TSTP Solution File: SEU890^5 by Duper---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : SEU890^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n031.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 16:44:14 EDT 2023
% Result : Theorem 6.96s 7.15s
% Output : Proof 7.04s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU890^5 : TPTP v8.1.2. Released v4.0.0.
% 0.13/0.14 % Command : duper %s
% 0.13/0.35 % Computer : n031.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 : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Wed Aug 23 12:45:19 EDT 2023
% 0.13/0.36 % CPUTime :
% 6.96/7.15 SZS status Theorem for theBenchmark.p
% 6.96/7.15 SZS output start Proof for theBenchmark.p
% 6.96/7.15 Clause #0 (by assumption #[]): Eq
% 6.96/7.15 (Not
% 6.96/7.15 (∀ (Xx : a),
% 6.96/7.15 Iff (Exists fun Xt => And (Exists fun Xt0 => And (cS Xt0) (Eq Xt (cG Xt0))) (Eq Xx (cF Xt)))
% 6.96/7.15 (Exists fun Xt => And (cS Xt) (Eq Xx (cF (cG Xt))))))
% 6.96/7.15 True
% 6.96/7.15 Clause #1 (by clausification #[0]): Eq
% 6.96/7.15 (∀ (Xx : a),
% 6.96/7.15 Iff (Exists fun Xt => And (Exists fun Xt0 => And (cS Xt0) (Eq Xt (cG Xt0))) (Eq Xx (cF Xt)))
% 6.96/7.15 (Exists fun Xt => And (cS Xt) (Eq Xx (cF (cG Xt)))))
% 6.96/7.15 False
% 6.96/7.15 Clause #2 (by clausification #[1]): ∀ (a_1 : a),
% 6.96/7.15 Eq
% 6.96/7.15 (Not
% 6.96/7.15 (Iff (Exists fun Xt => And (Exists fun Xt0 => And (cS Xt0) (Eq Xt (cG Xt0))) (Eq (skS.0 0 a_1) (cF Xt)))
% 6.96/7.15 (Exists fun Xt => And (cS Xt) (Eq (skS.0 0 a_1) (cF (cG Xt))))))
% 6.96/7.15 True
% 6.96/7.15 Clause #3 (by clausification #[2]): ∀ (a_1 : a),
% 6.96/7.15 Eq
% 6.96/7.15 (Iff (Exists fun Xt => And (Exists fun Xt0 => And (cS Xt0) (Eq Xt (cG Xt0))) (Eq (skS.0 0 a_1) (cF Xt)))
% 6.96/7.15 (Exists fun Xt => And (cS Xt) (Eq (skS.0 0 a_1) (cF (cG Xt)))))
% 6.96/7.15 False
% 6.96/7.15 Clause #4 (by clausification #[3]): ∀ (a_1 : a),
% 6.96/7.15 Or (Eq (Exists fun Xt => And (Exists fun Xt0 => And (cS Xt0) (Eq Xt (cG Xt0))) (Eq (skS.0 0 a_1) (cF Xt))) False)
% 6.96/7.15 (Eq (Exists fun Xt => And (cS Xt) (Eq (skS.0 0 a_1) (cF (cG Xt)))) False)
% 6.96/7.15 Clause #5 (by clausification #[3]): ∀ (a_1 : a),
% 6.96/7.15 Or (Eq (Exists fun Xt => And (Exists fun Xt0 => And (cS Xt0) (Eq Xt (cG Xt0))) (Eq (skS.0 0 a_1) (cF Xt))) True)
% 6.96/7.15 (Eq (Exists fun Xt => And (cS Xt) (Eq (skS.0 0 a_1) (cF (cG Xt)))) True)
% 6.96/7.15 Clause #6 (by clausification #[4]): ∀ (a_1 : a) (a_2 : b),
% 6.96/7.15 Or (Eq (Exists fun Xt => And (cS Xt) (Eq (skS.0 0 a_1) (cF (cG Xt)))) False)
% 6.96/7.15 (Eq (And (Exists fun Xt0 => And (cS Xt0) (Eq a_2 (cG Xt0))) (Eq (skS.0 0 a_1) (cF a_2))) False)
% 6.96/7.15 Clause #7 (by clausification #[6]): ∀ (a_1 : b) (a_2 : a) (a_3 : c),
% 6.96/7.15 Or (Eq (And (Exists fun Xt0 => And (cS Xt0) (Eq a_1 (cG Xt0))) (Eq (skS.0 0 a_2) (cF a_1))) False)
% 6.96/7.15 (Eq (And (cS a_3) (Eq (skS.0 0 a_2) (cF (cG a_3)))) False)
% 6.96/7.15 Clause #8 (by clausification #[7]): ∀ (a_1 : c) (a_2 : a) (a_3 : b),
% 6.96/7.15 Or (Eq (And (cS a_1) (Eq (skS.0 0 a_2) (cF (cG a_1)))) False)
% 6.96/7.15 (Or (Eq (Exists fun Xt0 => And (cS Xt0) (Eq a_3 (cG Xt0))) False) (Eq (Eq (skS.0 0 a_2) (cF a_3)) False))
% 6.96/7.15 Clause #9 (by clausification #[8]): ∀ (a_1 : b) (a_2 : a) (a_3 : c),
% 6.96/7.15 Or (Eq (Exists fun Xt0 => And (cS Xt0) (Eq a_1 (cG Xt0))) False)
% 6.96/7.15 (Or (Eq (Eq (skS.0 0 a_2) (cF a_1)) False) (Or (Eq (cS a_3) False) (Eq (Eq (skS.0 0 a_2) (cF (cG a_3))) False)))
% 6.96/7.15 Clause #10 (by clausification #[9]): ∀ (a_1 : a) (a_2 : b) (a_3 a_4 : c),
% 6.96/7.15 Or (Eq (Eq (skS.0 0 a_1) (cF a_2)) False)
% 6.96/7.15 (Or (Eq (cS a_3) False)
% 6.96/7.15 (Or (Eq (Eq (skS.0 0 a_1) (cF (cG a_3))) False) (Eq (And (cS a_4) (Eq a_2 (cG a_4))) False)))
% 6.96/7.15 Clause #11 (by clausification #[10]): ∀ (a_1 : c) (a_2 : a) (a_3 : c) (a_4 : b),
% 6.96/7.15 Or (Eq (cS a_1) False)
% 6.96/7.15 (Or (Eq (Eq (skS.0 0 a_2) (cF (cG a_1))) False)
% 6.96/7.15 (Or (Eq (And (cS a_3) (Eq a_4 (cG a_3))) False) (Ne (skS.0 0 a_2) (cF a_4))))
% 6.96/7.15 Clause #12 (by clausification #[11]): ∀ (a_1 a_2 : c) (a_3 : b) (a_4 : a),
% 6.96/7.15 Or (Eq (cS a_1) False)
% 6.96/7.15 (Or (Eq (And (cS a_2) (Eq a_3 (cG a_2))) False) (Or (Ne (skS.0 0 a_4) (cF a_3)) (Ne (skS.0 0 a_4) (cF (cG a_1)))))
% 6.96/7.15 Clause #13 (by clausification #[12]): ∀ (a_1 : c) (a_2 : a) (a_3 : b) (a_4 : c),
% 6.96/7.15 Or (Eq (cS a_1) False)
% 6.96/7.15 (Or (Ne (skS.0 0 a_2) (cF a_3))
% 6.96/7.15 (Or (Ne (skS.0 0 a_2) (cF (cG a_1))) (Or (Eq (cS a_4) False) (Eq (Eq a_3 (cG a_4)) False))))
% 6.96/7.15 Clause #14 (by clausification #[13]): ∀ (a_1 : c) (a_2 : a) (a_3 : b) (a_4 : c),
% 6.96/7.15 Or (Eq (cS a_1) False)
% 6.96/7.15 (Or (Ne (skS.0 0 a_2) (cF a_3)) (Or (Ne (skS.0 0 a_2) (cF (cG a_1))) (Or (Eq (cS a_4) False) (Ne a_3 (cG a_4)))))
% 6.96/7.15 Clause #15 (by destructive equality resolution #[14]): ∀ (a_1 : c) (a_2 : a) (a_3 : c),
% 6.96/7.15 Or (Eq (cS a_1) False) (Or (Ne (skS.0 0 a_2) (cF (cG a_3))) (Or (Ne (skS.0 0 a_2) (cF (cG a_1))) (Eq (cS a_3) False)))
% 6.96/7.15 Clause #16 (by clausification #[5]): ∀ (a_1 : a) (a_2 : b),
% 6.96/7.15 Or (Eq (Exists fun Xt => And (cS Xt) (Eq (skS.0 0 a_1) (cF (cG Xt)))) True)
% 6.96/7.15 (Eq (And (Exists fun Xt0 => And (cS Xt0) (Eq (skS.0 1 a_1 a_2) (cG Xt0))) (Eq (skS.0 0 a_1) (cF (skS.0 1 a_1 a_2))))
% 6.96/7.17 True)
% 6.96/7.17 Clause #17 (by clausification #[16]): ∀ (a_1 : a) (a_2 : b) (a_3 : c),
% 6.96/7.17 Or
% 6.96/7.17 (Eq (And (Exists fun Xt0 => And (cS Xt0) (Eq (skS.0 1 a_1 a_2) (cG Xt0))) (Eq (skS.0 0 a_1) (cF (skS.0 1 a_1 a_2))))
% 6.96/7.17 True)
% 6.96/7.17 (Eq (And (cS (skS.0 2 a_1 a_3)) (Eq (skS.0 0 a_1) (cF (cG (skS.0 2 a_1 a_3))))) True)
% 6.96/7.17 Clause #18 (by clausification #[17]): ∀ (a_1 : a) (a_2 : c) (a_3 : b),
% 6.96/7.17 Or (Eq (And (cS (skS.0 2 a_1 a_2)) (Eq (skS.0 0 a_1) (cF (cG (skS.0 2 a_1 a_2))))) True)
% 6.96/7.17 (Eq (Eq (skS.0 0 a_1) (cF (skS.0 1 a_1 a_3))) True)
% 6.96/7.17 Clause #19 (by clausification #[17]): ∀ (a_1 : a) (a_2 : c) (a_3 : b),
% 6.96/7.17 Or (Eq (And (cS (skS.0 2 a_1 a_2)) (Eq (skS.0 0 a_1) (cF (cG (skS.0 2 a_1 a_2))))) True)
% 6.96/7.17 (Eq (Exists fun Xt0 => And (cS Xt0) (Eq (skS.0 1 a_1 a_3) (cG Xt0))) True)
% 6.96/7.17 Clause #20 (by clausification #[18]): ∀ (a_1 : a) (a_2 : b) (a_3 : c),
% 6.96/7.17 Or (Eq (Eq (skS.0 0 a_1) (cF (skS.0 1 a_1 a_2))) True) (Eq (Eq (skS.0 0 a_1) (cF (cG (skS.0 2 a_1 a_3)))) True)
% 6.96/7.17 Clause #21 (by clausification #[18]): ∀ (a_1 : a) (a_2 : b) (a_3 : c), Or (Eq (Eq (skS.0 0 a_1) (cF (skS.0 1 a_1 a_2))) True) (Eq (cS (skS.0 2 a_1 a_3)) True)
% 6.96/7.17 Clause #22 (by clausification #[20]): ∀ (a_1 : a) (a_2 : c) (a_3 : b),
% 6.96/7.17 Or (Eq (Eq (skS.0 0 a_1) (cF (cG (skS.0 2 a_1 a_2)))) True) (Eq (skS.0 0 a_1) (cF (skS.0 1 a_1 a_3)))
% 6.96/7.17 Clause #23 (by clausification #[22]): ∀ (a_1 : a) (a_2 : b) (a_3 : c),
% 6.96/7.17 Or (Eq (skS.0 0 a_1) (cF (skS.0 1 a_1 a_2))) (Eq (skS.0 0 a_1) (cF (cG (skS.0 2 a_1 a_3))))
% 6.96/7.17 Clause #24 (by clausification #[21]): ∀ (a_1 : a) (a_2 : c) (a_3 : b), Or (Eq (cS (skS.0 2 a_1 a_2)) True) (Eq (skS.0 0 a_1) (cF (skS.0 1 a_1 a_3)))
% 6.96/7.17 Clause #25 (by superposition #[24, 15]): ∀ (a_1 : a) (a_2 : b) (a_3 : a) (a_4 a_5 : c),
% 6.96/7.17 Or (Eq (skS.0 0 a_1) (cF (skS.0 1 a_1 a_2)))
% 6.96/7.17 (Or (Eq True False)
% 6.96/7.17 (Or (Ne (skS.0 0 a_3) (cF (cG a_4))) (Or (Ne (skS.0 0 a_3) (cF (cG (skS.0 2 a_1 a_5)))) (Eq (cS a_4) False))))
% 6.96/7.17 Clause #26 (by clausification #[25]): ∀ (a_1 : a) (a_2 : b) (a_3 : a) (a_4 a_5 : c),
% 6.96/7.17 Or (Eq (skS.0 0 a_1) (cF (skS.0 1 a_1 a_2)))
% 6.96/7.17 (Or (Ne (skS.0 0 a_3) (cF (cG a_4))) (Or (Ne (skS.0 0 a_3) (cF (cG (skS.0 2 a_1 a_5)))) (Eq (cS a_4) False)))
% 6.96/7.17 Clause #27 (by superposition #[26, 23]): ∀ (a_1 : a) (a_2 : b) (a_3 : a) (a_4 : b) (a_5 : a) (a_6 a_7 : c),
% 6.96/7.17 Or (Eq (skS.0 0 a_1) (cF (skS.0 1 a_1 a_2)))
% 6.96/7.17 (Or (Eq (skS.0 0 a_3) (cF (skS.0 1 a_3 a_4)))
% 6.96/7.17 (Or (Ne (skS.0 0 a_5) (skS.0 0 a_1))
% 6.96/7.17 (Or (Ne (skS.0 0 a_5) (cF (cG (skS.0 2 a_3 a_6)))) (Eq (cS (skS.0 2 a_1 a_7)) False))))
% 6.96/7.17 Clause #28 (by clausification #[19]): ∀ (a_1 : a) (a_2 : b) (a_3 : c),
% 6.96/7.17 Or (Eq (Exists fun Xt0 => And (cS Xt0) (Eq (skS.0 1 a_1 a_2) (cG Xt0))) True)
% 6.96/7.17 (Eq (Eq (skS.0 0 a_1) (cF (cG (skS.0 2 a_1 a_3)))) True)
% 6.96/7.17 Clause #29 (by clausification #[19]): ∀ (a_1 : a) (a_2 : b) (a_3 : c),
% 6.96/7.17 Or (Eq (Exists fun Xt0 => And (cS Xt0) (Eq (skS.0 1 a_1 a_2) (cG Xt0))) True) (Eq (cS (skS.0 2 a_1 a_3)) True)
% 6.96/7.17 Clause #30 (by clausification #[28]): ∀ (a_1 : a) (a_2 : c) (a_3 : b) (a_4 : c),
% 6.96/7.17 Or (Eq (Eq (skS.0 0 a_1) (cF (cG (skS.0 2 a_1 a_2)))) True)
% 6.96/7.17 (Eq (And (cS (skS.0 3 a_1 a_3 a_4)) (Eq (skS.0 1 a_1 a_3) (cG (skS.0 3 a_1 a_3 a_4)))) True)
% 6.96/7.17 Clause #31 (by clausification #[30]): ∀ (a_1 : a) (a_2 : b) (a_3 a_4 : c),
% 6.96/7.17 Or (Eq (And (cS (skS.0 3 a_1 a_2 a_3)) (Eq (skS.0 1 a_1 a_2) (cG (skS.0 3 a_1 a_2 a_3)))) True)
% 6.96/7.17 (Eq (skS.0 0 a_1) (cF (cG (skS.0 2 a_1 a_4))))
% 6.96/7.17 Clause #32 (by clausification #[31]): ∀ (a_1 : a) (a_2 : c) (a_3 : b) (a_4 : c),
% 6.96/7.17 Or (Eq (skS.0 0 a_1) (cF (cG (skS.0 2 a_1 a_2)))) (Eq (Eq (skS.0 1 a_1 a_3) (cG (skS.0 3 a_1 a_3 a_4))) True)
% 6.96/7.17 Clause #33 (by clausification #[31]): ∀ (a_1 : a) (a_2 : c) (a_3 : b) (a_4 : c),
% 6.96/7.17 Or (Eq (skS.0 0 a_1) (cF (cG (skS.0 2 a_1 a_2)))) (Eq (cS (skS.0 3 a_1 a_3 a_4)) True)
% 6.96/7.17 Clause #34 (by clausification #[32]): ∀ (a_1 : a) (a_2 : c) (a_3 : b) (a_4 : c),
% 6.96/7.17 Or (Eq (skS.0 0 a_1) (cF (cG (skS.0 2 a_1 a_2)))) (Eq (skS.0 1 a_1 a_3) (cG (skS.0 3 a_1 a_3 a_4)))
% 6.96/7.17 Clause #37 (by equality resolution #[27]): ∀ (a_1 : a) (a_2 : b) (a_3 : a) (a_4 : b) (a_5 a_6 : c),
% 6.96/7.17 Or (Eq (skS.0 0 a_1) (cF (skS.0 1 a_1 a_2)))
% 7.04/7.20 (Or (Eq (skS.0 0 a_3) (cF (skS.0 1 a_3 a_4)))
% 7.04/7.20 (Or (Ne (skS.0 0 a_1) (cF (cG (skS.0 2 a_3 a_5)))) (Eq (cS (skS.0 2 a_1 a_6)) False)))
% 7.04/7.20 Clause #40 (by clausification #[29]): ∀ (a_1 : a) (a_2 : c) (a_3 : b) (a_4 : c),
% 7.04/7.20 Or (Eq (cS (skS.0 2 a_1 a_2)) True)
% 7.04/7.20 (Eq (And (cS (skS.0 4 a_1 a_3 a_4)) (Eq (skS.0 1 a_1 a_3) (cG (skS.0 4 a_1 a_3 a_4)))) True)
% 7.04/7.20 Clause #41 (by clausification #[40]): ∀ (a_1 : a) (a_2 : c) (a_3 : b) (a_4 : c),
% 7.04/7.20 Or (Eq (cS (skS.0 2 a_1 a_2)) True) (Eq (Eq (skS.0 1 a_1 a_3) (cG (skS.0 4 a_1 a_3 a_4))) True)
% 7.04/7.20 Clause #42 (by clausification #[40]): ∀ (a_1 : a) (a_2 : c) (a_3 : b) (a_4 : c), Or (Eq (cS (skS.0 2 a_1 a_2)) True) (Eq (cS (skS.0 4 a_1 a_3 a_4)) True)
% 7.04/7.20 Clause #43 (by clausification #[41]): ∀ (a_1 : a) (a_2 : c) (a_3 : b) (a_4 : c),
% 7.04/7.20 Or (Eq (cS (skS.0 2 a_1 a_2)) True) (Eq (skS.0 1 a_1 a_3) (cG (skS.0 4 a_1 a_3 a_4)))
% 7.04/7.20 Clause #47 (by superposition #[42, 15]): ∀ (a_1 : a) (a_2 : c) (a_3 : a) (a_4 : c) (a_5 : b) (a_6 : c),
% 7.04/7.20 Or (Eq (cS (skS.0 2 a_1 a_2)) True)
% 7.04/7.20 (Or (Eq True False)
% 7.04/7.20 (Or (Ne (skS.0 0 a_3) (cF (cG a_4))) (Or (Ne (skS.0 0 a_3) (cF (cG (skS.0 4 a_1 a_5 a_6)))) (Eq (cS a_4) False))))
% 7.04/7.20 Clause #54 (by clausification #[47]): ∀ (a_1 : a) (a_2 : c) (a_3 : a) (a_4 : c) (a_5 : b) (a_6 : c),
% 7.04/7.20 Or (Eq (cS (skS.0 2 a_1 a_2)) True)
% 7.04/7.20 (Or (Ne (skS.0 0 a_3) (cF (cG a_4))) (Or (Ne (skS.0 0 a_3) (cF (cG (skS.0 4 a_1 a_5 a_6)))) (Eq (cS a_4) False)))
% 7.04/7.20 Clause #59 (by superposition #[54, 43]): ∀ (a_1 : a) (a_2 : c) (a_3 : a) (a_4 : c) (a_5 : a) (a_6 a_7 : b) (a_8 a_9 : c),
% 7.04/7.20 Or (Eq (cS (skS.0 2 a_1 a_2)) True)
% 7.04/7.20 (Or (Eq (cS (skS.0 2 a_3 a_4)) True)
% 7.04/7.20 (Or (Ne (skS.0 0 a_5) (cF (skS.0 1 a_1 a_6)))
% 7.04/7.20 (Or (Ne (skS.0 0 a_5) (cF (cG (skS.0 4 a_3 a_7 a_8)))) (Eq (cS (skS.0 4 a_1 a_6 a_9)) False))))
% 7.04/7.20 Clause #73 (by superposition #[37, 23]): ∀ (a_1 : a) (a_2 : b) (a_3 : a) (a_4 a_5 : b) (a_6 : c),
% 7.04/7.20 Or (Eq (skS.0 0 a_1) (cF (skS.0 1 a_1 a_2)))
% 7.04/7.20 (Or (Eq (skS.0 0 a_3) (cF (skS.0 1 a_3 a_4)))
% 7.04/7.20 (Or (Eq (skS.0 0 a_1) (cF (skS.0 1 a_1 a_5)))
% 7.04/7.20 (Or (Ne (skS.0 0 a_3) (skS.0 0 a_1)) (Eq (cS (skS.0 2 a_3 a_6)) False))))
% 7.04/7.20 Clause #308 (by equality resolution #[73]): ∀ (a_1 : a) (a_2 a_3 a_4 : b) (a_5 : c),
% 7.04/7.20 Or (Eq (skS.0 0 a_1) (cF (skS.0 1 a_1 a_2)))
% 7.04/7.20 (Or (Eq (skS.0 0 a_1) (cF (skS.0 1 a_1 a_3)))
% 7.04/7.20 (Or (Eq (skS.0 0 a_1) (cF (skS.0 1 a_1 a_4))) (Eq (cS (skS.0 2 a_1 a_5)) False)))
% 7.04/7.20 Clause #309 (by superposition #[308, 24]): ∀ (a_1 : a) (a_2 a_3 a_4 a_5 : b),
% 7.04/7.20 Or (Eq (skS.0 0 a_1) (cF (skS.0 1 a_1 a_2)))
% 7.04/7.20 (Or (Eq (skS.0 0 a_1) (cF (skS.0 1 a_1 a_3)))
% 7.04/7.20 (Or (Eq (skS.0 0 a_1) (cF (skS.0 1 a_1 a_4))) (Or (Eq False True) (Eq (skS.0 0 a_1) (cF (skS.0 1 a_1 a_5))))))
% 7.04/7.20 Clause #314 (by clausification #[309]): ∀ (a_1 : a) (a_2 a_3 a_4 a_5 : b),
% 7.04/7.20 Or (Eq (skS.0 0 a_1) (cF (skS.0 1 a_1 a_2)))
% 7.04/7.20 (Or (Eq (skS.0 0 a_1) (cF (skS.0 1 a_1 a_3)))
% 7.04/7.20 (Or (Eq (skS.0 0 a_1) (cF (skS.0 1 a_1 a_4))) (Eq (skS.0 0 a_1) (cF (skS.0 1 a_1 a_5)))))
% 7.04/7.20 Clause #328 (by equality factoring #[314]): ∀ (a_1 : a) (a_2 a_3 a_4 : b),
% 7.04/7.20 Or (Eq (skS.0 0 a_1) (cF (skS.0 1 a_1 a_2)))
% 7.04/7.20 (Or (Eq (skS.0 0 a_1) (cF (skS.0 1 a_1 a_3)))
% 7.04/7.20 (Or (Ne (skS.0 0 a_1) (skS.0 0 a_1)) (Eq (skS.0 0 a_1) (cF (skS.0 1 a_1 a_4)))))
% 7.04/7.20 Clause #329 (by eliminate resolved literals #[328]): ∀ (a_1 : a) (a_2 a_3 a_4 : b),
% 7.04/7.20 Or (Eq (skS.0 0 a_1) (cF (skS.0 1 a_1 a_2)))
% 7.04/7.20 (Or (Eq (skS.0 0 a_1) (cF (skS.0 1 a_1 a_3))) (Eq (skS.0 0 a_1) (cF (skS.0 1 a_1 a_4))))
% 7.04/7.20 Clause #343 (by equality factoring #[329]): ∀ (a_1 : a) (a_2 a_3 : b),
% 7.04/7.20 Or (Eq (skS.0 0 a_1) (cF (skS.0 1 a_1 a_2)))
% 7.04/7.20 (Or (Ne (skS.0 0 a_1) (skS.0 0 a_1)) (Eq (skS.0 0 a_1) (cF (skS.0 1 a_1 a_3))))
% 7.04/7.20 Clause #344 (by eliminate resolved literals #[343]): ∀ (a_1 : a) (a_2 a_3 : b), Or (Eq (skS.0 0 a_1) (cF (skS.0 1 a_1 a_2))) (Eq (skS.0 0 a_1) (cF (skS.0 1 a_1 a_3)))
% 7.04/7.20 Clause #358 (by equality factoring #[344]): ∀ (a_1 : a) (a_2 : b), Or (Ne (skS.0 0 a_1) (skS.0 0 a_1)) (Eq (skS.0 0 a_1) (cF (skS.0 1 a_1 a_2)))
% 7.04/7.20 Clause #359 (by eliminate resolved literals #[358]): ∀ (a_1 : a) (a_2 : b), Eq (skS.0 0 a_1) (cF (skS.0 1 a_1 a_2))
% 7.04/7.20 Clause #369 (by backward demodulation #[359, 59]): ∀ (a_1 : a) (a_2 : c) (a_3 : a) (a_4 : c) (a_5 : a) (a_6 : b) (a_7 : c) (a_8 : b) (a_9 : c),
% 7.04/7.23 Or (Eq (cS (skS.0 2 a_1 a_2)) True)
% 7.04/7.23 (Or (Eq (cS (skS.0 2 a_3 a_4)) True)
% 7.04/7.23 (Or (Ne (skS.0 0 a_5) (skS.0 0 a_1))
% 7.04/7.23 (Or (Ne (skS.0 0 a_5) (cF (cG (skS.0 4 a_3 a_6 a_7)))) (Eq (cS (skS.0 4 a_1 a_8 a_9)) False))))
% 7.04/7.23 Clause #402 (by equality resolution #[369]): ∀ (a_1 : a) (a_2 : c) (a_3 : a) (a_4 : c) (a_5 : b) (a_6 : c) (a_7 : b) (a_8 : c),
% 7.04/7.23 Or (Eq (cS (skS.0 2 a_1 a_2)) True)
% 7.04/7.23 (Or (Eq (cS (skS.0 2 a_3 a_4)) True)
% 7.04/7.23 (Or (Ne (skS.0 0 a_1) (cF (cG (skS.0 4 a_3 a_5 a_6)))) (Eq (cS (skS.0 4 a_1 a_7 a_8)) False)))
% 7.04/7.23 Clause #403 (by superposition #[402, 43]): ∀ (a_1 : a) (a_2 : c) (a_3 : a) (a_4 a_5 : c) (a_6 a_7 : b) (a_8 : c),
% 7.04/7.23 Or (Eq (cS (skS.0 2 a_1 a_2)) True)
% 7.04/7.23 (Or (Eq (cS (skS.0 2 a_3 a_4)) True)
% 7.04/7.23 (Or (Eq (cS (skS.0 2 a_1 a_5)) True)
% 7.04/7.23 (Or (Ne (skS.0 0 a_3) (cF (skS.0 1 a_1 a_6))) (Eq (cS (skS.0 4 a_3 a_7 a_8)) False))))
% 7.04/7.23 Clause #404 (by forward demodulation #[403, 359]): ∀ (a_1 : a) (a_2 : c) (a_3 : a) (a_4 a_5 : c) (a_6 : b) (a_7 : c),
% 7.04/7.23 Or (Eq (cS (skS.0 2 a_1 a_2)) True)
% 7.04/7.23 (Or (Eq (cS (skS.0 2 a_3 a_4)) True)
% 7.04/7.23 (Or (Eq (cS (skS.0 2 a_1 a_5)) True) (Or (Ne (skS.0 0 a_3) (skS.0 0 a_1)) (Eq (cS (skS.0 4 a_3 a_6 a_7)) False))))
% 7.04/7.23 Clause #405 (by equality resolution #[404]): ∀ (a_1 : a) (a_2 a_3 a_4 : c) (a_5 : b) (a_6 : c),
% 7.04/7.23 Or (Eq (cS (skS.0 2 a_1 a_2)) True)
% 7.04/7.23 (Or (Eq (cS (skS.0 2 a_1 a_3)) True) (Or (Eq (cS (skS.0 2 a_1 a_4)) True) (Eq (cS (skS.0 4 a_1 a_5 a_6)) False)))
% 7.04/7.23 Clause #406 (by superposition #[405, 42]): ∀ (a_1 : a) (a_2 a_3 a_4 a_5 : c),
% 7.04/7.23 Or (Eq (cS (skS.0 2 a_1 a_2)) True)
% 7.04/7.23 (Or (Eq (cS (skS.0 2 a_1 a_3)) True)
% 7.04/7.23 (Or (Eq (cS (skS.0 2 a_1 a_4)) True) (Or (Eq (cS (skS.0 2 a_1 a_5)) True) (Eq False True))))
% 7.04/7.23 Clause #408 (by clausification #[406]): ∀ (a_1 : a) (a_2 a_3 a_4 a_5 : c),
% 7.04/7.23 Or (Eq (cS (skS.0 2 a_1 a_2)) True)
% 7.04/7.23 (Or (Eq (cS (skS.0 2 a_1 a_3)) True) (Or (Eq (cS (skS.0 2 a_1 a_4)) True) (Eq (cS (skS.0 2 a_1 a_5)) True)))
% 7.04/7.23 Clause #413 (by equality factoring #[408]): ∀ (a_1 : a) (a_2 a_3 a_4 : c),
% 7.04/7.23 Or (Eq (cS (skS.0 2 a_1 a_2)) True)
% 7.04/7.23 (Or (Eq (cS (skS.0 2 a_1 a_3)) True) (Or (Ne True True) (Eq (cS (skS.0 2 a_1 a_4)) True)))
% 7.04/7.23 Clause #414 (by clausification #[413]): ∀ (a_1 : a) (a_2 a_3 a_4 : c),
% 7.04/7.23 Or (Eq (cS (skS.0 2 a_1 a_2)) True)
% 7.04/7.23 (Or (Eq (cS (skS.0 2 a_1 a_3)) True) (Or (Eq (cS (skS.0 2 a_1 a_4)) True) (Or (Eq True False) (Eq True False))))
% 7.04/7.23 Clause #416 (by clausification #[414]): ∀ (a_1 : a) (a_2 a_3 a_4 : c),
% 7.04/7.23 Or (Eq (cS (skS.0 2 a_1 a_2)) True)
% 7.04/7.23 (Or (Eq (cS (skS.0 2 a_1 a_3)) True) (Or (Eq (cS (skS.0 2 a_1 a_4)) True) (Eq True False)))
% 7.04/7.23 Clause #417 (by clausification #[416]): ∀ (a_1 : a) (a_2 a_3 a_4 : c),
% 7.04/7.23 Or (Eq (cS (skS.0 2 a_1 a_2)) True) (Or (Eq (cS (skS.0 2 a_1 a_3)) True) (Eq (cS (skS.0 2 a_1 a_4)) True))
% 7.04/7.23 Clause #422 (by equality factoring #[417]): ∀ (a_1 : a) (a_2 a_3 : c), Or (Eq (cS (skS.0 2 a_1 a_2)) True) (Or (Ne True True) (Eq (cS (skS.0 2 a_1 a_3)) True))
% 7.04/7.23 Clause #423 (by clausification #[422]): ∀ (a_1 : a) (a_2 a_3 : c),
% 7.04/7.23 Or (Eq (cS (skS.0 2 a_1 a_2)) True) (Or (Eq (cS (skS.0 2 a_1 a_3)) True) (Or (Eq True False) (Eq True False)))
% 7.04/7.23 Clause #425 (by clausification #[423]): ∀ (a_1 : a) (a_2 a_3 : c), Or (Eq (cS (skS.0 2 a_1 a_2)) True) (Or (Eq (cS (skS.0 2 a_1 a_3)) True) (Eq True False))
% 7.04/7.23 Clause #426 (by clausification #[425]): ∀ (a_1 : a) (a_2 a_3 : c), Or (Eq (cS (skS.0 2 a_1 a_2)) True) (Eq (cS (skS.0 2 a_1 a_3)) True)
% 7.04/7.23 Clause #429 (by equality factoring #[426]): ∀ (a_1 : a) (a_2 : c), Or (Ne True True) (Eq (cS (skS.0 2 a_1 a_2)) True)
% 7.04/7.23 Clause #430 (by clausification #[429]): ∀ (a_1 : a) (a_2 : c), Or (Eq (cS (skS.0 2 a_1 a_2)) True) (Or (Eq True False) (Eq True False))
% 7.04/7.23 Clause #432 (by clausification #[430]): ∀ (a_1 : a) (a_2 : c), Or (Eq (cS (skS.0 2 a_1 a_2)) True) (Eq True False)
% 7.04/7.23 Clause #433 (by clausification #[432]): ∀ (a_1 : a) (a_2 : c), Eq (cS (skS.0 2 a_1 a_2)) True
% 7.04/7.23 Clause #434 (by superposition #[433, 15]): ∀ (a_1 : a) (a_2 : c) (a_3 : a) (a_4 : c),
% 7.04/7.23 Or (Eq True False)
% 7.04/7.25 (Or (Ne (skS.0 0 a_1) (cF (cG a_2))) (Or (Ne (skS.0 0 a_1) (cF (cG (skS.0 2 a_3 a_4)))) (Eq (cS a_2) False)))
% 7.04/7.25 Clause #435 (by clausification #[434]): ∀ (a_1 : a) (a_2 : c) (a_3 : a) (a_4 : c),
% 7.04/7.25 Or (Ne (skS.0 0 a_1) (cF (cG a_2))) (Or (Ne (skS.0 0 a_1) (cF (cG (skS.0 2 a_3 a_4)))) (Eq (cS a_2) False))
% 7.04/7.25 Clause #436 (by superposition #[435, 34]): ∀ (a_1 : a) (a_2 : b) (a_3 : c) (a_4 a_5 : a) (a_6 a_7 : c),
% 7.04/7.25 Or (Eq (skS.0 1 a_1 a_2) (cG (skS.0 3 a_1 a_2 a_3)))
% 7.04/7.25 (Or (Ne (skS.0 0 a_4) (skS.0 0 a_1))
% 7.04/7.25 (Or (Ne (skS.0 0 a_4) (cF (cG (skS.0 2 a_5 a_6)))) (Eq (cS (skS.0 2 a_1 a_7)) False)))
% 7.04/7.25 Clause #437 (by superposition #[435, 33]): ∀ (a_1 : a) (a_2 : b) (a_3 : c) (a_4 a_5 : a) (a_6 a_7 : c),
% 7.04/7.25 Or (Eq (cS (skS.0 3 a_1 a_2 a_3)) True)
% 7.04/7.25 (Or (Ne (skS.0 0 a_4) (skS.0 0 a_1))
% 7.04/7.25 (Or (Ne (skS.0 0 a_4) (cF (cG (skS.0 2 a_5 a_6)))) (Eq (cS (skS.0 2 a_1 a_7)) False)))
% 7.04/7.25 Clause #443 (by equality resolution #[437]): ∀ (a_1 : a) (a_2 : b) (a_3 : c) (a_4 : a) (a_5 a_6 : c),
% 7.04/7.25 Or (Eq (cS (skS.0 3 a_1 a_2 a_3)) True)
% 7.04/7.25 (Or (Ne (skS.0 0 a_1) (cF (cG (skS.0 2 a_4 a_5)))) (Eq (cS (skS.0 2 a_1 a_6)) False))
% 7.04/7.25 Clause #445 (by superposition #[443, 33]): ∀ (a_1 : a) (a_2 : b) (a_3 : c) (a_4 : a) (a_5 : b) (a_6 a_7 : c),
% 7.04/7.25 Or (Eq (cS (skS.0 3 a_1 a_2 a_3)) True)
% 7.04/7.25 (Or (Eq (cS (skS.0 3 a_4 a_5 a_6)) True) (Or (Ne (skS.0 0 a_4) (skS.0 0 a_1)) (Eq (cS (skS.0 2 a_4 a_7)) False)))
% 7.04/7.25 Clause #446 (by equality resolution #[445]): ∀ (a_1 : a) (a_2 : b) (a_3 : c) (a_4 : b) (a_5 a_6 : c),
% 7.04/7.25 Or (Eq (cS (skS.0 3 a_1 a_2 a_3)) True) (Or (Eq (cS (skS.0 3 a_1 a_4 a_5)) True) (Eq (cS (skS.0 2 a_1 a_6)) False))
% 7.04/7.25 Clause #447 (by superposition #[446, 433]): ∀ (a_1 : a) (a_2 : b) (a_3 : c) (a_4 : b) (a_5 : c),
% 7.04/7.25 Or (Eq (cS (skS.0 3 a_1 a_2 a_3)) True) (Or (Eq (cS (skS.0 3 a_1 a_4 a_5)) True) (Eq False True))
% 7.04/7.25 Clause #448 (by clausification #[447]): ∀ (a_1 : a) (a_2 : b) (a_3 : c) (a_4 : b) (a_5 : c),
% 7.04/7.25 Or (Eq (cS (skS.0 3 a_1 a_2 a_3)) True) (Eq (cS (skS.0 3 a_1 a_4 a_5)) True)
% 7.04/7.25 Clause #450 (by equality factoring #[448]): ∀ (a_1 : a) (a_2 : b) (a_3 : c), Or (Ne True True) (Eq (cS (skS.0 3 a_1 a_2 a_3)) True)
% 7.04/7.25 Clause #451 (by clausification #[450]): ∀ (a_1 : a) (a_2 : b) (a_3 : c), Or (Eq (cS (skS.0 3 a_1 a_2 a_3)) True) (Or (Eq True False) (Eq True False))
% 7.04/7.25 Clause #453 (by clausification #[451]): ∀ (a_1 : a) (a_2 : b) (a_3 : c), Or (Eq (cS (skS.0 3 a_1 a_2 a_3)) True) (Eq True False)
% 7.04/7.25 Clause #454 (by clausification #[453]): ∀ (a_1 : a) (a_2 : b) (a_3 : c), Eq (cS (skS.0 3 a_1 a_2 a_3)) True
% 7.04/7.25 Clause #455 (by superposition #[454, 15]): ∀ (a_1 : a) (a_2 : c) (a_3 : a) (a_4 : b) (a_5 : c),
% 7.04/7.25 Or (Eq True False)
% 7.04/7.25 (Or (Ne (skS.0 0 a_1) (cF (cG a_2))) (Or (Ne (skS.0 0 a_1) (cF (cG (skS.0 3 a_3 a_4 a_5)))) (Eq (cS a_2) False)))
% 7.04/7.25 Clause #456 (by clausification #[455]): ∀ (a_1 : a) (a_2 : c) (a_3 : a) (a_4 : b) (a_5 : c),
% 7.04/7.25 Or (Ne (skS.0 0 a_1) (cF (cG a_2))) (Or (Ne (skS.0 0 a_1) (cF (cG (skS.0 3 a_3 a_4 a_5)))) (Eq (cS a_2) False))
% 7.04/7.25 Clause #462 (by equality resolution #[436]): ∀ (a_1 : a) (a_2 : b) (a_3 : c) (a_4 : a) (a_5 a_6 : c),
% 7.04/7.25 Or (Eq (skS.0 1 a_1 a_2) (cG (skS.0 3 a_1 a_2 a_3)))
% 7.04/7.25 (Or (Ne (skS.0 0 a_1) (cF (cG (skS.0 2 a_4 a_5)))) (Eq (cS (skS.0 2 a_1 a_6)) False))
% 7.04/7.25 Clause #463 (by superposition #[462, 34]): ∀ (a_1 : a) (a_2 : b) (a_3 : c) (a_4 : a) (a_5 : b) (a_6 a_7 : c),
% 7.04/7.25 Or (Eq (skS.0 1 a_1 a_2) (cG (skS.0 3 a_1 a_2 a_3)))
% 7.04/7.25 (Or (Eq (skS.0 1 a_4 a_5) (cG (skS.0 3 a_4 a_5 a_6)))
% 7.04/7.25 (Or (Ne (skS.0 0 a_4) (skS.0 0 a_1)) (Eq (cS (skS.0 2 a_4 a_7)) False)))
% 7.04/7.25 Clause #473 (by equality resolution #[463]): ∀ (a_1 : a) (a_2 : b) (a_3 : c) (a_4 : b) (a_5 a_6 : c),
% 7.04/7.25 Or (Eq (skS.0 1 a_1 a_2) (cG (skS.0 3 a_1 a_2 a_3)))
% 7.04/7.25 (Or (Eq (skS.0 1 a_1 a_4) (cG (skS.0 3 a_1 a_4 a_5))) (Eq (cS (skS.0 2 a_1 a_6)) False))
% 7.04/7.25 Clause #474 (by superposition #[473, 433]): ∀ (a_1 : a) (a_2 : b) (a_3 : c) (a_4 : b) (a_5 : c),
% 7.04/7.25 Or (Eq (skS.0 1 a_1 a_2) (cG (skS.0 3 a_1 a_2 a_3)))
% 7.04/7.25 (Or (Eq (skS.0 1 a_1 a_4) (cG (skS.0 3 a_1 a_4 a_5))) (Eq False True))
% 7.04/7.25 Clause #475 (by clausification #[474]): ∀ (a_1 : a) (a_2 : b) (a_3 : c) (a_4 : b) (a_5 : c),
% 7.04/7.27 Or (Eq (skS.0 1 a_1 a_2) (cG (skS.0 3 a_1 a_2 a_3))) (Eq (skS.0 1 a_1 a_4) (cG (skS.0 3 a_1 a_4 a_5)))
% 7.04/7.27 Clause #479 (by equality factoring #[475]): ∀ (a_1 : a) (a_2 : b) (a_3 : c),
% 7.04/7.27 Or (Ne (skS.0 1 a_1 a_2) (skS.0 1 a_1 a_2)) (Eq (skS.0 1 a_1 a_2) (cG (skS.0 3 a_1 a_2 a_3)))
% 7.04/7.27 Clause #480 (by eliminate resolved literals #[479]): ∀ (a_1 : a) (a_2 : b) (a_3 : c), Eq (skS.0 1 a_1 a_2) (cG (skS.0 3 a_1 a_2 a_3))
% 7.04/7.27 Clause #481 (by backward demodulation #[480, 456]): ∀ (a_1 : a) (a_2 : c) (a_3 : a) (a_4 : b),
% 7.04/7.27 Or (Ne (skS.0 0 a_1) (cF (cG a_2))) (Or (Ne (skS.0 0 a_1) (cF (skS.0 1 a_3 a_4))) (Eq (cS a_2) False))
% 7.04/7.27 Clause #485 (by forward demodulation #[481, 359]): ∀ (a_1 : a) (a_2 : c) (a_3 : a),
% 7.04/7.27 Or (Ne (skS.0 0 a_1) (cF (cG a_2))) (Or (Ne (skS.0 0 a_1) (skS.0 0 a_3)) (Eq (cS a_2) False))
% 7.04/7.27 Clause #486 (by superposition #[485, 480]): ∀ (a_1 a_2 : a) (a_3 : b) (a_4 : a) (a_5 : c),
% 7.04/7.27 Or (Ne (skS.0 0 a_1) (cF (skS.0 1 a_2 a_3)))
% 7.04/7.27 (Or (Ne (skS.0 0 a_1) (skS.0 0 a_4)) (Eq (cS (skS.0 3 a_2 a_3 a_5)) False))
% 7.04/7.27 Clause #487 (by forward demodulation #[486, 359]): ∀ (a_1 a_2 a_3 : a) (a_4 : b) (a_5 : c),
% 7.04/7.27 Or (Ne (skS.0 0 a_1) (skS.0 0 a_2)) (Or (Ne (skS.0 0 a_1) (skS.0 0 a_3)) (Eq (cS (skS.0 3 a_2 a_4 a_5)) False))
% 7.04/7.27 Clause #488 (by equality resolution #[487]): ∀ (a_1 a_2 : a) (a_3 : b) (a_4 : c), Or (Ne (skS.0 0 a_1) (skS.0 0 a_2)) (Eq (cS (skS.0 3 a_1 a_3 a_4)) False)
% 7.04/7.27 Clause #489 (by equality resolution #[488]): ∀ (a_1 : a) (a_2 : b) (a_3 : c), Eq (cS (skS.0 3 a_1 a_2 a_3)) False
% 7.04/7.27 Clause #490 (by superposition #[489, 454]): Eq False True
% 7.04/7.27 Clause #491 (by clausification #[490]): False
% 7.04/7.27 SZS output end Proof for theBenchmark.p
%------------------------------------------------------------------------------