%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : NUN073+1 : TPTP v9.2.0. Released v7.3.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n005.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 07:57:49 PM UTC 2025 % Result : Theorem 15.68s 15.86s % Output : Proof 15.76s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.13 % Problem : NUN073+1 : TPTP v9.2.0. Released v7.3.0. % 0.07/0.14 % Command : duper %s % 0.14/0.35 % Computer : n005.cluster.edu % 0.14/0.35 % Model : x86_64 x86_64 % 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.35 % Memory : 8042.1875MB % 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.36 % CPULimit : 300 % 0.14/0.36 % WCLimit : 300 % 0.14/0.36 % DateTime : Thu Oct 2 11:30:53 EDT 2025 % 0.14/0.36 % CPUTime : % 15.68/15.86 SZS status Theorem for theBenchmark.p % 15.68/15.86 SZS output start Proof for theBenchmark.p % 15.68/15.86 Clause #1 (by assumption #[]): Eq % 15.68/15.86 (∀ (X11 : Iota), % 15.68/15.86 Exists fun Y21 => ∀ (X12 : Iota), Or (And (id X12 Y21) (r2 X11 X12)) (And (Not (r2 X11 X12)) (Not (id X12 Y21)))) % 15.68/15.86 True % 15.68/15.86 Clause #4 (by assumption #[]): Eq (∀ (X20 : Iota), id X20 X20) True % 15.68/15.86 Clause #8 (by assumption #[]): Eq % 15.68/15.86 (∀ (X28 X29 X30 X31 : Iota), % 15.68/15.86 Or (Or (Or (Not (id X28 X30)) (Not (id X29 X31))) (And (Not (r2 X28 X29)) (Not (r2 X30 X31)))) % 15.68/15.86 (And (r2 X28 X29) (r2 X30 X31))) % 15.68/15.86 True % 15.68/15.86 Clause #13 (by assumption #[]): Eq % 15.68/15.86 (∀ (X3 X10 : Iota), % 15.68/15.86 Or (∀ (Y12 : Iota), Or (∀ (Y13 : Iota), Or (Not (id Y13 Y12)) (Not (r2 X3 Y13))) (Not (r2 X10 Y12))) (id X3 X10)) % 15.68/15.86 True % 15.68/15.86 Clause #17 (by assumption #[]): Eq (∀ (X7 Y10 : Iota), Or (∀ (Y20 : Iota), Or (Not (id Y20 Y10)) (Not (r1 Y20))) (Not (r2 X7 Y10))) True % 15.68/15.86 Clause #18 (by assumption #[]): Eq % 15.68/15.86 (Not % 15.68/15.86 (∀ (Y1 : Iota), % 15.68/15.86 Or (∀ (Y2 : Iota), Or (∀ (Y4 : Iota), Or (Not (r1 Y4)) (Not (r2 Y4 Y2))) (Not (id Y2 Y1))) % 15.68/15.86 (∀ (Y3 : Iota), Or (∀ (Y5 : Iota), Or (Not (r1 Y5)) (Not (r2 Y5 Y3))) (Not (r2 Y3 Y1))))) % 15.68/15.86 True % 15.68/15.86 Clause #19 (by clausification #[4]): ∀ (a : Iota), Eq (id a a) True % 15.68/15.86 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 % 15.68/15.86 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 % 15.68/15.86 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) % 15.68/15.86 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) % 15.68/15.86 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) % 15.68/15.86 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)) % 15.68/15.86 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)) % 15.68/15.86 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)) % 15.68/15.86 Clause #63 (by clausification #[1]): ∀ (a : Iota), % 15.68/15.86 Eq (Exists fun Y21 => ∀ (X12 : Iota), Or (And (id X12 Y21) (r2 a X12)) (And (Not (r2 a X12)) (Not (id X12 Y21)))) True % 15.68/15.86 Clause #64 (by clausification #[63]): ∀ (a a_1 : Iota), % 15.68/15.86 Eq % 15.68/15.86 (∀ (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))))) % 15.68/15.86 True % 15.68/15.86 Clause #65 (by clausification #[64]): ∀ (a a_1 a_2 : Iota), % 15.68/15.86 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 % 15.68/15.86 Clause #66 (by clausification #[65]): ∀ (a a_1 a_2 : Iota), % 15.68/15.86 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) % 15.68/15.86 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) % 15.68/15.86 Clause #68 (by clausification #[66]): ∀ (a a_1 a_2 : Iota), % 15.68/15.86 Or (Eq (And (Not (r2 a a_1)) (Not (id a_1 (skS.0 3 a a_2)))) True) (Eq (id a_1 (skS.0 3 a a_2)) True) % 15.68/15.86 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) % 15.68/15.86 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) % 15.68/15.86 Clause #73 (by superposition #[71, 19]): ∀ (a a_1 : Iota), Or (Eq (r2 a (skS.0 3 a a_1)) True) (Eq False True) % 15.68/15.86 Clause #78 (by clausification #[73]): ∀ (a a_1 : Iota), Eq (r2 a (skS.0 3 a a_1)) True % 15.68/15.86 Clause #139 (by clausification #[8]): ∀ (a : Iota), % 15.68/15.86 Eq % 15.68/15.86 (∀ (X29 X30 X31 : Iota), % 15.68/15.86 Or (Or (Or (Not (id a X30)) (Not (id X29 X31))) (And (Not (r2 a X29)) (Not (r2 X30 X31)))) % 15.68/15.86 (And (r2 a X29) (r2 X30 X31))) % 15.68/15.86 True % 15.68/15.89 Clause #140 (by clausification #[139]): ∀ (a a_1 : Iota), % 15.68/15.89 Eq % 15.68/15.89 (∀ (X30 X31 : Iota), % 15.68/15.89 Or (Or (Or (Not (id a X30)) (Not (id a_1 X31))) (And (Not (r2 a a_1)) (Not (r2 X30 X31)))) % 15.68/15.89 (And (r2 a a_1) (r2 X30 X31))) % 15.68/15.89 True % 15.68/15.89 Clause #141 (by clausification #[140]): ∀ (a a_1 a_2 : Iota), % 15.68/15.89 Eq % 15.68/15.89 (∀ (X31 : Iota), % 15.68/15.89 Or (Or (Or (Not (id a a_1)) (Not (id a_2 X31))) (And (Not (r2 a a_2)) (Not (r2 a_1 X31)))) % 15.68/15.89 (And (r2 a a_2) (r2 a_1 X31))) % 15.68/15.89 True % 15.68/15.89 Clause #142 (by clausification #[141]): ∀ (a a_1 a_2 a_3 : Iota), % 15.68/15.89 Eq % 15.68/15.89 (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)))) % 15.68/15.89 (And (r2 a a_2) (r2 a_1 a_3))) % 15.68/15.89 True % 15.68/15.89 Clause #143 (by clausification #[142]): ∀ (a a_1 a_2 a_3 : Iota), % 15.68/15.89 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) % 15.68/15.89 (Eq (And (r2 a a_2) (r2 a_1 a_3)) True) % 15.68/15.89 Clause #144 (by clausification #[143]): ∀ (a a_1 a_2 a_3 : Iota), % 15.68/15.89 Or (Eq (And (r2 a a_1) (r2 a_2 a_3)) True) % 15.68/15.89 (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)) % 15.68/15.89 Clause #145 (by clausification #[144]): ∀ (a a_1 a_2 a_3 : Iota), % 15.68/15.89 Or (Eq (Or (Not (id a a_1)) (Not (id a_2 a_3))) True) % 15.68/15.89 (Or (Eq (And (Not (r2 a a_2)) (Not (r2 a_1 a_3))) True) (Eq (r2 a_1 a_3) True)) % 15.68/15.89 Clause #147 (by clausification #[145]): ∀ (a a_1 a_2 a_3 : Iota), % 15.68/15.89 Or (Eq (And (Not (r2 a a_1)) (Not (r2 a_2 a_3))) True) % 15.68/15.89 (Or (Eq (r2 a_2 a_3) True) (Or (Eq (Not (id a a_2)) True) (Eq (Not (id a_1 a_3)) True))) % 15.68/15.89 Clause #149 (by clausification #[147]): ∀ (a a_1 a_2 a_3 : Iota), % 15.68/15.89 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))) % 15.68/15.89 Clause #158 (by clausification #[149]): ∀ (a a_1 a_2 a_3 : Iota), % 15.68/15.89 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))) % 15.68/15.89 Clause #159 (by clausification #[158]): ∀ (a a_1 a_2 a_3 : Iota), % 15.68/15.89 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))) % 15.68/15.89 Clause #160 (by clausification #[159]): ∀ (a a_1 a_2 a_3 : Iota), % 15.68/15.89 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))) % 15.68/15.89 Clause #163 (by superposition #[160, 19]): ∀ (a a_1 a_2 : Iota), Or (Eq (r2 a a_1) True) (Or (Eq (id a_2 a_1) False) (Or (Eq (r2 a a_2) False) (Eq False True))) % 15.68/15.89 Clause #164 (by clausification #[163]): ∀ (a a_1 a_2 : Iota), Or (Eq (r2 a a_1) True) (Or (Eq (id a_2 a_1) False) (Eq (r2 a a_2) False)) % 15.68/15.89 Clause #284 (by clausification #[13]): ∀ (a : Iota), % 15.68/15.89 Eq % 15.68/15.89 (∀ (X10 : Iota), % 15.68/15.89 Or (∀ (Y12 : Iota), Or (∀ (Y13 : Iota), Or (Not (id Y13 Y12)) (Not (r2 a Y13))) (Not (r2 X10 Y12))) (id a X10)) % 15.68/15.89 True % 15.68/15.89 Clause #285 (by clausification #[284]): ∀ (a a_1 : Iota), % 15.68/15.89 Eq (Or (∀ (Y12 : Iota), Or (∀ (Y13 : Iota), Or (Not (id Y13 Y12)) (Not (r2 a Y13))) (Not (r2 a_1 Y12))) (id a a_1)) % 15.68/15.89 True % 15.68/15.89 Clause #286 (by clausification #[285]): ∀ (a a_1 : Iota), % 15.68/15.89 Or (Eq (∀ (Y12 : Iota), Or (∀ (Y13 : Iota), Or (Not (id Y13 Y12)) (Not (r2 a Y13))) (Not (r2 a_1 Y12))) True) % 15.68/15.89 (Eq (id a a_1) True) % 15.68/15.89 Clause #287 (by clausification #[286]): ∀ (a a_1 a_2 : Iota), % 15.68/15.89 Or (Eq (id a a_1) True) (Eq (Or (∀ (Y13 : Iota), Or (Not (id Y13 a_2)) (Not (r2 a Y13))) (Not (r2 a_1 a_2))) True) % 15.68/15.89 Clause #288 (by clausification #[287]): ∀ (a a_1 a_2 : Iota), % 15.68/15.89 Or (Eq (id a a_1) True) % 15.68/15.89 (Or (Eq (∀ (Y13 : Iota), Or (Not (id Y13 a_2)) (Not (r2 a Y13))) True) (Eq (Not (r2 a_1 a_2)) True)) % 15.68/15.89 Clause #289 (by clausification #[288]): ∀ (a a_1 a_2 a_3 : Iota), % 15.68/15.89 Or (Eq (id a a_1) True) (Or (Eq (Not (r2 a_1 a_2)) True) (Eq (Or (Not (id a_3 a_2)) (Not (r2 a a_3))) True)) % 15.68/15.89 Clause #290 (by clausification #[289]): ∀ (a a_1 a_2 a_3 : Iota), % 15.68/15.89 Or (Eq (id a a_1) True) (Or (Eq (Or (Not (id a_2 a_3)) (Not (r2 a a_2))) True) (Eq (r2 a_1 a_3) False)) % 15.68/15.89 Clause #291 (by clausification #[290]): ∀ (a a_1 a_2 a_3 : Iota), % 15.68/15.89 Or (Eq (id a a_1) True) (Or (Eq (r2 a_1 a_2) False) (Or (Eq (Not (id a_3 a_2)) True) (Eq (Not (r2 a a_3)) True))) % 15.76/15.92 Clause #292 (by clausification #[291]): ∀ (a a_1 a_2 a_3 : Iota), % 15.76/15.92 Or (Eq (id a a_1) True) (Or (Eq (r2 a_1 a_2) False) (Or (Eq (Not (r2 a a_3)) True) (Eq (id a_3 a_2) False))) % 15.76/15.92 Clause #293 (by clausification #[292]): ∀ (a a_1 a_2 a_3 : Iota), % 15.76/15.92 Or (Eq (id a a_1) True) (Or (Eq (r2 a_1 a_2) False) (Or (Eq (id a_3 a_2) False) (Eq (r2 a a_3) False))) % 15.76/15.92 Clause #295 (by superposition #[293, 78]): ∀ (a a_1 a_2 a_3 : Iota), % 15.76/15.92 Or (Eq (id a a_1) True) (Or (Eq (id a_2 (skS.0 3 a_1 a_3)) False) (Or (Eq (r2 a a_2) False) (Eq False True))) % 15.76/15.92 Clause #298 (by clausification #[295]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (id a a_1) True) (Or (Eq (id a_2 (skS.0 3 a_1 a_3)) False) (Eq (r2 a a_2) False)) % 15.76/15.92 Clause #372 (by clausification #[18]): Eq % 15.76/15.92 (∀ (Y1 : Iota), % 15.76/15.92 Or (∀ (Y2 : Iota), Or (∀ (Y4 : Iota), Or (Not (r1 Y4)) (Not (r2 Y4 Y2))) (Not (id Y2 Y1))) % 15.76/15.92 (∀ (Y3 : Iota), Or (∀ (Y5 : Iota), Or (Not (r1 Y5)) (Not (r2 Y5 Y3))) (Not (r2 Y3 Y1)))) % 15.76/15.92 False % 15.76/15.92 Clause #373 (by clausification #[372]): ∀ (a : Iota), % 15.76/15.92 Eq % 15.76/15.92 (Not % 15.76/15.92 (Or (∀ (Y2 : Iota), Or (∀ (Y4 : Iota), Or (Not (r1 Y4)) (Not (r2 Y4 Y2))) (Not (id Y2 (skS.0 16 a)))) % 15.76/15.92 (∀ (Y3 : Iota), Or (∀ (Y5 : Iota), Or (Not (r1 Y5)) (Not (r2 Y5 Y3))) (Not (r2 Y3 (skS.0 16 a)))))) % 15.76/15.92 True % 15.76/15.92 Clause #374 (by clausification #[373]): ∀ (a : Iota), % 15.76/15.92 Eq % 15.76/15.92 (Or (∀ (Y2 : Iota), Or (∀ (Y4 : Iota), Or (Not (r1 Y4)) (Not (r2 Y4 Y2))) (Not (id Y2 (skS.0 16 a)))) % 15.76/15.92 (∀ (Y3 : Iota), Or (∀ (Y5 : Iota), Or (Not (r1 Y5)) (Not (r2 Y5 Y3))) (Not (r2 Y3 (skS.0 16 a))))) % 15.76/15.92 False % 15.76/15.92 Clause #375 (by clausification #[374]): ∀ (a : Iota), Eq (∀ (Y3 : Iota), Or (∀ (Y5 : Iota), Or (Not (r1 Y5)) (Not (r2 Y5 Y3))) (Not (r2 Y3 (skS.0 16 a)))) False % 15.76/15.92 Clause #376 (by clausification #[374]): ∀ (a : Iota), Eq (∀ (Y2 : Iota), Or (∀ (Y4 : Iota), Or (Not (r1 Y4)) (Not (r2 Y4 Y2))) (Not (id Y2 (skS.0 16 a)))) False % 15.76/15.92 Clause #377 (by clausification #[375]): ∀ (a a_1 : Iota), % 15.76/15.92 Eq % 15.76/15.92 (Not (Or (∀ (Y5 : Iota), Or (Not (r1 Y5)) (Not (r2 Y5 (skS.0 17 a a_1)))) (Not (r2 (skS.0 17 a a_1) (skS.0 16 a))))) % 15.76/15.92 True % 15.76/15.92 Clause #378 (by clausification #[377]): ∀ (a a_1 : Iota), % 15.76/15.92 Eq (Or (∀ (Y5 : Iota), Or (Not (r1 Y5)) (Not (r2 Y5 (skS.0 17 a a_1)))) (Not (r2 (skS.0 17 a a_1) (skS.0 16 a)))) % 15.76/15.92 False % 15.76/15.92 Clause #379 (by clausification #[378]): ∀ (a a_1 : Iota), Eq (Not (r2 (skS.0 17 a a_1) (skS.0 16 a))) False % 15.76/15.92 Clause #380 (by clausification #[378]): ∀ (a a_1 : Iota), Eq (∀ (Y5 : Iota), Or (Not (r1 Y5)) (Not (r2 Y5 (skS.0 17 a a_1)))) False % 15.76/15.92 Clause #381 (by clausification #[379]): ∀ (a a_1 : Iota), Eq (r2 (skS.0 17 a a_1) (skS.0 16 a)) True % 15.76/15.92 Clause #391 (by clausification #[380]): ∀ (a a_1 a_2 : Iota), % 15.76/15.92 Eq (Not (Or (Not (r1 (skS.0 18 a a_1 a_2))) (Not (r2 (skS.0 18 a a_1 a_2) (skS.0 17 a a_1))))) True % 15.76/15.92 Clause #392 (by clausification #[391]): ∀ (a a_1 a_2 : Iota), Eq (Or (Not (r1 (skS.0 18 a a_1 a_2))) (Not (r2 (skS.0 18 a a_1 a_2) (skS.0 17 a a_1)))) False % 15.76/15.92 Clause #393 (by clausification #[392]): ∀ (a a_1 a_2 : Iota), Eq (Not (r2 (skS.0 18 a a_1 a_2) (skS.0 17 a a_1))) False % 15.76/15.92 Clause #395 (by clausification #[393]): ∀ (a a_1 a_2 : Iota), Eq (r2 (skS.0 18 a a_1 a_2) (skS.0 17 a a_1)) True % 15.76/15.92 Clause #396 (by superposition #[395, 52]): ∀ (a a_1 a_2 : Iota), Or (Eq True False) (Or (Eq (id a (skS.0 17 a_1 a_2)) False) (Eq (r1 a) False)) % 15.76/15.92 Clause #403 (by clausification #[396]): ∀ (a a_1 a_2 : Iota), Or (Eq (id a (skS.0 17 a_1 a_2)) False) (Eq (r1 a) False) % 15.76/15.92 Clause #434 (by clausification #[68]): ∀ (a a_1 a_2 : Iota), Or (Eq (id a (skS.0 3 a_1 a_2)) True) (Eq (Not (r2 a_1 a)) True) % 15.76/15.92 Clause #436 (by clausification #[434]): ∀ (a a_1 a_2 : Iota), Or (Eq (id a (skS.0 3 a_1 a_2)) True) (Eq (r2 a_1 a) False) % 15.76/15.92 Clause #439 (by superposition #[436, 381]): ∀ (a a_1 a_2 : Iota), Or (Eq (id (skS.0 16 a) (skS.0 3 (skS.0 17 a a_1) a_2)) True) (Eq False True) % 15.76/15.92 Clause #556 (by clausification #[376]): ∀ (a a_1 : Iota), % 15.76/15.92 Eq % 15.76/15.92 (Not (Or (∀ (Y4 : Iota), Or (Not (r1 Y4)) (Not (r2 Y4 (skS.0 19 a a_1)))) (Not (id (skS.0 19 a a_1) (skS.0 16 a))))) % 15.76/15.92 True % 15.76/15.92 Clause #557 (by clausification #[556]): ∀ (a a_1 : Iota), % 15.76/15.96 Eq (Or (∀ (Y4 : Iota), Or (Not (r1 Y4)) (Not (r2 Y4 (skS.0 19 a a_1)))) (Not (id (skS.0 19 a a_1) (skS.0 16 a)))) % 15.76/15.96 False % 15.76/15.96 Clause #558 (by clausification #[557]): ∀ (a a_1 : Iota), Eq (Not (id (skS.0 19 a a_1) (skS.0 16 a))) False % 15.76/15.96 Clause #559 (by clausification #[557]): ∀ (a a_1 : Iota), Eq (∀ (Y4 : Iota), Or (Not (r1 Y4)) (Not (r2 Y4 (skS.0 19 a a_1)))) False % 15.76/15.96 Clause #560 (by clausification #[558]): ∀ (a a_1 : Iota), Eq (id (skS.0 19 a a_1) (skS.0 16 a)) True % 15.76/15.96 Clause #568 (by superposition #[560, 164]): ∀ (a a_1 a_2 : Iota), Or (Eq (r2 a (skS.0 16 a_1)) True) (Or (Eq True False) (Eq (r2 a (skS.0 19 a_1 a_2)) False)) % 15.76/15.96 Clause #572 (by clausification #[559]): ∀ (a a_1 a_2 : Iota), % 15.76/15.96 Eq (Not (Or (Not (r1 (skS.0 20 a a_1 a_2))) (Not (r2 (skS.0 20 a a_1 a_2) (skS.0 19 a a_1))))) True % 15.76/15.96 Clause #573 (by clausification #[572]): ∀ (a a_1 a_2 : Iota), Eq (Or (Not (r1 (skS.0 20 a a_1 a_2))) (Not (r2 (skS.0 20 a a_1 a_2) (skS.0 19 a a_1)))) False % 15.76/15.96 Clause #574 (by clausification #[573]): ∀ (a a_1 a_2 : Iota), Eq (Not (r2 (skS.0 20 a a_1 a_2) (skS.0 19 a a_1))) False % 15.76/15.96 Clause #575 (by clausification #[573]): ∀ (a a_1 a_2 : Iota), Eq (Not (r1 (skS.0 20 a a_1 a_2))) False % 15.76/15.96 Clause #576 (by clausification #[574]): ∀ (a a_1 a_2 : Iota), Eq (r2 (skS.0 20 a a_1 a_2) (skS.0 19 a a_1)) True % 15.76/15.96 Clause #582 (by clausification #[575]): ∀ (a a_1 a_2 : Iota), Eq (r1 (skS.0 20 a a_1 a_2)) True % 15.76/15.96 Clause #911 (by clausification #[568]): ∀ (a a_1 a_2 : Iota), Or (Eq (r2 a (skS.0 16 a_1)) True) (Eq (r2 a (skS.0 19 a_1 a_2)) False) % 15.76/15.96 Clause #912 (by superposition #[911, 576]): ∀ (a a_1 a_2 : Iota), Or (Eq (r2 (skS.0 20 a a_1 a_2) (skS.0 16 a)) True) (Eq False True) % 15.76/15.96 Clause #915 (by clausification #[912]): ∀ (a a_1 a_2 : Iota), Eq (r2 (skS.0 20 a a_1 a_2) (skS.0 16 a)) True % 15.76/15.96 Clause #3205 (by clausification #[439]): ∀ (a a_1 a_2 : Iota), Eq (id (skS.0 16 a) (skS.0 3 (skS.0 17 a a_1) a_2)) True % 15.76/15.96 Clause #3206 (by superposition #[3205, 298]): ∀ (a a_1 a_2 : Iota), Or (Eq (id a (skS.0 17 a_1 a_2)) True) (Or (Eq True False) (Eq (r2 a (skS.0 16 a_1)) False)) % 15.76/15.96 Clause #3241 (by clausification #[3206]): ∀ (a a_1 a_2 : Iota), Or (Eq (id a (skS.0 17 a_1 a_2)) True) (Eq (r2 a (skS.0 16 a_1)) False) % 15.76/15.96 Clause #3243 (by superposition #[3241, 915]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (id (skS.0 20 a a_1 a_2) (skS.0 17 a a_3)) True) (Eq False True) % 15.76/15.96 Clause #3316 (by clausification #[3243]): ∀ (a a_1 a_2 a_3 : Iota), Eq (id (skS.0 20 a a_1 a_2) (skS.0 17 a a_3)) True % 15.76/15.96 Clause #3317 (by superposition #[3316, 403]): ∀ (a a_1 a_2 : Iota), Or (Eq True False) (Eq (r1 (skS.0 20 a a_1 a_2)) False) % 15.76/15.96 Clause #3350 (by clausification #[3317]): ∀ (a a_1 a_2 : Iota), Eq (r1 (skS.0 20 a a_1 a_2)) False % 15.76/15.96 Clause #3351 (by superposition #[3350, 582]): Eq False True % 15.76/15.96 Clause #3365 (by clausification #[3351]): False % 15.76/15.96 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------