%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : NUN070+1 : TPTP v9.2.0. Released v7.3.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n003.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 07:57:48 PM UTC 2025 % Result : Theorem 20.81s 21.02s % Output : Proof 20.99s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : NUN070+1 : TPTP v9.2.0. Released v7.3.0. % 0.03/0.13 % Command : duper %s % 0.13/0.34 % Computer : n003.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 11:42:23 EDT 2025 % 0.13/0.34 % CPUTime : % 20.81/21.02 SZS status Theorem for theBenchmark.p % 20.81/21.02 SZS output start Proof for theBenchmark.p % 20.81/21.02 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 % 20.81/21.02 Clause #1 (by assumption #[]): Eq % 20.81/21.02 (∀ (X11 : Iota), % 20.81/21.02 Exists fun Y21 => ∀ (X12 : Iota), Or (And (id X12 Y21) (r2 X11 X12)) (And (Not (r2 X11 X12)) (Not (id X12 Y21)))) % 20.81/21.02 True % 20.81/21.02 Clause #4 (by assumption #[]): Eq (∀ (X20 : Iota), id X20 X20) True % 20.81/21.02 Clause #5 (by assumption #[]): Eq (∀ (X21 X22 : Iota), Or (Not (id X21 X22)) (id X22 X21)) True % 20.81/21.02 Clause #8 (by assumption #[]): Eq % 20.81/21.02 (∀ (X28 X29 X30 X31 : Iota), % 20.81/21.02 Or (Or (Or (Not (id X28 X30)) (Not (id X29 X31))) (And (Not (r2 X28 X29)) (Not (r2 X30 X31)))) % 20.81/21.02 (And (r2 X28 X29) (r2 X30 X31))) % 20.81/21.02 True % 20.81/21.02 Clause #9 (by assumption #[]): Eq % 20.81/21.02 (∀ (X32 X33 X34 X35 X36 X37 : Iota), % 20.81/21.02 Or % 20.81/21.02 (Or (Or (Or (Not (id X32 X35)) (Not (id X33 X36))) (Not (id X34 X37))) % 20.81/21.02 (And (Not (r3 X32 X33 X34)) (Not (r3 X35 X36 X37)))) % 20.81/21.02 (And (r3 X32 X33 X34) (r3 X35 X36 X37))) % 20.81/21.02 True % 20.81/21.02 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 % 20.81/21.02 Clause #18 (by assumption #[]): Eq % 20.81/21.02 (Not % 20.81/21.02 (Exists fun Y1 => % 20.81/21.02 And (Exists fun Y2 => And (Exists fun Y4 => And (r1 Y4) (r3 Y2 Y4 Y1)) (Exists fun Y5 => And (r1 Y5) (r2 Y5 Y2))) % 20.81/21.02 (Exists fun Y3 => And (id Y1 Y3) (Exists fun Y6 => And (r1 Y6) (r2 Y6 Y3))))) % 20.81/21.02 True % 20.81/21.02 Clause #19 (by clausification #[4]): ∀ (a : Iota), Eq (id a a) True % 20.81/21.02 Clause #20 (by clausification #[5]): ∀ (a : Iota), Eq (∀ (X22 : Iota), Or (Not (id a X22)) (id X22 a)) True % 20.81/21.02 Clause #21 (by clausification #[20]): ∀ (a a_1 : Iota), Eq (Or (Not (id a a_1)) (id a_1 a)) True % 20.81/21.02 Clause #22 (by clausification #[21]): ∀ (a a_1 : Iota), Or (Eq (Not (id a a_1)) True) (Eq (id a_1 a) True) % 20.81/21.02 Clause #23 (by clausification #[22]): ∀ (a a_1 : Iota), Or (Eq (id a a_1) True) (Eq (id a_1 a) False) % 20.81/21.02 Clause #34 (by clausification #[0]): ∀ (a : Iota), % 20.81/21.02 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 % 20.81/21.02 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 % 20.81/21.02 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) % 20.81/21.02 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) % 20.81/21.02 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) % 20.81/21.02 Clause #39 (by clausification #[37]): ∀ (a a_1 : Iota), Or (Eq (r1 a) True) (Eq (Not (id a (skS.0 0 a_1))) True) % 20.81/21.02 Clause #41 (by clausification #[39]): ∀ (a a_1 : Iota), Or (Eq (r1 a) True) (Eq (id a (skS.0 0 a_1)) False) % 20.81/21.02 Clause #42 (by superposition #[41, 19]): ∀ (a : Iota), Or (Eq (r1 (skS.0 0 a)) True) (Eq False True) % 20.81/21.02 Clause #44 (by clausification #[42]): ∀ (a : Iota), Eq (r1 (skS.0 0 a)) True % 20.81/21.02 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 % 20.81/21.02 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 % 20.81/21.02 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 % 20.81/21.02 Clause #56 (by clausification #[54]): ∀ (a a_1 : Iota), Eq (id (skS.0 1 a a_1) a) True % 20.81/21.02 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 % 20.81/21.02 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 % 20.81/21.02 Clause #59 (by clausification #[57]): ∀ (a a_1 a_2 : Iota), Eq (r1 (skS.0 2 a a_1 a_2)) True % 20.81/21.02 Clause #61 (by superposition #[56, 23]): ∀ (a a_1 : Iota), Or (Eq (id a (skS.0 1 a a_1)) True) (Eq True False) % 20.89/21.05 Clause #63 (by clausification #[1]): ∀ (a : Iota), % 20.89/21.05 Eq (Exists fun Y21 => ∀ (X12 : Iota), Or (And (id X12 Y21) (r2 a X12)) (And (Not (r2 a X12)) (Not (id X12 Y21)))) True % 20.89/21.05 Clause #64 (by clausification #[63]): ∀ (a a_1 : Iota), % 20.89/21.05 Eq % 20.89/21.05 (∀ (X12 : Iota), Or (And (id X12 (skS.0 3 a a_1)) (r2 a X12)) (And (Not (r2 a X12)) (Not (id X12 (skS.0 3 a a_1))))) % 20.89/21.05 True % 20.89/21.05 Clause #65 (by clausification #[64]): ∀ (a a_1 a_2 : Iota), % 20.89/21.05 Eq (Or (And (id a (skS.0 3 a_1 a_2)) (r2 a_1 a)) (And (Not (r2 a_1 a)) (Not (id a (skS.0 3 a_1 a_2))))) True % 20.89/21.05 Clause #66 (by clausification #[65]): ∀ (a a_1 a_2 : Iota), % 20.89/21.05 Or (Eq (And (id a (skS.0 3 a_1 a_2)) (r2 a_1 a)) True) (Eq (And (Not (r2 a_1 a)) (Not (id a (skS.0 3 a_1 a_2)))) True) % 20.89/21.05 Clause #67 (by clausification #[66]): ∀ (a a_1 a_2 : Iota), Or (Eq (And (Not (r2 a a_1)) (Not (id a_1 (skS.0 3 a a_2)))) True) (Eq (r2 a a_1) True) % 20.89/21.05 Clause #69 (by clausification #[67]): ∀ (a a_1 a_2 : Iota), Or (Eq (r2 a a_1) True) (Eq (Not (id a_1 (skS.0 3 a a_2))) True) % 20.89/21.05 Clause #71 (by clausification #[69]): ∀ (a a_1 a_2 : Iota), Or (Eq (r2 a a_1) True) (Eq (id a_1 (skS.0 3 a a_2)) False) % 20.89/21.05 Clause #73 (by superposition #[71, 19]): ∀ (a a_1 : Iota), Or (Eq (r2 a (skS.0 3 a a_1)) True) (Eq False True) % 20.89/21.05 Clause #75 (by clausification #[61]): ∀ (a a_1 : Iota), Eq (id a (skS.0 1 a a_1)) True % 20.89/21.05 Clause #78 (by clausification #[73]): ∀ (a a_1 : Iota), Eq (r2 a (skS.0 3 a a_1)) True % 20.89/21.05 Clause #139 (by clausification #[8]): ∀ (a : Iota), % 20.89/21.05 Eq % 20.89/21.05 (∀ (X29 X30 X31 : Iota), % 20.89/21.05 Or (Or (Or (Not (id a X30)) (Not (id X29 X31))) (And (Not (r2 a X29)) (Not (r2 X30 X31)))) % 20.89/21.05 (And (r2 a X29) (r2 X30 X31))) % 20.89/21.05 True % 20.89/21.05 Clause #140 (by clausification #[139]): ∀ (a a_1 : Iota), % 20.89/21.05 Eq % 20.89/21.05 (∀ (X30 X31 : Iota), % 20.89/21.05 Or (Or (Or (Not (id a X30)) (Not (id a_1 X31))) (And (Not (r2 a a_1)) (Not (r2 X30 X31)))) % 20.89/21.05 (And (r2 a a_1) (r2 X30 X31))) % 20.89/21.05 True % 20.89/21.05 Clause #141 (by clausification #[140]): ∀ (a a_1 a_2 : Iota), % 20.89/21.05 Eq % 20.89/21.05 (∀ (X31 : Iota), % 20.89/21.05 Or (Or (Or (Not (id a a_1)) (Not (id a_2 X31))) (And (Not (r2 a a_2)) (Not (r2 a_1 X31)))) % 20.89/21.05 (And (r2 a a_2) (r2 a_1 X31))) % 20.89/21.05 True % 20.89/21.05 Clause #142 (by clausification #[141]): ∀ (a a_1 a_2 a_3 : Iota), % 20.89/21.05 Eq % 20.89/21.05 (Or (Or (Or (Not (id a a_1)) (Not (id a_2 a_3))) (And (Not (r2 a a_2)) (Not (r2 a_1 a_3)))) % 20.89/21.05 (And (r2 a a_2) (r2 a_1 a_3))) % 20.89/21.05 True % 20.89/21.05 Clause #143 (by clausification #[142]): ∀ (a a_1 a_2 a_3 : Iota), % 20.89/21.05 Or (Eq (Or (Or (Not (id a a_1)) (Not (id a_2 a_3))) (And (Not (r2 a a_2)) (Not (r2 a_1 a_3)))) True) % 20.89/21.05 (Eq (And (r2 a a_2) (r2 a_1 a_3)) True) % 20.89/21.05 Clause #144 (by clausification #[143]): ∀ (a a_1 a_2 a_3 : Iota), % 20.89/21.05 Or (Eq (And (r2 a a_1) (r2 a_2 a_3)) True) % 20.89/21.05 (Or (Eq (Or (Not (id a a_2)) (Not (id a_1 a_3))) True) (Eq (And (Not (r2 a a_1)) (Not (r2 a_2 a_3))) True)) % 20.89/21.05 Clause #145 (by clausification #[144]): ∀ (a a_1 a_2 a_3 : Iota), % 20.89/21.05 Or (Eq (Or (Not (id a a_1)) (Not (id a_2 a_3))) True) % 20.89/21.05 (Or (Eq (And (Not (r2 a a_2)) (Not (r2 a_1 a_3))) True) (Eq (r2 a_1 a_3) True)) % 20.89/21.05 Clause #147 (by clausification #[145]): ∀ (a a_1 a_2 a_3 : Iota), % 20.89/21.05 Or (Eq (And (Not (r2 a a_1)) (Not (r2 a_2 a_3))) True) % 20.89/21.05 (Or (Eq (r2 a_2 a_3) True) (Or (Eq (Not (id a a_2)) True) (Eq (Not (id a_1 a_3)) True))) % 20.89/21.05 Clause #149 (by clausification #[147]): ∀ (a a_1 a_2 a_3 : Iota), % 20.89/21.05 Or (Eq (r2 a a_1) True) (Or (Eq (Not (id a_2 a)) True) (Or (Eq (Not (id a_3 a_1)) True) (Eq (Not (r2 a_2 a_3)) True))) % 20.89/21.05 Clause #158 (by clausification #[149]): ∀ (a a_1 a_2 a_3 : Iota), % 20.89/21.05 Or (Eq (r2 a a_1) True) (Or (Eq (Not (id a_2 a_1)) True) (Or (Eq (Not (r2 a_3 a_2)) True) (Eq (id a_3 a) False))) % 20.89/21.05 Clause #159 (by clausification #[158]): ∀ (a a_1 a_2 a_3 : Iota), % 20.89/21.05 Or (Eq (r2 a a_1) True) (Or (Eq (Not (r2 a_2 a_3)) True) (Or (Eq (id a_2 a) False) (Eq (id a_3 a_1) False))) % 20.89/21.05 Clause #160 (by clausification #[159]): ∀ (a a_1 a_2 a_3 : Iota), % 20.89/21.05 Or (Eq (r2 a a_1) True) (Or (Eq (id a_2 a) False) (Or (Eq (id a_3 a_1) False) (Eq (r2 a_2 a_3) False))) % 20.89/21.05 Clause #168 (by clausification #[9]): ∀ (a : Iota), % 20.89/21.05 Eq % 20.89/21.05 (∀ (X33 X34 X35 X36 X37 : Iota), % 20.89/21.05 Or % 20.89/21.05 (Or (Or (Or (Not (id a X35)) (Not (id X33 X36))) (Not (id X34 X37))) % 20.89/21.08 (And (Not (r3 a X33 X34)) (Not (r3 X35 X36 X37)))) % 20.89/21.08 (And (r3 a X33 X34) (r3 X35 X36 X37))) % 20.89/21.08 True % 20.89/21.08 Clause #169 (by clausification #[168]): ∀ (a a_1 : Iota), % 20.89/21.08 Eq % 20.89/21.08 (∀ (X34 X35 X36 X37 : Iota), % 20.89/21.08 Or % 20.89/21.08 (Or (Or (Or (Not (id a X35)) (Not (id a_1 X36))) (Not (id X34 X37))) % 20.89/21.08 (And (Not (r3 a a_1 X34)) (Not (r3 X35 X36 X37)))) % 20.89/21.08 (And (r3 a a_1 X34) (r3 X35 X36 X37))) % 20.89/21.08 True % 20.89/21.08 Clause #170 (by clausification #[169]): ∀ (a a_1 a_2 : Iota), % 20.89/21.08 Eq % 20.89/21.08 (∀ (X35 X36 X37 : Iota), % 20.89/21.08 Or % 20.89/21.08 (Or (Or (Or (Not (id a X35)) (Not (id a_1 X36))) (Not (id a_2 X37))) % 20.89/21.08 (And (Not (r3 a a_1 a_2)) (Not (r3 X35 X36 X37)))) % 20.89/21.08 (And (r3 a a_1 a_2) (r3 X35 X36 X37))) % 20.89/21.08 True % 20.89/21.08 Clause #171 (by clausification #[170]): ∀ (a a_1 a_2 a_3 : Iota), % 20.89/21.08 Eq % 20.89/21.08 (∀ (X36 X37 : Iota), % 20.89/21.08 Or % 20.89/21.08 (Or (Or (Or (Not (id a a_1)) (Not (id a_2 X36))) (Not (id a_3 X37))) % 20.89/21.08 (And (Not (r3 a a_2 a_3)) (Not (r3 a_1 X36 X37)))) % 20.89/21.08 (And (r3 a a_2 a_3) (r3 a_1 X36 X37))) % 20.89/21.08 True % 20.89/21.08 Clause #172 (by clausification #[171]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 20.89/21.08 Eq % 20.89/21.08 (∀ (X37 : Iota), % 20.89/21.08 Or % 20.89/21.08 (Or (Or (Or (Not (id a a_1)) (Not (id a_2 a_3))) (Not (id a_4 X37))) % 20.89/21.08 (And (Not (r3 a a_2 a_4)) (Not (r3 a_1 a_3 X37)))) % 20.89/21.08 (And (r3 a a_2 a_4) (r3 a_1 a_3 X37))) % 20.89/21.08 True % 20.89/21.08 Clause #173 (by clausification #[172]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 20.89/21.08 Eq % 20.89/21.08 (Or % 20.89/21.08 (Or (Or (Or (Not (id a a_1)) (Not (id a_2 a_3))) (Not (id a_4 a_5))) % 20.89/21.08 (And (Not (r3 a a_2 a_4)) (Not (r3 a_1 a_3 a_5)))) % 20.89/21.08 (And (r3 a a_2 a_4) (r3 a_1 a_3 a_5))) % 20.89/21.08 True % 20.89/21.08 Clause #174 (by clausification #[173]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 20.89/21.08 Or % 20.89/21.08 (Eq % 20.89/21.08 (Or (Or (Or (Not (id a a_1)) (Not (id a_2 a_3))) (Not (id a_4 a_5))) % 20.89/21.08 (And (Not (r3 a a_2 a_4)) (Not (r3 a_1 a_3 a_5)))) % 20.89/21.08 True) % 20.89/21.08 (Eq (And (r3 a a_2 a_4) (r3 a_1 a_3 a_5)) True) % 20.89/21.08 Clause #175 (by clausification #[174]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 20.89/21.08 Or (Eq (And (r3 a a_1 a_2) (r3 a_3 a_4 a_5)) True) % 20.89/21.08 (Or (Eq (Or (Or (Not (id a a_3)) (Not (id a_1 a_4))) (Not (id a_2 a_5))) True) % 20.89/21.08 (Eq (And (Not (r3 a a_1 a_2)) (Not (r3 a_3 a_4 a_5))) True)) % 20.89/21.08 Clause #177 (by clausification #[175]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 20.89/21.08 Or (Eq (Or (Or (Not (id a a_1)) (Not (id a_2 a_3))) (Not (id a_4 a_5))) True) % 20.89/21.08 (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)) % 20.89/21.08 Clause #372 (by clausification #[18]): Eq % 20.89/21.08 (Exists fun Y1 => % 20.89/21.08 And (Exists fun Y2 => And (Exists fun Y4 => And (r1 Y4) (r3 Y2 Y4 Y1)) (Exists fun Y5 => And (r1 Y5) (r2 Y5 Y2))) % 20.89/21.08 (Exists fun Y3 => And (id Y1 Y3) (Exists fun Y6 => And (r1 Y6) (r2 Y6 Y3)))) % 20.89/21.08 False % 20.89/21.08 Clause #373 (by clausification #[372]): ∀ (a : Iota), % 20.89/21.08 Eq % 20.89/21.08 (And (Exists fun Y2 => And (Exists fun Y4 => And (r1 Y4) (r3 Y2 Y4 a)) (Exists fun Y5 => And (r1 Y5) (r2 Y5 Y2))) % 20.89/21.08 (Exists fun Y3 => And (id a Y3) (Exists fun Y6 => And (r1 Y6) (r2 Y6 Y3)))) % 20.89/21.08 False % 20.89/21.08 Clause #374 (by clausification #[373]): ∀ (a : Iota), % 20.89/21.08 Or % 20.89/21.08 (Eq (Exists fun Y2 => And (Exists fun Y4 => And (r1 Y4) (r3 Y2 Y4 a)) (Exists fun Y5 => And (r1 Y5) (r2 Y5 Y2))) % 20.89/21.08 False) % 20.89/21.08 (Eq (Exists fun Y3 => And (id a Y3) (Exists fun Y6 => And (r1 Y6) (r2 Y6 Y3))) False) % 20.89/21.08 Clause #375 (by clausification #[374]): ∀ (a a_1 : Iota), % 20.89/21.08 Or (Eq (Exists fun Y3 => And (id a Y3) (Exists fun Y6 => And (r1 Y6) (r2 Y6 Y3))) False) % 20.89/21.08 (Eq (And (Exists fun Y4 => And (r1 Y4) (r3 a_1 Y4 a)) (Exists fun Y5 => And (r1 Y5) (r2 Y5 a_1))) False) % 20.89/21.08 Clause #376 (by clausification #[375]): ∀ (a a_1 a_2 : Iota), % 20.89/21.08 Or (Eq (And (Exists fun Y4 => And (r1 Y4) (r3 a Y4 a_1)) (Exists fun Y5 => And (r1 Y5) (r2 Y5 a))) False) % 20.89/21.08 (Eq (And (id a_1 a_2) (Exists fun Y6 => And (r1 Y6) (r2 Y6 a_2))) False) % 20.89/21.08 Clause #377 (by clausification #[376]): ∀ (a a_1 a_2 : Iota), % 20.89/21.08 Or (Eq (And (id a a_1) (Exists fun Y6 => And (r1 Y6) (r2 Y6 a_1))) False) % 20.89/21.08 (Or (Eq (Exists fun Y4 => And (r1 Y4) (r3 a_2 Y4 a)) False) (Eq (Exists fun Y5 => And (r1 Y5) (r2 Y5 a_2)) False)) % 20.89/21.08 Clause #378 (by clausification #[377]): ∀ (a a_1 a_2 : Iota), % 20.89/21.11 Or (Eq (Exists fun Y4 => And (r1 Y4) (r3 a Y4 a_1)) False) % 20.89/21.11 (Or (Eq (Exists fun Y5 => And (r1 Y5) (r2 Y5 a)) False) % 20.89/21.11 (Or (Eq (id a_1 a_2) False) (Eq (Exists fun Y6 => And (r1 Y6) (r2 Y6 a_2)) False))) % 20.89/21.11 Clause #379 (by clausification #[378]): ∀ (a a_1 a_2 a_3 : Iota), % 20.89/21.11 Or (Eq (Exists fun Y5 => And (r1 Y5) (r2 Y5 a)) False) % 20.89/21.11 (Or (Eq (id a_1 a_2) False) % 20.89/21.11 (Or (Eq (Exists fun Y6 => And (r1 Y6) (r2 Y6 a_2)) False) (Eq (And (r1 a_3) (r3 a a_3 a_1)) False))) % 20.89/21.11 Clause #380 (by clausification #[379]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 20.89/21.11 Or (Eq (id a a_1) False) % 20.89/21.11 (Or (Eq (Exists fun Y6 => And (r1 Y6) (r2 Y6 a_1)) False) % 20.89/21.11 (Or (Eq (And (r1 a_2) (r3 a_3 a_2 a)) False) (Eq (And (r1 a_4) (r2 a_4 a_3)) False))) % 20.89/21.11 Clause #381 (by clausification #[380]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 20.89/21.11 Or (Eq (id a a_1) False) % 20.89/21.11 (Or (Eq (And (r1 a_2) (r3 a_3 a_2 a)) False) % 20.89/21.11 (Or (Eq (And (r1 a_4) (r2 a_4 a_3)) False) (Eq (And (r1 a_5) (r2 a_5 a_1)) False))) % 20.89/21.11 Clause #382 (by clausification #[381]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 20.89/21.11 Or (Eq (id a a_1) False) % 20.89/21.11 (Or (Eq (And (r1 a_2) (r2 a_2 a_3)) False) % 20.89/21.11 (Or (Eq (And (r1 a_4) (r2 a_4 a_1)) False) (Or (Eq (r1 a_5) False) (Eq (r3 a_3 a_5 a) False)))) % 20.89/21.11 Clause #383 (by clausification #[382]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 20.89/21.11 Or (Eq (id a a_1) False) % 20.89/21.11 (Or (Eq (And (r1 a_2) (r2 a_2 a_1)) False) % 20.89/21.11 (Or (Eq (r1 a_3) False) (Or (Eq (r3 a_4 a_3 a) False) (Or (Eq (r1 a_5) False) (Eq (r2 a_5 a_4) False))))) % 20.89/21.11 Clause #384 (by clausification #[383]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 20.89/21.11 Or (Eq (id a a_1) False) % 20.89/21.11 (Or (Eq (r1 a_2) False) % 20.89/21.11 (Or (Eq (r3 a_3 a_2 a) False) % 20.89/21.11 (Or (Eq (r1 a_4) False) (Or (Eq (r2 a_4 a_3) False) (Or (Eq (r1 a_5) False) (Eq (r2 a_5 a_1) False)))))) % 20.89/21.11 Clause #393 (by superposition #[384, 19]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 20.89/21.11 Or (Eq (r1 a) False) % 20.89/21.11 (Or (Eq (r3 a_1 a a_2) False) % 20.89/21.11 (Or (Eq (r1 a_3) False) % 20.89/21.11 (Or (Eq (r2 a_3 a_1) False) (Or (Eq (r1 a_4) False) (Or (Eq (r2 a_4 a_2) False) (Eq False True)))))) % 20.89/21.11 Clause #400 (by clausification #[38]): ∀ (a a_1 : Iota), Or (Eq (id a (skS.0 0 a_1)) True) (Eq (Not (r1 a)) True) % 20.89/21.11 Clause #402 (by clausification #[400]): ∀ (a a_1 : Iota), Or (Eq (id a (skS.0 0 a_1)) True) (Eq (r1 a) False) % 20.89/21.11 Clause #403 (by superposition #[402, 44]): ∀ (a a_1 : Iota), Or (Eq (id (skS.0 0 a) (skS.0 0 a_1)) True) (Eq False True) % 20.89/21.11 Clause #404 (by superposition #[402, 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) % 20.89/21.11 Clause #416 (by clausification #[403]): ∀ (a a_1 : Iota), Eq (id (skS.0 0 a) (skS.0 0 a_1)) True % 20.89/21.11 Clause #422 (by superposition #[416, 160]): ∀ (a a_1 a_2 a_3 : Iota), % 20.89/21.11 Or (Eq (r2 (skS.0 0 a) a_1) True) (Or (Eq True False) (Or (Eq (id a_2 a_1) False) (Eq (r2 (skS.0 0 a_3) a_2) False))) % 20.89/21.11 Clause #509 (by clausification #[404]): ∀ (a a_1 a_2 a_3 : Iota), Eq (id (skS.0 2 a a_1 a_2) (skS.0 0 a_3)) True % 20.89/21.11 Clause #511 (by superposition #[509, 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) % 20.89/21.11 Clause #560 (by clausification #[511]): ∀ (a a_1 a_2 a_3 : Iota), Eq (id (skS.0 0 a) (skS.0 2 a_1 a_2 a_3)) True % 20.89/21.11 Clause #569 (by clausification #[177]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 20.89/21.11 Or (Eq (And (Not (r3 a a_1 a_2)) (Not (r3 a_3 a_4 a_5))) True) % 20.89/21.11 (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))) % 20.89/21.11 Clause #570 (by clausification #[569]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 20.89/21.11 Or (Eq (r3 a a_1 a_2) True) % 20.89/21.11 (Or (Eq (Or (Not (id a a_3)) (Not (id a_1 a_4))) True) % 20.89/21.11 (Or (Eq (Not (id a_2 a_5)) True) (Eq (Not (r3 a_3 a_4 a_5)) True))) % 20.89/21.11 Clause #572 (by clausification #[570]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 20.89/21.11 Or (Eq (r3 a a_1 a_2) True) % 20.89/21.11 (Or (Eq (Not (id a_2 a_3)) True) % 20.89/21.11 (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)))) % 20.89/21.11 Clause #573 (by clausification #[572]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 20.89/21.11 Or (Eq (r3 a a_1 a_2) True) % 20.89/21.11 (Or (Eq (Not (r3 a_3 a_4 a_5)) True) % 20.95/21.14 (Or (Eq (Not (id a a_3)) True) (Or (Eq (Not (id a_1 a_4)) True) (Eq (id a_2 a_5) False)))) % 20.95/21.14 Clause #574 (by clausification #[573]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 20.95/21.14 Or (Eq (r3 a a_1 a_2) True) % 20.95/21.14 (Or (Eq (Not (id a a_3)) True) % 20.95/21.14 (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)))) % 20.95/21.14 Clause #575 (by clausification #[574]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 20.95/21.14 Or (Eq (r3 a a_1 a_2) True) % 20.95/21.14 (Or (Eq (Not (id a_1 a_3)) True) % 20.95/21.14 (Or (Eq (id a_2 a_4) False) (Or (Eq (r3 a_5 a_3 a_4) False) (Eq (id a a_5) False)))) % 20.95/21.14 Clause #576 (by clausification #[575]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 20.95/21.14 Or (Eq (r3 a a_1 a_2) True) % 20.95/21.14 (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)))) % 20.95/21.14 Clause #588 (by superposition #[576, 75]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 20.95/21.14 Or (Eq (r3 a a_1 a_2) True) % 20.95/21.14 (Or (Eq (r3 a_3 a_4 (skS.0 1 a_2 a_5)) False) % 20.95/21.14 (Or (Eq (id a a_3) False) (Or (Eq (id a_1 a_4) False) (Eq False True)))) % 20.95/21.14 Clause #723 (by clausification #[422]): ∀ (a a_1 a_2 a_3 : Iota), % 20.95/21.14 Or (Eq (r2 (skS.0 0 a) a_1) True) (Or (Eq (id a_2 a_1) False) (Eq (r2 (skS.0 0 a_3) a_2) False)) % 20.95/21.14 Clause #742 (by superposition #[723, 19]): ∀ (a a_1 a_2 : Iota), Or (Eq (r2 (skS.0 0 a) a_1) True) (Or (Eq (r2 (skS.0 0 a_2) a_1) False) (Eq False True)) % 20.95/21.14 Clause #743 (by clausification #[742]): ∀ (a a_1 a_2 : Iota), Or (Eq (r2 (skS.0 0 a) a_1) True) (Eq (r2 (skS.0 0 a_2) a_1) False) % 20.95/21.14 Clause #744 (by superposition #[743, 78]): ∀ (a a_1 a_2 : Iota), Or (Eq (r2 (skS.0 0 a) (skS.0 3 (skS.0 0 a_1) a_2)) True) (Eq False True) % 20.95/21.14 Clause #748 (by clausification #[744]): ∀ (a a_1 a_2 : Iota), Eq (r2 (skS.0 0 a) (skS.0 3 (skS.0 0 a_1) a_2)) True % 20.95/21.14 Clause #1745 (by clausification #[393]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 20.95/21.14 Or (Eq (r1 a) False) % 20.95/21.14 (Or (Eq (r3 a_1 a a_2) False) % 20.95/21.14 (Or (Eq (r1 a_3) False) (Or (Eq (r2 a_3 a_1) False) (Or (Eq (r1 a_4) False) (Eq (r2 a_4 a_2) False))))) % 20.95/21.14 Clause #1746 (by superposition #[1745, 44]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 20.95/21.14 Or (Eq (r3 a (skS.0 0 a_1) a_2) False) % 20.95/21.14 (Or (Eq (r1 a_3) False) % 20.95/21.14 (Or (Eq (r2 a_3 a) False) (Or (Eq (r1 a_4) False) (Or (Eq (r2 a_4 a_2) False) (Eq False True))))) % 20.95/21.14 Clause #2890 (by clausification #[1746]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 20.95/21.14 Or (Eq (r3 a (skS.0 0 a_1) a_2) False) % 20.95/21.14 (Or (Eq (r1 a_3) False) (Or (Eq (r2 a_3 a) False) (Or (Eq (r1 a_4) False) (Eq (r2 a_4 a_2) False)))) % 20.95/21.14 Clause #3887 (by clausification #[588]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 20.95/21.14 Or (Eq (r3 a a_1 a_2) True) % 20.95/21.14 (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))) % 20.95/21.14 Clause #3888 (by superposition #[3887, 58]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 20.95/21.14 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))) % 20.95/21.14 Clause #3902 (by clausification #[3888]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 20.95/21.14 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)) % 20.95/21.14 Clause #3972 (by superposition #[3902, 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)) % 20.95/21.14 Clause #3973 (by clausification #[3972]): ∀ (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) % 20.95/21.14 Clause #3974 (by superposition #[3973, 560]): ∀ (a a_1 : Iota), Or (Eq (r3 a (skS.0 0 a_1) a) True) (Eq False True) % 20.95/21.14 Clause #3988 (by clausification #[3974]): ∀ (a a_1 : Iota), Eq (r3 a (skS.0 0 a_1) a) True % 20.95/21.14 Clause #3990 (by superposition #[3988, 2890]): ∀ (a a_1 a_2 : Iota), % 20.95/21.14 Or (Eq True False) (Or (Eq (r1 a) False) (Or (Eq (r2 a a_1) False) (Or (Eq (r1 a_2) False) (Eq (r2 a_2 a_1) False)))) % 20.95/21.14 Clause #4018 (by clausification #[3990]): ∀ (a a_1 a_2 : Iota), Or (Eq (r1 a) False) (Or (Eq (r2 a a_1) False) (Or (Eq (r1 a_2) False) (Eq (r2 a_2 a_1) False))) % 20.95/21.14 Clause #4019 (by superposition #[4018, 44]): ∀ (a a_1 a_2 : Iota), % 20.95/21.14 Or (Eq (r2 (skS.0 0 a) a_1) False) (Or (Eq (r1 a_2) False) (Or (Eq (r2 a_2 a_1) False) (Eq False True))) % 20.95/21.14 Clause #4055 (by clausification #[4019]): ∀ (a a_1 a_2 : Iota), Or (Eq (r2 (skS.0 0 a) a_1) False) (Or (Eq (r1 a_2) False) (Eq (r2 a_2 a_1) False)) % 20.99/21.19 Clause #4056 (by superposition #[4055, 748]): ∀ (a a_1 a_2 : Iota), Or (Eq (r1 a) False) (Or (Eq (r2 a (skS.0 3 (skS.0 0 a_1) a_2)) False) (Eq False True)) % 20.99/21.19 Clause #4382 (by clausification #[4056]): ∀ (a a_1 a_2 : Iota), Or (Eq (r1 a) False) (Eq (r2 a (skS.0 3 (skS.0 0 a_1) a_2)) False) % 20.99/21.19 Clause #4383 (by superposition #[4382, 44]): ∀ (a a_1 a_2 : Iota), Or (Eq (r2 (skS.0 0 a) (skS.0 3 (skS.0 0 a_1) a_2)) False) (Eq False True) % 20.99/21.19 Clause #4828 (by clausification #[4383]): ∀ (a a_1 a_2 : Iota), Eq (r2 (skS.0 0 a) (skS.0 3 (skS.0 0 a_1) a_2)) False % 20.99/21.19 Clause #4829 (by superposition #[4828, 748]): Eq False True % 20.99/21.19 Clause #4830 (by clausification #[4829]): False % 20.99/21.19 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------