TSTP Solution File: SEU785^2 by Duper---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : SEU785^2 : TPTP v8.1.2. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n002.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 : Thu Aug 31 16:43:53 EDT 2023
% Result : Theorem 5.72s 5.88s
% Output : Proof 5.83s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU785^2 : TPTP v8.1.2. Released v3.7.0.
% 0.00/0.14 % Command : duper %s
% 0.14/0.36 % Computer : n002.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Wed Aug 23 21:22:31 EDT 2023
% 0.14/0.36 % CPUTime :
% 5.72/5.88 SZS status Theorem for theBenchmark.p
% 5.72/5.88 SZS output start Proof for theBenchmark.p
% 5.72/5.88 Clause #0 (by assumption #[]): Eq
% 5.72/5.88 (Eq breln1unionIL
% 5.72/5.88 (∀ (A R : Iota),
% 5.72/5.88 breln1 A R →
% 5.72/5.88 ∀ (S : Iota),
% 5.72/5.88 breln1 A S →
% 5.72/5.88 ∀ (Xx : Iota), in Xx A → ∀ (Xy : Iota), in Xy A → in (kpair Xx Xy) R → in (kpair Xx Xy) (binunion R S)))
% 5.72/5.88 True
% 5.72/5.88 Clause #1 (by assumption #[]): Eq
% 5.72/5.88 (Eq breln1unionIR
% 5.72/5.88 (∀ (A R : Iota),
% 5.72/5.88 breln1 A R →
% 5.72/5.88 ∀ (S : Iota),
% 5.72/5.88 breln1 A S →
% 5.72/5.88 ∀ (Xx : Iota), in Xx A → ∀ (Xy : Iota), in Xy A → in (kpair Xx Xy) S → in (kpair Xx Xy) (binunion R S)))
% 5.72/5.88 True
% 5.72/5.88 Clause #2 (by assumption #[]): Eq
% 5.72/5.88 (Not
% 5.72/5.88 (breln1unionIL →
% 5.72/5.88 breln1unionIR →
% 5.72/5.88 ∀ (A R : Iota),
% 5.72/5.88 breln1 A R →
% 5.72/5.88 ∀ (S : Iota),
% 5.72/5.88 breln1 A S →
% 5.72/5.88 ∀ (Xx : Iota),
% 5.72/5.88 in Xx A →
% 5.72/5.88 ∀ (Xy : Iota),
% 5.72/5.88 in Xy A → Or (in (kpair Xx Xy) R) (in (kpair Xx Xy) S) → in (kpair Xx Xy) (binunion R S)))
% 5.72/5.88 True
% 5.72/5.88 Clause #3 (by clausification #[2]): Eq
% 5.72/5.88 (breln1unionIL →
% 5.72/5.88 breln1unionIR →
% 5.72/5.88 ∀ (A R : Iota),
% 5.72/5.88 breln1 A R →
% 5.72/5.88 ∀ (S : Iota),
% 5.72/5.88 breln1 A S →
% 5.72/5.88 ∀ (Xx : Iota),
% 5.72/5.88 in Xx A →
% 5.72/5.88 ∀ (Xy : Iota),
% 5.72/5.88 in Xy A → Or (in (kpair Xx Xy) R) (in (kpair Xx Xy) S) → in (kpair Xx Xy) (binunion R S))
% 5.72/5.88 False
% 5.72/5.88 Clause #4 (by clausification #[3]): Eq breln1unionIL True
% 5.72/5.88 Clause #5 (by clausification #[3]): Eq
% 5.72/5.88 (breln1unionIR →
% 5.72/5.88 ∀ (A R : Iota),
% 5.72/5.88 breln1 A R →
% 5.72/5.88 ∀ (S : Iota),
% 5.72/5.88 breln1 A S →
% 5.72/5.88 ∀ (Xx : Iota),
% 5.72/5.88 in Xx A →
% 5.72/5.88 ∀ (Xy : Iota), in Xy A → Or (in (kpair Xx Xy) R) (in (kpair Xx Xy) S) → in (kpair Xx Xy) (binunion R S))
% 5.72/5.88 False
% 5.72/5.88 Clause #6 (by clausification #[5]): Eq breln1unionIR True
% 5.72/5.88 Clause #7 (by clausification #[5]): Eq
% 5.72/5.88 (∀ (A R : Iota),
% 5.72/5.88 breln1 A R →
% 5.72/5.88 ∀ (S : Iota),
% 5.72/5.88 breln1 A S →
% 5.72/5.88 ∀ (Xx : Iota),
% 5.72/5.88 in Xx A →
% 5.72/5.88 ∀ (Xy : Iota), in Xy A → Or (in (kpair Xx Xy) R) (in (kpair Xx Xy) S) → in (kpair Xx Xy) (binunion R S))
% 5.72/5.88 False
% 5.72/5.88 Clause #8 (by clausification #[7]): ∀ (a : Iota),
% 5.72/5.88 Eq
% 5.72/5.88 (Not
% 5.72/5.88 (∀ (R : Iota),
% 5.72/5.88 breln1 (skS.0 0 a) R →
% 5.72/5.88 ∀ (S : Iota),
% 5.72/5.88 breln1 (skS.0 0 a) S →
% 5.72/5.88 ∀ (Xx : Iota),
% 5.72/5.88 in Xx (skS.0 0 a) →
% 5.72/5.88 ∀ (Xy : Iota),
% 5.72/5.88 in Xy (skS.0 0 a) → Or (in (kpair Xx Xy) R) (in (kpair Xx Xy) S) → in (kpair Xx Xy) (binunion R S)))
% 5.72/5.88 True
% 5.72/5.88 Clause #9 (by clausification #[8]): ∀ (a : Iota),
% 5.72/5.88 Eq
% 5.72/5.88 (∀ (R : Iota),
% 5.72/5.88 breln1 (skS.0 0 a) R →
% 5.72/5.88 ∀ (S : Iota),
% 5.72/5.88 breln1 (skS.0 0 a) S →
% 5.72/5.88 ∀ (Xx : Iota),
% 5.72/5.88 in Xx (skS.0 0 a) →
% 5.72/5.88 ∀ (Xy : Iota),
% 5.72/5.88 in Xy (skS.0 0 a) → Or (in (kpair Xx Xy) R) (in (kpair Xx Xy) S) → in (kpair Xx Xy) (binunion R S))
% 5.72/5.88 False
% 5.72/5.88 Clause #10 (by clausification #[9]): ∀ (a a_1 : Iota),
% 5.72/5.89 Eq
% 5.72/5.89 (Not
% 5.72/5.89 (breln1 (skS.0 0 a) (skS.0 1 a a_1) →
% 5.72/5.89 ∀ (S : Iota),
% 5.72/5.89 breln1 (skS.0 0 a) S →
% 5.72/5.89 ∀ (Xx : Iota),
% 5.72/5.89 in Xx (skS.0 0 a) →
% 5.72/5.89 ∀ (Xy : Iota),
% 5.72/5.89 in Xy (skS.0 0 a) →
% 5.72/5.89 Or (in (kpair Xx Xy) (skS.0 1 a a_1)) (in (kpair Xx Xy) S) →
% 5.72/5.89 in (kpair Xx Xy) (binunion (skS.0 1 a a_1) S)))
% 5.72/5.89 True
% 5.72/5.89 Clause #11 (by clausification #[10]): ∀ (a a_1 : Iota),
% 5.72/5.89 Eq
% 5.72/5.89 (breln1 (skS.0 0 a) (skS.0 1 a a_1) →
% 5.72/5.89 ∀ (S : Iota),
% 5.72/5.89 breln1 (skS.0 0 a) S →
% 5.72/5.89 ∀ (Xx : Iota),
% 5.72/5.89 in Xx (skS.0 0 a) →
% 5.72/5.89 ∀ (Xy : Iota),
% 5.72/5.89 in Xy (skS.0 0 a) →
% 5.72/5.89 Or (in (kpair Xx Xy) (skS.0 1 a a_1)) (in (kpair Xx Xy) S) →
% 5.72/5.89 in (kpair Xx Xy) (binunion (skS.0 1 a a_1) S))
% 5.72/5.89 False
% 5.72/5.89 Clause #12 (by clausification #[11]): ∀ (a a_1 : Iota), Eq (breln1 (skS.0 0 a) (skS.0 1 a a_1)) True
% 5.72/5.89 Clause #13 (by clausification #[11]): ∀ (a a_1 : Iota),
% 5.72/5.91 Eq
% 5.72/5.91 (∀ (S : Iota),
% 5.72/5.91 breln1 (skS.0 0 a) S →
% 5.72/5.91 ∀ (Xx : Iota),
% 5.72/5.91 in Xx (skS.0 0 a) →
% 5.72/5.91 ∀ (Xy : Iota),
% 5.72/5.91 in Xy (skS.0 0 a) →
% 5.72/5.91 Or (in (kpair Xx Xy) (skS.0 1 a a_1)) (in (kpair Xx Xy) S) →
% 5.72/5.91 in (kpair Xx Xy) (binunion (skS.0 1 a a_1) S))
% 5.72/5.91 False
% 5.72/5.91 Clause #14 (by clausification #[1]): Eq breln1unionIR
% 5.72/5.91 (∀ (A R : Iota),
% 5.72/5.91 breln1 A R →
% 5.72/5.91 ∀ (S : Iota),
% 5.72/5.91 breln1 A S →
% 5.72/5.91 ∀ (Xx : Iota), in Xx A → ∀ (Xy : Iota), in Xy A → in (kpair Xx Xy) S → in (kpair Xx Xy) (binunion R S))
% 5.72/5.91 Clause #15 (by forward demodulation #[14, 6]): Eq True
% 5.72/5.91 (∀ (A R : Iota),
% 5.72/5.91 breln1 A R →
% 5.72/5.91 ∀ (S : Iota),
% 5.72/5.91 breln1 A S →
% 5.72/5.91 ∀ (Xx : Iota), in Xx A → ∀ (Xy : Iota), in Xy A → in (kpair Xx Xy) S → in (kpair Xx Xy) (binunion R S))
% 5.72/5.91 Clause #16 (by clausification #[15]): ∀ (a : Iota),
% 5.72/5.91 Eq
% 5.72/5.91 (∀ (R : Iota),
% 5.72/5.91 breln1 a R →
% 5.72/5.91 ∀ (S : Iota),
% 5.72/5.91 breln1 a S →
% 5.72/5.91 ∀ (Xx : Iota), in Xx a → ∀ (Xy : Iota), in Xy a → in (kpair Xx Xy) S → in (kpair Xx Xy) (binunion R S))
% 5.72/5.91 True
% 5.72/5.91 Clause #17 (by clausification #[16]): ∀ (a a_1 : Iota),
% 5.72/5.91 Eq
% 5.72/5.91 (breln1 a a_1 →
% 5.72/5.91 ∀ (S : Iota),
% 5.72/5.91 breln1 a S →
% 5.72/5.91 ∀ (Xx : Iota), in Xx a → ∀ (Xy : Iota), in Xy a → in (kpair Xx Xy) S → in (kpair Xx Xy) (binunion a_1 S))
% 5.72/5.91 True
% 5.72/5.91 Clause #18 (by clausification #[17]): ∀ (a a_1 : Iota),
% 5.72/5.91 Or (Eq (breln1 a a_1) False)
% 5.72/5.91 (Eq
% 5.72/5.91 (∀ (S : Iota),
% 5.72/5.91 breln1 a S →
% 5.72/5.91 ∀ (Xx : Iota), in Xx a → ∀ (Xy : Iota), in Xy a → in (kpair Xx Xy) S → in (kpair Xx Xy) (binunion a_1 S))
% 5.72/5.91 True)
% 5.72/5.91 Clause #19 (by clausification #[18]): ∀ (a a_1 a_2 : Iota),
% 5.72/5.91 Or (Eq (breln1 a a_1) False)
% 5.72/5.91 (Eq
% 5.72/5.91 (breln1 a a_2 →
% 5.72/5.91 ∀ (Xx : Iota), in Xx a → ∀ (Xy : Iota), in Xy a → in (kpair Xx Xy) a_2 → in (kpair Xx Xy) (binunion a_1 a_2))
% 5.72/5.91 True)
% 5.72/5.91 Clause #20 (by clausification #[19]): ∀ (a a_1 a_2 : Iota),
% 5.72/5.91 Or (Eq (breln1 a a_1) False)
% 5.72/5.91 (Or (Eq (breln1 a a_2) False)
% 5.72/5.91 (Eq (∀ (Xx : Iota), in Xx a → ∀ (Xy : Iota), in Xy a → in (kpair Xx Xy) a_2 → in (kpair Xx Xy) (binunion a_1 a_2))
% 5.72/5.91 True))
% 5.72/5.91 Clause #21 (by clausification #[20]): ∀ (a a_1 a_2 a_3 : Iota),
% 5.72/5.91 Or (Eq (breln1 a a_1) False)
% 5.72/5.91 (Or (Eq (breln1 a a_2) False)
% 5.72/5.91 (Eq (in a_3 a → ∀ (Xy : Iota), in Xy a → in (kpair a_3 Xy) a_2 → in (kpair a_3 Xy) (binunion a_1 a_2)) True))
% 5.72/5.91 Clause #22 (by clausification #[21]): ∀ (a a_1 a_2 a_3 : Iota),
% 5.72/5.91 Or (Eq (breln1 a a_1) False)
% 5.72/5.91 (Or (Eq (breln1 a a_2) False)
% 5.72/5.91 (Or (Eq (in a_3 a) False)
% 5.72/5.91 (Eq (∀ (Xy : Iota), in Xy a → in (kpair a_3 Xy) a_2 → in (kpair a_3 Xy) (binunion a_1 a_2)) True)))
% 5.72/5.91 Clause #23 (by clausification #[22]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 5.72/5.91 Or (Eq (breln1 a a_1) False)
% 5.72/5.91 (Or (Eq (breln1 a a_2) False)
% 5.72/5.91 (Or (Eq (in a_3 a) False) (Eq (in a_4 a → in (kpair a_3 a_4) a_2 → in (kpair a_3 a_4) (binunion a_1 a_2)) True)))
% 5.72/5.91 Clause #24 (by clausification #[23]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 5.72/5.91 Or (Eq (breln1 a a_1) False)
% 5.72/5.91 (Or (Eq (breln1 a a_2) False)
% 5.72/5.91 (Or (Eq (in a_3 a) False)
% 5.72/5.91 (Or (Eq (in a_4 a) False) (Eq (in (kpair a_3 a_4) a_2 → in (kpair a_3 a_4) (binunion a_1 a_2)) True))))
% 5.72/5.91 Clause #25 (by clausification #[24]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 5.72/5.91 Or (Eq (breln1 a a_1) False)
% 5.72/5.91 (Or (Eq (breln1 a a_2) False)
% 5.72/5.91 (Or (Eq (in a_3 a) False)
% 5.72/5.91 (Or (Eq (in a_4 a) False)
% 5.72/5.91 (Or (Eq (in (kpair a_3 a_4) a_2) False) (Eq (in (kpair a_3 a_4) (binunion a_1 a_2)) True)))))
% 5.72/5.91 Clause #26 (by superposition #[25, 12]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 5.72/5.91 Or (Eq (breln1 (skS.0 0 a) a_1) False)
% 5.72/5.91 (Or (Eq (in a_2 (skS.0 0 a)) False)
% 5.72/5.91 (Or (Eq (in a_3 (skS.0 0 a)) False)
% 5.72/5.91 (Or (Eq (in (kpair a_2 a_3) a_1) False)
% 5.72/5.91 (Or (Eq (in (kpair a_2 a_3) (binunion (skS.0 1 a a_4) a_1)) True) (Eq False True)))))
% 5.72/5.91 Clause #27 (by clausification #[0]): Eq breln1unionIL
% 5.72/5.91 (∀ (A R : Iota),
% 5.72/5.91 breln1 A R →
% 5.72/5.91 ∀ (S : Iota),
% 5.72/5.93 breln1 A S →
% 5.72/5.93 ∀ (Xx : Iota), in Xx A → ∀ (Xy : Iota), in Xy A → in (kpair Xx Xy) R → in (kpair Xx Xy) (binunion R S))
% 5.72/5.93 Clause #28 (by forward demodulation #[27, 4]): Eq True
% 5.72/5.93 (∀ (A R : Iota),
% 5.72/5.93 breln1 A R →
% 5.72/5.93 ∀ (S : Iota),
% 5.72/5.93 breln1 A S →
% 5.72/5.93 ∀ (Xx : Iota), in Xx A → ∀ (Xy : Iota), in Xy A → in (kpair Xx Xy) R → in (kpair Xx Xy) (binunion R S))
% 5.72/5.93 Clause #29 (by clausification #[28]): ∀ (a : Iota),
% 5.72/5.93 Eq
% 5.72/5.93 (∀ (R : Iota),
% 5.72/5.93 breln1 a R →
% 5.72/5.93 ∀ (S : Iota),
% 5.72/5.93 breln1 a S →
% 5.72/5.93 ∀ (Xx : Iota), in Xx a → ∀ (Xy : Iota), in Xy a → in (kpair Xx Xy) R → in (kpair Xx Xy) (binunion R S))
% 5.72/5.93 True
% 5.72/5.93 Clause #30 (by clausification #[29]): ∀ (a a_1 : Iota),
% 5.72/5.93 Eq
% 5.72/5.93 (breln1 a a_1 →
% 5.72/5.93 ∀ (S : Iota),
% 5.72/5.93 breln1 a S →
% 5.72/5.93 ∀ (Xx : Iota), in Xx a → ∀ (Xy : Iota), in Xy a → in (kpair Xx Xy) a_1 → in (kpair Xx Xy) (binunion a_1 S))
% 5.72/5.93 True
% 5.72/5.93 Clause #31 (by clausification #[30]): ∀ (a a_1 : Iota),
% 5.72/5.93 Or (Eq (breln1 a a_1) False)
% 5.72/5.93 (Eq
% 5.72/5.93 (∀ (S : Iota),
% 5.72/5.93 breln1 a S →
% 5.72/5.93 ∀ (Xx : Iota), in Xx a → ∀ (Xy : Iota), in Xy a → in (kpair Xx Xy) a_1 → in (kpair Xx Xy) (binunion a_1 S))
% 5.72/5.93 True)
% 5.72/5.93 Clause #32 (by clausification #[31]): ∀ (a a_1 a_2 : Iota),
% 5.72/5.93 Or (Eq (breln1 a a_1) False)
% 5.72/5.93 (Eq
% 5.72/5.93 (breln1 a a_2 →
% 5.72/5.93 ∀ (Xx : Iota), in Xx a → ∀ (Xy : Iota), in Xy a → in (kpair Xx Xy) a_1 → in (kpair Xx Xy) (binunion a_1 a_2))
% 5.72/5.93 True)
% 5.72/5.93 Clause #33 (by clausification #[32]): ∀ (a a_1 a_2 : Iota),
% 5.72/5.93 Or (Eq (breln1 a a_1) False)
% 5.72/5.93 (Or (Eq (breln1 a a_2) False)
% 5.72/5.93 (Eq (∀ (Xx : Iota), in Xx a → ∀ (Xy : Iota), in Xy a → in (kpair Xx Xy) a_1 → in (kpair Xx Xy) (binunion a_1 a_2))
% 5.72/5.93 True))
% 5.72/5.93 Clause #34 (by clausification #[33]): ∀ (a a_1 a_2 a_3 : Iota),
% 5.72/5.93 Or (Eq (breln1 a a_1) False)
% 5.72/5.93 (Or (Eq (breln1 a a_2) False)
% 5.72/5.93 (Eq (in a_3 a → ∀ (Xy : Iota), in Xy a → in (kpair a_3 Xy) a_1 → in (kpair a_3 Xy) (binunion a_1 a_2)) True))
% 5.72/5.93 Clause #35 (by clausification #[34]): ∀ (a a_1 a_2 a_3 : Iota),
% 5.72/5.93 Or (Eq (breln1 a a_1) False)
% 5.72/5.93 (Or (Eq (breln1 a a_2) False)
% 5.72/5.93 (Or (Eq (in a_3 a) False)
% 5.72/5.93 (Eq (∀ (Xy : Iota), in Xy a → in (kpair a_3 Xy) a_1 → in (kpair a_3 Xy) (binunion a_1 a_2)) True)))
% 5.72/5.93 Clause #36 (by clausification #[35]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 5.72/5.93 Or (Eq (breln1 a a_1) False)
% 5.72/5.93 (Or (Eq (breln1 a a_2) False)
% 5.72/5.93 (Or (Eq (in a_3 a) False) (Eq (in a_4 a → in (kpair a_3 a_4) a_1 → in (kpair a_3 a_4) (binunion a_1 a_2)) True)))
% 5.72/5.93 Clause #37 (by clausification #[36]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 5.72/5.93 Or (Eq (breln1 a a_1) False)
% 5.72/5.93 (Or (Eq (breln1 a a_2) False)
% 5.72/5.93 (Or (Eq (in a_3 a) False)
% 5.72/5.93 (Or (Eq (in a_4 a) False) (Eq (in (kpair a_3 a_4) a_1 → in (kpair a_3 a_4) (binunion a_1 a_2)) True))))
% 5.72/5.93 Clause #38 (by clausification #[37]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 5.72/5.93 Or (Eq (breln1 a a_1) False)
% 5.72/5.93 (Or (Eq (breln1 a a_2) False)
% 5.72/5.93 (Or (Eq (in a_3 a) False)
% 5.72/5.93 (Or (Eq (in a_4 a) False)
% 5.72/5.93 (Or (Eq (in (kpair a_3 a_4) a_1) False) (Eq (in (kpair a_3 a_4) (binunion a_1 a_2)) True)))))
% 5.72/5.93 Clause #39 (by superposition #[38, 12]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 5.72/5.93 Or (Eq (breln1 (skS.0 0 a) a_1) False)
% 5.72/5.93 (Or (Eq (in a_2 (skS.0 0 a)) False)
% 5.72/5.93 (Or (Eq (in a_3 (skS.0 0 a)) False)
% 5.72/5.93 (Or (Eq (in (kpair a_2 a_3) (skS.0 1 a a_4)) False)
% 5.72/5.93 (Or (Eq (in (kpair a_2 a_3) (binunion (skS.0 1 a a_4) a_1)) True) (Eq False True)))))
% 5.72/5.93 Clause #40 (by clausification #[13]): ∀ (a a_1 a_2 : Iota),
% 5.72/5.93 Eq
% 5.72/5.93 (Not
% 5.72/5.93 (breln1 (skS.0 0 a) (skS.0 2 a a_1 a_2) →
% 5.72/5.93 ∀ (Xx : Iota),
% 5.72/5.93 in Xx (skS.0 0 a) →
% 5.72/5.93 ∀ (Xy : Iota),
% 5.72/5.93 in Xy (skS.0 0 a) →
% 5.72/5.93 Or (in (kpair Xx Xy) (skS.0 1 a a_1)) (in (kpair Xx Xy) (skS.0 2 a a_1 a_2)) →
% 5.72/5.93 in (kpair Xx Xy) (binunion (skS.0 1 a a_1) (skS.0 2 a a_1 a_2))))
% 5.72/5.93 True
% 5.72/5.93 Clause #41 (by clausification #[40]): ∀ (a a_1 a_2 : Iota),
% 5.72/5.93 Eq
% 5.72/5.93 (breln1 (skS.0 0 a) (skS.0 2 a a_1 a_2) →
% 5.72/5.93 ∀ (Xx : Iota),
% 5.72/5.93 in Xx (skS.0 0 a) →
% 5.72/5.95 ∀ (Xy : Iota),
% 5.72/5.95 in Xy (skS.0 0 a) →
% 5.72/5.95 Or (in (kpair Xx Xy) (skS.0 1 a a_1)) (in (kpair Xx Xy) (skS.0 2 a a_1 a_2)) →
% 5.72/5.95 in (kpair Xx Xy) (binunion (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)))
% 5.72/5.95 False
% 5.72/5.95 Clause #42 (by clausification #[41]): ∀ (a a_1 a_2 : Iota), Eq (breln1 (skS.0 0 a) (skS.0 2 a a_1 a_2)) True
% 5.72/5.95 Clause #43 (by clausification #[41]): ∀ (a a_1 a_2 : Iota),
% 5.72/5.95 Eq
% 5.72/5.95 (∀ (Xx : Iota),
% 5.72/5.95 in Xx (skS.0 0 a) →
% 5.72/5.95 ∀ (Xy : Iota),
% 5.72/5.95 in Xy (skS.0 0 a) →
% 5.72/5.95 Or (in (kpair Xx Xy) (skS.0 1 a a_1)) (in (kpair Xx Xy) (skS.0 2 a a_1 a_2)) →
% 5.72/5.95 in (kpair Xx Xy) (binunion (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)))
% 5.72/5.95 False
% 5.72/5.95 Clause #46 (by clausification #[43]): ∀ (a a_1 a_2 a_3 : Iota),
% 5.72/5.95 Eq
% 5.72/5.95 (Not
% 5.72/5.95 (in (skS.0 3 a a_1 a_2 a_3) (skS.0 0 a) →
% 5.72/5.95 ∀ (Xy : Iota),
% 5.72/5.95 in Xy (skS.0 0 a) →
% 5.72/5.95 Or (in (kpair (skS.0 3 a a_1 a_2 a_3) Xy) (skS.0 1 a a_1))
% 5.72/5.95 (in (kpair (skS.0 3 a a_1 a_2 a_3) Xy) (skS.0 2 a a_1 a_2)) →
% 5.72/5.95 in (kpair (skS.0 3 a a_1 a_2 a_3) Xy) (binunion (skS.0 1 a a_1) (skS.0 2 a a_1 a_2))))
% 5.72/5.95 True
% 5.72/5.95 Clause #47 (by clausification #[46]): ∀ (a a_1 a_2 a_3 : Iota),
% 5.72/5.95 Eq
% 5.72/5.95 (in (skS.0 3 a a_1 a_2 a_3) (skS.0 0 a) →
% 5.72/5.95 ∀ (Xy : Iota),
% 5.72/5.95 in Xy (skS.0 0 a) →
% 5.72/5.95 Or (in (kpair (skS.0 3 a a_1 a_2 a_3) Xy) (skS.0 1 a a_1))
% 5.72/5.95 (in (kpair (skS.0 3 a a_1 a_2 a_3) Xy) (skS.0 2 a a_1 a_2)) →
% 5.72/5.95 in (kpair (skS.0 3 a a_1 a_2 a_3) Xy) (binunion (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)))
% 5.72/5.95 False
% 5.72/5.95 Clause #48 (by clausification #[47]): ∀ (a a_1 a_2 a_3 : Iota), Eq (in (skS.0 3 a a_1 a_2 a_3) (skS.0 0 a)) True
% 5.72/5.95 Clause #49 (by clausification #[47]): ∀ (a a_1 a_2 a_3 : Iota),
% 5.72/5.95 Eq
% 5.72/5.95 (∀ (Xy : Iota),
% 5.72/5.95 in Xy (skS.0 0 a) →
% 5.72/5.95 Or (in (kpair (skS.0 3 a a_1 a_2 a_3) Xy) (skS.0 1 a a_1))
% 5.72/5.95 (in (kpair (skS.0 3 a a_1 a_2 a_3) Xy) (skS.0 2 a a_1 a_2)) →
% 5.72/5.95 in (kpair (skS.0 3 a a_1 a_2 a_3) Xy) (binunion (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)))
% 5.72/5.95 False
% 5.72/5.95 Clause #50 (by clausification #[49]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 5.72/5.95 Eq
% 5.72/5.95 (Not
% 5.72/5.95 (in (skS.0 4 a a_1 a_2 a_3 a_4) (skS.0 0 a) →
% 5.72/5.95 Or (in (kpair (skS.0 3 a a_1 a_2 a_3) (skS.0 4 a a_1 a_2 a_3 a_4)) (skS.0 1 a a_1))
% 5.72/5.95 (in (kpair (skS.0 3 a a_1 a_2 a_3) (skS.0 4 a a_1 a_2 a_3 a_4)) (skS.0 2 a a_1 a_2)) →
% 5.72/5.95 in (kpair (skS.0 3 a a_1 a_2 a_3) (skS.0 4 a a_1 a_2 a_3 a_4))
% 5.72/5.95 (binunion (skS.0 1 a a_1) (skS.0 2 a a_1 a_2))))
% 5.72/5.95 True
% 5.72/5.95 Clause #51 (by clausification #[50]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 5.72/5.95 Eq
% 5.72/5.95 (in (skS.0 4 a a_1 a_2 a_3 a_4) (skS.0 0 a) →
% 5.72/5.95 Or (in (kpair (skS.0 3 a a_1 a_2 a_3) (skS.0 4 a a_1 a_2 a_3 a_4)) (skS.0 1 a a_1))
% 5.72/5.95 (in (kpair (skS.0 3 a a_1 a_2 a_3) (skS.0 4 a a_1 a_2 a_3 a_4)) (skS.0 2 a a_1 a_2)) →
% 5.72/5.95 in (kpair (skS.0 3 a a_1 a_2 a_3) (skS.0 4 a a_1 a_2 a_3 a_4)) (binunion (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)))
% 5.72/5.95 False
% 5.72/5.95 Clause #52 (by clausification #[51]): ∀ (a a_1 a_2 a_3 a_4 : Iota), Eq (in (skS.0 4 a a_1 a_2 a_3 a_4) (skS.0 0 a)) True
% 5.72/5.95 Clause #53 (by clausification #[51]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 5.72/5.95 Eq
% 5.72/5.95 (Or (in (kpair (skS.0 3 a a_1 a_2 a_3) (skS.0 4 a a_1 a_2 a_3 a_4)) (skS.0 1 a a_1))
% 5.72/5.95 (in (kpair (skS.0 3 a a_1 a_2 a_3) (skS.0 4 a a_1 a_2 a_3 a_4)) (skS.0 2 a a_1 a_2)) →
% 5.72/5.95 in (kpair (skS.0 3 a a_1 a_2 a_3) (skS.0 4 a a_1 a_2 a_3 a_4)) (binunion (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)))
% 5.72/5.95 False
% 5.72/5.95 Clause #54 (by clausification #[53]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 5.72/5.95 Eq
% 5.72/5.95 (Or (in (kpair (skS.0 3 a a_1 a_2 a_3) (skS.0 4 a a_1 a_2 a_3 a_4)) (skS.0 1 a a_1))
% 5.72/5.95 (in (kpair (skS.0 3 a a_1 a_2 a_3) (skS.0 4 a a_1 a_2 a_3 a_4)) (skS.0 2 a a_1 a_2)))
% 5.72/5.95 True
% 5.72/5.95 Clause #55 (by clausification #[53]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 5.72/5.95 Eq (in (kpair (skS.0 3 a a_1 a_2 a_3) (skS.0 4 a a_1 a_2 a_3 a_4)) (binunion (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)))
% 5.72/5.95 False
% 5.72/5.95 Clause #56 (by clausification #[54]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 5.72/5.95 Or (Eq (in (kpair (skS.0 3 a a_1 a_2 a_3) (skS.0 4 a a_1 a_2 a_3 a_4)) (skS.0 1 a a_1)) True)
% 5.81/5.98 (Eq (in (kpair (skS.0 3 a a_1 a_2 a_3) (skS.0 4 a a_1 a_2 a_3 a_4)) (skS.0 2 a a_1 a_2)) True)
% 5.81/5.98 Clause #57 (by clausification #[26]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 5.81/5.98 Or (Eq (breln1 (skS.0 0 a) a_1) False)
% 5.81/5.98 (Or (Eq (in a_2 (skS.0 0 a)) False)
% 5.81/5.98 (Or (Eq (in a_3 (skS.0 0 a)) False)
% 5.81/5.98 (Or (Eq (in (kpair a_2 a_3) a_1) False) (Eq (in (kpair a_2 a_3) (binunion (skS.0 1 a a_4) a_1)) True))))
% 5.81/5.98 Clause #59 (by superposition #[57, 42]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 5.81/5.98 Or (Eq (in a (skS.0 0 a_1)) False)
% 5.81/5.98 (Or (Eq (in a_2 (skS.0 0 a_1)) False)
% 5.81/5.98 (Or (Eq (in (kpair a a_2) (skS.0 2 a_1 a_3 a_4)) False)
% 5.81/5.98 (Or (Eq (in (kpair a a_2) (binunion (skS.0 1 a_1 a_5) (skS.0 2 a_1 a_3 a_4))) True) (Eq False True))))
% 5.81/5.98 Clause #60 (by clausification #[39]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 5.81/5.98 Or (Eq (breln1 (skS.0 0 a) a_1) False)
% 5.81/5.98 (Or (Eq (in a_2 (skS.0 0 a)) False)
% 5.81/5.98 (Or (Eq (in a_3 (skS.0 0 a)) False)
% 5.81/5.98 (Or (Eq (in (kpair a_2 a_3) (skS.0 1 a a_4)) False)
% 5.81/5.98 (Eq (in (kpair a_2 a_3) (binunion (skS.0 1 a a_4) a_1)) True))))
% 5.81/5.98 Clause #62 (by superposition #[60, 42]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 5.81/5.98 Or (Eq (in a (skS.0 0 a_1)) False)
% 5.81/5.98 (Or (Eq (in a_2 (skS.0 0 a_1)) False)
% 5.81/5.98 (Or (Eq (in (kpair a a_2) (skS.0 1 a_1 a_3)) False)
% 5.81/5.98 (Or (Eq (in (kpair a a_2) (binunion (skS.0 1 a_1 a_3) (skS.0 2 a_1 a_4 a_5))) True) (Eq False True))))
% 5.81/5.98 Clause #75 (by clausification #[62]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 5.81/5.98 Or (Eq (in a (skS.0 0 a_1)) False)
% 5.81/5.98 (Or (Eq (in a_2 (skS.0 0 a_1)) False)
% 5.81/5.98 (Or (Eq (in (kpair a a_2) (skS.0 1 a_1 a_3)) False)
% 5.81/5.98 (Eq (in (kpair a a_2) (binunion (skS.0 1 a_1 a_3) (skS.0 2 a_1 a_4 a_5))) True)))
% 5.81/5.98 Clause #76 (by superposition #[75, 48]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 : Iota),
% 5.81/5.98 Or (Eq (in a (skS.0 0 a_1)) False)
% 5.81/5.98 (Or (Eq (in (kpair (skS.0 3 a_1 a_2 a_3 a_4) a) (skS.0 1 a_1 a_5)) False)
% 5.81/5.98 (Or (Eq (in (kpair (skS.0 3 a_1 a_2 a_3 a_4) a) (binunion (skS.0 1 a_1 a_5) (skS.0 2 a_1 a_6 a_7))) True)
% 5.81/5.98 (Eq False True)))
% 5.81/5.98 Clause #84 (by clausification #[59]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 5.81/5.98 Or (Eq (in a (skS.0 0 a_1)) False)
% 5.81/5.98 (Or (Eq (in a_2 (skS.0 0 a_1)) False)
% 5.81/5.98 (Or (Eq (in (kpair a a_2) (skS.0 2 a_1 a_3 a_4)) False)
% 5.81/5.98 (Eq (in (kpair a a_2) (binunion (skS.0 1 a_1 a_5) (skS.0 2 a_1 a_3 a_4))) True)))
% 5.81/5.98 Clause #85 (by superposition #[84, 48]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 : Iota),
% 5.81/5.98 Or (Eq (in a (skS.0 0 a_1)) False)
% 5.81/5.98 (Or (Eq (in (kpair (skS.0 3 a_1 a_2 a_3 a_4) a) (skS.0 2 a_1 a_5 a_6)) False)
% 5.81/5.98 (Or (Eq (in (kpair (skS.0 3 a_1 a_2 a_3 a_4) a) (binunion (skS.0 1 a_1 a_7) (skS.0 2 a_1 a_5 a_6))) True)
% 5.81/5.98 (Eq False True)))
% 5.81/5.98 Clause #105 (by clausification #[76]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 : Iota),
% 5.81/5.98 Or (Eq (in a (skS.0 0 a_1)) False)
% 5.81/5.98 (Or (Eq (in (kpair (skS.0 3 a_1 a_2 a_3 a_4) a) (skS.0 1 a_1 a_5)) False)
% 5.81/5.98 (Eq (in (kpair (skS.0 3 a_1 a_2 a_3 a_4) a) (binunion (skS.0 1 a_1 a_5) (skS.0 2 a_1 a_6 a_7))) True))
% 5.81/5.98 Clause #107 (by superposition #[105, 52]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 a_8 a_9 a_10 : Iota),
% 5.81/5.98 Or (Eq (in (kpair (skS.0 3 a a_1 a_2 a_3) (skS.0 4 a a_4 a_5 a_6 a_7)) (skS.0 1 a a_8)) False)
% 5.81/5.98 (Or
% 5.81/5.98 (Eq
% 5.81/5.98 (in (kpair (skS.0 3 a a_1 a_2 a_3) (skS.0 4 a a_4 a_5 a_6 a_7)) (binunion (skS.0 1 a a_8) (skS.0 2 a a_9 a_10)))
% 5.81/5.98 True)
% 5.81/5.98 (Eq False True))
% 5.81/5.98 Clause #108 (by clausification #[85]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 : Iota),
% 5.81/5.98 Or (Eq (in a (skS.0 0 a_1)) False)
% 5.81/5.98 (Or (Eq (in (kpair (skS.0 3 a_1 a_2 a_3 a_4) a) (skS.0 2 a_1 a_5 a_6)) False)
% 5.81/5.98 (Eq (in (kpair (skS.0 3 a_1 a_2 a_3 a_4) a) (binunion (skS.0 1 a_1 a_7) (skS.0 2 a_1 a_5 a_6))) True))
% 5.81/5.98 Clause #110 (by superposition #[108, 52]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 a_8 a_9 a_10 : Iota),
% 5.81/5.98 Or (Eq (in (kpair (skS.0 3 a a_1 a_2 a_3) (skS.0 4 a a_4 a_5 a_6 a_7)) (skS.0 2 a a_8 a_9)) False)
% 5.81/5.98 (Or
% 5.81/5.98 (Eq
% 5.81/5.98 (in (kpair (skS.0 3 a a_1 a_2 a_3) (skS.0 4 a a_4 a_5 a_6 a_7)) (binunion (skS.0 1 a a_10) (skS.0 2 a a_8 a_9)))
% 5.81/5.98 True)
% 5.81/5.98 (Eq False True))
% 5.83/5.99 Clause #154 (by clausification #[107]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 a_8 a_9 a_10 : Iota),
% 5.83/5.99 Or (Eq (in (kpair (skS.0 3 a a_1 a_2 a_3) (skS.0 4 a a_4 a_5 a_6 a_7)) (skS.0 1 a a_8)) False)
% 5.83/5.99 (Eq (in (kpair (skS.0 3 a a_1 a_2 a_3) (skS.0 4 a a_4 a_5 a_6 a_7)) (binunion (skS.0 1 a a_8) (skS.0 2 a a_9 a_10)))
% 5.83/5.99 True)
% 5.83/5.99 Clause #163 (by clausification #[110]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 a_8 a_9 a_10 : Iota),
% 5.83/5.99 Or (Eq (in (kpair (skS.0 3 a a_1 a_2 a_3) (skS.0 4 a a_4 a_5 a_6 a_7)) (skS.0 2 a a_8 a_9)) False)
% 5.83/5.99 (Eq (in (kpair (skS.0 3 a a_1 a_2 a_3) (skS.0 4 a a_4 a_5 a_6 a_7)) (binunion (skS.0 1 a a_10) (skS.0 2 a a_8 a_9)))
% 5.83/5.99 True)
% 5.83/5.99 Clause #164 (by superposition #[163, 56]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 5.83/5.99 Or
% 5.83/5.99 (Eq (in (kpair (skS.0 3 a a_1 a_2 a_3) (skS.0 4 a a_1 a_2 a_3 a_4)) (binunion (skS.0 1 a a_5) (skS.0 2 a a_1 a_2)))
% 5.83/5.99 True)
% 5.83/5.99 (Or (Eq (in (kpair (skS.0 3 a a_1 a_2 a_3) (skS.0 4 a a_1 a_2 a_3 a_4)) (skS.0 1 a a_1)) True) (Eq False True))
% 5.83/5.99 Clause #165 (by clausification #[164]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 5.83/5.99 Or
% 5.83/5.99 (Eq (in (kpair (skS.0 3 a a_1 a_2 a_3) (skS.0 4 a a_1 a_2 a_3 a_4)) (binunion (skS.0 1 a a_5) (skS.0 2 a a_1 a_2)))
% 5.83/5.99 True)
% 5.83/5.99 (Eq (in (kpair (skS.0 3 a a_1 a_2 a_3) (skS.0 4 a a_1 a_2 a_3 a_4)) (skS.0 1 a a_1)) True)
% 5.83/5.99 Clause #166 (by superposition #[165, 55]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 5.83/5.99 Or (Eq (in (kpair (skS.0 3 a a_1 a_2 a_3) (skS.0 4 a a_1 a_2 a_3 a_4)) (skS.0 1 a a_1)) True) (Eq True False)
% 5.83/5.99 Clause #167 (by clausification #[166]): ∀ (a a_1 a_2 a_3 a_4 : Iota), Eq (in (kpair (skS.0 3 a a_1 a_2 a_3) (skS.0 4 a a_1 a_2 a_3 a_4)) (skS.0 1 a a_1)) True
% 5.83/5.99 Clause #172 (by superposition #[167, 154]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota),
% 5.83/5.99 Or (Eq True False)
% 5.83/5.99 (Eq (in (kpair (skS.0 3 a a_1 a_2 a_3) (skS.0 4 a a_1 a_2 a_3 a_4)) (binunion (skS.0 1 a a_1) (skS.0 2 a a_5 a_6)))
% 5.83/5.99 True)
% 5.83/5.99 Clause #178 (by clausification #[172]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota),
% 5.83/5.99 Eq (in (kpair (skS.0 3 a a_1 a_2 a_3) (skS.0 4 a a_1 a_2 a_3 a_4)) (binunion (skS.0 1 a a_1) (skS.0 2 a a_5 a_6)))
% 5.83/5.99 True
% 5.83/5.99 Clause #179 (by superposition #[178, 55]): Eq True False
% 5.83/5.99 Clause #180 (by clausification #[179]): False
% 5.83/5.99 SZS output end Proof for theBenchmark.p
%------------------------------------------------------------------------------