TSTP Solution File: REL002+1 by Duper---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : REL002+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n019.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 13:37:35 EDT 2023
% Result : Theorem 12.68s 12.94s
% Output : Proof 12.68s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : REL002+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : duper %s
% 0.13/0.35 % Computer : n019.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri Aug 25 19:15:13 EDT 2023
% 0.13/0.35 % CPUTime :
% 12.68/12.94 SZS status Theorem for theBenchmark.p
% 12.68/12.94 SZS output start Proof for theBenchmark.p
% 12.68/12.94 Clause #0 (by assumption #[]): Eq (∀ (X0 X1 : Iota), Eq (join X0 X1) (join X1 X0)) True
% 12.68/12.94 Clause #1 (by assumption #[]): Eq (∀ (X0 X1 X2 : Iota), Eq (join X0 (join X1 X2)) (join (join X0 X1) X2)) True
% 12.68/12.94 Clause #2 (by assumption #[]): Eq
% 12.68/12.94 (∀ (X0 X1 : Iota),
% 12.68/12.94 Eq X0 (join (complement (join (complement X0) (complement X1))) (complement (join (complement X0) X1))))
% 12.68/12.94 True
% 12.68/12.94 Clause #3 (by assumption #[]): Eq (∀ (X0 X1 : Iota), Eq (meet X0 X1) (complement (join (complement X0) (complement X1)))) True
% 12.68/12.94 Clause #11 (by assumption #[]): Eq (∀ (X0 : Iota), Eq top (join X0 (complement X0))) True
% 12.68/12.94 Clause #12 (by assumption #[]): Eq (∀ (X0 : Iota), Eq zero (meet X0 (complement X0))) True
% 12.68/12.94 Clause #13 (by assumption #[]): Eq (Not (∀ (X0 : Iota), Eq (join X0 top) top)) True
% 12.68/12.94 Clause #18 (by clausification #[13]): Eq (∀ (X0 : Iota), Eq (join X0 top) top) False
% 12.68/12.94 Clause #19 (by clausification #[18]): ∀ (a : Iota), Eq (Not (Eq (join (skS.0 0 a) top) top)) True
% 12.68/12.94 Clause #20 (by clausification #[19]): ∀ (a : Iota), Eq (Eq (join (skS.0 0 a) top) top) False
% 12.68/12.94 Clause #21 (by clausification #[20]): ∀ (a : Iota), Ne (join (skS.0 0 a) top) top
% 12.68/12.94 Clause #22 (by clausification #[12]): ∀ (a : Iota), Eq (Eq zero (meet a (complement a))) True
% 12.68/12.94 Clause #23 (by clausification #[22]): ∀ (a : Iota), Eq zero (meet a (complement a))
% 12.68/12.94 Clause #24 (by clausification #[11]): ∀ (a : Iota), Eq (Eq top (join a (complement a))) True
% 12.68/12.94 Clause #25 (by clausification #[24]): ∀ (a : Iota), Eq top (join a (complement a))
% 12.68/12.94 Clause #26 (by clausification #[0]): ∀ (a : Iota), Eq (∀ (X1 : Iota), Eq (join a X1) (join X1 a)) True
% 12.68/12.94 Clause #27 (by clausification #[26]): ∀ (a a_1 : Iota), Eq (Eq (join a a_1) (join a_1 a)) True
% 12.68/12.94 Clause #28 (by clausification #[27]): ∀ (a a_1 : Iota), Eq (join a a_1) (join a_1 a)
% 12.68/12.94 Clause #48 (by clausification #[1]): ∀ (a : Iota), Eq (∀ (X1 X2 : Iota), Eq (join a (join X1 X2)) (join (join a X1) X2)) True
% 12.68/12.94 Clause #49 (by clausification #[48]): ∀ (a a_1 : Iota), Eq (∀ (X2 : Iota), Eq (join a (join a_1 X2)) (join (join a a_1) X2)) True
% 12.68/12.94 Clause #50 (by clausification #[49]): ∀ (a a_1 a_2 : Iota), Eq (Eq (join a (join a_1 a_2)) (join (join a a_1) a_2)) True
% 12.68/12.94 Clause #51 (by clausification #[50]): ∀ (a a_1 a_2 : Iota), Eq (join a (join a_1 a_2)) (join (join a a_1) a_2)
% 12.68/12.94 Clause #52 (by superposition #[51, 25]): ∀ (a a_1 : Iota), Eq top (join a (join a_1 (complement (join a a_1))))
% 12.68/12.94 Clause #56 (by superposition #[51, 25]): ∀ (a a_1 : Iota), Eq (join a (join (complement a) a_1)) (join top a_1)
% 12.68/12.94 Clause #64 (by clausification #[2]): ∀ (a : Iota),
% 12.68/12.94 Eq
% 12.68/12.94 (∀ (X1 : Iota),
% 12.68/12.94 Eq a (join (complement (join (complement a) (complement X1))) (complement (join (complement a) X1))))
% 12.68/12.94 True
% 12.68/12.94 Clause #65 (by clausification #[64]): ∀ (a a_1 : Iota),
% 12.68/12.94 Eq (Eq a (join (complement (join (complement a) (complement a_1))) (complement (join (complement a) a_1)))) True
% 12.68/12.94 Clause #66 (by clausification #[65]): ∀ (a a_1 : Iota), Eq a (join (complement (join (complement a) (complement a_1))) (complement (join (complement a) a_1)))
% 12.68/12.94 Clause #69 (by superposition #[66, 28]): ∀ (a a_1 : Iota), Eq a (join (complement (join (complement a) a_1)) (complement (join (complement a) (complement a_1))))
% 12.68/12.94 Clause #74 (by superposition #[66, 25]): ∀ (a : Iota), Eq a (join (complement top) (complement (join (complement a) (complement a))))
% 12.68/12.94 Clause #85 (by superposition #[56, 25]): ∀ (a : Iota), Eq (join a top) (join top (complement (complement a)))
% 12.68/12.94 Clause #86 (by superposition #[56, 28]): ∀ (a a_1 : Iota), Eq (join a (join a_1 (complement a))) (join top a_1)
% 12.68/12.94 Clause #87 (by clausification #[3]): ∀ (a : Iota), Eq (∀ (X1 : Iota), Eq (meet a X1) (complement (join (complement a) (complement X1)))) True
% 12.68/12.94 Clause #88 (by clausification #[87]): ∀ (a a_1 : Iota), Eq (Eq (meet a a_1) (complement (join (complement a) (complement a_1)))) True
% 12.68/12.94 Clause #89 (by clausification #[88]): ∀ (a a_1 : Iota), Eq (meet a a_1) (complement (join (complement a) (complement a_1)))
% 12.68/12.94 Clause #92 (by superposition #[89, 25]): ∀ (a a_1 : Iota), Eq top (join (join (complement a) (complement a_1)) (meet a a_1))
% 12.68/12.97 Clause #96 (by superposition #[89, 25]): ∀ (a : Iota), Eq (meet a (complement a)) (complement top)
% 12.68/12.97 Clause #98 (by superposition #[96, 23]): Eq zero (complement top)
% 12.68/12.97 Clause #101 (by superposition #[98, 23]): Eq zero (meet top zero)
% 12.68/12.97 Clause #102 (by superposition #[98, 25]): Eq top (join top zero)
% 12.68/12.97 Clause #104 (by superposition #[98, 89]): ∀ (a : Iota), Eq (meet a top) (complement (join (complement a) zero))
% 12.68/12.97 Clause #105 (by superposition #[98, 89]): ∀ (a : Iota), Eq (meet top a) (complement (join zero (complement a)))
% 12.68/12.97 Clause #117 (by superposition #[105, 25]): ∀ (a : Iota), Eq top (join (join zero (complement a)) (meet top a))
% 12.68/12.97 Clause #315 (by forward demodulation #[104, 28]): ∀ (a : Iota), Eq (meet a top) (complement (join zero (complement a)))
% 12.68/12.97 Clause #326 (by superposition #[315, 25]): Eq (meet zero top) (complement top)
% 12.68/12.97 Clause #330 (by forward demodulation #[326, 98]): Eq (meet zero top) zero
% 12.68/12.97 Clause #337 (by superposition #[86, 85]): ∀ (a : Iota), Eq (join (complement a) (join a top)) (join top top)
% 12.68/12.97 Clause #380 (by superposition #[337, 28]): ∀ (a : Iota), Eq (join (complement a) (join top a)) (join top top)
% 12.68/12.97 Clause #387 (by superposition #[380, 102]): Eq (join (complement zero) top) (join top top)
% 12.68/12.97 Clause #404 (by superposition #[117, 28]): ∀ (a : Iota), Eq (join (meet top a) (join zero (complement a))) top
% 12.68/12.97 Clause #414 (by superposition #[404, 25]): Eq (join (meet top zero) top) top
% 12.68/12.97 Clause #423 (by forward demodulation #[414, 101]): Eq (join zero top) top
% 12.68/12.97 Clause #425 (by superposition #[423, 51]): ∀ (a : Iota), Eq (join zero (join top a)) (join top a)
% 12.68/12.97 Clause #468 (by superposition #[52, 25]): ∀ (a : Iota), Eq top (join a (join (complement a) (complement top)))
% 12.68/12.97 Clause #839 (by forward demodulation #[468, 98]): ∀ (a : Iota), Eq top (join a (join (complement a) zero))
% 12.68/12.97 Clause #840 (by forward demodulation #[839, 28]): ∀ (a : Iota), Eq top (join a (join zero (complement a)))
% 12.68/12.97 Clause #884 (by forward demodulation #[69, 89]): ∀ (a a_1 : Iota), Eq a (join (complement (join (complement a) a_1)) (meet a a_1))
% 12.68/12.97 Clause #895 (by superposition #[884, 330]): Eq zero (join (complement (join (complement zero) top)) zero)
% 12.68/12.97 Clause #926 (by forward demodulation #[895, 387]): Eq zero (join (complement (join top top)) zero)
% 12.68/12.97 Clause #933 (by superposition #[926, 28]): Eq (join zero (complement (join top top))) zero
% 12.68/12.97 Clause #942 (by superposition #[933, 840]): Eq top (join (join top top) zero)
% 12.68/12.97 Clause #951 (by superposition #[942, 28]): Eq (join zero (join top top)) top
% 12.68/12.97 Clause #956 (by superposition #[951, 425]): Eq top (join top top)
% 12.68/12.97 Clause #966 (by backward demodulation #[956, 933]): Eq (join zero (complement top)) zero
% 12.68/12.97 Clause #970 (by forward demodulation #[966, 98]): Eq (join zero zero) zero
% 12.68/12.97 Clause #976 (by superposition #[970, 51]): ∀ (a : Iota), Eq (join zero (join zero a)) (join zero a)
% 12.68/12.97 Clause #1088 (by forward demodulation #[74, 89]): ∀ (a : Iota), Eq a (join (complement top) (meet a a))
% 12.68/12.97 Clause #1089 (by forward demodulation #[1088, 98]): ∀ (a : Iota), Eq a (join zero (meet a a))
% 12.68/12.97 Clause #1571 (by superposition #[976, 1089]): ∀ (a : Iota), Eq (join zero a) a
% 12.68/12.97 Clause #1618 (by superposition #[1571, 1089]): ∀ (a : Iota), Eq a (meet a a)
% 12.68/12.97 Clause #1680 (by superposition #[1618, 92]): ∀ (a : Iota), Eq top (join (join (complement a) (complement a)) a)
% 12.68/12.97 Clause #4236 (by superposition #[1680, 28]): ∀ (a : Iota), Eq (join a (join (complement a) (complement a))) top
% 12.68/12.97 Clause #4442 (by superposition #[4236, 56]): ∀ (a : Iota), Eq top (join top (complement a))
% 12.68/12.97 Clause #4485 (by superposition #[4442, 52]): ∀ (a : Iota), Eq top (join a top)
% 12.68/12.97 Clause #4571 (by backward contextual literal cutting #[4485, 21]): False
% 12.68/12.97 SZS output end Proof for theBenchmark.p
%------------------------------------------------------------------------------