%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP127-1.004 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n012.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 10:12:46 AM UTC 2026
% Result : Unsatisfiable 0.63s 0.81s
% Output : Refutation 2.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 31
% Syntax : Number of formulae : 181 ( 39 unt; 15 def)
% Number of atoms : 414 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 471 ( 238 ~; 218 |; 0 &)
% ( 15 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 19 ( 18 usr; 16 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 78 ( 0 sgn 78 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
group_element(e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_1) ).
fof(f2,axiom,
group_element(e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_2) ).
fof(f3,axiom,
group_element(e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_3) ).
fof(f4,axiom,
group_element(e_4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_4) ).
fof(f5,axiom,
~ equalish(e_1,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_1_is_not_e_2) ).
fof(f6,axiom,
~ equalish(e_1,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_1_is_not_e_3) ).
fof(f7,axiom,
~ equalish(e_1,e_4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_1_is_not_e_4) ).
fof(f9,axiom,
~ equalish(e_2,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_2_is_not_e_3) ).
fof(f10,axiom,
~ equalish(e_2,e_4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_2_is_not_e_4) ).
fof(f13,axiom,
~ equalish(e_3,e_4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_is_not_e_4) ).
fof(f17,axiom,
! [X0,X1] :
( product(X0,X1,e_4)
| ~ group_element(X1)
| product(X0,X1,e_1)
| product(X0,X1,e_2)
| product(X0,X1,e_3)
| ~ group_element(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_total_function1) ).
fof(f18,axiom,
! [X2,X3,X0,X1] :
( equalish(X2,X3)
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_total_function2) ).
fof(f19,axiom,
! [X2,X3,X0,X1] :
( equalish(X1,X3)
| ~ product(X0,X3,X2)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_right_cancellation) ).
fof(f20,axiom,
! [X2,X3,X0,X1] :
( equalish(X0,X3)
| ~ product(X3,X1,X2)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_left_cancellation) ).
fof(f21,axiom,
! [X0] : product(X0,X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_idempotence) ).
fof(f22,negated_conjecture,
! [X2,X3,X0,X1] :
( product(X3,X0,X1)
| ~ product(X2,X0,X3)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qg3) ).
fof(f23,plain,
! [X0,X1] :
( ~ product(e_2,X0,X1)
| ~ product(e_1,X0,X1) ),
inference(resolution,[],[f5,f20]) ).
fof(f24,plain,
! [X0,X1] :
( ~ product(X0,e_2,X1)
| ~ product(X0,e_1,X1) ),
inference(resolution,[],[f5,f19]) ).
fof(f25,plain,
! [X0,X1] :
( ~ product(X0,X1,e_2)
| ~ product(X0,X1,e_1) ),
inference(resolution,[],[f5,f18]) ).
fof(f26,plain,
! [X0,X1] :
( ~ product(e_3,X0,X1)
| ~ product(e_1,X0,X1) ),
inference(resolution,[],[f6,f20]) ).
fof(f27,plain,
! [X0,X1] :
( ~ product(X0,e_3,X1)
| ~ product(X0,e_1,X1) ),
inference(resolution,[],[f6,f19]) ).
fof(f28,plain,
! [X0,X1] :
( ~ product(X0,X1,e_3)
| ~ product(X0,X1,e_1) ),
inference(resolution,[],[f6,f18]) ).
fof(f29,plain,
! [X0,X1] :
( ~ product(e_4,X0,X1)
| ~ product(e_1,X0,X1) ),
inference(resolution,[],[f7,f20]) ).
fof(f30,plain,
! [X0,X1] :
( ~ product(X0,e_4,X1)
| ~ product(X0,e_1,X1) ),
inference(resolution,[],[f7,f19]) ).
fof(f35,plain,
! [X0,X1] :
( ~ product(e_3,X0,X1)
| ~ product(e_2,X0,X1) ),
inference(resolution,[],[f9,f20]) ).
fof(f36,plain,
! [X0,X1] :
( ~ product(X0,e_3,X1)
| ~ product(X0,e_2,X1) ),
inference(resolution,[],[f9,f19]) ).
fof(f37,plain,
! [X0,X1] :
( ~ product(X0,X1,e_3)
| ~ product(X0,X1,e_2) ),
inference(resolution,[],[f9,f18]) ).
fof(f38,plain,
! [X0,X1] :
( ~ product(e_4,X0,X1)
| ~ product(e_2,X0,X1) ),
inference(resolution,[],[f10,f20]) ).
fof(f39,plain,
! [X0,X1] :
( ~ product(X0,e_4,X1)
| ~ product(X0,e_2,X1) ),
inference(resolution,[],[f10,f19]) ).
fof(f47,plain,
! [X0,X1] :
( ~ product(e_4,X0,X1)
| ~ product(e_3,X0,X1) ),
inference(resolution,[],[f13,f20]) ).
fof(f48,plain,
! [X0,X1] :
( ~ product(X0,e_4,X1)
| ~ product(X0,e_3,X1) ),
inference(resolution,[],[f13,f19]) ).
fof(f59,plain,
! [X2,X0,X1] :
( ~ product(X2,X0,e_2)
| ~ product(e_1,X0,X1)
| ~ product(X0,X1,X2) ),
inference(resolution,[],[f23,f22]) ).
fof(f65,plain,
~ product(e_2,e_1,e_2),
inference(resolution,[],[f24,f21]) ).
fof(f68,plain,
! [X0] :
( ~ product(e_2,X0,e_2)
| ~ product(e_1,e_2,X0) ),
inference(resolution,[],[f59,f21]) ).
fof(f71,plain,
! [X2,X0,X1] :
( ~ product(X0,X1,e_1)
| ~ product(X2,X1,X0)
| ~ product(X1,e_2,X2) ),
inference(resolution,[],[f25,f22]) ).
fof(f74,plain,
~ product(e_1,e_2,e_2),
inference(resolution,[],[f68,f21]) ).
fof(f75,plain,
! [X2,X0,X1] :
( ~ product(X2,X0,e_3)
| ~ product(e_1,X0,X1)
| ~ product(X0,X1,X2) ),
inference(resolution,[],[f26,f22]) ).
fof(f82,plain,
~ product(e_3,e_1,e_3),
inference(resolution,[],[f27,f21]) ).
fof(f85,plain,
! [X2,X0,X1] :
( ~ product(X0,X1,e_1)
| ~ product(X2,X1,X0)
| ~ product(X1,e_3,X2) ),
inference(resolution,[],[f28,f22]) ).
fof(f100,plain,
~ product(e_4,e_1,e_4),
inference(resolution,[],[f30,f21]) ).
fof(f106,plain,
! [X0] :
( ~ product(e_1,e_2,X0)
| ~ product(X0,e_1,e_1) ),
inference(resolution,[],[f71,f21]) ).
fof(f107,plain,
! [X0] :
( ~ product(X0,e_2,e_1)
| ~ product(e_1,X0,e_1) ),
inference(factoring,[],[f71]) ).
fof(f110,plain,
( ~ product(e_4,e_1,e_1)
| ~ group_element(e_2)
| product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_3)
| ~ group_element(e_1) ),
inference(resolution,[],[f106,f17]) ).
fof(f111,plain,
( ~ product(e_4,e_1,e_1)
| product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_3)
| ~ group_element(e_1) ),
inference(forward_subsumption_resolution,[],[f110,f2]) ).
fof(f112,plain,
( ~ product(e_4,e_1,e_1)
| product(e_1,e_2,e_1)
| product(e_1,e_2,e_3)
| ~ group_element(e_1) ),
inference(forward_subsumption_resolution,[],[f111,f74]) ).
fof(f113,plain,
( ~ product(e_4,e_1,e_1)
| product(e_1,e_2,e_1)
| product(e_1,e_2,e_3) ),
inference(forward_subsumption_resolution,[],[f112,f1]) ).
fof(f115,definition,
( spl0_1
<=> product(e_1,e_2,e_3) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f116,plain,
( ~ product(e_1,e_2,e_3)
| spl0_1 ),
inference(avatar_component_clause,[],[f115]) ).
fof(f117,plain,
( product(e_1,e_2,e_3)
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f115]) ).
fof(f119,definition,
( spl0_2
<=> product(e_1,e_2,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f121,plain,
( product(e_1,e_2,e_1)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f119]) ).
fof(f123,definition,
( spl0_3
<=> product(e_4,e_1,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f126,plain,
( spl0_1
| spl0_2
| ~ spl0_3 ),
inference(avatar_split_clause,[],[f113,f123,f119,f115]) ).
fof(f129,plain,
! [X2,X0,X1] :
( ~ product(X2,X0,e_3)
| ~ product(e_2,X0,X1)
| ~ product(X0,X1,X2) ),
inference(resolution,[],[f35,f22]) ).
fof(f141,plain,
! [X0] :
( ~ product(e_3,X0,e_3)
| ~ product(e_1,e_3,X0) ),
inference(resolution,[],[f75,f21]) ).
fof(f142,plain,
! [X0] :
( ~ product(e_1,X0,e_3)
| ~ product(X0,e_3,e_1) ),
inference(factoring,[],[f75]) ).
fof(f144,plain,
! [X2,X0,X1] :
( ~ product(X0,X1,e_2)
| ~ product(X2,X1,X0)
| ~ product(X1,e_3,X2) ),
inference(resolution,[],[f37,f22]) ).
fof(f147,plain,
~ product(e_1,e_3,e_3),
inference(resolution,[],[f141,f21]) ).
fof(f155,plain,
~ product(e_4,e_2,e_4),
inference(resolution,[],[f39,f21]) ).
fof(f170,plain,
! [X0] :
( ~ product(X0,e_3,e_1)
| ~ product(e_1,X0,e_1) ),
inference(factoring,[],[f85]) ).
fof(f188,plain,
~ product(e_4,e_3,e_4),
inference(resolution,[],[f48,f21]) ).
fof(f208,plain,
! [X0] :
( ~ product(e_3,X0,e_3)
| ~ product(e_2,e_3,X0) ),
inference(resolution,[],[f129,f21]) ).
fof(f212,plain,
~ product(e_2,e_3,e_3),
inference(resolution,[],[f208,f21]) ).
fof(f224,plain,
! [X0] :
( ~ product(e_2,e_3,X0)
| ~ product(X0,e_2,e_2) ),
inference(resolution,[],[f144,f21]) ).
fof(f225,plain,
! [X0] :
( ~ product(X0,e_3,e_2)
| ~ product(e_2,X0,e_2) ),
inference(factoring,[],[f144]) ).
fof(f234,plain,
( ~ product(e_4,e_2,e_2)
| ~ group_element(e_3)
| product(e_2,e_3,e_1)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_3)
| ~ group_element(e_2) ),
inference(resolution,[],[f224,f17]) ).
fof(f235,plain,
( ~ product(e_4,e_2,e_2)
| product(e_2,e_3,e_1)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_3)
| ~ group_element(e_2) ),
inference(forward_subsumption_resolution,[],[f234,f3]) ).
fof(f236,plain,
( ~ product(e_4,e_2,e_2)
| product(e_2,e_3,e_1)
| product(e_2,e_3,e_2)
| ~ group_element(e_2) ),
inference(forward_subsumption_resolution,[],[f235,f212]) ).
fof(f237,plain,
( ~ product(e_4,e_2,e_2)
| product(e_2,e_3,e_1)
| product(e_2,e_3,e_2) ),
inference(forward_subsumption_resolution,[],[f236,f2]) ).
fof(f239,definition,
( spl0_4
<=> product(e_2,e_3,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f241,plain,
( product(e_2,e_3,e_2)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f239]) ).
fof(f243,definition,
( spl0_5
<=> product(e_2,e_3,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f247,definition,
( spl0_6
<=> product(e_4,e_2,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f250,plain,
( spl0_4
| spl0_5
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f237,f247,f243,f239]) ).
fof(f290,definition,
( spl0_9
<=> product(e_4,e_3,e_3) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f291,plain,
( product(e_4,e_3,e_3)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f290]) ).
fof(f350,plain,
! [X0] :
( ~ product(e_1,e_2,X0)
| ~ product(X0,e_1,e_2) ),
inference(resolution,[],[f65,f22]) ).
fof(f364,plain,
! [X0] :
( ~ product(X0,e_1,e_3)
| ~ product(e_1,e_3,X0) ),
inference(resolution,[],[f82,f22]) ).
fof(f407,plain,
( ~ group_element(e_1)
| product(e_4,e_1,e_1)
| product(e_4,e_1,e_2)
| product(e_4,e_1,e_3)
| ~ group_element(e_4) ),
inference(resolution,[],[f100,f17]) ).
fof(f409,plain,
( product(e_4,e_1,e_1)
| product(e_4,e_1,e_2)
| product(e_4,e_1,e_3)
| ~ group_element(e_4) ),
inference(forward_subsumption_resolution,[],[f407,f1]) ).
fof(f413,definition,
( spl0_20
<=> product(e_4,e_1,e_3) ),
introduced(definition,[new_symbols(definition,[spl0_20])],[avatar_definition]) ).
fof(f415,plain,
( product(e_4,e_1,e_3)
| ~ spl0_20 ),
inference(avatar_component_clause,[],[f413]) ).
fof(f417,definition,
( spl0_21
<=> product(e_4,e_1,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_21])],[avatar_definition]) ).
fof(f427,plain,
( product(e_4,e_1,e_1)
| product(e_4,e_1,e_2)
| product(e_4,e_1,e_3) ),
inference(forward_subsumption_resolution,[],[f409,f4]) ).
fof(f429,plain,
( spl0_20
| spl0_21
| spl0_3 ),
inference(avatar_split_clause,[],[f427,f123,f417,f413]) ).
fof(f432,definition,
( spl0_23
<=> product(e_1,e_3,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_23])],[avatar_definition]) ).
fof(f433,plain,
( ~ product(e_1,e_3,e_2)
| spl0_23 ),
inference(avatar_component_clause,[],[f432]) ).
fof(f436,definition,
( spl0_24
<=> product(e_1,e_3,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_24])],[avatar_definition]) ).
fof(f438,plain,
( product(e_1,e_3,e_1)
| ~ spl0_24 ),
inference(avatar_component_clause,[],[f436]) ).
fof(f461,plain,
( ~ product(e_2,e_3,e_1)
| ~ spl0_1 ),
inference(resolution,[],[f117,f142]) ).
fof(f473,plain,
( ~ spl0_5
| ~ spl0_1 ),
inference(avatar_split_clause,[],[f461,f115,f243]) ).
fof(f484,plain,
( ~ group_element(e_2)
| product(e_4,e_2,e_1)
| product(e_4,e_2,e_2)
| product(e_4,e_2,e_3)
| ~ group_element(e_4) ),
inference(resolution,[],[f155,f17]) ).
fof(f486,plain,
( product(e_4,e_2,e_1)
| product(e_4,e_2,e_2)
| product(e_4,e_2,e_3)
| ~ group_element(e_4) ),
inference(forward_subsumption_resolution,[],[f484,f2]) ).
fof(f490,definition,
( spl0_25
<=> product(e_4,e_2,e_3) ),
introduced(definition,[new_symbols(definition,[spl0_25])],[avatar_definition]) ).
fof(f492,plain,
( product(e_4,e_2,e_3)
| ~ spl0_25 ),
inference(avatar_component_clause,[],[f490]) ).
fof(f494,definition,
( spl0_26
<=> product(e_4,e_2,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_26])],[avatar_definition]) ).
fof(f496,plain,
( product(e_4,e_2,e_1)
| ~ spl0_26 ),
inference(avatar_component_clause,[],[f494]) ).
fof(f503,plain,
( product(e_4,e_2,e_1)
| product(e_4,e_2,e_2)
| product(e_4,e_2,e_3) ),
inference(forward_subsumption_resolution,[],[f486,f4]) ).
fof(f504,plain,
( spl0_25
| spl0_6
| spl0_26 ),
inference(avatar_split_clause,[],[f503,f494,f247,f490]) ).
fof(f510,plain,
( ~ group_element(e_3)
| product(e_4,e_3,e_1)
| product(e_4,e_3,e_2)
| product(e_4,e_3,e_3)
| ~ group_element(e_4) ),
inference(resolution,[],[f188,f17]) ).
fof(f512,plain,
( product(e_4,e_3,e_1)
| product(e_4,e_3,e_2)
| product(e_4,e_3,e_3)
| ~ group_element(e_4) ),
inference(forward_subsumption_resolution,[],[f510,f3]) ).
fof(f516,definition,
( spl0_28
<=> product(e_4,e_3,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_28])],[avatar_definition]) ).
fof(f518,plain,
( product(e_4,e_3,e_2)
| ~ spl0_28 ),
inference(avatar_component_clause,[],[f516]) ).
fof(f520,definition,
( spl0_29
<=> product(e_4,e_3,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_29])],[avatar_definition]) ).
fof(f522,plain,
( product(e_4,e_3,e_1)
| ~ spl0_29 ),
inference(avatar_component_clause,[],[f520]) ).
fof(f524,plain,
( product(e_4,e_3,e_1)
| product(e_4,e_3,e_2)
| product(e_4,e_3,e_3) ),
inference(forward_subsumption_resolution,[],[f512,f4]) ).
fof(f525,plain,
( spl0_9
| spl0_28
| spl0_29 ),
inference(avatar_split_clause,[],[f524,f520,f516,f290]) ).
fof(f534,plain,
( ~ product(e_3,e_3,e_3)
| ~ spl0_9 ),
inference(resolution,[],[f291,f47]) ).
fof(f543,plain,
( $false
| ~ spl0_9 ),
inference(forward_subsumption_resolution,[],[f534,f21]) ).
fof(f544,plain,
~ spl0_9,
inference(avatar_contradiction_clause,[],[f543]) ).
fof(f563,plain,
( ~ product(e_1,e_3,e_2)
| ~ spl0_28 ),
inference(resolution,[],[f518,f29]) ).
fof(f566,plain,
( ~ product(e_4,e_1,e_2)
| ~ spl0_28 ),
inference(resolution,[],[f518,f27]) ).
fof(f568,plain,
( ~ spl0_23
| ~ spl0_28 ),
inference(avatar_split_clause,[],[f563,f516,f432]) ).
fof(f587,plain,
( ~ product(e_1,e_2,e_3)
| ~ spl0_25 ),
inference(resolution,[],[f492,f29]) ).
fof(f589,plain,
( ~ product(e_4,e_1,e_3)
| ~ spl0_25 ),
inference(resolution,[],[f492,f24]) ).
fof(f594,plain,
( ~ spl0_21
| ~ spl0_28 ),
inference(avatar_split_clause,[],[f566,f516,f417]) ).
fof(f595,plain,
( ~ spl0_20
| ~ spl0_25 ),
inference(avatar_split_clause,[],[f589,f490,f413]) ).
fof(f639,plain,
( ~ product(e_4,e_1,e_1)
| ~ spl0_26 ),
inference(resolution,[],[f496,f24]) ).
fof(f756,plain,
( ~ product(e_2,e_3,e_1)
| ~ spl0_29 ),
inference(resolution,[],[f522,f38]) ).
fof(f759,plain,
( ~ product(e_4,e_2,e_1)
| ~ spl0_29 ),
inference(resolution,[],[f522,f36]) ).
fof(f766,plain,
( ~ spl0_5
| ~ spl0_29 ),
inference(avatar_split_clause,[],[f756,f520,f243]) ).
fof(f811,plain,
( ~ product(e_4,e_1,e_2)
| ~ group_element(e_2)
| product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_3)
| ~ group_element(e_1) ),
inference(resolution,[],[f350,f17]) ).
fof(f819,plain,
( ~ spl0_26
| ~ spl0_29 ),
inference(avatar_split_clause,[],[f759,f520,f494]) ).
fof(f820,plain,
( ~ product(e_4,e_1,e_2)
| product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_3)
| ~ group_element(e_1) ),
inference(forward_subsumption_resolution,[],[f811,f2]) ).
fof(f826,plain,
( ~ spl0_1
| ~ spl0_25 ),
inference(avatar_split_clause,[],[f587,f490,f115]) ).
fof(f830,plain,
( ~ spl0_3
| ~ spl0_26 ),
inference(avatar_split_clause,[],[f639,f494,f123]) ).
fof(f891,plain,
( ~ product(e_2,e_2,e_2)
| ~ spl0_4 ),
inference(resolution,[],[f241,f225]) ).
fof(f909,plain,
( $false
| ~ spl0_4 ),
inference(forward_subsumption_resolution,[],[f891,f21]) ).
fof(f910,plain,
~ spl0_4,
inference(avatar_contradiction_clause,[],[f909]) ).
fof(f934,plain,
( ~ product(e_1,e_1,e_1)
| ~ spl0_2 ),
inference(resolution,[],[f121,f107]) ).
fof(f948,plain,
( $false
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f934,f21]) ).
fof(f949,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[],[f948]) ).
fof(f952,plain,
( ~ product(e_4,e_1,e_2)
| product(e_1,e_2,e_1)
| product(e_1,e_2,e_3)
| ~ group_element(e_1) ),
inference(forward_subsumption_resolution,[],[f820,f74]) ).
fof(f953,plain,
( ~ product(e_4,e_1,e_2)
| product(e_1,e_2,e_1)
| ~ group_element(e_1)
| spl0_1 ),
inference(forward_subsumption_resolution,[],[f952,f116]) ).
fof(f954,plain,
( ~ product(e_4,e_1,e_2)
| product(e_1,e_2,e_1)
| spl0_1 ),
inference(forward_subsumption_resolution,[],[f953,f1]) ).
fof(f955,plain,
( spl0_2
| ~ spl0_21
| spl0_1 ),
inference(avatar_split_clause,[],[f954,f115,f417,f119]) ).
fof(f956,plain,
( ~ product(e_1,e_3,e_4)
| ~ spl0_20 ),
inference(resolution,[],[f415,f364]) ).
fof(f1105,plain,
( ~ group_element(e_3)
| product(e_1,e_3,e_1)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_3)
| ~ group_element(e_1)
| ~ spl0_20 ),
inference(resolution,[],[f956,f17]) ).
fof(f1107,plain,
( product(e_1,e_3,e_1)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_3)
| ~ group_element(e_1)
| ~ spl0_20 ),
inference(forward_subsumption_resolution,[],[f1105,f3]) ).
fof(f1113,plain,
( product(e_1,e_3,e_1)
| product(e_1,e_3,e_3)
| ~ group_element(e_1)
| ~ spl0_20
| spl0_23 ),
inference(forward_subsumption_resolution,[],[f1107,f433]) ).
fof(f1114,plain,
( product(e_1,e_3,e_1)
| ~ group_element(e_1)
| ~ spl0_20
| spl0_23 ),
inference(forward_subsumption_resolution,[],[f1113,f147]) ).
fof(f1115,plain,
( product(e_1,e_3,e_1)
| ~ spl0_20
| spl0_23 ),
inference(forward_subsumption_resolution,[],[f1114,f1]) ).
fof(f1116,plain,
( spl0_24
| ~ spl0_20
| spl0_23 ),
inference(avatar_split_clause,[],[f1115,f432,f413,f436]) ).
fof(f1124,plain,
( ~ product(e_1,e_1,e_1)
| ~ spl0_24 ),
inference(resolution,[],[f438,f170]) ).
fof(f1142,plain,
( $false
| ~ spl0_24 ),
inference(forward_subsumption_resolution,[],[f1124,f21]) ).
fof(f1143,plain,
~ spl0_24,
inference(avatar_contradiction_clause,[],[f1142]) ).
cnf(s1,plain,
( spl0_1
| spl0_2
| ~ spl0_3 ),
inference(sat_conversion,[],[f126]) ).
cnf(s2,plain,
( spl0_4
| spl0_5
| ~ spl0_6 ),
inference(sat_conversion,[],[f250]) ).
cnf(s18,plain,
( spl0_3
| spl0_20
| spl0_21 ),
inference(sat_conversion,[],[f429]) ).
cnf(s24,plain,
( ~ spl0_1
| ~ spl0_5 ),
inference(sat_conversion,[],[f473]) ).
cnf(s30,plain,
( spl0_6
| spl0_25
| spl0_26 ),
inference(sat_conversion,[],[f504]) ).
cnf(s32,plain,
( spl0_9
| spl0_28
| spl0_29 ),
inference(sat_conversion,[],[f525]) ).
cnf(s35,plain,
~ spl0_9,
inference(sat_conversion,[],[f544]) ).
cnf(s39,plain,
( ~ spl0_23
| ~ spl0_28 ),
inference(sat_conversion,[],[f568]) ).
cnf(s46,plain,
( ~ spl0_21
| ~ spl0_28 ),
inference(sat_conversion,[],[f594]) ).
cnf(s47,plain,
( ~ spl0_20
| ~ spl0_25 ),
inference(sat_conversion,[],[f595]) ).
cnf(s67,plain,
( ~ spl0_5
| ~ spl0_29 ),
inference(sat_conversion,[],[f766]) ).
cnf(s75,plain,
( ~ spl0_26
| ~ spl0_29 ),
inference(sat_conversion,[],[f819]) ).
cnf(s77,plain,
( ~ spl0_1
| ~ spl0_25 ),
inference(sat_conversion,[],[f826]) ).
cnf(s88,plain,
( ~ spl0_3
| ~ spl0_26 ),
inference(sat_conversion,[],[f830]) ).
cnf(s105,plain,
~ spl0_4,
inference(sat_conversion,[],[f910]) ).
cnf(s116,plain,
~ spl0_2,
inference(sat_conversion,[],[f949]) ).
cnf(s129,plain,
( spl0_1
| spl0_2
| ~ spl0_21 ),
inference(sat_conversion,[],[f955]) ).
cnf(s143,plain,
( ~ spl0_20
| spl0_23
| spl0_24 ),
inference(sat_conversion,[],[f1116]) ).
cnf(s146,plain,
~ spl0_24,
inference(sat_conversion,[],[f1143]) ).
cnf(s147,plain,
( ~ spl0_20
| spl0_23 ),
inference(rat,[],[s143,s146]) ).
cnf(s153,plain,
( spl0_28
| spl0_29 ),
inference(rat,[],[s32,s35]) ).
cnf(s159,plain,
( spl0_5
| ~ spl0_6 ),
inference(rat,[],[s2,s105]) ).
cnf(s160,plain,
( spl0_1
| ~ spl0_3 ),
inference(rat,[],[s1,s116]) ).
cnf(s161,plain,
~ spl0_20,
inference(rat,[],[s159,s30,s67,s75,s153,s39,s47,s147]) ).
cnf(s162,plain,
spl0_1,
inference(rat,[],[s18,s160,s129,s161,s116]) ).
cnf(s163,plain,
~ spl0_25,
inference(rat,[],[s77,s162]) ).
cnf(s164,plain,
~ spl0_5,
inference(rat,[],[s24,s162]) ).
cnf(s165,plain,
~ spl0_6,
inference(rat,[],[s159,s164]) ).
cnf(s166,plain,
spl0_26,
inference(rat,[],[s30,s163,s165]) ).
cnf(s167,plain,
~ spl0_3,
inference(rat,[],[s88,s166]) ).
cnf(s168,plain,
~ spl0_29,
inference(rat,[],[s75,s166]) ).
cnf(s170,plain,
spl0_21,
inference(rat,[],[s18,s161,s167]) ).
cnf(s171,plain,
spl0_28,
inference(rat,[],[s153,s168]) ).
cnf(s172,plain,
$false,
inference(rat,[],[s46,s171,s170]) ).
fof(f1144,plain,
$false,
inference(avatar_sat_refutation,[],[s172]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : GRP127-1.004 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.02 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.03/0.30 % Computer : n012.cluster.edu
% 0.03/0.30 % Model : x86_64 x86_64
% 0.03/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.30 % Memory : 8046.5625MB
% 0.03/0.30 % OS : Linux 6.8.0-71-generic
% 0.03/0.30 % CPULimit : 300
% 0.03/0.30 % WCLimit : 300
% 0.03/0.30 % DateTime : Sun Sep 27 09:25:19 UTC 2026
% 0.03/0.30 % CPUTime :
% 0.03/0.30 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.03/0.32 Running first-order theorem proving
% 0.03/0.32 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.63/0.81 % (2112381)Input is clausal, will run a generic CNF schedule.
% 0.63/0.81 % (2112392)dis-21_1_sil=8000:lcm=predicate:random_seed=2728482740: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)
% 0.63/0.81 % (2112387)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3748241659:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 0.63/0.81 % (2112386)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=421614284:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 0.63/0.81 % (2112389)lrs+10_1_sil=8000:sp=occurrence:random_seed=2163973203:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 0.63/0.81 % (2112388)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=353176031:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 0.63/0.81 % (2112390)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1228735807:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 0.63/0.81 % (2112391)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3667365500:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 0.63/0.81 % (2112391)First to succeed.
% 0.63/0.81 % (2112391)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2112381"
% 0.63/0.81 % (2112390)Instruction limit reached!
% 0.63/0.81 % (2112390)------------------------------
% 0.63/0.81 % (2112390)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.63/0.81 % (2112390)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.63/0.81 % (2112390)CaDiCaL version: 2.1.3
% 0.63/0.81 % (2112390)Termination reason: Instruction limit
% 0.63/0.81 % (2112390)Termination phase: Saturation
% 0.63/0.81 % (2112390)Time elapsed: 0.029 s
% 0.63/0.81 % (2112390)Peak memory usage: 87 MB
% 0.63/0.81 % (2112390)Instructions burned: 117 (million)
% 0.63/0.81 % (2112389)Instruction limit reached!
% 0.63/0.81 % (2112389)------------------------------
% 0.63/0.81 % (2112389)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.63/0.81 % (2112389)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.63/0.81 % (2112389)CaDiCaL version: 2.1.3
% 0.63/0.81 % (2112389)Termination reason: Instruction limit
% 0.63/0.81 % (2112389)Termination phase: Saturation
% 0.63/0.81 % (2112389)Time elapsed: 0.033 s
% 0.63/0.81 % (2112389)Peak memory usage: 88 MB
% 0.63/0.81 % (2112389)Instructions burned: 108 (million)
% 0.63/0.81 % (2112392)Instruction limit reached!
% 0.63/0.81 % (2112392)------------------------------
% 0.63/0.81 % (2112392)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.63/0.81 % (2112392)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.63/0.81 % (2112392)CaDiCaL version: 2.1.3
% 0.63/0.81 % (2112392)Termination reason: Instruction limit
% 0.63/0.81 % (2112392)Termination phase: Saturation
% 0.63/0.81 % (2112392)Time elapsed: 0.042 s
% 0.63/0.81 % (2112392)Peak memory usage: 88 MB
% 0.63/0.81 % (2112392)Instructions burned: 119 (million)
% 0.63/0.81 % (2112402)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=366048767:st=4:i=219:sd=3:ss=axioms_2998 on theBenchmark for (2998ds/219Mi)
% 0.63/0.81 % (2112400)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=3801082395:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 0.63/0.81 % (2112401)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=994630617:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2998 on theBenchmark for (2998ds/189Mi)
% 0.63/0.81 % (2112401)Refutation not found, incomplete strategy
% 0.63/0.81 % (2112401)------------------------------
% 0.63/0.81 % (2112401)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.63/0.81 % (2112401)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.63/0.81 % (2112401)CaDiCaL version: 2.1.3
% 0.63/0.81 % (2112401)Termination reason: Refutation not found, incomplete strategy
% 0.63/0.81 % (2112401)Time elapsed: 0.001 s
% 0.63/0.81 % (2112401)Peak memory usage: 87 MB
% 0.63/0.81 % (2112401)Instructions burned: 1 (million)
% 0.63/0.81 % (2112400)Also succeeded, but the first one will report.
% 0.63/0.81 % (2112391)Refutation found. Thanks to Tanya!
% 0.63/0.81 % SZS status Unsatisfiable for theBenchmark
% 0.63/0.81 % SZS output start Proof for theBenchmark
% See solution above
% 2.27/0.91 % (2112391)------------------------------
% 2.27/0.91 % (2112391)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.27/0.91 % (2112391)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.27/0.91 % (2112391)CaDiCaL version: 2.1.3
% 2.27/0.91 % (2112391)Termination reason: Refutation
% 2.27/0.91 % (2112391)Time elapsed: 0.014 s
% 2.27/0.91 % (2112391)Peak memory usage: 89 MB
% 2.27/0.91 % (2112391)Instructions burned: 39 (million)
% 2.27/0.91 % (2112391)------------------------------
% 2.27/0.91 % (2112391)------------------------------
% 2.27/0.91 % (2112381)Success in time 0.292 s
% 2.27/0.91 % Vampire exiting
%------------------------------------------------------------------------------