TSTP Solution File: SYN056+1 by Duper---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : SYN056+1 : TPTP v8.1.2. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n023.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 02:10:21 EDT 2023
% Result : Theorem 3.71s 3.96s
% Output : Proof 3.85s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SYN056+1 : TPTP v8.1.2. Released v2.0.0.
% 0.11/0.13 % Command : duper %s
% 0.13/0.34 % Computer : n023.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.19/0.34 % CPULimit : 300
% 0.19/0.34 % WCLimit : 300
% 0.19/0.34 % DateTime : Sat Aug 26 19:34:56 EDT 2023
% 0.19/0.34 % CPUTime :
% 3.71/3.96 SZS status Theorem for theBenchmark.p
% 3.71/3.96 SZS output start Proof for theBenchmark.p
% 3.71/3.96 Clause #0 (by assumption #[]): Eq (Iff (Exists fun X => big_p X) (Exists fun Y => big_q Y)) True
% 3.71/3.96 Clause #1 (by assumption #[]): Eq (∀ (X Y : Iota), And (big_p X) (big_q Y) → Iff (big_r X) (big_s Y)) True
% 3.71/3.96 Clause #2 (by assumption #[]): Eq (Not (Iff (∀ (X : Iota), big_p X → big_r X) (∀ (Y : Iota), big_q Y → big_s Y))) True
% 3.71/3.96 Clause #3 (by clausification #[1]): ∀ (a : Iota), Eq (∀ (Y : Iota), And (big_p a) (big_q Y) → Iff (big_r a) (big_s Y)) True
% 3.71/3.96 Clause #4 (by clausification #[3]): ∀ (a a_1 : Iota), Eq (And (big_p a) (big_q a_1) → Iff (big_r a) (big_s a_1)) True
% 3.71/3.96 Clause #5 (by clausification #[4]): ∀ (a a_1 : Iota), Or (Eq (And (big_p a) (big_q a_1)) False) (Eq (Iff (big_r a) (big_s a_1)) True)
% 3.71/3.96 Clause #6 (by clausification #[5]): ∀ (a a_1 : Iota), Or (Eq (Iff (big_r a) (big_s a_1)) True) (Or (Eq (big_p a) False) (Eq (big_q a_1) False))
% 3.71/3.96 Clause #7 (by clausification #[6]): ∀ (a a_1 : Iota), Or (Eq (big_p a) False) (Or (Eq (big_q a_1) False) (Or (Eq (big_r a) True) (Eq (big_s a_1) False)))
% 3.71/3.96 Clause #8 (by clausification #[6]): ∀ (a a_1 : Iota), Or (Eq (big_p a) False) (Or (Eq (big_q a_1) False) (Or (Eq (big_r a) False) (Eq (big_s a_1) True)))
% 3.71/3.96 Clause #9 (by clausification #[2]): Eq (Iff (∀ (X : Iota), big_p X → big_r X) (∀ (Y : Iota), big_q Y → big_s Y)) False
% 3.71/3.96 Clause #10 (by clausification #[9]): Or (Eq (∀ (X : Iota), big_p X → big_r X) False) (Eq (∀ (Y : Iota), big_q Y → big_s Y) False)
% 3.71/3.96 Clause #11 (by clausification #[9]): Or (Eq (∀ (X : Iota), big_p X → big_r X) True) (Eq (∀ (Y : Iota), big_q Y → big_s Y) True)
% 3.71/3.96 Clause #12 (by clausification #[10]): ∀ (a : Iota), Or (Eq (∀ (Y : Iota), big_q Y → big_s Y) False) (Eq (Not (big_p (skS.0 0 a) → big_r (skS.0 0 a))) True)
% 3.71/3.96 Clause #13 (by clausification #[12]): ∀ (a a_1 : Iota),
% 3.71/3.96 Or (Eq (Not (big_p (skS.0 0 a) → big_r (skS.0 0 a))) True) (Eq (Not (big_q (skS.0 1 a_1) → big_s (skS.0 1 a_1))) True)
% 3.71/3.96 Clause #14 (by clausification #[13]): ∀ (a a_1 : Iota),
% 3.71/3.96 Or (Eq (Not (big_q (skS.0 1 a) → big_s (skS.0 1 a))) True) (Eq (big_p (skS.0 0 a_1) → big_r (skS.0 0 a_1)) False)
% 3.71/3.96 Clause #15 (by clausification #[14]): ∀ (a a_1 : Iota),
% 3.71/3.96 Or (Eq (big_p (skS.0 0 a) → big_r (skS.0 0 a)) False) (Eq (big_q (skS.0 1 a_1) → big_s (skS.0 1 a_1)) False)
% 3.71/3.96 Clause #16 (by clausification #[15]): ∀ (a a_1 : Iota), Or (Eq (big_q (skS.0 1 a) → big_s (skS.0 1 a)) False) (Eq (big_p (skS.0 0 a_1)) True)
% 3.71/3.96 Clause #17 (by clausification #[15]): ∀ (a a_1 : Iota), Or (Eq (big_q (skS.0 1 a) → big_s (skS.0 1 a)) False) (Eq (big_r (skS.0 0 a_1)) False)
% 3.71/3.96 Clause #18 (by clausification #[16]): ∀ (a a_1 : Iota), Or (Eq (big_p (skS.0 0 a)) True) (Eq (big_q (skS.0 1 a_1)) True)
% 3.71/3.96 Clause #19 (by clausification #[16]): ∀ (a a_1 : Iota), Or (Eq (big_p (skS.0 0 a)) True) (Eq (big_s (skS.0 1 a_1)) False)
% 3.71/3.96 Clause #20 (by superposition #[18, 7]): ∀ (a a_1 a_2 : Iota),
% 3.71/3.96 Or (Eq (big_q (skS.0 1 a)) True)
% 3.71/3.96 (Or (Eq True False) (Or (Eq (big_q a_1) False) (Or (Eq (big_r (skS.0 0 a_2)) True) (Eq (big_s a_1) False))))
% 3.71/3.96 Clause #21 (by clausification #[11]): ∀ (a : Iota), Or (Eq (∀ (Y : Iota), big_q Y → big_s Y) True) (Eq (big_p a → big_r a) True)
% 3.71/3.96 Clause #22 (by clausification #[21]): ∀ (a a_1 : Iota), Or (Eq (big_p a → big_r a) True) (Eq (big_q a_1 → big_s a_1) True)
% 3.71/3.96 Clause #23 (by clausification #[22]): ∀ (a a_1 : Iota), Or (Eq (big_q a → big_s a) True) (Or (Eq (big_p a_1) False) (Eq (big_r a_1) True))
% 3.71/3.96 Clause #24 (by clausification #[23]): ∀ (a a_1 : Iota), Or (Eq (big_p a) False) (Or (Eq (big_r a) True) (Or (Eq (big_q a_1) False) (Eq (big_s a_1) True)))
% 3.71/3.96 Clause #27 (by betaEtaReduce #[0]): Eq (Iff (Exists big_p) (Exists big_q)) True
% 3.71/3.96 Clause #28 (by clausification #[27]): Or (Eq (Exists big_p) True) (Eq (Exists big_q) False)
% 3.71/3.96 Clause #29 (by clausification #[27]): Or (Eq (Exists big_p) False) (Eq (Exists big_q) True)
% 3.71/3.96 Clause #30 (by clausification #[28]): ∀ (a : Iota), Or (Eq (Exists big_q) False) (Eq (big_p (skS.0 2 a)) True)
% 3.71/3.96 Clause #31 (by clausification #[30]): ∀ (a a_1 : Iota), Or (Eq (big_p (skS.0 2 a)) True) (Eq (big_q a_1) False)
% 3.81/3.98 Clause #33 (by clausification #[17]): ∀ (a a_1 : Iota), Or (Eq (big_r (skS.0 0 a)) False) (Eq (big_q (skS.0 1 a_1)) True)
% 3.81/3.98 Clause #34 (by clausification #[17]): ∀ (a a_1 : Iota), Or (Eq (big_r (skS.0 0 a)) False) (Eq (big_s (skS.0 1 a_1)) False)
% 3.81/3.98 Clause #35 (by clausification #[29]): ∀ (a : Iota), Or (Eq (Exists big_q) True) (Eq (big_p a) False)
% 3.81/3.98 Clause #36 (by clausification #[35]): ∀ (a a_1 : Iota), Or (Eq (big_p a) False) (Eq (big_q (skS.0 3 a_1)) True)
% 3.81/3.98 Clause #37 (by superposition #[36, 18]): ∀ (a a_1 : Iota), Or (Eq (big_q (skS.0 3 a)) True) (Or (Eq False True) (Eq (big_q (skS.0 1 a_1)) True))
% 3.81/3.98 Clause #38 (by clausification #[37]): ∀ (a a_1 : Iota), Or (Eq (big_q (skS.0 3 a)) True) (Eq (big_q (skS.0 1 a_1)) True)
% 3.81/3.98 Clause #40 (by superposition #[38, 31]): ∀ (a a_1 : Iota), Or (Eq (big_q (skS.0 3 a)) True) (Or (Eq (big_p (skS.0 2 a_1)) True) (Eq True False))
% 3.81/3.98 Clause #41 (by clausification #[40]): ∀ (a a_1 : Iota), Or (Eq (big_q (skS.0 3 a)) True) (Eq (big_p (skS.0 2 a_1)) True)
% 3.81/3.98 Clause #46 (by superposition #[41, 36]): ∀ (a a_1 : Iota), Or (Eq (big_q (skS.0 3 a)) True) (Or (Eq True False) (Eq (big_q (skS.0 3 a_1)) True))
% 3.81/3.98 Clause #47 (by clausification #[20]): ∀ (a a_1 a_2 : Iota),
% 3.81/3.98 Or (Eq (big_q (skS.0 1 a)) True)
% 3.81/3.98 (Or (Eq (big_q a_1) False) (Or (Eq (big_r (skS.0 0 a_2)) True) (Eq (big_s a_1) False)))
% 3.81/3.98 Clause #52 (by clausification #[46]): ∀ (a a_1 : Iota), Or (Eq (big_q (skS.0 3 a)) True) (Eq (big_q (skS.0 3 a_1)) True)
% 3.81/3.98 Clause #54 (by equality factoring #[52]): ∀ (a : Iota), Or (Ne True True) (Eq (big_q (skS.0 3 a)) True)
% 3.81/3.98 Clause #55 (by clausification #[54]): ∀ (a : Iota), Or (Eq (big_q (skS.0 3 a)) True) (Or (Eq True False) (Eq True False))
% 3.81/3.98 Clause #57 (by clausification #[55]): ∀ (a : Iota), Or (Eq (big_q (skS.0 3 a)) True) (Eq True False)
% 3.81/3.98 Clause #58 (by clausification #[57]): ∀ (a : Iota), Eq (big_q (skS.0 3 a)) True
% 3.81/3.98 Clause #59 (by superposition #[58, 31]): ∀ (a : Iota), Or (Eq (big_p (skS.0 2 a)) True) (Eq True False)
% 3.81/3.98 Clause #60 (by superposition #[58, 47]): ∀ (a a_1 a_2 : Iota),
% 3.81/3.98 Or (Eq (big_q (skS.0 1 a)) True)
% 3.81/3.98 (Or (Eq True False) (Or (Eq (big_r (skS.0 0 a_1)) True) (Eq (big_s (skS.0 3 a_2)) False)))
% 3.81/3.98 Clause #61 (by clausification #[59]): ∀ (a : Iota), Eq (big_p (skS.0 2 a)) True
% 3.81/3.98 Clause #62 (by superposition #[61, 7]): ∀ (a a_1 : Iota), Or (Eq True False) (Or (Eq (big_q a) False) (Or (Eq (big_r (skS.0 2 a_1)) True) (Eq (big_s a) False)))
% 3.81/3.98 Clause #63 (by superposition #[61, 24]): ∀ (a a_1 : Iota),
% 3.81/3.98 Or (Eq True False) (Or (Eq (big_r (skS.0 2 a)) True) (Or (Eq (big_q a_1) False) (Eq (big_s a_1) True)))
% 3.81/3.98 Clause #64 (by superposition #[61, 8]): ∀ (a a_1 : Iota), Or (Eq True False) (Or (Eq (big_q a) False) (Or (Eq (big_r (skS.0 2 a_1)) False) (Eq (big_s a) True)))
% 3.81/3.98 Clause #65 (by clausification #[64]): ∀ (a a_1 : Iota), Or (Eq (big_q a) False) (Or (Eq (big_r (skS.0 2 a_1)) False) (Eq (big_s a) True))
% 3.81/3.98 Clause #67 (by superposition #[65, 58]): ∀ (a a_1 : Iota), Or (Eq (big_r (skS.0 2 a)) False) (Or (Eq (big_s (skS.0 3 a_1)) True) (Eq False True))
% 3.81/3.98 Clause #71 (by clausification #[62]): ∀ (a a_1 : Iota), Or (Eq (big_q a) False) (Or (Eq (big_r (skS.0 2 a_1)) True) (Eq (big_s a) False))
% 3.81/3.98 Clause #73 (by superposition #[71, 58]): ∀ (a a_1 : Iota), Or (Eq (big_r (skS.0 2 a)) True) (Or (Eq (big_s (skS.0 3 a_1)) False) (Eq False True))
% 3.81/3.98 Clause #74 (by clausification #[63]): ∀ (a a_1 : Iota), Or (Eq (big_r (skS.0 2 a)) True) (Or (Eq (big_q a_1) False) (Eq (big_s a_1) True))
% 3.81/3.98 Clause #76 (by superposition #[74, 58]): ∀ (a a_1 : Iota), Or (Eq (big_r (skS.0 2 a)) True) (Or (Eq (big_s (skS.0 3 a_1)) True) (Eq False True))
% 3.81/3.98 Clause #77 (by clausification #[76]): ∀ (a a_1 : Iota), Or (Eq (big_r (skS.0 2 a)) True) (Eq (big_s (skS.0 3 a_1)) True)
% 3.81/3.98 Clause #78 (by clausification #[67]): ∀ (a a_1 : Iota), Or (Eq (big_r (skS.0 2 a)) False) (Eq (big_s (skS.0 3 a_1)) True)
% 3.81/3.98 Clause #79 (by superposition #[78, 77]): ∀ (a a_1 : Iota), Or (Eq (big_s (skS.0 3 a)) True) (Or (Eq False True) (Eq (big_s (skS.0 3 a_1)) True))
% 3.81/3.98 Clause #80 (by clausification #[79]): ∀ (a a_1 : Iota), Or (Eq (big_s (skS.0 3 a)) True) (Eq (big_s (skS.0 3 a_1)) True)
% 3.85/4.01 Clause #81 (by equality factoring #[80]): ∀ (a : Iota), Or (Ne True True) (Eq (big_s (skS.0 3 a)) True)
% 3.85/4.01 Clause #83 (by clausification #[81]): ∀ (a : Iota), Or (Eq (big_s (skS.0 3 a)) True) (Or (Eq True False) (Eq True False))
% 3.85/4.01 Clause #85 (by clausification #[83]): ∀ (a : Iota), Or (Eq (big_s (skS.0 3 a)) True) (Eq True False)
% 3.85/4.01 Clause #86 (by clausification #[85]): ∀ (a : Iota), Eq (big_s (skS.0 3 a)) True
% 3.85/4.01 Clause #87 (by clausification #[73]): ∀ (a a_1 : Iota), Or (Eq (big_r (skS.0 2 a)) True) (Eq (big_s (skS.0 3 a_1)) False)
% 3.85/4.01 Clause #88 (by superposition #[87, 86]): ∀ (a : Iota), Or (Eq (big_r (skS.0 2 a)) True) (Eq False True)
% 3.85/4.01 Clause #89 (by clausification #[88]): ∀ (a : Iota), Eq (big_r (skS.0 2 a)) True
% 3.85/4.01 Clause #99 (by clausification #[60]): ∀ (a a_1 a_2 : Iota),
% 3.85/4.01 Or (Eq (big_q (skS.0 1 a)) True) (Or (Eq (big_r (skS.0 0 a_1)) True) (Eq (big_s (skS.0 3 a_2)) False))
% 3.85/4.01 Clause #100 (by superposition #[99, 86]): ∀ (a a_1 : Iota), Or (Eq (big_q (skS.0 1 a)) True) (Or (Eq (big_r (skS.0 0 a_1)) True) (Eq False True))
% 3.85/4.01 Clause #101 (by clausification #[100]): ∀ (a a_1 : Iota), Or (Eq (big_q (skS.0 1 a)) True) (Eq (big_r (skS.0 0 a_1)) True)
% 3.85/4.01 Clause #103 (by superposition #[101, 33]): ∀ (a a_1 : Iota), Or (Eq (big_q (skS.0 1 a)) True) (Or (Eq True False) (Eq (big_q (skS.0 1 a_1)) True))
% 3.85/4.01 Clause #106 (by clausification #[103]): ∀ (a a_1 : Iota), Or (Eq (big_q (skS.0 1 a)) True) (Eq (big_q (skS.0 1 a_1)) True)
% 3.85/4.01 Clause #108 (by equality factoring #[106]): ∀ (a : Iota), Or (Ne True True) (Eq (big_q (skS.0 1 a)) True)
% 3.85/4.01 Clause #110 (by clausification #[108]): ∀ (a : Iota), Or (Eq (big_q (skS.0 1 a)) True) (Or (Eq True False) (Eq True False))
% 3.85/4.01 Clause #112 (by clausification #[110]): ∀ (a : Iota), Or (Eq (big_q (skS.0 1 a)) True) (Eq True False)
% 3.85/4.01 Clause #113 (by clausification #[112]): ∀ (a : Iota), Eq (big_q (skS.0 1 a)) True
% 3.85/4.01 Clause #114 (by superposition #[113, 65]): ∀ (a a_1 : Iota), Or (Eq True False) (Or (Eq (big_r (skS.0 2 a)) False) (Eq (big_s (skS.0 1 a_1)) True))
% 3.85/4.01 Clause #115 (by clausification #[114]): ∀ (a a_1 : Iota), Or (Eq (big_r (skS.0 2 a)) False) (Eq (big_s (skS.0 1 a_1)) True)
% 3.85/4.01 Clause #116 (by superposition #[115, 89]): ∀ (a : Iota), Or (Eq (big_s (skS.0 1 a)) True) (Eq False True)
% 3.85/4.01 Clause #117 (by clausification #[116]): ∀ (a : Iota), Eq (big_s (skS.0 1 a)) True
% 3.85/4.01 Clause #118 (by superposition #[117, 19]): ∀ (a : Iota), Or (Eq (big_p (skS.0 0 a)) True) (Eq True False)
% 3.85/4.01 Clause #119 (by clausification #[118]): ∀ (a : Iota), Eq (big_p (skS.0 0 a)) True
% 3.85/4.01 Clause #120 (by superposition #[119, 7]): ∀ (a a_1 : Iota), Or (Eq True False) (Or (Eq (big_q a) False) (Or (Eq (big_r (skS.0 0 a_1)) True) (Eq (big_s a) False)))
% 3.85/4.01 Clause #130 (by clausification #[120]): ∀ (a a_1 : Iota), Or (Eq (big_q a) False) (Or (Eq (big_r (skS.0 0 a_1)) True) (Eq (big_s a) False))
% 3.85/4.01 Clause #131 (by superposition #[130, 58]): ∀ (a a_1 : Iota), Or (Eq (big_r (skS.0 0 a)) True) (Or (Eq (big_s (skS.0 3 a_1)) False) (Eq False True))
% 3.85/4.01 Clause #133 (by clausification #[131]): ∀ (a a_1 : Iota), Or (Eq (big_r (skS.0 0 a)) True) (Eq (big_s (skS.0 3 a_1)) False)
% 3.85/4.01 Clause #134 (by superposition #[133, 86]): ∀ (a : Iota), Or (Eq (big_r (skS.0 0 a)) True) (Eq False True)
% 3.85/4.01 Clause #135 (by clausification #[134]): ∀ (a : Iota), Eq (big_r (skS.0 0 a)) True
% 3.85/4.01 Clause #136 (by superposition #[135, 34]): ∀ (a : Iota), Or (Eq True False) (Eq (big_s (skS.0 1 a)) False)
% 3.85/4.01 Clause #138 (by clausification #[136]): ∀ (a : Iota), Eq (big_s (skS.0 1 a)) False
% 3.85/4.01 Clause #139 (by superposition #[138, 117]): Eq False True
% 3.85/4.01 Clause #140 (by clausification #[139]): False
% 3.85/4.01 SZS output end Proof for theBenchmark.p
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