%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SYN377+1 : TPTP v9.2.0. Released v2.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n005.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 08:07:32 PM UTC 2025 % Result : Theorem 3.77s 3.93s % Output : Proof 3.77s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : SYN377+1 : TPTP v9.2.0. Released v2.0.0. % 0.06/0.13 % Command : duper %s % 0.12/0.34 % Computer : n005.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 300 % 0.12/0.34 % DateTime : Thu Oct 2 15:38:08 EDT 2025 % 0.12/0.34 % CPUTime : % 3.77/3.93 SZS status Theorem for theBenchmark.p % 3.77/3.93 SZS output start Proof for theBenchmark.p % 3.77/3.93 Clause #0 (by assumption #[]): Eq % 3.77/3.93 (Not % 3.77/3.93 (Iff (∀ (X : Iota), Iff (big_p X) (∀ (Y : Iota), big_p Y)) (Iff (Exists fun X => big_p X) (∀ (Y : Iota), big_p Y)))) % 3.77/3.93 True % 3.77/3.93 Clause #1 (by betaEtaReduce #[0]): Eq (Not (Iff (∀ (X : Iota), Iff (big_p X) (∀ (Y : Iota), big_p Y)) (Iff (Exists big_p) (∀ (Y : Iota), big_p Y)))) True % 3.77/3.93 Clause #2 (by clausification #[1]): Eq (Iff (∀ (X : Iota), Iff (big_p X) (∀ (Y : Iota), big_p Y)) (Iff (Exists big_p) (∀ (Y : Iota), big_p Y))) False % 3.77/3.93 Clause #3 (by clausification #[2]): Or (Eq (∀ (X : Iota), Iff (big_p X) (∀ (Y : Iota), big_p Y)) False) % 3.77/3.93 (Eq (Iff (Exists big_p) (∀ (Y : Iota), big_p Y)) False) % 3.77/3.93 Clause #4 (by clausification #[2]): Or (Eq (∀ (X : Iota), Iff (big_p X) (∀ (Y : Iota), big_p Y)) True) % 3.77/3.93 (Eq (Iff (Exists big_p) (∀ (Y : Iota), big_p Y)) True) % 3.77/3.93 Clause #5 (by clausification #[3]): ∀ (a : Iota), % 3.77/3.93 Or (Eq (Iff (Exists big_p) (∀ (Y : Iota), big_p Y)) False) % 3.77/3.93 (Eq (Not (Iff (big_p (skS.0 0 a)) (∀ (Y : Iota), big_p Y))) True) % 3.77/3.93 Clause #6 (by clausification #[5]): ∀ (a : Iota), % 3.77/3.93 Or (Eq (Not (Iff (big_p (skS.0 0 a)) (∀ (Y : Iota), big_p Y))) True) % 3.77/3.93 (Or (Eq (Exists big_p) False) (Eq (∀ (Y : Iota), big_p Y) False)) % 3.77/3.93 Clause #7 (by clausification #[5]): ∀ (a : Iota), % 3.77/3.93 Or (Eq (Not (Iff (big_p (skS.0 0 a)) (∀ (Y : Iota), big_p Y))) True) % 3.77/3.93 (Or (Eq (Exists big_p) True) (Eq (∀ (Y : Iota), big_p Y) True)) % 3.77/3.93 Clause #8 (by clausification #[6]): ∀ (a : Iota), % 3.77/3.93 Or (Eq (Exists big_p) False) % 3.77/3.93 (Or (Eq (∀ (Y : Iota), big_p Y) False) (Eq (Iff (big_p (skS.0 0 a)) (∀ (Y : Iota), big_p Y)) False)) % 3.77/3.93 Clause #9 (by clausification #[8]): ∀ (a a_1 : Iota), % 3.77/3.93 Or (Eq (∀ (Y : Iota), big_p Y) False) % 3.77/3.93 (Or (Eq (Iff (big_p (skS.0 0 a)) (∀ (Y : Iota), big_p Y)) False) (Eq (big_p a_1) False)) % 3.77/3.93 Clause #10 (by clausification #[9]): ∀ (a a_1 a_2 : Iota), % 3.77/3.93 Or (Eq (Iff (big_p (skS.0 0 a)) (∀ (Y : Iota), big_p Y)) False) % 3.77/3.93 (Or (Eq (big_p a_1) False) (Eq (Not (big_p (skS.0 1 a_2))) True)) % 3.77/3.93 Clause #11 (by clausification #[10]): ∀ (a a_1 a_2 : Iota), % 3.77/3.93 Or (Eq (big_p a) False) % 3.77/3.93 (Or (Eq (Not (big_p (skS.0 1 a_1))) True) (Or (Eq (big_p (skS.0 0 a_2)) False) (Eq (∀ (Y : Iota), big_p Y) False))) % 3.77/3.93 Clause #13 (by clausification #[11]): ∀ (a a_1 a_2 : Iota), % 3.77/3.93 Or (Eq (big_p a) False) % 3.77/3.93 (Or (Eq (big_p (skS.0 0 a_1)) False) (Or (Eq (∀ (Y : Iota), big_p Y) False) (Eq (big_p (skS.0 1 a_2)) False))) % 3.77/3.93 Clause #14 (by clausification #[13]): ∀ (a a_1 a_2 a_3 : Iota), % 3.77/3.93 Or (Eq (big_p a) False) % 3.77/3.93 (Or (Eq (big_p (skS.0 0 a_1)) False) (Or (Eq (big_p (skS.0 1 a_2)) False) (Eq (Not (big_p (skS.0 2 a_3))) True))) % 3.77/3.93 Clause #15 (by clausification #[14]): ∀ (a a_1 a_2 a_3 : Iota), % 3.77/3.93 Or (Eq (big_p a) False) % 3.77/3.93 (Or (Eq (big_p (skS.0 0 a_1)) False) (Or (Eq (big_p (skS.0 1 a_2)) False) (Eq (big_p (skS.0 2 a_3)) False))) % 3.77/3.93 Clause #16 (by clausification #[4]): ∀ (a : Iota), % 3.77/3.93 Or (Eq (Iff (Exists big_p) (∀ (Y : Iota), big_p Y)) True) (Eq (Iff (big_p a) (∀ (Y : Iota), big_p Y)) True) % 3.77/3.93 Clause #18 (by clausification #[16]): ∀ (a : Iota), % 3.77/3.93 Or (Eq (Iff (big_p a) (∀ (Y : Iota), big_p Y)) True) (Or (Eq (Exists big_p) False) (Eq (∀ (Y : Iota), big_p Y) True)) % 3.77/3.93 Clause #31 (by clausification #[18]): ∀ (a : Iota), % 3.77/3.93 Or (Eq (Exists big_p) False) % 3.77/3.93 (Or (Eq (∀ (Y : Iota), big_p Y) True) (Or (Eq (big_p a) False) (Eq (∀ (Y : Iota), big_p Y) True))) % 3.77/3.93 Clause #36 (by clausification #[31]): ∀ (a a_1 : Iota), % 3.77/3.93 Or (Eq (∀ (Y : Iota), big_p Y) True) % 3.77/3.93 (Or (Eq (big_p a) False) (Or (Eq (∀ (Y : Iota), big_p Y) True) (Eq (big_p a_1) False))) % 3.77/3.93 Clause #37 (by clausification #[36]): ∀ (a a_1 a_2 : Iota), % 3.77/3.93 Or (Eq (big_p a) False) (Or (Eq (∀ (Y : Iota), big_p Y) True) (Or (Eq (big_p a_1) False) (Eq (big_p a_2) True))) % 3.77/3.93 Clause #38 (by clausification #[37]): ∀ (a a_1 a_2 a_3 : Iota), % 3.77/3.93 Or (Eq (big_p a) False) (Or (Eq (big_p a_1) False) (Or (Eq (big_p a_2) True) (Eq (big_p a_3) True))) % 3.77/3.93 Clause #39 (by clausification #[7]): ∀ (a : Iota), % 3.77/3.93 Or (Eq (Exists big_p) True) % 3.77/3.93 (Or (Eq (∀ (Y : Iota), big_p Y) True) (Eq (Iff (big_p (skS.0 0 a)) (∀ (Y : Iota), big_p Y)) False)) % 3.77/3.96 Clause #40 (by clausification #[39]): ∀ (a a_1 : Iota), % 3.77/3.96 Or (Eq (∀ (Y : Iota), big_p Y) True) % 3.77/3.96 (Or (Eq (Iff (big_p (skS.0 0 a)) (∀ (Y : Iota), big_p Y)) False) (Eq (big_p (skS.0 9 a_1)) True)) % 3.77/3.96 Clause #41 (by clausification #[40]): ∀ (a a_1 a_2 : Iota), % 3.77/3.96 Or (Eq (Iff (big_p (skS.0 0 a)) (∀ (Y : Iota), big_p Y)) False) % 3.77/3.96 (Or (Eq (big_p (skS.0 9 a_1)) True) (Eq (big_p a_2) True)) % 3.77/3.96 Clause #43 (by clausification #[41]): ∀ (a a_1 a_2 : Iota), % 3.77/3.96 Or (Eq (big_p (skS.0 9 a)) True) % 3.77/3.96 (Or (Eq (big_p a_1) True) (Or (Eq (big_p (skS.0 0 a_2)) True) (Eq (∀ (Y : Iota), big_p Y) True))) % 3.77/3.96 Clause #46 (by clausification #[43]): ∀ (a a_1 a_2 a_3 : Iota), % 3.77/3.96 Or (Eq (big_p (skS.0 9 a)) True) (Or (Eq (big_p a_1) True) (Or (Eq (big_p (skS.0 0 a_2)) True) (Eq (big_p a_3) True))) % 3.77/3.96 Clause #58 (by equality factoring #[46]): ∀ (a a_1 a_2 : Iota), % 3.77/3.96 Or (Eq (big_p (skS.0 9 a)) True) (Or (Eq (big_p (skS.0 0 a_1)) True) (Or (Ne True True) (Eq (big_p a_2) True))) % 3.77/3.96 Clause #59 (by clausification #[58]): ∀ (a a_1 a_2 : Iota), % 3.77/3.96 Or (Eq (big_p (skS.0 9 a)) True) % 3.77/3.96 (Or (Eq (big_p (skS.0 0 a_1)) True) (Or (Eq (big_p a_2) True) (Or (Eq True False) (Eq True False)))) % 3.77/3.96 Clause #61 (by clausification #[59]): ∀ (a a_1 a_2 : Iota), % 3.77/3.96 Or (Eq (big_p (skS.0 9 a)) True) (Or (Eq (big_p (skS.0 0 a_1)) True) (Or (Eq (big_p a_2) True) (Eq True False))) % 3.77/3.96 Clause #62 (by clausification #[61]): ∀ (a a_1 a_2 : Iota), Or (Eq (big_p (skS.0 9 a)) True) (Or (Eq (big_p (skS.0 0 a_1)) True) (Eq (big_p a_2) True)) % 3.77/3.96 Clause #70 (by equality factoring #[62]): ∀ (a a_1 : Iota), Or (Eq (big_p (skS.0 9 a)) True) (Or (Ne True True) (Eq (big_p (skS.0 0 a_1)) True)) % 3.77/3.96 Clause #71 (by clausification #[70]): ∀ (a a_1 : Iota), % 3.77/3.96 Or (Eq (big_p (skS.0 9 a)) True) (Or (Eq (big_p (skS.0 0 a_1)) True) (Or (Eq True False) (Eq True False))) % 3.77/3.96 Clause #73 (by clausification #[71]): ∀ (a a_1 : Iota), Or (Eq (big_p (skS.0 9 a)) True) (Or (Eq (big_p (skS.0 0 a_1)) True) (Eq True False)) % 3.77/3.96 Clause #74 (by clausification #[73]): ∀ (a a_1 : Iota), Or (Eq (big_p (skS.0 9 a)) True) (Eq (big_p (skS.0 0 a_1)) True) % 3.77/3.96 Clause #78 (by superposition #[74, 38]): ∀ (a a_1 a_2 a_3 : Iota), % 3.77/3.96 Or (Eq (big_p (skS.0 9 a)) True) % 3.77/3.96 (Or (Eq True False) (Or (Eq (big_p a_1) False) (Or (Eq (big_p a_2) True) (Eq (big_p a_3) True)))) % 3.77/3.96 Clause #83 (by clausification #[78]): ∀ (a a_1 a_2 a_3 : Iota), % 3.77/3.96 Or (Eq (big_p (skS.0 9 a)) True) (Or (Eq (big_p a_1) False) (Or (Eq (big_p a_2) True) (Eq (big_p a_3) True))) % 3.77/3.96 Clause #85 (by superposition #[83, 74]): ∀ (a a_1 a_2 a_3 : Iota), % 3.77/3.96 Or (Eq (big_p (skS.0 9 a)) True) % 3.77/3.96 (Or (Eq (big_p a_1) True) (Or (Eq (big_p a_2) True) (Or (Eq (big_p (skS.0 9 a_3)) True) (Eq False True)))) % 3.77/3.96 Clause #107 (by clausification #[85]): ∀ (a a_1 a_2 a_3 : Iota), % 3.77/3.96 Or (Eq (big_p (skS.0 9 a)) True) (Or (Eq (big_p a_1) True) (Or (Eq (big_p a_2) True) (Eq (big_p (skS.0 9 a_3)) True))) % 3.77/3.96 Clause #119 (by equality factoring #[107]): ∀ (a a_1 a_2 : Iota), % 3.77/3.96 Or (Eq (big_p a) True) (Or (Eq (big_p a_1) True) (Or (Ne True True) (Eq (big_p (skS.0 9 a_2)) True))) % 3.77/3.96 Clause #122 (by clausification #[119]): ∀ (a a_1 a_2 : Iota), % 3.77/3.96 Or (Eq (big_p a) True) % 3.77/3.96 (Or (Eq (big_p a_1) True) (Or (Eq (big_p (skS.0 9 a_2)) True) (Or (Eq True False) (Eq True False)))) % 3.77/3.96 Clause #124 (by clausification #[122]): ∀ (a a_1 a_2 : Iota), % 3.77/3.96 Or (Eq (big_p a) True) (Or (Eq (big_p a_1) True) (Or (Eq (big_p (skS.0 9 a_2)) True) (Eq True False))) % 3.77/3.96 Clause #125 (by clausification #[124]): ∀ (a a_1 a_2 : Iota), Or (Eq (big_p a) True) (Or (Eq (big_p a_1) True) (Eq (big_p (skS.0 9 a_2)) True)) % 3.77/3.96 Clause #135 (by equality factoring #[125]): ∀ (a a_1 : Iota), Or (Eq (big_p a) True) (Or (Ne True True) (Eq (big_p (skS.0 9 a_1)) True)) % 3.77/3.96 Clause #136 (by clausification #[135]): ∀ (a a_1 : Iota), Or (Eq (big_p a) True) (Or (Eq (big_p (skS.0 9 a_1)) True) (Or (Eq True False) (Eq True False))) % 3.77/3.96 Clause #138 (by clausification #[136]): ∀ (a a_1 : Iota), Or (Eq (big_p a) True) (Or (Eq (big_p (skS.0 9 a_1)) True) (Eq True False)) % 3.77/3.96 Clause #139 (by clausification #[138]): ∀ (a a_1 : Iota), Or (Eq (big_p a) True) (Eq (big_p (skS.0 9 a_1)) True) % 3.77/3.98 Clause #146 (by equality factoring #[139]): ∀ (a : Iota), Or (Ne True True) (Eq (big_p (skS.0 9 a)) True) % 3.77/3.98 Clause #148 (by clausification #[146]): ∀ (a : Iota), Or (Eq (big_p (skS.0 9 a)) True) (Or (Eq True False) (Eq True False)) % 3.77/3.98 Clause #150 (by clausification #[148]): ∀ (a : Iota), Or (Eq (big_p (skS.0 9 a)) True) (Eq True False) % 3.77/3.98 Clause #151 (by clausification #[150]): ∀ (a : Iota), Eq (big_p (skS.0 9 a)) True % 3.77/3.98 Clause #152 (by superposition #[151, 15]): ∀ (a a_1 a_2 : Iota), % 3.77/3.98 Or (Eq True False) % 3.77/3.98 (Or (Eq (big_p (skS.0 0 a)) False) (Or (Eq (big_p (skS.0 1 a_1)) False) (Eq (big_p (skS.0 2 a_2)) False))) % 3.77/3.98 Clause #153 (by superposition #[151, 38]): ∀ (a a_1 a_2 : Iota), Or (Eq True False) (Or (Eq (big_p a) False) (Or (Eq (big_p a_1) True) (Eq (big_p a_2) True))) % 3.77/3.98 Clause #155 (by clausification #[153]): ∀ (a a_1 a_2 : Iota), Or (Eq (big_p a) False) (Or (Eq (big_p a_1) True) (Eq (big_p a_2) True)) % 3.77/3.98 Clause #156 (by superposition #[155, 151]): ∀ (a a_1 : Iota), Or (Eq (big_p a) True) (Or (Eq (big_p a_1) True) (Eq False True)) % 3.77/3.98 Clause #157 (by clausification #[156]): ∀ (a a_1 : Iota), Or (Eq (big_p a) True) (Eq (big_p a_1) True) % 3.77/3.98 Clause #158 (by equality factoring #[157]): ∀ (a : Iota), Or (Ne True True) (Eq (big_p a) True) % 3.77/3.98 Clause #159 (by clausification #[158]): ∀ (a : Iota), Or (Eq (big_p a) True) (Or (Eq True False) (Eq True False)) % 3.77/3.98 Clause #161 (by clausification #[159]): ∀ (a : Iota), Or (Eq (big_p a) True) (Eq True False) % 3.77/3.98 Clause #162 (by clausification #[161]): ∀ (a : Iota), Eq (big_p a) True % 3.77/3.98 Clause #199 (by clausification #[152]): ∀ (a a_1 a_2 : Iota), % 3.77/3.98 Or (Eq (big_p (skS.0 0 a)) False) (Or (Eq (big_p (skS.0 1 a_1)) False) (Eq (big_p (skS.0 2 a_2)) False)) % 3.77/3.98 Clause #200 (by superposition #[199, 162]): ∀ (a a_1 : Iota), Or (Eq (big_p (skS.0 1 a)) False) (Or (Eq (big_p (skS.0 2 a_1)) False) (Eq False True)) % 3.77/3.98 Clause #201 (by clausification #[200]): ∀ (a a_1 : Iota), Or (Eq (big_p (skS.0 1 a)) False) (Eq (big_p (skS.0 2 a_1)) False) % 3.77/3.98 Clause #202 (by superposition #[201, 162]): ∀ (a : Iota), Or (Eq (big_p (skS.0 2 a)) False) (Eq False True) % 3.77/3.98 Clause #203 (by clausification #[202]): ∀ (a : Iota), Eq (big_p (skS.0 2 a)) False % 3.77/3.98 Clause #204 (by superposition #[203, 162]): Eq False True % 3.77/3.98 Clause #205 (by clausification #[204]): False % 3.77/3.98 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------