TSTP Solution File: GRP124-3.004 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : GRP124-3.004 : TPTP v8.1.2. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n024.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 : Sun May 5 05:53:31 EDT 2024
% Result : Unsatisfiable 0.17s 0.37s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 58
% Syntax : Number of formulae : 211 ( 36 unt; 0 def)
% Number of atoms : 467 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 461 ( 205 ~; 220 |; 0 &)
% ( 36 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 40 ( 39 usr; 37 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 44 ( 44 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1022,plain,
$false,
inference(avatar_sat_refutation,[],[f138,f155,f172,f192,f213,f230,f247,f268,f285,f302,f317,f420,f440,f471,f500,f521,f571,f595,f608,f621,f633,f666,f676,f687,f708,f725,f750,f793,f806,f829,f857,f869,f886,f908,f957,f969,f982,f1017,f1021]) ).
fof(f1021,plain,
( ~ spl0_35
| ~ spl0_26 ),
inference(avatar_split_clause,[],[f1020,f215,f257]) ).
fof(f257,plain,
( spl0_35
<=> product(e_1,e_3,e_2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).
fof(f215,plain,
( spl0_26
<=> product(e_3,e_2,e_1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).
fof(f1020,plain,
( ~ product(e_1,e_3,e_2)
| ~ spl0_26 ),
inference(subsumption_resolution,[],[f988,f27]) ).
fof(f27,axiom,
~ equalish(e_1,e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_1_is_not_e_3) ).
fof(f988,plain,
( ~ product(e_1,e_3,e_2)
| equalish(e_1,e_3)
| ~ spl0_26 ),
inference(resolution,[],[f217,f110]) ).
fof(f110,plain,
! [X2,X0,X1] :
( ~ product(X1,X2,X0)
| ~ product(X0,X1,X2)
| equalish(X0,X1) ),
inference(resolution,[],[f98,f42]) ).
fof(f42,axiom,
! [X0] : product(X0,X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_idempotence) ).
fof(f98,plain,
! [X2,X3,X0,X1] :
( ~ product(X0,X3,X3)
| ~ product(X0,X1,X2)
| ~ product(X1,X2,X3)
| equalish(X3,X1) ),
inference(resolution,[],[f43,f42]) ).
fof(f43,axiom,
! [X8,X6,X9,X7,X4,X5] :
( ~ product(X6,X7,X4)
| ~ product(X5,X8,X9)
| ~ product(X5,X6,X7)
| ~ product(X8,X9,X4)
| equalish(X6,X8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qg2_1) ).
fof(f217,plain,
( product(e_3,e_2,e_1)
| ~ spl0_26 ),
inference(avatar_component_clause,[],[f215]) ).
fof(f1017,plain,
( ~ spl0_24
| ~ spl0_38 ),
inference(avatar_split_clause,[],[f1016,f270,f206]) ).
fof(f206,plain,
( spl0_24
<=> product(e_1,e_2,e_3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).
fof(f270,plain,
( spl0_38
<=> product(e_2,e_3,e_1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).
fof(f1016,plain,
( ~ product(e_1,e_2,e_3)
| ~ spl0_38 ),
inference(subsumption_resolution,[],[f1006,f26]) ).
fof(f26,axiom,
~ equalish(e_1,e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_1_is_not_e_2) ).
fof(f1006,plain,
( ~ product(e_1,e_2,e_3)
| equalish(e_1,e_2)
| ~ spl0_38 ),
inference(resolution,[],[f272,f110]) ).
fof(f272,plain,
( product(e_2,e_3,e_1)
| ~ spl0_38 ),
inference(avatar_component_clause,[],[f270]) ).
fof(f982,plain,
( ~ spl0_30
| ~ spl0_11 ),
inference(avatar_split_clause,[],[f981,f135,f232]) ).
fof(f232,plain,
( spl0_30
<=> product(e_4,e_2,e_1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).
fof(f135,plain,
( spl0_11
<=> product(e_2,e_1,e_4) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
fof(f981,plain,
( ~ product(e_4,e_2,e_1)
| ~ spl0_11 ),
inference(subsumption_resolution,[],[f977,f35]) ).
fof(f35,axiom,
~ equalish(e_4,e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_4_is_not_e_1) ).
fof(f977,plain,
( ~ product(e_4,e_2,e_1)
| equalish(e_4,e_1)
| ~ spl0_11 ),
inference(resolution,[],[f137,f112]) ).
fof(f112,plain,
! [X2,X0,X1] :
( ~ product(X1,X2,X0)
| ~ product(X0,X1,X2)
| equalish(X0,X2) ),
inference(resolution,[],[f99,f42]) ).
fof(f99,plain,
! [X2,X3,X0,X1] :
( ~ product(X0,X3,X3)
| ~ product(X0,X1,X2)
| ~ product(X1,X2,X3)
| equalish(X3,X2) ),
inference(resolution,[],[f44,f42]) ).
fof(f44,axiom,
! [X8,X6,X9,X7,X4,X5] :
( ~ product(X6,X7,X4)
| ~ product(X5,X8,X9)
| ~ product(X5,X6,X7)
| ~ product(X8,X9,X4)
| equalish(X7,X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qg2_2) ).
fof(f137,plain,
( product(e_2,e_1,e_4)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f135]) ).
fof(f969,plain,
~ spl0_44,
inference(avatar_contradiction_clause,[],[f968]) ).
fof(f968,plain,
( $false
| ~ spl0_44 ),
inference(subsumption_resolution,[],[f967,f34]) ).
fof(f34,axiom,
~ equalish(e_3,e_4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_3_is_not_e_4) ).
fof(f967,plain,
( equalish(e_3,e_4)
| ~ spl0_44 ),
inference(resolution,[],[f297,f50]) ).
fof(f50,plain,
! [X0,X1] :
( ~ product(X0,X1,X1)
| equalish(X1,X0) ),
inference(resolution,[],[f41,f42]) ).
fof(f41,axiom,
! [X2,X3,X0,X1] :
( ~ product(X3,X1,X0)
| ~ product(X2,X1,X0)
| equalish(X3,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_left_cancellation) ).
fof(f297,plain,
( product(e_4,e_3,e_3)
| ~ spl0_44 ),
inference(avatar_component_clause,[],[f295]) ).
fof(f295,plain,
( spl0_44
<=> product(e_4,e_3,e_3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).
fof(f957,plain,
~ spl0_45,
inference(avatar_contradiction_clause,[],[f956]) ).
fof(f956,plain,
( $false
| ~ spl0_45 ),
inference(subsumption_resolution,[],[f955,f37]) ).
fof(f37,axiom,
~ equalish(e_4,e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_4_is_not_e_3) ).
fof(f955,plain,
( equalish(e_4,e_3)
| ~ spl0_45 ),
inference(resolution,[],[f301,f48]) ).
fof(f48,plain,
! [X0,X1] :
( ~ product(X0,X1,X0)
| equalish(X0,X1) ),
inference(resolution,[],[f40,f42]) ).
fof(f40,axiom,
! [X2,X3,X0,X1] :
( ~ product(X0,X3,X1)
| ~ product(X0,X2,X1)
| equalish(X3,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_right_cancellation) ).
fof(f301,plain,
( product(e_4,e_3,e_4)
| ~ spl0_45 ),
inference(avatar_component_clause,[],[f299]) ).
fof(f299,plain,
( spl0_45
<=> product(e_4,e_3,e_4) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).
fof(f908,plain,
( ~ spl0_42
| ~ spl0_15 ),
inference(avatar_split_clause,[],[f907,f152,f287]) ).
fof(f287,plain,
( spl0_42
<=> product(e_4,e_3,e_1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).
fof(f152,plain,
( spl0_15
<=> product(e_3,e_1,e_4) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
fof(f907,plain,
( ~ product(e_4,e_3,e_1)
| ~ spl0_15 ),
inference(subsumption_resolution,[],[f903,f35]) ).
fof(f903,plain,
( ~ product(e_4,e_3,e_1)
| equalish(e_4,e_1)
| ~ spl0_15 ),
inference(resolution,[],[f154,f112]) ).
fof(f154,plain,
( product(e_3,e_1,e_4)
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f152]) ).
fof(f886,plain,
( ~ spl0_32
| ~ spl0_41 ),
inference(avatar_split_clause,[],[f885,f282,f240]) ).
fof(f240,plain,
( spl0_32
<=> product(e_4,e_2,e_3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).
fof(f282,plain,
( spl0_41
<=> product(e_2,e_3,e_4) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).
fof(f885,plain,
( ~ product(e_4,e_2,e_3)
| ~ spl0_41 ),
inference(subsumption_resolution,[],[f875,f36]) ).
fof(f36,axiom,
~ equalish(e_4,e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_4_is_not_e_2) ).
fof(f875,plain,
( ~ product(e_4,e_2,e_3)
| equalish(e_4,e_2)
| ~ spl0_41 ),
inference(resolution,[],[f284,f110]) ).
fof(f284,plain,
( product(e_2,e_3,e_4)
| ~ spl0_41 ),
inference(avatar_component_clause,[],[f282]) ).
fof(f869,plain,
~ spl0_40,
inference(avatar_contradiction_clause,[],[f868]) ).
fof(f868,plain,
( $false
| ~ spl0_40 ),
inference(subsumption_resolution,[],[f867,f33]) ).
fof(f33,axiom,
~ equalish(e_3,e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_3_is_not_e_2) ).
fof(f867,plain,
( equalish(e_3,e_2)
| ~ spl0_40 ),
inference(resolution,[],[f280,f50]) ).
fof(f280,plain,
( product(e_2,e_3,e_3)
| ~ spl0_40 ),
inference(avatar_component_clause,[],[f278]) ).
fof(f278,plain,
( spl0_40
<=> product(e_2,e_3,e_3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).
fof(f857,plain,
~ spl0_39,
inference(avatar_contradiction_clause,[],[f856]) ).
fof(f856,plain,
( $false
| ~ spl0_39 ),
inference(subsumption_resolution,[],[f855,f30]) ).
fof(f30,axiom,
~ equalish(e_2,e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_2_is_not_e_3) ).
fof(f855,plain,
( equalish(e_2,e_3)
| ~ spl0_39 ),
inference(resolution,[],[f276,f48]) ).
fof(f276,plain,
( product(e_2,e_3,e_2)
| ~ spl0_39 ),
inference(avatar_component_clause,[],[f274]) ).
fof(f274,plain,
( spl0_39
<=> product(e_2,e_3,e_2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).
fof(f829,plain,
~ spl0_33,
inference(avatar_contradiction_clause,[],[f828]) ).
fof(f828,plain,
( $false
| ~ spl0_33 ),
inference(subsumption_resolution,[],[f827,f36]) ).
fof(f827,plain,
( equalish(e_4,e_2)
| ~ spl0_33 ),
inference(resolution,[],[f246,f48]) ).
fof(f246,plain,
( product(e_4,e_2,e_4)
| ~ spl0_33 ),
inference(avatar_component_clause,[],[f244]) ).
fof(f244,plain,
( spl0_33
<=> product(e_4,e_2,e_4) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).
fof(f806,plain,
( ~ spl0_18
| ~ spl0_37 ),
inference(avatar_contradiction_clause,[],[f805]) ).
fof(f805,plain,
( $false
| ~ spl0_18
| ~ spl0_37 ),
inference(subsumption_resolution,[],[f804,f37]) ).
fof(f804,plain,
( equalish(e_4,e_3)
| ~ spl0_18
| ~ spl0_37 ),
inference(subsumption_resolution,[],[f800,f167]) ).
fof(f167,plain,
( product(e_4,e_1,e_3)
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f165]) ).
fof(f165,plain,
( spl0_18
<=> product(e_4,e_1,e_3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).
fof(f800,plain,
( ~ product(e_4,e_1,e_3)
| equalish(e_4,e_3)
| ~ spl0_37 ),
inference(resolution,[],[f267,f112]) ).
fof(f267,plain,
( product(e_1,e_3,e_4)
| ~ spl0_37 ),
inference(avatar_component_clause,[],[f265]) ).
fof(f265,plain,
( spl0_37
<=> product(e_1,e_3,e_4) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).
fof(f793,plain,
~ spl0_36,
inference(avatar_contradiction_clause,[],[f792]) ).
fof(f792,plain,
( $false
| ~ spl0_36 ),
inference(subsumption_resolution,[],[f791,f32]) ).
fof(f32,axiom,
~ equalish(e_3,e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_3_is_not_e_1) ).
fof(f791,plain,
( equalish(e_3,e_1)
| ~ spl0_36 ),
inference(resolution,[],[f263,f50]) ).
fof(f263,plain,
( product(e_1,e_3,e_3)
| ~ spl0_36 ),
inference(avatar_component_clause,[],[f261]) ).
fof(f261,plain,
( spl0_36
<=> product(e_1,e_3,e_3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).
fof(f750,plain,
~ spl0_31,
inference(avatar_contradiction_clause,[],[f749]) ).
fof(f749,plain,
( $false
| ~ spl0_31 ),
inference(subsumption_resolution,[],[f748,f31]) ).
fof(f31,axiom,
~ equalish(e_2,e_4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_2_is_not_e_4) ).
fof(f748,plain,
( equalish(e_2,e_4)
| ~ spl0_31 ),
inference(resolution,[],[f238,f50]) ).
fof(f238,plain,
( product(e_4,e_2,e_2)
| ~ spl0_31 ),
inference(avatar_component_clause,[],[f236]) ).
fof(f236,plain,
( spl0_31
<=> product(e_4,e_2,e_2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).
fof(f725,plain,
( ~ spl0_10
| ~ spl0_35 ),
inference(avatar_split_clause,[],[f724,f257,f131]) ).
fof(f131,plain,
( spl0_10
<=> product(e_2,e_1,e_3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
fof(f724,plain,
( ~ product(e_2,e_1,e_3)
| ~ spl0_35 ),
inference(subsumption_resolution,[],[f714,f29]) ).
fof(f29,axiom,
~ equalish(e_2,e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_2_is_not_e_1) ).
fof(f714,plain,
( ~ product(e_2,e_1,e_3)
| equalish(e_2,e_1)
| ~ spl0_35 ),
inference(resolution,[],[f259,f110]) ).
fof(f259,plain,
( product(e_1,e_3,e_2)
| ~ spl0_35 ),
inference(avatar_component_clause,[],[f257]) ).
fof(f708,plain,
~ spl0_34,
inference(avatar_contradiction_clause,[],[f707]) ).
fof(f707,plain,
( $false
| ~ spl0_34 ),
inference(subsumption_resolution,[],[f706,f27]) ).
fof(f706,plain,
( equalish(e_1,e_3)
| ~ spl0_34 ),
inference(resolution,[],[f255,f48]) ).
fof(f255,plain,
( product(e_1,e_3,e_1)
| ~ spl0_34 ),
inference(avatar_component_clause,[],[f253]) ).
fof(f253,plain,
( spl0_34
<=> product(e_1,e_3,e_1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).
fof(f687,plain,
( ~ spl0_43
| ~ spl0_29 ),
inference(avatar_split_clause,[],[f686,f227,f291]) ).
fof(f291,plain,
( spl0_43
<=> product(e_4,e_3,e_2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).
fof(f227,plain,
( spl0_29
<=> product(e_3,e_2,e_4) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).
fof(f686,plain,
( ~ product(e_4,e_3,e_2)
| ~ spl0_29 ),
inference(subsumption_resolution,[],[f683,f36]) ).
fof(f683,plain,
( ~ product(e_4,e_3,e_2)
| equalish(e_4,e_2)
| ~ spl0_29 ),
inference(resolution,[],[f229,f112]) ).
fof(f229,plain,
( product(e_3,e_2,e_4)
| ~ spl0_29 ),
inference(avatar_component_clause,[],[f227]) ).
fof(f676,plain,
~ spl0_28,
inference(avatar_contradiction_clause,[],[f675]) ).
fof(f675,plain,
( $false
| ~ spl0_28 ),
inference(subsumption_resolution,[],[f674,f33]) ).
fof(f674,plain,
( equalish(e_3,e_2)
| ~ spl0_28 ),
inference(resolution,[],[f225,f48]) ).
fof(f225,plain,
( product(e_3,e_2,e_3)
| ~ spl0_28 ),
inference(avatar_component_clause,[],[f223]) ).
fof(f223,plain,
( spl0_28
<=> product(e_3,e_2,e_3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).
fof(f666,plain,
~ spl0_27,
inference(avatar_contradiction_clause,[],[f665]) ).
fof(f665,plain,
( $false
| ~ spl0_27 ),
inference(subsumption_resolution,[],[f664,f30]) ).
fof(f664,plain,
( equalish(e_2,e_3)
| ~ spl0_27 ),
inference(resolution,[],[f221,f50]) ).
fof(f221,plain,
( product(e_3,e_2,e_2)
| ~ spl0_27 ),
inference(avatar_component_clause,[],[f219]) ).
fof(f219,plain,
( spl0_27
<=> product(e_3,e_2,e_2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).
fof(f633,plain,
~ spl0_23,
inference(avatar_contradiction_clause,[],[f632]) ).
fof(f632,plain,
( $false
| ~ spl0_23 ),
inference(subsumption_resolution,[],[f631,f29]) ).
fof(f631,plain,
( equalish(e_2,e_1)
| ~ spl0_23 ),
inference(resolution,[],[f204,f50]) ).
fof(f204,plain,
( product(e_1,e_2,e_2)
| ~ spl0_23 ),
inference(avatar_component_clause,[],[f202]) ).
fof(f202,plain,
( spl0_23
<=> product(e_1,e_2,e_2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).
fof(f621,plain,
( ~ spl0_17
| ~ spl0_25 ),
inference(avatar_contradiction_clause,[],[f620]) ).
fof(f620,plain,
( $false
| ~ spl0_17
| ~ spl0_25 ),
inference(subsumption_resolution,[],[f619,f36]) ).
fof(f619,plain,
( equalish(e_4,e_2)
| ~ spl0_17
| ~ spl0_25 ),
inference(subsumption_resolution,[],[f615,f163]) ).
fof(f163,plain,
( product(e_4,e_1,e_2)
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f161]) ).
fof(f161,plain,
( spl0_17
<=> product(e_4,e_1,e_2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).
fof(f615,plain,
( ~ product(e_4,e_1,e_2)
| equalish(e_4,e_2)
| ~ spl0_25 ),
inference(resolution,[],[f212,f112]) ).
fof(f212,plain,
( product(e_1,e_2,e_4)
| ~ spl0_25 ),
inference(avatar_component_clause,[],[f210]) ).
fof(f210,plain,
( spl0_25
<=> product(e_1,e_2,e_4) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).
fof(f608,plain,
( ~ spl0_13
| ~ spl0_24 ),
inference(avatar_contradiction_clause,[],[f607]) ).
fof(f607,plain,
( $false
| ~ spl0_13
| ~ spl0_24 ),
inference(subsumption_resolution,[],[f606,f33]) ).
fof(f606,plain,
( equalish(e_3,e_2)
| ~ spl0_13
| ~ spl0_24 ),
inference(subsumption_resolution,[],[f602,f146]) ).
fof(f146,plain,
( product(e_3,e_1,e_2)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f144]) ).
fof(f144,plain,
( spl0_13
<=> product(e_3,e_1,e_2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
fof(f602,plain,
( ~ product(e_3,e_1,e_2)
| equalish(e_3,e_2)
| ~ spl0_24 ),
inference(resolution,[],[f208,f112]) ).
fof(f208,plain,
( product(e_1,e_2,e_3)
| ~ spl0_24 ),
inference(avatar_component_clause,[],[f206]) ).
fof(f595,plain,
~ spl0_22,
inference(avatar_contradiction_clause,[],[f594]) ).
fof(f594,plain,
( $false
| ~ spl0_22 ),
inference(subsumption_resolution,[],[f593,f26]) ).
fof(f593,plain,
( equalish(e_1,e_2)
| ~ spl0_22 ),
inference(resolution,[],[f200,f48]) ).
fof(f200,plain,
( product(e_1,e_2,e_1)
| ~ spl0_22 ),
inference(avatar_component_clause,[],[f198]) ).
fof(f198,plain,
( spl0_22
<=> product(e_1,e_2,e_1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).
fof(f571,plain,
~ spl0_19,
inference(avatar_contradiction_clause,[],[f570]) ).
fof(f570,plain,
( $false
| ~ spl0_19 ),
inference(subsumption_resolution,[],[f565,f35]) ).
fof(f565,plain,
( equalish(e_4,e_1)
| ~ spl0_19 ),
inference(resolution,[],[f171,f48]) ).
fof(f171,plain,
( product(e_4,e_1,e_4)
| ~ spl0_19 ),
inference(avatar_component_clause,[],[f169]) ).
fof(f169,plain,
( spl0_19
<=> product(e_4,e_1,e_4) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).
fof(f521,plain,
~ spl0_16,
inference(avatar_contradiction_clause,[],[f520]) ).
fof(f520,plain,
( $false
| ~ spl0_16 ),
inference(subsumption_resolution,[],[f512,f28]) ).
fof(f28,axiom,
~ equalish(e_1,e_4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_1_is_not_e_4) ).
fof(f512,plain,
( equalish(e_1,e_4)
| ~ spl0_16 ),
inference(resolution,[],[f159,f50]) ).
fof(f159,plain,
( product(e_4,e_1,e_1)
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f157]) ).
fof(f157,plain,
( spl0_16
<=> product(e_4,e_1,e_1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
fof(f500,plain,
( ~ spl0_38
| ~ spl0_13 ),
inference(avatar_split_clause,[],[f499,f144,f270]) ).
fof(f499,plain,
( ~ product(e_2,e_3,e_1)
| ~ spl0_13 ),
inference(subsumption_resolution,[],[f495,f29]) ).
fof(f495,plain,
( ~ product(e_2,e_3,e_1)
| equalish(e_2,e_1)
| ~ spl0_13 ),
inference(resolution,[],[f146,f112]) ).
fof(f471,plain,
~ spl0_14,
inference(avatar_contradiction_clause,[],[f470]) ).
fof(f470,plain,
( $false
| ~ spl0_14 ),
inference(subsumption_resolution,[],[f465,f32]) ).
fof(f465,plain,
( equalish(e_3,e_1)
| ~ spl0_14 ),
inference(resolution,[],[f150,f48]) ).
fof(f150,plain,
( product(e_3,e_1,e_3)
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f148]) ).
fof(f148,plain,
( spl0_14
<=> product(e_3,e_1,e_3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
fof(f440,plain,
~ spl0_12,
inference(avatar_contradiction_clause,[],[f439]) ).
fof(f439,plain,
( $false
| ~ spl0_12 ),
inference(subsumption_resolution,[],[f431,f27]) ).
fof(f431,plain,
( equalish(e_1,e_3)
| ~ spl0_12 ),
inference(resolution,[],[f142,f50]) ).
fof(f142,plain,
( product(e_3,e_1,e_1)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f140]) ).
fof(f140,plain,
( spl0_12
<=> product(e_3,e_1,e_1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
fof(f420,plain,
( ~ spl0_26
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f419,f131,f215]) ).
fof(f419,plain,
( ~ product(e_3,e_2,e_1)
| ~ spl0_10 ),
inference(subsumption_resolution,[],[f415,f32]) ).
fof(f415,plain,
( ~ product(e_3,e_2,e_1)
| equalish(e_3,e_1)
| ~ spl0_10 ),
inference(resolution,[],[f133,f112]) ).
fof(f133,plain,
( product(e_2,e_1,e_3)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f131]) ).
fof(f317,plain,
~ spl0_9,
inference(avatar_contradiction_clause,[],[f316]) ).
fof(f316,plain,
( $false
| ~ spl0_9 ),
inference(subsumption_resolution,[],[f311,f29]) ).
fof(f311,plain,
( equalish(e_2,e_1)
| ~ spl0_9 ),
inference(resolution,[],[f129,f48]) ).
fof(f129,plain,
( product(e_2,e_1,e_2)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f127]) ).
fof(f127,plain,
( spl0_9
<=> product(e_2,e_1,e_2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
fof(f302,plain,
( spl0_42
| spl0_43
| spl0_44
| spl0_45 ),
inference(avatar_split_clause,[],[f251,f299,f295,f291,f287]) ).
fof(f251,plain,
( product(e_4,e_3,e_4)
| product(e_4,e_3,e_3)
| product(e_4,e_3,e_2)
| product(e_4,e_3,e_1) ),
inference(resolution,[],[f107,f25]) ).
fof(f25,axiom,
group_element(e_4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_4) ).
fof(f107,plain,
! [X0] :
( ~ group_element(X0)
| product(X0,e_3,e_4)
| product(X0,e_3,e_3)
| product(X0,e_3,e_2)
| product(X0,e_3,e_1) ),
inference(resolution,[],[f38,f24]) ).
fof(f24,axiom,
group_element(e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_3) ).
fof(f38,axiom,
! [X0,X1] :
( ~ group_element(X1)
| ~ group_element(X0)
| product(X0,X1,e_4)
| product(X0,X1,e_3)
| product(X0,X1,e_2)
| product(X0,X1,e_1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_total_function1) ).
fof(f285,plain,
( spl0_38
| spl0_39
| spl0_40
| spl0_41 ),
inference(avatar_split_clause,[],[f249,f282,f278,f274,f270]) ).
fof(f249,plain,
( product(e_2,e_3,e_4)
| product(e_2,e_3,e_3)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1) ),
inference(resolution,[],[f107,f23]) ).
fof(f23,axiom,
group_element(e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_2) ).
fof(f268,plain,
( spl0_34
| spl0_35
| spl0_36
| spl0_37 ),
inference(avatar_split_clause,[],[f248,f265,f261,f257,f253]) ).
fof(f248,plain,
( product(e_1,e_3,e_4)
| product(e_1,e_3,e_3)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1) ),
inference(resolution,[],[f107,f22]) ).
fof(f22,axiom,
group_element(e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_1) ).
fof(f247,plain,
( spl0_30
| spl0_31
| spl0_32
| spl0_33 ),
inference(avatar_split_clause,[],[f196,f244,f240,f236,f232]) ).
fof(f196,plain,
( product(e_4,e_2,e_4)
| product(e_4,e_2,e_3)
| product(e_4,e_2,e_2)
| product(e_4,e_2,e_1) ),
inference(resolution,[],[f106,f25]) ).
fof(f106,plain,
! [X0] :
( ~ group_element(X0)
| product(X0,e_2,e_4)
| product(X0,e_2,e_3)
| product(X0,e_2,e_2)
| product(X0,e_2,e_1) ),
inference(resolution,[],[f38,f23]) ).
fof(f230,plain,
( spl0_26
| spl0_27
| spl0_28
| spl0_29 ),
inference(avatar_split_clause,[],[f195,f227,f223,f219,f215]) ).
fof(f195,plain,
( product(e_3,e_2,e_4)
| product(e_3,e_2,e_3)
| product(e_3,e_2,e_2)
| product(e_3,e_2,e_1) ),
inference(resolution,[],[f106,f24]) ).
fof(f213,plain,
( spl0_22
| spl0_23
| spl0_24
| spl0_25 ),
inference(avatar_split_clause,[],[f193,f210,f206,f202,f198]) ).
fof(f193,plain,
( product(e_1,e_2,e_4)
| product(e_1,e_2,e_3)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1) ),
inference(resolution,[],[f106,f22]) ).
fof(f192,plain,
~ spl0_8,
inference(avatar_contradiction_clause,[],[f191]) ).
fof(f191,plain,
( $false
| ~ spl0_8 ),
inference(subsumption_resolution,[],[f183,f26]) ).
fof(f183,plain,
( equalish(e_1,e_2)
| ~ spl0_8 ),
inference(resolution,[],[f125,f50]) ).
fof(f125,plain,
( product(e_2,e_1,e_1)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f123]) ).
fof(f123,plain,
( spl0_8
<=> product(e_2,e_1,e_1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
fof(f172,plain,
( spl0_16
| spl0_17
| spl0_18
| spl0_19 ),
inference(avatar_split_clause,[],[f121,f169,f165,f161,f157]) ).
fof(f121,plain,
( product(e_4,e_1,e_4)
| product(e_4,e_1,e_3)
| product(e_4,e_1,e_2)
| product(e_4,e_1,e_1) ),
inference(resolution,[],[f105,f25]) ).
fof(f105,plain,
! [X0] :
( ~ group_element(X0)
| product(X0,e_1,e_4)
| product(X0,e_1,e_3)
| product(X0,e_1,e_2)
| product(X0,e_1,e_1) ),
inference(resolution,[],[f38,f22]) ).
fof(f155,plain,
( spl0_12
| spl0_13
| spl0_14
| spl0_15 ),
inference(avatar_split_clause,[],[f120,f152,f148,f144,f140]) ).
fof(f120,plain,
( product(e_3,e_1,e_4)
| product(e_3,e_1,e_3)
| product(e_3,e_1,e_2)
| product(e_3,e_1,e_1) ),
inference(resolution,[],[f105,f24]) ).
fof(f138,plain,
( spl0_8
| spl0_9
| spl0_10
| spl0_11 ),
inference(avatar_split_clause,[],[f119,f135,f131,f127,f123]) ).
fof(f119,plain,
( product(e_2,e_1,e_4)
| product(e_2,e_1,e_3)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_1) ),
inference(resolution,[],[f105,f23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : GRP124-3.004 : TPTP v8.1.2. Released v1.2.0.
% 0.11/0.12 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.11/0.33 % Computer : n024.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri May 3 20:40:38 EDT 2024
% 0.11/0.33 % CPUTime :
% 0.11/0.33 % (5261)Running in auto input_syntax mode. Trying TPTP
% 0.17/0.35 % (5263)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3_569 on theBenchmark for (569ds/0Mi)
% 0.17/0.35 % (5267)dis+11_4:5_nm=4_216 on theBenchmark for (216ds/0Mi)
% 0.17/0.35 % (5262)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2_1451 on theBenchmark for (1451ds/0Mi)
% 0.17/0.35 % (5265)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3:gsp=on:nm=4_470 on theBenchmark for (470ds/0Mi)
% 0.17/0.35 % (5266)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on theBenchmark for (396ds/0Mi)
% 0.17/0.35 % (5264)dis-2_2:3_amm=sco:anc=none:bce=on:fsr=off:gsp=on:nm=16:nwc=1.2:nicw=on:sac=on:sp=weighted_frequency_476 on theBenchmark for (476ds/0Mi)
% 0.17/0.35 % (5268)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2:si=on:rtra=on:rawr=on:rp=on:fmbksg=on_1451 on theBenchmark for (1451ds/0Mi)
% 0.17/0.35 Detected minimum model sizes of [1]
% 0.17/0.35 Detected maximum model sizes of [5]
% 0.17/0.35 TRYING [1]
% 0.17/0.35 TRYING [2]
% 0.17/0.35 Detected minimum model sizes of [1]
% 0.17/0.35 Detected maximum model sizes of [5]
% 0.17/0.35 TRYING [1]
% 0.17/0.35 Detected minimum model sizes of [1]
% 0.17/0.35 Detected maximum model sizes of [5]
% 0.17/0.35 Detected minimum model sizes of [1]
% 0.17/0.35 TRYING [1]
% 0.17/0.35 Detected maximum model sizes of [5]
% 0.17/0.35 TRYING [1]
% 0.17/0.35 TRYING [2]
% 0.17/0.35 TRYING [2]
% 0.17/0.35 TRYING [2]
% 0.17/0.35 TRYING [3]
% 0.17/0.35 TRYING [3]
% 0.17/0.35 TRYING [3]
% 0.17/0.35 TRYING [3]
% 0.17/0.36 TRYING [4]
% 0.17/0.36 TRYING [4]
% 0.17/0.36 TRYING [4]
% 0.17/0.36 TRYING [4]
% 0.17/0.36 TRYING [5]
% 0.17/0.37 TRYING [5]
% 0.17/0.37 TRYING [5]
% 0.17/0.37 TRYING [5]
% 0.17/0.37 % (5267)First to succeed.
% 0.17/0.37 % (5267)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-5261"
% 0.17/0.37 % (5267)Refutation found. Thanks to Tanya!
% 0.17/0.37 % SZS status Unsatisfiable for theBenchmark
% 0.17/0.37 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.37 % (5267)------------------------------
% 0.17/0.37 % (5267)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.17/0.37 % (5267)Termination reason: Refutation
% 0.17/0.37
% 0.17/0.37 % (5267)Memory used [KB]: 1087
% 0.17/0.37 % (5267)Time elapsed: 0.023 s
% 0.17/0.37 % (5267)Instructions burned: 44 (million)
% 0.17/0.37 % (5261)Success in time 0.037 s
%------------------------------------------------------------------------------