TSTP Solution File: REL015+1 by Duper---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : REL015+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n011.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 13:37:41 EDT 2023
% Result : Theorem 26.54s 26.72s
% Output : Proof 26.57s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : REL015+1 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.14 % Command : duper %s
% 0.15/0.35 % Computer : n011.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Fri Aug 25 19:17:23 EDT 2023
% 0.15/0.35 % CPUTime :
% 26.54/26.72 SZS status Theorem for theBenchmark.p
% 26.54/26.72 SZS output start Proof for theBenchmark.p
% 26.54/26.72 Clause #0 (by assumption #[]): Eq (∀ (X0 X1 : Iota), Eq (join X0 X1) (join X1 X0)) True
% 26.54/26.72 Clause #1 (by assumption #[]): Eq (∀ (X0 X1 X2 : Iota), Eq (join X0 (join X1 X2)) (join (join X0 X1) X2)) True
% 26.54/26.72 Clause #2 (by assumption #[]): Eq
% 26.54/26.72 (∀ (X0 X1 : Iota),
% 26.54/26.72 Eq X0 (join (complement (join (complement X0) (complement X1))) (complement (join (complement X0) X1))))
% 26.54/26.72 True
% 26.54/26.72 Clause #3 (by assumption #[]): Eq (∀ (X0 X1 : Iota), Eq (meet X0 X1) (complement (join (complement X0) (complement X1)))) True
% 26.54/26.72 Clause #5 (by assumption #[]): Eq (∀ (X0 : Iota), Eq (composition X0 one) X0) True
% 26.54/26.72 Clause #6 (by assumption #[]): Eq (∀ (X0 X1 X2 : Iota), Eq (composition (join X0 X1) X2) (join (composition X0 X2) (composition X1 X2))) True
% 26.54/26.72 Clause #7 (by assumption #[]): Eq (∀ (X0 : Iota), Eq (converse (converse X0)) X0) True
% 26.54/26.72 Clause #9 (by assumption #[]): Eq (∀ (X0 X1 : Iota), Eq (converse (composition X0 X1)) (composition (converse X1) (converse X0))) True
% 26.54/26.72 Clause #11 (by assumption #[]): Eq (∀ (X0 : Iota), Eq top (join X0 (complement X0))) True
% 26.54/26.72 Clause #12 (by assumption #[]): Eq (∀ (X0 : Iota), Eq zero (meet X0 (complement X0))) True
% 26.54/26.72 Clause #13 (by assumption #[]): Eq (Not (Eq (composition top top) top)) True
% 26.54/26.72 Clause #14 (by clausification #[13]): Eq (Eq (composition top top) top) False
% 26.54/26.72 Clause #15 (by clausification #[14]): Ne (composition top top) top
% 26.54/26.72 Clause #16 (by clausification #[7]): ∀ (a : Iota), Eq (Eq (converse (converse a)) a) True
% 26.54/26.72 Clause #17 (by clausification #[16]): ∀ (a : Iota), Eq (converse (converse a)) a
% 26.54/26.72 Clause #18 (by clausification #[5]): ∀ (a : Iota), Eq (Eq (composition a one) a) True
% 26.54/26.72 Clause #19 (by clausification #[18]): ∀ (a : Iota), Eq (composition a one) a
% 26.54/26.72 Clause #20 (by clausification #[12]): ∀ (a : Iota), Eq (Eq zero (meet a (complement a))) True
% 26.54/26.72 Clause #21 (by clausification #[20]): ∀ (a : Iota), Eq zero (meet a (complement a))
% 26.54/26.72 Clause #22 (by clausification #[11]): ∀ (a : Iota), Eq (Eq top (join a (complement a))) True
% 26.54/26.72 Clause #23 (by clausification #[22]): ∀ (a : Iota), Eq top (join a (complement a))
% 26.54/26.72 Clause #24 (by clausification #[0]): ∀ (a : Iota), Eq (∀ (X1 : Iota), Eq (join a X1) (join X1 a)) True
% 26.54/26.72 Clause #25 (by clausification #[24]): ∀ (a a_1 : Iota), Eq (Eq (join a a_1) (join a_1 a)) True
% 26.54/26.72 Clause #26 (by clausification #[25]): ∀ (a a_1 : Iota), Eq (join a a_1) (join a_1 a)
% 26.54/26.72 Clause #27 (by clausification #[9]): ∀ (a : Iota), Eq (∀ (X1 : Iota), Eq (converse (composition a X1)) (composition (converse X1) (converse a))) True
% 26.54/26.72 Clause #28 (by clausification #[27]): ∀ (a a_1 : Iota), Eq (Eq (converse (composition a a_1)) (composition (converse a_1) (converse a))) True
% 26.54/26.72 Clause #29 (by clausification #[28]): ∀ (a a_1 : Iota), Eq (converse (composition a a_1)) (composition (converse a_1) (converse a))
% 26.54/26.72 Clause #30 (by superposition #[29, 17]): ∀ (a a_1 : Iota), Eq (converse (composition (converse a) a_1)) (composition (converse a_1) a)
% 26.54/26.72 Clause #39 (by superposition #[30, 19]): ∀ (a : Iota), Eq (converse (converse a)) (composition (converse one) a)
% 26.54/26.72 Clause #40 (by forward demodulation #[39, 17]): ∀ (a : Iota), Eq a (composition (converse one) a)
% 26.54/26.72 Clause #42 (by superposition #[40, 19]): Eq one (converse one)
% 26.54/26.72 Clause #45 (by backward demodulation #[42, 40]): ∀ (a : Iota), Eq a (composition one a)
% 26.54/26.72 Clause #49 (by clausification #[1]): ∀ (a : Iota), Eq (∀ (X1 X2 : Iota), Eq (join a (join X1 X2)) (join (join a X1) X2)) True
% 26.54/26.72 Clause #50 (by clausification #[49]): ∀ (a a_1 : Iota), Eq (∀ (X2 : Iota), Eq (join a (join a_1 X2)) (join (join a a_1) X2)) True
% 26.54/26.72 Clause #51 (by clausification #[50]): ∀ (a a_1 a_2 : Iota), Eq (Eq (join a (join a_1 a_2)) (join (join a a_1) a_2)) True
% 26.54/26.72 Clause #52 (by clausification #[51]): ∀ (a a_1 a_2 : Iota), Eq (join a (join a_1 a_2)) (join (join a a_1) a_2)
% 26.54/26.72 Clause #53 (by superposition #[52, 23]): ∀ (a a_1 : Iota), Eq top (join a (join a_1 (complement (join a a_1))))
% 26.54/26.72 Clause #55 (by superposition #[52, 26]): ∀ (a a_1 a_2 : Iota), Eq (join a (join a_1 a_2)) (join a_1 (join a_2 a))
% 26.57/26.74 Clause #57 (by superposition #[52, 23]): ∀ (a a_1 : Iota), Eq (join a (join (complement a) a_1)) (join top a_1)
% 26.57/26.74 Clause #63 (by clausification #[2]): ∀ (a : Iota),
% 26.57/26.74 Eq
% 26.57/26.74 (∀ (X1 : Iota),
% 26.57/26.74 Eq a (join (complement (join (complement a) (complement X1))) (complement (join (complement a) X1))))
% 26.57/26.74 True
% 26.57/26.74 Clause #64 (by clausification #[63]): ∀ (a a_1 : Iota),
% 26.57/26.74 Eq (Eq a (join (complement (join (complement a) (complement a_1))) (complement (join (complement a) a_1)))) True
% 26.57/26.74 Clause #65 (by clausification #[64]): ∀ (a a_1 : Iota), Eq a (join (complement (join (complement a) (complement a_1))) (complement (join (complement a) a_1)))
% 26.57/26.74 Clause #68 (by superposition #[65, 26]): ∀ (a a_1 : Iota), Eq a (join (complement (join (complement a) a_1)) (complement (join (complement a) (complement a_1))))
% 26.57/26.74 Clause #72 (by superposition #[65, 26]): ∀ (a a_1 : Iota), Eq a (join (complement (join (complement a) (complement a_1))) (complement (join a_1 (complement a))))
% 26.57/26.74 Clause #83 (by superposition #[53, 23]): ∀ (a : Iota), Eq top (join a (join (complement a) (complement top)))
% 26.57/26.74 Clause #91 (by clausification #[3]): ∀ (a : Iota), Eq (∀ (X1 : Iota), Eq (meet a X1) (complement (join (complement a) (complement X1)))) True
% 26.57/26.74 Clause #92 (by clausification #[91]): ∀ (a a_1 : Iota), Eq (Eq (meet a a_1) (complement (join (complement a) (complement a_1)))) True
% 26.57/26.74 Clause #93 (by clausification #[92]): ∀ (a a_1 : Iota), Eq (meet a a_1) (complement (join (complement a) (complement a_1)))
% 26.57/26.74 Clause #97 (by superposition #[93, 23]): ∀ (a a_1 : Iota), Eq top (join (join (complement a) (complement a_1)) (meet a a_1))
% 26.57/26.74 Clause #101 (by superposition #[93, 23]): ∀ (a : Iota), Eq (meet a (complement a)) (complement top)
% 26.57/26.74 Clause #103 (by superposition #[101, 21]): Eq zero (complement top)
% 26.57/26.74 Clause #105 (by backward demodulation #[103, 83]): ∀ (a : Iota), Eq top (join a (join (complement a) zero))
% 26.57/26.74 Clause #109 (by superposition #[103, 93]): ∀ (a : Iota), Eq (meet a top) (complement (join (complement a) zero))
% 26.57/26.74 Clause #126 (by forward demodulation #[105, 26]): ∀ (a : Iota), Eq top (join a (join zero (complement a)))
% 26.57/26.74 Clause #130 (by superposition #[126, 23]): Eq top (join zero top)
% 26.57/26.74 Clause #133 (by superposition #[130, 52]): ∀ (a : Iota), Eq (join zero (join top a)) (join top a)
% 26.57/26.74 Clause #135 (by clausification #[6]): ∀ (a : Iota), Eq (∀ (X1 X2 : Iota), Eq (composition (join a X1) X2) (join (composition a X2) (composition X1 X2))) True
% 26.57/26.74 Clause #136 (by clausification #[135]): ∀ (a a_1 : Iota),
% 26.57/26.74 Eq (∀ (X2 : Iota), Eq (composition (join a a_1) X2) (join (composition a X2) (composition a_1 X2))) True
% 26.57/26.74 Clause #137 (by clausification #[136]): ∀ (a a_1 a_2 : Iota), Eq (Eq (composition (join a a_1) a_2) (join (composition a a_2) (composition a_1 a_2))) True
% 26.57/26.74 Clause #138 (by clausification #[137]): ∀ (a a_1 a_2 : Iota), Eq (composition (join a a_1) a_2) (join (composition a a_2) (composition a_1 a_2))
% 26.57/26.74 Clause #149 (by superposition #[138, 45]): ∀ (a a_1 : Iota), Eq (composition (join one a) a_1) (join a_1 (composition a a_1))
% 26.57/26.74 Clause #155 (by superposition #[133, 26]): ∀ (a : Iota), Eq (join zero (join a top)) (join a top)
% 26.57/26.74 Clause #381 (by forward demodulation #[109, 26]): ∀ (a : Iota), Eq (meet a top) (complement (join zero (complement a)))
% 26.57/26.74 Clause #392 (by superposition #[381, 23]): Eq (meet zero top) (complement top)
% 26.57/26.74 Clause #396 (by forward demodulation #[392, 103]): Eq (meet zero top) zero
% 26.57/26.74 Clause #410 (by superposition #[57, 155]): Eq (join (complement zero) top) (join top top)
% 26.57/26.74 Clause #554 (by superposition #[55, 130]): ∀ (a : Iota), Eq (join a top) (join zero (join top a))
% 26.57/26.74 Clause #786 (by forward demodulation #[68, 93]): ∀ (a a_1 : Iota), Eq a (join (complement (join (complement a) a_1)) (meet a a_1))
% 26.57/26.74 Clause #796 (by superposition #[786, 396]): Eq zero (join (complement (join (complement zero) top)) zero)
% 26.57/26.74 Clause #824 (by forward demodulation #[796, 410]): Eq zero (join (complement (join top top)) zero)
% 26.57/26.74 Clause #831 (by superposition #[824, 26]): Eq (join zero (complement (join top top))) zero
% 26.57/26.74 Clause #836 (by superposition #[831, 126]): Eq top (join (join top top) zero)
% 26.57/26.79 Clause #846 (by superposition #[836, 26]): Eq (join zero (join top top)) top
% 26.57/26.79 Clause #852 (by superposition #[846, 554]): Eq (join top top) top
% 26.57/26.79 Clause #861 (by backward demodulation #[852, 831]): Eq (join zero (complement top)) zero
% 26.57/26.79 Clause #865 (by forward demodulation #[861, 103]): Eq (join zero zero) zero
% 26.57/26.79 Clause #870 (by superposition #[865, 52]): ∀ (a : Iota), Eq (join zero (join zero a)) (join zero a)
% 26.57/26.79 Clause #940 (by forward demodulation #[72, 93]): ∀ (a a_1 : Iota), Eq a (join (meet a a_1) (complement (join a_1 (complement a))))
% 26.57/26.79 Clause #954 (by superposition #[940, 23]): ∀ (a : Iota), Eq a (join (meet a a) (complement top))
% 26.57/26.79 Clause #968 (by forward demodulation #[954, 103]): ∀ (a : Iota), Eq a (join (meet a a) zero)
% 26.57/26.79 Clause #972 (by superposition #[968, 26]): ∀ (a : Iota), Eq (join zero (meet a a)) a
% 26.57/26.79 Clause #2063 (by superposition #[870, 972]): ∀ (a : Iota), Eq (join zero a) a
% 26.57/26.79 Clause #2106 (by superposition #[2063, 972]): ∀ (a : Iota), Eq (meet a a) a
% 26.57/26.79 Clause #2250 (by superposition #[97, 2106]): ∀ (a : Iota), Eq top (join (join (complement a) (complement a)) a)
% 26.57/26.79 Clause #3646 (by superposition #[2250, 26]): ∀ (a : Iota), Eq (join a (join (complement a) (complement a))) top
% 26.57/26.79 Clause #3669 (by superposition #[3646, 57]): ∀ (a : Iota), Eq top (join top (complement a))
% 26.57/26.79 Clause #3705 (by superposition #[3669, 53]): ∀ (a : Iota), Eq top (join a top)
% 26.57/26.79 Clause #3741 (by superposition #[3705, 149]): ∀ (a : Iota), Eq (composition top a) (join a (composition top a))
% 26.57/26.79 Clause #3743 (by superposition #[3705, 26]): ∀ (a : Iota), Eq (join top a) top
% 26.57/26.79 Clause #10419 (by superposition #[3741, 3743]): Eq (composition top top) top
% 26.57/26.79 Clause #10422 (by forward contextual literal cutting #[10419, 15]): False
% 26.57/26.79 SZS output end Proof for theBenchmark.p
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