%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU785^2 : TPTP v9.2.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n031.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 5.87s 6.07s % Output : Proof 5.97s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.13 % Problem : SEU785^2 : TPTP v9.2.0. Released v3.7.0. % 0.04/0.14 % Command : duper %s % 0.14/0.36 % Computer : n031.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 : Fri Oct 3 05:43:38 EDT 2025 % 0.14/0.36 % CPUTime : % 5.87/6.07 SZS status Theorem for theBenchmark.p % 5.87/6.07 SZS output start Proof for theBenchmark.p % 5.87/6.07 Clause #0 (by assumption #[]): Eq % 5.87/6.07 (Eq breln1unionIL % 5.87/6.07 (∀ (A R : Iota), % 5.87/6.07 breln1 A R → % 5.87/6.07 ∀ (S : Iota), % 5.87/6.07 breln1 A S → % 5.87/6.07 ∀ (Xx : Iota), in Xx A → ∀ (Xy : Iota), in Xy A → in (kpair Xx Xy) R → in (kpair Xx Xy) (binunion R S))) % 5.87/6.07 True % 5.87/6.07 Clause #1 (by assumption #[]): Eq % 5.87/6.07 (Eq breln1unionIR % 5.87/6.07 (∀ (A R : Iota), % 5.87/6.07 breln1 A R → % 5.87/6.07 ∀ (S : Iota), % 5.87/6.07 breln1 A S → % 5.87/6.07 ∀ (Xx : Iota), in Xx A → ∀ (Xy : Iota), in Xy A → in (kpair Xx Xy) S → in (kpair Xx Xy) (binunion R S))) % 5.87/6.07 True % 5.87/6.07 Clause #2 (by assumption #[]): Eq % 5.87/6.07 (Not % 5.87/6.07 (breln1unionIL → % 5.87/6.07 breln1unionIR → % 5.87/6.07 ∀ (A R : Iota), % 5.87/6.07 breln1 A R → % 5.87/6.07 ∀ (S : Iota), % 5.87/6.07 breln1 A S → % 5.87/6.07 ∀ (Xx : Iota), % 5.87/6.07 in Xx A → % 5.87/6.07 ∀ (Xy : Iota), % 5.87/6.07 in Xy A → Or (in (kpair Xx Xy) R) (in (kpair Xx Xy) S) → in (kpair Xx Xy) (binunion R S))) % 5.87/6.07 True % 5.87/6.07 Clause #3 (by clausification #[2]): Eq % 5.87/6.07 (breln1unionIL → % 5.87/6.07 breln1unionIR → % 5.87/6.07 ∀ (A R : Iota), % 5.87/6.07 breln1 A R → % 5.87/6.07 ∀ (S : Iota), % 5.87/6.07 breln1 A S → % 5.87/6.07 ∀ (Xx : Iota), % 5.87/6.07 in Xx A → % 5.87/6.07 ∀ (Xy : Iota), % 5.87/6.07 in Xy A → Or (in (kpair Xx Xy) R) (in (kpair Xx Xy) S) → in (kpair Xx Xy) (binunion R S)) % 5.87/6.07 False % 5.87/6.07 Clause #4 (by clausification #[3]): Eq breln1unionIL True % 5.87/6.07 Clause #5 (by clausification #[3]): Eq % 5.87/6.07 (breln1unionIR → % 5.87/6.07 ∀ (A R : Iota), % 5.87/6.07 breln1 A R → % 5.87/6.07 ∀ (S : Iota), % 5.87/6.07 breln1 A S → % 5.87/6.07 ∀ (Xx : Iota), % 5.87/6.07 in Xx A → % 5.87/6.07 ∀ (Xy : Iota), in Xy A → Or (in (kpair Xx Xy) R) (in (kpair Xx Xy) S) → in (kpair Xx Xy) (binunion R S)) % 5.87/6.07 False % 5.87/6.07 Clause #6 (by clausification #[5]): Eq breln1unionIR True % 5.87/6.07 Clause #7 (by clausification #[5]): Eq % 5.87/6.07 (∀ (A R : Iota), % 5.87/6.07 breln1 A R → % 5.87/6.07 ∀ (S : Iota), % 5.87/6.07 breln1 A S → % 5.87/6.07 ∀ (Xx : Iota), % 5.87/6.07 in Xx A → % 5.87/6.07 ∀ (Xy : Iota), in Xy A → Or (in (kpair Xx Xy) R) (in (kpair Xx Xy) S) → in (kpair Xx Xy) (binunion R S)) % 5.87/6.07 False % 5.87/6.07 Clause #8 (by clausification #[7]): ∀ (a : Iota), % 5.87/6.07 Eq % 5.87/6.07 (Not % 5.87/6.07 (∀ (R : Iota), % 5.87/6.07 breln1 (skS.0 0 a) R → % 5.87/6.07 ∀ (S : Iota), % 5.87/6.07 breln1 (skS.0 0 a) S → % 5.87/6.07 ∀ (Xx : Iota), % 5.87/6.07 in Xx (skS.0 0 a) → % 5.87/6.07 ∀ (Xy : Iota), % 5.87/6.07 in Xy (skS.0 0 a) → Or (in (kpair Xx Xy) R) (in (kpair Xx Xy) S) → in (kpair Xx Xy) (binunion R S))) % 5.87/6.07 True % 5.87/6.07 Clause #9 (by clausification #[8]): ∀ (a : Iota), % 5.87/6.07 Eq % 5.87/6.07 (∀ (R : Iota), % 5.87/6.07 breln1 (skS.0 0 a) R → % 5.87/6.07 ∀ (S : Iota), % 5.87/6.07 breln1 (skS.0 0 a) S → % 5.87/6.07 ∀ (Xx : Iota), % 5.87/6.07 in Xx (skS.0 0 a) → % 5.87/6.07 ∀ (Xy : Iota), % 5.87/6.07 in Xy (skS.0 0 a) → Or (in (kpair Xx Xy) R) (in (kpair Xx Xy) S) → in (kpair Xx Xy) (binunion R S)) % 5.87/6.07 False % 5.87/6.07 Clause #10 (by clausification #[9]): ∀ (a a_1 : Iota), % 5.87/6.07 Eq % 5.87/6.07 (Not % 5.87/6.07 (breln1 (skS.0 0 a) (skS.0 1 a a_1) → % 5.87/6.07 ∀ (S : Iota), % 5.87/6.07 breln1 (skS.0 0 a) S → % 5.87/6.07 ∀ (Xx : Iota), % 5.87/6.07 in Xx (skS.0 0 a) → % 5.87/6.07 ∀ (Xy : Iota), % 5.87/6.07 in Xy (skS.0 0 a) → % 5.87/6.07 Or (in (kpair Xx Xy) (skS.0 1 a a_1)) (in (kpair Xx Xy) S) → % 5.87/6.07 in (kpair Xx Xy) (binunion (skS.0 1 a a_1) S))) % 5.87/6.07 True % 5.87/6.07 Clause #11 (by clausification #[10]): ∀ (a a_1 : Iota), % 5.87/6.07 Eq % 5.87/6.07 (breln1 (skS.0 0 a) (skS.0 1 a a_1) → % 5.87/6.07 ∀ (S : Iota), % 5.87/6.07 breln1 (skS.0 0 a) S → % 5.87/6.07 ∀ (Xx : Iota), % 5.87/6.07 in Xx (skS.0 0 a) → % 5.87/6.07 ∀ (Xy : Iota), % 5.87/6.07 in Xy (skS.0 0 a) → % 5.87/6.07 Or (in (kpair Xx Xy) (skS.0 1 a a_1)) (in (kpair Xx Xy) S) → % 5.87/6.07 in (kpair Xx Xy) (binunion (skS.0 1 a a_1) S)) % 5.87/6.07 False % 5.87/6.07 Clause #12 (by clausification #[11]): ∀ (a a_1 : Iota), Eq (breln1 (skS.0 0 a) (skS.0 1 a a_1)) True % 5.87/6.07 Clause #13 (by clausification #[11]): ∀ (a a_1 : Iota), % 5.87/6.09 Eq % 5.87/6.09 (∀ (S : Iota), % 5.87/6.09 breln1 (skS.0 0 a) S → % 5.87/6.09 ∀ (Xx : Iota), % 5.87/6.09 in Xx (skS.0 0 a) → % 5.87/6.09 ∀ (Xy : Iota), % 5.87/6.09 in Xy (skS.0 0 a) → % 5.87/6.09 Or (in (kpair Xx Xy) (skS.0 1 a a_1)) (in (kpair Xx Xy) S) → % 5.87/6.09 in (kpair Xx Xy) (binunion (skS.0 1 a a_1) S)) % 5.87/6.09 False % 5.87/6.09 Clause #14 (by clausification #[1]): Eq breln1unionIR % 5.87/6.09 (∀ (A R : Iota), % 5.87/6.09 breln1 A R → % 5.87/6.09 ∀ (S : Iota), % 5.87/6.09 breln1 A S → % 5.87/6.09 ∀ (Xx : Iota), in Xx A → ∀ (Xy : Iota), in Xy A → in (kpair Xx Xy) S → in (kpair Xx Xy) (binunion R S)) % 5.87/6.09 Clause #15 (by forward demodulation #[14, 6]): Eq True % 5.87/6.09 (∀ (A R : Iota), % 5.87/6.09 breln1 A R → % 5.87/6.09 ∀ (S : Iota), % 5.87/6.09 breln1 A S → % 5.87/6.09 ∀ (Xx : Iota), in Xx A → ∀ (Xy : Iota), in Xy A → in (kpair Xx Xy) S → in (kpair Xx Xy) (binunion R S)) % 5.87/6.09 Clause #16 (by clausification #[15]): ∀ (a : Iota), % 5.87/6.09 Eq % 5.87/6.09 (∀ (R : Iota), % 5.87/6.09 breln1 a R → % 5.87/6.09 ∀ (S : Iota), % 5.87/6.09 breln1 a S → % 5.87/6.09 ∀ (Xx : Iota), in Xx a → ∀ (Xy : Iota), in Xy a → in (kpair Xx Xy) S → in (kpair Xx Xy) (binunion R S)) % 5.87/6.09 True % 5.87/6.09 Clause #17 (by clausification #[16]): ∀ (a a_1 : Iota), % 5.87/6.09 Eq % 5.87/6.09 (breln1 a a_1 → % 5.87/6.09 ∀ (S : Iota), % 5.87/6.09 breln1 a S → % 5.87/6.09 ∀ (Xx : Iota), in Xx a → ∀ (Xy : Iota), in Xy a → in (kpair Xx Xy) S → in (kpair Xx Xy) (binunion a_1 S)) % 5.87/6.09 True % 5.87/6.09 Clause #18 (by clausification #[17]): ∀ (a a_1 : Iota), % 5.87/6.09 Or (Eq (breln1 a a_1) False) % 5.87/6.09 (Eq % 5.87/6.09 (∀ (S : Iota), % 5.87/6.09 breln1 a S → % 5.87/6.09 ∀ (Xx : Iota), in Xx a → ∀ (Xy : Iota), in Xy a → in (kpair Xx Xy) S → in (kpair Xx Xy) (binunion a_1 S)) % 5.87/6.09 True) % 5.87/6.09 Clause #19 (by clausification #[18]): ∀ (a a_1 a_2 : Iota), % 5.87/6.09 Or (Eq (breln1 a a_1) False) % 5.87/6.09 (Eq % 5.87/6.09 (breln1 a a_2 → % 5.87/6.09 ∀ (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)) % 5.87/6.09 True) % 5.87/6.09 Clause #20 (by clausification #[19]): ∀ (a a_1 a_2 : Iota), % 5.87/6.09 Or (Eq (breln1 a a_1) False) % 5.87/6.09 (Or (Eq (breln1 a a_2) False) % 5.87/6.09 (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)) % 5.87/6.09 True)) % 5.87/6.09 Clause #21 (by clausification #[20]): ∀ (a a_1 a_2 a_3 : Iota), % 5.87/6.09 Or (Eq (breln1 a a_1) False) % 5.87/6.09 (Or (Eq (breln1 a a_2) False) % 5.87/6.09 (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)) % 5.87/6.09 Clause #22 (by clausification #[21]): ∀ (a a_1 a_2 a_3 : Iota), % 5.87/6.09 Or (Eq (breln1 a a_1) False) % 5.87/6.09 (Or (Eq (breln1 a a_2) False) % 5.87/6.09 (Or (Eq (in a_3 a) False) % 5.87/6.09 (Eq (∀ (Xy : Iota), in Xy a → in (kpair a_3 Xy) a_2 → in (kpair a_3 Xy) (binunion a_1 a_2)) True))) % 5.87/6.09 Clause #23 (by clausification #[22]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 5.87/6.09 Or (Eq (breln1 a a_1) False) % 5.87/6.09 (Or (Eq (breln1 a a_2) False) % 5.87/6.09 (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))) % 5.87/6.09 Clause #24 (by clausification #[23]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 5.87/6.09 Or (Eq (breln1 a a_1) False) % 5.87/6.09 (Or (Eq (breln1 a a_2) False) % 5.87/6.09 (Or (Eq (in a_3 a) False) % 5.87/6.09 (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)))) % 5.87/6.09 Clause #25 (by clausification #[24]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 5.87/6.09 Or (Eq (breln1 a a_1) False) % 5.87/6.09 (Or (Eq (breln1 a a_2) False) % 5.87/6.09 (Or (Eq (in a_3 a) False) % 5.87/6.09 (Or (Eq (in a_4 a) False) % 5.87/6.09 (Or (Eq (in (kpair a_3 a_4) a_2) False) (Eq (in (kpair a_3 a_4) (binunion a_1 a_2)) True))))) % 5.87/6.09 Clause #26 (by superposition #[25, 12]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 5.87/6.09 Or (Eq (breln1 (skS.0 0 a) a_1) False) % 5.87/6.09 (Or (Eq (in a_2 (skS.0 0 a)) False) % 5.87/6.09 (Or (Eq (in a_3 (skS.0 0 a)) False) % 5.87/6.09 (Or (Eq (in (kpair a_2 a_3) a_1) False) % 5.87/6.09 (Or (Eq (in (kpair a_2 a_3) (binunion (skS.0 1 a a_4) a_1)) True) (Eq False True))))) % 5.87/6.09 Clause #27 (by clausification #[0]): Eq breln1unionIL % 5.87/6.09 (∀ (A R : Iota), % 5.87/6.09 breln1 A R → % 5.87/6.09 ∀ (S : Iota), % 5.87/6.12 breln1 A S → % 5.87/6.12 ∀ (Xx : Iota), in Xx A → ∀ (Xy : Iota), in Xy A → in (kpair Xx Xy) R → in (kpair Xx Xy) (binunion R S)) % 5.87/6.12 Clause #28 (by forward demodulation #[27, 4]): Eq True % 5.87/6.12 (∀ (A R : Iota), % 5.87/6.12 breln1 A R → % 5.87/6.12 ∀ (S : Iota), % 5.87/6.12 breln1 A S → % 5.87/6.12 ∀ (Xx : Iota), in Xx A → ∀ (Xy : Iota), in Xy A → in (kpair Xx Xy) R → in (kpair Xx Xy) (binunion R S)) % 5.87/6.12 Clause #29 (by clausification #[28]): ∀ (a : Iota), % 5.87/6.12 Eq % 5.87/6.12 (∀ (R : Iota), % 5.87/6.12 breln1 a R → % 5.87/6.12 ∀ (S : Iota), % 5.87/6.12 breln1 a S → % 5.87/6.12 ∀ (Xx : Iota), in Xx a → ∀ (Xy : Iota), in Xy a → in (kpair Xx Xy) R → in (kpair Xx Xy) (binunion R S)) % 5.87/6.12 True % 5.87/6.12 Clause #30 (by clausification #[29]): ∀ (a a_1 : Iota), % 5.87/6.12 Eq % 5.87/6.12 (breln1 a a_1 → % 5.87/6.12 ∀ (S : Iota), % 5.87/6.12 breln1 a S → % 5.87/6.12 ∀ (Xx : Iota), in Xx a → ∀ (Xy : Iota), in Xy a → in (kpair Xx Xy) a_1 → in (kpair Xx Xy) (binunion a_1 S)) % 5.87/6.12 True % 5.87/6.12 Clause #31 (by clausification #[30]): ∀ (a a_1 : Iota), % 5.87/6.12 Or (Eq (breln1 a a_1) False) % 5.87/6.12 (Eq % 5.87/6.12 (∀ (S : Iota), % 5.87/6.12 breln1 a S → % 5.87/6.12 ∀ (Xx : Iota), in Xx a → ∀ (Xy : Iota), in Xy a → in (kpair Xx Xy) a_1 → in (kpair Xx Xy) (binunion a_1 S)) % 5.87/6.12 True) % 5.87/6.12 Clause #32 (by clausification #[31]): ∀ (a a_1 a_2 : Iota), % 5.87/6.12 Or (Eq (breln1 a a_1) False) % 5.87/6.12 (Eq % 5.87/6.12 (breln1 a a_2 → % 5.87/6.12 ∀ (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)) % 5.87/6.12 True) % 5.87/6.12 Clause #33 (by clausification #[32]): ∀ (a a_1 a_2 : Iota), % 5.87/6.12 Or (Eq (breln1 a a_1) False) % 5.87/6.12 (Or (Eq (breln1 a a_2) False) % 5.87/6.12 (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)) % 5.87/6.12 True)) % 5.87/6.12 Clause #34 (by clausification #[33]): ∀ (a a_1 a_2 a_3 : Iota), % 5.87/6.12 Or (Eq (breln1 a a_1) False) % 5.87/6.12 (Or (Eq (breln1 a a_2) False) % 5.87/6.12 (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)) % 5.87/6.12 Clause #35 (by clausification #[34]): ∀ (a a_1 a_2 a_3 : Iota), % 5.87/6.12 Or (Eq (breln1 a a_1) False) % 5.87/6.12 (Or (Eq (breln1 a a_2) False) % 5.87/6.12 (Or (Eq (in a_3 a) False) % 5.87/6.12 (Eq (∀ (Xy : Iota), in Xy a → in (kpair a_3 Xy) a_1 → in (kpair a_3 Xy) (binunion a_1 a_2)) True))) % 5.87/6.12 Clause #36 (by clausification #[35]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 5.87/6.12 Or (Eq (breln1 a a_1) False) % 5.87/6.12 (Or (Eq (breln1 a a_2) False) % 5.87/6.12 (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))) % 5.87/6.12 Clause #37 (by clausification #[36]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 5.87/6.12 Or (Eq (breln1 a a_1) False) % 5.87/6.12 (Or (Eq (breln1 a a_2) False) % 5.87/6.12 (Or (Eq (in a_3 a) False) % 5.87/6.12 (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)))) % 5.87/6.12 Clause #38 (by clausification #[37]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 5.87/6.12 Or (Eq (breln1 a a_1) False) % 5.87/6.12 (Or (Eq (breln1 a a_2) False) % 5.87/6.12 (Or (Eq (in a_3 a) False) % 5.87/6.12 (Or (Eq (in a_4 a) False) % 5.87/6.12 (Or (Eq (in (kpair a_3 a_4) a_1) False) (Eq (in (kpair a_3 a_4) (binunion a_1 a_2)) True))))) % 5.87/6.12 Clause #39 (by superposition #[38, 12]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 5.87/6.12 Or (Eq (breln1 (skS.0 0 a) a_1) False) % 5.87/6.12 (Or (Eq (in a_2 (skS.0 0 a)) False) % 5.87/6.12 (Or (Eq (in a_3 (skS.0 0 a)) False) % 5.87/6.12 (Or (Eq (in (kpair a_2 a_3) (skS.0 1 a a_4)) False) % 5.87/6.12 (Or (Eq (in (kpair a_2 a_3) (binunion (skS.0 1 a a_4) a_1)) True) (Eq False True))))) % 5.87/6.12 Clause #40 (by clausification #[13]): ∀ (a a_1 a_2 : Iota), % 5.87/6.12 Eq % 5.87/6.12 (Not % 5.87/6.12 (breln1 (skS.0 0 a) (skS.0 2 a a_1 a_2) → % 5.87/6.12 ∀ (Xx : Iota), % 5.87/6.12 in Xx (skS.0 0 a) → % 5.87/6.12 ∀ (Xy : Iota), % 5.87/6.12 in Xy (skS.0 0 a) → % 5.87/6.12 Or (in (kpair Xx Xy) (skS.0 1 a a_1)) (in (kpair Xx Xy) (skS.0 2 a a_1 a_2)) → % 5.87/6.12 in (kpair Xx Xy) (binunion (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)))) % 5.87/6.12 True % 5.87/6.12 Clause #41 (by clausification #[40]): ∀ (a a_1 a_2 : Iota), % 5.87/6.12 Eq % 5.87/6.12 (breln1 (skS.0 0 a) (skS.0 2 a a_1 a_2) → % 5.87/6.12 ∀ (Xx : Iota), % 5.87/6.12 in Xx (skS.0 0 a) → % 5.87/6.14 ∀ (Xy : Iota), % 5.87/6.14 in Xy (skS.0 0 a) → % 5.87/6.14 Or (in (kpair Xx Xy) (skS.0 1 a a_1)) (in (kpair Xx Xy) (skS.0 2 a a_1 a_2)) → % 5.87/6.14 in (kpair Xx Xy) (binunion (skS.0 1 a a_1) (skS.0 2 a a_1 a_2))) % 5.87/6.14 False % 5.87/6.14 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 % 5.87/6.14 Clause #43 (by clausification #[41]): ∀ (a a_1 a_2 : Iota), % 5.87/6.14 Eq % 5.87/6.14 (∀ (Xx : Iota), % 5.87/6.14 in Xx (skS.0 0 a) → % 5.87/6.14 ∀ (Xy : Iota), % 5.87/6.14 in Xy (skS.0 0 a) → % 5.87/6.14 Or (in (kpair Xx Xy) (skS.0 1 a a_1)) (in (kpair Xx Xy) (skS.0 2 a a_1 a_2)) → % 5.87/6.14 in (kpair Xx Xy) (binunion (skS.0 1 a a_1) (skS.0 2 a a_1 a_2))) % 5.87/6.14 False % 5.87/6.14 Clause #46 (by clausification #[43]): ∀ (a a_1 a_2 a_3 : Iota), % 5.87/6.14 Eq % 5.87/6.14 (Not % 5.87/6.14 (in (skS.0 3 a a_1 a_2 a_3) (skS.0 0 a) → % 5.87/6.14 ∀ (Xy : Iota), % 5.87/6.14 in Xy (skS.0 0 a) → % 5.87/6.14 Or (in (kpair (skS.0 3 a a_1 a_2 a_3) Xy) (skS.0 1 a a_1)) % 5.87/6.14 (in (kpair (skS.0 3 a a_1 a_2 a_3) Xy) (skS.0 2 a a_1 a_2)) → % 5.87/6.14 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)))) % 5.87/6.14 True % 5.87/6.14 Clause #47 (by clausification #[46]): ∀ (a a_1 a_2 a_3 : Iota), % 5.87/6.14 Eq % 5.87/6.14 (in (skS.0 3 a a_1 a_2 a_3) (skS.0 0 a) → % 5.87/6.14 ∀ (Xy : Iota), % 5.87/6.14 in Xy (skS.0 0 a) → % 5.87/6.14 Or (in (kpair (skS.0 3 a a_1 a_2 a_3) Xy) (skS.0 1 a a_1)) % 5.87/6.14 (in (kpair (skS.0 3 a a_1 a_2 a_3) Xy) (skS.0 2 a a_1 a_2)) → % 5.87/6.14 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))) % 5.87/6.14 False % 5.87/6.14 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 % 5.87/6.14 Clause #49 (by clausification #[47]): ∀ (a a_1 a_2 a_3 : Iota), % 5.87/6.14 Eq % 5.87/6.14 (∀ (Xy : Iota), % 5.87/6.14 in Xy (skS.0 0 a) → % 5.87/6.14 Or (in (kpair (skS.0 3 a a_1 a_2 a_3) Xy) (skS.0 1 a a_1)) % 5.87/6.14 (in (kpair (skS.0 3 a a_1 a_2 a_3) Xy) (skS.0 2 a a_1 a_2)) → % 5.87/6.14 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))) % 5.87/6.14 False % 5.87/6.14 Clause #50 (by clausification #[49]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 5.87/6.14 Eq % 5.87/6.14 (Not % 5.87/6.14 (in (skS.0 4 a a_1 a_2 a_3 a_4) (skS.0 0 a) → % 5.87/6.14 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)) % 5.87/6.14 (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)) → % 5.87/6.14 in (kpair (skS.0 3 a a_1 a_2 a_3) (skS.0 4 a a_1 a_2 a_3 a_4)) % 5.87/6.14 (binunion (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)))) % 5.87/6.14 True % 5.87/6.14 Clause #51 (by clausification #[50]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 5.87/6.14 Eq % 5.87/6.14 (in (skS.0 4 a a_1 a_2 a_3 a_4) (skS.0 0 a) → % 5.87/6.14 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)) % 5.87/6.14 (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)) → % 5.87/6.14 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))) % 5.87/6.14 False % 5.87/6.14 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 % 5.87/6.14 Clause #53 (by clausification #[51]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 5.87/6.14 Eq % 5.87/6.14 (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)) % 5.87/6.14 (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)) → % 5.87/6.14 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))) % 5.87/6.14 False % 5.87/6.14 Clause #54 (by clausification #[53]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 5.87/6.14 Eq % 5.87/6.14 (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)) % 5.87/6.14 (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))) % 5.87/6.14 True % 5.87/6.14 Clause #55 (by clausification #[53]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 5.87/6.14 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))) % 5.87/6.14 False % 5.87/6.14 Clause #56 (by clausification #[54]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 5.87/6.14 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) % 5.97/6.17 (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) % 5.97/6.17 Clause #57 (by clausification #[26]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 5.97/6.17 Or (Eq (breln1 (skS.0 0 a) a_1) False) % 5.97/6.17 (Or (Eq (in a_2 (skS.0 0 a)) False) % 5.97/6.17 (Or (Eq (in a_3 (skS.0 0 a)) False) % 5.97/6.17 (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)))) % 5.97/6.17 Clause #59 (by superposition #[57, 42]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 5.97/6.17 Or (Eq (in a (skS.0 0 a_1)) False) % 5.97/6.17 (Or (Eq (in a_2 (skS.0 0 a_1)) False) % 5.97/6.17 (Or (Eq (in (kpair a a_2) (skS.0 2 a_1 a_3 a_4)) False) % 5.97/6.17 (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)))) % 5.97/6.17 Clause #60 (by clausification #[39]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 5.97/6.17 Or (Eq (breln1 (skS.0 0 a) a_1) False) % 5.97/6.17 (Or (Eq (in a_2 (skS.0 0 a)) False) % 5.97/6.17 (Or (Eq (in a_3 (skS.0 0 a)) False) % 5.97/6.17 (Or (Eq (in (kpair a_2 a_3) (skS.0 1 a a_4)) False) % 5.97/6.17 (Eq (in (kpair a_2 a_3) (binunion (skS.0 1 a a_4) a_1)) True)))) % 5.97/6.17 Clause #62 (by superposition #[60, 42]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 5.97/6.17 Or (Eq (in a (skS.0 0 a_1)) False) % 5.97/6.17 (Or (Eq (in a_2 (skS.0 0 a_1)) False) % 5.97/6.17 (Or (Eq (in (kpair a a_2) (skS.0 1 a_1 a_3)) False) % 5.97/6.17 (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)))) % 5.97/6.17 Clause #75 (by clausification #[62]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 5.97/6.17 Or (Eq (in a (skS.0 0 a_1)) False) % 5.97/6.17 (Or (Eq (in a_2 (skS.0 0 a_1)) False) % 5.97/6.17 (Or (Eq (in (kpair a a_2) (skS.0 1 a_1 a_3)) False) % 5.97/6.17 (Eq (in (kpair a a_2) (binunion (skS.0 1 a_1 a_3) (skS.0 2 a_1 a_4 a_5))) True))) % 5.97/6.17 Clause #76 (by superposition #[75, 48]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 : Iota), % 5.97/6.17 Or (Eq (in a (skS.0 0 a_1)) False) % 5.97/6.17 (Or (Eq (in (kpair (skS.0 3 a_1 a_2 a_3 a_4) a) (skS.0 1 a_1 a_5)) False) % 5.97/6.17 (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) % 5.97/6.17 (Eq False True))) % 5.97/6.17 Clause #84 (by clausification #[59]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 5.97/6.17 Or (Eq (in a (skS.0 0 a_1)) False) % 5.97/6.17 (Or (Eq (in a_2 (skS.0 0 a_1)) False) % 5.97/6.17 (Or (Eq (in (kpair a a_2) (skS.0 2 a_1 a_3 a_4)) False) % 5.97/6.17 (Eq (in (kpair a a_2) (binunion (skS.0 1 a_1 a_5) (skS.0 2 a_1 a_3 a_4))) True))) % 5.97/6.17 Clause #85 (by superposition #[84, 48]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 : Iota), % 5.97/6.17 Or (Eq (in a (skS.0 0 a_1)) False) % 5.97/6.17 (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) % 5.97/6.17 (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) % 5.97/6.17 (Eq False True))) % 5.97/6.17 Clause #105 (by clausification #[76]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 : Iota), % 5.97/6.17 Or (Eq (in a (skS.0 0 a_1)) False) % 5.97/6.17 (Or (Eq (in (kpair (skS.0 3 a_1 a_2 a_3 a_4) a) (skS.0 1 a_1 a_5)) False) % 5.97/6.17 (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)) % 5.97/6.17 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), % 5.97/6.17 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) % 5.97/6.17 (Or % 5.97/6.17 (Eq % 5.97/6.17 (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))) % 5.97/6.17 True) % 5.97/6.17 (Eq False True)) % 5.97/6.17 Clause #108 (by clausification #[85]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 : Iota), % 5.97/6.17 Or (Eq (in a (skS.0 0 a_1)) False) % 5.97/6.17 (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) % 5.97/6.17 (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)) % 5.97/6.17 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), % 5.97/6.17 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) % 5.97/6.17 (Or % 5.97/6.17 (Eq % 5.97/6.17 (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))) % 5.97/6.17 True) % 5.97/6.17 (Eq False True)) % 5.97/6.18 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), % 5.97/6.18 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) % 5.97/6.18 (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))) % 5.97/6.18 True) % 5.97/6.18 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), % 5.97/6.18 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) % 5.97/6.18 (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))) % 5.97/6.18 True) % 5.97/6.18 Clause #164 (by superposition #[163, 56]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 5.97/6.18 Or % 5.97/6.18 (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))) % 5.97/6.18 True) % 5.97/6.18 (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)) % 5.97/6.18 Clause #165 (by clausification #[164]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 5.97/6.18 Or % 5.97/6.18 (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))) % 5.97/6.18 True) % 5.97/6.18 (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) % 5.97/6.18 Clause #166 (by superposition #[165, 55]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 5.97/6.18 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) % 5.97/6.18 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 % 5.97/6.18 Clause #172 (by superposition #[167, 154]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota), % 5.97/6.18 Or (Eq True False) % 5.97/6.18 (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))) % 5.97/6.18 True) % 5.97/6.18 Clause #178 (by clausification #[172]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota), % 5.97/6.18 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))) % 5.97/6.18 True % 5.97/6.18 Clause #179 (by superposition #[178, 55]): Eq True False % 5.97/6.18 Clause #180 (by clausification #[179]): False % 5.97/6.18 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------