TSTP Solution File: SYO038^1.003.003 by Duper---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : SYO038^1.003.003 : TPTP v8.1.2. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n008.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 04:21:13 EDT 2023
% Result : Theorem 4.18s 4.36s
% Output : Proof 4.18s
% 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 : SYO038^1.003.003 : TPTP v8.1.2. Released v5.3.0.
% 0.00/0.14 % Command : duper %s
% 0.13/0.35 % Computer : n008.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 : Sat Aug 26 05:49:32 EDT 2023
% 0.13/0.35 % CPUTime :
% 4.18/4.36 SZS status Theorem for theBenchmark.p
% 4.18/4.36 SZS output start Proof for theBenchmark.p
% 4.18/4.36 Clause #0 (by assumption #[]): Eq (∀ (N : Iota), Eq (f N one) (s one)) True
% 4.18/4.36 Clause #1 (by assumption #[]): Eq (∀ (X : Iota), Eq (f one (s X)) (s (s (f one X)))) True
% 4.18/4.36 Clause #2 (by assumption #[]): Eq (∀ (N X : Iota), Eq (f (s N) (s X)) (f N (f (s N) X))) True
% 4.18/4.36 Clause #3 (by assumption #[]): Eq (d one) True
% 4.18/4.36 Clause #4 (by assumption #[]): Eq (∀ (X : Iota), d X → d (s X)) True
% 4.18/4.36 Clause #5 (by assumption #[]): Eq (Not (d (f (s (s one)) (s (s one))))) True
% 4.18/4.36 Clause #6 (by clausification #[4]): ∀ (a : Iota), Eq (d a → d (s a)) True
% 4.18/4.36 Clause #7 (by clausification #[6]): ∀ (a : Iota), Or (Eq (d a) False) (Eq (d (s a)) True)
% 4.18/4.36 Clause #8 (by superposition #[7, 3]): Or (Eq (d (s one)) True) (Eq False True)
% 4.18/4.36 Clause #9 (by clausification #[8]): Eq (d (s one)) True
% 4.18/4.36 Clause #10 (by superposition #[9, 7]): Or (Eq True False) (Eq (d (s (s one))) True)
% 4.18/4.36 Clause #11 (by clausification #[10]): Eq (d (s (s one))) True
% 4.18/4.36 Clause #12 (by superposition #[11, 7]): Or (Eq True False) (Eq (d (s (s (s one)))) True)
% 4.18/4.36 Clause #13 (by clausification #[12]): Eq (d (s (s (s one)))) True
% 4.18/4.36 Clause #14 (by superposition #[13, 7]): Or (Eq True False) (Eq (d (s (s (s (s one))))) True)
% 4.18/4.36 Clause #15 (by clausification #[0]): ∀ (a : Iota), Eq (Eq (f a one) (s one)) True
% 4.18/4.36 Clause #16 (by clausification #[15]): ∀ (a : Iota), Eq (f a one) (s one)
% 4.18/4.36 Clause #17 (by clausification #[14]): Eq (d (s (s (s (s one))))) True
% 4.18/4.36 Clause #18 (by superposition #[17, 7]): Or (Eq True False) (Eq (d (s (s (s (s (s one)))))) True)
% 4.18/4.36 Clause #19 (by clausification #[5]): Eq (d (f (s (s one)) (s (s one)))) False
% 4.18/4.36 Clause #20 (by clausification #[18]): Eq (d (s (s (s (s (s one)))))) True
% 4.18/4.36 Clause #21 (by superposition #[20, 7]): Or (Eq True False) (Eq (d (s (s (s (s (s (s one))))))) True)
% 4.18/4.36 Clause #22 (by clausification #[21]): Eq (d (s (s (s (s (s (s one))))))) True
% 4.18/4.36 Clause #23 (by superposition #[22, 7]): Or (Eq True False) (Eq (d (s (s (s (s (s (s (s one)))))))) True)
% 4.18/4.36 Clause #24 (by clausification #[23]): Eq (d (s (s (s (s (s (s (s one)))))))) True
% 4.18/4.36 Clause #25 (by superposition #[24, 7]): Or (Eq True False) (Eq (d (s (s (s (s (s (s (s (s one))))))))) True)
% 4.18/4.36 Clause #26 (by clausification #[1]): ∀ (a : Iota), Eq (Eq (f one (s a)) (s (s (f one a)))) True
% 4.18/4.36 Clause #27 (by clausification #[26]): ∀ (a : Iota), Eq (f one (s a)) (s (s (f one a)))
% 4.18/4.36 Clause #28 (by superposition #[27, 16]): Eq (f one (s one)) (s (s (s one)))
% 4.18/4.36 Clause #38 (by clausification #[2]): ∀ (a : Iota), Eq (∀ (X : Iota), Eq (f (s a) (s X)) (f a (f (s a) X))) True
% 4.18/4.36 Clause #39 (by clausification #[38]): ∀ (a a_1 : Iota), Eq (Eq (f (s a) (s a_1)) (f a (f (s a) a_1))) True
% 4.18/4.36 Clause #40 (by clausification #[39]): ∀ (a a_1 : Iota), Eq (f (s a) (s a_1)) (f a (f (s a) a_1))
% 4.18/4.36 Clause #43 (by superposition #[40, 16]): ∀ (a : Iota), Eq (f (s a) (s one)) (f a (s one))
% 4.18/4.36 Clause #46 (by superposition #[43, 40]): ∀ (a : Iota), Eq (f (s a) (s (s one))) (f a (f a (s one)))
% 4.18/4.36 Clause #55 (by clausification #[25]): Eq (d (s (s (s (s (s (s (s (s one))))))))) True
% 4.18/4.36 Clause #56 (by forward demodulation #[55, 28]): Eq (d (s (s (s (s (s (f one (s one)))))))) True
% 4.18/4.36 Clause #57 (by forward demodulation #[56, 27]): Eq (d (s (s (s (f one (s (s one))))))) True
% 4.18/4.36 Clause #58 (by forward demodulation #[57, 27]): Eq (d (s (f one (s (s (s one)))))) True
% 4.18/4.36 Clause #59 (by forward demodulation #[58, 28]): Eq (d (s (f one (f one (s one))))) True
% 4.18/4.36 Clause #60 (by superposition #[59, 7]): Or (Eq True False) (Eq (d (s (s (f one (f one (s one)))))) True)
% 4.18/4.36 Clause #61 (by clausification #[60]): Eq (d (s (s (f one (f one (s one)))))) True
% 4.18/4.36 Clause #62 (by forward demodulation #[61, 27]): Eq (d (f one (s (f one (s one))))) True
% 4.18/4.36 Clause #63 (by superposition #[62, 7]): Or (Eq True False) (Eq (d (s (f one (s (f one (s one)))))) True)
% 4.18/4.36 Clause #64 (by clausification #[63]): Eq (d (s (f one (s (f one (s one)))))) True
% 4.18/4.36 Clause #65 (by superposition #[64, 7]): Or (Eq True False) (Eq (d (s (s (f one (s (f one (s one))))))) True)
% 4.18/4.36 Clause #66 (by superposition #[46, 40]): ∀ (a : Iota), Eq (f (s a) (s (s (s one)))) (f a (f a (f a (s one))))
% 4.18/4.37 Clause #68 (by superposition #[46, 43]): ∀ (a : Iota), Eq (f (s (s a)) (s (s one))) (f (s a) (f a (s one)))
% 4.18/4.37 Clause #80 (by clausification #[65]): Eq (d (s (s (f one (s (f one (s one))))))) True
% 4.18/4.37 Clause #81 (by forward demodulation #[80, 27]): Eq (d (f one (s (s (f one (s one)))))) True
% 4.18/4.37 Clause #82 (by forward demodulation #[81, 27]): Eq (d (f one (f one (s (s one))))) True
% 4.18/4.37 Clause #83 (by superposition #[82, 7]): Or (Eq True False) (Eq (d (s (f one (f one (s (s one)))))) True)
% 4.18/4.37 Clause #84 (by clausification #[83]): Eq (d (s (f one (f one (s (s one)))))) True
% 4.18/4.37 Clause #85 (by superposition #[84, 7]): Or (Eq True False) (Eq (d (s (s (f one (f one (s (s one))))))) True)
% 4.18/4.37 Clause #86 (by clausification #[85]): Eq (d (s (s (f one (f one (s (s one))))))) True
% 4.18/4.37 Clause #87 (by forward demodulation #[86, 27]): Eq (d (f one (s (f one (s (s one)))))) True
% 4.18/4.37 Clause #88 (by superposition #[87, 7]): Or (Eq True False) (Eq (d (s (f one (s (f one (s (s one))))))) True)
% 4.18/4.37 Clause #101 (by clausification #[88]): Eq (d (s (f one (s (f one (s (s one))))))) True
% 4.18/4.37 Clause #102 (by superposition #[101, 7]): Or (Eq True False) (Eq (d (s (s (f one (s (f one (s (s one)))))))) True)
% 4.18/4.37 Clause #104 (by superposition #[68, 19]): Eq (d (f (s one) (f one (s one)))) False
% 4.18/4.37 Clause #114 (by clausification #[102]): Eq (d (s (s (f one (s (f one (s (s one)))))))) True
% 4.18/4.37 Clause #115 (by forward demodulation #[114, 27]): Eq (d (f one (s (s (f one (s (s one))))))) True
% 4.18/4.37 Clause #116 (by forward demodulation #[115, 27]): Eq (d (f one (f one (s (s (s one)))))) True
% 4.18/4.37 Clause #117 (by forward demodulation #[116, 28]): Eq (d (f one (f one (f one (s one))))) True
% 4.18/4.37 Clause #157 (by forward demodulation #[66, 28]): ∀ (a : Iota), Eq (f (s a) (f one (s one))) (f a (f a (f a (s one))))
% 4.18/4.37 Clause #158 (by backward demodulation #[157, 117]): Eq (d (f (s one) (f one (s one)))) True
% 4.18/4.37 Clause #170 (by superposition #[158, 104]): Eq True False
% 4.18/4.37 Clause #172 (by clausification #[170]): False
% 4.18/4.37 SZS output end Proof for theBenchmark.p
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