%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : KLE004+1 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n026.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 07:52:14 PM UTC 2025 % Result : Theorem 13.42s 13.59s % Output : Proof 13.48s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : KLE004+1 : TPTP v9.2.0. Released v4.0.0. % 0.11/0.13 % Command : duper %s % 0.13/0.34 % Computer : n026.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 16:53:53 EDT 2025 % 0.13/0.34 % CPUTime : % 13.42/13.59 SZS status Theorem for theBenchmark.p % 13.42/13.59 SZS output start Proof for theBenchmark.p % 13.42/13.59 Clause #0 (by assumption #[]): Eq (∀ (A B : Iota), Eq (addition A B) (addition B A)) True % 13.42/13.59 Clause #2 (by assumption #[]): Eq (∀ (A : Iota), Eq (addition A zero) A) True % 13.42/13.59 Clause #5 (by assumption #[]): Eq (∀ (A : Iota), Eq (multiplication A one) A) True % 13.42/13.59 Clause #9 (by assumption #[]): Eq (∀ (A : Iota), Eq (multiplication A zero) zero) True % 13.42/13.59 Clause #12 (by assumption #[]): Eq (∀ (X0 : Iota), Iff (test X0) (Exists fun X1 => complement X1 X0)) True % 13.42/13.59 Clause #13 (by assumption #[]): Eq % 13.42/13.59 (∀ (X0 X1 : Iota), % 13.42/13.59 Iff (complement X1 X0) % 13.42/13.59 (And (And (Eq (multiplication X0 X1) zero) (Eq (multiplication X1 X0) zero)) (Eq (addition X0 X1) one))) % 13.42/13.59 True % 13.42/13.59 Clause #14 (by assumption #[]): Eq (∀ (X0 X1 : Iota), test X0 → Iff (Eq (c X0) X1) (complement X0 X1)) True % 13.42/13.59 Clause #16 (by assumption #[]): Eq (Not (Eq (c zero) one)) True % 13.42/13.59 Clause #17 (by clausification #[16]): Eq (Eq (c zero) one) False % 13.42/13.59 Clause #18 (by clausification #[17]): Ne (c zero) one % 13.42/13.59 Clause #25 (by clausification #[9]): ∀ (a : Iota), Eq (Eq (multiplication a zero) zero) True % 13.42/13.59 Clause #26 (by clausification #[25]): ∀ (a : Iota), Eq (multiplication a zero) zero % 13.42/13.59 Clause #29 (by clausification #[0]): ∀ (a : Iota), Eq (∀ (B : Iota), Eq (addition a B) (addition B a)) True % 13.42/13.59 Clause #30 (by clausification #[29]): ∀ (a a_1 : Iota), Eq (Eq (addition a a_1) (addition a_1 a)) True % 13.42/13.59 Clause #31 (by clausification #[30]): ∀ (a a_1 : Iota), Eq (addition a a_1) (addition a_1 a) % 13.42/13.59 Clause #32 (by clausification #[5]): ∀ (a : Iota), Eq (Eq (multiplication a one) a) True % 13.42/13.59 Clause #33 (by clausification #[32]): ∀ (a : Iota), Eq (multiplication a one) a % 13.42/13.59 Clause #36 (by clausification #[2]): ∀ (a : Iota), Eq (Eq (addition a zero) a) True % 13.42/13.59 Clause #37 (by clausification #[36]): ∀ (a : Iota), Eq (addition a zero) a % 13.42/13.59 Clause #39 (by superposition #[37, 31]): ∀ (a : Iota), Eq (addition zero a) a % 13.42/13.59 Clause #177 (by clausification #[12]): ∀ (a : Iota), Eq (Iff (test a) (Exists fun X1 => complement X1 a)) True % 13.42/13.59 Clause #178 (by clausification #[177]): ∀ (a : Iota), Or (Eq (test a) True) (Eq (Exists fun X1 => complement X1 a) False) % 13.42/13.59 Clause #180 (by clausification #[178]): ∀ (a a_1 : Iota), Or (Eq (test a) True) (Eq (complement a_1 a) False) % 13.42/13.59 Clause #190 (by clausification #[13]): ∀ (a : Iota), % 13.42/13.59 Eq % 13.42/13.59 (∀ (X1 : Iota), % 13.42/13.59 Iff (complement X1 a) % 13.42/13.59 (And (And (Eq (multiplication a X1) zero) (Eq (multiplication X1 a) zero)) (Eq (addition a X1) one))) % 13.42/13.59 True % 13.42/13.59 Clause #191 (by clausification #[190]): ∀ (a a_1 : Iota), % 13.42/13.59 Eq % 13.42/13.59 (Iff (complement a a_1) % 13.42/13.59 (And (And (Eq (multiplication a_1 a) zero) (Eq (multiplication a a_1) zero)) (Eq (addition a_1 a) one))) % 13.42/13.59 True % 13.42/13.59 Clause #192 (by clausification #[191]): ∀ (a a_1 : Iota), % 13.42/13.59 Or (Eq (complement a a_1) True) % 13.42/13.59 (Eq (And (And (Eq (multiplication a_1 a) zero) (Eq (multiplication a a_1) zero)) (Eq (addition a_1 a) one)) False) % 13.42/13.59 Clause #194 (by clausification #[192]): ∀ (a a_1 : Iota), % 13.42/13.59 Or (Eq (complement a a_1) True) % 13.42/13.59 (Or (Eq (And (Eq (multiplication a_1 a) zero) (Eq (multiplication a a_1) zero)) False) % 13.42/13.59 (Eq (Eq (addition a_1 a) one) False)) % 13.42/13.59 Clause #195 (by clausification #[194]): ∀ (a a_1 : Iota), % 13.42/13.59 Or (Eq (complement a a_1) True) % 13.42/13.59 (Or (Eq (Eq (addition a_1 a) one) False) % 13.42/13.59 (Or (Eq (Eq (multiplication a_1 a) zero) False) (Eq (Eq (multiplication a a_1) zero) False))) % 13.42/13.59 Clause #196 (by clausification #[195]): ∀ (a a_1 : Iota), % 13.42/13.59 Or (Eq (complement a a_1) True) % 13.42/13.59 (Or (Eq (Eq (multiplication a_1 a) zero) False) % 13.42/13.59 (Or (Eq (Eq (multiplication a a_1) zero) False) (Ne (addition a_1 a) one))) % 13.42/13.59 Clause #197 (by clausification #[196]): ∀ (a a_1 : Iota), % 13.42/13.59 Or (Eq (complement a a_1) True) % 13.42/13.59 (Or (Eq (Eq (multiplication a a_1) zero) False) (Or (Ne (addition a_1 a) one) (Ne (multiplication a_1 a) zero))) % 13.42/13.59 Clause #198 (by clausification #[197]): ∀ (a a_1 : Iota), % 13.42/13.59 Or (Eq (complement a a_1) True) % 13.42/13.59 (Or (Ne (addition a_1 a) one) (Or (Ne (multiplication a_1 a) zero) (Ne (multiplication a a_1) zero))) % 13.42/13.59 Clause #201 (by superposition #[198, 37]): ∀ (a : Iota), % 13.48/13.64 Or (Eq (complement zero a) True) % 13.48/13.64 (Or (Ne a one) (Or (Ne (multiplication a zero) zero) (Ne (multiplication zero a) zero))) % 13.48/13.64 Clause #205 (by superposition #[198, 39]): ∀ (a : Iota), % 13.48/13.64 Or (Eq (complement a zero) True) % 13.48/13.64 (Or (Ne a one) (Or (Ne (multiplication zero a) zero) (Ne (multiplication a zero) zero))) % 13.48/13.64 Clause #227 (by clausification #[14]): ∀ (a : Iota), Eq (∀ (X1 : Iota), test a → Iff (Eq (c a) X1) (complement a X1)) True % 13.48/13.64 Clause #228 (by clausification #[227]): ∀ (a a_1 : Iota), Eq (test a → Iff (Eq (c a) a_1) (complement a a_1)) True % 13.48/13.64 Clause #229 (by clausification #[228]): ∀ (a a_1 : Iota), Or (Eq (test a) False) (Eq (Iff (Eq (c a) a_1) (complement a a_1)) True) % 13.48/13.64 Clause #230 (by clausification #[229]): ∀ (a a_1 : Iota), Or (Eq (test a) False) (Or (Eq (Eq (c a) a_1) True) (Eq (complement a a_1) False)) % 13.48/13.64 Clause #232 (by clausification #[230]): ∀ (a a_1 : Iota), Or (Eq (test a) False) (Or (Eq (complement a a_1) False) (Eq (c a) a_1)) % 13.48/13.64 Clause #6762 (by destructive equality resolution #[201]): Or (Eq (complement zero one) True) (Or (Ne (multiplication one zero) zero) (Ne (multiplication zero one) zero)) % 13.48/13.64 Clause #6763 (by forward demodulation #[6762, 26]): Or (Eq (complement zero one) True) (Or (Ne zero zero) (Ne (multiplication zero one) zero)) % 13.48/13.64 Clause #6764 (by eliminate resolved literals #[6763]): Or (Eq (complement zero one) True) (Ne (multiplication zero one) zero) % 13.48/13.64 Clause #6765 (by forward demodulation #[6764, 33]): Or (Eq (complement zero one) True) (Ne zero zero) % 13.48/13.64 Clause #6766 (by eliminate resolved literals #[6765]): Eq (complement zero one) True % 13.48/13.64 Clause #6926 (by destructive equality resolution #[205]): Or (Eq (complement one zero) True) (Or (Ne (multiplication zero one) zero) (Ne (multiplication one zero) zero)) % 13.48/13.64 Clause #6927 (by forward demodulation #[6926, 33]): Or (Eq (complement one zero) True) (Or (Ne zero zero) (Ne (multiplication one zero) zero)) % 13.48/13.64 Clause #6928 (by eliminate resolved literals #[6927]): Or (Eq (complement one zero) True) (Ne (multiplication one zero) zero) % 13.48/13.64 Clause #6929 (by forward demodulation #[6928, 26]): Or (Eq (complement one zero) True) (Ne zero zero) % 13.48/13.64 Clause #6930 (by eliminate resolved literals #[6929]): Eq (complement one zero) True % 13.48/13.64 Clause #6932 (by superposition #[6930, 180]): Or (Eq (test zero) True) (Eq True False) % 13.48/13.64 Clause #6934 (by clausification #[6932]): Eq (test zero) True % 13.48/13.64 Clause #6935 (by superposition #[6934, 232]): ∀ (a : Iota), Or (Eq True False) (Or (Eq (complement zero a) False) (Eq (c zero) a)) % 13.48/13.64 Clause #7047 (by clausification #[6935]): ∀ (a : Iota), Or (Eq (complement zero a) False) (Eq (c zero) a) % 13.48/13.64 Clause #7048 (by superposition #[7047, 6766]): Or (Eq (c zero) one) (Eq False True) % 13.48/13.64 Clause #7049 (by clausification #[7048]): Eq (c zero) one % 13.48/13.64 Clause #7050 (by forward contextual literal cutting #[7049, 18]): False % 13.48/13.64 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------