%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP125-4.003 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 10:12:44 AM UTC 2026
% Result : Unsatisfiable 2.68s 1.27s
% Output : Refutation 3.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 44
% Syntax : Number of formulae : 255 ( 31 unt; 32 def)
% Number of atoms : 753 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 897 ( 399 ~; 466 |; 0 &)
% ( 32 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 36 ( 35 usr; 33 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 83 ( 0 sgn 83 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( product(e_3,X0,X1)
| ~ group_element(X1)
| product(e_1,X0,X1)
| product(e_2,X0,X1)
| ~ group_element(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',row_surjectivity) ).
fof(f2,axiom,
! [X0,X1] :
( product(X0,e_3,X1)
| ~ group_element(X1)
| product(X0,e_1,X1)
| product(X0,e_2,X1)
| ~ group_element(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',column_surjectivity) ).
fof(f3,negated_conjecture,
! [X2,X3,X0,X1] :
( product(X0,X1,X2)
| ~ product(X2,X3,X0)
| ~ product(X1,X0,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qg3_1) ).
fof(f4,negated_conjecture,
! [X2,X3,X0,X1] :
( product(X0,X1,X2)
| ~ product(X3,X2,X1)
| ~ product(X1,X0,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qg3_2) ).
fof(f5,axiom,
group_element(e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_1) ).
fof(f6,axiom,
group_element(e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_2) ).
fof(f7,axiom,
group_element(e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_3) ).
fof(f8,axiom,
~ equalish(e_1,e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_1_is_not_e_2) ).
fof(f14,axiom,
! [X0,X1] :
( product(X0,X1,e_3)
| ~ group_element(X1)
| product(X0,X1,e_1)
| product(X0,X1,e_2)
| ~ group_element(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_total_function1) ).
fof(f15,axiom,
! [X2,X3,X0,X1] :
( equalish(X2,X3)
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_total_function2) ).
fof(f18,axiom,
! [X0] : product(X0,X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_idempotence) ).
fof(f19,negated_conjecture,
! [X2,X3,X0,X1] :
( product(X2,X3,X0)
| ~ product(X1,X0,X3)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qg3) ).
fof(f20,plain,
! [X0,X1] :
( ~ product(X0,X1,e_2)
| ~ product(X0,X1,e_1) ),
inference(resolution,[],[f15,f8]) ).
fof(f26,plain,
! [X2,X0,X1] :
( ~ product(X0,X1,e_1)
| ~ product(X2,e_2,X1)
| ~ product(e_2,X2,X0) ),
inference(resolution,[],[f20,f19]) ).
fof(f42,plain,
! [X0] :
( ~ product(X0,e_2,e_1)
| ~ product(e_2,e_2,X0) ),
inference(resolution,[],[f26,f18]) ).
fof(f60,plain,
~ product(e_2,e_2,e_1),
inference(resolution,[],[f42,f18]) ).
fof(f61,plain,
! [X0] :
( ~ group_element(e_2)
| product(e_1,X0,e_2)
| product(e_2,X0,e_2)
| ~ group_element(X0)
| ~ product(e_3,X0,e_1) ),
inference(resolution,[],[f1,f20]) ).
fof(f62,plain,
! [X0,X1] :
( ~ group_element(e_1)
| product(e_1,X0,e_1)
| product(e_2,X0,e_1)
| ~ group_element(X0)
| ~ product(X1,e_2,X0)
| ~ product(e_2,X1,e_3) ),
inference(resolution,[],[f1,f26]) ).
fof(f63,plain,
! [X0,X1] :
( ~ group_element(X0)
| product(e_1,e_2,X0)
| product(e_2,e_2,X0)
| ~ group_element(e_2)
| ~ product(X1,X0,e_1)
| ~ product(e_2,e_3,X1) ),
inference(resolution,[],[f1,f26]) ).
fof(f69,definition,
( spl0_2
<=> group_element(e_2) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f70,plain,
( ~ group_element(e_2)
| spl0_2 ),
inference(avatar_component_clause,[],[f69]) ).
fof(f72,definition,
( spl0_3
<=> product(e_2,e_2,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f73,plain,
( product(e_2,e_2,e_1)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f72]) ).
fof(f75,definition,
( spl0_4
<=> product(e_1,e_2,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f76,plain,
( product(e_1,e_2,e_1)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f75]) ).
fof(f78,definition,
( spl0_5
<=> group_element(e_1) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f79,plain,
( ~ group_element(e_1)
| spl0_5 ),
inference(avatar_component_clause,[],[f78]) ).
fof(f82,definition,
( spl0_6
<=> ! [X0,X1] :
( ~ group_element(X0)
| ~ product(e_2,e_3,X1)
| ~ product(X1,X0,e_1)
| product(e_2,e_2,X0)
| product(e_1,e_2,X0) ) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f83,plain,
( ! [X0,X1] :
( ~ group_element(X0)
| ~ product(e_2,e_3,X1)
| ~ product(X1,X0,e_1)
| product(e_2,e_2,X0)
| product(e_1,e_2,X0) )
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f82]) ).
fof(f84,plain,
( ~ spl0_2
| spl0_6 ),
inference(avatar_split_clause,[],[f63,f82,f69]) ).
fof(f86,definition,
( spl0_7
<=> ! [X0,X1] :
( product(e_1,X0,e_1)
| ~ product(e_2,X1,e_3)
| ~ product(X1,e_2,X0)
| ~ group_element(X0)
| product(e_2,X0,e_1) ) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f87,plain,
( ! [X0,X1] :
( ~ group_element(X0)
| ~ product(e_2,X1,e_3)
| ~ product(X1,e_2,X0)
| product(e_1,X0,e_1)
| product(e_2,X0,e_1) )
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f86]) ).
fof(f88,plain,
( spl0_7
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f62,f78,f86]) ).
fof(f90,definition,
( spl0_8
<=> ! [X0] :
( product(e_1,X0,e_2)
| ~ product(e_3,X0,e_1)
| ~ group_element(X0)
| product(e_2,X0,e_2) ) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f91,plain,
( ! [X0] :
( ~ group_element(X0)
| ~ product(e_3,X0,e_1)
| product(e_1,X0,e_2)
| product(e_2,X0,e_2) )
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f90]) ).
fof(f92,plain,
( spl0_8
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f61,f69,f90]) ).
fof(f93,plain,
( $false
| spl0_2 ),
inference(resolution,[],[f70,f6]) ).
fof(f94,plain,
spl0_2,
inference(avatar_contradiction_clause,[],[f93]) ).
fof(f95,plain,
( ~ product(e_3,e_1,e_1)
| product(e_1,e_1,e_2)
| product(e_2,e_1,e_2)
| ~ spl0_8 ),
inference(resolution,[],[f91,f5]) ).
fof(f97,plain,
( ~ product(e_3,e_3,e_1)
| product(e_1,e_3,e_2)
| product(e_2,e_3,e_2)
| ~ spl0_8 ),
inference(resolution,[],[f91,f7]) ).
fof(f99,definition,
( spl0_9
<=> product(e_2,e_3,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f100,plain,
( product(e_2,e_3,e_2)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f99]) ).
fof(f102,definition,
( spl0_10
<=> product(e_1,e_3,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f103,plain,
( product(e_1,e_3,e_2)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f102]) ).
fof(f105,definition,
( spl0_11
<=> product(e_3,e_3,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f106,plain,
( ~ product(e_3,e_3,e_1)
| spl0_11 ),
inference(avatar_component_clause,[],[f105]) ).
fof(f107,plain,
( spl0_9
| spl0_10
| ~ spl0_11
| ~ spl0_8 ),
inference(avatar_split_clause,[],[f97,f90,f105,f102,f99]) ).
fof(f109,definition,
( spl0_12
<=> product(e_2,e_1,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f110,plain,
( product(e_2,e_1,e_2)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f109]) ).
fof(f112,definition,
( spl0_13
<=> product(e_1,e_1,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f113,plain,
( product(e_1,e_1,e_2)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f112]) ).
fof(f115,definition,
( spl0_14
<=> product(e_3,e_1,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f116,plain,
( ~ product(e_3,e_1,e_1)
| spl0_14 ),
inference(avatar_component_clause,[],[f115]) ).
fof(f117,plain,
( spl0_12
| spl0_13
| ~ spl0_14
| ~ spl0_8 ),
inference(avatar_split_clause,[],[f95,f90,f115,f112,f109]) ).
fof(f118,plain,
( $false
| spl0_5 ),
inference(resolution,[],[f79,f5]) ).
fof(f119,plain,
spl0_5,
inference(avatar_contradiction_clause,[],[f118]) ).
fof(f120,plain,
( ! [X0] :
( ~ product(e_2,e_3,X0)
| ~ product(X0,e_1,e_1)
| product(e_2,e_2,e_1)
| product(e_1,e_2,e_1) )
| ~ spl0_6 ),
inference(resolution,[],[f83,f5]) ).
fof(f124,definition,
( spl0_15
<=> product(e_1,e_2,e_3) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f132,definition,
( spl0_17
<=> ! [X0] :
( ~ product(e_2,e_3,X0)
| ~ product(X0,e_1,e_1) ) ),
introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition]) ).
fof(f133,plain,
( ! [X0] :
( ~ product(e_2,e_3,X0)
| ~ product(X0,e_1,e_1) )
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f132]) ).
fof(f134,plain,
( spl0_4
| spl0_3
| spl0_17
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f120,f82,f132,f72,f75]) ).
fof(f136,plain,
( ! [X0] :
( ~ product(e_2,X0,e_3)
| ~ product(X0,e_2,e_2)
| product(e_1,e_2,e_1)
| product(e_2,e_2,e_1) )
| ~ spl0_7 ),
inference(resolution,[],[f87,f6]) ).
fof(f137,plain,
( ! [X0] :
( ~ product(e_2,X0,e_3)
| ~ product(X0,e_2,e_3)
| product(e_1,e_3,e_1)
| product(e_2,e_3,e_1) )
| ~ spl0_7 ),
inference(resolution,[],[f87,f7]) ).
fof(f139,definition,
( spl0_18
<=> product(e_2,e_3,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_18])],[avatar_definition]) ).
fof(f140,plain,
( product(e_2,e_3,e_1)
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f139]) ).
fof(f142,definition,
( spl0_19
<=> product(e_1,e_3,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_19])],[avatar_definition]) ).
fof(f143,plain,
( product(e_1,e_3,e_1)
| ~ spl0_19 ),
inference(avatar_component_clause,[],[f142]) ).
fof(f145,definition,
( spl0_20
<=> ! [X0] :
( ~ product(e_2,X0,e_3)
| ~ product(X0,e_2,e_3) ) ),
introduced(definition,[new_symbols(definition,[spl0_20])],[avatar_definition]) ).
fof(f146,plain,
( ! [X0] :
( ~ product(e_2,X0,e_3)
| ~ product(X0,e_2,e_3) )
| ~ spl0_20 ),
inference(avatar_component_clause,[],[f145]) ).
fof(f147,plain,
( spl0_18
| spl0_19
| spl0_20
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f137,f86,f145,f142,f139]) ).
fof(f150,plain,
( ! [X0] :
( ~ product(X0,e_1,e_3)
| ~ product(e_1,X0,e_3) )
| spl0_11 ),
inference(resolution,[],[f106,f19]) ).
fof(f151,plain,
( ! [X0] :
( ~ product(X0,e_1,e_3)
| ~ product(e_3,e_3,X0) )
| spl0_11 ),
inference(resolution,[],[f106,f4]) ).
fof(f152,plain,
( ! [X0] :
( ~ product(e_3,e_3,X0)
| ~ product(e_1,X0,e_3) )
| spl0_11 ),
inference(resolution,[],[f106,f3]) ).
fof(f154,definition,
( spl0_21
<=> group_element(e_3) ),
introduced(definition,[new_symbols(definition,[spl0_21])],[avatar_definition]) ).
fof(f155,plain,
( ~ group_element(e_3)
| spl0_21 ),
inference(avatar_component_clause,[],[f154]) ).
fof(f160,plain,
( ! [X0] :
( ~ product(X0,e_1,e_1)
| ~ product(e_1,e_3,X0) )
| spl0_14 ),
inference(resolution,[],[f116,f4]) ).
fof(f161,plain,
( ! [X0] :
( ~ product(e_1,X0,e_3)
| ~ product(e_1,e_3,X0) )
| spl0_14 ),
inference(resolution,[],[f116,f3]) ).
fof(f170,plain,
( ~ product(e_1,e_1,e_3)
| spl0_11 ),
inference(factoring,[],[f150]) ).
fof(f172,definition,
( spl0_22
<=> product(e_2,e_1,e_3) ),
introduced(definition,[new_symbols(definition,[spl0_22])],[avatar_definition]) ).
fof(f173,plain,
( product(e_2,e_1,e_3)
| ~ spl0_22 ),
inference(avatar_component_clause,[],[f172]) ).
fof(f175,definition,
( spl0_23
<=> product(e_1,e_1,e_3) ),
introduced(definition,[new_symbols(definition,[spl0_23])],[avatar_definition]) ).
fof(f176,plain,
( product(e_1,e_1,e_3)
| ~ spl0_23 ),
inference(avatar_component_clause,[],[f175]) ).
fof(f178,definition,
( spl0_24
<=> product(e_1,e_3,e_3) ),
introduced(definition,[new_symbols(definition,[spl0_24])],[avatar_definition]) ).
fof(f179,plain,
( ~ product(e_1,e_3,e_3)
| spl0_24 ),
inference(avatar_component_clause,[],[f178]) ).
fof(f188,plain,
( ~ product(e_3,e_1,e_3)
| spl0_11 ),
inference(resolution,[],[f151,f18]) ).
fof(f200,plain,
( ~ product(e_1,e_3,e_3)
| spl0_11 ),
inference(resolution,[],[f152,f18]) ).
fof(f201,plain,
( ~ spl0_24
| spl0_11 ),
inference(avatar_split_clause,[],[f200,f105,f178]) ).
fof(f220,plain,
( ~ group_element(e_3)
| product(e_1,e_1,e_3)
| product(e_2,e_1,e_3)
| ~ group_element(e_1)
| spl0_11 ),
inference(resolution,[],[f188,f1]) ).
fof(f224,plain,
( ~ spl0_5
| spl0_22
| spl0_23
| ~ spl0_21
| spl0_11 ),
inference(avatar_split_clause,[],[f220,f105,f154,f175,f172,f78]) ).
fof(f239,plain,
( ~ product(e_1,e_3,e_3)
| spl0_14 ),
inference(factoring,[],[f161]) ).
fof(f240,plain,
( $false
| spl0_21 ),
inference(resolution,[],[f155,f7]) ).
fof(f241,plain,
spl0_21,
inference(avatar_contradiction_clause,[],[f240]) ).
fof(f250,plain,
( ~ product(e_2,e_3,e_1)
| ~ spl0_9 ),
inference(resolution,[],[f100,f20]) ).
fof(f258,plain,
( ~ product(e_1,e_1,e_1)
| spl0_14
| ~ spl0_19 ),
inference(resolution,[],[f143,f160]) ).
fof(f268,plain,
( $false
| spl0_14
| ~ spl0_19 ),
inference(resolution,[],[f258,f18]) ).
fof(f269,plain,
( spl0_14
| ~ spl0_19 ),
inference(avatar_contradiction_clause,[],[f268]) ).
fof(f270,plain,
( ! [X0] :
( ~ product(e_2,X0,e_1)
| ~ product(e_1,e_2,X0) )
| ~ spl0_12 ),
inference(resolution,[],[f110,f26]) ).
fof(f279,plain,
! [X0] :
( ~ group_element(e_2)
| product(X0,e_1,e_2)
| product(X0,e_2,e_2)
| ~ group_element(X0)
| ~ product(X0,e_3,e_1) ),
inference(resolution,[],[f2,f20]) ).
fof(f280,plain,
! [X0,X1] :
( ~ group_element(e_1)
| product(X0,e_1,e_1)
| product(X0,e_2,e_1)
| ~ group_element(X0)
| ~ product(X1,e_2,e_3)
| ~ product(e_2,X1,X0) ),
inference(resolution,[],[f2,f26]) ).
fof(f281,plain,
( ~ group_element(e_3)
| product(e_1,e_1,e_3)
| product(e_1,e_2,e_3)
| ~ group_element(e_1)
| spl0_24 ),
inference(resolution,[],[f2,f179]) ).
fof(f282,plain,
( ~ group_element(e_1)
| product(e_2,e_1,e_1)
| product(e_2,e_2,e_1)
| ~ group_element(e_2)
| ~ spl0_9 ),
inference(resolution,[],[f2,f250]) ).
fof(f284,plain,
( ~ group_element(e_1)
| product(e_2,e_1,e_1)
| product(e_2,e_2,e_1)
| ~ group_element(e_2)
| ~ product(e_1,e_2,e_3)
| ~ spl0_12 ),
inference(resolution,[],[f2,f270]) ).
fof(f287,definition,
( spl0_27
<=> product(e_2,e_1,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_27])],[avatar_definition]) ).
fof(f288,plain,
( product(e_2,e_1,e_1)
| ~ spl0_27 ),
inference(avatar_component_clause,[],[f287]) ).
fof(f289,plain,
( ~ spl0_15
| ~ spl0_2
| spl0_3
| spl0_27
| ~ spl0_5
| ~ spl0_12 ),
inference(avatar_split_clause,[],[f284,f109,f78,f287,f72,f69,f124]) ).
fof(f294,plain,
( ~ spl0_2
| spl0_3
| spl0_27
| ~ spl0_5
| ~ spl0_9 ),
inference(avatar_split_clause,[],[f282,f99,f78,f287,f72,f69]) ).
fof(f295,plain,
( ~ spl0_5
| spl0_15
| spl0_23
| ~ spl0_21
| spl0_24 ),
inference(avatar_split_clause,[],[f281,f178,f154,f175,f124,f78]) ).
fof(f297,definition,
( spl0_29
<=> ! [X0,X1] :
( product(X0,e_1,e_1)
| ~ product(X1,e_2,e_3)
| ~ product(e_2,X1,X0)
| ~ group_element(X0)
| product(X0,e_2,e_1) ) ),
introduced(definition,[new_symbols(definition,[spl0_29])],[avatar_definition]) ).
fof(f298,plain,
( ! [X0,X1] :
( ~ group_element(X0)
| ~ product(X1,e_2,e_3)
| ~ product(e_2,X1,X0)
| product(X0,e_1,e_1)
| product(X0,e_2,e_1) )
| ~ spl0_29 ),
inference(avatar_component_clause,[],[f297]) ).
fof(f299,plain,
( spl0_29
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f280,f78,f297]) ).
fof(f301,definition,
( spl0_30
<=> ! [X0] :
( product(X0,e_1,e_2)
| ~ product(X0,e_3,e_1)
| ~ group_element(X0)
| product(X0,e_2,e_2) ) ),
introduced(definition,[new_symbols(definition,[spl0_30])],[avatar_definition]) ).
fof(f302,plain,
( ! [X0] :
( ~ group_element(X0)
| ~ product(X0,e_3,e_1)
| product(X0,e_1,e_2)
| product(X0,e_2,e_2) )
| ~ spl0_30 ),
inference(avatar_component_clause,[],[f301]) ).
fof(f303,plain,
( spl0_30
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f279,f69,f301]) ).
fof(f308,plain,
( $false
| ~ spl0_3 ),
inference(resolution,[],[f73,f60]) ).
fof(f315,plain,
~ spl0_3,
inference(avatar_contradiction_clause,[],[f308]) ).
fof(f316,plain,
( ~ product(e_1,e_3,e_1)
| product(e_1,e_1,e_2)
| product(e_1,e_2,e_2)
| ~ spl0_30 ),
inference(resolution,[],[f302,f5]) ).
fof(f318,plain,
( ~ product(e_3,e_3,e_1)
| product(e_3,e_1,e_2)
| product(e_3,e_2,e_2)
| ~ spl0_30 ),
inference(resolution,[],[f302,f7]) ).
fof(f320,definition,
( spl0_32
<=> product(e_3,e_2,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_32])],[avatar_definition]) ).
fof(f321,plain,
( product(e_3,e_2,e_2)
| ~ spl0_32 ),
inference(avatar_component_clause,[],[f320]) ).
fof(f323,definition,
( spl0_33
<=> product(e_3,e_1,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_33])],[avatar_definition]) ).
fof(f324,plain,
( product(e_3,e_1,e_2)
| ~ spl0_33 ),
inference(avatar_component_clause,[],[f323]) ).
fof(f325,plain,
( spl0_32
| spl0_33
| ~ spl0_11
| ~ spl0_30 ),
inference(avatar_split_clause,[],[f318,f301,f105,f323,f320]) ).
fof(f327,definition,
( spl0_34
<=> product(e_1,e_2,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_34])],[avatar_definition]) ).
fof(f328,plain,
( product(e_1,e_2,e_2)
| ~ spl0_34 ),
inference(avatar_component_clause,[],[f327]) ).
fof(f329,plain,
( ~ product(e_1,e_3,e_1)
| spl0_19 ),
inference(avatar_component_clause,[],[f142]) ).
fof(f330,plain,
( spl0_34
| spl0_13
| ~ spl0_19
| ~ spl0_30 ),
inference(avatar_split_clause,[],[f316,f301,f142,f112,f327]) ).
fof(f343,plain,
( ! [X0] :
( ~ product(X0,e_2,e_3)
| ~ product(e_2,X0,e_3)
| product(e_3,e_1,e_1)
| product(e_3,e_2,e_1) )
| ~ spl0_29 ),
inference(resolution,[],[f298,f7]) ).
fof(f345,definition,
( spl0_36
<=> product(e_3,e_2,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_36])],[avatar_definition]) ).
fof(f346,plain,
( product(e_3,e_2,e_1)
| ~ spl0_36 ),
inference(avatar_component_clause,[],[f345]) ).
fof(f347,plain,
( product(e_3,e_1,e_1)
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f115]) ).
fof(f348,plain,
( spl0_36
| spl0_14
| spl0_20
| ~ spl0_29 ),
inference(avatar_split_clause,[],[f343,f297,f145,f115,f345]) ).
fof(f353,plain,
( ~ product(e_1,e_3,e_1)
| ~ spl0_10 ),
inference(resolution,[],[f103,f20]) ).
fof(f354,plain,
( ~ spl0_19
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f353,f102,f142]) ).
fof(f356,plain,
( ! [X0] :
( ~ product(X0,e_1,e_3)
| ~ product(e_1,X0,e_1) )
| spl0_19 ),
inference(resolution,[],[f329,f19]) ).
fof(f357,plain,
( ! [X0] :
( ~ product(X0,e_1,e_3)
| ~ product(e_3,e_1,X0) )
| spl0_19 ),
inference(resolution,[],[f329,f4]) ).
fof(f358,plain,
( ! [X0] :
( ~ product(e_3,e_1,X0)
| ~ product(e_1,X0,e_1) )
| spl0_19 ),
inference(resolution,[],[f329,f3]) ).
fof(f360,plain,
( ~ product(e_1,e_1,e_1)
| ~ spl0_13 ),
inference(resolution,[],[f113,f20]) ).
fof(f368,plain,
( ~ product(e_1,e_2,e_3)
| ~ spl0_20
| ~ spl0_22 ),
inference(resolution,[],[f146,f173]) ).
fof(f377,plain,
( ~ spl0_15
| ~ spl0_20
| ~ spl0_22 ),
inference(avatar_split_clause,[],[f368,f172,f145,f124]) ).
fof(f379,definition,
( spl0_38
<=> ! [X0] :
( ~ product(e_3,e_2,X0)
| ~ product(e_3,X0,e_1) ) ),
introduced(definition,[new_symbols(definition,[spl0_38])],[avatar_definition]) ).
fof(f380,plain,
( ! [X0] :
( ~ product(e_3,e_2,X0)
| ~ product(e_3,X0,e_1) )
| ~ spl0_38 ),
inference(avatar_component_clause,[],[f379]) ).
fof(f396,plain,
( ~ product(e_3,e_1,e_3)
| spl0_19 ),
inference(factoring,[],[f357]) ).
fof(f409,plain,
( ~ group_element(e_3)
| product(e_1,e_1,e_3)
| product(e_2,e_1,e_3)
| ~ group_element(e_1)
| spl0_19 ),
inference(resolution,[],[f396,f1]) ).
fof(f413,plain,
( ~ spl0_5
| spl0_22
| spl0_23
| ~ spl0_21
| spl0_19 ),
inference(avatar_split_clause,[],[f409,f142,f154,f175,f172,f78]) ).
fof(f422,plain,
( ~ product(e_1,e_1,e_1)
| spl0_19
| ~ spl0_23 ),
inference(resolution,[],[f176,f356]) ).
fof(f438,plain,
( $false
| spl0_19
| ~ spl0_23 ),
inference(resolution,[],[f422,f18]) ).
fof(f439,plain,
( spl0_19
| ~ spl0_23 ),
inference(avatar_contradiction_clause,[],[f438]) ).
fof(f464,plain,
( ~ product(e_3,e_2,e_1)
| ~ spl0_32
| ~ spl0_38 ),
inference(resolution,[],[f380,f321]) ).
fof(f489,plain,
( ~ product(e_1,e_1,e_1)
| ~ spl0_14
| spl0_19 ),
inference(resolution,[],[f347,f358]) ).
fof(f499,plain,
( $false
| ~ spl0_13 ),
inference(resolution,[],[f360,f18]) ).
fof(f500,plain,
~ spl0_13,
inference(avatar_contradiction_clause,[],[f499]) ).
fof(f501,plain,
( ~ spl0_24
| spl0_14 ),
inference(avatar_split_clause,[],[f239,f115,f178]) ).
fof(f502,plain,
( ~ group_element(e_1)
| product(e_1,e_2,e_1)
| product(e_2,e_2,e_1)
| ~ group_element(e_2)
| ~ spl0_32
| ~ spl0_38 ),
inference(resolution,[],[f464,f1]) ).
fof(f506,plain,
( ! [X0] :
( ~ product(e_2,X0,e_1)
| ~ product(e_1,e_2,X0) )
| ~ spl0_12 ),
inference(resolution,[],[f110,f26]) ).
fof(f513,plain,
( ~ product(e_1,e_2,e_1)
| ~ spl0_12
| ~ spl0_27 ),
inference(resolution,[],[f506,f288]) ).
fof(f524,plain,
! [X0,X1] :
( ~ group_element(X0)
| product(e_2,X0,e_1)
| product(e_2,X0,e_2)
| ~ group_element(e_2)
| ~ product(e_3,X1,e_1)
| ~ product(X0,e_2,X1) ),
inference(resolution,[],[f14,f26]) ).
fof(f533,definition,
( spl0_48
<=> ! [X0,X1] :
( ~ group_element(X0)
| ~ product(X0,e_2,X1)
| ~ product(e_3,X1,e_1)
| product(e_2,X0,e_2)
| product(e_2,X0,e_1) ) ),
introduced(definition,[new_symbols(definition,[spl0_48])],[avatar_definition]) ).
fof(f534,plain,
( ! [X0,X1] :
( ~ group_element(X0)
| ~ product(X0,e_2,X1)
| ~ product(e_3,X1,e_1)
| product(e_2,X0,e_2)
| product(e_2,X0,e_1) )
| ~ spl0_48 ),
inference(avatar_component_clause,[],[f533]) ).
fof(f535,plain,
( ~ spl0_2
| spl0_48 ),
inference(avatar_split_clause,[],[f524,f533,f69]) ).
fof(f559,plain,
( $false
| ~ spl0_14
| spl0_19 ),
inference(resolution,[],[f489,f18]) ).
fof(f560,plain,
( ~ spl0_14
| spl0_19 ),
inference(avatar_contradiction_clause,[],[f559]) ).
fof(f563,plain,
( ! [X0] :
( ~ product(e_3,e_2,X0)
| ~ product(e_3,X0,e_1)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1) )
| ~ spl0_48 ),
inference(resolution,[],[f534,f7]) ).
fof(f575,plain,
( $false
| ~ spl0_4
| ~ spl0_12
| ~ spl0_27 ),
inference(resolution,[],[f513,f76]) ).
fof(f579,plain,
( ~ spl0_4
| ~ spl0_12
| ~ spl0_27 ),
inference(avatar_contradiction_clause,[],[f575]) ).
fof(f581,definition,
( spl0_54
<=> ! [X0] :
( ~ product(e_2,X0,e_3)
| ~ product(X0,e_2,e_2) ) ),
introduced(definition,[new_symbols(definition,[spl0_54])],[avatar_definition]) ).
fof(f582,plain,
( ! [X0] :
( ~ product(e_2,X0,e_3)
| ~ product(X0,e_2,e_2) )
| ~ spl0_54 ),
inference(avatar_component_clause,[],[f581]) ).
fof(f583,plain,
( spl0_3
| spl0_4
| spl0_54
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f136,f86,f581,f75,f72]) ).
fof(f584,plain,
( ~ spl0_2
| spl0_3
| spl0_4
| ~ spl0_5
| ~ spl0_32
| ~ spl0_38 ),
inference(avatar_split_clause,[],[f502,f379,f320,f78,f75,f72,f69]) ).
fof(f585,plain,
( ~ product(e_3,e_1,e_1)
| ~ spl0_33 ),
inference(resolution,[],[f324,f20]) ).
fof(f586,plain,
( ~ spl0_14
| ~ spl0_33 ),
inference(avatar_split_clause,[],[f585,f323,f115]) ).
fof(f587,plain,
( ~ product(e_2,e_1,e_1)
| ~ spl0_9
| ~ spl0_17 ),
inference(resolution,[],[f133,f100]) ).
fof(f603,plain,
( $false
| ~ spl0_9
| ~ spl0_17
| ~ spl0_27 ),
inference(resolution,[],[f587,f288]) ).
fof(f607,plain,
( ~ spl0_9
| ~ spl0_17
| ~ spl0_27 ),
inference(avatar_contradiction_clause,[],[f603]) ).
fof(f608,plain,
( spl0_18
| spl0_9
| spl0_38
| ~ spl0_48 ),
inference(avatar_split_clause,[],[f563,f533,f379,f99,f139]) ).
fof(f609,plain,
( ~ group_element(e_1)
| product(e_1,e_3,e_1)
| product(e_2,e_3,e_1)
| ~ group_element(e_3)
| spl0_11 ),
inference(resolution,[],[f106,f1]) ).
fof(f615,plain,
( $false
| spl0_11
| ~ spl0_23 ),
inference(resolution,[],[f170,f176]) ).
fof(f621,plain,
( spl0_11
| ~ spl0_23 ),
inference(avatar_contradiction_clause,[],[f615]) ).
fof(f632,plain,
( ~ group_element(e_3)
| product(e_1,e_3,e_1)
| product(e_1,e_3,e_2)
| ~ group_element(e_1)
| spl0_24 ),
inference(resolution,[],[f179,f14]) ).
fof(f654,plain,
( ~ product(e_1,e_2,e_2)
| ~ spl0_22
| ~ spl0_54 ),
inference(resolution,[],[f582,f173]) ).
fof(f668,plain,
( $false
| ~ spl0_22
| ~ spl0_34
| ~ spl0_54 ),
inference(resolution,[],[f654,f328]) ).
fof(f672,plain,
( ~ spl0_22
| ~ spl0_34
| ~ spl0_54 ),
inference(avatar_contradiction_clause,[],[f668]) ).
fof(f677,plain,
( ~ spl0_21
| spl0_18
| spl0_19
| ~ spl0_5
| spl0_11 ),
inference(avatar_split_clause,[],[f609,f105,f78,f142,f139,f154]) ).
fof(f678,plain,
( ~ spl0_5
| spl0_10
| spl0_19
| ~ spl0_21
| spl0_24 ),
inference(avatar_split_clause,[],[f632,f178,f154,f142,f102,f78]) ).
fof(f684,plain,
( ~ product(e_1,e_1,e_1)
| ~ spl0_17
| ~ spl0_18 ),
inference(resolution,[],[f140,f133]) ).
fof(f694,plain,
( ! [X0] :
( ~ product(X0,e_1,e_1)
| ~ product(e_2,e_3,X0) )
| ~ spl0_36 ),
inference(resolution,[],[f346,f26]) ).
fof(f705,plain,
( $false
| ~ spl0_17
| ~ spl0_18 ),
inference(resolution,[],[f684,f18]) ).
fof(f706,plain,
( ~ spl0_17
| ~ spl0_18 ),
inference(avatar_contradiction_clause,[],[f705]) ).
fof(f707,plain,
( spl0_17
| ~ spl0_36 ),
inference(avatar_split_clause,[],[f694,f345,f132]) ).
cnf(s2,plain,
( ~ spl0_2
| spl0_6 ),
inference(sat_conversion,[],[f84]) ).
cnf(s3,plain,
( ~ spl0_5
| spl0_7 ),
inference(sat_conversion,[],[f88]) ).
cnf(s4,plain,
( ~ spl0_2
| spl0_8 ),
inference(sat_conversion,[],[f92]) ).
cnf(s5,plain,
spl0_2,
inference(sat_conversion,[],[f94]) ).
cnf(s6,plain,
( ~ spl0_8
| spl0_9
| spl0_10
| ~ spl0_11 ),
inference(sat_conversion,[],[f107]) ).
cnf(s7,plain,
( ~ spl0_8
| spl0_12
| spl0_13
| ~ spl0_14 ),
inference(sat_conversion,[],[f117]) ).
cnf(s8,plain,
spl0_5,
inference(sat_conversion,[],[f119]) ).
cnf(s10,plain,
( spl0_3
| spl0_4
| ~ spl0_6
| spl0_17 ),
inference(sat_conversion,[],[f134]) ).
cnf(s11,plain,
( ~ spl0_7
| spl0_18
| spl0_19
| spl0_20 ),
inference(sat_conversion,[],[f147]) ).
cnf(s15,plain,
( spl0_11
| ~ spl0_24 ),
inference(sat_conversion,[],[f201]) ).
cnf(s17,plain,
( ~ spl0_5
| spl0_11
| ~ spl0_21
| spl0_22
| spl0_23 ),
inference(sat_conversion,[],[f224]) ).
cnf(s18,plain,
spl0_21,
inference(sat_conversion,[],[f241]) ).
cnf(s22,plain,
( spl0_14
| ~ spl0_19 ),
inference(sat_conversion,[],[f269]) ).
cnf(s23,plain,
( ~ spl0_2
| spl0_3
| ~ spl0_5
| ~ spl0_12
| ~ spl0_15
| spl0_27 ),
inference(sat_conversion,[],[f289]) ).
cnf(s25,plain,
( ~ spl0_2
| spl0_3
| ~ spl0_5
| ~ spl0_9
| spl0_27 ),
inference(sat_conversion,[],[f294]) ).
cnf(s26,plain,
( ~ spl0_5
| spl0_15
| ~ spl0_21
| spl0_23
| spl0_24 ),
inference(sat_conversion,[],[f295]) ).
cnf(s27,plain,
( ~ spl0_5
| spl0_29 ),
inference(sat_conversion,[],[f299]) ).
cnf(s28,plain,
( ~ spl0_2
| spl0_30 ),
inference(sat_conversion,[],[f303]) ).
cnf(s30,plain,
~ spl0_3,
inference(sat_conversion,[],[f315]) ).
cnf(s31,plain,
( ~ spl0_11
| ~ spl0_30
| spl0_32
| spl0_33 ),
inference(sat_conversion,[],[f325]) ).
cnf(s32,plain,
( spl0_13
| ~ spl0_19
| ~ spl0_30
| spl0_34 ),
inference(sat_conversion,[],[f330]) ).
cnf(s34,plain,
( spl0_14
| spl0_20
| ~ spl0_29
| spl0_36 ),
inference(sat_conversion,[],[f348]) ).
cnf(s36,plain,
( ~ spl0_10
| ~ spl0_19 ),
inference(sat_conversion,[],[f354]) ).
cnf(s37,plain,
( ~ spl0_15
| ~ spl0_20
| ~ spl0_22 ),
inference(sat_conversion,[],[f377]) ).
cnf(s40,plain,
( ~ spl0_5
| spl0_19
| ~ spl0_21
| spl0_22
| spl0_23 ),
inference(sat_conversion,[],[f413]) ).
cnf(s43,plain,
( spl0_19
| ~ spl0_23 ),
inference(sat_conversion,[],[f439]) ).
cnf(s53,plain,
~ spl0_13,
inference(sat_conversion,[],[f500]) ).
cnf(s54,plain,
( spl0_14
| ~ spl0_24 ),
inference(sat_conversion,[],[f501]) ).
cnf(s58,plain,
( ~ spl0_2
| spl0_48 ),
inference(sat_conversion,[],[f535]) ).
cnf(s64,plain,
( ~ spl0_14
| spl0_19 ),
inference(sat_conversion,[],[f560]) ).
cnf(s65,plain,
( ~ spl0_4
| ~ spl0_12
| ~ spl0_27 ),
inference(sat_conversion,[],[f579]) ).
cnf(s66,plain,
( spl0_3
| spl0_4
| ~ spl0_7
| spl0_54 ),
inference(sat_conversion,[],[f583]) ).
cnf(s67,plain,
( ~ spl0_2
| spl0_3
| spl0_4
| ~ spl0_5
| ~ spl0_32
| ~ spl0_38 ),
inference(sat_conversion,[],[f584]) ).
cnf(s68,plain,
( ~ spl0_14
| ~ spl0_33 ),
inference(sat_conversion,[],[f586]) ).
cnf(s70,plain,
( ~ spl0_9
| ~ spl0_17
| ~ spl0_27 ),
inference(sat_conversion,[],[f607]) ).
cnf(s72,plain,
( spl0_9
| spl0_18
| spl0_38
| ~ spl0_48 ),
inference(sat_conversion,[],[f608]) ).
cnf(s74,plain,
( spl0_11
| ~ spl0_23 ),
inference(sat_conversion,[],[f621]) ).
cnf(s80,plain,
( ~ spl0_22
| ~ spl0_34
| ~ spl0_54 ),
inference(sat_conversion,[],[f672]) ).
cnf(s83,plain,
( ~ spl0_5
| spl0_11
| spl0_18
| spl0_19
| ~ spl0_21 ),
inference(sat_conversion,[],[f677]) ).
cnf(s84,plain,
( ~ spl0_5
| spl0_10
| spl0_19
| ~ spl0_21
| spl0_24 ),
inference(sat_conversion,[],[f678]) ).
cnf(s89,plain,
( ~ spl0_17
| ~ spl0_18 ),
inference(sat_conversion,[],[f706]) ).
cnf(s90,plain,
( spl0_17
| ~ spl0_36 ),
inference(sat_conversion,[],[f707]) ).
cnf(s91,plain,
( ~ spl0_19
| ~ spl0_30
| spl0_34 ),
inference(rat,[],[s32,s53]) ).
cnf(s92,plain,
( ~ spl0_2
| ~ spl0_5
| ~ spl0_9
| spl0_27 ),
inference(rat,[],[s25,s30]) ).
cnf(s93,plain,
( ~ spl0_2
| ~ spl0_5
| ~ spl0_12
| ~ spl0_15
| spl0_27 ),
inference(rat,[],[s23,s30]) ).
cnf(s94,plain,
( ~ spl0_5
| spl0_11
| spl0_22
| spl0_23 ),
inference(rat,[],[s17,s18]) ).
cnf(s99,plain,
( spl0_4
| ~ spl0_6
| spl0_17 ),
inference(rat,[],[s10,s30]) ).
cnf(s100,plain,
spl0_29,
inference(rat,[],[s27,s8]) ).
cnf(s101,plain,
( ~ spl0_8
| spl0_12
| ~ spl0_14 ),
inference(rat,[],[s7,s53]) ).
cnf(s103,plain,
spl0_48,
inference(rat,[],[s58,s5]) ).
cnf(s104,plain,
spl0_30,
inference(rat,[],[s28,s5]) ).
cnf(s106,plain,
spl0_8,
inference(rat,[],[s4,s5]) ).
cnf(s107,plain,
spl0_7,
inference(rat,[],[s3,s8]) ).
cnf(s108,plain,
spl0_6,
inference(rat,[],[s2,s5]) ).
cnf(s110,plain,
( spl0_11
| spl0_4 ),
inference(rat,[],[s80,s91,s94,s74,s83,s66,s89,s99,s104,s8,s18,s108,s107,s30]) ).
cnf(s111,plain,
( spl0_9
| spl0_4 ),
inference(rat,[],[s37,s26,s11,s40,s43,s54,s36,s68,s6,s31,s67,s72,s89,s99,s110,s18,s8,s107,s106,s104,s30,s5,s103,s108]) ).
cnf(s112,plain,
( ~ spl0_9
| ~ spl0_17 ),
inference(rat,[],[s92,s70,s5,s8]) ).
cnf(s113,plain,
spl0_4,
inference(rat,[],[s112,s111,s99,s108]) ).
cnf(s114,plain,
( spl0_10
| spl0_9 ),
inference(rat,[],[s93,s65,s101,s22,s84,s26,s15,s74,s6,s18,s106,s113,s5,s8]) ).
cnf(s115,plain,
spl0_19,
inference(rat,[],[s89,s90,s11,s34,s37,s26,s54,s40,s43,s64,s107,s100,s18,s8]) ).
cnf(s116,plain,
~ spl0_10,
inference(rat,[],[s36,s115]) ).
cnf(s118,plain,
spl0_14,
inference(rat,[],[s22,s115]) ).
cnf(s119,plain,
spl0_9,
inference(rat,[],[s114,s116]) ).
cnf(s121,plain,
spl0_12,
inference(rat,[],[s101,s106,s118]) ).
cnf(s123,plain,
spl0_27,
inference(rat,[],[s92,s5,s8,s119]) ).
cnf(s124,plain,
$false,
inference(rat,[],[s65,s113,s123,s121]) ).
fof(f708,plain,
$false,
inference(avatar_sat_refutation,[],[s124]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP125-4.003 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.39 % Computer : n019.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Sun Sep 27 09:22:04 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.68/1.27 % (2828437)Input is clausal, will run a generic CNF schedule.
% 2.68/1.27 % (2828442)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=1795004695:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.68/1.27 % (2828446)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1784254216:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.68/1.27 % (2828445)lrs+10_1_sil=8000:sp=occurrence:random_seed=1845402645:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.68/1.27 % (2828443)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=4009854017:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.68/1.27 % (2828444)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2401087922:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.68/1.27 % (2828448)dis-21_1_sil=8000:lcm=predicate:random_seed=476271015:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 2.68/1.27 % (2828447)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3312679164:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.68/1.27 % (2828445)Refutation not found, incomplete strategy
% 2.68/1.27 % (2828445)------------------------------
% 2.68/1.27 % (2828445)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.68/1.27 % (2828445)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.68/1.27 % (2828445)CaDiCaL version: 2.1.3
% 2.68/1.27 % (2828445)Termination reason: Refutation not found, incomplete strategy
% 2.68/1.27 % (2828445)Time elapsed: 0.001 s
% 2.68/1.27 % (2828445)Peak memory usage: 87 MB
% 2.68/1.27 % (2828448)First to succeed.
% 2.68/1.27 % (2828448)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2828437"
% 2.68/1.27 % (2828447)Also succeeded, but the first one will report.
% 2.68/1.27 % (2828446)Instruction limit reached!
% 2.68/1.27 % (2828446)------------------------------
% 2.68/1.27 % (2828446)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.68/1.27 % (2828446)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.68/1.27 % (2828446)CaDiCaL version: 2.1.3
% 2.68/1.27 % (2828446)Termination reason: Instruction limit
% 2.68/1.27 % (2828446)Termination phase: Saturation
% 2.68/1.27 % (2828446)Time elapsed: 0.058 s
% 2.68/1.27 % (2828446)Peak memory usage: 87 MB
% 2.68/1.27 % (2828446)Instructions burned: 115 (million)
% 2.68/1.27 % (2828456)dis+1010_3_sil=8000:plsq=on:drc=off:fde=none:plsqc=1:bsd=on:plsqr=7,2:sos=on:spb=goal_then_units:random_seed=2013482607:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 2.68/1.27 % (2828456)Also succeeded, but the first one will report.
% 2.68/1.27 % (2828445)------------------------------
% 2.68/1.27 % (2828445)------------------------------
% 2.68/1.27 % (2828448)Refutation found. Thanks to Tanya!
% 2.68/1.27 % SZS status Unsatisfiable for theBenchmark
% 2.68/1.27 % SZS output start Proof for theBenchmark
% See solution above
% 3.50/1.47 % (2828448)------------------------------
% 3.50/1.47 % (2828448)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.50/1.47 % (2828448)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.50/1.47 % (2828448)CaDiCaL version: 2.1.3
% 3.50/1.47 % (2828448)Termination reason: Refutation
% 3.50/1.47 % (2828448)Time elapsed: 0.015 s
% 3.50/1.47 % (2828448)Peak memory usage: 89 MB
% 3.50/1.47 % (2828448)Instructions burned: 20 (million)
% 3.50/1.47 % (2828448)------------------------------
% 3.50/1.47 % (2828448)------------------------------
% 3.50/1.47 % (2828437)Success in time 0.412 s
% 3.50/1.47 % Vampire exiting
%------------------------------------------------------------------------------