%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEV413^5 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n003.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 08:03:09 PM UTC 2025 % Result : Theorem 4.83s 5.04s % Output : Proof 4.91s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.12 % Problem : SEV413^5 : TPTP v9.2.0. Released v4.0.0. % 0.12/0.14 % Command : duper %s % 0.14/0.35 % Computer : n003.cluster.edu % 0.14/0.35 % Model : x86_64 x86_64 % 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.35 % Memory : 8042.1875MB % 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.35 % CPULimit : 300 % 0.14/0.35 % WCLimit : 300 % 0.14/0.35 % DateTime : Fri Oct 3 01:20:53 EDT 2025 % 0.14/0.35 % CPUTime : % 4.83/5.04 SZS status Theorem for theBenchmark.p % 4.83/5.04 SZS output start Proof for theBenchmark.p % 4.83/5.04 Clause #0 (by assumption #[]): Eq % 4.83/5.04 (Not % 4.83/5.04 (Or (∀ (Xx : Iota), cA Xx → cB Xx) (∀ (Xx : Iota), cA Xx → cB Xx) → % 4.83/5.04 And (∀ (Xx : Iota), cA Xx → cB Xx) (∀ (Xx : Iota), cA Xx → cB Xx))) % 4.83/5.04 True % 4.83/5.04 Clause #1 (by clausification #[0]): Eq % 4.83/5.04 (Or (∀ (Xx : Iota), cA Xx → cB Xx) (∀ (Xx : Iota), cA Xx → cB Xx) → % 4.83/5.04 And (∀ (Xx : Iota), cA Xx → cB Xx) (∀ (Xx : Iota), cA Xx → cB Xx)) % 4.83/5.04 False % 4.83/5.04 Clause #2 (by clausification #[1]): Eq (Or (∀ (Xx : Iota), cA Xx → cB Xx) (∀ (Xx : Iota), cA Xx → cB Xx)) True % 4.83/5.04 Clause #3 (by clausification #[1]): Eq (And (∀ (Xx : Iota), cA Xx → cB Xx) (∀ (Xx : Iota), cA Xx → cB Xx)) False % 4.83/5.04 Clause #4 (by clausification #[2]): Or (Eq (∀ (Xx : Iota), cA Xx → cB Xx) True) (Eq (∀ (Xx : Iota), cA Xx → cB Xx) True) % 4.83/5.04 Clause #5 (by clausification #[4]): ∀ (a : Iota), Or (Eq (∀ (Xx : Iota), cA Xx → cB Xx) True) (Eq (cA a → cB a) True) % 4.83/5.04 Clause #6 (by clausification #[5]): ∀ (a a_1 : Iota), Or (Eq (cA a → cB a) True) (Eq (cA a_1 → cB a_1) True) % 4.83/5.04 Clause #7 (by clausification #[6]): ∀ (a a_1 : Iota), Or (Eq (cA a → cB a) True) (Or (Eq (cA a_1) False) (Eq (cB a_1) True)) % 4.83/5.04 Clause #8 (by clausification #[7]): ∀ (a a_1 : Iota), Or (Eq (cA a) False) (Or (Eq (cB a) True) (Or (Eq (cA a_1) False) (Eq (cB a_1) True))) % 4.83/5.04 Clause #9 (by clausification #[3]): Or (Eq (∀ (Xx : Iota), cA Xx → cB Xx) False) (Eq (∀ (Xx : Iota), cA Xx → cB Xx) False) % 4.83/5.04 Clause #10 (by clausification #[9]): ∀ (a : Iota), Or (Eq (∀ (Xx : Iota), cA Xx → cB Xx) False) (Eq (Not (cA (skS.0 0 a) → cB (skS.0 0 a))) True) % 4.83/5.04 Clause #11 (by clausification #[10]): ∀ (a a_1 : Iota), % 4.83/5.04 Or (Eq (Not (cA (skS.0 0 a) → cB (skS.0 0 a))) True) (Eq (Not (cA (skS.0 1 a_1) → cB (skS.0 1 a_1))) True) % 4.83/5.04 Clause #12 (by clausification #[11]): ∀ (a a_1 : Iota), Or (Eq (Not (cA (skS.0 1 a) → cB (skS.0 1 a))) True) (Eq (cA (skS.0 0 a_1) → cB (skS.0 0 a_1)) False) % 4.83/5.04 Clause #13 (by clausification #[12]): ∀ (a a_1 : Iota), Or (Eq (cA (skS.0 0 a) → cB (skS.0 0 a)) False) (Eq (cA (skS.0 1 a_1) → cB (skS.0 1 a_1)) False) % 4.83/5.04 Clause #14 (by clausification #[13]): ∀ (a a_1 : Iota), Or (Eq (cA (skS.0 1 a) → cB (skS.0 1 a)) False) (Eq (cA (skS.0 0 a_1)) True) % 4.83/5.04 Clause #15 (by clausification #[13]): ∀ (a a_1 : Iota), Or (Eq (cA (skS.0 1 a) → cB (skS.0 1 a)) False) (Eq (cB (skS.0 0 a_1)) False) % 4.83/5.04 Clause #16 (by clausification #[14]): ∀ (a a_1 : Iota), Or (Eq (cA (skS.0 0 a)) True) (Eq (cA (skS.0 1 a_1)) True) % 4.83/5.04 Clause #17 (by clausification #[14]): ∀ (a a_1 : Iota), Or (Eq (cA (skS.0 0 a)) True) (Eq (cB (skS.0 1 a_1)) False) % 4.83/5.04 Clause #18 (by superposition #[16, 8]): ∀ (a a_1 a_2 : Iota), % 4.83/5.04 Or (Eq (cA (skS.0 1 a)) True) % 4.83/5.04 (Or (Eq True False) (Or (Eq (cB (skS.0 0 a_1)) True) (Or (Eq (cA a_2) False) (Eq (cB a_2) True)))) % 4.83/5.04 Clause #20 (by clausification #[15]): ∀ (a a_1 : Iota), Or (Eq (cB (skS.0 0 a)) False) (Eq (cA (skS.0 1 a_1)) True) % 4.83/5.04 Clause #21 (by clausification #[15]): ∀ (a a_1 : Iota), Or (Eq (cB (skS.0 0 a)) False) (Eq (cB (skS.0 1 a_1)) False) % 4.83/5.04 Clause #22 (by clausification #[18]): ∀ (a a_1 a_2 : Iota), % 4.83/5.04 Or (Eq (cA (skS.0 1 a)) True) (Or (Eq (cB (skS.0 0 a_1)) True) (Or (Eq (cA a_2) False) (Eq (cB a_2) True))) % 4.83/5.04 Clause #23 (by superposition #[22, 16]): ∀ (a a_1 a_2 a_3 : Iota), % 4.83/5.04 Or (Eq (cA (skS.0 1 a)) True) % 4.83/5.04 (Or (Eq (cB (skS.0 0 a_1)) True) % 4.83/5.04 (Or (Eq (cB (skS.0 0 a_2)) True) (Or (Eq False True) (Eq (cA (skS.0 1 a_3)) True)))) % 4.83/5.04 Clause #29 (by clausification #[23]): ∀ (a a_1 a_2 a_3 : Iota), % 4.83/5.04 Or (Eq (cA (skS.0 1 a)) True) % 4.83/5.04 (Or (Eq (cB (skS.0 0 a_1)) True) (Or (Eq (cB (skS.0 0 a_2)) True) (Eq (cA (skS.0 1 a_3)) True))) % 4.83/5.04 Clause #39 (by equality factoring #[29]): ∀ (a a_1 a_2 : Iota), % 4.83/5.04 Or (Eq (cA (skS.0 1 a)) True) (Or (Eq (cA (skS.0 1 a_1)) True) (Or (Ne True True) (Eq (cB (skS.0 0 a_2)) True))) % 4.83/5.04 Clause #40 (by clausification #[39]): ∀ (a a_1 a_2 : Iota), % 4.83/5.04 Or (Eq (cA (skS.0 1 a)) True) % 4.83/5.04 (Or (Eq (cA (skS.0 1 a_1)) True) (Or (Eq (cB (skS.0 0 a_2)) True) (Or (Eq True False) (Eq True False)))) % 4.83/5.04 Clause #42 (by clausification #[40]): ∀ (a a_1 a_2 : Iota), % 4.91/5.07 Or (Eq (cA (skS.0 1 a)) True) (Or (Eq (cA (skS.0 1 a_1)) True) (Or (Eq (cB (skS.0 0 a_2)) True) (Eq True False))) % 4.91/5.07 Clause #43 (by clausification #[42]): ∀ (a a_1 a_2 : Iota), Or (Eq (cA (skS.0 1 a)) True) (Or (Eq (cA (skS.0 1 a_1)) True) (Eq (cB (skS.0 0 a_2)) True)) % 4.91/5.07 Clause #49 (by equality factoring #[43]): ∀ (a a_1 : Iota), Or (Eq (cB (skS.0 0 a)) True) (Or (Ne True True) (Eq (cA (skS.0 1 a_1)) True)) % 4.91/5.07 Clause #50 (by clausification #[49]): ∀ (a a_1 : Iota), Or (Eq (cB (skS.0 0 a)) True) (Or (Eq (cA (skS.0 1 a_1)) True) (Or (Eq True False) (Eq True False))) % 4.91/5.07 Clause #52 (by clausification #[50]): ∀ (a a_1 : Iota), Or (Eq (cB (skS.0 0 a)) True) (Or (Eq (cA (skS.0 1 a_1)) True) (Eq True False)) % 4.91/5.07 Clause #53 (by clausification #[52]): ∀ (a a_1 : Iota), Or (Eq (cB (skS.0 0 a)) True) (Eq (cA (skS.0 1 a_1)) True) % 4.91/5.07 Clause #54 (by superposition #[53, 20]): ∀ (a a_1 : Iota), Or (Eq (cA (skS.0 1 a)) True) (Or (Eq True False) (Eq (cA (skS.0 1 a_1)) True)) % 4.91/5.07 Clause #60 (by clausification #[54]): ∀ (a a_1 : Iota), Or (Eq (cA (skS.0 1 a)) True) (Eq (cA (skS.0 1 a_1)) True) % 4.91/5.07 Clause #63 (by equality factoring #[60]): ∀ (a : Iota), Or (Ne True True) (Eq (cA (skS.0 1 a)) True) % 4.91/5.07 Clause #64 (by clausification #[63]): ∀ (a : Iota), Or (Eq (cA (skS.0 1 a)) True) (Or (Eq True False) (Eq True False)) % 4.91/5.07 Clause #66 (by clausification #[64]): ∀ (a : Iota), Or (Eq (cA (skS.0 1 a)) True) (Eq True False) % 4.91/5.07 Clause #67 (by clausification #[66]): ∀ (a : Iota), Eq (cA (skS.0 1 a)) True % 4.91/5.07 Clause #68 (by superposition #[67, 8]): ∀ (a a_1 : Iota), Or (Eq True False) (Or (Eq (cB (skS.0 1 a)) True) (Or (Eq (cA a_1) False) (Eq (cB a_1) True))) % 4.91/5.07 Clause #70 (by clausification #[68]): ∀ (a a_1 : Iota), Or (Eq (cB (skS.0 1 a)) True) (Or (Eq (cA a_1) False) (Eq (cB a_1) True)) % 4.91/5.07 Clause #71 (by superposition #[70, 67]): ∀ (a a_1 : Iota), Or (Eq (cB (skS.0 1 a)) True) (Or (Eq (cB (skS.0 1 a_1)) True) (Eq False True)) % 4.91/5.07 Clause #80 (by clausification #[71]): ∀ (a a_1 : Iota), Or (Eq (cB (skS.0 1 a)) True) (Eq (cB (skS.0 1 a_1)) True) % 4.91/5.07 Clause #82 (by equality factoring #[80]): ∀ (a : Iota), Or (Ne True True) (Eq (cB (skS.0 1 a)) True) % 4.91/5.07 Clause #83 (by clausification #[82]): ∀ (a : Iota), Or (Eq (cB (skS.0 1 a)) True) (Or (Eq True False) (Eq True False)) % 4.91/5.07 Clause #85 (by clausification #[83]): ∀ (a : Iota), Or (Eq (cB (skS.0 1 a)) True) (Eq True False) % 4.91/5.07 Clause #86 (by clausification #[85]): ∀ (a : Iota), Eq (cB (skS.0 1 a)) True % 4.91/5.07 Clause #87 (by superposition #[86, 17]): ∀ (a : Iota), Or (Eq (cA (skS.0 0 a)) True) (Eq True False) % 4.91/5.07 Clause #88 (by clausification #[87]): ∀ (a : Iota), Eq (cA (skS.0 0 a)) True % 4.91/5.07 Clause #89 (by superposition #[88, 8]): ∀ (a a_1 : Iota), Or (Eq True False) (Or (Eq (cB (skS.0 0 a)) True) (Or (Eq (cA a_1) False) (Eq (cB a_1) True))) % 4.91/5.07 Clause #90 (by clausification #[89]): ∀ (a a_1 : Iota), Or (Eq (cB (skS.0 0 a)) True) (Or (Eq (cA a_1) False) (Eq (cB a_1) True)) % 4.91/5.07 Clause #92 (by superposition #[90, 88]): ∀ (a a_1 : Iota), Or (Eq (cB (skS.0 0 a)) True) (Or (Eq (cB (skS.0 0 a_1)) True) (Eq False True)) % 4.91/5.07 Clause #95 (by clausification #[92]): ∀ (a a_1 : Iota), Or (Eq (cB (skS.0 0 a)) True) (Eq (cB (skS.0 0 a_1)) True) % 4.91/5.07 Clause #97 (by equality factoring #[95]): ∀ (a : Iota), Or (Ne True True) (Eq (cB (skS.0 0 a)) True) % 4.91/5.07 Clause #98 (by clausification #[97]): ∀ (a : Iota), Or (Eq (cB (skS.0 0 a)) True) (Or (Eq True False) (Eq True False)) % 4.91/5.07 Clause #100 (by clausification #[98]): ∀ (a : Iota), Or (Eq (cB (skS.0 0 a)) True) (Eq True False) % 4.91/5.07 Clause #101 (by clausification #[100]): ∀ (a : Iota), Eq (cB (skS.0 0 a)) True % 4.91/5.07 Clause #102 (by superposition #[101, 21]): ∀ (a : Iota), Or (Eq True False) (Eq (cB (skS.0 1 a)) False) % 4.91/5.07 Clause #103 (by clausification #[102]): ∀ (a : Iota), Eq (cB (skS.0 1 a)) False % 4.91/5.07 Clause #104 (by superposition #[103, 86]): Eq False True % 4.91/5.07 Clause #105 (by clausification #[104]): False % 4.91/5.07 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------