TSTP Solution File: SYN354+1 by Duper---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : SYN354+1 : TPTP v8.1.2. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n004.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 02:11:22 EDT 2023
% Result : Theorem 3.99s 4.29s
% Output : Proof 3.99s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SYN354+1 : TPTP v8.1.2. Released v2.0.0.
% 0.00/0.14 % Command : duper %s
% 0.15/0.35 % Computer : n004.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Sat Aug 26 21:24:52 EDT 2023
% 0.15/0.35 % CPUTime :
% 3.99/4.29 SZS status Theorem for theBenchmark.p
% 3.99/4.29 SZS output start Proof for theBenchmark.p
% 3.99/4.29 Clause #0 (by assumption #[]): Eq
% 3.99/4.29 (Not
% 3.99/4.29 (∀ (X1 X2 : Iota),
% 3.99/4.29 Exists fun Y1 =>
% 3.99/4.29 Exists fun Y2 =>
% 3.99/4.29 ∀ (Z : Iota),
% 3.99/4.29 big_f X1 X2 →
% 3.99/4.29 big_g X1 X2 →
% 3.99/4.29 (Iff (big_g X2 Z) (big_g Y2 Z) → big_f Y1 Y2 → big_f X2 Y2) →
% 3.99/4.29 Iff (big_g X2 Z) (big_g Y1 Z) → And (And (big_f X1 Y1) (big_f X2 Y1)) (big_f Y1 Y2)))
% 3.99/4.29 True
% 3.99/4.29 Clause #1 (by clausification #[0]): Eq
% 3.99/4.29 (∀ (X1 X2 : Iota),
% 3.99/4.29 Exists fun Y1 =>
% 3.99/4.29 Exists fun Y2 =>
% 3.99/4.29 ∀ (Z : Iota),
% 3.99/4.29 big_f X1 X2 →
% 3.99/4.29 big_g X1 X2 →
% 3.99/4.29 (Iff (big_g X2 Z) (big_g Y2 Z) → big_f Y1 Y2 → big_f X2 Y2) →
% 3.99/4.29 Iff (big_g X2 Z) (big_g Y1 Z) → And (And (big_f X1 Y1) (big_f X2 Y1)) (big_f Y1 Y2))
% 3.99/4.29 False
% 3.99/4.29 Clause #2 (by clausification #[1]): ∀ (a : Iota),
% 3.99/4.29 Eq
% 3.99/4.29 (Not
% 3.99/4.29 (∀ (X2 : Iota),
% 3.99/4.29 Exists fun Y1 =>
% 3.99/4.29 Exists fun Y2 =>
% 3.99/4.29 ∀ (Z : Iota),
% 3.99/4.29 big_f (skS.0 0 a) X2 →
% 3.99/4.29 big_g (skS.0 0 a) X2 →
% 3.99/4.29 (Iff (big_g X2 Z) (big_g Y2 Z) → big_f Y1 Y2 → big_f X2 Y2) →
% 3.99/4.29 Iff (big_g X2 Z) (big_g Y1 Z) → And (And (big_f (skS.0 0 a) Y1) (big_f X2 Y1)) (big_f Y1 Y2)))
% 3.99/4.29 True
% 3.99/4.29 Clause #3 (by clausification #[2]): ∀ (a : Iota),
% 3.99/4.29 Eq
% 3.99/4.29 (∀ (X2 : Iota),
% 3.99/4.29 Exists fun Y1 =>
% 3.99/4.29 Exists fun Y2 =>
% 3.99/4.29 ∀ (Z : Iota),
% 3.99/4.29 big_f (skS.0 0 a) X2 →
% 3.99/4.29 big_g (skS.0 0 a) X2 →
% 3.99/4.29 (Iff (big_g X2 Z) (big_g Y2 Z) → big_f Y1 Y2 → big_f X2 Y2) →
% 3.99/4.29 Iff (big_g X2 Z) (big_g Y1 Z) → And (And (big_f (skS.0 0 a) Y1) (big_f X2 Y1)) (big_f Y1 Y2))
% 3.99/4.29 False
% 3.99/4.29 Clause #4 (by clausification #[3]): ∀ (a a_1 : Iota),
% 3.99/4.29 Eq
% 3.99/4.29 (Not
% 3.99/4.29 (Exists fun Y1 =>
% 3.99/4.29 Exists fun Y2 =>
% 3.99/4.29 ∀ (Z : Iota),
% 3.99/4.29 big_f (skS.0 0 a) (skS.0 1 a a_1) →
% 3.99/4.29 big_g (skS.0 0 a) (skS.0 1 a a_1) →
% 3.99/4.29 (Iff (big_g (skS.0 1 a a_1) Z) (big_g Y2 Z) → big_f Y1 Y2 → big_f (skS.0 1 a a_1) Y2) →
% 3.99/4.29 Iff (big_g (skS.0 1 a a_1) Z) (big_g Y1 Z) →
% 3.99/4.29 And (And (big_f (skS.0 0 a) Y1) (big_f (skS.0 1 a a_1) Y1)) (big_f Y1 Y2)))
% 3.99/4.29 True
% 3.99/4.29 Clause #5 (by clausification #[4]): ∀ (a a_1 : Iota),
% 3.99/4.29 Eq
% 3.99/4.29 (Exists fun Y1 =>
% 3.99/4.29 Exists fun Y2 =>
% 3.99/4.29 ∀ (Z : Iota),
% 3.99/4.29 big_f (skS.0 0 a) (skS.0 1 a a_1) →
% 3.99/4.29 big_g (skS.0 0 a) (skS.0 1 a a_1) →
% 3.99/4.29 (Iff (big_g (skS.0 1 a a_1) Z) (big_g Y2 Z) → big_f Y1 Y2 → big_f (skS.0 1 a a_1) Y2) →
% 3.99/4.29 Iff (big_g (skS.0 1 a a_1) Z) (big_g Y1 Z) →
% 3.99/4.29 And (And (big_f (skS.0 0 a) Y1) (big_f (skS.0 1 a a_1) Y1)) (big_f Y1 Y2))
% 3.99/4.29 False
% 3.99/4.29 Clause #6 (by clausification #[5]): ∀ (a a_1 a_2 : Iota),
% 3.99/4.29 Eq
% 3.99/4.29 (Exists fun Y2 =>
% 3.99/4.29 ∀ (Z : Iota),
% 3.99/4.29 big_f (skS.0 0 a) (skS.0 1 a a_1) →
% 3.99/4.29 big_g (skS.0 0 a) (skS.0 1 a a_1) →
% 3.99/4.29 (Iff (big_g (skS.0 1 a a_1) Z) (big_g Y2 Z) → big_f a_2 Y2 → big_f (skS.0 1 a a_1) Y2) →
% 3.99/4.29 Iff (big_g (skS.0 1 a a_1) Z) (big_g a_2 Z) →
% 3.99/4.29 And (And (big_f (skS.0 0 a) a_2) (big_f (skS.0 1 a a_1) a_2)) (big_f a_2 Y2))
% 3.99/4.29 False
% 3.99/4.29 Clause #7 (by clausification #[6]): ∀ (a a_1 a_2 a_3 : Iota),
% 3.99/4.29 Eq
% 3.99/4.29 (∀ (Z : Iota),
% 3.99/4.29 big_f (skS.0 0 a) (skS.0 1 a a_1) →
% 3.99/4.29 big_g (skS.0 0 a) (skS.0 1 a a_1) →
% 3.99/4.29 (Iff (big_g (skS.0 1 a a_1) Z) (big_g a_2 Z) → big_f a_3 a_2 → big_f (skS.0 1 a a_1) a_2) →
% 3.99/4.29 Iff (big_g (skS.0 1 a a_1) Z) (big_g a_3 Z) →
% 3.99/4.29 And (And (big_f (skS.0 0 a) a_3) (big_f (skS.0 1 a a_1) a_3)) (big_f a_3 a_2))
% 3.99/4.29 False
% 3.99/4.29 Clause #8 (by clausification #[7]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 3.99/4.29 Eq
% 3.99/4.29 (Not
% 3.99/4.29 (big_f (skS.0 0 a) (skS.0 1 a a_1) →
% 3.99/4.29 big_g (skS.0 0 a) (skS.0 1 a a_1) →
% 3.99/4.29 (Iff (big_g (skS.0 1 a a_1) (skS.0 2 a a_1 a_2 a_3 a_4)) (big_g a_2 (skS.0 2 a a_1 a_2 a_3 a_4)) →
% 3.99/4.29 big_f a_3 a_2 → big_f (skS.0 1 a a_1) a_2) →
% 3.99/4.29 Iff (big_g (skS.0 1 a a_1) (skS.0 2 a a_1 a_2 a_3 a_4)) (big_g a_3 (skS.0 2 a a_1 a_2 a_3 a_4)) →
% 3.99/4.32 And (And (big_f (skS.0 0 a) a_3) (big_f (skS.0 1 a a_1) a_3)) (big_f a_3 a_2)))
% 3.99/4.32 True
% 3.99/4.32 Clause #9 (by clausification #[8]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 3.99/4.32 Eq
% 3.99/4.32 (big_f (skS.0 0 a) (skS.0 1 a a_1) →
% 3.99/4.32 big_g (skS.0 0 a) (skS.0 1 a a_1) →
% 3.99/4.32 (Iff (big_g (skS.0 1 a a_1) (skS.0 2 a a_1 a_2 a_3 a_4)) (big_g a_2 (skS.0 2 a a_1 a_2 a_3 a_4)) →
% 3.99/4.32 big_f a_3 a_2 → big_f (skS.0 1 a a_1) a_2) →
% 3.99/4.32 Iff (big_g (skS.0 1 a a_1) (skS.0 2 a a_1 a_2 a_3 a_4)) (big_g a_3 (skS.0 2 a a_1 a_2 a_3 a_4)) →
% 3.99/4.32 And (And (big_f (skS.0 0 a) a_3) (big_f (skS.0 1 a a_1) a_3)) (big_f a_3 a_2))
% 3.99/4.32 False
% 3.99/4.32 Clause #10 (by clausification #[9]): ∀ (a a_1 : Iota), Eq (big_f (skS.0 0 a) (skS.0 1 a a_1)) True
% 3.99/4.32 Clause #11 (by clausification #[9]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 3.99/4.32 Eq
% 3.99/4.32 (big_g (skS.0 0 a) (skS.0 1 a a_1) →
% 3.99/4.32 (Iff (big_g (skS.0 1 a a_1) (skS.0 2 a a_1 a_2 a_3 a_4)) (big_g a_2 (skS.0 2 a a_1 a_2 a_3 a_4)) →
% 3.99/4.32 big_f a_3 a_2 → big_f (skS.0 1 a a_1) a_2) →
% 3.99/4.32 Iff (big_g (skS.0 1 a a_1) (skS.0 2 a a_1 a_2 a_3 a_4)) (big_g a_3 (skS.0 2 a a_1 a_2 a_3 a_4)) →
% 3.99/4.32 And (And (big_f (skS.0 0 a) a_3) (big_f (skS.0 1 a a_1) a_3)) (big_f a_3 a_2))
% 3.99/4.32 False
% 3.99/4.32 Clause #13 (by clausification #[11]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 3.99/4.32 Eq
% 3.99/4.32 ((Iff (big_g (skS.0 1 a a_1) (skS.0 2 a a_1 a_2 a_3 a_4)) (big_g a_2 (skS.0 2 a a_1 a_2 a_3 a_4)) →
% 3.99/4.32 big_f a_3 a_2 → big_f (skS.0 1 a a_1) a_2) →
% 3.99/4.32 Iff (big_g (skS.0 1 a a_1) (skS.0 2 a a_1 a_2 a_3 a_4)) (big_g a_3 (skS.0 2 a a_1 a_2 a_3 a_4)) →
% 3.99/4.32 And (And (big_f (skS.0 0 a) a_3) (big_f (skS.0 1 a a_1) a_3)) (big_f a_3 a_2))
% 3.99/4.32 False
% 3.99/4.32 Clause #14 (by clausification #[13]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 3.99/4.32 Eq
% 3.99/4.32 (Iff (big_g (skS.0 1 a a_1) (skS.0 2 a a_1 a_2 a_3 a_4)) (big_g a_2 (skS.0 2 a a_1 a_2 a_3 a_4)) →
% 3.99/4.32 big_f a_3 a_2 → big_f (skS.0 1 a a_1) a_2)
% 3.99/4.32 True
% 3.99/4.32 Clause #15 (by clausification #[13]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 3.99/4.32 Eq
% 3.99/4.32 (Iff (big_g (skS.0 1 a a_1) (skS.0 2 a a_1 a_2 a_3 a_4)) (big_g a_3 (skS.0 2 a a_1 a_2 a_3 a_4)) →
% 3.99/4.32 And (And (big_f (skS.0 0 a) a_3) (big_f (skS.0 1 a a_1) a_3)) (big_f a_3 a_2))
% 3.99/4.32 False
% 3.99/4.32 Clause #16 (by clausification #[14]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 3.99/4.32 Or (Eq (Iff (big_g (skS.0 1 a a_1) (skS.0 2 a a_1 a_2 a_3 a_4)) (big_g a_2 (skS.0 2 a a_1 a_2 a_3 a_4))) False)
% 3.99/4.32 (Eq (big_f a_3 a_2 → big_f (skS.0 1 a a_1) a_2) True)
% 3.99/4.32 Clause #17 (by clausification #[16]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 3.99/4.32 Or (Eq (big_f a a_1 → big_f (skS.0 1 a_2 a_3) a_1) True)
% 3.99/4.32 (Or (Eq (big_g (skS.0 1 a_2 a_3) (skS.0 2 a_2 a_3 a_1 a a_4)) False)
% 3.99/4.32 (Eq (big_g a_1 (skS.0 2 a_2 a_3 a_1 a a_4)) False))
% 3.99/4.32 Clause #18 (by clausification #[16]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 3.99/4.32 Or (Eq (big_f a a_1 → big_f (skS.0 1 a_2 a_3) a_1) True)
% 3.99/4.32 (Or (Eq (big_g (skS.0 1 a_2 a_3) (skS.0 2 a_2 a_3 a_1 a a_4)) True)
% 3.99/4.32 (Eq (big_g a_1 (skS.0 2 a_2 a_3 a_1 a a_4)) True))
% 3.99/4.32 Clause #19 (by clausification #[17]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 3.99/4.32 Or (Eq (big_g (skS.0 1 a a_1) (skS.0 2 a a_1 a_2 a_3 a_4)) False)
% 3.99/4.32 (Or (Eq (big_g a_2 (skS.0 2 a a_1 a_2 a_3 a_4)) False)
% 3.99/4.32 (Or (Eq (big_f a_3 a_2) False) (Eq (big_f (skS.0 1 a a_1) a_2) True)))
% 3.99/4.32 Clause #21 (by clausification #[15]): ∀ (a a_1 a_2 a_3 : Iota), Eq (And (And (big_f (skS.0 0 a) a_1) (big_f (skS.0 1 a a_2) a_1)) (big_f a_1 a_3)) False
% 3.99/4.32 Clause #24 (by clausification #[21]): ∀ (a a_1 a_2 a_3 : Iota),
% 3.99/4.32 Or (Eq (And (big_f (skS.0 0 a) a_1) (big_f (skS.0 1 a a_2) a_1)) False) (Eq (big_f a_1 a_3) False)
% 3.99/4.32 Clause #25 (by clausification #[24]): ∀ (a a_1 a_2 a_3 : Iota),
% 3.99/4.32 Or (Eq (big_f a a_1) False) (Or (Eq (big_f (skS.0 0 a_2) a) False) (Eq (big_f (skS.0 1 a_2 a_3) a) False))
% 3.99/4.32 Clause #27 (by clausification #[18]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 3.99/4.32 Or (Eq (big_g (skS.0 1 a a_1) (skS.0 2 a a_1 a_2 a_3 a_4)) True)
% 3.99/4.32 (Or (Eq (big_g a_2 (skS.0 2 a a_1 a_2 a_3 a_4)) True)
% 3.99/4.32 (Or (Eq (big_f a_3 a_2) False) (Eq (big_f (skS.0 1 a a_1) a_2) True)))
% 3.99/4.32 Clause #28 (by superposition #[27, 10]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 3.99/4.34 Or (Eq (big_g (skS.0 1 a a_1) (skS.0 2 a a_1 (skS.0 1 a_2 a_3) (skS.0 0 a_2) a_4)) True)
% 3.99/4.34 (Or (Eq (big_g (skS.0 1 a_2 a_3) (skS.0 2 a a_1 (skS.0 1 a_2 a_3) (skS.0 0 a_2) a_4)) True)
% 3.99/4.34 (Or (Eq (big_f (skS.0 1 a a_1) (skS.0 1 a_2 a_3)) True) (Eq False True)))
% 3.99/4.34 Clause #30 (by clausification #[28]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 3.99/4.34 Or (Eq (big_g (skS.0 1 a a_1) (skS.0 2 a a_1 (skS.0 1 a_2 a_3) (skS.0 0 a_2) a_4)) True)
% 3.99/4.34 (Or (Eq (big_g (skS.0 1 a_2 a_3) (skS.0 2 a a_1 (skS.0 1 a_2 a_3) (skS.0 0 a_2) a_4)) True)
% 3.99/4.34 (Eq (big_f (skS.0 1 a a_1) (skS.0 1 a_2 a_3)) True))
% 3.99/4.34 Clause #33 (by equality factoring #[30]): ∀ (a a_1 a_2 : Iota),
% 3.99/4.34 Or (Eq (big_f (skS.0 1 a a_1) (skS.0 1 a a_1)) True)
% 3.99/4.34 (Or (Ne True True) (Eq (big_g (skS.0 1 a a_1) (skS.0 2 a a_1 (skS.0 1 a a_1) (skS.0 0 a) a_2)) True))
% 3.99/4.34 Clause #34 (by clausification #[33]): ∀ (a a_1 a_2 : Iota),
% 3.99/4.34 Or (Eq (big_f (skS.0 1 a a_1) (skS.0 1 a a_1)) True)
% 3.99/4.34 (Or (Eq (big_g (skS.0 1 a a_1) (skS.0 2 a a_1 (skS.0 1 a a_1) (skS.0 0 a) a_2)) True)
% 3.99/4.34 (Or (Eq True False) (Eq True False)))
% 3.99/4.34 Clause #36 (by clausification #[34]): ∀ (a a_1 a_2 : Iota),
% 3.99/4.34 Or (Eq (big_f (skS.0 1 a a_1) (skS.0 1 a a_1)) True)
% 3.99/4.34 (Or (Eq (big_g (skS.0 1 a a_1) (skS.0 2 a a_1 (skS.0 1 a a_1) (skS.0 0 a) a_2)) True) (Eq True False))
% 3.99/4.34 Clause #37 (by clausification #[36]): ∀ (a a_1 a_2 : Iota),
% 3.99/4.34 Or (Eq (big_f (skS.0 1 a a_1) (skS.0 1 a a_1)) True)
% 3.99/4.34 (Eq (big_g (skS.0 1 a a_1) (skS.0 2 a a_1 (skS.0 1 a a_1) (skS.0 0 a) a_2)) True)
% 3.99/4.34 Clause #38 (by superposition #[37, 19]): ∀ (a a_1 : Iota),
% 3.99/4.34 Or (Eq (big_f (skS.0 1 a a_1) (skS.0 1 a a_1)) True)
% 3.99/4.34 (Or (Eq True False)
% 3.99/4.34 (Or (Eq True False)
% 3.99/4.34 (Or (Eq (big_f (skS.0 0 a) (skS.0 1 a a_1)) False) (Eq (big_f (skS.0 1 a a_1) (skS.0 1 a a_1)) True))))
% 3.99/4.34 Clause #42 (by clausification #[38]): ∀ (a a_1 : Iota),
% 3.99/4.34 Or (Eq (big_f (skS.0 1 a a_1) (skS.0 1 a a_1)) True)
% 3.99/4.34 (Or (Eq True False)
% 3.99/4.34 (Or (Eq (big_f (skS.0 0 a) (skS.0 1 a a_1)) False) (Eq (big_f (skS.0 1 a a_1) (skS.0 1 a a_1)) True)))
% 3.99/4.34 Clause #43 (by clausification #[42]): ∀ (a a_1 : Iota),
% 3.99/4.34 Or (Eq (big_f (skS.0 1 a a_1) (skS.0 1 a a_1)) True)
% 3.99/4.34 (Or (Eq (big_f (skS.0 0 a) (skS.0 1 a a_1)) False) (Eq (big_f (skS.0 1 a a_1) (skS.0 1 a a_1)) True))
% 3.99/4.34 Clause #44 (by eliminate duplicate literals #[43]): ∀ (a a_1 : Iota), Or (Eq (big_f (skS.0 1 a a_1) (skS.0 1 a a_1)) True) (Eq (big_f (skS.0 0 a) (skS.0 1 a a_1)) False)
% 3.99/4.34 Clause #45 (by forward demodulation #[44, 10]): ∀ (a a_1 : Iota), Or (Eq (big_f (skS.0 1 a a_1) (skS.0 1 a a_1)) True) (Eq True False)
% 3.99/4.34 Clause #46 (by clausification #[45]): ∀ (a a_1 : Iota), Eq (big_f (skS.0 1 a a_1) (skS.0 1 a a_1)) True
% 3.99/4.34 Clause #49 (by superposition #[46, 25]): ∀ (a a_1 a_2 a_3 : Iota),
% 3.99/4.34 Or (Eq True False)
% 3.99/4.34 (Or (Eq (big_f (skS.0 0 a) (skS.0 1 a_1 a_2)) False) (Eq (big_f (skS.0 1 a a_3) (skS.0 1 a_1 a_2)) False))
% 3.99/4.34 Clause #51 (by clausification #[49]): ∀ (a a_1 a_2 a_3 : Iota),
% 3.99/4.34 Or (Eq (big_f (skS.0 0 a) (skS.0 1 a_1 a_2)) False) (Eq (big_f (skS.0 1 a a_3) (skS.0 1 a_1 a_2)) False)
% 3.99/4.34 Clause #52 (by superposition #[51, 10]): ∀ (a a_1 a_2 : Iota), Or (Eq (big_f (skS.0 1 a a_1) (skS.0 1 a a_2)) False) (Eq False True)
% 3.99/4.34 Clause #53 (by clausification #[52]): ∀ (a a_1 a_2 : Iota), Eq (big_f (skS.0 1 a a_1) (skS.0 1 a a_2)) False
% 3.99/4.34 Clause #54 (by superposition #[53, 46]): Eq False True
% 3.99/4.34 Clause #55 (by clausification #[54]): False
% 3.99/4.34 SZS output end Proof for theBenchmark.p
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