%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU787^2 : TPTP v9.2.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n006.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 Oct 3 08:02:26 PM UTC 2025 % Result : Theorem 5.49s 5.65s % Output : Proof 5.59s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.11 % Problem : SEU787^2 : TPTP v9.2.0. Released v3.7.0. % 0.06/0.13 % Command : duper %s % 0.12/0.33 % Computer : n006.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 300 % 0.12/0.33 % DateTime : Fri Oct 3 05:11:23 EDT 2025 % 0.12/0.33 % CPUTime : % 5.49/5.65 SZS status Theorem for theBenchmark.p % 5.49/5.65 SZS output start Proof for theBenchmark.p % 5.49/5.65 Clause #0 (by assumption #[]): Eq % 5.49/5.65 (Eq breln1unionE % 5.49/5.65 (∀ (A R : Iota), % 5.49/5.65 breln1 A R → % 5.49/5.65 ∀ (S : Iota), % 5.49/5.65 breln1 A S → % 5.49/5.65 ∀ (Xx : Iota), % 5.49/5.65 in Xx A → % 5.49/5.65 ∀ (Xy : Iota), % 5.49/5.65 in Xy A → in (kpair Xx Xy) (binunion R S) → Or (in (kpair Xx Xy) R) (in (kpair Xx Xy) S))) % 5.49/5.65 True % 5.49/5.65 Clause #1 (by assumption #[]): Eq % 5.49/5.65 (Not % 5.49/5.65 (breln1unionE → % 5.49/5.65 ∀ (A R : Iota), % 5.49/5.65 breln1 A R → % 5.49/5.65 ∀ (S : Iota), % 5.49/5.65 breln1 A S → % 5.49/5.65 ∀ (Xx : Iota), % 5.49/5.65 in Xx A → % 5.49/5.65 ∀ (Xy : Iota), % 5.49/5.65 in Xy A → % 5.49/5.65 in (kpair Xx Xy) (binunion R S) → % 5.49/5.65 ∀ (Xphi : Prop), (in (kpair Xx Xy) R → Xphi) → (in (kpair Xx Xy) S → Xphi) → Xphi)) % 5.49/5.65 True % 5.49/5.65 Clause #2 (by clausification #[1]): Eq % 5.49/5.65 (breln1unionE → % 5.49/5.65 ∀ (A R : Iota), % 5.49/5.65 breln1 A R → % 5.49/5.65 ∀ (S : Iota), % 5.49/5.65 breln1 A S → % 5.49/5.65 ∀ (Xx : Iota), % 5.49/5.65 in Xx A → % 5.49/5.65 ∀ (Xy : Iota), % 5.49/5.65 in Xy A → % 5.49/5.65 in (kpair Xx Xy) (binunion R S) → % 5.49/5.65 ∀ (Xphi : Prop), (in (kpair Xx Xy) R → Xphi) → (in (kpair Xx Xy) S → Xphi) → Xphi) % 5.49/5.65 False % 5.49/5.65 Clause #3 (by clausification #[2]): Eq breln1unionE True % 5.49/5.65 Clause #4 (by clausification #[2]): Eq % 5.49/5.65 (∀ (A R : Iota), % 5.49/5.65 breln1 A R → % 5.49/5.65 ∀ (S : Iota), % 5.49/5.65 breln1 A S → % 5.49/5.65 ∀ (Xx : Iota), % 5.49/5.65 in Xx A → % 5.49/5.65 ∀ (Xy : Iota), % 5.49/5.65 in Xy A → % 5.49/5.65 in (kpair Xx Xy) (binunion R S) → % 5.49/5.65 ∀ (Xphi : Prop), (in (kpair Xx Xy) R → Xphi) → (in (kpair Xx Xy) S → Xphi) → Xphi) % 5.49/5.65 False % 5.49/5.65 Clause #5 (by clausification #[4]): ∀ (a : Iota), % 5.49/5.65 Eq % 5.49/5.65 (Not % 5.49/5.65 (∀ (R : Iota), % 5.49/5.65 breln1 (skS.0 0 a) R → % 5.49/5.65 ∀ (S : Iota), % 5.49/5.65 breln1 (skS.0 0 a) S → % 5.49/5.65 ∀ (Xx : Iota), % 5.49/5.65 in Xx (skS.0 0 a) → % 5.49/5.65 ∀ (Xy : Iota), % 5.49/5.65 in Xy (skS.0 0 a) → % 5.49/5.65 in (kpair Xx Xy) (binunion R S) → % 5.49/5.65 ∀ (Xphi : Prop), (in (kpair Xx Xy) R → Xphi) → (in (kpair Xx Xy) S → Xphi) → Xphi)) % 5.49/5.65 True % 5.49/5.65 Clause #6 (by clausification #[5]): ∀ (a : Iota), % 5.49/5.65 Eq % 5.49/5.65 (∀ (R : Iota), % 5.49/5.65 breln1 (skS.0 0 a) R → % 5.49/5.65 ∀ (S : Iota), % 5.49/5.65 breln1 (skS.0 0 a) S → % 5.49/5.65 ∀ (Xx : Iota), % 5.49/5.65 in Xx (skS.0 0 a) → % 5.49/5.65 ∀ (Xy : Iota), % 5.49/5.65 in Xy (skS.0 0 a) → % 5.49/5.65 in (kpair Xx Xy) (binunion R S) → % 5.49/5.65 ∀ (Xphi : Prop), (in (kpair Xx Xy) R → Xphi) → (in (kpair Xx Xy) S → Xphi) → Xphi) % 5.49/5.65 False % 5.49/5.65 Clause #7 (by clausification #[6]): ∀ (a a_1 : Iota), % 5.49/5.65 Eq % 5.49/5.65 (Not % 5.49/5.65 (breln1 (skS.0 0 a) (skS.0 1 a a_1) → % 5.49/5.65 ∀ (S : Iota), % 5.49/5.65 breln1 (skS.0 0 a) S → % 5.49/5.65 ∀ (Xx : Iota), % 5.49/5.65 in Xx (skS.0 0 a) → % 5.49/5.65 ∀ (Xy : Iota), % 5.49/5.65 in Xy (skS.0 0 a) → % 5.49/5.65 in (kpair Xx Xy) (binunion (skS.0 1 a a_1) S) → % 5.49/5.65 ∀ (Xphi : Prop), (in (kpair Xx Xy) (skS.0 1 a a_1) → Xphi) → (in (kpair Xx Xy) S → Xphi) → Xphi)) % 5.49/5.65 True % 5.49/5.65 Clause #8 (by clausification #[7]): ∀ (a a_1 : Iota), % 5.49/5.65 Eq % 5.49/5.65 (breln1 (skS.0 0 a) (skS.0 1 a a_1) → % 5.49/5.65 ∀ (S : Iota), % 5.49/5.65 breln1 (skS.0 0 a) S → % 5.49/5.65 ∀ (Xx : Iota), % 5.49/5.65 in Xx (skS.0 0 a) → % 5.49/5.65 ∀ (Xy : Iota), % 5.49/5.65 in Xy (skS.0 0 a) → % 5.49/5.65 in (kpair Xx Xy) (binunion (skS.0 1 a a_1) S) → % 5.49/5.65 ∀ (Xphi : Prop), (in (kpair Xx Xy) (skS.0 1 a a_1) → Xphi) → (in (kpair Xx Xy) S → Xphi) → Xphi) % 5.49/5.65 False % 5.49/5.65 Clause #9 (by clausification #[8]): ∀ (a a_1 : Iota), Eq (breln1 (skS.0 0 a) (skS.0 1 a a_1)) True % 5.49/5.65 Clause #10 (by clausification #[8]): ∀ (a a_1 : Iota), % 5.49/5.65 Eq % 5.49/5.65 (∀ (S : Iota), % 5.49/5.65 breln1 (skS.0 0 a) S → % 5.49/5.65 ∀ (Xx : Iota), % 5.49/5.65 in Xx (skS.0 0 a) → % 5.52/5.68 ∀ (Xy : Iota), % 5.52/5.68 in Xy (skS.0 0 a) → % 5.52/5.68 in (kpair Xx Xy) (binunion (skS.0 1 a a_1) S) → % 5.52/5.68 ∀ (Xphi : Prop), (in (kpair Xx Xy) (skS.0 1 a a_1) → Xphi) → (in (kpair Xx Xy) S → Xphi) → Xphi) % 5.52/5.68 False % 5.52/5.68 Clause #11 (by clausification #[10]): ∀ (a a_1 a_2 : Iota), % 5.52/5.68 Eq % 5.52/5.68 (Not % 5.52/5.68 (breln1 (skS.0 0 a) (skS.0 2 a a_1 a_2) → % 5.52/5.68 ∀ (Xx : Iota), % 5.52/5.68 in Xx (skS.0 0 a) → % 5.52/5.68 ∀ (Xy : Iota), % 5.52/5.68 in Xy (skS.0 0 a) → % 5.52/5.68 in (kpair Xx Xy) (binunion (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)) → % 5.52/5.68 ∀ (Xphi : Prop), % 5.52/5.68 (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)) % 5.52/5.68 True % 5.52/5.68 Clause #12 (by clausification #[11]): ∀ (a a_1 a_2 : Iota), % 5.52/5.68 Eq % 5.52/5.68 (breln1 (skS.0 0 a) (skS.0 2 a a_1 a_2) → % 5.52/5.68 ∀ (Xx : Iota), % 5.52/5.68 in Xx (skS.0 0 a) → % 5.52/5.68 ∀ (Xy : Iota), % 5.52/5.68 in Xy (skS.0 0 a) → % 5.52/5.68 in (kpair Xx Xy) (binunion (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)) → % 5.52/5.68 ∀ (Xphi : Prop), % 5.52/5.68 (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) % 5.52/5.68 False % 5.52/5.68 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 % 5.52/5.68 Clause #14 (by clausification #[12]): ∀ (a a_1 a_2 : Iota), % 5.52/5.68 Eq % 5.52/5.68 (∀ (Xx : Iota), % 5.52/5.68 in Xx (skS.0 0 a) → % 5.52/5.68 ∀ (Xy : Iota), % 5.52/5.68 in Xy (skS.0 0 a) → % 5.52/5.68 in (kpair Xx Xy) (binunion (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)) → % 5.52/5.68 ∀ (Xphi : Prop), % 5.52/5.68 (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) % 5.52/5.68 False % 5.52/5.68 Clause #15 (by clausification #[14]): ∀ (a a_1 a_2 a_3 : Iota), % 5.52/5.68 Eq % 5.52/5.68 (Not % 5.52/5.68 (in (skS.0 3 a a_1 a_2 a_3) (skS.0 0 a) → % 5.52/5.68 ∀ (Xy : Iota), % 5.52/5.68 in Xy (skS.0 0 a) → % 5.52/5.68 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)) → % 5.52/5.68 ∀ (Xphi : Prop), % 5.52/5.68 (in (kpair (skS.0 3 a a_1 a_2 a_3) Xy) (skS.0 1 a a_1) → Xphi) → % 5.52/5.68 (in (kpair (skS.0 3 a a_1 a_2 a_3) Xy) (skS.0 2 a a_1 a_2) → Xphi) → Xphi)) % 5.52/5.68 True % 5.52/5.68 Clause #16 (by clausification #[15]): ∀ (a a_1 a_2 a_3 : Iota), % 5.52/5.68 Eq % 5.52/5.68 (in (skS.0 3 a a_1 a_2 a_3) (skS.0 0 a) → % 5.52/5.68 ∀ (Xy : Iota), % 5.52/5.68 in Xy (skS.0 0 a) → % 5.52/5.68 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)) → % 5.52/5.68 ∀ (Xphi : Prop), % 5.52/5.68 (in (kpair (skS.0 3 a a_1 a_2 a_3) Xy) (skS.0 1 a a_1) → Xphi) → % 5.52/5.68 (in (kpair (skS.0 3 a a_1 a_2 a_3) Xy) (skS.0 2 a a_1 a_2) → Xphi) → Xphi) % 5.52/5.68 False % 5.52/5.68 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 % 5.52/5.68 Clause #18 (by clausification #[16]): ∀ (a a_1 a_2 a_3 : Iota), % 5.52/5.68 Eq % 5.52/5.68 (∀ (Xy : Iota), % 5.52/5.68 in Xy (skS.0 0 a) → % 5.52/5.68 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)) → % 5.52/5.68 ∀ (Xphi : Prop), % 5.52/5.68 (in (kpair (skS.0 3 a a_1 a_2 a_3) Xy) (skS.0 1 a a_1) → Xphi) → % 5.52/5.68 (in (kpair (skS.0 3 a a_1 a_2 a_3) Xy) (skS.0 2 a a_1 a_2) → Xphi) → Xphi) % 5.52/5.68 False % 5.52/5.68 Clause #19 (by clausification #[18]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 5.52/5.68 Eq % 5.52/5.68 (Not % 5.52/5.68 (in (skS.0 4 a a_1 a_2 a_3 a_4) (skS.0 0 a) → % 5.52/5.68 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)) → % 5.52/5.68 ∀ (Xphi : Prop), % 5.52/5.68 (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) → % 5.52/5.68 (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)) % 5.52/5.68 True % 5.52/5.68 Clause #20 (by clausification #[19]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 5.52/5.68 Eq % 5.52/5.68 (in (skS.0 4 a a_1 a_2 a_3 a_4) (skS.0 0 a) → % 5.52/5.68 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)) → % 5.52/5.70 ∀ (Xphi : Prop), % 5.52/5.70 (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) → % 5.52/5.70 (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) % 5.52/5.70 False % 5.52/5.70 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 % 5.52/5.70 Clause #22 (by clausification #[20]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 5.52/5.70 Eq % 5.52/5.70 (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)) → % 5.52/5.70 ∀ (Xphi : Prop), % 5.52/5.70 (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) → % 5.52/5.70 (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) % 5.52/5.70 False % 5.52/5.70 Clause #23 (by clausification #[0]): Eq breln1unionE % 5.52/5.70 (∀ (A R : Iota), % 5.52/5.70 breln1 A R → % 5.52/5.70 ∀ (S : Iota), % 5.52/5.70 breln1 A S → % 5.52/5.70 ∀ (Xx : Iota), % 5.52/5.70 in Xx A → % 5.52/5.70 ∀ (Xy : Iota), in Xy A → in (kpair Xx Xy) (binunion R S) → Or (in (kpair Xx Xy) R) (in (kpair Xx Xy) S)) % 5.52/5.70 Clause #24 (by forward demodulation #[23, 3]): Eq True % 5.52/5.70 (∀ (A R : Iota), % 5.52/5.70 breln1 A R → % 5.52/5.70 ∀ (S : Iota), % 5.52/5.70 breln1 A S → % 5.52/5.70 ∀ (Xx : Iota), % 5.52/5.70 in Xx A → % 5.52/5.70 ∀ (Xy : Iota), in Xy A → in (kpair Xx Xy) (binunion R S) → Or (in (kpair Xx Xy) R) (in (kpair Xx Xy) S)) % 5.52/5.70 Clause #25 (by clausification #[24]): ∀ (a : Iota), % 5.52/5.70 Eq % 5.52/5.70 (∀ (R : Iota), % 5.52/5.70 breln1 a R → % 5.52/5.70 ∀ (S : Iota), % 5.52/5.70 breln1 a S → % 5.52/5.70 ∀ (Xx : Iota), % 5.52/5.70 in Xx a → % 5.52/5.70 ∀ (Xy : Iota), in Xy a → in (kpair Xx Xy) (binunion R S) → Or (in (kpair Xx Xy) R) (in (kpair Xx Xy) S)) % 5.52/5.70 True % 5.52/5.70 Clause #26 (by clausification #[25]): ∀ (a a_1 : Iota), % 5.52/5.70 Eq % 5.52/5.70 (breln1 a a_1 → % 5.52/5.70 ∀ (S : Iota), % 5.52/5.70 breln1 a S → % 5.52/5.70 ∀ (Xx : Iota), % 5.52/5.70 in Xx a → % 5.52/5.70 ∀ (Xy : Iota), % 5.52/5.70 in Xy a → in (kpair Xx Xy) (binunion a_1 S) → Or (in (kpair Xx Xy) a_1) (in (kpair Xx Xy) S)) % 5.52/5.70 True % 5.52/5.70 Clause #27 (by clausification #[26]): ∀ (a a_1 : Iota), % 5.52/5.70 Or (Eq (breln1 a a_1) False) % 5.52/5.70 (Eq % 5.52/5.70 (∀ (S : Iota), % 5.52/5.70 breln1 a S → % 5.52/5.70 ∀ (Xx : Iota), % 5.52/5.70 in Xx a → % 5.52/5.70 ∀ (Xy : Iota), % 5.52/5.70 in Xy a → in (kpair Xx Xy) (binunion a_1 S) → Or (in (kpair Xx Xy) a_1) (in (kpair Xx Xy) S)) % 5.52/5.70 True) % 5.52/5.70 Clause #28 (by clausification #[27]): ∀ (a a_1 a_2 : Iota), % 5.52/5.70 Or (Eq (breln1 a a_1) False) % 5.52/5.70 (Eq % 5.52/5.70 (breln1 a a_2 → % 5.52/5.70 ∀ (Xx : Iota), % 5.52/5.70 in Xx a → % 5.52/5.70 ∀ (Xy : Iota), % 5.52/5.70 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)) % 5.52/5.70 True) % 5.52/5.70 Clause #29 (by clausification #[28]): ∀ (a a_1 a_2 : Iota), % 5.52/5.70 Or (Eq (breln1 a a_1) False) % 5.52/5.70 (Or (Eq (breln1 a a_2) False) % 5.52/5.70 (Eq % 5.52/5.70 (∀ (Xx : Iota), % 5.52/5.70 in Xx a → % 5.52/5.70 ∀ (Xy : Iota), % 5.52/5.70 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)) % 5.52/5.70 True)) % 5.52/5.70 Clause #30 (by clausification #[29]): ∀ (a a_1 a_2 a_3 : Iota), % 5.52/5.70 Or (Eq (breln1 a a_1) False) % 5.52/5.70 (Or (Eq (breln1 a a_2) False) % 5.52/5.70 (Eq % 5.52/5.70 (in a_3 a → % 5.52/5.70 ∀ (Xy : Iota), % 5.52/5.70 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)) % 5.52/5.70 True)) % 5.52/5.70 Clause #31 (by clausification #[30]): ∀ (a a_1 a_2 a_3 : Iota), % 5.52/5.70 Or (Eq (breln1 a a_1) False) % 5.52/5.70 (Or (Eq (breln1 a a_2) False) % 5.52/5.70 (Or (Eq (in a_3 a) False) % 5.52/5.70 (Eq % 5.52/5.70 (∀ (Xy : Iota), % 5.52/5.70 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)) % 5.52/5.70 True))) % 5.52/5.70 Clause #32 (by clausification #[31]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 5.52/5.70 Or (Eq (breln1 a a_1) False) % 5.52/5.70 (Or (Eq (breln1 a a_2) False) % 5.52/5.70 (Or (Eq (in a_3 a) False) % 5.52/5.70 (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)) % 5.52/5.73 True))) % 5.52/5.73 Clause #33 (by clausification #[32]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 5.52/5.73 Or (Eq (breln1 a a_1) False) % 5.52/5.73 (Or (Eq (breln1 a a_2) False) % 5.52/5.73 (Or (Eq (in a_3 a) False) % 5.52/5.73 (Or (Eq (in a_4 a) False) % 5.52/5.73 (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)))) % 5.52/5.73 Clause #34 (by clausification #[33]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 5.52/5.73 Or (Eq (breln1 a a_1) False) % 5.52/5.73 (Or (Eq (breln1 a a_2) False) % 5.52/5.73 (Or (Eq (in a_3 a) False) % 5.52/5.73 (Or (Eq (in a_4 a) False) % 5.52/5.73 (Or (Eq (in (kpair a_3 a_4) (binunion a_1 a_2)) False) % 5.52/5.73 (Eq (Or (in (kpair a_3 a_4) a_1) (in (kpair a_3 a_4) a_2)) True))))) % 5.52/5.73 Clause #35 (by clausification #[34]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 5.52/5.73 Or (Eq (breln1 a a_1) False) % 5.52/5.73 (Or (Eq (breln1 a a_2) False) % 5.52/5.73 (Or (Eq (in a_3 a) False) % 5.52/5.73 (Or (Eq (in a_4 a) False) % 5.52/5.73 (Or (Eq (in (kpair a_3 a_4) (binunion a_1 a_2)) False) % 5.52/5.73 (Or (Eq (in (kpair a_3 a_4) a_1) True) (Eq (in (kpair a_3 a_4) a_2) True)))))) % 5.57/5.73 Clause #36 (by superposition #[35, 9]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 5.57/5.73 Or (Eq (breln1 (skS.0 0 a) a_1) False) % 5.57/5.73 (Or (Eq (in a_2 (skS.0 0 a)) False) % 5.57/5.73 (Or (Eq (in a_3 (skS.0 0 a)) False) % 5.57/5.73 (Or (Eq (in (kpair a_2 a_3) (binunion (skS.0 1 a a_4) a_1)) False) % 5.57/5.73 (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)))))) % 5.57/5.73 Clause #38 (by clausification #[22]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 5.57/5.73 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))) % 5.57/5.73 True % 5.57/5.73 Clause #39 (by clausification #[22]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 5.57/5.73 Eq % 5.57/5.73 (∀ (Xphi : Prop), % 5.57/5.73 (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) → % 5.57/5.73 (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) % 5.57/5.73 False % 5.57/5.73 Clause #40 (by clausification #[39]): ∀ (a a_1 a_2 a_3 a_4 : Iota) (a_5 : Prop), % 5.57/5.73 Eq % 5.57/5.73 (Not % 5.57/5.73 ((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) → % 5.57/5.73 skS.0 5 a a_1 a_2 a_3 a_4 a_5) → % 5.57/5.73 (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) → % 5.57/5.73 skS.0 5 a a_1 a_2 a_3 a_4 a_5) → % 5.57/5.73 skS.0 5 a a_1 a_2 a_3 a_4 a_5)) % 5.57/5.73 True % 5.57/5.73 Clause #41 (by clausification #[40]): ∀ (a a_1 a_2 a_3 a_4 : Iota) (a_5 : Prop), % 5.57/5.73 Eq % 5.57/5.73 ((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) → skS.0 5 a a_1 a_2 a_3 a_4 a_5) → % 5.57/5.73 (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) → % 5.57/5.73 skS.0 5 a a_1 a_2 a_3 a_4 a_5) → % 5.57/5.73 skS.0 5 a a_1 a_2 a_3 a_4 a_5) % 5.57/5.73 False % 5.57/5.73 Clause #42 (by clausification #[41]): ∀ (a a_1 a_2 a_3 a_4 : Iota) (a_5 : Prop), % 5.57/5.73 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) % 5.57/5.73 True % 5.57/5.73 Clause #43 (by clausification #[41]): ∀ (a a_1 a_2 a_3 a_4 : Iota) (a_5 : Prop), % 5.57/5.73 Eq % 5.57/5.73 ((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) → % 5.57/5.73 skS.0 5 a a_1 a_2 a_3 a_4 a_5) → % 5.57/5.73 skS.0 5 a a_1 a_2 a_3 a_4 a_5) % 5.57/5.73 False % 5.57/5.73 Clause #44 (by clausification #[42]): ∀ (a a_1 a_2 a_3 a_4 : Iota) (a_5 : Prop), % 5.57/5.73 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) % 5.57/5.73 (Eq (skS.0 5 a a_1 a_2 a_3 a_4 a_5) True) % 5.57/5.73 Clause #46 (by identity boolHoist #[44]): ∀ (a a_1 a_2 a_3 a_4 : Iota) (a_5 : Prop), % 5.57/5.73 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) % 5.57/5.73 (Or (Eq (skS.0 5 a a_1 a_2 a_3 a_4 False) True) (Eq a_5 True)) % 5.57/5.73 Clause #47 (by clausification #[43]): ∀ (a a_1 a_2 a_3 a_4 : Iota) (a_5 : Prop), % 5.57/5.73 Eq % 5.57/5.73 (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) → skS.0 5 a a_1 a_2 a_3 a_4 a_5) % 5.57/5.73 True % 5.57/5.73 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 % 5.59/5.76 Clause #49 (by clausification #[47]): ∀ (a a_1 a_2 a_3 a_4 : Iota) (a_5 : Prop), % 5.59/5.76 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) % 5.59/5.76 (Eq (skS.0 5 a a_1 a_2 a_3 a_4 a_5) True) % 5.59/5.76 Clause #51 (by identity boolHoist #[49]): ∀ (a a_1 a_2 a_3 a_4 : Iota) (a_5 : Prop), % 5.59/5.76 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) % 5.59/5.76 (Or (Eq (skS.0 5 a a_1 a_2 a_3 a_4 False) True) (Eq a_5 True)) % 5.59/5.76 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) % 5.59/5.76 Clause #54 (by clausification #[36]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 5.59/5.76 Or (Eq (breln1 (skS.0 0 a) a_1) False) % 5.59/5.76 (Or (Eq (in a_2 (skS.0 0 a)) False) % 5.59/5.76 (Or (Eq (in a_3 (skS.0 0 a)) False) % 5.59/5.76 (Or (Eq (in (kpair a_2 a_3) (binunion (skS.0 1 a a_4) a_1)) False) % 5.59/5.76 (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))))) % 5.59/5.76 Clause #56 (by superposition #[54, 13]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 5.59/5.76 Or (Eq (in a (skS.0 0 a_1)) False) % 5.59/5.76 (Or (Eq (in a_2 (skS.0 0 a_1)) False) % 5.59/5.76 (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) % 5.59/5.76 (Or (Eq (in (kpair a a_2) (skS.0 1 a_1 a_3)) True) % 5.59/5.76 (Or (Eq (in (kpair a a_2) (skS.0 2 a_1 a_4 a_5)) True) (Eq False True))))) % 5.59/5.76 Clause #63 (by clausification #[56]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 5.59/5.76 Or (Eq (in a (skS.0 0 a_1)) False) % 5.59/5.76 (Or (Eq (in a_2 (skS.0 0 a_1)) False) % 5.59/5.76 (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) % 5.59/5.76 (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)))) % 5.59/5.76 Clause #64 (by superposition #[63, 17]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 : Iota), % 5.59/5.76 Or (Eq (in a (skS.0 0 a_1)) False) % 5.59/5.76 (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) % 5.59/5.76 (Or (Eq (in (kpair (skS.0 3 a_1 a_2 a_3 a_4) a) (skS.0 1 a_1 a_5)) True) % 5.59/5.76 (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)))) % 5.59/5.76 Clause #78 (by clausification #[64]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 : Iota), % 5.59/5.76 Or (Eq (in a (skS.0 0 a_1)) False) % 5.59/5.76 (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) % 5.59/5.76 (Or (Eq (in (kpair (skS.0 3 a_1 a_2 a_3 a_4) a) (skS.0 1 a_1 a_5)) True) % 5.59/5.76 (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))) % 5.59/5.76 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), % 5.59/5.76 Or % 5.59/5.76 (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))) % 5.59/5.76 False) % 5.59/5.76 (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) % 5.59/5.76 (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) % 5.59/5.76 (Eq False True))) % 5.59/5.76 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), % 5.59/5.76 Or % 5.59/5.76 (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))) % 5.59/5.76 False) % 5.59/5.76 (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) % 5.59/5.76 (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)) % 5.59/5.76 Clause #104 (by superposition #[103, 38]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 5.59/5.76 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) % 5.59/5.76 (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)) % 5.59/5.76 Clause #106 (by clausification #[104]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 5.59/5.76 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) % 5.59/5.76 (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) % 5.59/5.76 Clause #108 (by superposition #[106, 51]): ∀ (a a_1 a_2 a_3 a_4 : Iota) (a_5 : Prop), % 5.59/5.77 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) % 5.59/5.77 (Or (Eq True False) (Or (Eq (skS.0 5 a a_1 a_2 a_3 a_4 False) True) (Eq a_5 True))) % 5.59/5.77 Clause #109 (by clausification #[108]): ∀ (a a_1 a_2 a_3 a_4 : Iota) (a_5 : Prop), % 5.59/5.77 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) % 5.59/5.77 (Or (Eq (skS.0 5 a a_1 a_2 a_3 a_4 False) True) (Eq a_5 True)) % 5.59/5.77 Clause #111 (by superposition #[109, 46]): ∀ (a a_1 a_2 a_3 a_4 : Iota) (a_5 a_6 : Prop), % 5.59/5.77 Or (Eq (skS.0 5 a a_1 a_2 a_3 a_4 False) True) % 5.59/5.77 (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)))) % 5.59/5.77 Clause #143 (by clausification #[111]): ∀ (a a_1 a_2 a_3 a_4 : Iota) (a_5 a_6 : Prop), % 5.59/5.77 Or (Eq (skS.0 5 a a_1 a_2 a_3 a_4 False) True) % 5.59/5.77 (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))) % 5.59/5.77 Clause #144 (by eliminate duplicate literals #[143]): ∀ (a a_1 a_2 a_3 a_4 : Iota) (a_5 a_6 : Prop), % 5.59/5.77 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)) % 5.59/5.77 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))) % 5.59/5.77 Clause #179 (by clausification #[145]): ∀ (a a_1 a_2 : Prop), Or (Eq a True) (Or (Eq a_1 True) (Eq a_2 True)) % 5.59/5.77 Clause #211 (by falseElim #[179]): ∀ (a a_1 : Prop), Or (Eq a True) (Eq a_1 True) % 5.59/5.77 Clause #219 (by falseElim #[211]): ∀ (a : Prop), Eq a True % 5.59/5.77 Clause #222 (by falseElim #[219]): False % 5.59/5.77 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------