TSTP Solution File: SEU787^2 by Duper---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : SEU787^2 : TPTP v8.1.2. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n022.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 5.54s 5.71s
% Output : Proof 5.62s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU787^2 : TPTP v8.1.2. Released v3.7.0.
% 0.12/0.13 % Command : duper %s
% 0.12/0.34 % Computer : n022.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Wed Aug 23 16:06:41 EDT 2023
% 0.12/0.34 % CPUTime :
% 5.54/5.71 SZS status Theorem for theBenchmark.p
% 5.54/5.71 SZS output start Proof for theBenchmark.p
% 5.54/5.71 Clause #0 (by assumption #[]): Eq
% 5.54/5.71 (Eq breln1unionE
% 5.54/5.71 (∀ (A R : Iota),
% 5.54/5.71 breln1 A R →
% 5.54/5.71 ∀ (S : Iota),
% 5.54/5.71 breln1 A S →
% 5.54/5.71 ∀ (Xx : Iota),
% 5.54/5.71 in Xx A →
% 5.54/5.71 ∀ (Xy : Iota),
% 5.54/5.71 in Xy A → in (kpair Xx Xy) (binunion R S) → Or (in (kpair Xx Xy) R) (in (kpair Xx Xy) S)))
% 5.54/5.71 True
% 5.54/5.71 Clause #1 (by assumption #[]): Eq
% 5.54/5.71 (Not
% 5.54/5.71 (breln1unionE →
% 5.54/5.71 ∀ (A R : Iota),
% 5.54/5.71 breln1 A R →
% 5.54/5.71 ∀ (S : Iota),
% 5.54/5.71 breln1 A S →
% 5.54/5.71 ∀ (Xx : Iota),
% 5.54/5.71 in Xx A →
% 5.54/5.71 ∀ (Xy : Iota),
% 5.54/5.71 in Xy A →
% 5.54/5.71 in (kpair Xx Xy) (binunion R S) →
% 5.54/5.71 ∀ (Xphi : Prop), (in (kpair Xx Xy) R → Xphi) → (in (kpair Xx Xy) S → Xphi) → Xphi))
% 5.54/5.71 True
% 5.54/5.71 Clause #2 (by clausification #[1]): Eq
% 5.54/5.71 (breln1unionE →
% 5.54/5.71 ∀ (A R : Iota),
% 5.54/5.71 breln1 A R →
% 5.54/5.71 ∀ (S : Iota),
% 5.54/5.71 breln1 A S →
% 5.54/5.71 ∀ (Xx : Iota),
% 5.54/5.71 in Xx A →
% 5.54/5.71 ∀ (Xy : Iota),
% 5.54/5.71 in Xy A →
% 5.54/5.71 in (kpair Xx Xy) (binunion R S) →
% 5.54/5.71 ∀ (Xphi : Prop), (in (kpair Xx Xy) R → Xphi) → (in (kpair Xx Xy) S → Xphi) → Xphi)
% 5.54/5.71 False
% 5.54/5.71 Clause #3 (by clausification #[2]): Eq breln1unionE True
% 5.54/5.71 Clause #4 (by clausification #[2]): Eq
% 5.54/5.71 (∀ (A R : Iota),
% 5.54/5.71 breln1 A R →
% 5.54/5.71 ∀ (S : Iota),
% 5.54/5.71 breln1 A S →
% 5.54/5.71 ∀ (Xx : Iota),
% 5.54/5.71 in Xx A →
% 5.54/5.71 ∀ (Xy : Iota),
% 5.54/5.71 in Xy A →
% 5.54/5.71 in (kpair Xx Xy) (binunion R S) →
% 5.54/5.71 ∀ (Xphi : Prop), (in (kpair Xx Xy) R → Xphi) → (in (kpair Xx Xy) S → Xphi) → Xphi)
% 5.54/5.71 False
% 5.54/5.71 Clause #5 (by clausification #[4]): ∀ (a : Iota),
% 5.54/5.71 Eq
% 5.54/5.71 (Not
% 5.54/5.71 (∀ (R : Iota),
% 5.54/5.71 breln1 (skS.0 0 a) R →
% 5.54/5.71 ∀ (S : Iota),
% 5.54/5.71 breln1 (skS.0 0 a) S →
% 5.54/5.71 ∀ (Xx : Iota),
% 5.54/5.71 in Xx (skS.0 0 a) →
% 5.54/5.71 ∀ (Xy : Iota),
% 5.54/5.71 in Xy (skS.0 0 a) →
% 5.54/5.71 in (kpair Xx Xy) (binunion R S) →
% 5.54/5.71 ∀ (Xphi : Prop), (in (kpair Xx Xy) R → Xphi) → (in (kpair Xx Xy) S → Xphi) → Xphi))
% 5.54/5.71 True
% 5.54/5.71 Clause #6 (by clausification #[5]): ∀ (a : Iota),
% 5.54/5.71 Eq
% 5.54/5.71 (∀ (R : Iota),
% 5.54/5.71 breln1 (skS.0 0 a) R →
% 5.54/5.71 ∀ (S : Iota),
% 5.54/5.71 breln1 (skS.0 0 a) S →
% 5.54/5.71 ∀ (Xx : Iota),
% 5.54/5.71 in Xx (skS.0 0 a) →
% 5.54/5.71 ∀ (Xy : Iota),
% 5.54/5.71 in Xy (skS.0 0 a) →
% 5.54/5.71 in (kpair Xx Xy) (binunion R S) →
% 5.54/5.71 ∀ (Xphi : Prop), (in (kpair Xx Xy) R → Xphi) → (in (kpair Xx Xy) S → Xphi) → Xphi)
% 5.54/5.71 False
% 5.54/5.71 Clause #7 (by clausification #[6]): ∀ (a a_1 : Iota),
% 5.54/5.71 Eq
% 5.54/5.71 (Not
% 5.54/5.71 (breln1 (skS.0 0 a) (skS.0 1 a a_1) →
% 5.54/5.71 ∀ (S : Iota),
% 5.54/5.71 breln1 (skS.0 0 a) S →
% 5.54/5.71 ∀ (Xx : Iota),
% 5.54/5.71 in Xx (skS.0 0 a) →
% 5.54/5.71 ∀ (Xy : Iota),
% 5.54/5.71 in Xy (skS.0 0 a) →
% 5.54/5.71 in (kpair Xx Xy) (binunion (skS.0 1 a a_1) S) →
% 5.54/5.71 ∀ (Xphi : Prop), (in (kpair Xx Xy) (skS.0 1 a a_1) → Xphi) → (in (kpair Xx Xy) S → Xphi) → Xphi))
% 5.54/5.71 True
% 5.54/5.71 Clause #8 (by clausification #[7]): ∀ (a a_1 : Iota),
% 5.54/5.71 Eq
% 5.54/5.71 (breln1 (skS.0 0 a) (skS.0 1 a a_1) →
% 5.54/5.71 ∀ (S : Iota),
% 5.54/5.71 breln1 (skS.0 0 a) S →
% 5.54/5.71 ∀ (Xx : Iota),
% 5.54/5.71 in Xx (skS.0 0 a) →
% 5.54/5.71 ∀ (Xy : Iota),
% 5.54/5.71 in Xy (skS.0 0 a) →
% 5.54/5.71 in (kpair Xx Xy) (binunion (skS.0 1 a a_1) S) →
% 5.54/5.71 ∀ (Xphi : Prop), (in (kpair Xx Xy) (skS.0 1 a a_1) → Xphi) → (in (kpair Xx Xy) S → Xphi) → Xphi)
% 5.54/5.71 False
% 5.54/5.71 Clause #9 (by clausification #[8]): ∀ (a a_1 : Iota), Eq (breln1 (skS.0 0 a) (skS.0 1 a a_1)) True
% 5.54/5.71 Clause #10 (by clausification #[8]): ∀ (a a_1 : Iota),
% 5.54/5.71 Eq
% 5.54/5.71 (∀ (S : Iota),
% 5.54/5.71 breln1 (skS.0 0 a) S →
% 5.54/5.71 ∀ (Xx : Iota),
% 5.54/5.71 in Xx (skS.0 0 a) →
% 5.54/5.73 ∀ (Xy : Iota),
% 5.54/5.73 in Xy (skS.0 0 a) →
% 5.54/5.73 in (kpair Xx Xy) (binunion (skS.0 1 a a_1) S) →
% 5.54/5.73 ∀ (Xphi : Prop), (in (kpair Xx Xy) (skS.0 1 a a_1) → Xphi) → (in (kpair Xx Xy) S → Xphi) → Xphi)
% 5.54/5.73 False
% 5.54/5.73 Clause #11 (by clausification #[10]): ∀ (a a_1 a_2 : Iota),
% 5.54/5.73 Eq
% 5.54/5.73 (Not
% 5.54/5.73 (breln1 (skS.0 0 a) (skS.0 2 a a_1 a_2) →
% 5.54/5.73 ∀ (Xx : Iota),
% 5.54/5.73 in Xx (skS.0 0 a) →
% 5.54/5.73 ∀ (Xy : Iota),
% 5.54/5.73 in Xy (skS.0 0 a) →
% 5.54/5.73 in (kpair Xx Xy) (binunion (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)) →
% 5.54/5.73 ∀ (Xphi : Prop),
% 5.54/5.73 (in (kpair Xx Xy) (skS.0 1 a a_1) → Xphi) → (in (kpair Xx Xy) (skS.0 2 a a_1 a_2) → Xphi) → Xphi))
% 5.54/5.73 True
% 5.54/5.73 Clause #12 (by clausification #[11]): ∀ (a a_1 a_2 : Iota),
% 5.54/5.73 Eq
% 5.54/5.73 (breln1 (skS.0 0 a) (skS.0 2 a a_1 a_2) →
% 5.54/5.73 ∀ (Xx : Iota),
% 5.54/5.73 in Xx (skS.0 0 a) →
% 5.54/5.73 ∀ (Xy : Iota),
% 5.54/5.73 in Xy (skS.0 0 a) →
% 5.54/5.73 in (kpair Xx Xy) (binunion (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)) →
% 5.54/5.73 ∀ (Xphi : Prop),
% 5.54/5.73 (in (kpair Xx Xy) (skS.0 1 a a_1) → Xphi) → (in (kpair Xx Xy) (skS.0 2 a a_1 a_2) → Xphi) → Xphi)
% 5.54/5.73 False
% 5.54/5.73 Clause #13 (by clausification #[12]): ∀ (a a_1 a_2 : Iota), Eq (breln1 (skS.0 0 a) (skS.0 2 a a_1 a_2)) True
% 5.54/5.73 Clause #14 (by clausification #[12]): ∀ (a a_1 a_2 : Iota),
% 5.54/5.73 Eq
% 5.54/5.73 (∀ (Xx : Iota),
% 5.54/5.73 in Xx (skS.0 0 a) →
% 5.54/5.73 ∀ (Xy : Iota),
% 5.54/5.73 in Xy (skS.0 0 a) →
% 5.54/5.73 in (kpair Xx Xy) (binunion (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)) →
% 5.54/5.73 ∀ (Xphi : Prop),
% 5.54/5.73 (in (kpair Xx Xy) (skS.0 1 a a_1) → Xphi) → (in (kpair Xx Xy) (skS.0 2 a a_1 a_2) → Xphi) → Xphi)
% 5.54/5.73 False
% 5.54/5.73 Clause #15 (by clausification #[14]): ∀ (a a_1 a_2 a_3 : Iota),
% 5.54/5.73 Eq
% 5.54/5.73 (Not
% 5.54/5.73 (in (skS.0 3 a a_1 a_2 a_3) (skS.0 0 a) →
% 5.54/5.73 ∀ (Xy : Iota),
% 5.54/5.73 in Xy (skS.0 0 a) →
% 5.54/5.73 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)) →
% 5.54/5.73 ∀ (Xphi : Prop),
% 5.54/5.73 (in (kpair (skS.0 3 a a_1 a_2 a_3) Xy) (skS.0 1 a a_1) → Xphi) →
% 5.54/5.73 (in (kpair (skS.0 3 a a_1 a_2 a_3) Xy) (skS.0 2 a a_1 a_2) → Xphi) → Xphi))
% 5.54/5.73 True
% 5.54/5.73 Clause #16 (by clausification #[15]): ∀ (a a_1 a_2 a_3 : Iota),
% 5.54/5.73 Eq
% 5.54/5.73 (in (skS.0 3 a a_1 a_2 a_3) (skS.0 0 a) →
% 5.54/5.73 ∀ (Xy : Iota),
% 5.54/5.73 in Xy (skS.0 0 a) →
% 5.54/5.73 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)) →
% 5.54/5.73 ∀ (Xphi : Prop),
% 5.54/5.73 (in (kpair (skS.0 3 a a_1 a_2 a_3) Xy) (skS.0 1 a a_1) → Xphi) →
% 5.54/5.73 (in (kpair (skS.0 3 a a_1 a_2 a_3) Xy) (skS.0 2 a a_1 a_2) → Xphi) → Xphi)
% 5.54/5.73 False
% 5.54/5.73 Clause #17 (by clausification #[16]): ∀ (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
% 5.54/5.73 Clause #18 (by clausification #[16]): ∀ (a a_1 a_2 a_3 : Iota),
% 5.54/5.73 Eq
% 5.54/5.73 (∀ (Xy : Iota),
% 5.54/5.73 in Xy (skS.0 0 a) →
% 5.54/5.73 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)) →
% 5.54/5.73 ∀ (Xphi : Prop),
% 5.54/5.73 (in (kpair (skS.0 3 a a_1 a_2 a_3) Xy) (skS.0 1 a a_1) → Xphi) →
% 5.54/5.73 (in (kpair (skS.0 3 a a_1 a_2 a_3) Xy) (skS.0 2 a a_1 a_2) → Xphi) → Xphi)
% 5.54/5.73 False
% 5.54/5.73 Clause #19 (by clausification #[18]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 5.54/5.73 Eq
% 5.54/5.73 (Not
% 5.54/5.73 (in (skS.0 4 a a_1 a_2 a_3 a_4) (skS.0 0 a) →
% 5.54/5.73 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)) →
% 5.54/5.73 ∀ (Xphi : Prop),
% 5.54/5.73 (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) → Xphi) →
% 5.54/5.73 (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) → Xphi) → Xphi))
% 5.54/5.73 True
% 5.54/5.73 Clause #20 (by clausification #[19]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 5.54/5.73 Eq
% 5.54/5.73 (in (skS.0 4 a a_1 a_2 a_3 a_4) (skS.0 0 a) →
% 5.54/5.73 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)) →
% 5.54/5.76 ∀ (Xphi : Prop),
% 5.54/5.76 (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) → Xphi) →
% 5.54/5.76 (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) → Xphi) → Xphi)
% 5.54/5.76 False
% 5.54/5.76 Clause #21 (by clausification #[20]): ∀ (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
% 5.54/5.76 Clause #22 (by clausification #[20]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 5.54/5.76 Eq
% 5.54/5.76 (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)) →
% 5.54/5.76 ∀ (Xphi : Prop),
% 5.54/5.76 (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) → Xphi) →
% 5.54/5.76 (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) → Xphi) → Xphi)
% 5.54/5.76 False
% 5.54/5.76 Clause #23 (by clausification #[0]): Eq breln1unionE
% 5.54/5.76 (∀ (A R : Iota),
% 5.54/5.76 breln1 A R →
% 5.54/5.76 ∀ (S : Iota),
% 5.54/5.76 breln1 A S →
% 5.54/5.76 ∀ (Xx : Iota),
% 5.54/5.76 in Xx A →
% 5.54/5.76 ∀ (Xy : Iota), in Xy A → in (kpair Xx Xy) (binunion R S) → Or (in (kpair Xx Xy) R) (in (kpair Xx Xy) S))
% 5.54/5.76 Clause #24 (by forward demodulation #[23, 3]): Eq True
% 5.54/5.76 (∀ (A R : Iota),
% 5.54/5.76 breln1 A R →
% 5.54/5.76 ∀ (S : Iota),
% 5.54/5.76 breln1 A S →
% 5.54/5.76 ∀ (Xx : Iota),
% 5.54/5.76 in Xx A →
% 5.54/5.76 ∀ (Xy : Iota), in Xy A → in (kpair Xx Xy) (binunion R S) → Or (in (kpair Xx Xy) R) (in (kpair Xx Xy) S))
% 5.54/5.76 Clause #25 (by clausification #[24]): ∀ (a : Iota),
% 5.54/5.76 Eq
% 5.54/5.76 (∀ (R : Iota),
% 5.54/5.76 breln1 a R →
% 5.54/5.76 ∀ (S : Iota),
% 5.54/5.76 breln1 a S →
% 5.54/5.76 ∀ (Xx : Iota),
% 5.54/5.76 in Xx a →
% 5.54/5.76 ∀ (Xy : Iota), in Xy a → in (kpair Xx Xy) (binunion R S) → Or (in (kpair Xx Xy) R) (in (kpair Xx Xy) S))
% 5.54/5.76 True
% 5.54/5.76 Clause #26 (by clausification #[25]): ∀ (a a_1 : Iota),
% 5.54/5.76 Eq
% 5.54/5.76 (breln1 a a_1 →
% 5.54/5.76 ∀ (S : Iota),
% 5.54/5.76 breln1 a S →
% 5.54/5.76 ∀ (Xx : Iota),
% 5.54/5.76 in Xx a →
% 5.54/5.76 ∀ (Xy : Iota),
% 5.54/5.76 in Xy a → in (kpair Xx Xy) (binunion a_1 S) → Or (in (kpair Xx Xy) a_1) (in (kpair Xx Xy) S))
% 5.54/5.76 True
% 5.54/5.76 Clause #27 (by clausification #[26]): ∀ (a a_1 : Iota),
% 5.54/5.76 Or (Eq (breln1 a a_1) False)
% 5.54/5.76 (Eq
% 5.54/5.76 (∀ (S : Iota),
% 5.54/5.76 breln1 a S →
% 5.54/5.76 ∀ (Xx : Iota),
% 5.54/5.76 in Xx a →
% 5.54/5.76 ∀ (Xy : Iota),
% 5.54/5.76 in Xy a → in (kpair Xx Xy) (binunion a_1 S) → Or (in (kpair Xx Xy) a_1) (in (kpair Xx Xy) S))
% 5.54/5.76 True)
% 5.54/5.76 Clause #28 (by clausification #[27]): ∀ (a a_1 a_2 : Iota),
% 5.54/5.76 Or (Eq (breln1 a a_1) False)
% 5.54/5.76 (Eq
% 5.54/5.76 (breln1 a a_2 →
% 5.54/5.76 ∀ (Xx : Iota),
% 5.54/5.76 in Xx a →
% 5.54/5.76 ∀ (Xy : Iota),
% 5.54/5.76 in Xy a → in (kpair Xx Xy) (binunion a_1 a_2) → Or (in (kpair Xx Xy) a_1) (in (kpair Xx Xy) a_2))
% 5.54/5.76 True)
% 5.54/5.76 Clause #29 (by clausification #[28]): ∀ (a a_1 a_2 : Iota),
% 5.54/5.76 Or (Eq (breln1 a a_1) False)
% 5.54/5.76 (Or (Eq (breln1 a a_2) False)
% 5.54/5.76 (Eq
% 5.54/5.76 (∀ (Xx : Iota),
% 5.54/5.76 in Xx a →
% 5.54/5.76 ∀ (Xy : Iota),
% 5.54/5.76 in Xy a → in (kpair Xx Xy) (binunion a_1 a_2) → Or (in (kpair Xx Xy) a_1) (in (kpair Xx Xy) a_2))
% 5.54/5.76 True))
% 5.54/5.76 Clause #30 (by clausification #[29]): ∀ (a a_1 a_2 a_3 : Iota),
% 5.54/5.76 Or (Eq (breln1 a a_1) False)
% 5.54/5.76 (Or (Eq (breln1 a a_2) False)
% 5.54/5.76 (Eq
% 5.54/5.76 (in a_3 a →
% 5.54/5.76 ∀ (Xy : Iota),
% 5.54/5.76 in Xy a → in (kpair a_3 Xy) (binunion a_1 a_2) → Or (in (kpair a_3 Xy) a_1) (in (kpair a_3 Xy) a_2))
% 5.54/5.76 True))
% 5.54/5.76 Clause #31 (by clausification #[30]): ∀ (a a_1 a_2 a_3 : Iota),
% 5.54/5.76 Or (Eq (breln1 a a_1) False)
% 5.54/5.76 (Or (Eq (breln1 a a_2) False)
% 5.54/5.76 (Or (Eq (in a_3 a) False)
% 5.54/5.76 (Eq
% 5.54/5.76 (∀ (Xy : Iota),
% 5.54/5.76 in Xy a → in (kpair a_3 Xy) (binunion a_1 a_2) → Or (in (kpair a_3 Xy) a_1) (in (kpair a_3 Xy) a_2))
% 5.54/5.76 True)))
% 5.54/5.76 Clause #32 (by clausification #[31]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 5.54/5.76 Or (Eq (breln1 a a_1) False)
% 5.54/5.76 (Or (Eq (breln1 a a_2) False)
% 5.54/5.76 (Or (Eq (in a_3 a) False)
% 5.54/5.76 (Eq (in a_4 a → in (kpair a_3 a_4) (binunion a_1 a_2) → Or (in (kpair a_3 a_4) a_1) (in (kpair a_3 a_4) a_2))
% 5.62/5.78 True)))
% 5.62/5.78 Clause #33 (by clausification #[32]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 5.62/5.78 Or (Eq (breln1 a a_1) False)
% 5.62/5.78 (Or (Eq (breln1 a a_2) False)
% 5.62/5.78 (Or (Eq (in a_3 a) False)
% 5.62/5.78 (Or (Eq (in a_4 a) False)
% 5.62/5.78 (Eq (in (kpair a_3 a_4) (binunion a_1 a_2) → Or (in (kpair a_3 a_4) a_1) (in (kpair a_3 a_4) a_2)) True))))
% 5.62/5.78 Clause #34 (by clausification #[33]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 5.62/5.78 Or (Eq (breln1 a a_1) False)
% 5.62/5.78 (Or (Eq (breln1 a a_2) False)
% 5.62/5.78 (Or (Eq (in a_3 a) False)
% 5.62/5.78 (Or (Eq (in a_4 a) False)
% 5.62/5.78 (Or (Eq (in (kpair a_3 a_4) (binunion a_1 a_2)) False)
% 5.62/5.78 (Eq (Or (in (kpair a_3 a_4) a_1) (in (kpair a_3 a_4) a_2)) True)))))
% 5.62/5.78 Clause #35 (by clausification #[34]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 5.62/5.78 Or (Eq (breln1 a a_1) False)
% 5.62/5.78 (Or (Eq (breln1 a a_2) False)
% 5.62/5.78 (Or (Eq (in a_3 a) False)
% 5.62/5.78 (Or (Eq (in a_4 a) False)
% 5.62/5.78 (Or (Eq (in (kpair a_3 a_4) (binunion a_1 a_2)) False)
% 5.62/5.78 (Or (Eq (in (kpair a_3 a_4) a_1) True) (Eq (in (kpair a_3 a_4) a_2) True))))))
% 5.62/5.78 Clause #36 (by superposition #[35, 9]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 5.62/5.78 Or (Eq (breln1 (skS.0 0 a) a_1) False)
% 5.62/5.78 (Or (Eq (in a_2 (skS.0 0 a)) False)
% 5.62/5.78 (Or (Eq (in a_3 (skS.0 0 a)) False)
% 5.62/5.78 (Or (Eq (in (kpair a_2 a_3) (binunion (skS.0 1 a a_4) a_1)) False)
% 5.62/5.78 (Or (Eq (in (kpair a_2 a_3) (skS.0 1 a a_4)) True) (Or (Eq (in (kpair a_2 a_3) a_1) True) (Eq False True))))))
% 5.62/5.78 Clause #38 (by clausification #[22]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 5.62/5.78 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)))
% 5.62/5.78 True
% 5.62/5.78 Clause #39 (by clausification #[22]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 5.62/5.78 Eq
% 5.62/5.78 (∀ (Xphi : Prop),
% 5.62/5.78 (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) → Xphi) →
% 5.62/5.78 (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) → Xphi) → Xphi)
% 5.62/5.78 False
% 5.62/5.78 Clause #40 (by clausification #[39]): ∀ (a a_1 a_2 a_3 a_4 : Iota) (a_5 : Prop),
% 5.62/5.78 Eq
% 5.62/5.78 (Not
% 5.62/5.78 ((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) →
% 5.62/5.78 skS.0 5 a a_1 a_2 a_3 a_4 a_5) →
% 5.62/5.78 (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) →
% 5.62/5.78 skS.0 5 a a_1 a_2 a_3 a_4 a_5) →
% 5.62/5.78 skS.0 5 a a_1 a_2 a_3 a_4 a_5))
% 5.62/5.78 True
% 5.62/5.78 Clause #41 (by clausification #[40]): ∀ (a a_1 a_2 a_3 a_4 : Iota) (a_5 : Prop),
% 5.62/5.78 Eq
% 5.62/5.78 ((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) → skS.0 5 a a_1 a_2 a_3 a_4 a_5) →
% 5.62/5.78 (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) →
% 5.62/5.78 skS.0 5 a a_1 a_2 a_3 a_4 a_5) →
% 5.62/5.78 skS.0 5 a a_1 a_2 a_3 a_4 a_5)
% 5.62/5.78 False
% 5.62/5.78 Clause #42 (by clausification #[41]): ∀ (a a_1 a_2 a_3 a_4 : Iota) (a_5 : Prop),
% 5.62/5.78 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) → skS.0 5 a a_1 a_2 a_3 a_4 a_5)
% 5.62/5.78 True
% 5.62/5.78 Clause #43 (by clausification #[41]): ∀ (a a_1 a_2 a_3 a_4 : Iota) (a_5 : Prop),
% 5.62/5.78 Eq
% 5.62/5.78 ((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) →
% 5.62/5.78 skS.0 5 a a_1 a_2 a_3 a_4 a_5) →
% 5.62/5.78 skS.0 5 a a_1 a_2 a_3 a_4 a_5)
% 5.62/5.78 False
% 5.62/5.78 Clause #44 (by clausification #[42]): ∀ (a a_1 a_2 a_3 a_4 : Iota) (a_5 : Prop),
% 5.62/5.78 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)) False)
% 5.62/5.78 (Eq (skS.0 5 a a_1 a_2 a_3 a_4 a_5) True)
% 5.62/5.78 Clause #46 (by identity boolHoist #[44]): ∀ (a a_1 a_2 a_3 a_4 : Iota) (a_5 : Prop),
% 5.62/5.78 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)) False)
% 5.62/5.78 (Or (Eq (skS.0 5 a a_1 a_2 a_3 a_4 False) True) (Eq a_5 True))
% 5.62/5.78 Clause #47 (by clausification #[43]): ∀ (a a_1 a_2 a_3 a_4 : Iota) (a_5 : Prop),
% 5.62/5.78 Eq
% 5.62/5.78 (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) → skS.0 5 a a_1 a_2 a_3 a_4 a_5)
% 5.62/5.78 True
% 5.62/5.78 Clause #48 (by clausification #[43]): ∀ (a a_1 a_2 a_3 a_4 : Iota) (a_5 : Prop), Eq (skS.0 5 a a_1 a_2 a_3 a_4 a_5) False
% 5.62/5.81 Clause #49 (by clausification #[47]): ∀ (a a_1 a_2 a_3 a_4 : Iota) (a_5 : Prop),
% 5.62/5.81 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 2 a a_1 a_2)) False)
% 5.62/5.81 (Eq (skS.0 5 a a_1 a_2 a_3 a_4 a_5) True)
% 5.62/5.81 Clause #51 (by identity boolHoist #[49]): ∀ (a a_1 a_2 a_3 a_4 : Iota) (a_5 : Prop),
% 5.62/5.81 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 2 a a_1 a_2)) False)
% 5.62/5.81 (Or (Eq (skS.0 5 a a_1 a_2 a_3 a_4 False) True) (Eq a_5 True))
% 5.62/5.81 Clause #53 (by identity boolHoist #[48]): ∀ (a a_1 a_2 a_3 a_4 : Iota) (a_5 : Prop), Or (Eq (skS.0 5 a a_1 a_2 a_3 a_4 False) False) (Eq a_5 True)
% 5.62/5.81 Clause #54 (by clausification #[36]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 5.62/5.81 Or (Eq (breln1 (skS.0 0 a) a_1) False)
% 5.62/5.81 (Or (Eq (in a_2 (skS.0 0 a)) False)
% 5.62/5.81 (Or (Eq (in a_3 (skS.0 0 a)) False)
% 5.62/5.81 (Or (Eq (in (kpair a_2 a_3) (binunion (skS.0 1 a a_4) a_1)) False)
% 5.62/5.81 (Or (Eq (in (kpair a_2 a_3) (skS.0 1 a a_4)) True) (Eq (in (kpair a_2 a_3) a_1) True)))))
% 5.62/5.81 Clause #56 (by superposition #[54, 13]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 5.62/5.81 Or (Eq (in a (skS.0 0 a_1)) False)
% 5.62/5.81 (Or (Eq (in a_2 (skS.0 0 a_1)) False)
% 5.62/5.81 (Or (Eq (in (kpair a a_2) (binunion (skS.0 1 a_1 a_3) (skS.0 2 a_1 a_4 a_5))) False)
% 5.62/5.81 (Or (Eq (in (kpair a a_2) (skS.0 1 a_1 a_3)) True)
% 5.62/5.81 (Or (Eq (in (kpair a a_2) (skS.0 2 a_1 a_4 a_5)) True) (Eq False True)))))
% 5.62/5.81 Clause #63 (by clausification #[56]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 5.62/5.81 Or (Eq (in a (skS.0 0 a_1)) False)
% 5.62/5.81 (Or (Eq (in a_2 (skS.0 0 a_1)) False)
% 5.62/5.81 (Or (Eq (in (kpair a a_2) (binunion (skS.0 1 a_1 a_3) (skS.0 2 a_1 a_4 a_5))) False)
% 5.62/5.81 (Or (Eq (in (kpair a a_2) (skS.0 1 a_1 a_3)) True) (Eq (in (kpair a a_2) (skS.0 2 a_1 a_4 a_5)) True))))
% 5.62/5.81 Clause #64 (by superposition #[63, 17]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 : Iota),
% 5.62/5.81 Or (Eq (in a (skS.0 0 a_1)) False)
% 5.62/5.81 (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))) False)
% 5.62/5.81 (Or (Eq (in (kpair (skS.0 3 a_1 a_2 a_3 a_4) a) (skS.0 1 a_1 a_5)) True)
% 5.62/5.81 (Or (Eq (in (kpair (skS.0 3 a_1 a_2 a_3 a_4) a) (skS.0 2 a_1 a_6 a_7)) True) (Eq False True))))
% 5.62/5.81 Clause #78 (by clausification #[64]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 : Iota),
% 5.62/5.81 Or (Eq (in a (skS.0 0 a_1)) False)
% 5.62/5.81 (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))) False)
% 5.62/5.81 (Or (Eq (in (kpair (skS.0 3 a_1 a_2 a_3 a_4) a) (skS.0 1 a_1 a_5)) True)
% 5.62/5.81 (Eq (in (kpair (skS.0 3 a_1 a_2 a_3 a_4) a) (skS.0 2 a_1 a_6 a_7)) True)))
% 5.62/5.81 Clause #80 (by superposition #[78, 21]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 a_8 a_9 a_10 : Iota),
% 5.62/5.81 Or
% 5.62/5.81 (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)))
% 5.62/5.81 False)
% 5.62/5.81 (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)) True)
% 5.62/5.81 (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_9 a_10)) True)
% 5.62/5.81 (Eq False True)))
% 5.62/5.81 Clause #103 (by clausification #[80]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 a_8 a_9 a_10 : Iota),
% 5.62/5.81 Or
% 5.62/5.81 (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)))
% 5.62/5.81 False)
% 5.62/5.81 (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)) True)
% 5.62/5.81 (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_9 a_10)) True))
% 5.62/5.81 Clause #104 (by superposition #[103, 38]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 5.62/5.81 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)
% 5.62/5.81 (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 2 a a_1 a_2)) True) (Eq False True))
% 5.62/5.81 Clause #106 (by clausification #[104]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 5.62/5.81 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)
% 5.62/5.81 (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)
% 5.62/5.81 Clause #108 (by superposition #[106, 51]): ∀ (a a_1 a_2 a_3 a_4 : Iota) (a_5 : Prop),
% 5.62/5.82 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)
% 5.62/5.82 (Or (Eq True False) (Or (Eq (skS.0 5 a a_1 a_2 a_3 a_4 False) True) (Eq a_5 True)))
% 5.62/5.82 Clause #109 (by clausification #[108]): ∀ (a a_1 a_2 a_3 a_4 : Iota) (a_5 : Prop),
% 5.62/5.82 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)
% 5.62/5.82 (Or (Eq (skS.0 5 a a_1 a_2 a_3 a_4 False) True) (Eq a_5 True))
% 5.62/5.82 Clause #111 (by superposition #[109, 46]): ∀ (a a_1 a_2 a_3 a_4 : Iota) (a_5 a_6 : Prop),
% 5.62/5.82 Or (Eq (skS.0 5 a a_1 a_2 a_3 a_4 False) True)
% 5.62/5.82 (Or (Eq a_5 True) (Or (Eq True False) (Or (Eq (skS.0 5 a a_1 a_2 a_3 a_4 False) True) (Eq a_6 True))))
% 5.62/5.82 Clause #143 (by clausification #[111]): ∀ (a a_1 a_2 a_3 a_4 : Iota) (a_5 a_6 : Prop),
% 5.62/5.82 Or (Eq (skS.0 5 a a_1 a_2 a_3 a_4 False) True)
% 5.62/5.82 (Or (Eq a_5 True) (Or (Eq (skS.0 5 a a_1 a_2 a_3 a_4 False) True) (Eq a_6 True)))
% 5.62/5.82 Clause #144 (by eliminate duplicate literals #[143]): ∀ (a a_1 a_2 a_3 a_4 : Iota) (a_5 a_6 : Prop),
% 5.62/5.82 Or (Eq (skS.0 5 a a_1 a_2 a_3 a_4 False) True) (Or (Eq a_5 True) (Eq a_6 True))
% 5.62/5.82 Clause #145 (by superposition #[144, 53]): ∀ (a a_1 a_2 : Prop), Or (Eq a True) (Or (Eq a_1 True) (Or (Eq True False) (Eq a_2 True)))
% 5.62/5.82 Clause #179 (by clausification #[145]): ∀ (a a_1 a_2 : Prop), Or (Eq a True) (Or (Eq a_1 True) (Eq a_2 True))
% 5.62/5.82 Clause #211 (by falseElim #[179]): ∀ (a a_1 : Prop), Or (Eq a True) (Eq a_1 True)
% 5.62/5.82 Clause #219 (by falseElim #[211]): ∀ (a : Prop), Eq a True
% 5.62/5.82 Clause #222 (by falseElim #[219]): False
% 5.62/5.82 SZS output end Proof for theBenchmark.p
%------------------------------------------------------------------------------