TSTP Solution File: SYN058^5 by Duper---1.0
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% File : Duper---1.0
% Problem : SYN058^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n005.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 : Fri Sep 1 02:10:22 EDT 2023
% Result : Theorem 3.65s 3.90s
% Output : Proof 3.65s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SYN058^5 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.14 % Command : duper %s
% 0.21/0.35 % Computer : n005.cluster.edu
% 0.21/0.35 % Model : x86_64 x86_64
% 0.21/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.21/0.35 % Memory : 8042.1875MB
% 0.21/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.21/0.35 % CPULimit : 300
% 0.21/0.35 % WCLimit : 300
% 0.21/0.35 % DateTime : Sat Aug 26 21:37:38 EDT 2023
% 0.21/0.35 % CPUTime :
% 3.65/3.90 SZS status Theorem for theBenchmark.p
% 3.65/3.90 SZS output start Proof for theBenchmark.p
% 3.65/3.90 Clause #0 (by assumption #[]): Eq
% 3.65/3.90 (Not
% 3.65/3.90 (And
% 3.65/3.90 (And (∀ (Xx : Iota), cP Xx → ∀ (Xx0 : Iota), cQ Xx0)
% 3.65/3.90 ((∀ (Xx : Iota), Or (cQ Xx) (cR Xx)) → Exists fun Xx => And (cQ Xx) (cS Xx)))
% 3.65/3.90 ((Exists fun Xx => cS Xx) → ∀ (Xx : Iota), cF Xx → cG Xx) →
% 3.65/3.90 ∀ (Xx : Iota), And (cP Xx) (cF Xx) → cG Xx))
% 3.65/3.90 True
% 3.65/3.90 Clause #1 (by betaEtaReduce #[0]): Eq
% 3.65/3.90 (Not
% 3.65/3.90 (And
% 3.65/3.90 (And (∀ (Xx : Iota), cP Xx → ∀ (Xx0 : Iota), cQ Xx0)
% 3.65/3.90 ((∀ (Xx : Iota), Or (cQ Xx) (cR Xx)) → Exists fun Xx => And (cQ Xx) (cS Xx)))
% 3.65/3.90 (Exists cS → ∀ (Xx : Iota), cF Xx → cG Xx) →
% 3.65/3.90 ∀ (Xx : Iota), And (cP Xx) (cF Xx) → cG Xx))
% 3.65/3.90 True
% 3.65/3.90 Clause #2 (by clausification #[1]): Eq
% 3.65/3.90 (And
% 3.65/3.90 (And (∀ (Xx : Iota), cP Xx → ∀ (Xx0 : Iota), cQ Xx0)
% 3.65/3.90 ((∀ (Xx : Iota), Or (cQ Xx) (cR Xx)) → Exists fun Xx => And (cQ Xx) (cS Xx)))
% 3.65/3.90 (Exists cS → ∀ (Xx : Iota), cF Xx → cG Xx) →
% 3.65/3.90 ∀ (Xx : Iota), And (cP Xx) (cF Xx) → cG Xx)
% 3.65/3.90 False
% 3.65/3.90 Clause #3 (by clausification #[2]): Eq
% 3.65/3.90 (And
% 3.65/3.90 (And (∀ (Xx : Iota), cP Xx → ∀ (Xx0 : Iota), cQ Xx0)
% 3.65/3.90 ((∀ (Xx : Iota), Or (cQ Xx) (cR Xx)) → Exists fun Xx => And (cQ Xx) (cS Xx)))
% 3.65/3.90 (Exists cS → ∀ (Xx : Iota), cF Xx → cG Xx))
% 3.65/3.90 True
% 3.65/3.90 Clause #4 (by clausification #[2]): Eq (∀ (Xx : Iota), And (cP Xx) (cF Xx) → cG Xx) False
% 3.65/3.90 Clause #5 (by clausification #[3]): Eq (Exists cS → ∀ (Xx : Iota), cF Xx → cG Xx) True
% 3.65/3.90 Clause #6 (by clausification #[3]): Eq
% 3.65/3.90 (And (∀ (Xx : Iota), cP Xx → ∀ (Xx0 : Iota), cQ Xx0)
% 3.65/3.90 ((∀ (Xx : Iota), Or (cQ Xx) (cR Xx)) → Exists fun Xx => And (cQ Xx) (cS Xx)))
% 3.65/3.90 True
% 3.65/3.90 Clause #7 (by clausification #[5]): Or (Eq (Exists cS) False) (Eq (∀ (Xx : Iota), cF Xx → cG Xx) True)
% 3.65/3.90 Clause #8 (by clausification #[7]): ∀ (a : Iota), Or (Eq (∀ (Xx : Iota), cF Xx → cG Xx) True) (Eq (cS a) False)
% 3.65/3.90 Clause #9 (by clausification #[8]): ∀ (a a_1 : Iota), Or (Eq (cS a) False) (Eq (cF a_1 → cG a_1) True)
% 3.65/3.90 Clause #10 (by clausification #[9]): ∀ (a a_1 : Iota), Or (Eq (cS a) False) (Or (Eq (cF a_1) False) (Eq (cG a_1) True))
% 3.65/3.90 Clause #11 (by clausification #[4]): ∀ (a : Iota), Eq (Not (And (cP (skS.0 0 a)) (cF (skS.0 0 a)) → cG (skS.0 0 a))) True
% 3.65/3.90 Clause #12 (by clausification #[11]): ∀ (a : Iota), Eq (And (cP (skS.0 0 a)) (cF (skS.0 0 a)) → cG (skS.0 0 a)) False
% 3.65/3.90 Clause #13 (by clausification #[12]): ∀ (a : Iota), Eq (And (cP (skS.0 0 a)) (cF (skS.0 0 a))) True
% 3.65/3.90 Clause #14 (by clausification #[12]): ∀ (a : Iota), Eq (cG (skS.0 0 a)) False
% 3.65/3.90 Clause #15 (by clausification #[13]): ∀ (a : Iota), Eq (cF (skS.0 0 a)) True
% 3.65/3.90 Clause #16 (by clausification #[13]): ∀ (a : Iota), Eq (cP (skS.0 0 a)) True
% 3.65/3.90 Clause #17 (by clausification #[6]): Eq ((∀ (Xx : Iota), Or (cQ Xx) (cR Xx)) → Exists fun Xx => And (cQ Xx) (cS Xx)) True
% 3.65/3.90 Clause #18 (by clausification #[6]): Eq (∀ (Xx : Iota), cP Xx → ∀ (Xx0 : Iota), cQ Xx0) True
% 3.65/3.90 Clause #19 (by clausification #[17]): Or (Eq (∀ (Xx : Iota), Or (cQ Xx) (cR Xx)) False) (Eq (Exists fun Xx => And (cQ Xx) (cS Xx)) True)
% 3.65/3.90 Clause #20 (by clausification #[19]): ∀ (a : Iota), Or (Eq (Exists fun Xx => And (cQ Xx) (cS Xx)) True) (Eq (Not (Or (cQ (skS.0 1 a)) (cR (skS.0 1 a)))) True)
% 3.65/3.90 Clause #21 (by clausification #[20]): ∀ (a a_1 : Iota),
% 3.65/3.90 Or (Eq (Not (Or (cQ (skS.0 1 a)) (cR (skS.0 1 a)))) True) (Eq (And (cQ (skS.0 2 a_1)) (cS (skS.0 2 a_1))) True)
% 3.65/3.90 Clause #22 (by clausification #[21]): ∀ (a a_1 : Iota),
% 3.65/3.90 Or (Eq (And (cQ (skS.0 2 a)) (cS (skS.0 2 a))) True) (Eq (Or (cQ (skS.0 1 a_1)) (cR (skS.0 1 a_1))) False)
% 3.65/3.90 Clause #23 (by clausification #[22]): ∀ (a a_1 : Iota), Or (Eq (Or (cQ (skS.0 1 a)) (cR (skS.0 1 a))) False) (Eq (cS (skS.0 2 a_1)) True)
% 3.65/3.90 Clause #26 (by clausification #[23]): ∀ (a a_1 : Iota), Or (Eq (cS (skS.0 2 a)) True) (Eq (cQ (skS.0 1 a_1)) False)
% 3.65/3.90 Clause #27 (by clausification #[18]): ∀ (a : Iota), Eq (cP a → ∀ (Xx0 : Iota), cQ Xx0) True
% 3.65/3.90 Clause #28 (by clausification #[27]): ∀ (a : Iota), Or (Eq (cP a) False) (Eq (∀ (Xx0 : Iota), cQ Xx0) True)
% 3.65/3.90 Clause #29 (by clausification #[28]): ∀ (a a_1 : Iota), Or (Eq (cP a) False) (Eq (cQ a_1) True)
% 3.65/3.91 Clause #30 (by superposition #[29, 16]): ∀ (a : Iota), Or (Eq (cQ a) True) (Eq False True)
% 3.65/3.91 Clause #31 (by clausification #[30]): ∀ (a : Iota), Eq (cQ a) True
% 3.65/3.91 Clause #32 (by superposition #[26, 31]): ∀ (a : Iota), Or (Eq (cS (skS.0 2 a)) True) (Eq True False)
% 3.65/3.91 Clause #33 (by clausification #[32]): ∀ (a : Iota), Eq (cS (skS.0 2 a)) True
% 3.65/3.91 Clause #34 (by superposition #[33, 10]): ∀ (a : Iota), Or (Eq True False) (Or (Eq (cF a) False) (Eq (cG a) True))
% 3.65/3.91 Clause #35 (by clausification #[34]): ∀ (a : Iota), Or (Eq (cF a) False) (Eq (cG a) True)
% 3.65/3.91 Clause #36 (by superposition #[35, 15]): ∀ (a : Iota), Or (Eq (cG (skS.0 0 a)) True) (Eq False True)
% 3.65/3.91 Clause #37 (by clausification #[36]): ∀ (a : Iota), Eq (cG (skS.0 0 a)) True
% 3.65/3.91 Clause #38 (by superposition #[37, 14]): Eq True False
% 3.65/3.91 Clause #41 (by clausification #[38]): False
% 3.65/3.91 SZS output end Proof for theBenchmark.p
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