%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : NUN059+1 : TPTP v9.2.0. Bugfixed v7.4.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n020.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 07:57:47 PM UTC 2025 % Result : Theorem 189.37s 189.64s % Output : Proof 189.90s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : NUN059+1 : TPTP v9.2.0. Bugfixed v7.4.0. % 0.03/0.13 % Command : duper %s % 0.13/0.34 % Computer : n020.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Thu Oct 2 11:36:08 EDT 2025 % 0.13/0.34 % CPUTime : % 189.37/189.64 SZS status Theorem for theBenchmark.p % 189.37/189.64 SZS output start Proof for theBenchmark.p % 189.37/189.64 Clause #0 (by assumption #[]): Eq (Exists fun Y24 => ∀ (X19 : Iota), Or (And (id X19 Y24) (r1 X19)) (And (Not (r1 X19)) (Not (id X19 Y24)))) True % 189.37/189.64 Clause #3 (by assumption #[]): Eq % 189.37/189.64 (∀ (X16 X17 : Iota), % 189.37/189.64 Exists fun Y23 => % 189.37/189.64 ∀ (X18 : Iota), Or (And (id X18 Y23) (r4 X16 X17 X18)) (And (Not (r4 X16 X17 X18)) (Not (id X18 Y23)))) % 189.37/189.64 True % 189.37/189.64 Clause #4 (by assumption #[]): Eq (∀ (X20 : Iota), id X20 X20) True % 189.37/189.64 Clause #5 (by assumption #[]): Eq (∀ (X21 X22 : Iota), Or (Not (id X21 X22)) (id X22 X21)) True % 189.37/189.64 Clause #6 (by assumption #[]): Eq (∀ (X23 X24 X25 : Iota), Or (Or (Not (id X23 X24)) (id X23 X25)) (Not (id X24 X25))) True % 189.37/189.64 Clause #7 (by assumption #[]): Eq (∀ (X26 X27 : Iota), Or (Or (Not (id X26 X27)) (And (Not (r1 X26)) (Not (r1 X27)))) (And (r1 X26) (r1 X27))) True % 189.37/189.64 Clause #9 (by assumption #[]): Eq % 189.37/189.64 (∀ (X32 X33 X34 X35 X36 X37 : Iota), % 189.37/189.64 Or % 189.37/189.64 (Or (Or (Or (Not (id X32 X35)) (Not (id X33 X36))) (Not (id X34 X37))) % 189.37/189.64 (And (Not (r3 X32 X33 X34)) (Not (r3 X35 X36 X37)))) % 189.37/189.64 (And (r3 X32 X33 X34) (r3 X35 X36 X37))) % 189.37/189.64 True % 189.37/189.64 Clause #10 (by assumption #[]): Eq % 189.37/189.64 (∀ (X38 X39 X40 X41 X42 X43 : Iota), % 189.37/189.64 Or % 189.37/189.64 (Or (Or (Or (Not (id X38 X41)) (Not (id X39 X42))) (Not (id X40 X43))) % 189.37/189.64 (And (Not (r4 X38 X39 X40)) (Not (r4 X41 X42 X43)))) % 189.37/189.64 (And (r4 X38 X39 X40) (r4 X41 X42 X43))) % 189.37/189.64 True % 189.37/189.64 Clause #14 (by assumption #[]): Eq (∀ (X4 : Iota), Exists fun Y9 => And (id Y9 X4) (Exists fun Y16 => And (r1 Y16) (r3 X4 Y16 Y9))) True % 189.37/189.64 Clause #15 (by assumption #[]): Eq % 189.37/189.64 (∀ (X5 : Iota), % 189.37/189.64 Exists fun Y8 => And (Exists fun Y17 => And (r1 Y17) (r4 X5 Y17 Y8)) (Exists fun Y18 => And (id Y8 Y18) (r1 Y18))) % 189.37/189.64 True % 189.37/189.64 Clause #18 (by assumption #[]): Eq % 189.37/189.64 (Not % 189.37/189.64 (Exists fun Y1 => % 189.37/189.64 Exists fun Y3 => % 189.37/189.64 Exists fun Y2 => % 189.37/189.64 Exists fun Y4 => % 189.37/189.64 And (Exists fun Y5 => And (id Y4 Y5) (r4 Y2 Y2 Y5)) % 189.37/189.64 (Exists fun Y6 => And (r4 Y3 Y3 Y6) (Exists fun Y7 => And (r4 Y1 Y1 Y7) (r3 Y7 Y6 Y4))))) % 189.37/189.64 True % 189.37/189.64 Clause #19 (by clausification #[4]): ∀ (a : Iota), Eq (id a a) True % 189.37/189.64 Clause #20 (by clausification #[5]): ∀ (a : Iota), Eq (∀ (X22 : Iota), Or (Not (id a X22)) (id X22 a)) True % 189.37/189.64 Clause #21 (by clausification #[20]): ∀ (a a_1 : Iota), Eq (Or (Not (id a a_1)) (id a_1 a)) True % 189.37/189.64 Clause #22 (by clausification #[21]): ∀ (a a_1 : Iota), Or (Eq (Not (id a a_1)) True) (Eq (id a_1 a) True) % 189.37/189.64 Clause #23 (by clausification #[22]): ∀ (a a_1 : Iota), Or (Eq (id a a_1) True) (Eq (id a_1 a) False) % 189.37/189.64 Clause #25 (by clausification #[6]): ∀ (a : Iota), Eq (∀ (X24 X25 : Iota), Or (Or (Not (id a X24)) (id a X25)) (Not (id X24 X25))) True % 189.37/189.64 Clause #26 (by clausification #[25]): ∀ (a a_1 : Iota), Eq (∀ (X25 : Iota), Or (Or (Not (id a a_1)) (id a X25)) (Not (id a_1 X25))) True % 189.37/189.64 Clause #27 (by clausification #[26]): ∀ (a a_1 a_2 : Iota), Eq (Or (Or (Not (id a a_1)) (id a a_2)) (Not (id a_1 a_2))) True % 189.37/189.64 Clause #28 (by clausification #[27]): ∀ (a a_1 a_2 : Iota), Or (Eq (Or (Not (id a a_1)) (id a a_2)) True) (Eq (Not (id a_1 a_2)) True) % 189.37/189.64 Clause #29 (by clausification #[28]): ∀ (a a_1 a_2 : Iota), Or (Eq (Not (id a a_1)) True) (Or (Eq (Not (id a_2 a)) True) (Eq (id a_2 a_1) True)) % 189.37/189.64 Clause #30 (by clausification #[29]): ∀ (a a_1 a_2 : Iota), Or (Eq (Not (id a a_1)) True) (Or (Eq (id a a_2) True) (Eq (id a_1 a_2) False)) % 189.37/189.64 Clause #31 (by clausification #[30]): ∀ (a a_1 a_2 : Iota), Or (Eq (id a a_1) True) (Or (Eq (id a_2 a_1) False) (Eq (id a a_2) False)) % 189.37/189.64 Clause #34 (by clausification #[0]): ∀ (a : Iota), % 189.37/189.64 Eq (∀ (X19 : Iota), Or (And (id X19 (skS.0 0 a)) (r1 X19)) (And (Not (r1 X19)) (Not (id X19 (skS.0 0 a))))) True % 189.37/189.64 Clause #35 (by clausification #[34]): ∀ (a a_1 : Iota), Eq (Or (And (id a (skS.0 0 a_1)) (r1 a)) (And (Not (r1 a)) (Not (id a (skS.0 0 a_1))))) True % 189.37/189.64 Clause #36 (by clausification #[35]): ∀ (a a_1 : Iota), Or (Eq (And (id a (skS.0 0 a_1)) (r1 a)) True) (Eq (And (Not (r1 a)) (Not (id a (skS.0 0 a_1)))) True) % 189.37/189.64 Clause #37 (by clausification #[36]): ∀ (a a_1 : Iota), Or (Eq (And (Not (r1 a)) (Not (id a (skS.0 0 a_1)))) True) (Eq (r1 a) True) % 189.45/189.67 Clause #38 (by clausification #[36]): ∀ (a a_1 : Iota), Or (Eq (And (Not (r1 a)) (Not (id a (skS.0 0 a_1)))) True) (Eq (id a (skS.0 0 a_1)) True) % 189.45/189.67 Clause #39 (by clausification #[37]): ∀ (a a_1 : Iota), Or (Eq (r1 a) True) (Eq (Not (id a (skS.0 0 a_1))) True) % 189.45/189.67 Clause #41 (by clausification #[39]): ∀ (a a_1 : Iota), Or (Eq (r1 a) True) (Eq (id a (skS.0 0 a_1)) False) % 189.45/189.67 Clause #42 (by superposition #[41, 19]): ∀ (a : Iota), Or (Eq (r1 (skS.0 0 a)) True) (Eq False True) % 189.45/189.67 Clause #44 (by clausification #[42]): ∀ (a : Iota), Eq (r1 (skS.0 0 a)) True % 189.45/189.67 Clause #53 (by clausification #[14]): ∀ (a : Iota), Eq (Exists fun Y9 => And (id Y9 a) (Exists fun Y16 => And (r1 Y16) (r3 a Y16 Y9))) True % 189.45/189.67 Clause #54 (by clausification #[53]): ∀ (a a_1 : Iota), Eq (And (id (skS.0 1 a a_1) a) (Exists fun Y16 => And (r1 Y16) (r3 a Y16 (skS.0 1 a a_1)))) True % 189.45/189.67 Clause #55 (by clausification #[54]): ∀ (a a_1 : Iota), Eq (Exists fun Y16 => And (r1 Y16) (r3 a Y16 (skS.0 1 a a_1))) True % 189.45/189.67 Clause #56 (by clausification #[54]): ∀ (a a_1 : Iota), Eq (id (skS.0 1 a a_1) a) True % 189.45/189.67 Clause #57 (by clausification #[55]): ∀ (a a_1 a_2 : Iota), Eq (And (r1 (skS.0 2 a a_1 a_2)) (r3 a (skS.0 2 a a_1 a_2) (skS.0 1 a a_1))) True % 189.45/189.67 Clause #58 (by clausification #[57]): ∀ (a a_1 a_2 : Iota), Eq (r3 a (skS.0 2 a a_1 a_2) (skS.0 1 a a_1)) True % 189.45/189.67 Clause #59 (by clausification #[57]): ∀ (a a_1 a_2 : Iota), Eq (r1 (skS.0 2 a a_1 a_2)) True % 189.45/189.67 Clause #61 (by superposition #[56, 23]): ∀ (a a_1 : Iota), Or (Eq (id a (skS.0 1 a a_1)) True) (Eq True False) % 189.45/189.67 Clause #75 (by clausification #[61]): ∀ (a a_1 : Iota), Eq (id a (skS.0 1 a a_1)) True % 189.45/189.67 Clause #99 (by clausification #[3]): ∀ (a : Iota), % 189.45/189.67 Eq % 189.45/189.67 (∀ (X17 : Iota), % 189.45/189.67 Exists fun Y23 => % 189.45/189.67 ∀ (X18 : Iota), Or (And (id X18 Y23) (r4 a X17 X18)) (And (Not (r4 a X17 X18)) (Not (id X18 Y23)))) % 189.45/189.67 True % 189.45/189.67 Clause #100 (by clausification #[99]): ∀ (a a_1 : Iota), % 189.45/189.67 Eq % 189.45/189.67 (Exists fun Y23 => % 189.45/189.67 ∀ (X18 : Iota), Or (And (id X18 Y23) (r4 a a_1 X18)) (And (Not (r4 a a_1 X18)) (Not (id X18 Y23)))) % 189.45/189.67 True % 189.45/189.67 Clause #101 (by clausification #[100]): ∀ (a a_1 a_2 : Iota), % 189.45/189.67 Eq % 189.45/189.67 (∀ (X18 : Iota), % 189.45/189.67 Or (And (id X18 (skS.0 5 a a_1 a_2)) (r4 a a_1 X18)) % 189.45/189.67 (And (Not (r4 a a_1 X18)) (Not (id X18 (skS.0 5 a a_1 a_2))))) % 189.45/189.67 True % 189.45/189.67 Clause #102 (by clausification #[101]): ∀ (a a_1 a_2 a_3 : Iota), % 189.45/189.67 Eq % 189.45/189.67 (Or (And (id a (skS.0 5 a_1 a_2 a_3)) (r4 a_1 a_2 a)) (And (Not (r4 a_1 a_2 a)) (Not (id a (skS.0 5 a_1 a_2 a_3))))) % 189.45/189.67 True % 189.45/189.67 Clause #103 (by clausification #[102]): ∀ (a a_1 a_2 a_3 : Iota), % 189.45/189.67 Or (Eq (And (id a (skS.0 5 a_1 a_2 a_3)) (r4 a_1 a_2 a)) True) % 189.45/189.67 (Eq (And (Not (r4 a_1 a_2 a)) (Not (id a (skS.0 5 a_1 a_2 a_3)))) True) % 189.45/189.67 Clause #104 (by clausification #[103]): ∀ (a a_1 a_2 a_3 : Iota), % 189.45/189.67 Or (Eq (And (Not (r4 a a_1 a_2)) (Not (id a_2 (skS.0 5 a a_1 a_3)))) True) (Eq (r4 a a_1 a_2) True) % 189.45/189.67 Clause #105 (by clausification #[103]): ∀ (a a_1 a_2 a_3 : Iota), % 189.45/189.67 Or (Eq (And (Not (r4 a a_1 a_2)) (Not (id a_2 (skS.0 5 a a_1 a_3)))) True) (Eq (id a_2 (skS.0 5 a a_1 a_3)) True) % 189.45/189.67 Clause #106 (by clausification #[104]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (r4 a a_1 a_2) True) (Eq (Not (id a_2 (skS.0 5 a a_1 a_3))) True) % 189.45/189.67 Clause #108 (by clausification #[106]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (r4 a a_1 a_2) True) (Eq (id a_2 (skS.0 5 a a_1 a_3)) False) % 189.45/189.67 Clause #120 (by clausification #[7]): ∀ (a : Iota), Eq (∀ (X27 : Iota), Or (Or (Not (id a X27)) (And (Not (r1 a)) (Not (r1 X27)))) (And (r1 a) (r1 X27))) True % 189.45/189.67 Clause #121 (by clausification #[120]): ∀ (a a_1 : Iota), Eq (Or (Or (Not (id a a_1)) (And (Not (r1 a)) (Not (r1 a_1)))) (And (r1 a) (r1 a_1))) True % 189.45/189.67 Clause #122 (by clausification #[121]): ∀ (a a_1 : Iota), Or (Eq (Or (Not (id a a_1)) (And (Not (r1 a)) (Not (r1 a_1)))) True) (Eq (And (r1 a) (r1 a_1)) True) % 189.45/189.67 Clause #123 (by clausification #[122]): ∀ (a a_1 : Iota), % 189.45/189.67 Or (Eq (And (r1 a) (r1 a_1)) True) (Or (Eq (Not (id a a_1)) True) (Eq (And (Not (r1 a)) (Not (r1 a_1))) True)) % 189.45/189.67 Clause #125 (by clausification #[123]): ∀ (a a_1 : Iota), Or (Eq (Not (id a a_1)) True) (Or (Eq (And (Not (r1 a)) (Not (r1 a_1))) True) (Eq (r1 a) True)) % 189.45/189.69 Clause #153 (by clausification #[125]): ∀ (a a_1 : Iota), Or (Eq (And (Not (r1 a)) (Not (r1 a_1))) True) (Or (Eq (r1 a) True) (Eq (id a a_1) False)) % 189.45/189.69 Clause #154 (by clausification #[153]): ∀ (a a_1 : Iota), Or (Eq (r1 a) True) (Or (Eq (id a a_1) False) (Eq (Not (r1 a_1)) True)) % 189.45/189.69 Clause #156 (by clausification #[154]): ∀ (a a_1 : Iota), Or (Eq (r1 a) True) (Or (Eq (id a a_1) False) (Eq (r1 a_1) False)) % 189.45/189.69 Clause #168 (by clausification #[9]): ∀ (a : Iota), % 189.45/189.69 Eq % 189.45/189.69 (∀ (X33 X34 X35 X36 X37 : Iota), % 189.45/189.69 Or % 189.45/189.69 (Or (Or (Or (Not (id a X35)) (Not (id X33 X36))) (Not (id X34 X37))) % 189.45/189.69 (And (Not (r3 a X33 X34)) (Not (r3 X35 X36 X37)))) % 189.45/189.69 (And (r3 a X33 X34) (r3 X35 X36 X37))) % 189.45/189.69 True % 189.45/189.69 Clause #169 (by clausification #[168]): ∀ (a a_1 : Iota), % 189.45/189.69 Eq % 189.45/189.69 (∀ (X34 X35 X36 X37 : Iota), % 189.45/189.69 Or % 189.45/189.69 (Or (Or (Or (Not (id a X35)) (Not (id a_1 X36))) (Not (id X34 X37))) % 189.45/189.69 (And (Not (r3 a a_1 X34)) (Not (r3 X35 X36 X37)))) % 189.45/189.69 (And (r3 a a_1 X34) (r3 X35 X36 X37))) % 189.45/189.69 True % 189.45/189.69 Clause #170 (by clausification #[169]): ∀ (a a_1 a_2 : Iota), % 189.45/189.69 Eq % 189.45/189.69 (∀ (X35 X36 X37 : Iota), % 189.45/189.69 Or % 189.45/189.69 (Or (Or (Or (Not (id a X35)) (Not (id a_1 X36))) (Not (id a_2 X37))) % 189.45/189.69 (And (Not (r3 a a_1 a_2)) (Not (r3 X35 X36 X37)))) % 189.45/189.69 (And (r3 a a_1 a_2) (r3 X35 X36 X37))) % 189.45/189.69 True % 189.45/189.69 Clause #171 (by clausification #[170]): ∀ (a a_1 a_2 a_3 : Iota), % 189.45/189.69 Eq % 189.45/189.69 (∀ (X36 X37 : Iota), % 189.45/189.69 Or % 189.45/189.69 (Or (Or (Or (Not (id a a_1)) (Not (id a_2 X36))) (Not (id a_3 X37))) % 189.45/189.69 (And (Not (r3 a a_2 a_3)) (Not (r3 a_1 X36 X37)))) % 189.45/189.69 (And (r3 a a_2 a_3) (r3 a_1 X36 X37))) % 189.45/189.69 True % 189.45/189.69 Clause #172 (by clausification #[171]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 189.45/189.69 Eq % 189.45/189.69 (∀ (X37 : Iota), % 189.45/189.69 Or % 189.45/189.69 (Or (Or (Or (Not (id a a_1)) (Not (id a_2 a_3))) (Not (id a_4 X37))) % 189.45/189.69 (And (Not (r3 a a_2 a_4)) (Not (r3 a_1 a_3 X37)))) % 189.45/189.69 (And (r3 a a_2 a_4) (r3 a_1 a_3 X37))) % 189.45/189.69 True % 189.45/189.69 Clause #173 (by clausification #[172]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 189.45/189.69 Eq % 189.45/189.69 (Or % 189.45/189.69 (Or (Or (Or (Not (id a a_1)) (Not (id a_2 a_3))) (Not (id a_4 a_5))) % 189.45/189.69 (And (Not (r3 a a_2 a_4)) (Not (r3 a_1 a_3 a_5)))) % 189.45/189.69 (And (r3 a a_2 a_4) (r3 a_1 a_3 a_5))) % 189.45/189.69 True % 189.45/189.69 Clause #174 (by clausification #[173]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 189.45/189.69 Or % 189.45/189.69 (Eq % 189.45/189.69 (Or (Or (Or (Not (id a a_1)) (Not (id a_2 a_3))) (Not (id a_4 a_5))) % 189.45/189.69 (And (Not (r3 a a_2 a_4)) (Not (r3 a_1 a_3 a_5)))) % 189.45/189.69 True) % 189.45/189.69 (Eq (And (r3 a a_2 a_4) (r3 a_1 a_3 a_5)) True) % 189.45/189.69 Clause #175 (by clausification #[174]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 189.45/189.69 Or (Eq (And (r3 a a_1 a_2) (r3 a_3 a_4 a_5)) True) % 189.45/189.69 (Or (Eq (Or (Or (Not (id a a_3)) (Not (id a_1 a_4))) (Not (id a_2 a_5))) True) % 189.45/189.69 (Eq (And (Not (r3 a a_1 a_2)) (Not (r3 a_3 a_4 a_5))) True)) % 189.45/189.69 Clause #176 (by clausification #[175]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 189.45/189.69 Or (Eq (Or (Or (Not (id a a_1)) (Not (id a_2 a_3))) (Not (id a_4 a_5))) True) % 189.45/189.69 (Or (Eq (And (Not (r3 a a_2 a_4)) (Not (r3 a_1 a_3 a_5))) True) (Eq (r3 a_1 a_3 a_5) True)) % 189.45/189.69 Clause #177 (by clausification #[175]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 189.45/189.69 Or (Eq (Or (Or (Not (id a a_1)) (Not (id a_2 a_3))) (Not (id a_4 a_5))) True) % 189.45/189.69 (Or (Eq (And (Not (r3 a a_2 a_4)) (Not (r3 a_1 a_3 a_5))) True) (Eq (r3 a a_2 a_4) True)) % 189.45/189.69 Clause #178 (by clausification #[176]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 189.45/189.69 Or (Eq (And (Not (r3 a a_1 a_2)) (Not (r3 a_3 a_4 a_5))) True) % 189.45/189.69 (Or (Eq (r3 a_3 a_4 a_5) True) (Or (Eq (Or (Not (id a a_3)) (Not (id a_1 a_4))) True) (Eq (Not (id a_2 a_5)) True))) % 189.45/189.69 Clause #180 (by clausification #[178]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 189.45/189.69 Or (Eq (r3 a a_1 a_2) True) % 189.45/189.69 (Or (Eq (Or (Not (id a_3 a)) (Not (id a_4 a_1))) True) % 189.45/189.69 (Or (Eq (Not (id a_5 a_2)) True) (Eq (Not (r3 a_3 a_4 a_5)) True))) % 189.45/189.69 Clause #193 (by clausification #[10]): ∀ (a : Iota), % 189.45/189.69 Eq % 189.45/189.69 (∀ (X39 X40 X41 X42 X43 : Iota), % 189.45/189.69 Or % 189.45/189.69 (Or (Or (Or (Not (id a X41)) (Not (id X39 X42))) (Not (id X40 X43))) % 189.45/189.69 (And (Not (r4 a X39 X40)) (Not (r4 X41 X42 X43)))) % 189.45/189.69 (And (r4 a X39 X40) (r4 X41 X42 X43))) % 189.50/189.72 True % 189.50/189.72 Clause #194 (by clausification #[193]): ∀ (a a_1 : Iota), % 189.50/189.72 Eq % 189.50/189.72 (∀ (X40 X41 X42 X43 : Iota), % 189.50/189.72 Or % 189.50/189.72 (Or (Or (Or (Not (id a X41)) (Not (id a_1 X42))) (Not (id X40 X43))) % 189.50/189.72 (And (Not (r4 a a_1 X40)) (Not (r4 X41 X42 X43)))) % 189.50/189.72 (And (r4 a a_1 X40) (r4 X41 X42 X43))) % 189.50/189.72 True % 189.50/189.72 Clause #195 (by clausification #[194]): ∀ (a a_1 a_2 : Iota), % 189.50/189.72 Eq % 189.50/189.72 (∀ (X41 X42 X43 : Iota), % 189.50/189.72 Or % 189.50/189.72 (Or (Or (Or (Not (id a X41)) (Not (id a_1 X42))) (Not (id a_2 X43))) % 189.50/189.72 (And (Not (r4 a a_1 a_2)) (Not (r4 X41 X42 X43)))) % 189.50/189.72 (And (r4 a a_1 a_2) (r4 X41 X42 X43))) % 189.50/189.72 True % 189.50/189.72 Clause #196 (by clausification #[195]): ∀ (a a_1 a_2 a_3 : Iota), % 189.50/189.72 Eq % 189.50/189.72 (∀ (X42 X43 : Iota), % 189.50/189.72 Or % 189.50/189.72 (Or (Or (Or (Not (id a a_1)) (Not (id a_2 X42))) (Not (id a_3 X43))) % 189.50/189.72 (And (Not (r4 a a_2 a_3)) (Not (r4 a_1 X42 X43)))) % 189.50/189.72 (And (r4 a a_2 a_3) (r4 a_1 X42 X43))) % 189.50/189.72 True % 189.50/189.72 Clause #197 (by clausification #[196]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 189.50/189.72 Eq % 189.50/189.72 (∀ (X43 : Iota), % 189.50/189.72 Or % 189.50/189.72 (Or (Or (Or (Not (id a a_1)) (Not (id a_2 a_3))) (Not (id a_4 X43))) % 189.50/189.72 (And (Not (r4 a a_2 a_4)) (Not (r4 a_1 a_3 X43)))) % 189.50/189.72 (And (r4 a a_2 a_4) (r4 a_1 a_3 X43))) % 189.50/189.72 True % 189.50/189.72 Clause #198 (by clausification #[197]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 189.50/189.72 Eq % 189.50/189.72 (Or % 189.50/189.72 (Or (Or (Or (Not (id a a_1)) (Not (id a_2 a_3))) (Not (id a_4 a_5))) % 189.50/189.72 (And (Not (r4 a a_2 a_4)) (Not (r4 a_1 a_3 a_5)))) % 189.50/189.72 (And (r4 a a_2 a_4) (r4 a_1 a_3 a_5))) % 189.50/189.72 True % 189.50/189.72 Clause #199 (by clausification #[198]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 189.50/189.72 Or % 189.50/189.72 (Eq % 189.50/189.72 (Or (Or (Or (Not (id a a_1)) (Not (id a_2 a_3))) (Not (id a_4 a_5))) % 189.50/189.72 (And (Not (r4 a a_2 a_4)) (Not (r4 a_1 a_3 a_5)))) % 189.50/189.72 True) % 189.50/189.72 (Eq (And (r4 a a_2 a_4) (r4 a_1 a_3 a_5)) True) % 189.50/189.72 Clause #200 (by clausification #[199]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 189.50/189.72 Or (Eq (And (r4 a a_1 a_2) (r4 a_3 a_4 a_5)) True) % 189.50/189.72 (Or (Eq (Or (Or (Not (id a a_3)) (Not (id a_1 a_4))) (Not (id a_2 a_5))) True) % 189.50/189.72 (Eq (And (Not (r4 a a_1 a_2)) (Not (r4 a_3 a_4 a_5))) True)) % 189.50/189.72 Clause #202 (by clausification #[200]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 189.50/189.72 Or (Eq (Or (Or (Not (id a a_1)) (Not (id a_2 a_3))) (Not (id a_4 a_5))) True) % 189.50/189.72 (Or (Eq (And (Not (r4 a a_2 a_4)) (Not (r4 a_1 a_3 a_5))) True) (Eq (r4 a a_2 a_4) True)) % 189.50/189.72 Clause #309 (by clausification #[15]): ∀ (a : Iota), % 189.50/189.72 Eq (Exists fun Y8 => And (Exists fun Y17 => And (r1 Y17) (r4 a Y17 Y8)) (Exists fun Y18 => And (id Y8 Y18) (r1 Y18))) % 189.50/189.72 True % 189.50/189.72 Clause #310 (by clausification #[309]): ∀ (a a_1 : Iota), % 189.50/189.72 Eq % 189.50/189.72 (And (Exists fun Y17 => And (r1 Y17) (r4 a Y17 (skS.0 10 a a_1))) % 189.50/189.72 (Exists fun Y18 => And (id (skS.0 10 a a_1) Y18) (r1 Y18))) % 189.50/189.72 True % 189.50/189.72 Clause #311 (by clausification #[310]): ∀ (a a_1 : Iota), Eq (Exists fun Y18 => And (id (skS.0 10 a a_1) Y18) (r1 Y18)) True % 189.50/189.72 Clause #312 (by clausification #[310]): ∀ (a a_1 : Iota), Eq (Exists fun Y17 => And (r1 Y17) (r4 a Y17 (skS.0 10 a a_1))) True % 189.50/189.72 Clause #313 (by clausification #[311]): ∀ (a a_1 a_2 : Iota), Eq (And (id (skS.0 10 a a_1) (skS.0 11 a a_1 a_2)) (r1 (skS.0 11 a a_1 a_2))) True % 189.50/189.72 Clause #314 (by clausification #[313]): ∀ (a a_1 a_2 : Iota), Eq (r1 (skS.0 11 a a_1 a_2)) True % 189.50/189.72 Clause #315 (by clausification #[313]): ∀ (a a_1 a_2 : Iota), Eq (id (skS.0 10 a a_1) (skS.0 11 a a_1 a_2)) True % 189.50/189.72 Clause #318 (by clausification #[312]): ∀ (a a_1 a_2 : Iota), Eq (And (r1 (skS.0 12 a a_1 a_2)) (r4 a (skS.0 12 a a_1 a_2) (skS.0 10 a a_1))) True % 189.50/189.72 Clause #319 (by clausification #[318]): ∀ (a a_1 a_2 : Iota), Eq (r4 a (skS.0 12 a a_1 a_2) (skS.0 10 a a_1)) True % 189.50/189.72 Clause #320 (by clausification #[318]): ∀ (a a_1 a_2 : Iota), Eq (r1 (skS.0 12 a a_1 a_2)) True % 189.50/189.72 Clause #327 (by superposition #[315, 156]): ∀ (a a_1 a_2 : Iota), Or (Eq (r1 (skS.0 10 a a_1)) True) (Or (Eq True False) (Eq (r1 (skS.0 11 a a_1 a_2)) False)) % 189.50/189.72 Clause #372 (by clausification #[18]): Eq % 189.50/189.72 (Exists fun Y1 => % 189.50/189.72 Exists fun Y3 => % 189.50/189.72 Exists fun Y2 => % 189.50/189.72 Exists fun Y4 => % 189.50/189.72 And (Exists fun Y5 => And (id Y4 Y5) (r4 Y2 Y2 Y5)) % 189.50/189.72 (Exists fun Y6 => And (r4 Y3 Y3 Y6) (Exists fun Y7 => And (r4 Y1 Y1 Y7) (r3 Y7 Y6 Y4)))) % 189.53/189.75 False % 189.53/189.75 Clause #373 (by clausification #[372]): ∀ (a : Iota), % 189.53/189.75 Eq % 189.53/189.75 (Exists fun Y3 => % 189.53/189.75 Exists fun Y2 => % 189.53/189.75 Exists fun Y4 => % 189.53/189.75 And (Exists fun Y5 => And (id Y4 Y5) (r4 Y2 Y2 Y5)) % 189.53/189.75 (Exists fun Y6 => And (r4 Y3 Y3 Y6) (Exists fun Y7 => And (r4 a a Y7) (r3 Y7 Y6 Y4)))) % 189.53/189.75 False % 189.53/189.75 Clause #374 (by clausification #[373]): ∀ (a a_1 : Iota), % 189.53/189.75 Eq % 189.53/189.75 (Exists fun Y2 => % 189.53/189.75 Exists fun Y4 => % 189.53/189.75 And (Exists fun Y5 => And (id Y4 Y5) (r4 Y2 Y2 Y5)) % 189.53/189.75 (Exists fun Y6 => And (r4 a a Y6) (Exists fun Y7 => And (r4 a_1 a_1 Y7) (r3 Y7 Y6 Y4)))) % 189.53/189.75 False % 189.53/189.75 Clause #375 (by clausification #[374]): ∀ (a a_1 a_2 : Iota), % 189.53/189.75 Eq % 189.53/189.75 (Exists fun Y4 => % 189.53/189.75 And (Exists fun Y5 => And (id Y4 Y5) (r4 a a Y5)) % 189.53/189.75 (Exists fun Y6 => And (r4 a_1 a_1 Y6) (Exists fun Y7 => And (r4 a_2 a_2 Y7) (r3 Y7 Y6 Y4)))) % 189.53/189.75 False % 189.53/189.75 Clause #376 (by clausification #[375]): ∀ (a a_1 a_2 a_3 : Iota), % 189.53/189.75 Eq % 189.53/189.75 (And (Exists fun Y5 => And (id a Y5) (r4 a_1 a_1 Y5)) % 189.53/189.75 (Exists fun Y6 => And (r4 a_2 a_2 Y6) (Exists fun Y7 => And (r4 a_3 a_3 Y7) (r3 Y7 Y6 a)))) % 189.53/189.75 False % 189.53/189.75 Clause #377 (by clausification #[376]): ∀ (a a_1 a_2 a_3 : Iota), % 189.53/189.75 Or (Eq (Exists fun Y5 => And (id a Y5) (r4 a_1 a_1 Y5)) False) % 189.53/189.75 (Eq (Exists fun Y6 => And (r4 a_2 a_2 Y6) (Exists fun Y7 => And (r4 a_3 a_3 Y7) (r3 Y7 Y6 a))) False) % 189.53/189.75 Clause #378 (by clausification #[377]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 189.53/189.75 Or (Eq (Exists fun Y6 => And (r4 a a Y6) (Exists fun Y7 => And (r4 a_1 a_1 Y7) (r3 Y7 Y6 a_2))) False) % 189.53/189.75 (Eq (And (id a_2 a_3) (r4 a_4 a_4 a_3)) False) % 189.53/189.75 Clause #379 (by clausification #[378]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 189.53/189.75 Or (Eq (And (id a a_1) (r4 a_2 a_2 a_1)) False) % 189.53/189.75 (Eq (And (r4 a_3 a_3 a_4) (Exists fun Y7 => And (r4 a_5 a_5 Y7) (r3 Y7 a_4 a))) False) % 189.53/189.75 Clause #380 (by clausification #[379]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 189.53/189.75 Or (Eq (And (r4 a a a_1) (Exists fun Y7 => And (r4 a_2 a_2 Y7) (r3 Y7 a_1 a_3))) False) % 189.53/189.75 (Or (Eq (id a_3 a_4) False) (Eq (r4 a_5 a_5 a_4) False)) % 189.53/189.75 Clause #381 (by clausification #[380]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 189.53/189.75 Or (Eq (id a a_1) False) % 189.53/189.75 (Or (Eq (r4 a_2 a_2 a_1) False) % 189.53/189.75 (Or (Eq (r4 a_3 a_3 a_4) False) (Eq (Exists fun Y7 => And (r4 a_5 a_5 Y7) (r3 Y7 a_4 a)) False))) % 189.53/189.75 Clause #382 (by clausification #[381]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota), % 189.53/189.75 Or (Eq (id a a_1) False) % 189.53/189.75 (Or (Eq (r4 a_2 a_2 a_1) False) (Or (Eq (r4 a_3 a_3 a_4) False) (Eq (And (r4 a_5 a_5 a_6) (r3 a_6 a_4 a)) False))) % 189.53/189.75 Clause #383 (by clausification #[382]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota), % 189.53/189.75 Or (Eq (id a a_1) False) % 189.53/189.75 (Or (Eq (r4 a_2 a_2 a_1) False) % 189.53/189.75 (Or (Eq (r4 a_3 a_3 a_4) False) (Or (Eq (r4 a_5 a_5 a_6) False) (Eq (r3 a_6 a_4 a) False)))) % 189.53/189.75 Clause #403 (by clausification #[38]): ∀ (a a_1 : Iota), Or (Eq (id a (skS.0 0 a_1)) True) (Eq (Not (r1 a)) True) % 189.53/189.75 Clause #408 (by clausification #[403]): ∀ (a a_1 : Iota), Or (Eq (id a (skS.0 0 a_1)) True) (Eq (r1 a) False) % 189.53/189.75 Clause #409 (by superposition #[408, 44]): ∀ (a a_1 : Iota), Or (Eq (id (skS.0 0 a) (skS.0 0 a_1)) True) (Eq False True) % 189.53/189.75 Clause #410 (by superposition #[408, 59]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (id (skS.0 2 a a_1 a_2) (skS.0 0 a_3)) True) (Eq False True) % 189.53/189.75 Clause #414 (by superposition #[408, 320]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (id (skS.0 12 a a_1 a_2) (skS.0 0 a_3)) True) (Eq False True) % 189.53/189.75 Clause #425 (by clausification #[409]): ∀ (a a_1 : Iota), Eq (id (skS.0 0 a) (skS.0 0 a_1)) True % 189.53/189.75 Clause #435 (by superposition #[425, 383]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota), % 189.53/189.75 Or (Eq True False) % 189.53/189.75 (Or (Eq (r4 a a (skS.0 0 a_1)) False) % 189.53/189.75 (Or (Eq (r4 a_2 a_2 a_3) False) (Or (Eq (r4 a_4 a_4 a_5) False) (Eq (r3 a_5 a_3 (skS.0 0 a_6)) False)))) % 189.53/189.75 Clause #448 (by clausification #[410]): ∀ (a a_1 a_2 a_3 : Iota), Eq (id (skS.0 2 a a_1 a_2) (skS.0 0 a_3)) True % 189.53/189.75 Clause #450 (by superposition #[448, 23]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (id (skS.0 0 a) (skS.0 2 a_1 a_2 a_3)) True) (Eq True False) % 189.53/189.75 Clause #461 (by clausification #[105]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (id a (skS.0 5 a_1 a_2 a_3)) True) (Eq (Not (r4 a_1 a_2 a)) True) % 189.53/189.78 Clause #463 (by clausification #[461]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (id a (skS.0 5 a_1 a_2 a_3)) True) (Eq (r4 a_1 a_2 a) False) % 189.53/189.78 Clause #468 (by clausification #[450]): ∀ (a a_1 a_2 a_3 : Iota), Eq (id (skS.0 0 a) (skS.0 2 a_1 a_2 a_3)) True % 189.53/189.78 Clause #492 (by clausification #[414]): ∀ (a a_1 a_2 a_3 : Iota), Eq (id (skS.0 12 a a_1 a_2) (skS.0 0 a_3)) True % 189.53/189.78 Clause #494 (by superposition #[492, 23]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (id (skS.0 0 a) (skS.0 12 a_1 a_2 a_3)) True) (Eq True False) % 189.53/189.78 Clause #504 (by clausification #[494]): ∀ (a a_1 a_2 a_3 : Iota), Eq (id (skS.0 0 a) (skS.0 12 a_1 a_2 a_3)) True % 189.53/189.78 Clause #571 (by clausification #[177]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 189.53/189.78 Or (Eq (And (Not (r3 a a_1 a_2)) (Not (r3 a_3 a_4 a_5))) True) % 189.53/189.78 (Or (Eq (r3 a a_1 a_2) True) (Or (Eq (Or (Not (id a a_3)) (Not (id a_1 a_4))) True) (Eq (Not (id a_2 a_5)) True))) % 189.53/189.78 Clause #572 (by clausification #[571]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 189.53/189.78 Or (Eq (r3 a a_1 a_2) True) % 189.53/189.78 (Or (Eq (Or (Not (id a a_3)) (Not (id a_1 a_4))) True) % 189.53/189.78 (Or (Eq (Not (id a_2 a_5)) True) (Eq (Not (r3 a_3 a_4 a_5)) True))) % 189.53/189.78 Clause #574 (by clausification #[572]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 189.53/189.78 Or (Eq (r3 a a_1 a_2) True) % 189.53/189.78 (Or (Eq (Not (id a_2 a_3)) True) % 189.53/189.78 (Or (Eq (Not (r3 a_4 a_5 a_3)) True) (Or (Eq (Not (id a a_4)) True) (Eq (Not (id a_1 a_5)) True)))) % 189.53/189.78 Clause #575 (by clausification #[574]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 189.53/189.78 Or (Eq (r3 a a_1 a_2) True) % 189.53/189.78 (Or (Eq (Not (r3 a_3 a_4 a_5)) True) % 189.53/189.78 (Or (Eq (Not (id a a_3)) True) (Or (Eq (Not (id a_1 a_4)) True) (Eq (id a_2 a_5) False)))) % 189.53/189.78 Clause #576 (by clausification #[575]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 189.53/189.78 Or (Eq (r3 a a_1 a_2) True) % 189.53/189.78 (Or (Eq (Not (id a a_3)) True) % 189.53/189.78 (Or (Eq (Not (id a_1 a_4)) True) (Or (Eq (id a_2 a_5) False) (Eq (r3 a_3 a_4 a_5) False)))) % 189.53/189.78 Clause #577 (by clausification #[576]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 189.53/189.78 Or (Eq (r3 a a_1 a_2) True) % 189.53/189.78 (Or (Eq (Not (id a_1 a_3)) True) % 189.53/189.78 (Or (Eq (id a_2 a_4) False) (Or (Eq (r3 a_5 a_3 a_4) False) (Eq (id a a_5) False)))) % 189.53/189.78 Clause #578 (by clausification #[577]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 189.53/189.78 Or (Eq (r3 a a_1 a_2) True) % 189.53/189.78 (Or (Eq (id a_2 a_3) False) (Or (Eq (r3 a_4 a_5 a_3) False) (Or (Eq (id a a_4) False) (Eq (id a_1 a_5) False)))) % 189.53/189.78 Clause #590 (by superposition #[578, 75]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 189.53/189.78 Or (Eq (r3 a a_1 a_2) True) % 189.53/189.78 (Or (Eq (r3 a_3 a_4 (skS.0 1 a_2 a_5)) False) % 189.53/189.78 (Or (Eq (id a a_3) False) (Or (Eq (id a_1 a_4) False) (Eq False True)))) % 189.53/189.78 Clause #626 (by clausification #[180]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 189.53/189.78 Or (Eq (r3 a a_1 a_2) True) % 189.53/189.78 (Or (Eq (Not (id a_3 a_2)) True) % 189.53/189.78 (Or (Eq (Not (r3 a_4 a_5 a_3)) True) (Or (Eq (Not (id a_4 a)) True) (Eq (Not (id a_5 a_1)) True)))) % 189.53/189.78 Clause #627 (by clausification #[626]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 189.53/189.78 Or (Eq (r3 a a_1 a_2) True) % 189.53/189.78 (Or (Eq (Not (r3 a_3 a_4 a_5)) True) % 189.53/189.78 (Or (Eq (Not (id a_3 a)) True) (Or (Eq (Not (id a_4 a_1)) True) (Eq (id a_5 a_2) False)))) % 189.53/189.78 Clause #628 (by clausification #[627]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 189.53/189.78 Or (Eq (r3 a a_1 a_2) True) % 189.53/189.78 (Or (Eq (Not (id a_3 a)) True) % 189.53/189.78 (Or (Eq (Not (id a_4 a_1)) True) (Or (Eq (id a_5 a_2) False) (Eq (r3 a_3 a_4 a_5) False)))) % 189.53/189.78 Clause #629 (by clausification #[628]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 189.53/189.78 Or (Eq (r3 a a_1 a_2) True) % 189.53/189.78 (Or (Eq (Not (id a_3 a_1)) True) % 189.53/189.78 (Or (Eq (id a_4 a_2) False) (Or (Eq (r3 a_5 a_3 a_4) False) (Eq (id a_5 a) False)))) % 189.53/189.78 Clause #630 (by clausification #[629]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 189.53/189.78 Or (Eq (r3 a a_1 a_2) True) % 189.53/189.78 (Or (Eq (id a_3 a_2) False) (Or (Eq (r3 a_4 a_5 a_3) False) (Or (Eq (id a_4 a) False) (Eq (id a_5 a_1) False)))) % 189.53/189.78 Clause #647 (by superposition #[630, 19]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 189.53/189.78 Or (Eq (r3 a a_1 a_2) True) % 189.53/189.78 (Or (Eq (r3 a_3 a_4 a_2) False) (Or (Eq (id a_3 a) False) (Or (Eq (id a_4 a_1) False) (Eq False True)))) % 189.53/189.78 Clause #648 (by clausification #[647]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 189.53/189.81 Or (Eq (r3 a a_1 a_2) True) (Or (Eq (r3 a_3 a_4 a_2) False) (Or (Eq (id a_3 a) False) (Eq (id a_4 a_1) False))) % 189.53/189.81 Clause #692 (by clausification #[202]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 189.53/189.81 Or (Eq (And (Not (r4 a a_1 a_2)) (Not (r4 a_3 a_4 a_5))) True) % 189.53/189.81 (Or (Eq (r4 a a_1 a_2) True) (Or (Eq (Or (Not (id a a_3)) (Not (id a_1 a_4))) True) (Eq (Not (id a_2 a_5)) True))) % 189.53/189.81 Clause #693 (by clausification #[692]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 189.53/189.81 Or (Eq (r4 a a_1 a_2) True) % 189.53/189.81 (Or (Eq (Or (Not (id a a_3)) (Not (id a_1 a_4))) True) % 189.53/189.81 (Or (Eq (Not (id a_2 a_5)) True) (Eq (Not (r4 a_3 a_4 a_5)) True))) % 189.53/189.81 Clause #695 (by clausification #[693]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 189.53/189.81 Or (Eq (r4 a a_1 a_2) True) % 189.53/189.81 (Or (Eq (Not (id a_2 a_3)) True) % 189.53/189.81 (Or (Eq (Not (r4 a_4 a_5 a_3)) True) (Or (Eq (Not (id a a_4)) True) (Eq (Not (id a_1 a_5)) True)))) % 189.53/189.81 Clause #696 (by clausification #[695]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 189.53/189.81 Or (Eq (r4 a a_1 a_2) True) % 189.53/189.81 (Or (Eq (Not (r4 a_3 a_4 a_5)) True) % 189.53/189.81 (Or (Eq (Not (id a a_3)) True) (Or (Eq (Not (id a_1 a_4)) True) (Eq (id a_2 a_5) False)))) % 189.53/189.81 Clause #697 (by clausification #[696]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 189.53/189.81 Or (Eq (r4 a a_1 a_2) True) % 189.53/189.81 (Or (Eq (Not (id a a_3)) True) % 189.53/189.81 (Or (Eq (Not (id a_1 a_4)) True) (Or (Eq (id a_2 a_5) False) (Eq (r4 a_3 a_4 a_5) False)))) % 189.53/189.81 Clause #698 (by clausification #[697]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 189.53/189.81 Or (Eq (r4 a a_1 a_2) True) % 189.53/189.81 (Or (Eq (Not (id a_1 a_3)) True) % 189.53/189.81 (Or (Eq (id a_2 a_4) False) (Or (Eq (r4 a_5 a_3 a_4) False) (Eq (id a a_5) False)))) % 189.53/189.81 Clause #699 (by clausification #[698]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 189.53/189.81 Or (Eq (r4 a a_1 a_2) True) % 189.53/189.81 (Or (Eq (id a_2 a_3) False) (Or (Eq (r4 a_4 a_5 a_3) False) (Or (Eq (id a a_4) False) (Eq (id a_1 a_5) False)))) % 189.53/189.81 Clause #718 (by superposition #[699, 19]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 189.53/189.81 Or (Eq (r4 a a_1 a_2) True) % 189.53/189.81 (Or (Eq (r4 a_3 a_4 a_2) False) (Or (Eq (id a a_3) False) (Or (Eq (id a_1 a_4) False) (Eq False True)))) % 189.53/189.81 Clause #719 (by clausification #[718]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 189.53/189.81 Or (Eq (r4 a a_1 a_2) True) (Or (Eq (r4 a_3 a_4 a_2) False) (Or (Eq (id a a_3) False) (Eq (id a_1 a_4) False))) % 189.53/189.81 Clause #720 (by superposition #[719, 319]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 189.53/189.81 Or (Eq (r4 a a_1 (skS.0 10 a_2 a_3)) True) % 189.53/189.81 (Or (Eq (id a a_2) False) (Or (Eq (id a_1 (skS.0 12 a_2 a_3 a_4)) False) (Eq False True))) % 189.53/189.81 Clause #1314 (by clausification #[327]): ∀ (a a_1 a_2 : Iota), Or (Eq (r1 (skS.0 10 a a_1)) True) (Eq (r1 (skS.0 11 a a_1 a_2)) False) % 189.53/189.81 Clause #1315 (by superposition #[1314, 314]): ∀ (a a_1 : Iota), Or (Eq (r1 (skS.0 10 a a_1)) True) (Eq False True) % 189.53/189.81 Clause #1316 (by clausification #[1315]): ∀ (a a_1 : Iota), Eq (r1 (skS.0 10 a a_1)) True % 189.53/189.81 Clause #1320 (by superposition #[1316, 408]): ∀ (a a_1 a_2 : Iota), Or (Eq (id (skS.0 10 a a_1) (skS.0 0 a_2)) True) (Eq True False) % 189.53/189.81 Clause #1321 (by clausification #[1320]): ∀ (a a_1 a_2 : Iota), Eq (id (skS.0 10 a a_1) (skS.0 0 a_2)) True % 189.53/189.81 Clause #1326 (by superposition #[1321, 31]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (id a (skS.0 0 a_1)) True) (Or (Eq True False) (Eq (id a (skS.0 10 a_2 a_3)) False)) % 189.53/189.81 Clause #1674 (by clausification #[1326]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (id a (skS.0 0 a_1)) True) (Eq (id a (skS.0 10 a_2 a_3)) False) % 189.53/189.81 Clause #4859 (by clausification #[590]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 189.53/189.81 Or (Eq (r3 a a_1 a_2) True) % 189.53/189.81 (Or (Eq (r3 a_3 a_4 (skS.0 1 a_2 a_5)) False) (Or (Eq (id a a_3) False) (Eq (id a_1 a_4) False))) % 189.53/189.81 Clause #4860 (by superposition #[4859, 58]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 189.53/189.81 Or (Eq (r3 a a_1 a_2) True) (Or (Eq (id a a_2) False) (Or (Eq (id a_1 (skS.0 2 a_2 a_3 a_4)) False) (Eq False True))) % 189.53/189.81 Clause #4861 (by clausification #[4860]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 189.53/189.81 Or (Eq (r3 a a_1 a_2) True) (Or (Eq (id a a_2) False) (Eq (id a_1 (skS.0 2 a_2 a_3 a_4)) False)) % 189.53/189.81 Clause #4942 (by superposition #[4861, 19]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (r3 a a_1 a) True) (Or (Eq (id a_1 (skS.0 2 a a_2 a_3)) False) (Eq False True)) % 189.53/189.81 Clause #4943 (by clausification #[4942]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (r3 a a_1 a) True) (Eq (id a_1 (skS.0 2 a a_2 a_3)) False) % 189.62/189.83 Clause #4944 (by superposition #[4943, 468]): ∀ (a a_1 : Iota), Or (Eq (r3 a (skS.0 0 a_1) a) True) (Eq False True) % 189.62/189.83 Clause #4959 (by clausification #[4944]): ∀ (a a_1 : Iota), Eq (r3 a (skS.0 0 a_1) a) True % 189.62/189.83 Clause #4963 (by superposition #[4959, 648]): ∀ (a a_1 a_2 a_3 : Iota), % 189.62/189.83 Or (Eq (r3 a a_1 a_2) True) (Or (Eq True False) (Or (Eq (id a_2 a) False) (Eq (id (skS.0 0 a_3) a_1) False))) % 189.62/189.83 Clause #4998 (by clausification #[4963]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (r3 a a_1 a_2) True) (Or (Eq (id a_2 a) False) (Eq (id (skS.0 0 a_3) a_1) False)) % 189.62/189.83 Clause #5000 (by superposition #[4998, 425]): ∀ (a a_1 a_2 a_3 : Iota), % 189.62/189.83 Or (Eq (r3 (skS.0 0 a) a_1 (skS.0 0 a_2)) True) (Or (Eq (id (skS.0 0 a_3) a_1) False) (Eq False True)) % 189.62/189.83 Clause #8338 (by clausification #[5000]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (r3 (skS.0 0 a) a_1 (skS.0 0 a_2)) True) (Eq (id (skS.0 0 a_3) a_1) False) % 189.62/189.83 Clause #8339 (by superposition #[8338, 425]): ∀ (a a_1 a_2 : Iota), Or (Eq (r3 (skS.0 0 a) (skS.0 0 a_1) (skS.0 0 a_2)) True) (Eq False True) % 189.62/189.83 Clause #8366 (by clausification #[8339]): ∀ (a a_1 a_2 : Iota), Eq (r3 (skS.0 0 a) (skS.0 0 a_1) (skS.0 0 a_2)) True % 189.62/189.83 Clause #9212 (by clausification #[435]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota), % 189.62/189.83 Or (Eq (r4 a a (skS.0 0 a_1)) False) % 189.62/189.83 (Or (Eq (r4 a_2 a_2 a_3) False) (Or (Eq (r4 a_4 a_4 a_5) False) (Eq (r3 a_5 a_3 (skS.0 0 a_6)) False))) % 189.62/189.83 Clause #30058 (by clausification #[720]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 189.62/189.83 Or (Eq (r4 a a_1 (skS.0 10 a_2 a_3)) True) (Or (Eq (id a a_2) False) (Eq (id a_1 (skS.0 12 a_2 a_3 a_4)) False)) % 189.62/189.83 Clause #30223 (by superposition #[30058, 19]): ∀ (a a_1 a_2 a_3 : Iota), % 189.62/189.83 Or (Eq (r4 a a_1 (skS.0 10 a a_2)) True) (Or (Eq (id a_1 (skS.0 12 a a_2 a_3)) False) (Eq False True)) % 189.62/189.83 Clause #30224 (by clausification #[30223]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (r4 a a_1 (skS.0 10 a a_2)) True) (Eq (id a_1 (skS.0 12 a a_2 a_3)) False) % 189.62/189.83 Clause #30225 (by superposition #[30224, 504]): ∀ (a a_1 a_2 : Iota), Or (Eq (r4 a (skS.0 0 a_1) (skS.0 10 a a_2)) True) (Eq False True) % 189.62/189.83 Clause #30261 (by clausification #[30225]): ∀ (a a_1 a_2 : Iota), Eq (r4 a (skS.0 0 a_1) (skS.0 10 a a_2)) True % 189.62/189.83 Clause #30265 (by superposition #[30261, 463]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (id (skS.0 10 a a_1) (skS.0 5 a (skS.0 0 a_2) a_3)) True) (Eq True False) % 189.62/189.83 Clause #31228 (by clausification #[30265]): ∀ (a a_1 a_2 a_3 : Iota), Eq (id (skS.0 10 a a_1) (skS.0 5 a (skS.0 0 a_2) a_3)) True % 189.62/189.83 Clause #31235 (by superposition #[31228, 23]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (id (skS.0 5 a (skS.0 0 a_1) a_2) (skS.0 10 a a_3)) True) (Eq True False) % 189.62/189.83 Clause #31585 (by clausification #[31235]): ∀ (a a_1 a_2 a_3 : Iota), Eq (id (skS.0 5 a (skS.0 0 a_1) a_2) (skS.0 10 a a_3)) True % 189.62/189.83 Clause #31586 (by superposition #[31585, 1674]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (id (skS.0 5 a (skS.0 0 a_1) a_2) (skS.0 0 a_3)) True) (Eq True False) % 189.62/189.83 Clause #31663 (by clausification #[31586]): ∀ (a a_1 a_2 a_3 : Iota), Eq (id (skS.0 5 a (skS.0 0 a_1) a_2) (skS.0 0 a_3)) True % 189.62/189.83 Clause #31677 (by superposition #[31663, 23]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (id (skS.0 0 a) (skS.0 5 a_1 (skS.0 0 a_2) a_3)) True) (Eq True False) % 189.62/189.83 Clause #32044 (by clausification #[31677]): ∀ (a a_1 a_2 a_3 : Iota), Eq (id (skS.0 0 a) (skS.0 5 a_1 (skS.0 0 a_2) a_3)) True % 189.62/189.83 Clause #32045 (by superposition #[32044, 108]): ∀ (a a_1 a_2 : Iota), Or (Eq (r4 a (skS.0 0 a_1) (skS.0 0 a_2)) True) (Eq True False) % 189.62/189.83 Clause #32119 (by clausification #[32045]): ∀ (a a_1 a_2 : Iota), Eq (r4 a (skS.0 0 a_1) (skS.0 0 a_2)) True % 189.62/189.83 Clause #32120 (by superposition #[32119, 9212]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 189.62/189.83 Or (Eq True False) (Or (Eq (r4 a a a_1) False) (Or (Eq (r4 a_2 a_2 a_3) False) (Eq (r3 a_3 a_1 (skS.0 0 a_4)) False))) % 189.62/189.83 Clause #32138 (by clausification #[32120]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 189.62/189.83 Or (Eq (r4 a a a_1) False) (Or (Eq (r4 a_2 a_2 a_3) False) (Eq (r3 a_3 a_1 (skS.0 0 a_4)) False)) % 189.62/189.83 Clause #32156 (by superposition #[32138, 32119]): ∀ (a a_1 a_2 a_3 : Iota), % 189.90/190.13 Or (Eq (r4 a a a_1) False) (Or (Eq (r3 a_1 (skS.0 0 a_2) (skS.0 0 a_3)) False) (Eq False True)) % 189.90/190.13 Clause #32163 (by clausification #[32156]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (r4 a a a_1) False) (Eq (r3 a_1 (skS.0 0 a_2) (skS.0 0 a_3)) False) % 189.90/190.13 Clause #32181 (by superposition #[32163, 32119]): ∀ (a a_1 a_2 : Iota), Or (Eq (r3 (skS.0 0 a) (skS.0 0 a_1) (skS.0 0 a_2)) False) (Eq False True) % 189.90/190.13 Clause #32188 (by clausification #[32181]): ∀ (a a_1 a_2 : Iota), Eq (r3 (skS.0 0 a) (skS.0 0 a_1) (skS.0 0 a_2)) False % 189.90/190.13 Clause #32189 (by superposition #[32188, 8366]): Eq False True % 189.90/190.13 Clause #32225 (by clausification #[32189]): False % 189.90/190.13 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------