TSTP Solution File: LCL414+1 by Duper---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : LCL414+1 : TPTP v8.1.2. Released v2.5.0.
% 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 07:09:40 EDT 2023
% Result : Theorem 4.98s 5.22s
% Output : Proof 4.99s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL414+1 : TPTP v8.1.2. Released v2.5.0.
% 0.00/0.13 % Command : duper %s
% 0.14/0.34 % Computer : n018.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Fri Aug 25 04:35:28 EDT 2023
% 0.14/0.34 % CPUTime :
% 4.98/5.22 SZS status Theorem for theBenchmark.p
% 4.98/5.22 SZS output start Proof for theBenchmark.p
% 4.98/5.22 Clause #0 (by assumption #[]): Eq
% 4.98/5.22 (Not
% 4.98/5.22 (Not
% 4.98/5.22 (And
% 4.98/5.22 (And
% 4.98/5.22 (And
% 4.98/5.22 (And (∀ (P Q : Iota), Or (Or (Not (a_truth (implies P Q))) (Not (a_truth P))) (a_truth Q))
% 4.98/5.22 (∀ (P Q : Iota), a_truth (implies P (implies Q P))))
% 4.98/5.22 (∀ (P Q R : Iota), a_truth (implies (implies P (implies Q R)) (implies (implies P Q) (implies P R)))))
% 4.98/5.22 (∀ (P Q : Iota), a_truth (implies (implies (not P) (not Q)) (implies Q P))))
% 4.98/5.22 (Exists fun A => Not (a_truth (implies A A))))))
% 4.98/5.22 True
% 4.98/5.22 Clause #1 (by clausification #[0]): Eq
% 4.98/5.22 (Not
% 4.98/5.22 (And
% 4.98/5.22 (And
% 4.98/5.22 (And
% 4.98/5.22 (And (∀ (P Q : Iota), Or (Or (Not (a_truth (implies P Q))) (Not (a_truth P))) (a_truth Q))
% 4.98/5.22 (∀ (P Q : Iota), a_truth (implies P (implies Q P))))
% 4.98/5.22 (∀ (P Q R : Iota), a_truth (implies (implies P (implies Q R)) (implies (implies P Q) (implies P R)))))
% 4.98/5.22 (∀ (P Q : Iota), a_truth (implies (implies (not P) (not Q)) (implies Q P))))
% 4.98/5.22 (Exists fun A => Not (a_truth (implies A A)))))
% 4.98/5.22 False
% 4.98/5.22 Clause #2 (by clausification #[1]): Eq
% 4.98/5.22 (And
% 4.98/5.22 (And
% 4.98/5.22 (And
% 4.98/5.22 (And (∀ (P Q : Iota), Or (Or (Not (a_truth (implies P Q))) (Not (a_truth P))) (a_truth Q))
% 4.98/5.22 (∀ (P Q : Iota), a_truth (implies P (implies Q P))))
% 4.98/5.22 (∀ (P Q R : Iota), a_truth (implies (implies P (implies Q R)) (implies (implies P Q) (implies P R)))))
% 4.98/5.22 (∀ (P Q : Iota), a_truth (implies (implies (not P) (not Q)) (implies Q P))))
% 4.98/5.22 (Exists fun A => Not (a_truth (implies A A))))
% 4.98/5.22 True
% 4.98/5.22 Clause #3 (by clausification #[2]): Eq (Exists fun A => Not (a_truth (implies A A))) True
% 4.98/5.22 Clause #4 (by clausification #[2]): Eq
% 4.98/5.22 (And
% 4.98/5.22 (And
% 4.98/5.22 (And (∀ (P Q : Iota), Or (Or (Not (a_truth (implies P Q))) (Not (a_truth P))) (a_truth Q))
% 4.98/5.22 (∀ (P Q : Iota), a_truth (implies P (implies Q P))))
% 4.98/5.22 (∀ (P Q R : Iota), a_truth (implies (implies P (implies Q R)) (implies (implies P Q) (implies P R)))))
% 4.98/5.22 (∀ (P Q : Iota), a_truth (implies (implies (not P) (not Q)) (implies Q P))))
% 4.98/5.22 True
% 4.98/5.22 Clause #5 (by clausification #[3]): ∀ (a : Iota), Eq (Not (a_truth (implies (skS.0 0 a) (skS.0 0 a)))) True
% 4.98/5.22 Clause #6 (by clausification #[5]): ∀ (a : Iota), Eq (a_truth (implies (skS.0 0 a) (skS.0 0 a))) False
% 4.98/5.22 Clause #8 (by clausification #[4]): Eq
% 4.98/5.22 (And
% 4.98/5.22 (And (∀ (P Q : Iota), Or (Or (Not (a_truth (implies P Q))) (Not (a_truth P))) (a_truth Q))
% 4.98/5.22 (∀ (P Q : Iota), a_truth (implies P (implies Q P))))
% 4.98/5.22 (∀ (P Q R : Iota), a_truth (implies (implies P (implies Q R)) (implies (implies P Q) (implies P R)))))
% 4.98/5.22 True
% 4.98/5.22 Clause #11 (by clausification #[8]): Eq (∀ (P Q R : Iota), a_truth (implies (implies P (implies Q R)) (implies (implies P Q) (implies P R)))) True
% 4.98/5.22 Clause #12 (by clausification #[8]): Eq
% 4.98/5.22 (And (∀ (P Q : Iota), Or (Or (Not (a_truth (implies P Q))) (Not (a_truth P))) (a_truth Q))
% 4.98/5.22 (∀ (P Q : Iota), a_truth (implies P (implies Q P))))
% 4.98/5.22 True
% 4.98/5.22 Clause #13 (by clausification #[11]): ∀ (a : Iota),
% 4.98/5.22 Eq (∀ (Q R : Iota), a_truth (implies (implies a (implies Q R)) (implies (implies a Q) (implies a R)))) True
% 4.98/5.22 Clause #14 (by clausification #[13]): ∀ (a a_1 : Iota),
% 4.98/5.22 Eq (∀ (R : Iota), a_truth (implies (implies a (implies a_1 R)) (implies (implies a a_1) (implies a R)))) True
% 4.98/5.22 Clause #15 (by clausification #[14]): ∀ (a a_1 a_2 : Iota),
% 4.98/5.22 Eq (a_truth (implies (implies a (implies a_1 a_2)) (implies (implies a a_1) (implies a a_2)))) True
% 4.98/5.22 Clause #16 (by clausification #[12]): Eq (∀ (P Q : Iota), a_truth (implies P (implies Q P))) True
% 4.98/5.22 Clause #17 (by clausification #[12]): Eq (∀ (P Q : Iota), Or (Or (Not (a_truth (implies P Q))) (Not (a_truth P))) (a_truth Q)) True
% 4.98/5.22 Clause #18 (by clausification #[16]): ∀ (a : Iota), Eq (∀ (Q : Iota), a_truth (implies a (implies Q a))) True
% 4.98/5.22 Clause #19 (by clausification #[18]): ∀ (a a_1 : Iota), Eq (a_truth (implies a (implies a_1 a))) True
% 4.98/5.22 Clause #20 (by clausification #[17]): ∀ (a : Iota), Eq (∀ (Q : Iota), Or (Or (Not (a_truth (implies a Q))) (Not (a_truth a))) (a_truth Q)) True
% 4.99/5.24 Clause #21 (by clausification #[20]): ∀ (a a_1 : Iota), Eq (Or (Or (Not (a_truth (implies a a_1))) (Not (a_truth a))) (a_truth a_1)) True
% 4.99/5.24 Clause #22 (by clausification #[21]): ∀ (a a_1 : Iota), Or (Eq (Or (Not (a_truth (implies a a_1))) (Not (a_truth a))) True) (Eq (a_truth a_1) True)
% 4.99/5.24 Clause #23 (by clausification #[22]): ∀ (a a_1 : Iota), Or (Eq (a_truth a) True) (Or (Eq (Not (a_truth (implies a_1 a))) True) (Eq (Not (a_truth a_1)) True))
% 4.99/5.24 Clause #24 (by clausification #[23]): ∀ (a a_1 : Iota), Or (Eq (a_truth a) True) (Or (Eq (Not (a_truth a_1)) True) (Eq (a_truth (implies a_1 a)) False))
% 4.99/5.24 Clause #25 (by clausification #[24]): ∀ (a a_1 : Iota), Or (Eq (a_truth a) True) (Or (Eq (a_truth (implies a_1 a)) False) (Eq (a_truth a_1) False))
% 4.99/5.24 Clause #27 (by superposition #[25, 15]): ∀ (a a_1 a_2 : Iota),
% 4.99/5.24 Or (Eq (a_truth (implies (implies a a_1) (implies a a_2))) True)
% 4.99/5.24 (Or (Eq (a_truth (implies a (implies a_1 a_2))) False) (Eq False True))
% 4.99/5.24 Clause #42 (by clausification #[27]): ∀ (a a_1 a_2 : Iota),
% 4.99/5.24 Or (Eq (a_truth (implies (implies a a_1) (implies a a_2))) True) (Eq (a_truth (implies a (implies a_1 a_2))) False)
% 4.99/5.24 Clause #45 (by superposition #[42, 19]): ∀ (a a_1 : Iota), Or (Eq (a_truth (implies (implies a a_1) (implies a a))) True) (Eq False True)
% 4.99/5.24 Clause #48 (by clausification #[45]): ∀ (a a_1 : Iota), Eq (a_truth (implies (implies a a_1) (implies a a))) True
% 4.99/5.24 Clause #49 (by superposition #[48, 25]): ∀ (a a_1 : Iota), Or (Eq (a_truth (implies a a)) True) (Or (Eq True False) (Eq (a_truth (implies a a_1)) False))
% 4.99/5.24 Clause #52 (by clausification #[49]): ∀ (a a_1 : Iota), Or (Eq (a_truth (implies a a)) True) (Eq (a_truth (implies a a_1)) False)
% 4.99/5.24 Clause #55 (by superposition #[52, 19]): ∀ (a : Iota), Or (Eq (a_truth (implies a a)) True) (Eq False True)
% 4.99/5.24 Clause #57 (by clausification #[55]): ∀ (a : Iota), Eq (a_truth (implies a a)) True
% 4.99/5.24 Clause #58 (by superposition #[57, 6]): Eq True False
% 4.99/5.24 Clause #63 (by clausification #[58]): False
% 4.99/5.24 SZS output end Proof for theBenchmark.p
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