%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : KRS127+1 : TPTP v9.2.0. Released v3.1.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n015.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 07:52:40 PM UTC 2025 % Result : Unsatisfiable 3.91s 4.09s % Output : Proof 3.91s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : KRS127+1 : TPTP v9.2.0. Released v3.1.0. % 0.03/0.14 % Command : duper %s % 0.14/0.35 % Computer : n015.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 : Thu Oct 2 10:11:53 EDT 2025 % 0.14/0.35 % CPUTime : % 3.91/4.09 SZS status Theorem for theBenchmark.p % 3.91/4.09 SZS output start Proof for theBenchmark.p % 3.91/4.09 Clause #14 (by assumption #[]): Eq % 3.91/4.09 (∀ (X : Iota), % 3.91/4.09 Iff (cUnsatisfiable X) % 3.91/4.09 (And (And (Exists fun Y => And (rr X Y) (cc Y)) (Exists fun Y => And (rr X Y) (cd Y))) % 3.91/4.09 (∀ (Y0 Y1 : Iota), And (rr X Y0) (rr X Y1) → Eq Y0 Y1))) % 3.91/4.09 True % 3.91/4.09 Clause #15 (by assumption #[]): Eq (∀ (X : Iota), cc X → cdxcomp X) True % 3.91/4.09 Clause #16 (by assumption #[]): Eq (∀ (X : Iota), Iff (cd X) (Not (Exists fun Y => ra_Px1 X Y))) True % 3.91/4.09 Clause #17 (by assumption #[]): Eq (∀ (X : Iota), Iff (cdxcomp X) (Exists fun Y0 => ra_Px1 X Y0)) True % 3.91/4.09 Clause #18 (by assumption #[]): Eq (cUnsatisfiable i2003_11_14_17_22_27794) True % 3.91/4.09 Clause #19 (by clausification #[15]): ∀ (a : Iota), Eq (cc a → cdxcomp a) True % 3.91/4.09 Clause #20 (by clausification #[19]): ∀ (a : Iota), Or (Eq (cc a) False) (Eq (cdxcomp a) True) % 3.91/4.09 Clause #104 (by clausification #[14]): ∀ (a : Iota), % 3.91/4.09 Eq % 3.91/4.09 (Iff (cUnsatisfiable a) % 3.91/4.09 (And (And (Exists fun Y => And (rr a Y) (cc Y)) (Exists fun Y => And (rr a Y) (cd Y))) % 3.91/4.09 (∀ (Y0 Y1 : Iota), And (rr a Y0) (rr a Y1) → Eq Y0 Y1))) % 3.91/4.09 True % 3.91/4.09 Clause #106 (by clausification #[104]): ∀ (a : Iota), % 3.91/4.09 Or (Eq (cUnsatisfiable a) False) % 3.91/4.09 (Eq % 3.91/4.09 (And (And (Exists fun Y => And (rr a Y) (cc Y)) (Exists fun Y => And (rr a Y) (cd Y))) % 3.91/4.09 (∀ (Y0 Y1 : Iota), And (rr a Y0) (rr a Y1) → Eq Y0 Y1)) % 3.91/4.09 True) % 3.91/4.09 Clause #121 (by betaEtaReduce #[17]): Eq (∀ (X : Iota), Iff (cdxcomp X) (Exists (ra_Px1 X))) True % 3.91/4.09 Clause #122 (by clausification #[121]): ∀ (a : Iota), Eq (Iff (cdxcomp a) (Exists (ra_Px1 a))) True % 3.91/4.09 Clause #124 (by clausification #[122]): ∀ (a : Iota), Or (Eq (cdxcomp a) False) (Eq (Exists (ra_Px1 a)) True) % 3.91/4.09 Clause #126 (by clausification #[124]): ∀ (a a_1 : Iota), Or (Eq (cdxcomp a) False) (Eq (ra_Px1 a (skS.0 2 a a_1)) True) % 3.91/4.09 Clause #127 (by betaEtaReduce #[16]): Eq (∀ (X : Iota), Iff (cd X) (Not (Exists (ra_Px1 X)))) True % 3.91/4.09 Clause #128 (by clausification #[127]): ∀ (a : Iota), Eq (Iff (cd a) (Not (Exists (ra_Px1 a)))) True % 3.91/4.09 Clause #130 (by clausification #[128]): ∀ (a : Iota), Or (Eq (cd a) False) (Eq (Not (Exists (ra_Px1 a))) True) % 3.91/4.09 Clause #136 (by clausification #[106]): ∀ (a : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (∀ (Y0 Y1 : Iota), And (rr a Y0) (rr a Y1) → Eq Y0 Y1) True) % 3.91/4.09 Clause #137 (by clausification #[106]): ∀ (a : Iota), % 3.91/4.09 Or (Eq (cUnsatisfiable a) False) % 3.91/4.09 (Eq (And (Exists fun Y => And (rr a Y) (cc Y)) (Exists fun Y => And (rr a Y) (cd Y))) True) % 3.91/4.09 Clause #138 (by clausification #[136]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (∀ (Y1 : Iota), And (rr a a_1) (rr a Y1) → Eq a_1 Y1) True) % 3.91/4.09 Clause #139 (by clausification #[138]): ∀ (a a_1 a_2 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (And (rr a a_1) (rr a a_2) → Eq a_1 a_2) True) % 3.91/4.09 Clause #140 (by clausification #[139]): ∀ (a a_1 a_2 : Iota), % 3.91/4.09 Or (Eq (cUnsatisfiable a) False) (Or (Eq (And (rr a a_1) (rr a a_2)) False) (Eq (Eq a_1 a_2) True)) % 3.91/4.09 Clause #141 (by clausification #[140]): ∀ (a a_1 a_2 : Iota), % 3.91/4.09 Or (Eq (cUnsatisfiable a) False) (Or (Eq (Eq a_1 a_2) True) (Or (Eq (rr a a_1) False) (Eq (rr a a_2) False))) % 3.91/4.09 Clause #142 (by clausification #[141]): ∀ (a a_1 a_2 : Iota), % 3.91/4.09 Or (Eq (cUnsatisfiable a) False) (Or (Eq (rr a a_1) False) (Or (Eq (rr a a_2) False) (Eq a_1 a_2))) % 3.91/4.09 Clause #143 (by superposition #[142, 18]): ∀ (a a_1 : Iota), % 3.91/4.09 Or (Eq (rr i2003_11_14_17_22_27794 a) False) % 3.91/4.09 (Or (Eq (rr i2003_11_14_17_22_27794 a_1) False) (Or (Eq a a_1) (Eq False True))) % 3.91/4.09 Clause #144 (by clausification #[130]): ∀ (a : Iota), Or (Eq (cd a) False) (Eq (Exists (ra_Px1 a)) False) % 3.91/4.09 Clause #145 (by clausification #[144]): ∀ (a a_1 : Iota), Or (Eq (cd a) False) (Eq (ra_Px1 a a_1) False) % 3.91/4.09 Clause #146 (by clausification #[143]): ∀ (a a_1 : Iota), % 3.91/4.09 Or (Eq (rr i2003_11_14_17_22_27794 a) False) (Or (Eq (rr i2003_11_14_17_22_27794 a_1) False) (Eq a a_1)) % 3.91/4.09 Clause #148 (by clausification #[137]): ∀ (a : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (Exists fun Y => And (rr a Y) (cd Y)) True) % 3.91/4.09 Clause #149 (by clausification #[137]): ∀ (a : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (Exists fun Y => And (rr a Y) (cc Y)) True) % 3.91/4.11 Clause #150 (by clausification #[148]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (And (rr a (skS.0 4 a a_1)) (cd (skS.0 4 a a_1))) True) % 3.91/4.11 Clause #151 (by clausification #[150]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (cd (skS.0 4 a a_1)) True) % 3.91/4.11 Clause #152 (by clausification #[150]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (rr a (skS.0 4 a a_1)) True) % 3.91/4.11 Clause #153 (by superposition #[151, 18]): ∀ (a : Iota), Or (Eq (cd (skS.0 4 i2003_11_14_17_22_27794 a)) True) (Eq False True) % 3.91/4.11 Clause #154 (by clausification #[153]): ∀ (a : Iota), Eq (cd (skS.0 4 i2003_11_14_17_22_27794 a)) True % 3.91/4.11 Clause #155 (by superposition #[154, 145]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (ra_Px1 (skS.0 4 i2003_11_14_17_22_27794 a) a_1) False) % 3.91/4.11 Clause #157 (by clausification #[149]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (And (rr a (skS.0 5 a a_1)) (cc (skS.0 5 a a_1))) True) % 3.91/4.11 Clause #158 (by clausification #[157]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (cc (skS.0 5 a a_1)) True) % 3.91/4.11 Clause #159 (by clausification #[157]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (rr a (skS.0 5 a a_1)) True) % 3.91/4.11 Clause #160 (by superposition #[158, 18]): ∀ (a : Iota), Or (Eq (cc (skS.0 5 i2003_11_14_17_22_27794 a)) True) (Eq False True) % 3.91/4.11 Clause #161 (by clausification #[160]): ∀ (a : Iota), Eq (cc (skS.0 5 i2003_11_14_17_22_27794 a)) True % 3.91/4.11 Clause #162 (by superposition #[161, 20]): ∀ (a : Iota), Or (Eq True False) (Eq (cdxcomp (skS.0 5 i2003_11_14_17_22_27794 a)) True) % 3.91/4.11 Clause #163 (by clausification #[162]): ∀ (a : Iota), Eq (cdxcomp (skS.0 5 i2003_11_14_17_22_27794 a)) True % 3.91/4.11 Clause #164 (by superposition #[163, 126]): ∀ (a a_1 : Iota), % 3.91/4.11 Or (Eq True False) % 3.91/4.11 (Eq (ra_Px1 (skS.0 5 i2003_11_14_17_22_27794 a) (skS.0 2 (skS.0 5 i2003_11_14_17_22_27794 a) a_1)) True) % 3.91/4.11 Clause #165 (by clausification #[155]): ∀ (a a_1 : Iota), Eq (ra_Px1 (skS.0 4 i2003_11_14_17_22_27794 a) a_1) False % 3.91/4.11 Clause #166 (by superposition #[159, 18]): ∀ (a : Iota), Or (Eq (rr i2003_11_14_17_22_27794 (skS.0 5 i2003_11_14_17_22_27794 a)) True) (Eq False True) % 3.91/4.11 Clause #167 (by clausification #[166]): ∀ (a : Iota), Eq (rr i2003_11_14_17_22_27794 (skS.0 5 i2003_11_14_17_22_27794 a)) True % 3.91/4.11 Clause #172 (by superposition #[152, 18]): ∀ (a : Iota), Or (Eq (rr i2003_11_14_17_22_27794 (skS.0 4 i2003_11_14_17_22_27794 a)) True) (Eq False True) % 3.91/4.11 Clause #173 (by clausification #[172]): ∀ (a : Iota), Eq (rr i2003_11_14_17_22_27794 (skS.0 4 i2003_11_14_17_22_27794 a)) True % 3.91/4.11 Clause #174 (by superposition #[173, 146]): ∀ (a a_1 : Iota), % 3.91/4.11 Or (Eq True False) (Or (Eq (rr i2003_11_14_17_22_27794 a) False) (Eq (skS.0 4 i2003_11_14_17_22_27794 a_1) a)) % 3.91/4.11 Clause #178 (by clausification #[174]): ∀ (a a_1 : Iota), Or (Eq (rr i2003_11_14_17_22_27794 a) False) (Eq (skS.0 4 i2003_11_14_17_22_27794 a_1) a) % 3.91/4.11 Clause #179 (by superposition #[178, 167]): ∀ (a a_1 : Iota), Or (Eq (skS.0 4 i2003_11_14_17_22_27794 a) (skS.0 5 i2003_11_14_17_22_27794 a_1)) (Eq False True) % 3.91/4.11 Clause #184 (by clausification #[164]): ∀ (a a_1 : Iota), Eq (ra_Px1 (skS.0 5 i2003_11_14_17_22_27794 a) (skS.0 2 (skS.0 5 i2003_11_14_17_22_27794 a) a_1)) True % 3.91/4.11 Clause #188 (by clausification #[179]): ∀ (a a_1 : Iota), Eq (skS.0 4 i2003_11_14_17_22_27794 a) (skS.0 5 i2003_11_14_17_22_27794 a_1) % 3.91/4.11 Clause #190 (by superposition #[188, 165]): ∀ (a a_1 : Iota), Eq (ra_Px1 (skS.0 5 i2003_11_14_17_22_27794 a) a_1) False % 3.91/4.11 Clause #200 (by superposition #[190, 184]): Eq False True % 3.91/4.11 Clause #202 (by clausification #[200]): False % 3.91/4.11 SZS output end Proof for theBenchmark.p 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