Eq (Not (Ne (cP (skS.0 3 a) (skS.0 5 a a_1)) c0)) True) % 4.56/4.73 (Eq % 4.56/4.73 (∀ (Xu Xv : iS), % 4.56/4.73 Eq (cP (skS.0 2 a_2) Xu) (cP (skS.0 4 a_2 a_3) Xv) → And (Eq (skS.0 2 a_2) (skS.0 4 a_2 a_3)) (Eq Xu Xv)) % 4.56/4.73 False) % 4.56/4.73 Clause #54 (by clausification #[53]): ∀ (a a_1 a_2 a_3 : iS), % 4.56/4.73 Or % 4.56/4.73 (Eq % 4.56/4.73 (∀ (Xu Xv : iS), Eq (cP (skS.0 2 a) Xu) (cP (skS.0 4 a a_1) Xv) → And (Eq (skS.0 2 a) (skS.0 4 a a_1)) (Eq Xu Xv)) % 4.56/4.73 False) % 4.56/4.73 (Eq (Ne (cP (skS.0 3 a_2) (skS.0 5 a_2 a_3)) c0) False) % 4.56/4.73 Clause #55 (by clausification #[54]): ∀ (a a_1 a_2 a_3 a_4 : iS), % 4.56/4.73 Or (Eq (Ne (cP (skS.0 3 a) (skS.0 5 a a_1)) c0) False) % 4.56/4.73 (Eq % 4.56/4.73 (Not % 4.56/4.73 (∀ (Xv : iS), % 4.56/4.73 Eq (cP (skS.0 2 a_2) (skS.0 6 a_2 a_3 a_4)) (cP (skS.0 4 a_2 a_3) Xv) → % 4.56/4.75 And (Eq (skS.0 2 a_2) (skS.0 4 a_2 a_3)) (Eq (skS.0 6 a_2 a_3 a_4) Xv))) % 4.56/4.75 True) % 4.56/4.75 Clause #56 (by clausification #[55]): ∀ (a a_1 a_2 a_3 a_4 : iS), % 4.56/4.75 Or % 4.56/4.75 (Eq % 4.56/4.75 (Not % 4.56/4.75 (∀ (Xv : iS), % 4.56/4.75 Eq (cP (skS.0 2 a) (skS.0 6 a a_1 a_2)) (cP (skS.0 4 a a_1) Xv) → % 4.56/4.75 And (Eq (skS.0 2 a) (skS.0 4 a a_1)) (Eq (skS.0 6 a a_1 a_2) Xv))) % 4.56/4.75 True) % 4.56/4.75 (Eq (cP (skS.0 3 a_3) (skS.0 5 a_3 a_4)) c0) % 4.56/4.75 Clause #57 (by clausification #[56]): ∀ (a a_1 a_2 a_3 a_4 : iS), % 4.56/4.75 Or (Eq (cP (skS.0 3 a) (skS.0 5 a a_1)) c0) % 4.56/4.75 (Eq % 4.56/4.75 (∀ (Xv : iS), % 4.56/4.75 Eq (cP (skS.0 2 a_2) (skS.0 6 a_2 a_3 a_4)) (cP (skS.0 4 a_2 a_3) Xv) → % 4.56/4.75 And (Eq (skS.0 2 a_2) (skS.0 4 a_2 a_3)) (Eq (skS.0 6 a_2 a_3 a_4) Xv)) % 4.56/4.75 False) % 4.56/4.75 Clause #58 (by clausification #[57]): ∀ (a a_1 a_2 a_3 a_4 a_5 : iS), % 4.56/4.75 Or (Eq (cP (skS.0 3 a) (skS.0 5 a a_1)) c0) % 4.56/4.75 (Eq % 4.56/4.75 (Not % 4.56/4.75 (Eq (cP (skS.0 2 a_2) (skS.0 6 a_2 a_3 a_4)) (cP (skS.0 4 a_2 a_3) (skS.0 7 a_2 a_3 a_4 a_5)) → % 4.56/4.75 And (Eq (skS.0 2 a_2) (skS.0 4 a_2 a_3)) (Eq (skS.0 6 a_2 a_3 a_4) (skS.0 7 a_2 a_3 a_4 a_5)))) % 4.56/4.75 True) % 4.56/4.75 Clause #59 (by clausification #[58]): ∀ (a a_1 a_2 a_3 a_4 a_5 : iS), % 4.56/4.75 Or (Eq (cP (skS.0 3 a) (skS.0 5 a a_1)) c0) % 4.56/4.75 (Eq % 4.56/4.75 (Eq (cP (skS.0 2 a_2) (skS.0 6 a_2 a_3 a_4)) (cP (skS.0 4 a_2 a_3) (skS.0 7 a_2 a_3 a_4 a_5)) → % 4.56/4.75 And (Eq (skS.0 2 a_2) (skS.0 4 a_2 a_3)) (Eq (skS.0 6 a_2 a_3 a_4) (skS.0 7 a_2 a_3 a_4 a_5))) % 4.56/4.75 False) % 4.56/4.75 Clause #60 (by clausification #[59]): ∀ (a a_1 a_2 a_3 a_4 a_5 : iS), % 4.56/4.75 Or (Eq (cP (skS.0 3 a) (skS.0 5 a a_1)) c0) % 4.56/4.75 (Eq (Eq (cP (skS.0 2 a_2) (skS.0 6 a_2 a_3 a_4)) (cP (skS.0 4 a_2 a_3) (skS.0 7 a_2 a_3 a_4 a_5))) True) % 4.56/4.75 Clause #61 (by clausification #[59]): ∀ (a a_1 a_2 a_3 a_4 a_5 : iS), % 4.56/4.75 Or (Eq (cP (skS.0 3 a) (skS.0 5 a a_1)) c0) % 4.56/4.75 (Eq (And (Eq (skS.0 2 a_2) (skS.0 4 a_2 a_3)) (Eq (skS.0 6 a_2 a_3 a_4) (skS.0 7 a_2 a_3 a_4 a_5))) False) % 4.56/4.75 Clause #62 (by clausification #[60]): ∀ (a a_1 a_2 a_3 a_4 a_5 : iS), % 4.56/4.75 Or (Eq (cP (skS.0 3 a) (skS.0 5 a a_1)) c0) % 4.56/4.75 (Eq (cP (skS.0 2 a_2) (skS.0 6 a_2 a_3 a_4)) (cP (skS.0 4 a_2 a_3) (skS.0 7 a_2 a_3 a_4 a_5))) % 4.56/4.75 Clause #79 (by clausification #[5]): Eq (∀ (Xx Xy Xu Xv : iS), Eq (cP Xx Xu) (cP Xy Xv) → And (Eq Xx Xy) (Eq Xu Xv)) True % 4.56/4.75 Clause #80 (by clausification #[5]): Eq (∀ (Xx Xy : iS), Ne (cP Xx Xy) c0) True % 4.56/4.75 Clause #81 (by clausification #[79]): ∀ (a : iS), Eq (∀ (Xy Xu Xv : iS), Eq (cP a Xu) (cP Xy Xv) → And (Eq a Xy) (Eq Xu Xv)) True % 4.56/4.75 Clause #82 (by clausification #[81]): ∀ (a a_1 : iS), Eq (∀ (Xu Xv : iS), Eq (cP a Xu) (cP a_1 Xv) → And (Eq a a_1) (Eq Xu Xv)) True % 4.56/4.75 Clause #83 (by clausification #[82]): ∀ (a a_1 a_2 : iS), Eq (∀ (Xv : iS), Eq (cP a a_1) (cP a_2 Xv) → And (Eq a a_2) (Eq a_1 Xv)) True % 4.56/4.75 Clause #84 (by clausification #[83]): ∀ (a a_1 a_2 a_3 : iS), Eq (Eq (cP a a_1) (cP a_2 a_3) → And (Eq a a_2) (Eq a_1 a_3)) True % 4.56/4.75 Clause #85 (by clausification #[84]): ∀ (a a_1 a_2 a_3 : iS), Or (Eq (Eq (cP a a_1) (cP a_2 a_3)) False) (Eq (And (Eq a a_2) (Eq a_1 a_3)) True) % 4.56/4.75 Clause #86 (by clausification #[85]): ∀ (a a_1 a_2 a_3 : iS), Or (Eq (And (Eq a a_1) (Eq a_2 a_3)) True) (Ne (cP a a_2) (cP a_1 a_3)) % 4.56/4.75 Clause #87 (by clausification #[86]): ∀ (a a_1 a_2 a_3 : iS), Or (Ne (cP a a_1) (cP a_2 a_3)) (Eq (Eq a_1 a_3) True) % 4.56/4.75 Clause #88 (by clausification #[86]): ∀ (a a_1 a_2 a_3 : iS), Or (Ne (cP a a_1) (cP a_2 a_3)) (Eq (Eq a a_2) True) % 4.56/4.75 Clause #89 (by clausification #[87]): ∀ (a a_1 a_2 a_3 : iS), Or (Ne (cP a a_1) (cP a_2 a_3)) (Eq a_1 a_3) % 4.56/4.75 Clause #95 (by clausification #[80]): ∀ (a : iS), Eq (∀ (Xy : iS), Ne (cP a Xy) c0) True % 4.56/4.75 Clause #96 (by clausification #[95]): ∀ (a a_1 : iS), Eq (Ne (cP a a_1) c0) True % 4.56/4.75 Clause #97 (by clausification #[96]): ∀ (a a_1 : iS), Ne (cP a a_1) c0 % 4.56/4.75 Clause #98 (by backward contextual literal cutting #[97, 62]): ∀ (a a_1 a_2 a_3 : iS), Eq (cP (skS.0 2 a) (skS.0 6 a a_1 a_2)) (cP (skS.0 4 a a_1) (skS.0 7 a a_1 a_2 a_3)) % 4.56/4.75 Clause #103 (by clausification #[88]): ∀ (a a_1 a_2 a_3 : iS), Or (Ne (cP a a_1) (cP a_2 a_3)) (Eq a a_2) % 4.56/4.78 Clause #208 (by superposition #[98, 89]): ∀ (a a_1 a_2 a_3 a_4 a_5 : iS), % 4.56/4.78 Or (Ne (cP (skS.0 2 a) (skS.0 6 a a_1 a_2)) (cP a_3 a_4)) (Eq (skS.0 7 a a_1 a_2 a_5) a_4) % 4.56/4.78 Clause #212 (by superposition #[98, 103]): ∀ (a a_1 a_2 a_3 a_4 : iS), Or (Ne (cP a a_1) (cP (skS.0 2 a_2) (skS.0 6 a_2 a_3 a_4))) (Eq a (skS.0 4 a_2 a_3)) % 4.56/4.78 Clause #234 (by equality resolution #[212]): ∀ (a a_1 : iS), Eq (skS.0 2 a) (skS.0 4 a a_1) % 4.56/4.78 Clause #299 (by equality resolution #[208]): ∀ (a a_1 a_2 a_3 : iS), Eq (skS.0 7 a a_1 a_2 a_3) (skS.0 6 a a_1 a_2) % 4.56/4.78 Clause #333 (by clausification #[61]): ∀ (a a_1 a_2 a_3 a_4 a_5 : iS), % 4.56/4.78 Or (Eq (cP (skS.0 3 a) (skS.0 5 a a_1)) c0) % 4.56/4.78 (Or (Eq (Eq (skS.0 2 a_2) (skS.0 4 a_2 a_3)) False) (Eq (Eq (skS.0 6 a_2 a_3 a_4) (skS.0 7 a_2 a_3 a_4 a_5)) False)) % 4.56/4.78 Clause #334 (by clausification #[333]): ∀ (a a_1 a_2 a_3 a_4 a_5 : iS), % 4.56/4.78 Or (Eq (cP (skS.0 3 a) (skS.0 5 a a_1)) c0) % 4.56/4.78 (Or (Eq (Eq (skS.0 6 a_2 a_3 a_4) (skS.0 7 a_2 a_3 a_4 a_5)) False) (Ne (skS.0 2 a_2) (skS.0 4 a_2 a_3))) % 4.56/4.78 Clause #335 (by clausification #[334]): ∀ (a a_1 a_2 a_3 a_4 a_5 : iS), % 4.56/4.78 Or (Eq (cP (skS.0 3 a) (skS.0 5 a a_1)) c0) % 4.56/4.78 (Or (Ne (skS.0 2 a_2) (skS.0 4 a_2 a_3)) (Ne (skS.0 6 a_2 a_3 a_4) (skS.0 7 a_2 a_3 a_4 a_5))) % 4.56/4.78 Clause #336 (by forward demodulation #[335, 234]): ∀ (a a_1 a_2 a_3 a_4 a_5 : iS), % 4.56/4.78 Or (Eq (cP (skS.0 3 a) (skS.0 5 a a_1)) c0) % 4.56/4.78 (Or (Ne (skS.0 2 a_2) (skS.0 2 a_2)) (Ne (skS.0 6 a_2 a_3 a_4) (skS.0 7 a_2 a_3 a_4 a_5))) % 4.56/4.78 Clause #337 (by eliminate resolved literals #[336]): ∀ (a a_1 a_2 a_3 a_4 a_5 : iS), % 4.56/4.78 Or (Eq (cP (skS.0 3 a) (skS.0 5 a a_1)) c0) (Ne (skS.0 6 a_2 a_3 a_4) (skS.0 7 a_2 a_3 a_4 a_5)) % 4.56/4.78 Clause #338 (by forward demodulation #[337, 299]): ∀ (a a_1 a_2 a_3 a_4 : iS), Or (Eq (cP (skS.0 3 a) (skS.0 5 a a_1)) c0) (Ne (skS.0 6 a_2 a_3 a_4) (skS.0 6 a_2 a_3 a_4)) % 4.56/4.78 Clause #339 (by eliminate resolved literals #[338]): ∀ (a a_1 : iS), Eq (cP (skS.0 3 a) (skS.0 5 a a_1)) c0 % 4.56/4.78 Clause #340 (by forward contextual literal cutting #[339, 97]): False % 4.56/4.78 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------