TSTP Solution File: KLE005+1 by Duper---1.0
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%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : KLE005+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n018.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 05:28:15 EDT 2023
% Result : Theorem 12.64s 12.88s
% Output : Proof 12.73s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : KLE005+1 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.13 % Command : duper %s
% 0.13/0.35 % Computer : n018.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 : Tue Aug 29 11:18:47 EDT 2023
% 0.13/0.35 % CPUTime :
% 12.64/12.88 SZS status Theorem for theBenchmark.p
% 12.64/12.88 SZS output start Proof for theBenchmark.p
% 12.64/12.88 Clause #0 (by assumption #[]): Eq (∀ (A B : Iota), Eq (addition A B) (addition B A)) True
% 12.64/12.88 Clause #2 (by assumption #[]): Eq (∀ (A : Iota), Eq (addition A zero) A) True
% 12.64/12.88 Clause #5 (by assumption #[]): Eq (∀ (A : Iota), Eq (multiplication A one) A) True
% 12.64/12.88 Clause #9 (by assumption #[]): Eq (∀ (A : Iota), Eq (multiplication A zero) zero) True
% 12.64/12.88 Clause #12 (by assumption #[]): Eq (∀ (X0 : Iota), Iff (test X0) (Exists fun X1 => complement X1 X0)) True
% 12.64/12.88 Clause #13 (by assumption #[]): Eq
% 12.64/12.88 (∀ (X0 X1 : Iota),
% 12.64/12.88 Iff (complement X1 X0)
% 12.64/12.88 (And (And (Eq (multiplication X0 X1) zero) (Eq (multiplication X1 X0) zero)) (Eq (addition X0 X1) one)))
% 12.64/12.88 True
% 12.64/12.88 Clause #14 (by assumption #[]): Eq (∀ (X0 X1 : Iota), test X0 → Iff (Eq (c X0) X1) (complement X0 X1)) True
% 12.64/12.88 Clause #16 (by assumption #[]): Eq (Not (Eq (c one) zero)) True
% 12.64/12.88 Clause #17 (by clausification #[16]): Eq (Eq (c one) zero) False
% 12.64/12.88 Clause #18 (by clausification #[17]): Ne (c one) zero
% 12.64/12.88 Clause #25 (by clausification #[9]): ∀ (a : Iota), Eq (Eq (multiplication a zero) zero) True
% 12.64/12.88 Clause #26 (by clausification #[25]): ∀ (a : Iota), Eq (multiplication a zero) zero
% 12.64/12.88 Clause #29 (by clausification #[0]): ∀ (a : Iota), Eq (∀ (B : Iota), Eq (addition a B) (addition B a)) True
% 12.64/12.88 Clause #30 (by clausification #[29]): ∀ (a a_1 : Iota), Eq (Eq (addition a a_1) (addition a_1 a)) True
% 12.64/12.88 Clause #31 (by clausification #[30]): ∀ (a a_1 : Iota), Eq (addition a a_1) (addition a_1 a)
% 12.64/12.88 Clause #32 (by clausification #[5]): ∀ (a : Iota), Eq (Eq (multiplication a one) a) True
% 12.64/12.88 Clause #33 (by clausification #[32]): ∀ (a : Iota), Eq (multiplication a one) a
% 12.64/12.88 Clause #36 (by clausification #[2]): ∀ (a : Iota), Eq (Eq (addition a zero) a) True
% 12.64/12.88 Clause #37 (by clausification #[36]): ∀ (a : Iota), Eq (addition a zero) a
% 12.64/12.88 Clause #39 (by superposition #[37, 31]): ∀ (a : Iota), Eq (addition zero a) a
% 12.64/12.88 Clause #177 (by clausification #[12]): ∀ (a : Iota), Eq (Iff (test a) (Exists fun X1 => complement X1 a)) True
% 12.64/12.88 Clause #178 (by clausification #[177]): ∀ (a : Iota), Or (Eq (test a) True) (Eq (Exists fun X1 => complement X1 a) False)
% 12.64/12.88 Clause #180 (by clausification #[178]): ∀ (a a_1 : Iota), Or (Eq (test a) True) (Eq (complement a_1 a) False)
% 12.64/12.88 Clause #190 (by clausification #[13]): ∀ (a : Iota),
% 12.64/12.88 Eq
% 12.64/12.88 (∀ (X1 : Iota),
% 12.64/12.88 Iff (complement X1 a)
% 12.64/12.88 (And (And (Eq (multiplication a X1) zero) (Eq (multiplication X1 a) zero)) (Eq (addition a X1) one)))
% 12.64/12.88 True
% 12.64/12.88 Clause #191 (by clausification #[190]): ∀ (a a_1 : Iota),
% 12.64/12.88 Eq
% 12.64/12.88 (Iff (complement a a_1)
% 12.64/12.88 (And (And (Eq (multiplication a_1 a) zero) (Eq (multiplication a a_1) zero)) (Eq (addition a_1 a) one)))
% 12.64/12.88 True
% 12.64/12.88 Clause #192 (by clausification #[191]): ∀ (a a_1 : Iota),
% 12.64/12.88 Or (Eq (complement a a_1) True)
% 12.64/12.88 (Eq (And (And (Eq (multiplication a_1 a) zero) (Eq (multiplication a a_1) zero)) (Eq (addition a_1 a) one)) False)
% 12.64/12.88 Clause #194 (by clausification #[192]): ∀ (a a_1 : Iota),
% 12.64/12.88 Or (Eq (complement a a_1) True)
% 12.64/12.88 (Or (Eq (And (Eq (multiplication a_1 a) zero) (Eq (multiplication a a_1) zero)) False)
% 12.64/12.88 (Eq (Eq (addition a_1 a) one) False))
% 12.64/12.88 Clause #195 (by clausification #[194]): ∀ (a a_1 : Iota),
% 12.64/12.88 Or (Eq (complement a a_1) True)
% 12.64/12.88 (Or (Eq (Eq (addition a_1 a) one) False)
% 12.64/12.88 (Or (Eq (Eq (multiplication a_1 a) zero) False) (Eq (Eq (multiplication a a_1) zero) False)))
% 12.64/12.88 Clause #196 (by clausification #[195]): ∀ (a a_1 : Iota),
% 12.64/12.88 Or (Eq (complement a a_1) True)
% 12.64/12.88 (Or (Eq (Eq (multiplication a_1 a) zero) False)
% 12.64/12.88 (Or (Eq (Eq (multiplication a a_1) zero) False) (Ne (addition a_1 a) one)))
% 12.64/12.88 Clause #197 (by clausification #[196]): ∀ (a a_1 : Iota),
% 12.64/12.88 Or (Eq (complement a a_1) True)
% 12.64/12.88 (Or (Eq (Eq (multiplication a a_1) zero) False) (Or (Ne (addition a_1 a) one) (Ne (multiplication a_1 a) zero)))
% 12.64/12.88 Clause #198 (by clausification #[197]): ∀ (a a_1 : Iota),
% 12.64/12.88 Or (Eq (complement a a_1) True)
% 12.64/12.88 (Or (Ne (addition a_1 a) one) (Or (Ne (multiplication a_1 a) zero) (Ne (multiplication a a_1) zero)))
% 12.64/12.88 Clause #201 (by superposition #[198, 37]): ∀ (a : Iota),
% 12.73/12.92 Or (Eq (complement zero a) True)
% 12.73/12.92 (Or (Ne a one) (Or (Ne (multiplication a zero) zero) (Ne (multiplication zero a) zero)))
% 12.73/12.92 Clause #205 (by superposition #[198, 39]): ∀ (a : Iota),
% 12.73/12.92 Or (Eq (complement a zero) True)
% 12.73/12.92 (Or (Ne a one) (Or (Ne (multiplication zero a) zero) (Ne (multiplication a zero) zero)))
% 12.73/12.92 Clause #227 (by clausification #[14]): ∀ (a : Iota), Eq (∀ (X1 : Iota), test a → Iff (Eq (c a) X1) (complement a X1)) True
% 12.73/12.92 Clause #228 (by clausification #[227]): ∀ (a a_1 : Iota), Eq (test a → Iff (Eq (c a) a_1) (complement a a_1)) True
% 12.73/12.92 Clause #229 (by clausification #[228]): ∀ (a a_1 : Iota), Or (Eq (test a) False) (Eq (Iff (Eq (c a) a_1) (complement a a_1)) True)
% 12.73/12.92 Clause #230 (by clausification #[229]): ∀ (a a_1 : Iota), Or (Eq (test a) False) (Or (Eq (Eq (c a) a_1) True) (Eq (complement a a_1) False))
% 12.73/12.92 Clause #232 (by clausification #[230]): ∀ (a a_1 : Iota), Or (Eq (test a) False) (Or (Eq (complement a a_1) False) (Eq (c a) a_1))
% 12.73/12.92 Clause #6762 (by destructive equality resolution #[201]): Or (Eq (complement zero one) True) (Or (Ne (multiplication one zero) zero) (Ne (multiplication zero one) zero))
% 12.73/12.92 Clause #6763 (by forward demodulation #[6762, 26]): Or (Eq (complement zero one) True) (Or (Ne zero zero) (Ne (multiplication zero one) zero))
% 12.73/12.92 Clause #6764 (by eliminate resolved literals #[6763]): Or (Eq (complement zero one) True) (Ne (multiplication zero one) zero)
% 12.73/12.92 Clause #6765 (by forward demodulation #[6764, 33]): Or (Eq (complement zero one) True) (Ne zero zero)
% 12.73/12.92 Clause #6766 (by eliminate resolved literals #[6765]): Eq (complement zero one) True
% 12.73/12.92 Clause #6767 (by superposition #[6766, 180]): Or (Eq (test one) True) (Eq True False)
% 12.73/12.92 Clause #6769 (by clausification #[6767]): Eq (test one) True
% 12.73/12.92 Clause #6770 (by superposition #[6769, 232]): ∀ (a : Iota), Or (Eq True False) (Or (Eq (complement one a) False) (Eq (c one) a))
% 12.73/12.92 Clause #6773 (by clausification #[6770]): ∀ (a : Iota), Or (Eq (complement one a) False) (Eq (c one) a)
% 12.73/12.92 Clause #6926 (by destructive equality resolution #[205]): Or (Eq (complement one zero) True) (Or (Ne (multiplication zero one) zero) (Ne (multiplication one zero) zero))
% 12.73/12.92 Clause #6927 (by forward demodulation #[6926, 33]): Or (Eq (complement one zero) True) (Or (Ne zero zero) (Ne (multiplication one zero) zero))
% 12.73/12.92 Clause #6928 (by eliminate resolved literals #[6927]): Or (Eq (complement one zero) True) (Ne (multiplication one zero) zero)
% 12.73/12.92 Clause #6929 (by forward demodulation #[6928, 26]): Or (Eq (complement one zero) True) (Ne zero zero)
% 12.73/12.92 Clause #6930 (by eliminate resolved literals #[6929]): Eq (complement one zero) True
% 12.73/12.92 Clause #6931 (by superposition #[6930, 6773]): Or (Eq True False) (Eq (c one) zero)
% 12.73/12.92 Clause #6937 (by clausification #[6931]): Eq (c one) zero
% 12.73/12.92 Clause #6938 (by forward contextual literal cutting #[6937, 18]): False
% 12.73/12.92 SZS output end Proof for theBenchmark.p
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