%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SYO104^5 : 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 08:08:36 PM UTC 2025 % Result : Theorem 4.00s 4.15s % Output : Proof 4.00s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SYO104^5 : TPTP v9.2.0. Released v4.0.0. % 0.07/0.13 % Command : duper %s % 0.13/0.34 % Computer : n003.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Fri Oct 3 13:01:38 EDT 2025 % 0.13/0.34 % CPUTime : % 4.00/4.15 SZS status Theorem for theBenchmark.p % 4.00/4.15 SZS output start Proof for theBenchmark.p % 4.00/4.15 Clause #0 (by assumption #[]): Eq (Not (Iff (∀ (Xx : Iota), And (cP Xx y) (cQ Xx y)) (And (∀ (Xx : Iota), cP Xx y) (∀ (Xx : Iota), cQ Xx y)))) True % 4.00/4.15 Clause #1 (by clausification #[0]): Eq (Iff (∀ (Xx : Iota), And (cP Xx y) (cQ Xx y)) (And (∀ (Xx : Iota), cP Xx y) (∀ (Xx : Iota), cQ Xx y))) False % 4.00/4.15 Clause #2 (by clausification #[1]): Or (Eq (∀ (Xx : Iota), And (cP Xx y) (cQ Xx y)) False) % 4.00/4.15 (Eq (And (∀ (Xx : Iota), cP Xx y) (∀ (Xx : Iota), cQ Xx y)) False) % 4.00/4.15 Clause #3 (by clausification #[1]): Or (Eq (∀ (Xx : Iota), And (cP Xx y) (cQ Xx y)) True) (Eq (And (∀ (Xx : Iota), cP Xx y) (∀ (Xx : Iota), cQ Xx y)) True) % 4.00/4.15 Clause #4 (by clausification #[2]): ∀ (a : Iota), % 4.00/4.15 Or (Eq (And (∀ (Xx : Iota), cP Xx y) (∀ (Xx : Iota), cQ Xx y)) False) % 4.00/4.15 (Eq (Not (And (cP (skS.0 0 a) y) (cQ (skS.0 0 a) y))) True) % 4.00/4.15 Clause #5 (by clausification #[4]): ∀ (a : Iota), % 4.00/4.15 Or (Eq (Not (And (cP (skS.0 0 a) y) (cQ (skS.0 0 a) y))) True) % 4.00/4.15 (Or (Eq (∀ (Xx : Iota), cP Xx y) False) (Eq (∀ (Xx : Iota), cQ Xx y) False)) % 4.00/4.15 Clause #6 (by clausification #[5]): ∀ (a : Iota), % 4.00/4.15 Or (Eq (∀ (Xx : Iota), cP Xx y) False) % 4.00/4.15 (Or (Eq (∀ (Xx : Iota), cQ Xx y) False) (Eq (And (cP (skS.0 0 a) y) (cQ (skS.0 0 a) y)) False)) % 4.00/4.15 Clause #7 (by clausification #[6]): ∀ (a a_1 : Iota), % 4.00/4.15 Or (Eq (∀ (Xx : Iota), cQ Xx y) False) % 4.00/4.15 (Or (Eq (And (cP (skS.0 0 a) y) (cQ (skS.0 0 a) y)) False) (Eq (Not (cP (skS.0 1 a_1) y)) True)) % 4.00/4.15 Clause #8 (by clausification #[7]): ∀ (a a_1 a_2 : Iota), % 4.00/4.15 Or (Eq (And (cP (skS.0 0 a) y) (cQ (skS.0 0 a) y)) False) % 4.00/4.15 (Or (Eq (Not (cP (skS.0 1 a_1) y)) True) (Eq (Not (cQ (skS.0 2 a_2) y)) True)) % 4.00/4.15 Clause #9 (by clausification #[8]): ∀ (a a_1 a_2 : Iota), % 4.00/4.15 Or (Eq (Not (cP (skS.0 1 a) y)) True) % 4.00/4.15 (Or (Eq (Not (cQ (skS.0 2 a_1) y)) True) (Or (Eq (cP (skS.0 0 a_2) y) False) (Eq (cQ (skS.0 0 a_2) y) False))) % 4.00/4.15 Clause #10 (by clausification #[9]): ∀ (a a_1 a_2 : Iota), % 4.00/4.15 Or (Eq (Not (cQ (skS.0 2 a) y)) True) % 4.00/4.15 (Or (Eq (cP (skS.0 0 a_1) y) False) (Or (Eq (cQ (skS.0 0 a_1) y) False) (Eq (cP (skS.0 1 a_2) y) False))) % 4.00/4.15 Clause #11 (by clausification #[10]): ∀ (a a_1 a_2 : Iota), % 4.00/4.15 Or (Eq (cP (skS.0 0 a) y) False) % 4.00/4.15 (Or (Eq (cQ (skS.0 0 a) y) False) (Or (Eq (cP (skS.0 1 a_1) y) False) (Eq (cQ (skS.0 2 a_2) y) False))) % 4.00/4.15 Clause #12 (by clausification #[3]): ∀ (a : Iota), Or (Eq (And (∀ (Xx : Iota), cP Xx y) (∀ (Xx : Iota), cQ Xx y)) True) (Eq (And (cP a y) (cQ a y)) True) % 4.00/4.15 Clause #13 (by clausification #[12]): ∀ (a : Iota), Or (Eq (And (cP a y) (cQ a y)) True) (Eq (∀ (Xx : Iota), cQ Xx y) True) % 4.00/4.15 Clause #14 (by clausification #[12]): ∀ (a : Iota), Or (Eq (And (cP a y) (cQ a y)) True) (Eq (∀ (Xx : Iota), cP Xx y) True) % 4.00/4.15 Clause #15 (by clausification #[13]): ∀ (a : Iota), Or (Eq (∀ (Xx : Iota), cQ Xx y) True) (Eq (cQ a y) True) % 4.00/4.15 Clause #17 (by clausification #[15]): ∀ (a a_1 : Iota), Or (Eq (cQ a y) True) (Eq (cQ a_1 y) True) % 4.00/4.15 Clause #18 (by equality factoring #[17]): ∀ (a : Iota), Or (Ne True True) (Eq (cQ a y) True) % 4.00/4.15 Clause #19 (by clausification #[18]): ∀ (a : Iota), Or (Eq (cQ a y) True) (Or (Eq True False) (Eq True False)) % 4.00/4.15 Clause #21 (by clausification #[19]): ∀ (a : Iota), Or (Eq (cQ a y) True) (Eq True False) % 4.00/4.15 Clause #22 (by clausification #[21]): ∀ (a : Iota), Eq (cQ a y) True % 4.00/4.15 Clause #25 (by clausification #[14]): ∀ (a : Iota), Or (Eq (∀ (Xx : Iota), cP Xx y) True) (Eq (cP a y) True) % 4.00/4.15 Clause #27 (by clausification #[25]): ∀ (a a_1 : Iota), Or (Eq (cP a y) True) (Eq (cP a_1 y) True) % 4.00/4.15 Clause #29 (by equality factoring #[27]): ∀ (a : Iota), Or (Ne True True) (Eq (cP a y) True) % 4.00/4.15 Clause #30 (by clausification #[29]): ∀ (a : Iota), Or (Eq (cP a y) True) (Or (Eq True False) (Eq True False)) % 4.00/4.15 Clause #32 (by clausification #[30]): ∀ (a : Iota), Or (Eq (cP a y) True) (Eq True False) % 4.00/4.15 Clause #33 (by clausification #[32]): ∀ (a : Iota), Eq (cP a y) True % 4.00/4.15 Clause #34 (by backward demodulation #[33, 11]): ∀ (a a_1 a_2 : Iota), % 4.00/4.15 Or (Eq True False) % 4.00/4.15 (Or (Eq (cQ (skS.0 0 a) y) False) (Or (Eq (cP (skS.0 1 a_1) y) False) (Eq (cQ (skS.0 2 a_2) y) False))) % 4.00/4.16 Clause #35 (by clausification #[34]): ∀ (a a_1 a_2 : Iota), % 4.00/4.16 Or (Eq (cQ (skS.0 0 a) y) False) (Or (Eq (cP (skS.0 1 a_1) y) False) (Eq (cQ (skS.0 2 a_2) y) False)) % 4.00/4.16 Clause #36 (by superposition #[35, 22]): ∀ (a a_1 : Iota), Or (Eq (cP (skS.0 1 a) y) False) (Or (Eq (cQ (skS.0 2 a_1) y) False) (Eq False True)) % 4.00/4.16 Clause #37 (by clausification #[36]): ∀ (a a_1 : Iota), Or (Eq (cP (skS.0 1 a) y) False) (Eq (cQ (skS.0 2 a_1) y) False) % 4.00/4.16 Clause #38 (by superposition #[37, 33]): ∀ (a : Iota), Or (Eq (cQ (skS.0 2 a) y) False) (Eq False True) % 4.00/4.16 Clause #40 (by clausification #[38]): ∀ (a : Iota), Eq (cQ (skS.0 2 a) y) False % 4.00/4.16 Clause #41 (by superposition #[40, 22]): Eq False True % 4.00/4.16 Clause #42 (by clausification #[41]): False % 4.00/4.16 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------