0.11/0.13 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.11/0.14 % Command : duper %s 0.13/0.35 % Computer : n005.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 : 1440 0.13/0.35 % WCLimit : 180 0.13/0.35 % DateTime : Mon Jul 3 03:57:15 EDT 2023 0.13/0.35 % CPUTime : 5.57/5.79 SZS status Theorem for theBenchmark.p 5.57/5.79 SZS output start Proof for theBenchmark.p 5.57/5.79 Clause #0 (by assumption #[]): Eq 5.57/5.79 (Not 5.57/5.79 (And 5.57/5.79 (And 5.57/5.79 (And 5.57/5.79 (And 5.57/5.79 (And 5.57/5.79 (And 5.57/5.79 (And 5.57/5.79 (And 5.57/5.79 (And 5.57/5.79 (And 5.57/5.79 (And 5.57/5.79 (And 5.57/5.79 (And (And (cP cS cS cS cS cO) (∀ (T2 : b), cP cS cS cN cS T2 → cP cN cS cN cS (cL T2))) 5.57/5.79 (∀ (T4 : b), cP cS cS cS cN T4 → cP cN cN cS cN (cW T4))) 5.57/5.79 (∀ (X1 Y1 : a) (V : b), cP cN X1 cN Y1 V → cP cS X1 cS Y1 (cG V))) 5.57/5.79 (∀ (T8 : b), cP cS cN cS cS T8 → cP cN cN cS cN (cD T8))) 5.57/5.79 (∀ (V1 : b), cP cN cS cN cN V1 → cP cS cS cN cS (cD V1))) 5.57/5.79 (∀ (U1 : b), cP cS cS cN cS U1 → cP cN cS cN cN (cD U1))) 5.57/5.79 (∀ (T9 : b), cP cN cN cS cN T9 → cP cS cN cS cS (cD T9))) 5.57/5.79 (∀ (X Y : a) (U : b), cP cS X cS Y U → cP cN X cN Y (cG U))) 5.57/5.79 (∀ (T7 : b), cP cN cN cN cS T7 → cP cS cS cN cS (cW T7))) 5.57/5.79 (∀ (T6 : b), cP cS cS cN cS T6 → cP cN cN cN cS (cW T6))) 5.57/5.79 (∀ (T5 : b), cP cN cN cS cN T5 → cP cS cS cS cN (cW T5))) 5.57/5.79 (∀ (T3 : b), cP cN cS cN cS T3 → cP cS cS cN cS (cL T3))) 5.57/5.79 (∀ (T1 : b), cP cN cN cS cN T1 → cP cS cN cS cN (cL T1))) 5.57/5.79 (∀ (T : b), cP cS cN cS cN T → cP cN cN cS cN (cL T)) → 5.57/5.79 Exists fun Z => cP cN cN cN cN Z)) 5.57/5.79 True 5.57/5.79 Clause #1 (by betaEtaReduce #[0]): Eq 5.57/5.79 (Not 5.57/5.79 (And 5.57/5.79 (And 5.57/5.79 (And 5.57/5.79 (And 5.57/5.79 (And 5.57/5.79 (And 5.57/5.79 (And 5.57/5.79 (And 5.57/5.79 (And 5.57/5.79 (And 5.57/5.79 (And 5.57/5.79 (And 5.57/5.79 (And (And (cP cS cS cS cS cO) (∀ (T2 : b), cP cS cS cN cS T2 → cP cN cS cN cS (cL T2))) 5.57/5.79 (∀ (T4 : b), cP cS cS cS cN T4 → cP cN cN cS cN (cW T4))) 5.57/5.79 (∀ (X1 Y1 : a) (V : b), cP cN X1 cN Y1 V → cP cS X1 cS Y1 (cG V))) 5.57/5.79 (∀ (T8 : b), cP cS cN cS cS T8 → cP cN cN cS cN (cD T8))) 5.57/5.79 (∀ (V1 : b), cP cN cS cN cN V1 → cP cS cS cN cS (cD V1))) 5.57/5.79 (∀ (U1 : b), cP cS cS cN cS U1 → cP cN cS cN cN (cD U1))) 5.57/5.79 (∀ (T9 : b), cP cN cN cS cN T9 → cP cS cN cS cS (cD T9))) 5.57/5.79 (∀ (X Y : a) (U : b), cP cS X cS Y U → cP cN X cN Y (cG U))) 5.57/5.79 (∀ (T7 : b), cP cN cN cN cS T7 → cP cS cS cN cS (cW T7))) 5.57/5.79 (∀ (T6 : b), cP cS cS cN cS T6 → cP cN cN cN cS (cW T6))) 5.57/5.79 (∀ (T5 : b), cP cN cN cS cN T5 → cP cS cS cS cN (cW T5))) 5.57/5.79 (∀ (T3 : b), cP cN cS cN cS T3 → cP cS cS cN cS (cL T3))) 5.57/5.79 (∀ (T1 : b), cP cN cN cS cN T1 → cP cS cN cS cN (cL T1))) 5.57/5.79 (∀ (T : b), cP cS cN cS cN T → cP cN cN cS cN (cL T)) → 5.57/5.79 Exists (cP cN cN cN cN))) 5.57/5.79 True 5.57/5.79 Clause #2 (by clausification #[1]): Eq 5.57/5.79 (And 5.57/5.79 (And 5.57/5.79 (And 5.57/5.79 (And 5.57/5.79 (And 5.57/5.79 (And 5.57/5.79 (And 5.57/5.79 (And 5.57/5.79 (And 5.57/5.79 (And 5.57/5.79 (And 5.57/5.79 (And 5.57/5.79 (And (And (cP cS cS cS cS cO) (∀ (T2 : b), cP cS cS cN cS T2 → cP cN cS cN cS (cL T2))) 5.57/5.79 (∀ (T4 : b), cP cS cS cS cN T4 → cP cN cN cS cN (cW T4))) 5.57/5.79 (∀ (X1 Y1 : a) (V : b), cP cN X1 cN Y1 V → cP cS X1 cS Y1 (cG V))) 5.57/5.79 (∀ (T8 : b), cP cS cN cS cS T8 → cP cN cN cS cN (cD T8))) 5.57/5.79 (∀ (V1 : b), cP cN cS cN cN V1 → cP cS cS cN cS (cD V1))) 5.57/5.79 (∀ (U1 : b), cP cS cS cN cS U1 → cP cN cS cN cN (cD U1))) 5.57/5.79 (∀ (T9 : b), cP cN cN cS cN T9 → cP cS cN cS cS (cD T9))) 5.65/5.81 (∀ (X Y : a) (U : b), cP cS X cS Y U → cP cN X cN Y (cG U))) 5.65/5.81 (∀ (T7 : b), cP cN cN cN cS T7 → cP cS cS cN cS (cW T7))) 5.65/5.81 (∀ (T6 : b), cP cS cS cN cS T6 → cP cN cN cN cS (cW T6))) 5.65/5.81 (∀ (T5 : b), cP cN cN cS cN T5 → cP cS cS cS cN (cW T5))) 5.65/5.81 (∀ (T3 : b), cP cN cS cN cS T3 → cP cS cS cN cS (cL T3))) 5.65/5.81 (∀ (T1 : b), cP cN cN cS cN T1 → cP cS cN cS cN (cL T1))) 5.65/5.81 (∀ (T : b), cP cS cN cS cN T → cP cN cN cS cN (cL T)) → 5.65/5.81 Exists (cP cN cN cN cN)) 5.65/5.81 False 5.65/5.81 Clause #3 (by clausification #[2]): Eq 5.65/5.81 (And 5.65/5.81 (And 5.65/5.81 (And 5.65/5.81 (And 5.65/5.81 (And 5.65/5.81 (And 5.65/5.81 (And 5.65/5.81 (And 5.65/5.81 (And 5.65/5.81 (And 5.65/5.81 (And 5.65/5.81 (And 5.65/5.81 (And (And (cP cS cS cS cS cO) (∀ (T2 : b), cP cS cS cN cS T2 → cP cN cS cN cS (cL T2))) 5.65/5.81 (∀ (T4 : b), cP cS cS cS cN T4 → cP cN cN cS cN (cW T4))) 5.65/5.81 (∀ (X1 Y1 : a) (V : b), cP cN X1 cN Y1 V → cP cS X1 cS Y1 (cG V))) 5.65/5.81 (∀ (T8 : b), cP cS cN cS cS T8 → cP cN cN cS cN (cD T8))) 5.65/5.81 (∀ (V1 : b), cP cN cS cN cN V1 → cP cS cS cN cS (cD V1))) 5.65/5.81 (∀ (U1 : b), cP cS cS cN cS U1 → cP cN cS cN cN (cD U1))) 5.65/5.81 (∀ (T9 : b), cP cN cN cS cN T9 → cP cS cN cS cS (cD T9))) 5.65/5.81 (∀ (X Y : a) (U : b), cP cS X cS Y U → cP cN X cN Y (cG U))) 5.65/5.81 (∀ (T7 : b), cP cN cN cN cS T7 → cP cS cS cN cS (cW T7))) 5.65/5.81 (∀ (T6 : b), cP cS cS cN cS T6 → cP cN cN cN cS (cW T6))) 5.65/5.81 (∀ (T5 : b), cP cN cN cS cN T5 → cP cS cS cS cN (cW T5))) 5.65/5.81 (∀ (T3 : b), cP cN cS cN cS T3 → cP cS cS cN cS (cL T3))) 5.65/5.81 (∀ (T1 : b), cP cN cN cS cN T1 → cP cS cN cS cN (cL T1))) 5.65/5.81 (∀ (T : b), cP cS cN cS cN T → cP cN cN cS cN (cL T))) 5.65/5.81 True 5.65/5.81 Clause #4 (by clausification #[2]): Eq (Exists (cP cN cN cN cN)) False 5.65/5.81 Clause #6 (by clausification #[3]): Eq 5.65/5.81 (And 5.65/5.81 (And 5.65/5.81 (And 5.65/5.81 (And 5.65/5.81 (And 5.65/5.81 (And 5.65/5.81 (And 5.65/5.81 (And 5.65/5.81 (And 5.65/5.81 (And 5.65/5.81 (And 5.65/5.81 (And (And (cP cS cS cS cS cO) (∀ (T2 : b), cP cS cS cN cS T2 → cP cN cS cN cS (cL T2))) 5.65/5.81 (∀ (T4 : b), cP cS cS cS cN T4 → cP cN cN cS cN (cW T4))) 5.65/5.81 (∀ (X1 Y1 : a) (V : b), cP cN X1 cN Y1 V → cP cS X1 cS Y1 (cG V))) 5.65/5.81 (∀ (T8 : b), cP cS cN cS cS T8 → cP cN cN cS cN (cD T8))) 5.65/5.81 (∀ (V1 : b), cP cN cS cN cN V1 → cP cS cS cN cS (cD V1))) 5.65/5.81 (∀ (U1 : b), cP cS cS cN cS U1 → cP cN cS cN cN (cD U1))) 5.65/5.81 (∀ (T9 : b), cP cN cN cS cN T9 → cP cS cN cS cS (cD T9))) 5.65/5.81 (∀ (X Y : a) (U : b), cP cS X cS Y U → cP cN X cN Y (cG U))) 5.65/5.81 (∀ (T7 : b), cP cN cN cN cS T7 → cP cS cS cN cS (cW T7))) 5.65/5.81 (∀ (T6 : b), cP cS cS cN cS T6 → cP cN cN cN cS (cW T6))) 5.65/5.81 (∀ (T5 : b), cP cN cN cS cN T5 → cP cS cS cS cN (cW T5))) 5.65/5.81 (∀ (T3 : b), cP cN cS cN cS T3 → cP cS cS cN cS (cL T3))) 5.65/5.81 (∀ (T1 : b), cP cN cN cS cN T1 → cP cS cN cS cN (cL T1))) 5.65/5.81 True 5.65/5.81 Clause #9 (by clausification #[4]): ∀ (a : b), Eq (cP cN cN cN cN a) False 5.65/5.81 Clause #10 (by clausification #[6]): Eq (∀ (T1 : b), cP cN cN cS cN T1 → cP cS cN cS cN (cL T1)) True 5.65/5.81 Clause #11 (by clausification #[6]): Eq 5.65/5.81 (And 5.65/5.81 (And 5.65/5.81 (And 5.65/5.81 (And 5.65/5.81 (And 5.65/5.81 (And 5.65/5.81 (And 5.65/5.81 (And 5.65/5.81 (And 5.65/5.81 (And 5.65/5.81 (And (And (cP cS cS cS cS cO) (∀ (T2 : b), cP cS cS cN cS T2 → cP cN cS cN cS (cL T2))) 5.65/5.81 (∀ (T4 : b), cP cS cS cS cN T4 → cP cN cN cS cN (cW T4))) 5.65/5.81 (∀ (X1 Y1 : a) (V : b), cP cN X1 cN Y1 V → cP cS X1 cS Y1 (cG V))) 5.65/5.81 (∀ (T8 : b), cP cS cN cS cS T8 → cP cN cN cS cN (cD T8))) 5.65/5.81 (∀ (V1 : b), cP cN cS cN cN V1 → cP cS cS cN cS (cD V1))) 5.65/5.83 (∀ (U1 : b), cP cS cS cN cS U1 → cP cN cS cN cN (cD U1))) 5.65/5.83 (∀ (T9 : b), cP cN cN cS cN T9 → cP cS cN cS cS (cD T9))) 5.65/5.83 (∀ (X Y : a) (U : b), cP cS X cS Y U → cP cN X cN Y (cG U))) 5.65/5.83 (∀ (T7 : b), cP cN cN cN cS T7 → cP cS cS cN cS (cW T7))) 5.65/5.83 (∀ (T6 : b), cP cS cS cN cS T6 → cP cN cN cN cS (cW T6))) 5.65/5.83 (∀ (T5 : b), cP cN cN cS cN T5 → cP cS cS cS cN (cW T5))) 5.65/5.83 (∀ (T3 : b), cP cN cS cN cS T3 → cP cS cS cN cS (cL T3))) 5.65/5.83 True 5.65/5.83 Clause #12 (by clausification #[10]): ∀ (a : b), Eq (cP cN cN cS cN a → cP cS cN cS cN (cL a)) True 5.65/5.83 Clause #13 (by clausification #[12]): ∀ (a : b), Or (Eq (cP cN cN cS cN a) False) (Eq (cP cS cN cS cN (cL a)) True) 5.65/5.83 Clause #14 (by clausification #[11]): Eq (∀ (T3 : b), cP cN cS cN cS T3 → cP cS cS cN cS (cL T3)) True 5.65/5.83 Clause #15 (by clausification #[11]): Eq 5.65/5.83 (And 5.65/5.83 (And 5.65/5.83 (And 5.65/5.83 (And 5.65/5.83 (And 5.65/5.83 (And 5.65/5.83 (And 5.65/5.83 (And 5.65/5.83 (And 5.65/5.83 (And (And (cP cS cS cS cS cO) (∀ (T2 : b), cP cS cS cN cS T2 → cP cN cS cN cS (cL T2))) 5.65/5.83 (∀ (T4 : b), cP cS cS cS cN T4 → cP cN cN cS cN (cW T4))) 5.65/5.83 (∀ (X1 Y1 : a) (V : b), cP cN X1 cN Y1 V → cP cS X1 cS Y1 (cG V))) 5.65/5.83 (∀ (T8 : b), cP cS cN cS cS T8 → cP cN cN cS cN (cD T8))) 5.65/5.83 (∀ (V1 : b), cP cN cS cN cN V1 → cP cS cS cN cS (cD V1))) 5.65/5.83 (∀ (U1 : b), cP cS cS cN cS U1 → cP cN cS cN cN (cD U1))) 5.65/5.83 (∀ (T9 : b), cP cN cN cS cN T9 → cP cS cN cS cS (cD T9))) 5.65/5.83 (∀ (X Y : a) (U : b), cP cS X cS Y U → cP cN X cN Y (cG U))) 5.65/5.83 (∀ (T7 : b), cP cN cN cN cS T7 → cP cS cS cN cS (cW T7))) 5.65/5.83 (∀ (T6 : b), cP cS cS cN cS T6 → cP cN cN cN cS (cW T6))) 5.65/5.83 (∀ (T5 : b), cP cN cN cS cN T5 → cP cS cS cS cN (cW T5))) 5.65/5.83 True 5.65/5.83 Clause #16 (by clausification #[14]): ∀ (a : b), Eq (cP cN cS cN cS a → cP cS cS cN cS (cL a)) True 5.65/5.83 Clause #17 (by clausification #[16]): ∀ (a : b), Or (Eq (cP cN cS cN cS a) False) (Eq (cP cS cS cN cS (cL a)) True) 5.65/5.83 Clause #19 (by clausification #[15]): Eq 5.65/5.83 (And 5.65/5.83 (And 5.65/5.83 (And 5.65/5.83 (And 5.65/5.83 (And 5.65/5.83 (And 5.65/5.83 (And 5.65/5.83 (And 5.65/5.83 (And (And (cP cS cS cS cS cO) (∀ (T2 : b), cP cS cS cN cS T2 → cP cN cS cN cS (cL T2))) 5.65/5.83 (∀ (T4 : b), cP cS cS cS cN T4 → cP cN cN cS cN (cW T4))) 5.65/5.83 (∀ (X1 Y1 : a) (V : b), cP cN X1 cN Y1 V → cP cS X1 cS Y1 (cG V))) 5.65/5.83 (∀ (T8 : b), cP cS cN cS cS T8 → cP cN cN cS cN (cD T8))) 5.65/5.83 (∀ (V1 : b), cP cN cS cN cN V1 → cP cS cS cN cS (cD V1))) 5.65/5.83 (∀ (U1 : b), cP cS cS cN cS U1 → cP cN cS cN cN (cD U1))) 5.65/5.83 (∀ (T9 : b), cP cN cN cS cN T9 → cP cS cN cS cS (cD T9))) 5.65/5.83 (∀ (X Y : a) (U : b), cP cS X cS Y U → cP cN X cN Y (cG U))) 5.65/5.83 (∀ (T7 : b), cP cN cN cN cS T7 → cP cS cS cN cS (cW T7))) 5.65/5.83 (∀ (T6 : b), cP cS cS cN cS T6 → cP cN cN cN cS (cW T6))) 5.65/5.83 True 5.65/5.83 Clause #22 (by clausification #[19]): Eq (∀ (T6 : b), cP cS cS cN cS T6 → cP cN cN cN cS (cW T6)) True 5.65/5.83 Clause #23 (by clausification #[19]): Eq 5.65/5.83 (And 5.65/5.83 (And 5.65/5.83 (And 5.65/5.83 (And 5.65/5.83 (And 5.65/5.83 (And 5.65/5.83 (And 5.65/5.83 (And (And (cP cS cS cS cS cO) (∀ (T2 : b), cP cS cS cN cS T2 → cP cN cS cN cS (cL T2))) 5.65/5.83 (∀ (T4 : b), cP cS cS cS cN T4 → cP cN cN cS cN (cW T4))) 5.65/5.83 (∀ (X1 Y1 : a) (V : b), cP cN X1 cN Y1 V → cP cS X1 cS Y1 (cG V))) 5.65/5.83 (∀ (T8 : b), cP cS cN cS cS T8 → cP cN cN cS cN (cD T8))) 5.65/5.83 (∀ (V1 : b), cP cN cS cN cN V1 → cP cS cS cN cS (cD V1))) 5.65/5.83 (∀ (U1 : b), cP cS cS cN cS U1 → cP cN cS cN cN (cD U1))) 5.65/5.83 (∀ (T9 : b), cP cN cN cS cN T9 → cP cS cN cS cS (cD T9))) 5.65/5.83 (∀ (X Y : a) (U : b), cP cS X cS Y U → cP cN X cN Y (cG U))) 5.65/5.83 (∀ (T7 : b), cP cN cN cN cS T7 → cP cS cS cN cS (cW T7))) 5.65/5.83 True 5.65/5.83 Clause #24 (by clausification #[22]): ∀ (a : b), Eq (cP cS cS cN cS a → cP cN cN cN cS (cW a)) True 5.65/5.85 Clause #25 (by clausification #[24]): ∀ (a : b), Or (Eq (cP cS cS cN cS a) False) (Eq (cP cN cN cN cS (cW a)) True) 5.65/5.85 Clause #27 (by clausification #[23]): Eq 5.65/5.85 (And 5.65/5.85 (And 5.65/5.85 (And 5.65/5.85 (And 5.65/5.85 (And 5.65/5.85 (And 5.65/5.85 (And (And (cP cS cS cS cS cO) (∀ (T2 : b), cP cS cS cN cS T2 → cP cN cS cN cS (cL T2))) 5.65/5.85 (∀ (T4 : b), cP cS cS cS cN T4 → cP cN cN cS cN (cW T4))) 5.65/5.85 (∀ (X1 Y1 : a) (V : b), cP cN X1 cN Y1 V → cP cS X1 cS Y1 (cG V))) 5.65/5.85 (∀ (T8 : b), cP cS cN cS cS T8 → cP cN cN cS cN (cD T8))) 5.65/5.85 (∀ (V1 : b), cP cN cS cN cN V1 → cP cS cS cN cS (cD V1))) 5.65/5.85 (∀ (U1 : b), cP cS cS cN cS U1 → cP cN cS cN cN (cD U1))) 5.65/5.85 (∀ (T9 : b), cP cN cN cS cN T9 → cP cS cN cS cS (cD T9))) 5.65/5.85 (∀ (X Y : a) (U : b), cP cS X cS Y U → cP cN X cN Y (cG U))) 5.65/5.85 True 5.65/5.85 Clause #30 (by clausification #[27]): Eq (∀ (X Y : a) (U : b), cP cS X cS Y U → cP cN X cN Y (cG U)) True 5.65/5.85 Clause #31 (by clausification #[27]): Eq 5.65/5.85 (And 5.65/5.85 (And 5.65/5.85 (And 5.65/5.85 (And 5.65/5.85 (And 5.65/5.85 (And (And (cP cS cS cS cS cO) (∀ (T2 : b), cP cS cS cN cS T2 → cP cN cS cN cS (cL T2))) 5.65/5.85 (∀ (T4 : b), cP cS cS cS cN T4 → cP cN cN cS cN (cW T4))) 5.65/5.85 (∀ (X1 Y1 : a) (V : b), cP cN X1 cN Y1 V → cP cS X1 cS Y1 (cG V))) 5.65/5.85 (∀ (T8 : b), cP cS cN cS cS T8 → cP cN cN cS cN (cD T8))) 5.65/5.85 (∀ (V1 : b), cP cN cS cN cN V1 → cP cS cS cN cS (cD V1))) 5.65/5.85 (∀ (U1 : b), cP cS cS cN cS U1 → cP cN cS cN cN (cD U1))) 5.65/5.85 (∀ (T9 : b), cP cN cN cS cN T9 → cP cS cN cS cS (cD T9))) 5.65/5.85 True 5.65/5.85 Clause #32 (by clausification #[30]): ∀ (a_1 : a), Eq (∀ (Y : a) (U : b), cP cS a_1 cS Y U → cP cN a_1 cN Y (cG U)) True 5.65/5.85 Clause #33 (by clausification #[32]): ∀ (a_1 a : a), Eq (∀ (U : b), cP cS a_1 cS a U → cP cN a_1 cN a (cG U)) True 5.65/5.85 Clause #34 (by clausification #[33]): ∀ (a_1 a : a) (a_2 : b), Eq (cP cS a_1 cS a a_2 → cP cN a_1 cN a (cG a_2)) True 5.65/5.85 Clause #35 (by clausification #[34]): ∀ (a_1 a : a) (a_2 : b), Or (Eq (cP cS a_1 cS a a_2) False) (Eq (cP cN a_1 cN a (cG a_2)) True) 5.65/5.85 Clause #37 (by clausification #[31]): Eq 5.65/5.85 (And 5.65/5.85 (And 5.65/5.85 (And 5.65/5.85 (And 5.65/5.85 (And (And (cP cS cS cS cS cO) (∀ (T2 : b), cP cS cS cN cS T2 → cP cN cS cN cS (cL T2))) 5.65/5.85 (∀ (T4 : b), cP cS cS cS cN T4 → cP cN cN cS cN (cW T4))) 5.65/5.85 (∀ (X1 Y1 : a) (V : b), cP cN X1 cN Y1 V → cP cS X1 cS Y1 (cG V))) 5.65/5.85 (∀ (T8 : b), cP cS cN cS cS T8 → cP cN cN cS cN (cD T8))) 5.65/5.85 (∀ (V1 : b), cP cN cS cN cN V1 → cP cS cS cN cS (cD V1))) 5.65/5.85 (∀ (U1 : b), cP cS cS cN cS U1 → cP cN cS cN cN (cD U1))) 5.65/5.85 True 5.65/5.85 Clause #41 (by clausification #[37]): Eq 5.65/5.85 (And 5.65/5.85 (And 5.65/5.85 (And 5.65/5.85 (And (And (cP cS cS cS cS cO) (∀ (T2 : b), cP cS cS cN cS T2 → cP cN cS cN cS (cL T2))) 5.65/5.85 (∀ (T4 : b), cP cS cS cS cN T4 → cP cN cN cS cN (cW T4))) 5.65/5.85 (∀ (X1 Y1 : a) (V : b), cP cN X1 cN Y1 V → cP cS X1 cS Y1 (cG V))) 5.65/5.85 (∀ (T8 : b), cP cS cN cS cS T8 → cP cN cN cS cN (cD T8))) 5.65/5.85 (∀ (V1 : b), cP cN cS cN cN V1 → cP cS cS cN cS (cD V1))) 5.65/5.85 True 5.65/5.85 Clause #45 (by clausification #[41]): Eq 5.65/5.85 (And 5.65/5.85 (And 5.65/5.85 (And (And (cP cS cS cS cS cO) (∀ (T2 : b), cP cS cS cN cS T2 → cP cN cS cN cS (cL T2))) 5.65/5.85 (∀ (T4 : b), cP cS cS cS cN T4 → cP cN cN cS cN (cW T4))) 5.65/5.85 (∀ (X1 Y1 : a) (V : b), cP cN X1 cN Y1 V → cP cS X1 cS Y1 (cG V))) 5.65/5.85 (∀ (T8 : b), cP cS cN cS cS T8 → cP cN cN cS cN (cD T8))) 5.65/5.85 True 5.65/5.85 Clause #48 (by clausification #[45]): Eq (∀ (T8 : b), cP cS cN cS cS T8 → cP cN cN cS cN (cD T8)) True 5.65/5.85 Clause #49 (by clausification #[45]): Eq 5.65/5.85 (And 5.65/5.85 (And (And (cP cS cS cS cS cO) (∀ (T2 : b), cP cS cS cN cS T2 → cP cN cS cN cS (cL T2))) 5.65/5.85 (∀ (T4 : b), cP cS cS cS cN T4 → cP cN cN cS cN (cW T4))) 5.65/5.85 (∀ (X1 Y1 : a) (V : b), cP cN X1 cN Y1 V → cP cS X1 cS Y1 (cG V))) 5.65/5.85 True 5.65/5.85 Clause #50 (by clausification #[48]): ∀ (a : b), Eq (cP cS cN cS cS a → cP cN cN cS cN (cD a)) True 5.65/5.87 Clause #51 (by clausification #[50]): ∀ (a : b), Or (Eq (cP cS cN cS cS a) False) (Eq (cP cN cN cS cN (cD a)) True) 5.65/5.87 Clause #52 (by clausification #[49]): Eq (∀ (X1 Y1 : a) (V : b), cP cN X1 cN Y1 V → cP cS X1 cS Y1 (cG V)) True 5.65/5.87 Clause #53 (by clausification #[49]): Eq 5.65/5.87 (And (And (cP cS cS cS cS cO) (∀ (T2 : b), cP cS cS cN cS T2 → cP cN cS cN cS (cL T2))) 5.65/5.87 (∀ (T4 : b), cP cS cS cS cN T4 → cP cN cN cS cN (cW T4))) 5.65/5.87 True 5.65/5.87 Clause #54 (by clausification #[52]): ∀ (a_1 : a), Eq (∀ (Y1 : a) (V : b), cP cN a_1 cN Y1 V → cP cS a_1 cS Y1 (cG V)) True 5.65/5.87 Clause #55 (by clausification #[54]): ∀ (a_1 a : a), Eq (∀ (V : b), cP cN a_1 cN a V → cP cS a_1 cS a (cG V)) True 5.65/5.87 Clause #56 (by clausification #[55]): ∀ (a_1 a : a) (a_2 : b), Eq (cP cN a_1 cN a a_2 → cP cS a_1 cS a (cG a_2)) True 5.65/5.87 Clause #57 (by clausification #[56]): ∀ (a_1 a : a) (a_2 : b), Or (Eq (cP cN a_1 cN a a_2) False) (Eq (cP cS a_1 cS a (cG a_2)) True) 5.65/5.87 Clause #59 (by clausification #[53]): Eq (And (cP cS cS cS cS cO) (∀ (T2 : b), cP cS cS cN cS T2 → cP cN cS cN cS (cL T2))) True 5.65/5.87 Clause #63 (by clausification #[59]): Eq (cP cS cS cS cS cO) True 5.65/5.87 Clause #66 (by superposition #[63, 35]): Or (Eq True False) (Eq (cP cN cS cN cS (cG cO)) True) 5.65/5.87 Clause #67 (by clausification #[66]): Eq (cP cN cS cN cS (cG cO)) True 5.65/5.87 Clause #68 (by superposition #[67, 17]): Or (Eq True False) (Eq (cP cS cS cN cS (cL (cG cO))) True) 5.65/5.87 Clause #70 (by clausification #[68]): Eq (cP cS cS cN cS (cL (cG cO))) True 5.65/5.87 Clause #71 (by superposition #[70, 25]): Or (Eq True False) (Eq (cP cN cN cN cS (cW (cL (cG cO)))) True) 5.65/5.87 Clause #82 (by clausification #[71]): Eq (cP cN cN cN cS (cW (cL (cG cO)))) True 5.65/5.87 Clause #84 (by superposition #[82, 57]): Or (Eq True False) (Eq (cP cS cN cS cS (cG (cW (cL (cG cO))))) True) 5.65/5.87 Clause #98 (by clausification #[84]): Eq (cP cS cN cS cS (cG (cW (cL (cG cO))))) True 5.65/5.87 Clause #99 (by superposition #[98, 51]): Or (Eq True False) (Eq (cP cN cN cS cN (cD (cG (cW (cL (cG cO)))))) True) 5.65/5.87 Clause #153 (by clausification #[99]): Eq (cP cN cN cS cN (cD (cG (cW (cL (cG cO)))))) True 5.65/5.87 Clause #154 (by superposition #[153, 13]): Or (Eq True False) (Eq (cP cS cN cS cN (cL (cD (cG (cW (cL (cG cO))))))) True) 5.65/5.87 Clause #278 (by clausification #[154]): Eq (cP cS cN cS cN (cL (cD (cG (cW (cL (cG cO))))))) True 5.65/5.87 Clause #280 (by superposition #[278, 35]): Or (Eq True False) (Eq (cP cN cN cN cN (cG (cL (cD (cG (cW (cL (cG cO)))))))) True) 5.65/5.87 Clause #370 (by clausification #[280]): Eq (cP cN cN cN cN (cG (cL (cD (cG (cW (cL (cG cO)))))))) True 5.65/5.87 Clause #371 (by superposition #[370, 9]): Eq True False 5.65/5.87 Clause #373 (by clausification #[371]): False 5.65/5.87 SZS output end Proof for theBenchmark.p 5.65/5.87 EOF