TSTP Solution File: SYN352+1 by Duper---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : SYN352+1 : TPTP v8.1.2. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n032.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 02:11:21 EDT 2023
% Result : Theorem 7.65s 7.91s
% Output : Proof 7.65s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SYN352+1 : TPTP v8.1.2. Released v2.0.0.
% 0.00/0.10 % Command : duper %s
% 0.10/0.30 % Computer : n032.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 300
% 0.10/0.30 % DateTime : Sat Aug 26 18:07:29 EDT 2023
% 0.10/0.30 % CPUTime :
% 7.65/7.91 SZS status Theorem for theBenchmark.p
% 7.65/7.91 SZS output start Proof for theBenchmark.p
% 7.65/7.91 Clause #0 (by assumption #[]): Eq
% 7.65/7.91 (Not
% 7.65/7.91 (∀ (X1 X2 : Iota),
% 7.65/7.91 Exists fun Y1 =>
% 7.65/7.91 Exists fun Y2 =>
% 7.65/7.91 ∀ (Z : Iota),
% 7.65/7.91 big_f X1 X2 →
% 7.65/7.91 (big_f Y1 Y2 → Or (big_f X2 Z) (big_f Y2 Z)) →
% 7.65/7.91 ((big_f Y1 Y2 → Iff (big_f X2 Z) (big_f Y1 Z)) → big_f Z Z) →
% 7.65/7.91 And (big_f Y1 Y2) (Iff (big_f Y1 Z) (big_f Y2 Z))))
% 7.65/7.91 True
% 7.65/7.91 Clause #1 (by clausification #[0]): Eq
% 7.65/7.91 (∀ (X1 X2 : Iota),
% 7.65/7.91 Exists fun Y1 =>
% 7.65/7.91 Exists fun Y2 =>
% 7.65/7.91 ∀ (Z : Iota),
% 7.65/7.91 big_f X1 X2 →
% 7.65/7.91 (big_f Y1 Y2 → Or (big_f X2 Z) (big_f Y2 Z)) →
% 7.65/7.91 ((big_f Y1 Y2 → Iff (big_f X2 Z) (big_f Y1 Z)) → big_f Z Z) →
% 7.65/7.91 And (big_f Y1 Y2) (Iff (big_f Y1 Z) (big_f Y2 Z)))
% 7.65/7.91 False
% 7.65/7.91 Clause #2 (by clausification #[1]): ∀ (a : Iota),
% 7.65/7.91 Eq
% 7.65/7.91 (Not
% 7.65/7.91 (∀ (X2 : Iota),
% 7.65/7.91 Exists fun Y1 =>
% 7.65/7.91 Exists fun Y2 =>
% 7.65/7.91 ∀ (Z : Iota),
% 7.65/7.91 big_f (skS.0 0 a) X2 →
% 7.65/7.91 (big_f Y1 Y2 → Or (big_f X2 Z) (big_f Y2 Z)) →
% 7.65/7.91 ((big_f Y1 Y2 → Iff (big_f X2 Z) (big_f Y1 Z)) → big_f Z Z) →
% 7.65/7.91 And (big_f Y1 Y2) (Iff (big_f Y1 Z) (big_f Y2 Z))))
% 7.65/7.91 True
% 7.65/7.91 Clause #3 (by clausification #[2]): ∀ (a : Iota),
% 7.65/7.91 Eq
% 7.65/7.91 (∀ (X2 : Iota),
% 7.65/7.91 Exists fun Y1 =>
% 7.65/7.91 Exists fun Y2 =>
% 7.65/7.91 ∀ (Z : Iota),
% 7.65/7.91 big_f (skS.0 0 a) X2 →
% 7.65/7.91 (big_f Y1 Y2 → Or (big_f X2 Z) (big_f Y2 Z)) →
% 7.65/7.91 ((big_f Y1 Y2 → Iff (big_f X2 Z) (big_f Y1 Z)) → big_f Z Z) →
% 7.65/7.91 And (big_f Y1 Y2) (Iff (big_f Y1 Z) (big_f Y2 Z)))
% 7.65/7.91 False
% 7.65/7.91 Clause #4 (by clausification #[3]): ∀ (a a_1 : Iota),
% 7.65/7.91 Eq
% 7.65/7.91 (Not
% 7.65/7.91 (Exists fun Y1 =>
% 7.65/7.91 Exists fun Y2 =>
% 7.65/7.91 ∀ (Z : Iota),
% 7.65/7.91 big_f (skS.0 0 a) (skS.0 1 a a_1) →
% 7.65/7.91 (big_f Y1 Y2 → Or (big_f (skS.0 1 a a_1) Z) (big_f Y2 Z)) →
% 7.65/7.91 ((big_f Y1 Y2 → Iff (big_f (skS.0 1 a a_1) Z) (big_f Y1 Z)) → big_f Z Z) →
% 7.65/7.91 And (big_f Y1 Y2) (Iff (big_f Y1 Z) (big_f Y2 Z))))
% 7.65/7.91 True
% 7.65/7.91 Clause #5 (by clausification #[4]): ∀ (a a_1 : Iota),
% 7.65/7.91 Eq
% 7.65/7.91 (Exists fun Y1 =>
% 7.65/7.91 Exists fun Y2 =>
% 7.65/7.91 ∀ (Z : Iota),
% 7.65/7.91 big_f (skS.0 0 a) (skS.0 1 a a_1) →
% 7.65/7.91 (big_f Y1 Y2 → Or (big_f (skS.0 1 a a_1) Z) (big_f Y2 Z)) →
% 7.65/7.91 ((big_f Y1 Y2 → Iff (big_f (skS.0 1 a a_1) Z) (big_f Y1 Z)) → big_f Z Z) →
% 7.65/7.91 And (big_f Y1 Y2) (Iff (big_f Y1 Z) (big_f Y2 Z)))
% 7.65/7.91 False
% 7.65/7.91 Clause #6 (by clausification #[5]): ∀ (a a_1 a_2 : Iota),
% 7.65/7.91 Eq
% 7.65/7.91 (Exists fun Y2 =>
% 7.65/7.91 ∀ (Z : Iota),
% 7.65/7.91 big_f (skS.0 0 a) (skS.0 1 a a_1) →
% 7.65/7.91 (big_f a_2 Y2 → Or (big_f (skS.0 1 a a_1) Z) (big_f Y2 Z)) →
% 7.65/7.91 ((big_f a_2 Y2 → Iff (big_f (skS.0 1 a a_1) Z) (big_f a_2 Z)) → big_f Z Z) →
% 7.65/7.91 And (big_f a_2 Y2) (Iff (big_f a_2 Z) (big_f Y2 Z)))
% 7.65/7.91 False
% 7.65/7.91 Clause #7 (by clausification #[6]): ∀ (a a_1 a_2 a_3 : Iota),
% 7.65/7.91 Eq
% 7.65/7.91 (∀ (Z : Iota),
% 7.65/7.91 big_f (skS.0 0 a) (skS.0 1 a a_1) →
% 7.65/7.91 (big_f a_2 a_3 → Or (big_f (skS.0 1 a a_1) Z) (big_f a_3 Z)) →
% 7.65/7.91 ((big_f a_2 a_3 → Iff (big_f (skS.0 1 a a_1) Z) (big_f a_2 Z)) → big_f Z Z) →
% 7.65/7.91 And (big_f a_2 a_3) (Iff (big_f a_2 Z) (big_f a_3 Z)))
% 7.65/7.91 False
% 7.65/7.91 Clause #8 (by clausification #[7]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 7.65/7.91 Eq
% 7.65/7.91 (Not
% 7.65/7.91 (big_f (skS.0 0 a) (skS.0 1 a a_1) →
% 7.65/7.91 (big_f a_2 a_3 →
% 7.65/7.91 Or (big_f (skS.0 1 a a_1) (skS.0 2 a a_1 a_2 a_3 a_4)) (big_f a_3 (skS.0 2 a a_1 a_2 a_3 a_4))) →
% 7.65/7.91 ((big_f a_2 a_3 →
% 7.65/7.91 Iff (big_f (skS.0 1 a a_1) (skS.0 2 a a_1 a_2 a_3 a_4)) (big_f a_2 (skS.0 2 a a_1 a_2 a_3 a_4))) →
% 7.65/7.91 big_f (skS.0 2 a a_1 a_2 a_3 a_4) (skS.0 2 a a_1 a_2 a_3 a_4)) →
% 7.65/7.91 And (big_f a_2 a_3) (Iff (big_f a_2 (skS.0 2 a a_1 a_2 a_3 a_4)) (big_f a_3 (skS.0 2 a a_1 a_2 a_3 a_4)))))
% 7.65/7.91 True
% 7.65/7.91 Clause #9 (by clausification #[8]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 7.65/7.91 Eq
% 7.65/7.91 (big_f (skS.0 0 a) (skS.0 1 a a_1) →
% 7.65/7.93 (big_f a_2 a_3 → Or (big_f (skS.0 1 a a_1) (skS.0 2 a a_1 a_2 a_3 a_4)) (big_f a_3 (skS.0 2 a a_1 a_2 a_3 a_4))) →
% 7.65/7.93 ((big_f a_2 a_3 →
% 7.65/7.93 Iff (big_f (skS.0 1 a a_1) (skS.0 2 a a_1 a_2 a_3 a_4)) (big_f a_2 (skS.0 2 a a_1 a_2 a_3 a_4))) →
% 7.65/7.93 big_f (skS.0 2 a a_1 a_2 a_3 a_4) (skS.0 2 a a_1 a_2 a_3 a_4)) →
% 7.65/7.93 And (big_f a_2 a_3) (Iff (big_f a_2 (skS.0 2 a a_1 a_2 a_3 a_4)) (big_f a_3 (skS.0 2 a a_1 a_2 a_3 a_4))))
% 7.65/7.93 False
% 7.65/7.93 Clause #11 (by clausification #[9]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 7.65/7.93 Eq
% 7.65/7.93 ((big_f a a_1 → Or (big_f (skS.0 1 a_2 a_3) (skS.0 2 a_2 a_3 a a_1 a_4)) (big_f a_1 (skS.0 2 a_2 a_3 a a_1 a_4))) →
% 7.65/7.93 ((big_f a a_1 → Iff (big_f (skS.0 1 a_2 a_3) (skS.0 2 a_2 a_3 a a_1 a_4)) (big_f a (skS.0 2 a_2 a_3 a a_1 a_4))) →
% 7.65/7.93 big_f (skS.0 2 a_2 a_3 a a_1 a_4) (skS.0 2 a_2 a_3 a a_1 a_4)) →
% 7.65/7.93 And (big_f a a_1) (Iff (big_f a (skS.0 2 a_2 a_3 a a_1 a_4)) (big_f a_1 (skS.0 2 a_2 a_3 a a_1 a_4))))
% 7.65/7.93 False
% 7.65/7.93 Clause #13 (by clausification #[11]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 7.65/7.93 Eq
% 7.65/7.93 (((big_f a a_1 → Iff (big_f (skS.0 1 a_2 a_3) (skS.0 2 a_2 a_3 a a_1 a_4)) (big_f a (skS.0 2 a_2 a_3 a a_1 a_4))) →
% 7.65/7.93 big_f (skS.0 2 a_2 a_3 a a_1 a_4) (skS.0 2 a_2 a_3 a a_1 a_4)) →
% 7.65/7.93 And (big_f a a_1) (Iff (big_f a (skS.0 2 a_2 a_3 a a_1 a_4)) (big_f a_1 (skS.0 2 a_2 a_3 a a_1 a_4))))
% 7.65/7.93 False
% 7.65/7.93 Clause #17 (by clausification #[13]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 7.65/7.93 Eq
% 7.65/7.93 ((big_f a a_1 → Iff (big_f (skS.0 1 a_2 a_3) (skS.0 2 a_2 a_3 a a_1 a_4)) (big_f a (skS.0 2 a_2 a_3 a a_1 a_4))) →
% 7.65/7.93 big_f (skS.0 2 a_2 a_3 a a_1 a_4) (skS.0 2 a_2 a_3 a a_1 a_4))
% 7.65/7.93 True
% 7.65/7.93 Clause #18 (by clausification #[13]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 7.65/7.93 Eq (And (big_f a a_1) (Iff (big_f a (skS.0 2 a_2 a_3 a a_1 a_4)) (big_f a_1 (skS.0 2 a_2 a_3 a a_1 a_4)))) False
% 7.65/7.93 Clause #19 (by clausification #[17]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 7.65/7.93 Or
% 7.65/7.93 (Eq (big_f a a_1 → Iff (big_f (skS.0 1 a_2 a_3) (skS.0 2 a_2 a_3 a a_1 a_4)) (big_f a (skS.0 2 a_2 a_3 a a_1 a_4)))
% 7.65/7.93 False)
% 7.65/7.93 (Eq (big_f (skS.0 2 a_2 a_3 a a_1 a_4) (skS.0 2 a_2 a_3 a a_1 a_4)) True)
% 7.65/7.93 Clause #20 (by clausification #[19]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 7.65/7.93 Or (Eq (big_f (skS.0 2 a a_1 a_2 a_3 a_4) (skS.0 2 a a_1 a_2 a_3 a_4)) True) (Eq (big_f a_2 a_3) True)
% 7.65/7.93 Clause #23 (by clausification #[18]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 7.65/7.93 Or (Eq (big_f a a_1) False)
% 7.65/7.93 (Eq (Iff (big_f a (skS.0 2 a_2 a_3 a a_1 a_4)) (big_f a_1 (skS.0 2 a_2 a_3 a a_1 a_4))) False)
% 7.65/7.93 Clause #24 (by clausification #[23]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 7.65/7.93 Or (Eq (big_f a a_1) False)
% 7.65/7.93 (Or (Eq (big_f a (skS.0 2 a_2 a_3 a a_1 a_4)) False) (Eq (big_f a_1 (skS.0 2 a_2 a_3 a a_1 a_4)) False))
% 7.65/7.93 Clause #25 (by clausification #[23]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 7.65/7.93 Or (Eq (big_f a a_1) False)
% 7.65/7.93 (Or (Eq (big_f a (skS.0 2 a_2 a_3 a a_1 a_4)) True) (Eq (big_f a_1 (skS.0 2 a_2 a_3 a a_1 a_4)) True))
% 7.65/7.93 Clause #27 (by superposition #[24, 20]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 : Iota),
% 7.65/7.93 Or
% 7.65/7.93 (Eq
% 7.65/7.93 (big_f (skS.0 2 a a_1 a_2 a_3 a_4) (skS.0 2 a_5 a_6 (skS.0 2 a a_1 a_2 a_3 a_4) (skS.0 2 a a_1 a_2 a_3 a_4) a_7))
% 7.65/7.93 False)
% 7.65/7.93 (Or
% 7.65/7.93 (Eq
% 7.65/7.93 (big_f (skS.0 2 a a_1 a_2 a_3 a_4)
% 7.65/7.93 (skS.0 2 a_5 a_6 (skS.0 2 a a_1 a_2 a_3 a_4) (skS.0 2 a a_1 a_2 a_3 a_4) a_7))
% 7.65/7.93 False)
% 7.65/7.93 (Or (Eq False True) (Eq (big_f a_2 a_3) True)))
% 7.65/7.93 Clause #29 (by superposition #[25, 20]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 : Iota),
% 7.65/7.93 Or
% 7.65/7.93 (Eq
% 7.65/7.93 (big_f (skS.0 2 a a_1 a_2 a_3 a_4) (skS.0 2 a_5 a_6 (skS.0 2 a a_1 a_2 a_3 a_4) (skS.0 2 a a_1 a_2 a_3 a_4) a_7))
% 7.65/7.93 True)
% 7.65/7.93 (Or
% 7.65/7.93 (Eq
% 7.65/7.93 (big_f (skS.0 2 a a_1 a_2 a_3 a_4)
% 7.65/7.93 (skS.0 2 a_5 a_6 (skS.0 2 a a_1 a_2 a_3 a_4) (skS.0 2 a a_1 a_2 a_3 a_4) a_7))
% 7.65/7.93 True)
% 7.65/7.93 (Or (Eq False True) (Eq (big_f a_2 a_3) True)))
% 7.65/7.93 Clause #67 (by clausification #[29]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 : Iota),
% 7.65/7.93 Or
% 7.65/7.93 (Eq
% 7.65/7.93 (big_f (skS.0 2 a a_1 a_2 a_3 a_4) (skS.0 2 a_5 a_6 (skS.0 2 a a_1 a_2 a_3 a_4) (skS.0 2 a a_1 a_2 a_3 a_4) a_7))
% 7.65/7.93 True)
% 7.65/7.93 (Or
% 7.65/7.93 (Eq
% 7.65/7.93 (big_f (skS.0 2 a a_1 a_2 a_3 a_4)
% 7.65/7.95 (skS.0 2 a_5 a_6 (skS.0 2 a a_1 a_2 a_3 a_4) (skS.0 2 a a_1 a_2 a_3 a_4) a_7))
% 7.65/7.95 True)
% 7.65/7.95 (Eq (big_f a_2 a_3) True))
% 7.65/7.95 Clause #68 (by eliminate duplicate literals #[67]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 : Iota),
% 7.65/7.95 Or
% 7.65/7.95 (Eq
% 7.65/7.95 (big_f (skS.0 2 a a_1 a_2 a_3 a_4) (skS.0 2 a_5 a_6 (skS.0 2 a a_1 a_2 a_3 a_4) (skS.0 2 a a_1 a_2 a_3 a_4) a_7))
% 7.65/7.95 True)
% 7.65/7.95 (Eq (big_f a_2 a_3) True)
% 7.65/7.95 Clause #72 (by clausification #[27]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 : Iota),
% 7.65/7.95 Or
% 7.65/7.95 (Eq
% 7.65/7.95 (big_f (skS.0 2 a a_1 a_2 a_3 a_4) (skS.0 2 a_5 a_6 (skS.0 2 a a_1 a_2 a_3 a_4) (skS.0 2 a a_1 a_2 a_3 a_4) a_7))
% 7.65/7.95 False)
% 7.65/7.95 (Or
% 7.65/7.95 (Eq
% 7.65/7.95 (big_f (skS.0 2 a a_1 a_2 a_3 a_4)
% 7.65/7.95 (skS.0 2 a_5 a_6 (skS.0 2 a a_1 a_2 a_3 a_4) (skS.0 2 a a_1 a_2 a_3 a_4) a_7))
% 7.65/7.95 False)
% 7.65/7.95 (Eq (big_f a_2 a_3) True))
% 7.65/7.95 Clause #73 (by eliminate duplicate literals #[72]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 : Iota),
% 7.65/7.95 Or
% 7.65/7.95 (Eq
% 7.65/7.95 (big_f (skS.0 2 a a_1 a_2 a_3 a_4) (skS.0 2 a_5 a_6 (skS.0 2 a a_1 a_2 a_3 a_4) (skS.0 2 a a_1 a_2 a_3 a_4) a_7))
% 7.65/7.95 False)
% 7.65/7.95 (Eq (big_f a_2 a_3) True)
% 7.65/7.95 Clause #74 (by superposition #[73, 68]): ∀ (a a_1 : Iota), Or (Eq (big_f a a_1) True) (Or (Eq False True) (Eq (big_f a a_1) True))
% 7.65/7.95 Clause #75 (by clausification #[74]): ∀ (a a_1 : Iota), Or (Eq (big_f a a_1) True) (Eq (big_f a a_1) True)
% 7.65/7.95 Clause #76 (by eliminate duplicate literals #[75]): ∀ (a a_1 : Iota), Eq (big_f a a_1) True
% 7.65/7.95 Clause #84 (by backward demodulation #[76, 24]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 7.65/7.95 Or (Eq True False)
% 7.65/7.95 (Or (Eq (big_f a (skS.0 2 a_1 a_2 a a_3 a_4)) False) (Eq (big_f a_3 (skS.0 2 a_1 a_2 a a_3 a_4)) False))
% 7.65/7.95 Clause #91 (by clausification #[84]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 7.65/7.95 Or (Eq (big_f a (skS.0 2 a_1 a_2 a a_3 a_4)) False) (Eq (big_f a_3 (skS.0 2 a_1 a_2 a a_3 a_4)) False)
% 7.65/7.95 Clause #92 (by superposition #[91, 76]): ∀ (a a_1 a_2 a_3 a_4 : Iota), Or (Eq (big_f a (skS.0 2 a_1 a_2 a_3 a a_4)) False) (Eq False True)
% 7.65/7.95 Clause #93 (by clausification #[92]): ∀ (a a_1 a_2 a_3 a_4 : Iota), Eq (big_f a (skS.0 2 a_1 a_2 a_3 a a_4)) False
% 7.65/7.95 Clause #94 (by superposition #[93, 76]): Eq False True
% 7.65/7.95 Clause #95 (by clausification #[94]): False
% 7.65/7.95 SZS output end Proof for theBenchmark.p
%------------------------------------------------------------------------------