%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SYN724+1 : TPTP v9.2.0. Released v2.5.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n029.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 08:08:02 PM UTC 2025 % Result : Theorem 3.94s 4.09s % Output : Proof 3.94s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : SYN724+1 : TPTP v9.2.0. Released v2.5.0. % 0.11/0.13 % Command : duper %s % 0.13/0.35 % Computer : n029.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 : Thu Oct 2 15:29:08 EDT 2025 % 0.13/0.35 % CPUTime : % 3.94/4.09 SZS status Theorem for theBenchmark.p % 3.94/4.09 SZS output start Proof for theBenchmark.p % 3.94/4.09 Clause #0 (by assumption #[]): Eq (Not (Iff (∀ (X : Iota), r X → s X) (∀ (X : Iota), Iff (And (r X) (s X)) (r X)))) True % 3.94/4.09 Clause #1 (by clausification #[0]): Eq (Iff (∀ (X : Iota), r X → s X) (∀ (X : Iota), Iff (And (r X) (s X)) (r X))) False % 3.94/4.09 Clause #2 (by clausification #[1]): Or (Eq (∀ (X : Iota), r X → s X) False) (Eq (∀ (X : Iota), Iff (And (r X) (s X)) (r X)) False) % 3.94/4.09 Clause #3 (by clausification #[1]): Or (Eq (∀ (X : Iota), r X → s X) True) (Eq (∀ (X : Iota), Iff (And (r X) (s X)) (r X)) True) % 3.94/4.09 Clause #4 (by clausification #[2]): ∀ (a : Iota), Or (Eq (∀ (X : Iota), Iff (And (r X) (s X)) (r X)) False) (Eq (Not (r (skS.0 0 a) → s (skS.0 0 a))) True) % 3.94/4.09 Clause #5 (by clausification #[4]): ∀ (a a_1 : Iota), % 3.94/4.09 Or (Eq (Not (r (skS.0 0 a) → s (skS.0 0 a))) True) % 3.94/4.09 (Eq (Not (Iff (And (r (skS.0 1 a_1)) (s (skS.0 1 a_1))) (r (skS.0 1 a_1)))) True) % 3.94/4.09 Clause #6 (by clausification #[5]): ∀ (a a_1 : Iota), % 3.94/4.09 Or (Eq (Not (Iff (And (r (skS.0 1 a)) (s (skS.0 1 a))) (r (skS.0 1 a)))) True) % 3.94/4.09 (Eq (r (skS.0 0 a_1) → s (skS.0 0 a_1)) False) % 3.94/4.09 Clause #7 (by clausification #[6]): ∀ (a a_1 : Iota), % 3.94/4.09 Or (Eq (r (skS.0 0 a) → s (skS.0 0 a)) False) % 3.94/4.09 (Eq (Iff (And (r (skS.0 1 a_1)) (s (skS.0 1 a_1))) (r (skS.0 1 a_1))) False) % 3.94/4.09 Clause #8 (by clausification #[7]): ∀ (a a_1 : Iota), Or (Eq (Iff (And (r (skS.0 1 a)) (s (skS.0 1 a))) (r (skS.0 1 a))) False) (Eq (r (skS.0 0 a_1)) True) % 3.94/4.09 Clause #9 (by clausification #[7]): ∀ (a a_1 : Iota), Or (Eq (Iff (And (r (skS.0 1 a)) (s (skS.0 1 a))) (r (skS.0 1 a))) False) (Eq (s (skS.0 0 a_1)) False) % 3.94/4.09 Clause #10 (by clausification #[8]): ∀ (a a_1 : Iota), % 3.94/4.09 Or (Eq (r (skS.0 0 a)) True) (Or (Eq (And (r (skS.0 1 a_1)) (s (skS.0 1 a_1))) False) (Eq (r (skS.0 1 a_1)) False)) % 3.94/4.09 Clause #11 (by clausification #[8]): ∀ (a a_1 : Iota), % 3.94/4.09 Or (Eq (r (skS.0 0 a)) True) (Or (Eq (And (r (skS.0 1 a_1)) (s (skS.0 1 a_1))) True) (Eq (r (skS.0 1 a_1)) True)) % 3.94/4.09 Clause #12 (by clausification #[10]): ∀ (a a_1 : Iota), % 3.94/4.09 Or (Eq (r (skS.0 0 a)) True) % 3.94/4.09 (Or (Eq (r (skS.0 1 a_1)) False) (Or (Eq (r (skS.0 1 a_1)) False) (Eq (s (skS.0 1 a_1)) False))) % 3.94/4.09 Clause #13 (by eliminate duplicate literals #[12]): ∀ (a a_1 : Iota), Or (Eq (r (skS.0 0 a)) True) (Or (Eq (r (skS.0 1 a_1)) False) (Eq (s (skS.0 1 a_1)) False)) % 3.94/4.09 Clause #14 (by clausification #[3]): ∀ (a : Iota), Or (Eq (∀ (X : Iota), Iff (And (r X) (s X)) (r X)) True) (Eq (r a → s a) True) % 3.94/4.09 Clause #15 (by clausification #[14]): ∀ (a a_1 : Iota), Or (Eq (r a → s a) True) (Eq (Iff (And (r a_1) (s a_1)) (r a_1)) True) % 3.94/4.09 Clause #16 (by clausification #[15]): ∀ (a a_1 : Iota), Or (Eq (Iff (And (r a) (s a)) (r a)) True) (Or (Eq (r a_1) False) (Eq (s a_1) True)) % 3.94/4.09 Clause #17 (by clausification #[16]): ∀ (a a_1 : Iota), Or (Eq (r a) False) (Or (Eq (s a) True) (Or (Eq (And (r a_1) (s a_1)) True) (Eq (r a_1) False))) % 3.94/4.09 Clause #19 (by clausification #[17]): ∀ (a a_1 : Iota), Or (Eq (r a) False) (Or (Eq (s a) True) (Or (Eq (r a_1) False) (Eq (s a_1) True))) % 3.94/4.09 Clause #23 (by clausification #[11]): ∀ (a a_1 : Iota), Or (Eq (r (skS.0 0 a)) True) (Or (Eq (r (skS.0 1 a_1)) True) (Eq (r (skS.0 1 a_1)) True)) % 3.94/4.09 Clause #25 (by clausification #[9]): ∀ (a a_1 : Iota), % 3.94/4.09 Or (Eq (s (skS.0 0 a)) False) (Or (Eq (And (r (skS.0 1 a_1)) (s (skS.0 1 a_1))) False) (Eq (r (skS.0 1 a_1)) False)) % 3.94/4.09 Clause #26 (by clausification #[9]): ∀ (a a_1 : Iota), % 3.94/4.09 Or (Eq (s (skS.0 0 a)) False) (Or (Eq (And (r (skS.0 1 a_1)) (s (skS.0 1 a_1))) True) (Eq (r (skS.0 1 a_1)) True)) % 3.94/4.09 Clause #27 (by clausification #[25]): ∀ (a a_1 : Iota), % 3.94/4.09 Or (Eq (s (skS.0 0 a)) False) % 3.94/4.09 (Or (Eq (r (skS.0 1 a_1)) False) (Or (Eq (r (skS.0 1 a_1)) False) (Eq (s (skS.0 1 a_1)) False))) % 3.94/4.09 Clause #28 (by eliminate duplicate literals #[27]): ∀ (a a_1 : Iota), Or (Eq (s (skS.0 0 a)) False) (Or (Eq (r (skS.0 1 a_1)) False) (Eq (s (skS.0 1 a_1)) False)) % 3.94/4.09 Clause #29 (by eliminate duplicate literals #[23]): ∀ (a a_1 : Iota), Or (Eq (r (skS.0 0 a)) True) (Eq (r (skS.0 1 a_1)) True) % 3.94/4.09 Clause #31 (by superposition #[29, 13]): ∀ (a a_1 a_2 : Iota), % 3.94/4.12 Or (Eq (r (skS.0 0 a)) True) (Or (Eq (r (skS.0 0 a_1)) True) (Or (Eq True False) (Eq (s (skS.0 1 a_2)) False))) % 3.94/4.12 Clause #32 (by superposition #[29, 19]): ∀ (a a_1 a_2 : Iota), % 3.94/4.12 Or (Eq (r (skS.0 0 a)) True) % 3.94/4.12 (Or (Eq True False) (Or (Eq (s (skS.0 1 a_1)) True) (Or (Eq (r a_2) False) (Eq (s a_2) True)))) % 3.94/4.12 Clause #33 (by clausification #[32]): ∀ (a a_1 a_2 : Iota), % 3.94/4.12 Or (Eq (r (skS.0 0 a)) True) (Or (Eq (s (skS.0 1 a_1)) True) (Or (Eq (r a_2) False) (Eq (s a_2) True))) % 3.94/4.12 Clause #35 (by superposition #[33, 29]): ∀ (a a_1 a_2 a_3 : Iota), % 3.94/4.12 Or (Eq (r (skS.0 0 a)) True) % 3.94/4.12 (Or (Eq (s (skS.0 1 a_1)) True) (Or (Eq (s (skS.0 1 a_2)) True) (Or (Eq (r (skS.0 0 a_3)) True) (Eq False True)))) % 3.94/4.12 Clause #39 (by clausification #[31]): ∀ (a a_1 a_2 : Iota), Or (Eq (r (skS.0 0 a)) True) (Or (Eq (r (skS.0 0 a_1)) True) (Eq (s (skS.0 1 a_2)) False)) % 3.94/4.12 Clause #42 (by clausification #[26]): ∀ (a a_1 : Iota), Or (Eq (s (skS.0 0 a)) False) (Or (Eq (r (skS.0 1 a_1)) True) (Eq (r (skS.0 1 a_1)) True)) % 3.94/4.12 Clause #43 (by eliminate duplicate literals #[42]): ∀ (a a_1 : Iota), Or (Eq (s (skS.0 0 a)) False) (Eq (r (skS.0 1 a_1)) True) % 3.94/4.12 Clause #44 (by clausification #[35]): ∀ (a a_1 a_2 a_3 : Iota), % 3.94/4.12 Or (Eq (r (skS.0 0 a)) True) % 3.94/4.12 (Or (Eq (s (skS.0 1 a_1)) True) (Or (Eq (s (skS.0 1 a_2)) True) (Eq (r (skS.0 0 a_3)) True))) % 3.94/4.12 Clause #53 (by equality factoring #[44]): ∀ (a a_1 a_2 : Iota), % 3.94/4.12 Or (Eq (r (skS.0 0 a)) True) (Or (Eq (r (skS.0 0 a_1)) True) (Or (Ne True True) (Eq (s (skS.0 1 a_2)) True))) % 3.94/4.12 Clause #54 (by clausification #[53]): ∀ (a a_1 a_2 : Iota), % 3.94/4.12 Or (Eq (r (skS.0 0 a)) True) % 3.94/4.12 (Or (Eq (r (skS.0 0 a_1)) True) (Or (Eq (s (skS.0 1 a_2)) True) (Or (Eq True False) (Eq True False)))) % 3.94/4.12 Clause #56 (by clausification #[54]): ∀ (a a_1 a_2 : Iota), % 3.94/4.12 Or (Eq (r (skS.0 0 a)) True) (Or (Eq (r (skS.0 0 a_1)) True) (Or (Eq (s (skS.0 1 a_2)) True) (Eq True False))) % 3.94/4.12 Clause #57 (by clausification #[56]): ∀ (a a_1 a_2 : Iota), Or (Eq (r (skS.0 0 a)) True) (Or (Eq (r (skS.0 0 a_1)) True) (Eq (s (skS.0 1 a_2)) True)) % 3.94/4.12 Clause #62 (by equality factoring #[57]): ∀ (a a_1 : Iota), Or (Eq (s (skS.0 1 a)) True) (Or (Ne True True) (Eq (r (skS.0 0 a_1)) True)) % 3.94/4.12 Clause #63 (by clausification #[62]): ∀ (a a_1 : Iota), Or (Eq (s (skS.0 1 a)) True) (Or (Eq (r (skS.0 0 a_1)) True) (Or (Eq True False) (Eq True False))) % 3.94/4.12 Clause #65 (by clausification #[63]): ∀ (a a_1 : Iota), Or (Eq (s (skS.0 1 a)) True) (Or (Eq (r (skS.0 0 a_1)) True) (Eq True False)) % 3.94/4.12 Clause #66 (by clausification #[65]): ∀ (a a_1 : Iota), Or (Eq (s (skS.0 1 a)) True) (Eq (r (skS.0 0 a_1)) True) % 3.94/4.12 Clause #67 (by superposition #[66, 39]): ∀ (a a_1 a_2 : Iota), % 3.94/4.12 Or (Eq (r (skS.0 0 a)) True) (Or (Eq (r (skS.0 0 a_1)) True) (Or (Eq (r (skS.0 0 a_2)) True) (Eq True False))) % 3.94/4.12 Clause #75 (by clausification #[67]): ∀ (a a_1 a_2 : Iota), Or (Eq (r (skS.0 0 a)) True) (Or (Eq (r (skS.0 0 a_1)) True) (Eq (r (skS.0 0 a_2)) True)) % 3.94/4.12 Clause #79 (by equality factoring #[75]): ∀ (a a_1 : Iota), Or (Eq (r (skS.0 0 a)) True) (Or (Ne True True) (Eq (r (skS.0 0 a_1)) True)) % 3.94/4.12 Clause #80 (by clausification #[79]): ∀ (a a_1 : Iota), Or (Eq (r (skS.0 0 a)) True) (Or (Eq (r (skS.0 0 a_1)) True) (Or (Eq True False) (Eq True False))) % 3.94/4.12 Clause #82 (by clausification #[80]): ∀ (a a_1 : Iota), Or (Eq (r (skS.0 0 a)) True) (Or (Eq (r (skS.0 0 a_1)) True) (Eq True False)) % 3.94/4.12 Clause #83 (by clausification #[82]): ∀ (a a_1 : Iota), Or (Eq (r (skS.0 0 a)) True) (Eq (r (skS.0 0 a_1)) True) % 3.94/4.12 Clause #87 (by equality factoring #[83]): ∀ (a : Iota), Or (Ne True True) (Eq (r (skS.0 0 a)) True) % 3.94/4.12 Clause #88 (by clausification #[87]): ∀ (a : Iota), Or (Eq (r (skS.0 0 a)) True) (Or (Eq True False) (Eq True False)) % 3.94/4.12 Clause #90 (by clausification #[88]): ∀ (a : Iota), Or (Eq (r (skS.0 0 a)) True) (Eq True False) % 3.94/4.12 Clause #91 (by clausification #[90]): ∀ (a : Iota), Eq (r (skS.0 0 a)) True % 3.94/4.12 Clause #92 (by superposition #[91, 19]): ∀ (a a_1 : Iota), Or (Eq True False) (Or (Eq (s (skS.0 0 a)) True) (Or (Eq (r a_1) False) (Eq (s a_1) True))) % 3.94/4.12 Clause #106 (by clausification #[92]): ∀ (a a_1 : Iota), Or (Eq (s (skS.0 0 a)) True) (Or (Eq (r a_1) False) (Eq (s a_1) True)) % 3.94/4.13 Clause #107 (by superposition #[106, 91]): ∀ (a a_1 : Iota), Or (Eq (s (skS.0 0 a)) True) (Or (Eq (s (skS.0 0 a_1)) True) (Eq False True)) % 3.94/4.13 Clause #110 (by clausification #[107]): ∀ (a a_1 : Iota), Or (Eq (s (skS.0 0 a)) True) (Eq (s (skS.0 0 a_1)) True) % 3.94/4.13 Clause #113 (by equality factoring #[110]): ∀ (a : Iota), Or (Ne True True) (Eq (s (skS.0 0 a)) True) % 3.94/4.13 Clause #114 (by clausification #[113]): ∀ (a : Iota), Or (Eq (s (skS.0 0 a)) True) (Or (Eq True False) (Eq True False)) % 3.94/4.13 Clause #116 (by clausification #[114]): ∀ (a : Iota), Or (Eq (s (skS.0 0 a)) True) (Eq True False) % 3.94/4.13 Clause #117 (by clausification #[116]): ∀ (a : Iota), Eq (s (skS.0 0 a)) True % 3.94/4.13 Clause #118 (by superposition #[117, 28]): ∀ (a : Iota), Or (Eq True False) (Or (Eq (r (skS.0 1 a)) False) (Eq (s (skS.0 1 a)) False)) % 3.94/4.13 Clause #119 (by superposition #[117, 43]): ∀ (a : Iota), Or (Eq True False) (Eq (r (skS.0 1 a)) True) % 3.94/4.13 Clause #120 (by clausification #[119]): ∀ (a : Iota), Eq (r (skS.0 1 a)) True % 3.94/4.13 Clause #122 (by superposition #[120, 19]): ∀ (a a_1 : Iota), Or (Eq True False) (Or (Eq (s (skS.0 1 a)) True) (Or (Eq (r a_1) False) (Eq (s a_1) True))) % 3.94/4.13 Clause #124 (by clausification #[122]): ∀ (a a_1 : Iota), Or (Eq (s (skS.0 1 a)) True) (Or (Eq (r a_1) False) (Eq (s a_1) True)) % 3.94/4.13 Clause #126 (by superposition #[124, 120]): ∀ (a a_1 : Iota), Or (Eq (s (skS.0 1 a)) True) (Or (Eq (s (skS.0 1 a_1)) True) (Eq False True)) % 3.94/4.13 Clause #128 (by clausification #[118]): ∀ (a : Iota), Or (Eq (r (skS.0 1 a)) False) (Eq (s (skS.0 1 a)) False) % 3.94/4.13 Clause #129 (by forward demodulation #[128, 120]): ∀ (a : Iota), Or (Eq True False) (Eq (s (skS.0 1 a)) False) % 3.94/4.13 Clause #130 (by clausification #[129]): ∀ (a : Iota), Eq (s (skS.0 1 a)) False % 3.94/4.13 Clause #132 (by clausification #[126]): ∀ (a a_1 : Iota), Or (Eq (s (skS.0 1 a)) True) (Eq (s (skS.0 1 a_1)) True) % 3.94/4.13 Clause #133 (by superposition #[132, 130]): ∀ (a : Iota), Or (Eq (s (skS.0 1 a)) True) (Eq True False) % 3.94/4.13 Clause #138 (by clausification #[133]): ∀ (a : Iota), Eq (s (skS.0 1 a)) True % 3.94/4.13 Clause #139 (by superposition #[138, 130]): Eq True False % 3.94/4.13 Clause #140 (by clausification #[139]): False % 3.94/4.13 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------