TSTP Solution File: NUN023^2 by Duper---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : NUN023^2 : TPTP v8.1.2. Released v6.4.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n013.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 : Thu Aug 31 12:47:09 EDT 2023
% Result : Theorem 105.50s 105.71s
% Output : Proof 105.85s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUN023^2 : TPTP v8.1.2. Released v6.4.0.
% 0.00/0.14 % Command : duper %s
% 0.17/0.34 % Computer : n013.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Sun Aug 27 08:54:47 EDT 2023
% 0.17/0.34 % CPUTime :
% 105.50/105.71 SZS status Theorem for theBenchmark.p
% 105.50/105.71 SZS output start Proof for theBenchmark.p
% 105.50/105.71 Clause #0 (by assumption #[]): Eq
% 105.50/105.71 (Not
% 105.50/105.71 (And
% 105.50/105.71 (And (∀ (X100 : Prop) (U V : Iota), X100 → Eq (ite X100 U V) U)
% 105.50/105.71 (∀ (X100 : Prop) (U V : Iota), Not X100 → Eq (ite X100 U V) V))
% 105.50/105.71 (∀ (X : Iota), Eq (h X) (ite (Eq X zero) (s zero) zero)) →
% 105.50/105.71 Exists fun H => And (Eq (H zero) (s zero)) (Eq (H (s zero)) zero)))
% 105.50/105.71 True
% 105.50/105.71 Clause #1 (by clausification #[0]): Eq
% 105.50/105.71 (And
% 105.50/105.71 (And (∀ (X100 : Prop) (U V : Iota), X100 → Eq (ite X100 U V) U)
% 105.50/105.71 (∀ (X100 : Prop) (U V : Iota), Not X100 → Eq (ite X100 U V) V))
% 105.50/105.71 (∀ (X : Iota), Eq (h X) (ite (Eq X zero) (s zero) zero)) →
% 105.50/105.71 Exists fun H => And (Eq (H zero) (s zero)) (Eq (H (s zero)) zero))
% 105.50/105.71 False
% 105.50/105.71 Clause #2 (by clausification #[1]): Eq
% 105.50/105.71 (And
% 105.50/105.71 (And (∀ (X100 : Prop) (U V : Iota), X100 → Eq (ite X100 U V) U)
% 105.50/105.71 (∀ (X100 : Prop) (U V : Iota), Not X100 → Eq (ite X100 U V) V))
% 105.50/105.71 (∀ (X : Iota), Eq (h X) (ite (Eq X zero) (s zero) zero)))
% 105.50/105.71 True
% 105.50/105.71 Clause #3 (by clausification #[1]): Eq (Exists fun H => And (Eq (H zero) (s zero)) (Eq (H (s zero)) zero)) False
% 105.50/105.71 Clause #4 (by clausification #[2]): Eq (∀ (X : Iota), Eq (h X) (ite (Eq X zero) (s zero) zero)) True
% 105.50/105.71 Clause #5 (by clausification #[2]): Eq
% 105.50/105.71 (And (∀ (X100 : Prop) (U V : Iota), X100 → Eq (ite X100 U V) U)
% 105.50/105.71 (∀ (X100 : Prop) (U V : Iota), Not X100 → Eq (ite X100 U V) V))
% 105.50/105.71 True
% 105.50/105.71 Clause #6 (by clausification #[4]): ∀ (a : Iota), Eq (Eq (h a) (ite (Eq a zero) (s zero) zero)) True
% 105.50/105.71 Clause #7 (by clausification #[6]): ∀ (a : Iota), Eq (h a) (ite (Eq a zero) (s zero) zero)
% 105.50/105.71 Clause #8 (by identity loobHoist #[7]): ∀ (a : Iota), Or (Eq (h a) (ite True (s zero) zero)) (Eq (Eq a zero) False)
% 105.50/105.71 Clause #9 (by identity boolHoist #[7]): ∀ (a : Iota), Or (Eq (h a) (ite False (s zero) zero)) (Eq (Eq a zero) True)
% 105.50/105.71 Clause #10 (by clausification #[8]): ∀ (a : Iota), Or (Eq (h a) (ite True (s zero) zero)) (Ne a zero)
% 105.50/105.71 Clause #11 (by destructive equality resolution #[10]): Eq (h zero) (ite True (s zero) zero)
% 105.50/105.71 Clause #12 (by clausification #[9]): ∀ (a : Iota), Or (Eq (h a) (ite False (s zero) zero)) (Eq a zero)
% 105.50/105.71 Clause #13 (by superposition #[12, 12]): ∀ (a a_1 : Iota), Or (Eq a zero) (Or (Eq (h a_1) (h a)) (Eq a_1 zero))
% 105.50/105.71 Clause #48 (by clausification #[3]): ∀ (a : Iota → Iota), Eq (And (Eq (a zero) (s zero)) (Eq (a (s zero)) zero)) False
% 105.50/105.71 Clause #49 (by clausification #[48]): ∀ (a : Iota → Iota), Or (Eq (Eq (a zero) (s zero)) False) (Eq (Eq (a (s zero)) zero) False)
% 105.50/105.71 Clause #50 (by clausification #[49]): ∀ (a : Iota → Iota), Or (Eq (Eq (a (s zero)) zero) False) (Ne (a zero) (s zero))
% 105.50/105.71 Clause #51 (by clausification #[50]): ∀ (a : Iota → Iota), Or (Ne (a zero) (s zero)) (Ne (a (s zero)) zero)
% 105.50/105.71 Clause #52 (by equality resolution #[51]): Ne ((fun x => s zero) (s zero)) zero
% 105.50/105.71 Clause #61 (by betaEtaReduce #[52]): Ne (s zero) zero
% 105.50/105.71 Clause #63 (by superposition #[61, 13]): ∀ (a : Iota), Or (Eq a zero) (Or (Eq (h (s zero)) (h a)) (Ne zero zero))
% 105.50/105.71 Clause #79 (by clausification #[5]): Eq (∀ (X100 : Prop) (U V : Iota), Not X100 → Eq (ite X100 U V) V) True
% 105.50/105.71 Clause #80 (by clausification #[5]): Eq (∀ (X100 : Prop) (U V : Iota), X100 → Eq (ite X100 U V) U) True
% 105.50/105.71 Clause #81 (by clausification #[79]): ∀ (a : Prop), Eq (∀ (U V : Iota), Not a → Eq (ite a U V) V) True
% 105.50/105.71 Clause #82 (by clausification #[81]): ∀ (a : Prop) (a_1 : Iota), Eq (∀ (V : Iota), Not a → Eq (ite a a_1 V) V) True
% 105.50/105.71 Clause #83 (by clausification #[82]): ∀ (a : Prop) (a_1 a_2 : Iota), Eq (Not a → Eq (ite a a_1 a_2) a_2) True
% 105.50/105.71 Clause #84 (by clausification #[83]): ∀ (a : Prop) (a_1 a_2 : Iota), Or (Eq (Not a) False) (Eq (Eq (ite a a_1 a_2) a_2) True)
% 105.50/105.71 Clause #85 (by clausification #[84]): ∀ (a : Prop) (a_1 a_2 : Iota), Or (Eq (Eq (ite a a_1 a_2) a_2) True) (Eq a True)
% 105.50/105.71 Clause #86 (by clausification #[85]): ∀ (a : Prop) (a_1 a_2 : Iota), Or (Eq a True) (Eq (ite a a_1 a_2) a_2)
% 105.50/105.71 Clause #88 (by identity boolHoist #[86]): ∀ (a : Prop) (a_1 a_2 : Iota), Or (Eq a True) (Or (Eq (ite False a_1 a_2) a_2) (Eq a True))
% 105.85/106.02 Clause #89 (by eliminate duplicate literals #[88]): ∀ (a : Prop) (a_1 a_2 : Iota), Or (Eq a True) (Eq (ite False a_1 a_2) a_2)
% 105.85/106.02 Clause #91 (by falseElim #[89]): ∀ (a a_1 : Iota), Eq (ite False a a_1) a_1
% 105.85/106.02 Clause #92 (by backward demodulation #[91, 12]): ∀ (a : Iota), Or (Eq (h a) zero) (Eq a zero)
% 105.85/106.02 Clause #243 (by eliminate resolved literals #[63]): ∀ (a : Iota), Or (Eq a zero) (Eq (h (s zero)) (h a))
% 105.85/106.02 Clause #274 (by superposition #[243, 92]): ∀ (a : Iota), Or (Eq a zero) (Or (Eq (h (s zero)) zero) (Eq a zero))
% 105.85/106.02 Clause #291 (by eliminate duplicate literals #[274]): ∀ (a : Iota), Or (Eq a zero) (Eq (h (s zero)) zero)
% 105.85/106.02 Clause #331 (by equality factoring #[291]): Or (Ne zero zero) (Eq (h (s zero)) zero)
% 105.85/106.02 Clause #333 (by eliminate resolved literals #[331]): Eq (h (s zero)) zero
% 105.85/106.02 Clause #4342 (by clausification #[80]): ∀ (a : Prop), Eq (∀ (U V : Iota), a → Eq (ite a U V) U) True
% 105.85/106.02 Clause #4343 (by clausification #[4342]): ∀ (a : Prop) (a_1 : Iota), Eq (∀ (V : Iota), a → Eq (ite a a_1 V) a_1) True
% 105.85/106.02 Clause #4344 (by clausification #[4343]): ∀ (a : Prop) (a_1 a_2 : Iota), Eq (a → Eq (ite a a_1 a_2) a_1) True
% 105.85/106.02 Clause #4345 (by clausification #[4344]): ∀ (a : Prop) (a_1 a_2 : Iota), Or (Eq a False) (Eq (Eq (ite a a_1 a_2) a_1) True)
% 105.85/106.02 Clause #4346 (by clausification #[4345]): ∀ (a : Prop) (a_1 a_2 : Iota), Or (Eq a False) (Eq (ite a a_1 a_2) a_1)
% 105.85/106.02 Clause #4347 (by identity loobHoist #[4346]): ∀ (a : Prop) (a_1 a_2 : Iota), Or (Eq a False) (Or (Eq (ite True a_1 a_2) a_1) (Eq a False))
% 105.85/106.02 Clause #4349 (by eliminate duplicate literals #[4347]): ∀ (a : Prop) (a_1 a_2 : Iota), Or (Eq a False) (Eq (ite True a_1 a_2) a_1)
% 105.85/106.02 Clause #4350 (by falseElim #[4349]): ∀ (a a_1 : Iota), Eq (ite True a a_1) a
% 105.85/106.02 Clause #4351 (by superposition #[4350, 11]): Eq (h zero) (s zero)
% 105.85/106.02 Clause #4355 (by backward demodulation #[4351, 51]): ∀ (a : Iota → Iota), Or (Ne (a zero) (h zero)) (Ne (a (s zero)) zero)
% 105.85/106.02 Clause #4356 (by backward demodulation #[4351, 61]): Ne (h zero) zero
% 105.85/106.02 Clause #4358 (by backward demodulation #[4351, 333]): Eq (h (h zero)) zero
% 105.85/106.02 Clause #5246 (by forward demodulation #[4355, 4351]): ∀ (a : Iota → Iota), Or (Ne (a zero) (h zero)) (Ne (a (h zero)) zero)
% 105.85/106.02 Clause #5250 (by superposition #[5246, 92]): ∀ (a : Iota) (a_1 : Iota → Iota), Or (Eq (h a) zero) (Or (Ne (a_1 zero) (h a)) (Ne (a_1 (h zero)) a))
% 105.85/106.02 Clause #29957 (by equality resolution #[5250]): ∀ (a : Iota → Iota), Or (Eq (h (a zero)) zero) (Ne ((fun x => h (a x)) (h zero)) (a zero))
% 105.85/106.02 Clause #44655 (by betaEtaReduce #[29957]): ∀ (a : Iota → Iota), Or (Eq (h (a zero)) zero) (Ne (h (a (h zero))) (a zero))
% 105.85/106.02 Clause #44661 (by superposition #[44655, 4358]): Or (Eq (h zero) zero) (Ne zero zero)
% 105.85/106.02 Clause #45354 (by eliminate resolved literals #[44661]): Eq (h zero) zero
% 105.85/106.02 Clause #45355 (by forward contextual literal cutting #[45354, 4356]): False
% 105.85/106.02 SZS output end Proof for theBenchmark.p
%------------------------------------------------------------------------------