TSTP Solution File: KLE072+1 by Duper---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : KLE072+1 : 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 05:28:31 EDT 2023
% Result : Theorem 3.83s 4.04s
% Output : Proof 3.83s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : KLE072+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14 % Command : duper %s
% 0.15/0.34 % Computer : n031.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Tue Aug 29 11:42:26 EDT 2023
% 0.15/0.35 % CPUTime :
% 3.83/4.04 SZS status Theorem for theBenchmark.p
% 3.83/4.04 SZS output start Proof for theBenchmark.p
% 3.83/4.04 Clause #8 (by assumption #[]): Eq (∀ (A B C : Iota), Eq (multiplication (addition A B) C) (addition (multiplication A C) (multiplication B C))) True
% 3.83/4.04 Clause #13 (by assumption #[]): Eq (∀ (X0 X1 : Iota), Eq (domain (multiplication X0 X1)) (domain (multiplication X0 (domain X1)))) True
% 3.83/4.04 Clause #16 (by assumption #[]): Eq (∀ (X0 X1 : Iota), Eq (domain (addition X0 X1)) (addition (domain X0) (domain X1))) True
% 3.83/4.04 Clause #17 (by assumption #[]): Eq
% 3.83/4.04 (Not
% 3.83/4.04 (∀ (X0 X1 X2 : Iota),
% 3.83/4.04 Eq (domain (multiplication (addition X0 X1) (domain X2)))
% 3.83/4.04 (addition (domain (multiplication X0 (domain X2))) (domain (multiplication X1 (domain X2))))))
% 3.83/4.04 True
% 3.83/4.04 Clause #101 (by clausification #[8]): ∀ (a : Iota),
% 3.83/4.04 Eq (∀ (B C : Iota), Eq (multiplication (addition a B) C) (addition (multiplication a C) (multiplication B C))) True
% 3.83/4.04 Clause #102 (by clausification #[101]): ∀ (a a_1 : Iota),
% 3.83/4.04 Eq (∀ (C : Iota), Eq (multiplication (addition a a_1) C) (addition (multiplication a C) (multiplication a_1 C))) True
% 3.83/4.04 Clause #103 (by clausification #[102]): ∀ (a a_1 a_2 : Iota),
% 3.83/4.04 Eq (Eq (multiplication (addition a a_1) a_2) (addition (multiplication a a_2) (multiplication a_1 a_2))) True
% 3.83/4.04 Clause #104 (by clausification #[103]): ∀ (a a_1 a_2 : Iota),
% 3.83/4.04 Eq (multiplication (addition a a_1) a_2) (addition (multiplication a a_2) (multiplication a_1 a_2))
% 3.83/4.04 Clause #171 (by clausification #[13]): ∀ (a : Iota), Eq (∀ (X1 : Iota), Eq (domain (multiplication a X1)) (domain (multiplication a (domain X1)))) True
% 3.83/4.04 Clause #172 (by clausification #[171]): ∀ (a a_1 : Iota), Eq (Eq (domain (multiplication a a_1)) (domain (multiplication a (domain a_1)))) True
% 3.83/4.04 Clause #173 (by clausification #[172]): ∀ (a a_1 : Iota), Eq (domain (multiplication a a_1)) (domain (multiplication a (domain a_1)))
% 3.83/4.04 Clause #189 (by clausification #[16]): ∀ (a : Iota), Eq (∀ (X1 : Iota), Eq (domain (addition a X1)) (addition (domain a) (domain X1))) True
% 3.83/4.04 Clause #190 (by clausification #[189]): ∀ (a a_1 : Iota), Eq (Eq (domain (addition a a_1)) (addition (domain a) (domain a_1))) True
% 3.83/4.04 Clause #191 (by clausification #[190]): ∀ (a a_1 : Iota), Eq (domain (addition a a_1)) (addition (domain a) (domain a_1))
% 3.83/4.04 Clause #210 (by clausification #[17]): Eq
% 3.83/4.04 (∀ (X0 X1 X2 : Iota),
% 3.83/4.04 Eq (domain (multiplication (addition X0 X1) (domain X2)))
% 3.83/4.04 (addition (domain (multiplication X0 (domain X2))) (domain (multiplication X1 (domain X2)))))
% 3.83/4.04 False
% 3.83/4.04 Clause #211 (by clausification #[210]): ∀ (a : Iota),
% 3.83/4.04 Eq
% 3.83/4.04 (Not
% 3.83/4.04 (∀ (X1 X2 : Iota),
% 3.83/4.04 Eq (domain (multiplication (addition (skS.0 0 a) X1) (domain X2)))
% 3.83/4.04 (addition (domain (multiplication (skS.0 0 a) (domain X2))) (domain (multiplication X1 (domain X2))))))
% 3.83/4.04 True
% 3.83/4.04 Clause #212 (by clausification #[211]): ∀ (a : Iota),
% 3.83/4.04 Eq
% 3.83/4.04 (∀ (X1 X2 : Iota),
% 3.83/4.04 Eq (domain (multiplication (addition (skS.0 0 a) X1) (domain X2)))
% 3.83/4.04 (addition (domain (multiplication (skS.0 0 a) (domain X2))) (domain (multiplication X1 (domain X2)))))
% 3.83/4.04 False
% 3.83/4.04 Clause #213 (by clausification #[212]): ∀ (a a_1 : Iota),
% 3.83/4.04 Eq
% 3.83/4.04 (Not
% 3.83/4.04 (∀ (X2 : Iota),
% 3.83/4.04 Eq (domain (multiplication (addition (skS.0 0 a) (skS.0 1 a a_1)) (domain X2)))
% 3.83/4.04 (addition (domain (multiplication (skS.0 0 a) (domain X2)))
% 3.83/4.04 (domain (multiplication (skS.0 1 a a_1) (domain X2))))))
% 3.83/4.04 True
% 3.83/4.04 Clause #214 (by clausification #[213]): ∀ (a a_1 : Iota),
% 3.83/4.04 Eq
% 3.83/4.04 (∀ (X2 : Iota),
% 3.83/4.04 Eq (domain (multiplication (addition (skS.0 0 a) (skS.0 1 a a_1)) (domain X2)))
% 3.83/4.04 (addition (domain (multiplication (skS.0 0 a) (domain X2)))
% 3.83/4.04 (domain (multiplication (skS.0 1 a a_1) (domain X2)))))
% 3.83/4.04 False
% 3.83/4.04 Clause #215 (by clausification #[214]): ∀ (a a_1 a_2 : Iota),
% 3.83/4.04 Eq
% 3.83/4.04 (Not
% 3.83/4.04 (Eq (domain (multiplication (addition (skS.0 0 a) (skS.0 1 a a_1)) (domain (skS.0 2 a a_1 a_2))))
% 3.83/4.04 (addition (domain (multiplication (skS.0 0 a) (domain (skS.0 2 a a_1 a_2))))
% 3.83/4.04 (domain (multiplication (skS.0 1 a a_1) (domain (skS.0 2 a a_1 a_2)))))))
% 3.83/4.04 True
% 3.83/4.05 Clause #216 (by clausification #[215]): ∀ (a a_1 a_2 : Iota),
% 3.83/4.05 Eq
% 3.83/4.05 (Eq (domain (multiplication (addition (skS.0 0 a) (skS.0 1 a a_1)) (domain (skS.0 2 a a_1 a_2))))
% 3.83/4.05 (addition (domain (multiplication (skS.0 0 a) (domain (skS.0 2 a a_1 a_2))))
% 3.83/4.05 (domain (multiplication (skS.0 1 a a_1) (domain (skS.0 2 a a_1 a_2))))))
% 3.83/4.05 False
% 3.83/4.05 Clause #217 (by clausification #[216]): ∀ (a a_1 a_2 : Iota),
% 3.83/4.05 Ne (domain (multiplication (addition (skS.0 0 a) (skS.0 1 a a_1)) (domain (skS.0 2 a a_1 a_2))))
% 3.83/4.05 (addition (domain (multiplication (skS.0 0 a) (domain (skS.0 2 a a_1 a_2))))
% 3.83/4.05 (domain (multiplication (skS.0 1 a a_1) (domain (skS.0 2 a a_1 a_2)))))
% 3.83/4.05 Clause #218 (by forward demodulation #[217, 173]): ∀ (a a_1 a_2 : Iota),
% 3.83/4.05 Ne (domain (multiplication (addition (skS.0 0 a) (skS.0 1 a a_1)) (skS.0 2 a a_1 a_2)))
% 3.83/4.05 (addition (domain (multiplication (skS.0 0 a) (domain (skS.0 2 a a_1 a_2))))
% 3.83/4.05 (domain (multiplication (skS.0 1 a a_1) (domain (skS.0 2 a a_1 a_2)))))
% 3.83/4.05 Clause #219 (by forward demodulation #[218, 191]): ∀ (a a_1 a_2 : Iota),
% 3.83/4.05 Ne (domain (multiplication (addition (skS.0 0 a) (skS.0 1 a a_1)) (skS.0 2 a a_1 a_2)))
% 3.83/4.05 (domain
% 3.83/4.05 (addition (multiplication (skS.0 0 a) (domain (skS.0 2 a a_1 a_2)))
% 3.83/4.05 (multiplication (skS.0 1 a a_1) (domain (skS.0 2 a a_1 a_2)))))
% 3.83/4.05 Clause #220 (by forward demodulation #[219, 104]): ∀ (a a_1 a_2 : Iota),
% 3.83/4.05 Ne (domain (multiplication (addition (skS.0 0 a) (skS.0 1 a a_1)) (skS.0 2 a a_1 a_2)))
% 3.83/4.05 (domain (multiplication (addition (skS.0 0 a) (skS.0 1 a a_1)) (domain (skS.0 2 a a_1 a_2))))
% 3.83/4.05 Clause #221 (by forward demodulation #[220, 173]): ∀ (a a_1 a_2 : Iota),
% 3.83/4.05 Ne (domain (multiplication (addition (skS.0 0 a) (skS.0 1 a a_1)) (skS.0 2 a a_1 a_2)))
% 3.83/4.05 (domain (multiplication (addition (skS.0 0 a) (skS.0 1 a a_1)) (skS.0 2 a a_1 a_2)))
% 3.83/4.05 Clause #222 (by eliminate resolved literals #[221]): False
% 3.83/4.05 SZS output end Proof for theBenchmark.p
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