%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : NUN081+1 : TPTP v9.2.0. Released v7.3.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n018.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 07:57:50 PM UTC 2025 % Result : Theorem 25.50s 25.72s % Output : Proof 25.62s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : NUN081+1 : TPTP v9.2.0. Released v7.3.0. % 0.06/0.13 % Command : duper %s % 0.12/0.34 % Computer : n018.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 300 % 0.12/0.34 % DateTime : Thu Oct 2 11:33:53 EDT 2025 % 0.12/0.34 % CPUTime : % 25.50/25.72 SZS status Theorem for theBenchmark.p % 25.50/25.72 SZS output start Proof for theBenchmark.p % 25.50/25.72 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 % 25.50/25.72 Clause #1 (by assumption #[]): Eq % 25.50/25.72 (∀ (X11 : Iota), % 25.50/25.72 Exists fun Y21 => ∀ (X12 : Iota), Or (And (id X12 Y21) (r2 X11 X12)) (And (Not (r2 X11 X12)) (Not (id X12 Y21)))) % 25.50/25.72 True % 25.50/25.72 Clause #4 (by assumption #[]): Eq (∀ (X20 : Iota), id X20 X20) True % 25.50/25.72 Clause #8 (by assumption #[]): Eq % 25.50/25.72 (∀ (X28 X29 X30 X31 : Iota), % 25.50/25.72 Or (Or (Or (Not (id X28 X30)) (Not (id X29 X31))) (And (Not (r2 X28 X29)) (Not (r2 X30 X31)))) % 25.50/25.72 (And (r2 X28 X29) (r2 X30 X31))) % 25.50/25.72 True % 25.50/25.72 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 % 25.50/25.72 Clause #18 (by assumption #[]): Eq % 25.50/25.72 (Not % 25.50/25.72 (Exists fun Y1 => % 25.50/25.72 Exists fun Y2 => % 25.50/25.72 Exists fun Y3 => % 25.50/25.72 And (r3 Y1 Y2 Y3) % 25.50/25.72 (Exists fun Y4 => % 25.50/25.72 And (id Y3 Y4) % 25.50/25.72 (Exists fun Y5 => % 25.50/25.72 And (r2 Y5 Y4) (Exists fun Y6 => And (r2 Y6 Y5) (Exists fun Y7 => And (r1 Y7) (r2 Y7 Y6))))))) % 25.50/25.72 True % 25.50/25.72 Clause #19 (by clausification #[4]): ∀ (a : Iota), Eq (id a a) True % 25.50/25.72 Clause #34 (by clausification #[0]): ∀ (a : Iota), % 25.50/25.72 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 % 25.50/25.72 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 % 25.50/25.72 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) % 25.50/25.72 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) % 25.50/25.72 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) % 25.50/25.72 Clause #39 (by clausification #[37]): ∀ (a a_1 : Iota), Or (Eq (r1 a) True) (Eq (Not (id a (skS.0 0 a_1))) True) % 25.50/25.72 Clause #41 (by clausification #[39]): ∀ (a a_1 : Iota), Or (Eq (r1 a) True) (Eq (id a (skS.0 0 a_1)) False) % 25.50/25.72 Clause #42 (by superposition #[41, 19]): ∀ (a : Iota), Or (Eq (r1 (skS.0 0 a)) True) (Eq False True) % 25.50/25.72 Clause #44 (by clausification #[42]): ∀ (a : Iota), Eq (r1 (skS.0 0 a)) True % 25.50/25.72 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 % 25.50/25.72 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 % 25.50/25.72 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 % 25.50/25.72 Clause #56 (by clausification #[54]): ∀ (a a_1 : Iota), Eq (id (skS.0 1 a a_1) a) True % 25.50/25.72 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 % 25.50/25.72 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 % 25.50/25.72 Clause #63 (by clausification #[1]): ∀ (a : Iota), % 25.50/25.72 Eq (Exists fun Y21 => ∀ (X12 : Iota), Or (And (id X12 Y21) (r2 a X12)) (And (Not (r2 a X12)) (Not (id X12 Y21)))) True % 25.50/25.72 Clause #64 (by clausification #[63]): ∀ (a a_1 : Iota), % 25.50/25.72 Eq % 25.50/25.72 (∀ (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))))) % 25.50/25.72 True % 25.50/25.72 Clause #65 (by clausification #[64]): ∀ (a a_1 a_2 : Iota), % 25.50/25.72 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 % 25.50/25.72 Clause #66 (by clausification #[65]): ∀ (a a_1 a_2 : Iota), % 25.50/25.72 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) % 25.50/25.72 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) % 25.50/25.72 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) % 25.57/25.75 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) % 25.57/25.75 Clause #73 (by superposition #[71, 19]): ∀ (a a_1 : Iota), Or (Eq (r2 a (skS.0 3 a a_1)) True) (Eq False True) % 25.57/25.75 Clause #78 (by clausification #[73]): ∀ (a a_1 : Iota), Eq (r2 a (skS.0 3 a a_1)) True % 25.57/25.75 Clause #139 (by clausification #[8]): ∀ (a : Iota), % 25.57/25.75 Eq % 25.57/25.75 (∀ (X29 X30 X31 : Iota), % 25.57/25.75 Or (Or (Or (Not (id a X30)) (Not (id X29 X31))) (And (Not (r2 a X29)) (Not (r2 X30 X31)))) % 25.57/25.75 (And (r2 a X29) (r2 X30 X31))) % 25.57/25.75 True % 25.57/25.75 Clause #140 (by clausification #[139]): ∀ (a a_1 : Iota), % 25.57/25.75 Eq % 25.57/25.75 (∀ (X30 X31 : Iota), % 25.57/25.75 Or (Or (Or (Not (id a X30)) (Not (id a_1 X31))) (And (Not (r2 a a_1)) (Not (r2 X30 X31)))) % 25.57/25.75 (And (r2 a a_1) (r2 X30 X31))) % 25.57/25.75 True % 25.57/25.75 Clause #141 (by clausification #[140]): ∀ (a a_1 a_2 : Iota), % 25.57/25.75 Eq % 25.57/25.75 (∀ (X31 : Iota), % 25.57/25.75 Or (Or (Or (Not (id a a_1)) (Not (id a_2 X31))) (And (Not (r2 a a_2)) (Not (r2 a_1 X31)))) % 25.57/25.75 (And (r2 a a_2) (r2 a_1 X31))) % 25.57/25.75 True % 25.57/25.75 Clause #142 (by clausification #[141]): ∀ (a a_1 a_2 a_3 : Iota), % 25.57/25.75 Eq % 25.57/25.75 (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)))) % 25.57/25.75 (And (r2 a a_2) (r2 a_1 a_3))) % 25.57/25.75 True % 25.57/25.75 Clause #143 (by clausification #[142]): ∀ (a a_1 a_2 a_3 : Iota), % 25.57/25.75 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) % 25.57/25.75 (Eq (And (r2 a a_2) (r2 a_1 a_3)) True) % 25.57/25.75 Clause #144 (by clausification #[143]): ∀ (a a_1 a_2 a_3 : Iota), % 25.57/25.75 Or (Eq (And (r2 a a_1) (r2 a_2 a_3)) True) % 25.57/25.75 (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)) % 25.57/25.75 Clause #146 (by clausification #[144]): ∀ (a a_1 a_2 a_3 : Iota), % 25.57/25.75 Or (Eq (Or (Not (id a a_1)) (Not (id a_2 a_3))) True) % 25.57/25.75 (Or (Eq (And (Not (r2 a a_2)) (Not (r2 a_1 a_3))) True) (Eq (r2 a a_2) True)) % 25.57/25.75 Clause #372 (by clausification #[18]): Eq % 25.57/25.75 (Exists fun Y1 => % 25.57/25.75 Exists fun Y2 => % 25.57/25.75 Exists fun Y3 => % 25.57/25.75 And (r3 Y1 Y2 Y3) % 25.57/25.75 (Exists fun Y4 => % 25.57/25.75 And (id Y3 Y4) % 25.57/25.75 (Exists fun Y5 => % 25.57/25.75 And (r2 Y5 Y4) (Exists fun Y6 => And (r2 Y6 Y5) (Exists fun Y7 => And (r1 Y7) (r2 Y7 Y6)))))) % 25.57/25.75 False % 25.57/25.75 Clause #373 (by clausification #[372]): ∀ (a : Iota), % 25.57/25.75 Eq % 25.57/25.75 (Exists fun Y2 => % 25.57/25.75 Exists fun Y3 => % 25.57/25.75 And (r3 a Y2 Y3) % 25.57/25.75 (Exists fun Y4 => % 25.57/25.75 And (id Y3 Y4) % 25.57/25.75 (Exists fun Y5 => % 25.57/25.75 And (r2 Y5 Y4) (Exists fun Y6 => And (r2 Y6 Y5) (Exists fun Y7 => And (r1 Y7) (r2 Y7 Y6)))))) % 25.57/25.75 False % 25.57/25.75 Clause #374 (by clausification #[373]): ∀ (a a_1 : Iota), % 25.57/25.75 Eq % 25.57/25.75 (Exists fun Y3 => % 25.57/25.75 And (r3 a a_1 Y3) % 25.57/25.75 (Exists fun Y4 => % 25.57/25.75 And (id Y3 Y4) % 25.57/25.75 (Exists fun Y5 => % 25.57/25.75 And (r2 Y5 Y4) (Exists fun Y6 => And (r2 Y6 Y5) (Exists fun Y7 => And (r1 Y7) (r2 Y7 Y6)))))) % 25.57/25.75 False % 25.57/25.75 Clause #375 (by clausification #[374]): ∀ (a a_1 a_2 : Iota), % 25.57/25.75 Eq % 25.57/25.75 (And (r3 a a_1 a_2) % 25.57/25.75 (Exists fun Y4 => % 25.57/25.75 And (id a_2 Y4) % 25.57/25.75 (Exists fun Y5 => % 25.57/25.75 And (r2 Y5 Y4) (Exists fun Y6 => And (r2 Y6 Y5) (Exists fun Y7 => And (r1 Y7) (r2 Y7 Y6)))))) % 25.57/25.75 False % 25.57/25.75 Clause #376 (by clausification #[375]): ∀ (a a_1 a_2 : Iota), % 25.57/25.75 Or (Eq (r3 a a_1 a_2) False) % 25.57/25.75 (Eq % 25.57/25.75 (Exists fun Y4 => % 25.57/25.75 And (id a_2 Y4) % 25.57/25.75 (Exists fun Y5 => And (r2 Y5 Y4) (Exists fun Y6 => And (r2 Y6 Y5) (Exists fun Y7 => And (r1 Y7) (r2 Y7 Y6))))) % 25.57/25.75 False) % 25.57/25.75 Clause #377 (by clausification #[376]): ∀ (a a_1 a_2 a_3 : Iota), % 25.57/25.75 Or (Eq (r3 a a_1 a_2) False) % 25.57/25.75 (Eq % 25.57/25.75 (And (id a_2 a_3) % 25.57/25.75 (Exists fun Y5 => And (r2 Y5 a_3) (Exists fun Y6 => And (r2 Y6 Y5) (Exists fun Y7 => And (r1 Y7) (r2 Y7 Y6))))) % 25.57/25.75 False) % 25.57/25.75 Clause #378 (by clausification #[377]): ∀ (a a_1 a_2 a_3 : Iota), % 25.57/25.75 Or (Eq (r3 a a_1 a_2) False) % 25.57/25.75 (Or (Eq (id a_2 a_3) False) % 25.57/25.75 (Eq (Exists fun Y5 => And (r2 Y5 a_3) (Exists fun Y6 => And (r2 Y6 Y5) (Exists fun Y7 => And (r1 Y7) (r2 Y7 Y6)))) % 25.57/25.75 False)) % 25.57/25.75 Clause #379 (by clausification #[378]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 25.57/25.78 Or (Eq (r3 a a_1 a_2) False) % 25.57/25.78 (Or (Eq (id a_2 a_3) False) % 25.57/25.78 (Eq (And (r2 a_4 a_3) (Exists fun Y6 => And (r2 Y6 a_4) (Exists fun Y7 => And (r1 Y7) (r2 Y7 Y6)))) False)) % 25.57/25.78 Clause #380 (by clausification #[379]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 25.57/25.78 Or (Eq (r3 a a_1 a_2) False) % 25.57/25.78 (Or (Eq (id a_2 a_3) False) % 25.57/25.78 (Or (Eq (r2 a_4 a_3) False) % 25.57/25.78 (Eq (Exists fun Y6 => And (r2 Y6 a_4) (Exists fun Y7 => And (r1 Y7) (r2 Y7 Y6))) False))) % 25.57/25.78 Clause #381 (by clausification #[380]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 25.57/25.78 Or (Eq (r3 a a_1 a_2) False) % 25.57/25.78 (Or (Eq (id a_2 a_3) False) % 25.57/25.78 (Or (Eq (r2 a_4 a_3) False) (Eq (And (r2 a_5 a_4) (Exists fun Y7 => And (r1 Y7) (r2 Y7 a_5))) False))) % 25.57/25.78 Clause #382 (by clausification #[381]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 25.57/25.78 Or (Eq (r3 a a_1 a_2) False) % 25.57/25.78 (Or (Eq (id a_2 a_3) False) % 25.57/25.78 (Or (Eq (r2 a_4 a_3) False) (Or (Eq (r2 a_5 a_4) False) (Eq (Exists fun Y7 => And (r1 Y7) (r2 Y7 a_5)) False)))) % 25.57/25.78 Clause #383 (by clausification #[382]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota), % 25.57/25.78 Or (Eq (r3 a a_1 a_2) False) % 25.57/25.78 (Or (Eq (id a_2 a_3) False) % 25.57/25.78 (Or (Eq (r2 a_4 a_3) False) (Or (Eq (r2 a_5 a_4) False) (Eq (And (r1 a_6) (r2 a_6 a_5)) False)))) % 25.57/25.78 Clause #384 (by clausification #[383]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota), % 25.57/25.78 Or (Eq (r3 a a_1 a_2) False) % 25.57/25.78 (Or (Eq (id a_2 a_3) False) % 25.57/25.78 (Or (Eq (r2 a_4 a_3) False) (Or (Eq (r2 a_5 a_4) False) (Or (Eq (r1 a_6) False) (Eq (r2 a_6 a_5) False))))) % 25.57/25.78 Clause #385 (by superposition #[384, 58]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 25.57/25.78 Or (Eq (id (skS.0 1 a a_1) a_2) False) % 25.57/25.78 (Or (Eq (r2 a_3 a_2) False) % 25.57/25.78 (Or (Eq (r2 a_4 a_3) False) (Or (Eq (r1 a_5) False) (Or (Eq (r2 a_5 a_4) False) (Eq False True))))) % 25.57/25.78 Clause #395 (by clausification #[38]): ∀ (a a_1 : Iota), Or (Eq (id a (skS.0 0 a_1)) True) (Eq (Not (r1 a)) True) % 25.57/25.78 Clause #397 (by clausification #[395]): ∀ (a a_1 : Iota), Or (Eq (id a (skS.0 0 a_1)) True) (Eq (r1 a) False) % 25.57/25.78 Clause #398 (by superposition #[397, 44]): ∀ (a a_1 : Iota), Or (Eq (id (skS.0 0 a) (skS.0 0 a_1)) True) (Eq False True) % 25.57/25.78 Clause #411 (by clausification #[398]): ∀ (a a_1 : Iota), Eq (id (skS.0 0 a) (skS.0 0 a_1)) True % 25.57/25.78 Clause #516 (by clausification #[146]): ∀ (a a_1 a_2 a_3 : Iota), % 25.57/25.78 Or (Eq (And (Not (r2 a a_1)) (Not (r2 a_2 a_3))) True) % 25.57/25.78 (Or (Eq (r2 a a_1) True) (Or (Eq (Not (id a a_2)) True) (Eq (Not (id a_1 a_3)) True))) % 25.57/25.78 Clause #517 (by clausification #[516]): ∀ (a a_1 a_2 a_3 : Iota), % 25.57/25.78 Or (Eq (r2 a a_1) True) (Or (Eq (Not (id a a_2)) True) (Or (Eq (Not (id a_1 a_3)) True) (Eq (Not (r2 a_2 a_3)) True))) % 25.57/25.78 Clause #519 (by clausification #[517]): ∀ (a a_1 a_2 a_3 : Iota), % 25.57/25.78 Or (Eq (r2 a a_1) True) (Or (Eq (Not (id a_1 a_2)) True) (Or (Eq (Not (r2 a_3 a_2)) True) (Eq (id a a_3) False))) % 25.57/25.78 Clause #520 (by clausification #[519]): ∀ (a a_1 a_2 a_3 : Iota), % 25.57/25.78 Or (Eq (r2 a a_1) True) (Or (Eq (Not (r2 a_2 a_3)) True) (Or (Eq (id a a_2) False) (Eq (id a_1 a_3) False))) % 25.57/25.78 Clause #521 (by clausification #[520]): ∀ (a a_1 a_2 a_3 : Iota), % 25.57/25.78 Or (Eq (r2 a a_1) True) (Or (Eq (id a a_2) False) (Or (Eq (id a_1 a_3) False) (Eq (r2 a_2 a_3) False))) % 25.57/25.78 Clause #525 (by superposition #[521, 411]): ∀ (a a_1 a_2 a_3 : Iota), % 25.57/25.78 Or (Eq (r2 (skS.0 0 a) a_1) True) (Or (Eq (id a_1 a_2) False) (Or (Eq (r2 (skS.0 0 a_3) a_2) False) (Eq False True))) % 25.57/25.78 Clause #1030 (by clausification #[525]): ∀ (a a_1 a_2 a_3 : Iota), % 25.57/25.78 Or (Eq (r2 (skS.0 0 a) a_1) True) (Or (Eq (id a_1 a_2) False) (Eq (r2 (skS.0 0 a_3) a_2) False)) % 25.57/25.78 Clause #1059 (by superposition #[1030, 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)) % 25.57/25.78 Clause #1090 (by clausification #[1059]): ∀ (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) % 25.57/25.78 Clause #1091 (by superposition #[1090, 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) % 25.57/25.78 Clause #1095 (by clausification #[1091]): ∀ (a a_1 a_2 : Iota), Eq (r2 (skS.0 0 a) (skS.0 3 (skS.0 0 a_1) a_2)) True % 25.57/25.78 Clause #5751 (by clausification #[385]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 25.62/25.83 Or (Eq (id (skS.0 1 a a_1) a_2) False) % 25.62/25.83 (Or (Eq (r2 a_3 a_2) False) (Or (Eq (r2 a_4 a_3) False) (Or (Eq (r1 a_5) False) (Eq (r2 a_5 a_4) False)))) % 25.62/25.83 Clause #5771 (by superposition #[5751, 56]): ∀ (a a_1 a_2 a_3 : Iota), % 25.62/25.83 Or (Eq (r2 a a_1) False) % 25.62/25.83 (Or (Eq (r2 a_2 a) False) (Or (Eq (r1 a_3) False) (Or (Eq (r2 a_3 a_2) False) (Eq False True)))) % 25.62/25.83 Clause #5772 (by clausification #[5771]): ∀ (a a_1 a_2 a_3 : Iota), % 25.62/25.83 Or (Eq (r2 a a_1) False) (Or (Eq (r2 a_2 a) False) (Or (Eq (r1 a_3) False) (Eq (r2 a_3 a_2) False))) % 25.62/25.83 Clause #5784 (by superposition #[5772, 78]): ∀ (a a_1 a_2 : Iota), Or (Eq (r2 a a_1) False) (Or (Eq (r1 a_2) False) (Or (Eq (r2 a_2 a) False) (Eq False True))) % 25.62/25.83 Clause #5785 (by clausification #[5784]): ∀ (a a_1 a_2 : Iota), Or (Eq (r2 a a_1) False) (Or (Eq (r1 a_2) False) (Eq (r2 a_2 a) False)) % 25.62/25.83 Clause #5797 (by superposition #[5785, 78]): ∀ (a a_1 : Iota), Or (Eq (r1 a) False) (Or (Eq (r2 a a_1) False) (Eq False True)) % 25.62/25.83 Clause #5798 (by clausification #[5797]): ∀ (a a_1 : Iota), Or (Eq (r1 a) False) (Eq (r2 a a_1) False) % 25.62/25.83 Clause #5799 (by superposition #[5798, 44]): ∀ (a a_1 : Iota), Or (Eq (r2 (skS.0 0 a) a_1) False) (Eq False True) % 25.62/25.83 Clause #5828 (by clausification #[5799]): ∀ (a a_1 : Iota), Eq (r2 (skS.0 0 a) a_1) False % 25.62/25.83 Clause #5829 (by superposition #[5828, 1095]): Eq False True % 25.62/25.83 Clause #5830 (by clausification #[5829]): False % 25.62/25.83 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------