TSTP Solution File: SYN918+1 by Duper---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : SYN918+1 : TPTP v8.1.2. Released v3.1.0.
% 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 : Fri Sep 1 02:13:16 EDT 2023
% Result : Theorem 3.66s 3.84s
% Output : Proof 3.66s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYN918+1 : TPTP v8.1.2. Released v3.1.0.
% 0.00/0.14 % Command : duper %s
% 0.14/0.35 % Computer : n018.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sat Aug 26 18:47:00 EDT 2023
% 0.14/0.35 % CPUTime :
% 3.66/3.84 SZS status Theorem for theBenchmark.p
% 3.66/3.84 SZS output start Proof for theBenchmark.p
% 3.66/3.84 Clause #0 (by assumption #[]): Eq
% 3.66/3.84 (Not
% 3.66/3.84 (And (∀ (X : Iota), (And (f X) (g X) → h X) → Exists fun Y => And (f Y) (Not (g Y)))
% 3.66/3.84 (Or (∀ (W : Iota), f W → g W) (∀ (Z : Iota), f Z → h Z)) →
% 3.66/3.84 (∀ (R : Iota), And (f R) (h R) → g R) → Exists fun V => And (And (f V) (g V)) (Not (h V))))
% 3.66/3.84 True
% 3.66/3.84 Clause #1 (by clausification #[0]): Eq
% 3.66/3.84 (And (∀ (X : Iota), (And (f X) (g X) → h X) → Exists fun Y => And (f Y) (Not (g Y)))
% 3.66/3.84 (Or (∀ (W : Iota), f W → g W) (∀ (Z : Iota), f Z → h Z)) →
% 3.66/3.84 (∀ (R : Iota), And (f R) (h R) → g R) → Exists fun V => And (And (f V) (g V)) (Not (h V)))
% 3.66/3.84 False
% 3.66/3.84 Clause #2 (by clausification #[1]): Eq
% 3.66/3.84 (And (∀ (X : Iota), (And (f X) (g X) → h X) → Exists fun Y => And (f Y) (Not (g Y)))
% 3.66/3.84 (Or (∀ (W : Iota), f W → g W) (∀ (Z : Iota), f Z → h Z)))
% 3.66/3.84 True
% 3.66/3.84 Clause #3 (by clausification #[1]): Eq ((∀ (R : Iota), And (f R) (h R) → g R) → Exists fun V => And (And (f V) (g V)) (Not (h V))) False
% 3.66/3.84 Clause #4 (by clausification #[2]): Eq (Or (∀ (W : Iota), f W → g W) (∀ (Z : Iota), f Z → h Z)) True
% 3.66/3.84 Clause #5 (by clausification #[2]): Eq (∀ (X : Iota), (And (f X) (g X) → h X) → Exists fun Y => And (f Y) (Not (g Y))) True
% 3.66/3.84 Clause #6 (by clausification #[4]): Or (Eq (∀ (W : Iota), f W → g W) True) (Eq (∀ (Z : Iota), f Z → h Z) True)
% 3.66/3.84 Clause #7 (by clausification #[6]): ∀ (a : Iota), Or (Eq (∀ (Z : Iota), f Z → h Z) True) (Eq (f a → g a) True)
% 3.66/3.84 Clause #8 (by clausification #[7]): ∀ (a a_1 : Iota), Or (Eq (f a → g a) True) (Eq (f a_1 → h a_1) True)
% 3.66/3.84 Clause #9 (by clausification #[8]): ∀ (a a_1 : Iota), Or (Eq (f a → h a) True) (Or (Eq (f a_1) False) (Eq (g a_1) True))
% 3.66/3.84 Clause #10 (by clausification #[9]): ∀ (a a_1 : Iota), Or (Eq (f a) False) (Or (Eq (g a) True) (Or (Eq (f a_1) False) (Eq (h a_1) True)))
% 3.66/3.84 Clause #11 (by clausification #[5]): ∀ (a : Iota), Eq ((And (f a) (g a) → h a) → Exists fun Y => And (f Y) (Not (g Y))) True
% 3.66/3.84 Clause #12 (by clausification #[11]): ∀ (a : Iota), Or (Eq (And (f a) (g a) → h a) False) (Eq (Exists fun Y => And (f Y) (Not (g Y))) True)
% 3.66/3.84 Clause #13 (by clausification #[12]): ∀ (a : Iota), Or (Eq (Exists fun Y => And (f Y) (Not (g Y))) True) (Eq (And (f a) (g a)) True)
% 3.66/3.84 Clause #14 (by clausification #[12]): ∀ (a : Iota), Or (Eq (Exists fun Y => And (f Y) (Not (g Y))) True) (Eq (h a) False)
% 3.66/3.84 Clause #15 (by clausification #[13]): ∀ (a a_1 : Iota), Or (Eq (And (f a) (g a)) True) (Eq (And (f (skS.0 0 a_1)) (Not (g (skS.0 0 a_1)))) True)
% 3.66/3.84 Clause #16 (by clausification #[15]): ∀ (a a_1 : Iota), Or (Eq (And (f (skS.0 0 a)) (Not (g (skS.0 0 a)))) True) (Eq (g a_1) True)
% 3.66/3.84 Clause #17 (by clausification #[15]): ∀ (a a_1 : Iota), Or (Eq (And (f (skS.0 0 a)) (Not (g (skS.0 0 a)))) True) (Eq (f a_1) True)
% 3.66/3.84 Clause #18 (by clausification #[16]): ∀ (a a_1 : Iota), Or (Eq (g a) True) (Eq (Not (g (skS.0 0 a_1))) True)
% 3.66/3.84 Clause #20 (by clausification #[18]): ∀ (a a_1 : Iota), Or (Eq (g a) True) (Eq (g (skS.0 0 a_1)) False)
% 3.66/3.84 Clause #23 (by clausification #[14]): ∀ (a a_1 : Iota), Or (Eq (h a) False) (Eq (And (f (skS.0 1 a_1)) (Not (g (skS.0 1 a_1)))) True)
% 3.66/3.84 Clause #24 (by clausification #[23]): ∀ (a a_1 : Iota), Or (Eq (h a) False) (Eq (Not (g (skS.0 1 a_1))) True)
% 3.66/3.84 Clause #26 (by clausification #[24]): ∀ (a a_1 : Iota), Or (Eq (h a) False) (Eq (g (skS.0 1 a_1)) False)
% 3.66/3.84 Clause #27 (by clausification #[3]): Eq (∀ (R : Iota), And (f R) (h R) → g R) True
% 3.66/3.84 Clause #28 (by clausification #[3]): Eq (Exists fun V => And (And (f V) (g V)) (Not (h V))) False
% 3.66/3.84 Clause #29 (by clausification #[27]): ∀ (a : Iota), Eq (And (f a) (h a) → g a) True
% 3.66/3.84 Clause #30 (by clausification #[29]): ∀ (a : Iota), Or (Eq (And (f a) (h a)) False) (Eq (g a) True)
% 3.66/3.84 Clause #31 (by clausification #[30]): ∀ (a : Iota), Or (Eq (g a) True) (Or (Eq (f a) False) (Eq (h a) False))
% 3.66/3.84 Clause #33 (by clausification #[28]): ∀ (a : Iota), Eq (And (And (f a) (g a)) (Not (h a))) False
% 3.66/3.84 Clause #34 (by clausification #[33]): ∀ (a : Iota), Or (Eq (And (f a) (g a)) False) (Eq (Not (h a)) False)
% 3.66/3.87 Clause #35 (by clausification #[34]): ∀ (a : Iota), Or (Eq (Not (h a)) False) (Or (Eq (f a) False) (Eq (g a) False))
% 3.66/3.87 Clause #36 (by clausification #[35]): ∀ (a : Iota), Or (Eq (f a) False) (Or (Eq (g a) False) (Eq (h a) True))
% 3.66/3.87 Clause #40 (by clausification #[17]): ∀ (a a_1 : Iota), Or (Eq (f a) True) (Eq (Not (g (skS.0 0 a_1))) True)
% 3.66/3.87 Clause #41 (by clausification #[17]): ∀ (a a_1 : Iota), Or (Eq (f a) True) (Eq (f (skS.0 0 a_1)) True)
% 3.66/3.87 Clause #42 (by clausification #[40]): ∀ (a a_1 : Iota), Or (Eq (f a) True) (Eq (g (skS.0 0 a_1)) False)
% 3.66/3.87 Clause #52 (by equality factoring #[41]): ∀ (a : Iota), Or (Ne True True) (Eq (f (skS.0 0 a)) True)
% 3.66/3.87 Clause #54 (by clausification #[52]): ∀ (a : Iota), Or (Eq (f (skS.0 0 a)) True) (Or (Eq True False) (Eq True False))
% 3.66/3.87 Clause #56 (by clausification #[54]): ∀ (a : Iota), Or (Eq (f (skS.0 0 a)) True) (Eq True False)
% 3.66/3.87 Clause #57 (by clausification #[56]): ∀ (a : Iota), Eq (f (skS.0 0 a)) True
% 3.66/3.87 Clause #58 (by superposition #[57, 10]): ∀ (a a_1 : Iota), Or (Eq True False) (Or (Eq (g (skS.0 0 a)) True) (Or (Eq (f a_1) False) (Eq (h a_1) True)))
% 3.66/3.87 Clause #59 (by superposition #[57, 31]): ∀ (a : Iota), Or (Eq (g (skS.0 0 a)) True) (Or (Eq True False) (Eq (h (skS.0 0 a)) False))
% 3.66/3.87 Clause #63 (by clausification #[58]): ∀ (a a_1 : Iota), Or (Eq (g (skS.0 0 a)) True) (Or (Eq (f a_1) False) (Eq (h a_1) True))
% 3.66/3.87 Clause #64 (by superposition #[63, 57]): ∀ (a a_1 : Iota), Or (Eq (g (skS.0 0 a)) True) (Or (Eq (h (skS.0 0 a_1)) True) (Eq False True))
% 3.66/3.87 Clause #67 (by clausification #[59]): ∀ (a : Iota), Or (Eq (g (skS.0 0 a)) True) (Eq (h (skS.0 0 a)) False)
% 3.66/3.87 Clause #69 (by clausification #[64]): ∀ (a a_1 : Iota), Or (Eq (g (skS.0 0 a)) True) (Eq (h (skS.0 0 a_1)) True)
% 3.66/3.87 Clause #70 (by superposition #[69, 20]): ∀ (a a_1 : Iota), Or (Eq (h (skS.0 0 a)) True) (Or (Eq (g a_1) True) (Eq True False))
% 3.66/3.87 Clause #103 (by clausification #[70]): ∀ (a a_1 : Iota), Or (Eq (h (skS.0 0 a)) True) (Eq (g a_1) True)
% 3.66/3.87 Clause #104 (by superposition #[103, 67]): ∀ (a a_1 : Iota), Or (Eq (g a) True) (Or (Eq (g (skS.0 0 a_1)) True) (Eq True False))
% 3.66/3.87 Clause #110 (by clausification #[104]): ∀ (a a_1 : Iota), Or (Eq (g a) True) (Eq (g (skS.0 0 a_1)) True)
% 3.66/3.87 Clause #114 (by superposition #[110, 20]): ∀ (a a_1 : Iota), Or (Eq (g a) True) (Or (Eq (g a_1) True) (Eq True False))
% 3.66/3.87 Clause #115 (by superposition #[110, 42]): ∀ (a a_1 : Iota), Or (Eq (g a) True) (Or (Eq (f a_1) True) (Eq True False))
% 3.66/3.87 Clause #118 (by clausification #[115]): ∀ (a a_1 : Iota), Or (Eq (g a) True) (Eq (f a_1) True)
% 3.66/3.87 Clause #120 (by superposition #[118, 42]): ∀ (a a_1 : Iota), Or (Eq (f a) True) (Or (Eq (f a_1) True) (Eq True False))
% 3.66/3.87 Clause #126 (by clausification #[120]): ∀ (a a_1 : Iota), Or (Eq (f a) True) (Eq (f a_1) True)
% 3.66/3.87 Clause #131 (by equality factoring #[126]): ∀ (a : Iota), Or (Ne True True) (Eq (f a) True)
% 3.66/3.87 Clause #132 (by clausification #[131]): ∀ (a : Iota), Or (Eq (f a) True) (Or (Eq True False) (Eq True False))
% 3.66/3.87 Clause #134 (by clausification #[132]): ∀ (a : Iota), Or (Eq (f a) True) (Eq True False)
% 3.66/3.87 Clause #135 (by clausification #[134]): ∀ (a : Iota), Eq (f a) True
% 3.66/3.87 Clause #138 (by backward demodulation #[135, 36]): ∀ (a : Iota), Or (Eq True False) (Or (Eq (g a) False) (Eq (h a) True))
% 3.66/3.87 Clause #141 (by clausification #[138]): ∀ (a : Iota), Or (Eq (g a) False) (Eq (h a) True)
% 3.66/3.87 Clause #148 (by clausification #[114]): ∀ (a a_1 : Iota), Or (Eq (g a) True) (Eq (g a_1) True)
% 3.66/3.87 Clause #150 (by equality factoring #[148]): ∀ (a : Iota), Or (Ne True True) (Eq (g a) True)
% 3.66/3.87 Clause #153 (by clausification #[150]): ∀ (a : Iota), Or (Eq (g a) True) (Or (Eq True False) (Eq True False))
% 3.66/3.87 Clause #155 (by clausification #[153]): ∀ (a : Iota), Or (Eq (g a) True) (Eq True False)
% 3.66/3.87 Clause #156 (by clausification #[155]): ∀ (a : Iota), Eq (g a) True
% 3.66/3.87 Clause #157 (by backward demodulation #[156, 141]): ∀ (a : Iota), Or (Eq True False) (Eq (h a) True)
% 3.66/3.87 Clause #159 (by clausification #[157]): ∀ (a : Iota), Eq (h a) True
% 3.66/3.87 Clause #160 (by superposition #[159, 26]): ∀ (a : Iota), Or (Eq True False) (Eq (g (skS.0 1 a)) False)
% 3.66/3.87 Clause #164 (by clausification #[160]): ∀ (a : Iota), Eq (g (skS.0 1 a)) False
% 3.66/3.87 Clause #165 (by superposition #[164, 156]): Eq False True
% 3.66/3.87 Clause #166 (by clausification #[165]): False
% 3.66/3.87 SZS output end Proof for theBenchmark.p
%------------------------------------------------------------------------------