TSTP Solution File: PUZ047^5 by Duper---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : PUZ047^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n027.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 : Thu Aug 31 13:14:32 EDT 2023
% Result : Theorem 5.28s 5.48s
% Output : Proof 5.36s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : PUZ047^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : duper %s
% 0.16/0.35 % Computer : n027.cluster.edu
% 0.16/0.35 % Model : x86_64 x86_64
% 0.16/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.35 % Memory : 8042.1875MB
% 0.16/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.35 % CPULimit : 300
% 0.16/0.35 % WCLimit : 300
% 0.16/0.35 % DateTime : Sat Aug 26 23:11:05 EDT 2023
% 0.16/0.35 % CPUTime :
% 5.28/5.48 SZS status Theorem for theBenchmark.p
% 5.28/5.48 SZS output start Proof for theBenchmark.p
% 5.28/5.48 Clause #0 (by assumption #[]): Eq
% 5.28/5.48 (Not
% 5.28/5.48 (And
% 5.28/5.48 (And
% 5.28/5.48 (And
% 5.28/5.48 (And
% 5.28/5.48 (And
% 5.28/5.48 (And
% 5.28/5.48 (And
% 5.28/5.48 (And
% 5.28/5.48 (And
% 5.28/5.48 (And
% 5.28/5.48 (And
% 5.28/5.48 (And
% 5.28/5.48 (And (And (cP cS cS cS cS cO) (∀ (T : b), cP cS cN cS cN T → cP cN cN cS cN (cL T)))
% 5.28/5.48 (∀ (T1 : b), cP cN cN cS cN T1 → cP cS cN cS cN (cL T1)))
% 5.28/5.48 (∀ (T2 : b), cP cS cS cN cS T2 → cP cN cS cN cS (cL T2)))
% 5.28/5.48 (∀ (T3 : b), cP cN cS cN cS T3 → cP cS cS cN cS (cL T3)))
% 5.28/5.48 (∀ (T4 : b), cP cS cS cS cN T4 → cP cN cN cS cN (cW T4)))
% 5.28/5.48 (∀ (T5 : b), cP cN cN cS cN T5 → cP cS cS cS cN (cW T5)))
% 5.28/5.48 (∀ (T6 : b), cP cS cS cN cS T6 → cP cN cN cN cS (cW T6)))
% 5.28/5.48 (∀ (T7 : b), cP cN cN cN cS T7 → cP cS cS cN cS (cW T7)))
% 5.28/5.48 (∀ (X Y : a) (U : b), cP cS X cS Y U → cP cN X cN Y (cG U)))
% 5.28/5.48 (∀ (X1 Y1 : a) (V : b), cP cN X1 cN Y1 V → cP cS X1 cS Y1 (cG V)))
% 5.28/5.48 (∀ (T8 : b), cP cS cN cS cS T8 → cP cN cN cS cN (cD T8)))
% 5.28/5.48 (∀ (T9 : b), cP cN cN cS cN T9 → cP cS cN cS cS (cD T9)))
% 5.28/5.48 (∀ (U1 : b), cP cS cS cN cS U1 → cP cN cS cN cN (cD U1)))
% 5.28/5.48 (∀ (V1 : b), cP cN cS cN cN V1 → cP cS cS cN cS (cD V1)) →
% 5.28/5.48 Exists fun Z => cP cN cN cN cN Z))
% 5.28/5.48 True
% 5.28/5.48 Clause #1 (by betaEtaReduce #[0]): Eq
% 5.28/5.48 (Not
% 5.28/5.48 (And
% 5.28/5.48 (And
% 5.28/5.48 (And
% 5.28/5.48 (And
% 5.28/5.48 (And
% 5.28/5.48 (And
% 5.28/5.48 (And
% 5.28/5.48 (And
% 5.28/5.48 (And
% 5.28/5.48 (And
% 5.28/5.48 (And
% 5.28/5.48 (And
% 5.28/5.48 (And (And (cP cS cS cS cS cO) (∀ (T : b), cP cS cN cS cN T → cP cN cN cS cN (cL T)))
% 5.28/5.48 (∀ (T1 : b), cP cN cN cS cN T1 → cP cS cN cS cN (cL T1)))
% 5.28/5.48 (∀ (T2 : b), cP cS cS cN cS T2 → cP cN cS cN cS (cL T2)))
% 5.28/5.48 (∀ (T3 : b), cP cN cS cN cS T3 → cP cS cS cN cS (cL T3)))
% 5.28/5.48 (∀ (T4 : b), cP cS cS cS cN T4 → cP cN cN cS cN (cW T4)))
% 5.28/5.48 (∀ (T5 : b), cP cN cN cS cN T5 → cP cS cS cS cN (cW T5)))
% 5.28/5.48 (∀ (T6 : b), cP cS cS cN cS T6 → cP cN cN cN cS (cW T6)))
% 5.28/5.48 (∀ (T7 : b), cP cN cN cN cS T7 → cP cS cS cN cS (cW T7)))
% 5.28/5.48 (∀ (X Y : a) (U : b), cP cS X cS Y U → cP cN X cN Y (cG U)))
% 5.28/5.48 (∀ (X1 Y1 : a) (V : b), cP cN X1 cN Y1 V → cP cS X1 cS Y1 (cG V)))
% 5.28/5.48 (∀ (T8 : b), cP cS cN cS cS T8 → cP cN cN cS cN (cD T8)))
% 5.28/5.48 (∀ (T9 : b), cP cN cN cS cN T9 → cP cS cN cS cS (cD T9)))
% 5.28/5.48 (∀ (U1 : b), cP cS cS cN cS U1 → cP cN cS cN cN (cD U1)))
% 5.28/5.48 (∀ (V1 : b), cP cN cS cN cN V1 → cP cS cS cN cS (cD V1)) →
% 5.28/5.48 Exists (cP cN cN cN cN)))
% 5.28/5.48 True
% 5.28/5.48 Clause #2 (by clausification #[1]): Eq
% 5.28/5.48 (And
% 5.28/5.48 (And
% 5.28/5.48 (And
% 5.28/5.48 (And
% 5.28/5.48 (And
% 5.28/5.48 (And
% 5.28/5.48 (And
% 5.28/5.48 (And
% 5.28/5.48 (And
% 5.28/5.48 (And
% 5.28/5.48 (And
% 5.28/5.48 (And
% 5.28/5.48 (And (And (cP cS cS cS cS cO) (∀ (T : b), cP cS cN cS cN T → cP cN cN cS cN (cL T)))
% 5.28/5.48 (∀ (T1 : b), cP cN cN cS cN T1 → cP cS cN cS cN (cL T1)))
% 5.28/5.48 (∀ (T2 : b), cP cS cS cN cS T2 → cP cN cS cN cS (cL T2)))
% 5.28/5.48 (∀ (T3 : b), cP cN cS cN cS T3 → cP cS cS cN cS (cL T3)))
% 5.28/5.48 (∀ (T4 : b), cP cS cS cS cN T4 → cP cN cN cS cN (cW T4)))
% 5.28/5.48 (∀ (T5 : b), cP cN cN cS cN T5 → cP cS cS cS cN (cW T5)))
% 5.28/5.48 (∀ (T6 : b), cP cS cS cN cS T6 → cP cN cN cN cS (cW T6)))
% 5.28/5.48 (∀ (T7 : b), cP cN cN cN cS T7 → cP cS cS cN cS (cW T7)))
% 5.28/5.50 (∀ (X Y : a) (U : b), cP cS X cS Y U → cP cN X cN Y (cG U)))
% 5.28/5.50 (∀ (X1 Y1 : a) (V : b), cP cN X1 cN Y1 V → cP cS X1 cS Y1 (cG V)))
% 5.28/5.50 (∀ (T8 : b), cP cS cN cS cS T8 → cP cN cN cS cN (cD T8)))
% 5.28/5.50 (∀ (T9 : b), cP cN cN cS cN T9 → cP cS cN cS cS (cD T9)))
% 5.28/5.50 (∀ (U1 : b), cP cS cS cN cS U1 → cP cN cS cN cN (cD U1)))
% 5.28/5.50 (∀ (V1 : b), cP cN cS cN cN V1 → cP cS cS cN cS (cD V1)) →
% 5.28/5.50 Exists (cP cN cN cN cN))
% 5.28/5.50 False
% 5.28/5.50 Clause #3 (by clausification #[2]): Eq
% 5.28/5.50 (And
% 5.28/5.50 (And
% 5.28/5.50 (And
% 5.28/5.50 (And
% 5.28/5.50 (And
% 5.28/5.50 (And
% 5.28/5.50 (And
% 5.28/5.50 (And
% 5.28/5.50 (And
% 5.28/5.50 (And
% 5.28/5.50 (And
% 5.28/5.50 (And
% 5.28/5.50 (And (And (cP cS cS cS cS cO) (∀ (T : b), cP cS cN cS cN T → cP cN cN cS cN (cL T)))
% 5.28/5.50 (∀ (T1 : b), cP cN cN cS cN T1 → cP cS cN cS cN (cL T1)))
% 5.28/5.50 (∀ (T2 : b), cP cS cS cN cS T2 → cP cN cS cN cS (cL T2)))
% 5.28/5.50 (∀ (T3 : b), cP cN cS cN cS T3 → cP cS cS cN cS (cL T3)))
% 5.28/5.50 (∀ (T4 : b), cP cS cS cS cN T4 → cP cN cN cS cN (cW T4)))
% 5.28/5.50 (∀ (T5 : b), cP cN cN cS cN T5 → cP cS cS cS cN (cW T5)))
% 5.28/5.50 (∀ (T6 : b), cP cS cS cN cS T6 → cP cN cN cN cS (cW T6)))
% 5.28/5.50 (∀ (T7 : b), cP cN cN cN cS T7 → cP cS cS cN cS (cW T7)))
% 5.28/5.50 (∀ (X Y : a) (U : b), cP cS X cS Y U → cP cN X cN Y (cG U)))
% 5.28/5.50 (∀ (X1 Y1 : a) (V : b), cP cN X1 cN Y1 V → cP cS X1 cS Y1 (cG V)))
% 5.28/5.50 (∀ (T8 : b), cP cS cN cS cS T8 → cP cN cN cS cN (cD T8)))
% 5.28/5.50 (∀ (T9 : b), cP cN cN cS cN T9 → cP cS cN cS cS (cD T9)))
% 5.28/5.50 (∀ (U1 : b), cP cS cS cN cS U1 → cP cN cS cN cN (cD U1)))
% 5.28/5.50 (∀ (V1 : b), cP cN cS cN cN V1 → cP cS cS cN cS (cD V1)))
% 5.28/5.50 True
% 5.28/5.50 Clause #4 (by clausification #[2]): Eq (Exists (cP cN cN cN cN)) False
% 5.28/5.50 Clause #6 (by clausification #[3]): Eq
% 5.28/5.50 (And
% 5.28/5.50 (And
% 5.28/5.50 (And
% 5.28/5.50 (And
% 5.28/5.50 (And
% 5.28/5.50 (And
% 5.28/5.50 (And
% 5.28/5.50 (And
% 5.28/5.50 (And
% 5.28/5.50 (And
% 5.28/5.50 (And
% 5.28/5.50 (And (And (cP cS cS cS cS cO) (∀ (T : b), cP cS cN cS cN T → cP cN cN cS cN (cL T)))
% 5.28/5.50 (∀ (T1 : b), cP cN cN cS cN T1 → cP cS cN cS cN (cL T1)))
% 5.28/5.50 (∀ (T2 : b), cP cS cS cN cS T2 → cP cN cS cN cS (cL T2)))
% 5.28/5.50 (∀ (T3 : b), cP cN cS cN cS T3 → cP cS cS cN cS (cL T3)))
% 5.28/5.50 (∀ (T4 : b), cP cS cS cS cN T4 → cP cN cN cS cN (cW T4)))
% 5.28/5.50 (∀ (T5 : b), cP cN cN cS cN T5 → cP cS cS cS cN (cW T5)))
% 5.28/5.50 (∀ (T6 : b), cP cS cS cN cS T6 → cP cN cN cN cS (cW T6)))
% 5.28/5.50 (∀ (T7 : b), cP cN cN cN cS T7 → cP cS cS cN cS (cW T7)))
% 5.28/5.50 (∀ (X Y : a) (U : b), cP cS X cS Y U → cP cN X cN Y (cG U)))
% 5.28/5.50 (∀ (X1 Y1 : a) (V : b), cP cN X1 cN Y1 V → cP cS X1 cS Y1 (cG V)))
% 5.28/5.50 (∀ (T8 : b), cP cS cN cS cS T8 → cP cN cN cS cN (cD T8)))
% 5.28/5.50 (∀ (T9 : b), cP cN cN cS cN T9 → cP cS cN cS cS (cD T9)))
% 5.28/5.50 (∀ (U1 : b), cP cS cS cN cS U1 → cP cN cS cN cN (cD U1)))
% 5.28/5.50 True
% 5.28/5.50 Clause #9 (by clausification #[4]): ∀ (a : b), Eq (cP cN cN cN cN a) False
% 5.28/5.50 Clause #11 (by clausification #[6]): Eq
% 5.28/5.50 (And
% 5.28/5.50 (And
% 5.28/5.50 (And
% 5.28/5.50 (And
% 5.28/5.50 (And
% 5.28/5.50 (And
% 5.28/5.50 (And
% 5.28/5.50 (And
% 5.28/5.50 (And
% 5.28/5.50 (And
% 5.28/5.50 (And (And (cP cS cS cS cS cO) (∀ (T : b), cP cS cN cS cN T → cP cN cN cS cN (cL T)))
% 5.28/5.50 (∀ (T1 : b), cP cN cN cS cN T1 → cP cS cN cS cN (cL T1)))
% 5.28/5.50 (∀ (T2 : b), cP cS cS cN cS T2 → cP cN cS cN cS (cL T2)))
% 5.28/5.50 (∀ (T3 : b), cP cN cS cN cS T3 → cP cS cS cN cS (cL T3)))
% 5.28/5.50 (∀ (T4 : b), cP cS cS cS cN T4 → cP cN cN cS cN (cW T4)))
% 5.28/5.50 (∀ (T5 : b), cP cN cN cS cN T5 → cP cS cS cS cN (cW T5)))
% 5.36/5.52 (∀ (T6 : b), cP cS cS cN cS T6 → cP cN cN cN cS (cW T6)))
% 5.36/5.52 (∀ (T7 : b), cP cN cN cN cS T7 → cP cS cS cN cS (cW T7)))
% 5.36/5.52 (∀ (X Y : a) (U : b), cP cS X cS Y U → cP cN X cN Y (cG U)))
% 5.36/5.52 (∀ (X1 Y1 : a) (V : b), cP cN X1 cN Y1 V → cP cS X1 cS Y1 (cG V)))
% 5.36/5.52 (∀ (T8 : b), cP cS cN cS cS T8 → cP cN cN cS cN (cD T8)))
% 5.36/5.52 (∀ (T9 : b), cP cN cN cS cN T9 → cP cS cN cS cS (cD T9)))
% 5.36/5.52 True
% 5.36/5.52 Clause #15 (by clausification #[11]): Eq
% 5.36/5.52 (And
% 5.36/5.52 (And
% 5.36/5.52 (And
% 5.36/5.52 (And
% 5.36/5.52 (And
% 5.36/5.52 (And
% 5.36/5.52 (And
% 5.36/5.52 (And
% 5.36/5.52 (And
% 5.36/5.52 (And (And (cP cS cS cS cS cO) (∀ (T : b), cP cS cN cS cN T → cP cN cN cS cN (cL T)))
% 5.36/5.52 (∀ (T1 : b), cP cN cN cS cN T1 → cP cS cN cS cN (cL T1)))
% 5.36/5.52 (∀ (T2 : b), cP cS cS cN cS T2 → cP cN cS cN cS (cL T2)))
% 5.36/5.52 (∀ (T3 : b), cP cN cS cN cS T3 → cP cS cS cN cS (cL T3)))
% 5.36/5.52 (∀ (T4 : b), cP cS cS cS cN T4 → cP cN cN cS cN (cW T4)))
% 5.36/5.52 (∀ (T5 : b), cP cN cN cS cN T5 → cP cS cS cS cN (cW T5)))
% 5.36/5.52 (∀ (T6 : b), cP cS cS cN cS T6 → cP cN cN cN cS (cW T6)))
% 5.36/5.52 (∀ (T7 : b), cP cN cN cN cS T7 → cP cS cS cN cS (cW T7)))
% 5.36/5.52 (∀ (X Y : a) (U : b), cP cS X cS Y U → cP cN X cN Y (cG U)))
% 5.36/5.52 (∀ (X1 Y1 : a) (V : b), cP cN X1 cN Y1 V → cP cS X1 cS Y1 (cG V)))
% 5.36/5.52 (∀ (T8 : b), cP cS cN cS cS T8 → cP cN cN cS cN (cD T8)))
% 5.36/5.52 True
% 5.36/5.52 Clause #18 (by clausification #[15]): Eq (∀ (T8 : b), cP cS cN cS cS T8 → cP cN cN cS cN (cD T8)) True
% 5.36/5.52 Clause #19 (by clausification #[15]): Eq
% 5.36/5.52 (And
% 5.36/5.52 (And
% 5.36/5.52 (And
% 5.36/5.52 (And
% 5.36/5.52 (And
% 5.36/5.52 (And
% 5.36/5.52 (And
% 5.36/5.52 (And
% 5.36/5.52 (And (And (cP cS cS cS cS cO) (∀ (T : b), cP cS cN cS cN T → cP cN cN cS cN (cL T)))
% 5.36/5.52 (∀ (T1 : b), cP cN cN cS cN T1 → cP cS cN cS cN (cL T1)))
% 5.36/5.52 (∀ (T2 : b), cP cS cS cN cS T2 → cP cN cS cN cS (cL T2)))
% 5.36/5.52 (∀ (T3 : b), cP cN cS cN cS T3 → cP cS cS cN cS (cL T3)))
% 5.36/5.52 (∀ (T4 : b), cP cS cS cS cN T4 → cP cN cN cS cN (cW T4)))
% 5.36/5.52 (∀ (T5 : b), cP cN cN cS cN T5 → cP cS cS cS cN (cW T5)))
% 5.36/5.52 (∀ (T6 : b), cP cS cS cN cS T6 → cP cN cN cN cS (cW T6)))
% 5.36/5.52 (∀ (T7 : b), cP cN cN cN cS T7 → cP cS cS cN cS (cW T7)))
% 5.36/5.52 (∀ (X Y : a) (U : b), cP cS X cS Y U → cP cN X cN Y (cG U)))
% 5.36/5.52 (∀ (X1 Y1 : a) (V : b), cP cN X1 cN Y1 V → cP cS X1 cS Y1 (cG V)))
% 5.36/5.52 True
% 5.36/5.52 Clause #20 (by clausification #[18]): ∀ (a : b), Eq (cP cS cN cS cS a → cP cN cN cS cN (cD a)) True
% 5.36/5.52 Clause #21 (by clausification #[20]): ∀ (a : b), Or (Eq (cP cS cN cS cS a) False) (Eq (cP cN cN cS cN (cD a)) True)
% 5.36/5.52 Clause #22 (by clausification #[19]): Eq (∀ (X1 Y1 : a) (V : b), cP cN X1 cN Y1 V → cP cS X1 cS Y1 (cG V)) True
% 5.36/5.52 Clause #23 (by clausification #[19]): Eq
% 5.36/5.52 (And
% 5.36/5.52 (And
% 5.36/5.52 (And
% 5.36/5.52 (And
% 5.36/5.52 (And
% 5.36/5.52 (And
% 5.36/5.52 (And
% 5.36/5.52 (And (And (cP cS cS cS cS cO) (∀ (T : b), cP cS cN cS cN T → cP cN cN cS cN (cL T)))
% 5.36/5.52 (∀ (T1 : b), cP cN cN cS cN T1 → cP cS cN cS cN (cL T1)))
% 5.36/5.52 (∀ (T2 : b), cP cS cS cN cS T2 → cP cN cS cN cS (cL T2)))
% 5.36/5.52 (∀ (T3 : b), cP cN cS cN cS T3 → cP cS cS cN cS (cL T3)))
% 5.36/5.52 (∀ (T4 : b), cP cS cS cS cN T4 → cP cN cN cS cN (cW T4)))
% 5.36/5.52 (∀ (T5 : b), cP cN cN cS cN T5 → cP cS cS cS cN (cW T5)))
% 5.36/5.52 (∀ (T6 : b), cP cS cS cN cS T6 → cP cN cN cN cS (cW T6)))
% 5.36/5.52 (∀ (T7 : b), cP cN cN cN cS T7 → cP cS cS cN cS (cW T7)))
% 5.36/5.52 (∀ (X Y : a) (U : b), cP cS X cS Y U → cP cN X cN Y (cG U)))
% 5.36/5.52 True
% 5.36/5.52 Clause #24 (by clausification #[22]): ∀ (a_1 : a), Eq (∀ (Y1 : a) (V : b), cP cN a_1 cN Y1 V → cP cS a_1 cS Y1 (cG V)) True
% 5.36/5.52 Clause #25 (by clausification #[24]): ∀ (a_1 a : a), Eq (∀ (V : b), cP cN a_1 cN a V → cP cS a_1 cS a (cG V)) True
% 5.36/5.52 Clause #26 (by clausification #[25]): ∀ (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
% 5.36/5.54 Clause #27 (by clausification #[26]): ∀ (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)
% 5.36/5.54 Clause #28 (by clausification #[23]): Eq (∀ (X Y : a) (U : b), cP cS X cS Y U → cP cN X cN Y (cG U)) True
% 5.36/5.54 Clause #29 (by clausification #[23]): Eq
% 5.36/5.54 (And
% 5.36/5.54 (And
% 5.36/5.54 (And
% 5.36/5.54 (And
% 5.36/5.54 (And
% 5.36/5.54 (And
% 5.36/5.54 (And (And (cP cS cS cS cS cO) (∀ (T : b), cP cS cN cS cN T → cP cN cN cS cN (cL T)))
% 5.36/5.54 (∀ (T1 : b), cP cN cN cS cN T1 → cP cS cN cS cN (cL T1)))
% 5.36/5.54 (∀ (T2 : b), cP cS cS cN cS T2 → cP cN cS cN cS (cL T2)))
% 5.36/5.54 (∀ (T3 : b), cP cN cS cN cS T3 → cP cS cS cN cS (cL T3)))
% 5.36/5.54 (∀ (T4 : b), cP cS cS cS cN T4 → cP cN cN cS cN (cW T4)))
% 5.36/5.54 (∀ (T5 : b), cP cN cN cS cN T5 → cP cS cS cS cN (cW T5)))
% 5.36/5.54 (∀ (T6 : b), cP cS cS cN cS T6 → cP cN cN cN cS (cW T6)))
% 5.36/5.54 (∀ (T7 : b), cP cN cN cN cS T7 → cP cS cS cN cS (cW T7)))
% 5.36/5.54 True
% 5.36/5.54 Clause #30 (by clausification #[28]): ∀ (a_1 : a), Eq (∀ (Y : a) (U : b), cP cS a_1 cS Y U → cP cN a_1 cN Y (cG U)) True
% 5.36/5.54 Clause #31 (by clausification #[30]): ∀ (a_1 a : a), Eq (∀ (U : b), cP cS a_1 cS a U → cP cN a_1 cN a (cG U)) True
% 5.36/5.54 Clause #32 (by clausification #[31]): ∀ (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
% 5.36/5.54 Clause #33 (by clausification #[32]): ∀ (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)
% 5.36/5.54 Clause #35 (by clausification #[29]): Eq
% 5.36/5.54 (And
% 5.36/5.54 (And
% 5.36/5.54 (And
% 5.36/5.54 (And
% 5.36/5.54 (And
% 5.36/5.54 (And (And (cP cS cS cS cS cO) (∀ (T : b), cP cS cN cS cN T → cP cN cN cS cN (cL T)))
% 5.36/5.54 (∀ (T1 : b), cP cN cN cS cN T1 → cP cS cN cS cN (cL T1)))
% 5.36/5.54 (∀ (T2 : b), cP cS cS cN cS T2 → cP cN cS cN cS (cL T2)))
% 5.36/5.54 (∀ (T3 : b), cP cN cS cN cS T3 → cP cS cS cN cS (cL T3)))
% 5.36/5.54 (∀ (T4 : b), cP cS cS cS cN T4 → cP cN cN cS cN (cW T4)))
% 5.36/5.54 (∀ (T5 : b), cP cN cN cS cN T5 → cP cS cS cS cN (cW T5)))
% 5.36/5.54 (∀ (T6 : b), cP cS cS cN cS T6 → cP cN cN cN cS (cW T6)))
% 5.36/5.54 True
% 5.36/5.54 Clause #38 (by clausification #[35]): Eq (∀ (T6 : b), cP cS cS cN cS T6 → cP cN cN cN cS (cW T6)) True
% 5.36/5.54 Clause #39 (by clausification #[35]): Eq
% 5.36/5.54 (And
% 5.36/5.54 (And
% 5.36/5.54 (And
% 5.36/5.54 (And
% 5.36/5.54 (And (And (cP cS cS cS cS cO) (∀ (T : b), cP cS cN cS cN T → cP cN cN cS cN (cL T)))
% 5.36/5.54 (∀ (T1 : b), cP cN cN cS cN T1 → cP cS cN cS cN (cL T1)))
% 5.36/5.54 (∀ (T2 : b), cP cS cS cN cS T2 → cP cN cS cN cS (cL T2)))
% 5.36/5.54 (∀ (T3 : b), cP cN cS cN cS T3 → cP cS cS cN cS (cL T3)))
% 5.36/5.54 (∀ (T4 : b), cP cS cS cS cN T4 → cP cN cN cS cN (cW T4)))
% 5.36/5.54 (∀ (T5 : b), cP cN cN cS cN T5 → cP cS cS cS cN (cW T5)))
% 5.36/5.54 True
% 5.36/5.54 Clause #40 (by clausification #[38]): ∀ (a : b), Eq (cP cS cS cN cS a → cP cN cN cN cS (cW a)) True
% 5.36/5.54 Clause #41 (by clausification #[40]): ∀ (a : b), Or (Eq (cP cS cS cN cS a) False) (Eq (cP cN cN cN cS (cW a)) True)
% 5.36/5.54 Clause #43 (by clausification #[39]): Eq
% 5.36/5.54 (And
% 5.36/5.54 (And
% 5.36/5.54 (And
% 5.36/5.54 (And (And (cP cS cS cS cS cO) (∀ (T : b), cP cS cN cS cN T → cP cN cN cS cN (cL T)))
% 5.36/5.54 (∀ (T1 : b), cP cN cN cS cN T1 → cP cS cN cS cN (cL T1)))
% 5.36/5.54 (∀ (T2 : b), cP cS cS cN cS T2 → cP cN cS cN cS (cL T2)))
% 5.36/5.54 (∀ (T3 : b), cP cN cS cN cS T3 → cP cS cS cN cS (cL T3)))
% 5.36/5.54 (∀ (T4 : b), cP cS cS cS cN T4 → cP cN cN cS cN (cW T4)))
% 5.36/5.54 True
% 5.36/5.54 Clause #47 (by clausification #[43]): Eq
% 5.36/5.54 (And
% 5.36/5.54 (And
% 5.36/5.54 (And (And (cP cS cS cS cS cO) (∀ (T : b), cP cS cN cS cN T → cP cN cN cS cN (cL T)))
% 5.36/5.54 (∀ (T1 : b), cP cN cN cS cN T1 → cP cS cN cS cN (cL T1)))
% 5.36/5.54 (∀ (T2 : b), cP cS cS cN cS T2 → cP cN cS cN cS (cL T2)))
% 5.36/5.54 (∀ (T3 : b), cP cN cS cN cS T3 → cP cS cS cN cS (cL T3)))
% 5.36/5.54 True
% 5.36/5.54 Clause #50 (by clausification #[47]): Eq (∀ (T3 : b), cP cN cS cN cS T3 → cP cS cS cN cS (cL T3)) True
% 5.36/5.54 Clause #51 (by clausification #[47]): Eq
% 5.36/5.54 (And
% 5.36/5.54 (And (And (cP cS cS cS cS cO) (∀ (T : b), cP cS cN cS cN T → cP cN cN cS cN (cL T)))
% 5.36/5.54 (∀ (T1 : b), cP cN cN cS cN T1 → cP cS cN cS cN (cL T1)))
% 5.36/5.55 (∀ (T2 : b), cP cS cS cN cS T2 → cP cN cS cN cS (cL T2)))
% 5.36/5.55 True
% 5.36/5.55 Clause #52 (by clausification #[50]): ∀ (a : b), Eq (cP cN cS cN cS a → cP cS cS cN cS (cL a)) True
% 5.36/5.55 Clause #53 (by clausification #[52]): ∀ (a : b), Or (Eq (cP cN cS cN cS a) False) (Eq (cP cS cS cN cS (cL a)) True)
% 5.36/5.55 Clause #55 (by clausification #[51]): Eq
% 5.36/5.55 (And (And (cP cS cS cS cS cO) (∀ (T : b), cP cS cN cS cN T → cP cN cN cS cN (cL T)))
% 5.36/5.55 (∀ (T1 : b), cP cN cN cS cN T1 → cP cS cN cS cN (cL T1)))
% 5.36/5.55 True
% 5.36/5.55 Clause #58 (by clausification #[55]): Eq (∀ (T1 : b), cP cN cN cS cN T1 → cP cS cN cS cN (cL T1)) True
% 5.36/5.55 Clause #59 (by clausification #[55]): Eq (And (cP cS cS cS cS cO) (∀ (T : b), cP cS cN cS cN T → cP cN cN cS cN (cL T))) True
% 5.36/5.55 Clause #60 (by clausification #[58]): ∀ (a : b), Eq (cP cN cN cS cN a → cP cS cN cS cN (cL a)) True
% 5.36/5.55 Clause #61 (by clausification #[60]): ∀ (a : b), Or (Eq (cP cN cN cS cN a) False) (Eq (cP cS cN cS cN (cL a)) True)
% 5.36/5.55 Clause #63 (by clausification #[59]): Eq (cP cS cS cS cS cO) True
% 5.36/5.55 Clause #66 (by superposition #[63, 33]): Or (Eq True False) (Eq (cP cN cS cN cS (cG cO)) True)
% 5.36/5.55 Clause #67 (by clausification #[66]): Eq (cP cN cS cN cS (cG cO)) True
% 5.36/5.55 Clause #68 (by superposition #[67, 53]): Or (Eq True False) (Eq (cP cS cS cN cS (cL (cG cO))) True)
% 5.36/5.55 Clause #70 (by clausification #[68]): Eq (cP cS cS cN cS (cL (cG cO))) True
% 5.36/5.55 Clause #72 (by superposition #[70, 41]): Or (Eq True False) (Eq (cP cN cN cN cS (cW (cL (cG cO)))) True)
% 5.36/5.55 Clause #79 (by clausification #[72]): Eq (cP cN cN cN cS (cW (cL (cG cO)))) True
% 5.36/5.55 Clause #81 (by superposition #[79, 27]): Or (Eq True False) (Eq (cP cS cN cS cS (cG (cW (cL (cG cO))))) True)
% 5.36/5.55 Clause #105 (by clausification #[81]): Eq (cP cS cN cS cS (cG (cW (cL (cG cO))))) True
% 5.36/5.55 Clause #106 (by superposition #[105, 21]): Or (Eq True False) (Eq (cP cN cN cS cN (cD (cG (cW (cL (cG cO)))))) True)
% 5.36/5.55 Clause #166 (by clausification #[106]): Eq (cP cN cN cS cN (cD (cG (cW (cL (cG cO)))))) True
% 5.36/5.55 Clause #169 (by superposition #[166, 61]): Or (Eq True False) (Eq (cP cS cN cS cN (cL (cD (cG (cW (cL (cG cO))))))) True)
% 5.36/5.55 Clause #170 (by clausification #[169]): Eq (cP cS cN cS cN (cL (cD (cG (cW (cL (cG cO))))))) True
% 5.36/5.55 Clause #172 (by superposition #[170, 33]): Or (Eq True False) (Eq (cP cN cN cN cN (cG (cL (cD (cG (cW (cL (cG cO)))))))) True)
% 5.36/5.55 Clause #319 (by clausification #[172]): Eq (cP cN cN cN cN (cG (cL (cD (cG (cW (cL (cG cO)))))))) True
% 5.36/5.55 Clause #320 (by superposition #[319, 9]): Eq True False
% 5.36/5.55 Clause #322 (by clausification #[320]): False
% 5.36/5.55 SZS output end Proof for theBenchmark.p
%------------------------------------------------------------------------------