TSTP Solution File: NUM651^1 by Duper---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : NUM651^1 : TPTP v8.1.2. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n017.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 10:56:45 EDT 2023
% Result : Theorem 5.32s 5.50s
% Output : Proof 5.38s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : NUM651^1 : TPTP v8.1.2. Released v3.7.0.
% 0.11/0.13 % Command : duper %s
% 0.13/0.34 % Computer : n017.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 Aug 25 15:32:10 EDT 2023
% 0.13/0.35 % CPUTime :
% 5.32/5.50 SZS status Theorem for theBenchmark.p
% 5.32/5.50 SZS output start Proof for theBenchmark.p
% 5.32/5.50 Clause #0 (by assumption #[]): Eq (∀ (Xx Xy : nat), Ne Xy (pl Xx Xy)) True
% 5.32/5.50 Clause #1 (by assumption #[]): Eq (∀ (Xx Xy : nat), Eq (pl Xx Xy) (pl Xy Xx)) True
% 5.32/5.50 Clause #3 (by assumption #[]): Eq (∀ (Xx Xy Xz : nat), Eq (pl (pl Xx Xy) Xz) (pl Xx (pl Xy Xz))) True
% 5.32/5.50 Clause #4 (by assumption #[]): Eq
% 5.32/5.50 (Not
% 5.32/5.50 (Not
% 5.32/5.50 ((Eq x y → Not (Not (∀ (Xx_0 : nat), Ne x (pl y Xx_0)))) →
% 5.32/5.50 Not
% 5.32/5.50 (Not
% 5.32/5.50 ((Not (∀ (Xx_0 : nat), Ne x (pl y Xx_0)) → Not (Not (∀ (Xx_0 : nat), Ne y (pl x Xx_0)))) →
% 5.32/5.50 Not (Not (∀ (Xx_0 : nat), Ne y (pl x Xx_0)) → Ne x y))))))
% 5.32/5.50 True
% 5.32/5.50 Clause #9 (by clausification #[0]): ∀ (a : nat), Eq (∀ (Xy : nat), Ne Xy (pl a Xy)) True
% 5.32/5.50 Clause #10 (by clausification #[9]): ∀ (a a_1 : nat), Eq (Ne a (pl a_1 a)) True
% 5.32/5.50 Clause #11 (by clausification #[10]): ∀ (a a_1 : nat), Ne a (pl a_1 a)
% 5.32/5.50 Clause #12 (by clausification #[1]): ∀ (a : nat), Eq (∀ (Xy : nat), Eq (pl a Xy) (pl Xy a)) True
% 5.32/5.50 Clause #13 (by clausification #[12]): ∀ (a a_1 : nat), Eq (Eq (pl a a_1) (pl a_1 a)) True
% 5.32/5.50 Clause #14 (by clausification #[13]): ∀ (a a_1 : nat), Eq (pl a a_1) (pl a_1 a)
% 5.32/5.50 Clause #15 (by superposition #[14, 11]): ∀ (a a_1 : nat), Ne a (pl a a_1)
% 5.32/5.50 Clause #16 (by clausification #[4]): Eq
% 5.32/5.50 (Not
% 5.32/5.50 ((Eq x y → Not (Not (∀ (Xx_0 : nat), Ne x (pl y Xx_0)))) →
% 5.32/5.50 Not
% 5.32/5.50 (Not
% 5.32/5.50 ((Not (∀ (Xx_0 : nat), Ne x (pl y Xx_0)) → Not (Not (∀ (Xx_0 : nat), Ne y (pl x Xx_0)))) →
% 5.32/5.50 Not (Not (∀ (Xx_0 : nat), Ne y (pl x Xx_0)) → Ne x y)))))
% 5.32/5.50 False
% 5.32/5.50 Clause #17 (by clausification #[16]): Eq
% 5.32/5.50 ((Eq x y → Not (Not (∀ (Xx_0 : nat), Ne x (pl y Xx_0)))) →
% 5.32/5.50 Not
% 5.32/5.50 (Not
% 5.32/5.50 ((Not (∀ (Xx_0 : nat), Ne x (pl y Xx_0)) → Not (Not (∀ (Xx_0 : nat), Ne y (pl x Xx_0)))) →
% 5.32/5.50 Not (Not (∀ (Xx_0 : nat), Ne y (pl x Xx_0)) → Ne x y))))
% 5.32/5.50 True
% 5.32/5.50 Clause #18 (by clausification #[17]): Or (Eq (Eq x y → Not (Not (∀ (Xx_0 : nat), Ne x (pl y Xx_0)))) False)
% 5.32/5.50 (Eq
% 5.32/5.50 (Not
% 5.32/5.50 (Not
% 5.32/5.50 ((Not (∀ (Xx_0 : nat), Ne x (pl y Xx_0)) → Not (Not (∀ (Xx_0 : nat), Ne y (pl x Xx_0)))) →
% 5.32/5.50 Not (Not (∀ (Xx_0 : nat), Ne y (pl x Xx_0)) → Ne x y))))
% 5.32/5.50 True)
% 5.32/5.50 Clause #19 (by clausification #[18]): Or
% 5.32/5.50 (Eq
% 5.32/5.50 (Not
% 5.32/5.50 (Not
% 5.32/5.50 ((Not (∀ (Xx_0 : nat), Ne x (pl y Xx_0)) → Not (Not (∀ (Xx_0 : nat), Ne y (pl x Xx_0)))) →
% 5.32/5.50 Not (Not (∀ (Xx_0 : nat), Ne y (pl x Xx_0)) → Ne x y))))
% 5.32/5.50 True)
% 5.32/5.50 (Eq (Eq x y) True)
% 5.32/5.50 Clause #20 (by clausification #[18]): Or
% 5.32/5.50 (Eq
% 5.32/5.50 (Not
% 5.32/5.50 (Not
% 5.32/5.50 ((Not (∀ (Xx_0 : nat), Ne x (pl y Xx_0)) → Not (Not (∀ (Xx_0 : nat), Ne y (pl x Xx_0)))) →
% 5.32/5.50 Not (Not (∀ (Xx_0 : nat), Ne y (pl x Xx_0)) → Ne x y))))
% 5.32/5.50 True)
% 5.32/5.50 (Eq (Not (Not (∀ (Xx_0 : nat), Ne x (pl y Xx_0)))) False)
% 5.32/5.50 Clause #21 (by clausification #[19]): Or (Eq (Eq x y) True)
% 5.32/5.50 (Eq
% 5.32/5.50 (Not
% 5.32/5.50 ((Not (∀ (Xx_0 : nat), Ne x (pl y Xx_0)) → Not (Not (∀ (Xx_0 : nat), Ne y (pl x Xx_0)))) →
% 5.32/5.50 Not (Not (∀ (Xx_0 : nat), Ne y (pl x Xx_0)) → Ne x y)))
% 5.32/5.50 False)
% 5.32/5.50 Clause #22 (by clausification #[21]): Or
% 5.32/5.50 (Eq
% 5.32/5.50 (Not
% 5.32/5.50 ((Not (∀ (Xx_0 : nat), Ne x (pl y Xx_0)) → Not (Not (∀ (Xx_0 : nat), Ne y (pl x Xx_0)))) →
% 5.32/5.50 Not (Not (∀ (Xx_0 : nat), Ne y (pl x Xx_0)) → Ne x y)))
% 5.32/5.50 False)
% 5.32/5.50 (Eq x y)
% 5.32/5.50 Clause #23 (by clausification #[22]): Or (Eq x y)
% 5.32/5.50 (Eq
% 5.32/5.50 ((Not (∀ (Xx_0 : nat), Ne x (pl y Xx_0)) → Not (Not (∀ (Xx_0 : nat), Ne y (pl x Xx_0)))) →
% 5.32/5.50 Not (Not (∀ (Xx_0 : nat), Ne y (pl x Xx_0)) → Ne x y))
% 5.32/5.50 True)
% 5.32/5.50 Clause #24 (by clausification #[23]): Or (Eq x y)
% 5.32/5.50 (Or (Eq (Not (∀ (Xx_0 : nat), Ne x (pl y Xx_0)) → Not (Not (∀ (Xx_0 : nat), Ne y (pl x Xx_0)))) False)
% 5.32/5.50 (Eq (Not (Not (∀ (Xx_0 : nat), Ne y (pl x Xx_0)) → Ne x y)) True))
% 5.32/5.50 Clause #25 (by clausification #[24]): Or (Eq x y)
% 5.32/5.50 (Or (Eq (Not (Not (∀ (Xx_0 : nat), Ne y (pl x Xx_0)) → Ne x y)) True)
% 5.32/5.50 (Eq (Not (∀ (Xx_0 : nat), Ne x (pl y Xx_0))) True))
% 5.32/5.50 Clause #26 (by clausification #[24]): Or (Eq x y)
% 5.32/5.50 (Or (Eq (Not (Not (∀ (Xx_0 : nat), Ne y (pl x Xx_0)) → Ne x y)) True)
% 5.36/5.53 (Eq (Not (Not (∀ (Xx_0 : nat), Ne y (pl x Xx_0)))) False))
% 5.36/5.53 Clause #27 (by clausification #[25]): Or (Eq x y)
% 5.36/5.53 (Or (Eq (Not (∀ (Xx_0 : nat), Ne x (pl y Xx_0))) True) (Eq (Not (∀ (Xx_0 : nat), Ne y (pl x Xx_0)) → Ne x y) False))
% 5.36/5.53 Clause #28 (by clausification #[27]): Or (Eq x y)
% 5.36/5.53 (Or (Eq (Not (∀ (Xx_0 : nat), Ne y (pl x Xx_0)) → Ne x y) False) (Eq (∀ (Xx_0 : nat), Ne x (pl y Xx_0)) False))
% 5.36/5.53 Clause #30 (by clausification #[28]): Or (Eq x y) (Or (Eq (∀ (Xx_0 : nat), Ne x (pl y Xx_0)) False) (Eq (Ne x y) False))
% 5.36/5.53 Clause #42 (by clausification #[3]): ∀ (a : nat), Eq (∀ (Xy Xz : nat), Eq (pl (pl a Xy) Xz) (pl a (pl Xy Xz))) True
% 5.36/5.53 Clause #43 (by clausification #[42]): ∀ (a a_1 : nat), Eq (∀ (Xz : nat), Eq (pl (pl a a_1) Xz) (pl a (pl a_1 Xz))) True
% 5.36/5.53 Clause #44 (by clausification #[43]): ∀ (a a_1 a_2 : nat), Eq (Eq (pl (pl a a_1) a_2) (pl a (pl a_1 a_2))) True
% 5.36/5.53 Clause #45 (by clausification #[44]): ∀ (a a_1 a_2 : nat), Eq (pl (pl a a_1) a_2) (pl a (pl a_1 a_2))
% 5.36/5.53 Clause #46 (by superposition #[45, 11]): ∀ (a a_1 a_2 : nat), Ne a (pl a_1 (pl a_2 a))
% 5.36/5.53 Clause #49 (by superposition #[45, 15]): ∀ (a a_1 a_2 : nat), Ne (pl a a_1) (pl a (pl a_1 a_2))
% 5.36/5.53 Clause #58 (by superposition #[46, 14]): ∀ (a a_1 a_2 : nat), Ne a (pl a_1 (pl a a_2))
% 5.36/5.53 Clause #70 (by superposition #[49, 14]): ∀ (a a_1 a_2 : nat), Ne (pl a a_1) (pl a (pl a_2 a_1))
% 5.36/5.53 Clause #71 (by clausification #[20]): Or (Eq (Not (Not (∀ (Xx_0 : nat), Ne x (pl y Xx_0)))) False)
% 5.36/5.53 (Eq
% 5.36/5.53 (Not
% 5.36/5.53 ((Not (∀ (Xx_0 : nat), Ne x (pl y Xx_0)) → Not (Not (∀ (Xx_0 : nat), Ne y (pl x Xx_0)))) →
% 5.36/5.53 Not (Not (∀ (Xx_0 : nat), Ne y (pl x Xx_0)) → Ne x y)))
% 5.36/5.53 False)
% 5.36/5.53 Clause #72 (by clausification #[71]): Or
% 5.36/5.53 (Eq
% 5.36/5.53 (Not
% 5.36/5.53 ((Not (∀ (Xx_0 : nat), Ne x (pl y Xx_0)) → Not (Not (∀ (Xx_0 : nat), Ne y (pl x Xx_0)))) →
% 5.36/5.53 Not (Not (∀ (Xx_0 : nat), Ne y (pl x Xx_0)) → Ne x y)))
% 5.36/5.53 False)
% 5.36/5.53 (Eq (Not (∀ (Xx_0 : nat), Ne x (pl y Xx_0))) True)
% 5.36/5.53 Clause #73 (by clausification #[72]): Or (Eq (Not (∀ (Xx_0 : nat), Ne x (pl y Xx_0))) True)
% 5.36/5.53 (Eq
% 5.36/5.53 ((Not (∀ (Xx_0 : nat), Ne x (pl y Xx_0)) → Not (Not (∀ (Xx_0 : nat), Ne y (pl x Xx_0)))) →
% 5.36/5.53 Not (Not (∀ (Xx_0 : nat), Ne y (pl x Xx_0)) → Ne x y))
% 5.36/5.53 True)
% 5.36/5.53 Clause #74 (by clausification #[73]): Or
% 5.36/5.53 (Eq
% 5.36/5.53 ((Not (∀ (Xx_0 : nat), Ne x (pl y Xx_0)) → Not (Not (∀ (Xx_0 : nat), Ne y (pl x Xx_0)))) →
% 5.36/5.53 Not (Not (∀ (Xx_0 : nat), Ne y (pl x Xx_0)) → Ne x y))
% 5.36/5.53 True)
% 5.36/5.53 (Eq (∀ (Xx_0 : nat), Ne x (pl y Xx_0)) False)
% 5.36/5.53 Clause #75 (by clausification #[74]): Or (Eq (∀ (Xx_0 : nat), Ne x (pl y Xx_0)) False)
% 5.36/5.53 (Or (Eq (Not (∀ (Xx_0 : nat), Ne x (pl y Xx_0)) → Not (Not (∀ (Xx_0 : nat), Ne y (pl x Xx_0)))) False)
% 5.36/5.53 (Eq (Not (Not (∀ (Xx_0 : nat), Ne y (pl x Xx_0)) → Ne x y)) True))
% 5.36/5.53 Clause #76 (by clausification #[75]): ∀ (a : nat),
% 5.36/5.53 Or (Eq (Not (∀ (Xx_0 : nat), Ne x (pl y Xx_0)) → Not (Not (∀ (Xx_0 : nat), Ne y (pl x Xx_0)))) False)
% 5.36/5.53 (Or (Eq (Not (Not (∀ (Xx_0 : nat), Ne y (pl x Xx_0)) → Ne x y)) True) (Eq (Not (Ne x (pl y (skS.0 2 a)))) True))
% 5.36/5.53 Clause #77 (by clausification #[76]): ∀ (a : nat),
% 5.36/5.53 Or (Eq (Not (Not (∀ (Xx_0 : nat), Ne y (pl x Xx_0)) → Ne x y)) True)
% 5.36/5.53 (Or (Eq (Not (Ne x (pl y (skS.0 2 a)))) True) (Eq (Not (∀ (Xx_0 : nat), Ne x (pl y Xx_0))) True))
% 5.36/5.53 Clause #79 (by clausification #[77]): ∀ (a : nat),
% 5.36/5.53 Or (Eq (Not (Ne x (pl y (skS.0 2 a)))) True)
% 5.36/5.53 (Or (Eq (Not (∀ (Xx_0 : nat), Ne x (pl y Xx_0))) True) (Eq (Not (∀ (Xx_0 : nat), Ne y (pl x Xx_0)) → Ne x y) False))
% 5.36/5.53 Clause #80 (by clausification #[79]): ∀ (a : nat),
% 5.36/5.53 Or (Eq (Not (∀ (Xx_0 : nat), Ne x (pl y Xx_0))) True)
% 5.36/5.53 (Or (Eq (Not (∀ (Xx_0 : nat), Ne y (pl x Xx_0)) → Ne x y) False) (Eq (Ne x (pl y (skS.0 2 a))) False))
% 5.36/5.53 Clause #81 (by clausification #[80]): ∀ (a : nat),
% 5.36/5.53 Or (Eq (Not (∀ (Xx_0 : nat), Ne y (pl x Xx_0)) → Ne x y) False)
% 5.36/5.53 (Or (Eq (Ne x (pl y (skS.0 2 a))) False) (Eq (∀ (Xx_0 : nat), Ne x (pl y Xx_0)) False))
% 5.36/5.53 Clause #82 (by clausification #[81]): ∀ (a : nat),
% 5.36/5.53 Or (Eq (Ne x (pl y (skS.0 2 a))) False)
% 5.38/5.56 (Or (Eq (∀ (Xx_0 : nat), Ne x (pl y Xx_0)) False) (Eq (Not (∀ (Xx_0 : nat), Ne y (pl x Xx_0))) True))
% 5.38/5.56 Clause #84 (by clausification #[82]): ∀ (a : nat),
% 5.38/5.56 Or (Eq (∀ (Xx_0 : nat), Ne x (pl y Xx_0)) False)
% 5.38/5.56 (Or (Eq (Not (∀ (Xx_0 : nat), Ne y (pl x Xx_0))) True) (Eq x (pl y (skS.0 2 a))))
% 5.38/5.56 Clause #85 (by clausification #[84]): ∀ (a a_1 : nat),
% 5.38/5.56 Or (Eq (Not (∀ (Xx_0 : nat), Ne y (pl x Xx_0))) True)
% 5.38/5.56 (Or (Eq x (pl y (skS.0 2 a))) (Eq (Not (Ne x (pl y (skS.0 3 a_1)))) True))
% 5.38/5.56 Clause #86 (by clausification #[85]): ∀ (a a_1 : nat),
% 5.38/5.56 Or (Eq x (pl y (skS.0 2 a)))
% 5.38/5.56 (Or (Eq (Not (Ne x (pl y (skS.0 3 a_1)))) True) (Eq (∀ (Xx_0 : nat), Ne y (pl x Xx_0)) False))
% 5.38/5.56 Clause #87 (by clausification #[86]): ∀ (a a_1 : nat),
% 5.38/5.56 Or (Eq x (pl y (skS.0 2 a))) (Or (Eq (∀ (Xx_0 : nat), Ne y (pl x Xx_0)) False) (Eq (Ne x (pl y (skS.0 3 a_1))) False))
% 5.38/5.56 Clause #88 (by clausification #[87]): ∀ (a a_1 a_2 : nat),
% 5.38/5.56 Or (Eq x (pl y (skS.0 2 a))) (Or (Eq (Ne x (pl y (skS.0 3 a_1))) False) (Eq (Not (Ne y (pl x (skS.0 4 a_2)))) True))
% 5.38/5.56 Clause #89 (by clausification #[88]): ∀ (a a_1 a_2 : nat),
% 5.38/5.56 Or (Eq x (pl y (skS.0 2 a))) (Or (Eq (Not (Ne y (pl x (skS.0 4 a_1)))) True) (Eq x (pl y (skS.0 3 a_2))))
% 5.38/5.56 Clause #90 (by clausification #[89]): ∀ (a a_1 a_2 : nat),
% 5.38/5.56 Or (Eq x (pl y (skS.0 2 a))) (Or (Eq x (pl y (skS.0 3 a_1))) (Eq (Ne y (pl x (skS.0 4 a_2))) False))
% 5.38/5.56 Clause #91 (by clausification #[90]): ∀ (a a_1 a_2 : nat), Or (Eq x (pl y (skS.0 2 a))) (Or (Eq x (pl y (skS.0 3 a_1))) (Eq y (pl x (skS.0 4 a_2))))
% 5.38/5.56 Clause #94 (by superposition #[91, 45]): ∀ (a a_1 a_2 a_3 : nat),
% 5.38/5.56 Or (Eq x (pl y (skS.0 3 a))) (Or (Eq y (pl x (skS.0 4 a_1))) (Eq (pl x a_2) (pl y (pl (skS.0 2 a_3) a_2))))
% 5.38/5.56 Clause #146 (by clausification #[26]): Or (Eq x y)
% 5.38/5.56 (Or (Eq (Not (Not (∀ (Xx_0 : nat), Ne y (pl x Xx_0)))) False)
% 5.38/5.56 (Eq (Not (∀ (Xx_0 : nat), Ne y (pl x Xx_0)) → Ne x y) False))
% 5.38/5.56 Clause #147 (by clausification #[146]): Or (Eq x y)
% 5.38/5.56 (Or (Eq (Not (∀ (Xx_0 : nat), Ne y (pl x Xx_0)) → Ne x y) False) (Eq (Not (∀ (Xx_0 : nat), Ne y (pl x Xx_0))) True))
% 5.38/5.56 Clause #148 (by clausification #[147]): Or (Eq x y) (Or (Eq (Not (∀ (Xx_0 : nat), Ne y (pl x Xx_0))) True) (Eq (Not (∀ (Xx_0 : nat), Ne y (pl x Xx_0))) True))
% 5.38/5.56 Clause #150 (by clausification #[148]): Or (Eq x y) (Or (Eq (Not (∀ (Xx_0 : nat), Ne y (pl x Xx_0))) True) (Eq (∀ (Xx_0 : nat), Ne y (pl x Xx_0)) False))
% 5.38/5.56 Clause #151 (by clausification #[150]): Or (Eq x y) (Or (Eq (∀ (Xx_0 : nat), Ne y (pl x Xx_0)) False) (Eq (∀ (Xx_0 : nat), Ne y (pl x Xx_0)) False))
% 5.38/5.56 Clause #152 (by clausification #[151]): ∀ (a : nat), Or (Eq x y) (Or (Eq (∀ (Xx_0 : nat), Ne y (pl x Xx_0)) False) (Eq (Not (Ne y (pl x (skS.0 5 a)))) True))
% 5.38/5.56 Clause #153 (by clausification #[152]): ∀ (a a_1 : nat), Or (Eq x y) (Or (Eq (Not (Ne y (pl x (skS.0 5 a)))) True) (Eq (Not (Ne y (pl x (skS.0 6 a_1)))) True))
% 5.38/5.56 Clause #154 (by clausification #[153]): ∀ (a a_1 : nat), Or (Eq x y) (Or (Eq (Not (Ne y (pl x (skS.0 6 a)))) True) (Eq (Ne y (pl x (skS.0 5 a_1))) False))
% 5.38/5.56 Clause #155 (by clausification #[154]): ∀ (a a_1 : nat), Or (Eq x y) (Or (Eq (Ne y (pl x (skS.0 5 a))) False) (Eq (Ne y (pl x (skS.0 6 a_1))) False))
% 5.38/5.56 Clause #156 (by clausification #[155]): ∀ (a a_1 : nat), Or (Eq x y) (Or (Eq (Ne y (pl x (skS.0 6 a))) False) (Eq y (pl x (skS.0 5 a_1))))
% 5.38/5.56 Clause #157 (by clausification #[156]): ∀ (a a_1 : nat), Or (Eq x y) (Or (Eq y (pl x (skS.0 5 a))) (Eq y (pl x (skS.0 6 a_1))))
% 5.38/5.56 Clause #200 (by clausification #[30]): ∀ (a : nat), Or (Eq x y) (Or (Eq (Ne x y) False) (Eq (Not (Ne x (pl y (skS.0 7 a)))) True))
% 5.38/5.56 Clause #201 (by clausification #[200]): ∀ (a : nat), Or (Eq x y) (Or (Eq (Not (Ne x (pl y (skS.0 7 a)))) True) (Eq x y))
% 5.38/5.56 Clause #202 (by clausification #[201]): ∀ (a : nat), Or (Eq x y) (Or (Eq x y) (Eq (Ne x (pl y (skS.0 7 a))) False))
% 5.38/5.56 Clause #203 (by clausification #[202]): ∀ (a : nat), Or (Eq x y) (Or (Eq x y) (Eq x (pl y (skS.0 7 a))))
% 5.38/5.56 Clause #204 (by eliminate duplicate literals #[203]): ∀ (a : nat), Or (Eq x y) (Eq x (pl y (skS.0 7 a)))
% 5.38/5.56 Clause #209 (by superposition #[204, 58]): ∀ (a : nat), Or (Eq x y) (Ne y (pl a x))
% 5.38/5.57 Clause #217 (by superposition #[209, 14]): ∀ (a : nat), Or (Eq x y) (Ne y (pl x a))
% 5.38/5.57 Clause #219 (by backward contextual literal cutting #[217, 157]): ∀ (a : nat), Or (Eq x y) (Eq y (pl x (skS.0 6 a)))
% 5.38/5.57 Clause #1155 (by forward contextual literal cutting #[219, 217]): Eq x y
% 5.38/5.57 Clause #1194 (by forward demodulation #[94, 1155]): ∀ (a a_1 a_2 a_3 : nat),
% 5.38/5.57 Or (Eq y (pl y (skS.0 3 a))) (Or (Eq y (pl x (skS.0 4 a_1))) (Eq (pl x a_2) (pl y (pl (skS.0 2 a_3) a_2))))
% 5.38/5.57 Clause #1195 (by forward demodulation #[1194, 1155]): ∀ (a a_1 a_2 a_3 : nat),
% 5.38/5.57 Or (Eq y (pl y (skS.0 3 a))) (Or (Eq y (pl y (skS.0 4 a_1))) (Eq (pl x a_2) (pl y (pl (skS.0 2 a_3) a_2))))
% 5.38/5.57 Clause #1196 (by forward demodulation #[1195, 1155]): ∀ (a a_1 a_2 a_3 : nat),
% 5.38/5.57 Or (Eq y (pl y (skS.0 3 a))) (Or (Eq y (pl y (skS.0 4 a_1))) (Eq (pl y a_2) (pl y (pl (skS.0 2 a_3) a_2))))
% 5.38/5.57 Clause #1197 (by forward contextual literal cutting #[1196, 15]): ∀ (a a_1 a_2 : nat), Or (Eq y (pl y (skS.0 4 a))) (Eq (pl y a_1) (pl y (pl (skS.0 2 a_2) a_1)))
% 5.38/5.57 Clause #1198 (by forward contextual literal cutting #[1197, 15]): ∀ (a a_1 : nat), Eq (pl y a) (pl y (pl (skS.0 2 a_1) a))
% 5.38/5.57 Clause #1199 (by forward contextual literal cutting #[1198, 70]): False
% 5.38/5.57 SZS output end Proof for theBenchmark.p
%------------------------------------------------------------------------------