%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : NUN062+1 : TPTP v9.2.0. Bugfixed v7.4.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n025.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 13.74s 13.94s % Output : Proof 13.78s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : NUN062+1 : TPTP v9.2.0. Bugfixed v7.4.0. % 0.03/0.13 % Command : duper %s % 0.13/0.34 % Computer : n025.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 11:34:23 EDT 2025 % 0.13/0.34 % CPUTime : % 13.74/13.94 SZS status Theorem for theBenchmark.p % 13.74/13.94 SZS output start Proof for theBenchmark.p % 13.74/13.94 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 % 13.74/13.94 Clause #1 (by assumption #[]): Eq % 13.74/13.94 (∀ (X11 : Iota), % 13.74/13.94 Exists fun Y21 => ∀ (X12 : Iota), Or (And (id X12 Y21) (r2 X11 X12)) (And (Not (r2 X11 X12)) (Not (id X12 Y21)))) % 13.74/13.94 True % 13.74/13.94 Clause #2 (by assumption #[]): Eq % 13.74/13.94 (∀ (X13 X14 : Iota), % 13.74/13.94 Exists fun Y22 => % 13.74/13.94 ∀ (X15 : Iota), Or (And (id X15 Y22) (r3 X13 X14 X15)) (And (Not (r3 X13 X14 X15)) (Not (id X15 Y22)))) % 13.74/13.94 True % 13.74/13.94 Clause #4 (by assumption #[]): Eq (∀ (X20 : Iota), id X20 X20) True % 13.74/13.94 Clause #5 (by assumption #[]): Eq (∀ (X21 X22 : Iota), Or (Not (id X21 X22)) (id X22 X21)) True % 13.74/13.94 Clause #6 (by assumption #[]): Eq (∀ (X23 X24 X25 : Iota), Or (Or (Not (id X23 X24)) (id X23 X25)) (Not (id X24 X25))) True % 13.74/13.94 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 % 13.74/13.94 Clause #17 (by assumption #[]): Eq (∀ (X7 Y10 : Iota), Or (∀ (Y20 : Iota), Or (Not (id Y20 Y10)) (Not (r1 Y20))) (Not (r2 X7 Y10))) True % 13.74/13.94 Clause #18 (by assumption #[]): Eq % 13.74/13.94 (Not % 13.74/13.94 (∀ (X1 : Iota), % 13.74/13.94 Exists fun Y2 => % 13.74/13.94 Exists fun Y1 => % 13.74/13.94 And (∀ (Y4 : Iota), Or (Not (id Y1 Y4)) (Not (r1 Y4))) (Exists fun Y3 => And (id Y3 Y2) (r3 X1 Y1 Y3)))) % 13.74/13.94 True % 13.74/13.94 Clause #19 (by clausification #[4]): ∀ (a : Iota), Eq (id a a) True % 13.74/13.94 Clause #20 (by clausification #[5]): ∀ (a : Iota), Eq (∀ (X22 : Iota), Or (Not (id a X22)) (id X22 a)) True % 13.74/13.94 Clause #21 (by clausification #[20]): ∀ (a a_1 : Iota), Eq (Or (Not (id a a_1)) (id a_1 a)) True % 13.74/13.94 Clause #22 (by clausification #[21]): ∀ (a a_1 : Iota), Or (Eq (Not (id a a_1)) True) (Eq (id a_1 a) True) % 13.74/13.94 Clause #23 (by clausification #[22]): ∀ (a a_1 : Iota), Or (Eq (id a a_1) True) (Eq (id a_1 a) False) % 13.74/13.94 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 % 13.74/13.94 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 % 13.74/13.94 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 % 13.74/13.94 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) % 13.74/13.94 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)) % 13.74/13.94 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)) % 13.74/13.94 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)) % 13.74/13.94 Clause #34 (by clausification #[0]): ∀ (a : Iota), % 13.74/13.94 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 % 13.74/13.94 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 % 13.74/13.94 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) % 13.74/13.94 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) % 13.74/13.94 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) % 13.74/13.94 Clause #39 (by clausification #[37]): ∀ (a a_1 : Iota), Or (Eq (r1 a) True) (Eq (Not (id a (skS.0 0 a_1))) True) % 13.74/13.94 Clause #41 (by clausification #[39]): ∀ (a a_1 : Iota), Or (Eq (r1 a) True) (Eq (id a (skS.0 0 a_1)) False) % 13.74/13.94 Clause #45 (by clausification #[17]): ∀ (a : Iota), Eq (∀ (Y10 : Iota), Or (∀ (Y20 : Iota), Or (Not (id Y20 Y10)) (Not (r1 Y20))) (Not (r2 a Y10))) True % 13.74/13.94 Clause #46 (by clausification #[45]): ∀ (a a_1 : Iota), Eq (Or (∀ (Y20 : Iota), Or (Not (id Y20 a)) (Not (r1 Y20))) (Not (r2 a_1 a))) True % 13.78/13.97 Clause #47 (by clausification #[46]): ∀ (a a_1 : Iota), Or (Eq (∀ (Y20 : Iota), Or (Not (id Y20 a)) (Not (r1 Y20))) True) (Eq (Not (r2 a_1 a)) True) % 13.78/13.97 Clause #48 (by clausification #[47]): ∀ (a a_1 a_2 : Iota), Or (Eq (Not (r2 a a_1)) True) (Eq (Or (Not (id a_2 a_1)) (Not (r1 a_2))) True) % 13.78/13.97 Clause #49 (by clausification #[48]): ∀ (a a_1 a_2 : Iota), Or (Eq (Or (Not (id a a_1)) (Not (r1 a))) True) (Eq (r2 a_2 a_1) False) % 13.78/13.97 Clause #50 (by clausification #[49]): ∀ (a a_1 a_2 : Iota), Or (Eq (r2 a a_1) False) (Or (Eq (Not (id a_2 a_1)) True) (Eq (Not (r1 a_2)) True)) % 13.78/13.97 Clause #51 (by clausification #[50]): ∀ (a a_1 a_2 : Iota), Or (Eq (r2 a a_1) False) (Or (Eq (Not (r1 a_2)) True) (Eq (id a_2 a_1) False)) % 13.78/13.97 Clause #52 (by clausification #[51]): ∀ (a a_1 a_2 : Iota), Or (Eq (r2 a a_1) False) (Or (Eq (id a_2 a_1) False) (Eq (r1 a_2) False)) % 13.78/13.97 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 % 13.78/13.97 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 % 13.78/13.97 Clause #56 (by clausification #[54]): ∀ (a a_1 : Iota), Eq (id (skS.0 1 a a_1) a) True % 13.78/13.97 Clause #61 (by superposition #[56, 23]): ∀ (a a_1 : Iota), Or (Eq (id a (skS.0 1 a a_1)) True) (Eq True False) % 13.78/13.97 Clause #63 (by clausification #[1]): ∀ (a : Iota), % 13.78/13.97 Eq (Exists fun Y21 => ∀ (X12 : Iota), Or (And (id X12 Y21) (r2 a X12)) (And (Not (r2 a X12)) (Not (id X12 Y21)))) True % 13.78/13.97 Clause #64 (by clausification #[63]): ∀ (a a_1 : Iota), % 13.78/13.97 Eq % 13.78/13.97 (∀ (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))))) % 13.78/13.97 True % 13.78/13.97 Clause #65 (by clausification #[64]): ∀ (a a_1 a_2 : Iota), % 13.78/13.97 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 % 13.78/13.97 Clause #66 (by clausification #[65]): ∀ (a a_1 a_2 : Iota), % 13.78/13.97 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) % 13.78/13.97 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) % 13.78/13.97 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) % 13.78/13.97 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) % 13.78/13.97 Clause #73 (by superposition #[71, 19]): ∀ (a a_1 : Iota), Or (Eq (r2 a (skS.0 3 a a_1)) True) (Eq False True) % 13.78/13.97 Clause #75 (by clausification #[61]): ∀ (a a_1 : Iota), Eq (id a (skS.0 1 a a_1)) True % 13.78/13.97 Clause #78 (by clausification #[73]): ∀ (a a_1 : Iota), Eq (r2 a (skS.0 3 a a_1)) True % 13.78/13.97 Clause #79 (by superposition #[78, 52]): ∀ (a a_1 a_2 : Iota), Or (Eq True False) (Or (Eq (id a (skS.0 3 a_1 a_2)) False) (Eq (r1 a) False)) % 13.78/13.97 Clause #80 (by clausification #[2]): ∀ (a : Iota), % 13.78/13.97 Eq % 13.78/13.97 (∀ (X14 : Iota), % 13.78/13.97 Exists fun Y22 => % 13.78/13.97 ∀ (X15 : Iota), Or (And (id X15 Y22) (r3 a X14 X15)) (And (Not (r3 a X14 X15)) (Not (id X15 Y22)))) % 13.78/13.97 True % 13.78/13.97 Clause #81 (by clausification #[80]): ∀ (a a_1 : Iota), % 13.78/13.97 Eq % 13.78/13.97 (Exists fun Y22 => % 13.78/13.97 ∀ (X15 : Iota), Or (And (id X15 Y22) (r3 a a_1 X15)) (And (Not (r3 a a_1 X15)) (Not (id X15 Y22)))) % 13.78/13.97 True % 13.78/13.97 Clause #82 (by clausification #[81]): ∀ (a a_1 a_2 : Iota), % 13.78/13.97 Eq % 13.78/13.97 (∀ (X15 : Iota), % 13.78/13.97 Or (And (id X15 (skS.0 4 a a_1 a_2)) (r3 a a_1 X15)) % 13.78/13.97 (And (Not (r3 a a_1 X15)) (Not (id X15 (skS.0 4 a a_1 a_2))))) % 13.78/13.97 True % 13.78/13.97 Clause #83 (by clausification #[82]): ∀ (a a_1 a_2 a_3 : Iota), % 13.78/13.97 Eq % 13.78/13.97 (Or (And (id a (skS.0 4 a_1 a_2 a_3)) (r3 a_1 a_2 a)) (And (Not (r3 a_1 a_2 a)) (Not (id a (skS.0 4 a_1 a_2 a_3))))) % 13.78/13.97 True % 13.78/13.97 Clause #84 (by clausification #[83]): ∀ (a a_1 a_2 a_3 : Iota), % 13.78/13.97 Or (Eq (And (id a (skS.0 4 a_1 a_2 a_3)) (r3 a_1 a_2 a)) True) % 13.78/13.97 (Eq (And (Not (r3 a_1 a_2 a)) (Not (id a (skS.0 4 a_1 a_2 a_3)))) True) % 13.78/13.97 Clause #85 (by clausification #[84]): ∀ (a a_1 a_2 a_3 : Iota), % 13.78/13.99 Or (Eq (And (Not (r3 a a_1 a_2)) (Not (id a_2 (skS.0 4 a a_1 a_3)))) True) (Eq (r3 a a_1 a_2) True) % 13.78/13.99 Clause #87 (by clausification #[85]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (r3 a a_1 a_2) True) (Eq (Not (id a_2 (skS.0 4 a a_1 a_3))) True) % 13.78/13.99 Clause #89 (by clausification #[87]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (r3 a a_1 a_2) True) (Eq (id a_2 (skS.0 4 a a_1 a_3)) False) % 13.78/13.99 Clause #91 (by superposition #[89, 19]): ∀ (a a_1 a_2 : Iota), Or (Eq (r3 a a_1 (skS.0 4 a a_1 a_2)) True) (Eq False True) % 13.78/13.99 Clause #93 (by clausification #[79]): ∀ (a a_1 a_2 : Iota), Or (Eq (id a (skS.0 3 a_1 a_2)) False) (Eq (r1 a) False) % 13.78/13.99 Clause #95 (by superposition #[93, 19]): ∀ (a a_1 : Iota), Or (Eq (r1 (skS.0 3 a a_1)) False) (Eq False True) % 13.78/13.99 Clause #96 (by clausification #[95]): ∀ (a a_1 : Iota), Eq (r1 (skS.0 3 a a_1)) False % 13.78/13.99 Clause #97 (by clausification #[91]): ∀ (a a_1 a_2 : Iota), Eq (r3 a a_1 (skS.0 4 a a_1 a_2)) True % 13.78/13.99 Clause #372 (by clausification #[18]): Eq % 13.78/13.99 (∀ (X1 : Iota), % 13.78/13.99 Exists fun Y2 => % 13.78/13.99 Exists fun Y1 => % 13.78/13.99 And (∀ (Y4 : Iota), Or (Not (id Y1 Y4)) (Not (r1 Y4))) (Exists fun Y3 => And (id Y3 Y2) (r3 X1 Y1 Y3))) % 13.78/13.99 False % 13.78/13.99 Clause #373 (by clausification #[372]): ∀ (a : Iota), % 13.78/13.99 Eq % 13.78/13.99 (Not % 13.78/13.99 (Exists fun Y2 => % 13.78/13.99 Exists fun Y1 => % 13.78/13.99 And (∀ (Y4 : Iota), Or (Not (id Y1 Y4)) (Not (r1 Y4))) % 13.78/13.99 (Exists fun Y3 => And (id Y3 Y2) (r3 (skS.0 16 a) Y1 Y3)))) % 13.78/13.99 True % 13.78/13.99 Clause #374 (by clausification #[373]): ∀ (a : Iota), % 13.78/13.99 Eq % 13.78/13.99 (Exists fun Y2 => % 13.78/13.99 Exists fun Y1 => % 13.78/13.99 And (∀ (Y4 : Iota), Or (Not (id Y1 Y4)) (Not (r1 Y4))) % 13.78/13.99 (Exists fun Y3 => And (id Y3 Y2) (r3 (skS.0 16 a) Y1 Y3))) % 13.78/13.99 False % 13.78/13.99 Clause #375 (by clausification #[374]): ∀ (a a_1 : Iota), % 13.78/13.99 Eq % 13.78/13.99 (Exists fun Y1 => % 13.78/13.99 And (∀ (Y4 : Iota), Or (Not (id Y1 Y4)) (Not (r1 Y4))) (Exists fun Y3 => And (id Y3 a) (r3 (skS.0 16 a_1) Y1 Y3))) % 13.78/13.99 False % 13.78/13.99 Clause #376 (by clausification #[375]): ∀ (a a_1 a_2 : Iota), % 13.78/13.99 Eq (And (∀ (Y4 : Iota), Or (Not (id a Y4)) (Not (r1 Y4))) (Exists fun Y3 => And (id Y3 a_1) (r3 (skS.0 16 a_2) a Y3))) % 13.78/13.99 False % 13.78/13.99 Clause #377 (by clausification #[376]): ∀ (a a_1 a_2 : Iota), % 13.78/13.99 Or (Eq (∀ (Y4 : Iota), Or (Not (id a Y4)) (Not (r1 Y4))) False) % 13.78/13.99 (Eq (Exists fun Y3 => And (id Y3 a_1) (r3 (skS.0 16 a_2) a Y3)) False) % 13.78/13.99 Clause #378 (by clausification #[377]): ∀ (a a_1 a_2 a_3 : Iota), % 13.78/13.99 Or (Eq (Exists fun Y3 => And (id Y3 a) (r3 (skS.0 16 a_1) a_2 Y3)) False) % 13.78/13.99 (Eq (Not (Or (Not (id a_2 (skS.0 17 a_2 a_3))) (Not (r1 (skS.0 17 a_2 a_3))))) True) % 13.78/13.99 Clause #379 (by clausification #[378]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 13.78/13.99 Or (Eq (Not (Or (Not (id a (skS.0 17 a a_1))) (Not (r1 (skS.0 17 a a_1))))) True) % 13.78/13.99 (Eq (And (id a_2 a_3) (r3 (skS.0 16 a_4) a a_2)) False) % 13.78/13.99 Clause #380 (by clausification #[379]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 13.78/13.99 Or (Eq (And (id a a_1) (r3 (skS.0 16 a_2) a_3 a)) False) % 13.78/13.99 (Eq (Or (Not (id a_3 (skS.0 17 a_3 a_4))) (Not (r1 (skS.0 17 a_3 a_4)))) False) % 13.78/13.99 Clause #381 (by clausification #[380]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 13.78/13.99 Or (Eq (Or (Not (id a (skS.0 17 a a_1))) (Not (r1 (skS.0 17 a a_1)))) False) % 13.78/13.99 (Or (Eq (id a_2 a_3) False) (Eq (r3 (skS.0 16 a_4) a a_2) False)) % 13.78/13.99 Clause #382 (by clausification #[381]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 13.78/13.99 Or (Eq (id a a_1) False) (Or (Eq (r3 (skS.0 16 a_2) a_3 a) False) (Eq (Not (r1 (skS.0 17 a_3 a_4))) False)) % 13.78/13.99 Clause #383 (by clausification #[381]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 13.78/13.99 Or (Eq (id a a_1) False) (Or (Eq (r3 (skS.0 16 a_2) a_3 a) False) (Eq (Not (id a_3 (skS.0 17 a_3 a_4))) False)) % 13.78/13.99 Clause #384 (by clausification #[382]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 13.78/13.99 Or (Eq (id a a_1) False) (Or (Eq (r3 (skS.0 16 a_2) a_3 a) False) (Eq (r1 (skS.0 17 a_3 a_4)) True)) % 13.78/13.99 Clause #388 (by superposition #[384, 75]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (r3 (skS.0 16 a) a_1 a_2) False) (Or (Eq (r1 (skS.0 17 a_1 a_3)) True) (Eq False True)) % 13.78/13.99 Clause #391 (by clausification #[388]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (r3 (skS.0 16 a) a_1 a_2) False) (Eq (r1 (skS.0 17 a_1 a_3)) True) % 13.78/13.99 Clause #393 (by superposition #[391, 97]): ∀ (a a_1 : Iota), Or (Eq (r1 (skS.0 17 a a_1)) True) (Eq False True) % 13.78/14.02 Clause #394 (by clausification #[393]): ∀ (a a_1 : Iota), Eq (r1 (skS.0 17 a a_1)) True % 13.78/14.02 Clause #404 (by clausification #[38]): ∀ (a a_1 : Iota), Or (Eq (id a (skS.0 0 a_1)) True) (Eq (Not (r1 a)) True) % 13.78/14.02 Clause #406 (by clausification #[404]): ∀ (a a_1 : Iota), Or (Eq (id a (skS.0 0 a_1)) True) (Eq (r1 a) False) % 13.78/14.02 Clause #417 (by superposition #[406, 394]): ∀ (a a_1 a_2 : Iota), Or (Eq (id (skS.0 17 a a_1) (skS.0 0 a_2)) True) (Eq False True) % 13.78/14.02 Clause #429 (by clausification #[417]): ∀ (a a_1 a_2 : Iota), Eq (id (skS.0 17 a a_1) (skS.0 0 a_2)) True % 13.78/14.02 Clause #431 (by superposition #[429, 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 17 a_2 a_3)) False)) % 13.78/14.02 Clause #868 (by clausification #[431]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (id a (skS.0 0 a_1)) True) (Eq (id a (skS.0 17 a_2 a_3)) False) % 13.78/14.02 Clause #2752 (by clausification #[383]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 13.78/14.02 Or (Eq (id a a_1) False) (Or (Eq (r3 (skS.0 16 a_2) a_3 a) False) (Eq (id a_3 (skS.0 17 a_3 a_4)) True)) % 13.78/14.02 Clause #2770 (by superposition #[2752, 75]): ∀ (a a_1 a_2 a_3 : Iota), % 13.78/14.02 Or (Eq (r3 (skS.0 16 a) a_1 a_2) False) (Or (Eq (id a_1 (skS.0 17 a_1 a_3)) True) (Eq False True)) % 13.78/14.02 Clause #2774 (by clausification #[2770]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (r3 (skS.0 16 a) a_1 a_2) False) (Eq (id a_1 (skS.0 17 a_1 a_3)) True) % 13.78/14.02 Clause #2778 (by superposition #[2774, 97]): ∀ (a a_1 : Iota), Or (Eq (id a (skS.0 17 a a_1)) True) (Eq False True) % 13.78/14.02 Clause #2779 (by clausification #[2778]): ∀ (a a_1 : Iota), Eq (id a (skS.0 17 a a_1)) True % 13.78/14.02 Clause #2780 (by superposition #[2779, 868]): ∀ (a a_1 : Iota), Or (Eq (id a (skS.0 0 a_1)) True) (Eq True False) % 13.78/14.02 Clause #2815 (by clausification #[2780]): ∀ (a a_1 : Iota), Eq (id a (skS.0 0 a_1)) True % 13.78/14.02 Clause #2816 (by superposition #[2815, 41]): ∀ (a : Iota), Or (Eq (r1 a) True) (Eq True False) % 13.78/14.02 Clause #2852 (by clausification #[2816]): ∀ (a : Iota), Eq (r1 a) True % 13.78/14.02 Clause #2866 (by superposition #[2852, 96]): Eq True False % 13.78/14.02 Clause #2867 (by clausification #[2866]): False % 13.78/14.02 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------