TSTP Solution File: NUM686^1 by Duper---1.0
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% File : Duper---1.0
% Problem : NUM686^1 : TPTP v8.1.2. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n032.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 10:57:02 EDT 2023
% Result : Theorem 4.69s 4.95s
% Output : Proof 4.69s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : NUM686^1 : TPTP v8.1.2. Released v3.7.0.
% 0.00/0.11 % Command : duper %s
% 0.10/0.30 % Computer : n032.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 300
% 0.10/0.30 % DateTime : Fri Aug 25 13:32:13 EDT 2023
% 0.10/0.30 % CPUTime :
% 4.69/4.95 SZS status Theorem for theBenchmark.p
% 4.69/4.95 SZS output start Proof for theBenchmark.p
% 4.69/4.95 Clause #0 (by assumption #[]): Eq (some fun Xu => diffprop x y Xu) True
% 4.69/4.95 Clause #1 (by assumption #[]): Eq (some fun Xu_0 => diffprop z u Xu_0) True
% 4.69/4.95 Clause #2 (by assumption #[]): Eq
% 4.69/4.95 (∀ (Xx Xy Xz : nat),
% 4.69/4.95 (some fun Xv => diffprop Xy Xx Xv) → (some fun Xv => diffprop Xz Xy Xv) → some fun Xv => diffprop Xz Xx Xv)
% 4.69/4.95 True
% 4.69/4.95 Clause #3 (by assumption #[]): Eq (∀ (Xx Xy Xz : nat), (some fun Xu => diffprop Xx Xy Xu) → some fun Xu => diffprop (pl Xx Xz) (pl Xy Xz) Xu) True
% 4.69/4.95 Clause #4 (by assumption #[]): Eq (∀ (Xx Xy : nat), Eq (pl Xx Xy) (pl Xy Xx)) True
% 4.69/4.95 Clause #5 (by assumption #[]): Eq (Not (some fun Xu_0 => diffprop (pl x z) (pl y u) Xu_0)) True
% 4.69/4.95 Clause #6 (by betaEtaReduce #[1]): Eq (some (diffprop z u)) True
% 4.69/4.95 Clause #7 (by betaEtaReduce #[0]): Eq (some (diffprop x y)) True
% 4.69/4.95 Clause #8 (by clausification #[4]): ∀ (a : nat), Eq (∀ (Xy : nat), Eq (pl a Xy) (pl Xy a)) True
% 4.69/4.95 Clause #9 (by clausification #[8]): ∀ (a a_1 : nat), Eq (Eq (pl a a_1) (pl a_1 a)) True
% 4.69/4.95 Clause #10 (by clausification #[9]): ∀ (a a_1 : nat), Eq (pl a a_1) (pl a_1 a)
% 4.69/4.95 Clause #11 (by betaEtaReduce #[5]): Eq (Not (some (diffprop (pl x z) (pl y u)))) True
% 4.69/4.95 Clause #12 (by clausification #[11]): Eq (some (diffprop (pl x z) (pl y u))) False
% 4.69/4.95 Clause #13 (by forward demodulation #[12, 10]): Eq (some (diffprop (pl x z) (pl u y))) False
% 4.69/4.95 Clause #14 (by forward demodulation #[13, 10]): Eq (some (diffprop (pl z x) (pl u y))) False
% 4.69/4.95 Clause #15 (by betaEtaReduce #[2]): Eq (∀ (Xx Xy Xz : nat), some (diffprop Xy Xx) → some (diffprop Xz Xy) → some (diffprop Xz Xx)) True
% 4.69/4.95 Clause #16 (by clausification #[15]): ∀ (a : nat), Eq (∀ (Xy Xz : nat), some (diffprop Xy a) → some (diffprop Xz Xy) → some (diffprop Xz a)) True
% 4.69/4.95 Clause #17 (by clausification #[16]): ∀ (a a_1 : nat), Eq (∀ (Xz : nat), some (diffprop a a_1) → some (diffprop Xz a) → some (diffprop Xz a_1)) True
% 4.69/4.95 Clause #18 (by clausification #[17]): ∀ (a a_1 a_2 : nat), Eq (some (diffprop a a_1) → some (diffprop a_2 a) → some (diffprop a_2 a_1)) True
% 4.69/4.95 Clause #19 (by clausification #[18]): ∀ (a a_1 a_2 : nat), Or (Eq (some (diffprop a a_1)) False) (Eq (some (diffprop a_2 a) → some (diffprop a_2 a_1)) True)
% 4.69/4.95 Clause #20 (by clausification #[19]): ∀ (a a_1 a_2 : nat),
% 4.69/4.95 Or (Eq (some (diffprop a a_1)) False) (Or (Eq (some (diffprop a_2 a)) False) (Eq (some (diffprop a_2 a_1)) True))
% 4.69/4.95 Clause #23 (by betaEtaReduce #[3]): Eq (∀ (Xx Xy Xz : nat), some (diffprop Xx Xy) → some (diffprop (pl Xx Xz) (pl Xy Xz))) True
% 4.69/4.95 Clause #24 (by clausification #[23]): ∀ (a : nat), Eq (∀ (Xy Xz : nat), some (diffprop a Xy) → some (diffprop (pl a Xz) (pl Xy Xz))) True
% 4.69/4.95 Clause #25 (by clausification #[24]): ∀ (a a_1 : nat), Eq (∀ (Xz : nat), some (diffprop a a_1) → some (diffprop (pl a Xz) (pl a_1 Xz))) True
% 4.69/4.95 Clause #26 (by clausification #[25]): ∀ (a a_1 a_2 : nat), Eq (some (diffprop a a_1) → some (diffprop (pl a a_2) (pl a_1 a_2))) True
% 4.69/4.95 Clause #27 (by clausification #[26]): ∀ (a a_1 a_2 : nat), Or (Eq (some (diffprop a a_1)) False) (Eq (some (diffprop (pl a a_2) (pl a_1 a_2))) True)
% 4.69/4.95 Clause #28 (by superposition #[27, 6]): ∀ (a : nat), Or (Eq (some (diffprop (pl z a) (pl u a))) True) (Eq False True)
% 4.69/4.95 Clause #29 (by superposition #[27, 7]): ∀ (a : nat), Or (Eq (some (diffprop (pl x a) (pl y a))) True) (Eq False True)
% 4.69/4.95 Clause #30 (by clausification #[29]): ∀ (a : nat), Eq (some (diffprop (pl x a) (pl y a))) True
% 4.69/4.95 Clause #31 (by superposition #[30, 20]): ∀ (a a_1 : nat),
% 4.69/4.95 Or (Eq True False) (Or (Eq (some (diffprop a (pl x a_1))) False) (Eq (some (diffprop a (pl y a_1))) True))
% 4.69/4.95 Clause #42 (by clausification #[28]): ∀ (a : nat), Eq (some (diffprop (pl z a) (pl u a))) True
% 4.69/4.95 Clause #45 (by superposition #[42, 10]): ∀ (a : nat), Eq (some (diffprop (pl z a) (pl a u))) True
% 4.69/4.95 Clause #61 (by clausification #[31]): ∀ (a a_1 : nat), Or (Eq (some (diffprop a (pl x a_1))) False) (Eq (some (diffprop a (pl y a_1))) True)
% 4.69/4.95 Clause #64 (by superposition #[61, 45]): Or (Eq (some (diffprop (pl z x) (pl y u))) True) (Eq False True)
% 4.69/4.95 Clause #68 (by clausification #[64]): Eq (some (diffprop (pl z x) (pl y u))) True
% 4.69/4.95 Clause #69 (by forward demodulation #[68, 10]): Eq (some (diffprop (pl z x) (pl u y))) True
% 4.69/4.95 Clause #70 (by superposition #[69, 14]): Eq True False
% 4.69/4.95 Clause #73 (by clausification #[70]): False
% 4.69/4.95 SZS output end Proof for theBenchmark.p
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