%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP126-4.004 : 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 : n006.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 10:12:45 AM UTC 2026
% Result : Unsatisfiable 2.72s 1.36s
% Output : Refutation 3.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 37
% Syntax : Number of formulae : 163 ( 44 unt; 17 def)
% Number of atoms : 403 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 421 ( 181 ~; 223 |; 0 &)
% ( 17 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 21 ( 20 usr; 18 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 66 ( 0 sgn 66 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( product(e_4,X0,X1)
| ~ group_element(X1)
| product(e_1,X0,X1)
| product(e_2,X0,X1)
| product(e_3,X0,X1)
| ~ group_element(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',row_surjectivity) ).
fof(f2,axiom,
! [X0,X1] :
( product(X0,e_4,X1)
| ~ group_element(X1)
| product(X0,e_1,X1)
| product(X0,e_2,X1)
| product(X0,e_3,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,X1)
| ~ product(X1,X0,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qg4_1) ).
fof(f4,negated_conjecture,
! [X2,X3,X0,X1] :
( product(X0,X1,X2)
| ~ product(X3,X2,X0)
| ~ product(X1,X0,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qg4_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,
group_element(e_4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_4) ).
fof(f9,axiom,
~ equalish(e_1,e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_1_is_not_e_2) ).
fof(f10,axiom,
~ equalish(e_1,e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_1_is_not_e_3) ).
fof(f11,axiom,
~ equalish(e_1,e_4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_1_is_not_e_4) ).
fof(f13,axiom,
~ equalish(e_2,e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_2_is_not_e_3) ).
fof(f14,axiom,
~ equalish(e_2,e_4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_2_is_not_e_4) ).
fof(f17,axiom,
~ equalish(e_3,e_4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_3_is_not_e_4) ).
fof(f21,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/sandbox2/benchmark/theBenchmark.p',product_total_function1) ).
fof(f22,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(f23,axiom,
! [X2,X3,X0,X1] :
( equalish(X1,X3)
| ~ product(X0,X3,X2)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_right_cancellation) ).
fof(f24,axiom,
! [X2,X3,X0,X1] :
( equalish(X0,X3)
| ~ product(X3,X1,X2)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_left_cancellation) ).
fof(f25,axiom,
! [X0] : product(X0,X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_idempotence) ).
fof(f26,negated_conjecture,
! [X2,X3,X0,X1] :
( product(X2,X3,X1)
| ~ product(X1,X0,X3)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qg4) ).
fof(f27,plain,
! [X0,X1] :
( ~ product(e_2,X0,X1)
| ~ product(e_1,X0,X1) ),
inference(resolution,[],[f9,f24]) ).
fof(f28,plain,
! [X0,X1] :
( ~ product(X0,e_2,X1)
| ~ product(X0,e_1,X1) ),
inference(resolution,[],[f9,f23]) ).
fof(f30,plain,
! [X0,X1] :
( ~ product(e_3,X0,X1)
| ~ product(e_1,X0,X1) ),
inference(resolution,[],[f10,f24]) ).
fof(f33,plain,
! [X0,X1] :
( ~ product(e_1,X0,X1)
| ~ product(e_4,X0,X1) ),
inference(resolution,[],[f11,f24]) ).
fof(f35,plain,
! [X0,X1] :
( ~ product(X0,X1,e_1)
| ~ product(X0,X1,e_4) ),
inference(resolution,[],[f11,f22]) ).
fof(f39,plain,
! [X0,X1] :
( ~ product(e_3,X0,X1)
| ~ product(e_2,X0,X1) ),
inference(resolution,[],[f13,f24]) ).
fof(f40,plain,
! [X0,X1] :
( ~ product(X0,e_2,X1)
| ~ product(X0,e_3,X1) ),
inference(resolution,[],[f13,f23]) ).
fof(f44,plain,
! [X0,X1] :
( ~ product(X0,X1,e_2)
| ~ product(X0,X1,e_4) ),
inference(resolution,[],[f14,f22]) ).
fof(f51,plain,
! [X0,X1] :
( ~ product(e_3,X0,X1)
| ~ product(e_4,X0,X1) ),
inference(resolution,[],[f17,f24]) ).
fof(f53,plain,
! [X0,X1] :
( ~ product(X0,X1,e_3)
| ~ product(X0,X1,e_4) ),
inference(resolution,[],[f17,f22]) ).
fof(f63,plain,
! [X2,X0,X1] :
( ~ product(e_1,X0,X1)
| ~ product(X1,X2,X0)
| ~ product(X2,X1,e_2) ),
inference(resolution,[],[f27,f26]) ).
fof(f64,plain,
! [X2,X0,X1] :
( ~ product(e_1,X0,X1)
| ~ product(X2,X1,e_2)
| ~ product(X0,e_2,X2) ),
inference(resolution,[],[f27,f4]) ).
fof(f66,plain,
! [X0] :
( ~ product(e_1,X0,e_4)
| ~ group_element(X0)
| product(e_2,X0,e_1)
| product(e_2,X0,e_2)
| product(e_2,X0,e_3)
| ~ group_element(e_2) ),
inference(resolution,[],[f27,f21]) ).
fof(f67,plain,
~ product(e_1,e_2,e_2),
inference(resolution,[],[f27,f25]) ).
fof(f70,plain,
! [X0] :
( ~ group_element(X0)
| ~ product(e_1,X0,e_4)
| product(e_2,X0,e_1)
| product(e_2,X0,e_2)
| product(e_2,X0,e_3) ),
inference(forward_subsumption_resolution,[],[f66,f6]) ).
fof(f71,plain,
! [X2,X0,X1] :
( ~ product(X1,X2,e_2)
| ~ product(X0,e_1,X1)
| ~ product(X2,X1,X0) ),
inference(resolution,[],[f28,f26]) ).
fof(f85,plain,
( ~ product(e_1,e_1,e_1)
| ~ product(e_1,e_1,e_2) ),
inference(factoring,[],[f63]) ).
fof(f88,definition,
( spl0_1
<=> product(e_2,e_1,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f90,plain,
( ~ product(e_2,e_1,e_2)
| spl0_1 ),
inference(avatar_component_clause,[],[f88]) ).
fof(f92,definition,
( spl0_2
<=> product(e_1,e_2,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f94,plain,
( ~ product(e_1,e_2,e_2)
| spl0_2 ),
inference(avatar_component_clause,[],[f92]) ).
fof(f96,plain,
~ product(e_1,e_1,e_2),
inference(forward_subsumption_resolution,[],[f85,f25]) ).
fof(f109,plain,
( ! [X0] :
( ~ product(e_2,X0,e_1)
| ~ product(e_1,e_2,X0) )
| spl0_1 ),
inference(resolution,[],[f90,f3]) ).
fof(f119,plain,
! [X0] :
( ~ product(X0,e_2,e_1)
| ~ product(e_1,e_1,X0) ),
inference(resolution,[],[f96,f4]) ).
fof(f138,definition,
( spl0_3
<=> product(e_3,e_1,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f139,plain,
( ~ product(e_3,e_1,e_2)
| spl0_3 ),
inference(avatar_component_clause,[],[f138]) ).
fof(f140,plain,
( product(e_3,e_1,e_2)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f138]) ).
fof(f174,definition,
( spl0_5
<=> product(e_2,e_3,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f176,plain,
( product(e_2,e_3,e_1)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f174]) ).
fof(f206,plain,
~ product(e_1,e_1,e_4),
inference(resolution,[],[f35,f25]) ).
fof(f222,definition,
( spl0_9
<=> product(e_1,e_2,e_4) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f224,plain,
( ~ product(e_1,e_2,e_4)
| spl0_9 ),
inference(avatar_component_clause,[],[f222]) ).
fof(f233,definition,
( spl0_10
<=> product(e_1,e_2,e_3) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f235,plain,
( product(e_1,e_2,e_3)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f233]) ).
fof(f237,definition,
( spl0_11
<=> product(e_1,e_2,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f238,plain,
( ~ product(e_1,e_2,e_1)
| spl0_11 ),
inference(avatar_component_clause,[],[f237]) ).
fof(f239,plain,
( product(e_1,e_2,e_1)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f237]) ).
fof(f241,plain,
( ~ product(e_1,e_2,e_3)
| spl0_1
| ~ spl0_5 ),
inference(resolution,[],[f176,f109]) ).
fof(f247,plain,
( ~ spl0_10
| spl0_1
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f241,f174,f88,f233]) ).
fof(f252,plain,
~ product(e_2,e_3,e_3),
inference(resolution,[],[f39,f25]) ).
fof(f263,plain,
~ product(e_2,e_3,e_2),
inference(resolution,[],[f40,f25]) ).
fof(f392,plain,
( ~ 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)
| spl0_9 ),
inference(resolution,[],[f224,f21]) ).
fof(f396,plain,
( 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)
| spl0_9 ),
inference(forward_subsumption_resolution,[],[f392,f6]) ).
fof(f397,plain,
( product(e_1,e_2,e_1)
| product(e_1,e_2,e_3)
| ~ group_element(e_1)
| spl0_2
| spl0_9 ),
inference(forward_subsumption_resolution,[],[f396,f94]) ).
fof(f398,plain,
( product(e_1,e_2,e_1)
| product(e_1,e_2,e_3)
| spl0_2
| spl0_9 ),
inference(forward_subsumption_resolution,[],[f397,f5]) ).
fof(f399,plain,
( spl0_10
| spl0_11
| spl0_2
| spl0_9 ),
inference(avatar_split_clause,[],[f398,f222,f92,f237,f233]) ).
fof(f403,plain,
~ product(e_3,e_3,e_4),
inference(resolution,[],[f53,f25]) ).
fof(f408,plain,
( ~ product(e_1,e_2,e_4)
| ~ spl0_10 ),
inference(resolution,[],[f235,f53]) ).
fof(f465,definition,
( spl0_16
<=> product(e_1,e_1,e_4) ),
introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition]) ).
fof(f467,plain,
( ~ product(e_1,e_1,e_4)
| spl0_16 ),
inference(avatar_component_clause,[],[f465]) ).
fof(f479,plain,
! [X0] :
( ~ product(e_1,e_2,X0)
| ~ product(X0,e_1,e_2) ),
inference(resolution,[],[f64,f25]) ).
fof(f488,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,[],[f479,f21]) ).
fof(f506,plain,
! [X0] :
( ~ product(e_2,e_2,X0)
| ~ product(X0,e_1,e_2) ),
inference(resolution,[],[f71,f25]) ).
fof(f533,plain,
~ product(e_2,e_1,e_2),
inference(resolution,[],[f506,f25]) ).
fof(f538,plain,
~ spl0_1,
inference(avatar_split_clause,[],[f533,f88]) ).
fof(f544,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,[],[f488,f6]) ).
fof(f558,definition,
( spl0_19
<=> product(e_4,e_1,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_19])],[avatar_definition]) ).
fof(f560,plain,
( ~ product(e_4,e_1,e_2)
| spl0_19 ),
inference(avatar_component_clause,[],[f558]) ).
fof(f613,plain,
( ~ product(e_1,e_1,e_1)
| ~ spl0_11 ),
inference(resolution,[],[f239,f119]) ).
fof(f630,plain,
( $false
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f613,f25]) ).
fof(f631,plain,
~ spl0_11,
inference(avatar_contradiction_clause,[],[f630]) ).
fof(f680,plain,
( ~ group_element(e_2)
| product(e_1,e_1,e_2)
| product(e_2,e_1,e_2)
| product(e_3,e_1,e_2)
| ~ group_element(e_1)
| spl0_19 ),
inference(resolution,[],[f560,f1]) ).
fof(f684,plain,
( product(e_1,e_1,e_2)
| product(e_2,e_1,e_2)
| product(e_3,e_1,e_2)
| ~ group_element(e_1)
| spl0_19 ),
inference(forward_subsumption_resolution,[],[f680,f6]) ).
fof(f685,plain,
( product(e_2,e_1,e_2)
| product(e_3,e_1,e_2)
| ~ group_element(e_1)
| spl0_19 ),
inference(forward_subsumption_resolution,[],[f684,f96]) ).
fof(f686,plain,
( product(e_3,e_1,e_2)
| ~ group_element(e_1)
| spl0_1
| spl0_19 ),
inference(forward_subsumption_resolution,[],[f685,f90]) ).
fof(f687,plain,
( ~ group_element(e_1)
| spl0_1
| spl0_3
| spl0_19 ),
inference(forward_subsumption_resolution,[],[f686,f139]) ).
fof(f688,plain,
( $false
| spl0_1
| spl0_3
| spl0_19 ),
inference(forward_subsumption_resolution,[],[f687,f5]) ).
fof(f689,plain,
( spl0_1
| spl0_3
| spl0_19 ),
inference(avatar_contradiction_clause,[],[f688]) ).
fof(f804,definition,
( spl0_25
<=> product(e_3,e_1,e_4) ),
introduced(definition,[new_symbols(definition,[spl0_25])],[avatar_definition]) ).
fof(f827,plain,
( ~ product(e_3,e_1,e_4)
| ~ spl0_3 ),
inference(resolution,[],[f140,f44]) ).
fof(f839,plain,
( ~ spl0_25
| ~ spl0_3 ),
inference(avatar_split_clause,[],[f827,f138,f804]) ).
fof(f925,definition,
( spl0_28
<=> product(e_1,e_4,e_4) ),
introduced(definition,[new_symbols(definition,[spl0_28])],[avatar_definition]) ).
fof(f926,plain,
( product(e_1,e_4,e_4)
| ~ spl0_28 ),
inference(avatar_component_clause,[],[f925]) ).
fof(f927,plain,
( ~ product(e_1,e_4,e_4)
| spl0_28 ),
inference(avatar_component_clause,[],[f925]) ).
fof(f985,plain,
( ~ product(e_4,e_4,e_4)
| ~ spl0_28 ),
inference(resolution,[],[f926,f33]) ).
fof(f998,plain,
( $false
| ~ spl0_28 ),
inference(forward_subsumption_resolution,[],[f985,f25]) ).
fof(f999,plain,
~ spl0_28,
inference(avatar_contradiction_clause,[],[f998]) ).
fof(f1010,definition,
( spl0_32
<=> product(e_2,e_3,e_3) ),
introduced(definition,[new_symbols(definition,[spl0_32])],[avatar_definition]) ).
fof(f1016,plain,
( ~ group_element(e_4)
| product(e_1,e_1,e_4)
| product(e_1,e_2,e_4)
| product(e_1,e_3,e_4)
| ~ group_element(e_1)
| spl0_28 ),
inference(resolution,[],[f927,f2]) ).
fof(f1022,plain,
( product(e_1,e_1,e_4)
| product(e_1,e_2,e_4)
| product(e_1,e_3,e_4)
| ~ group_element(e_1)
| spl0_28 ),
inference(forward_subsumption_resolution,[],[f1016,f8]) ).
fof(f1024,plain,
( product(e_1,e_2,e_4)
| product(e_1,e_3,e_4)
| ~ group_element(e_1)
| spl0_16
| spl0_28 ),
inference(forward_subsumption_resolution,[],[f1022,f467]) ).
fof(f1026,plain,
( product(e_1,e_3,e_4)
| ~ group_element(e_1)
| spl0_9
| spl0_16
| spl0_28 ),
inference(forward_subsumption_resolution,[],[f1024,f224]) ).
fof(f1027,plain,
( product(e_1,e_3,e_4)
| spl0_9
| spl0_16
| spl0_28 ),
inference(forward_subsumption_resolution,[],[f1026,f5]) ).
fof(f1064,definition,
( spl0_34
<=> product(e_1,e_3,e_4) ),
introduced(definition,[new_symbols(definition,[spl0_34])],[avatar_definition]) ).
fof(f1232,definition,
( spl0_38
<=> product(e_3,e_2,e_4) ),
introduced(definition,[new_symbols(definition,[spl0_38])],[avatar_definition]) ).
fof(f1234,plain,
( product(e_3,e_2,e_4)
| ~ spl0_38 ),
inference(avatar_component_clause,[],[f1232]) ).
fof(f1289,definition,
( spl0_45
<=> product(e_2,e_3,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_45])],[avatar_definition]) ).
fof(f1291,plain,
( ~ product(e_2,e_3,e_2)
| spl0_45 ),
inference(avatar_component_clause,[],[f1289]) ).
fof(f1398,plain,
( ~ spl0_9
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f408,f233,f222]) ).
fof(f1401,plain,
( ~ product(e_4,e_1,e_2)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_3)
| ~ group_element(e_1)
| spl0_11 ),
inference(forward_subsumption_resolution,[],[f544,f238]) ).
fof(f1468,definition,
( spl0_51
<=> product(e_3,e_3,e_4) ),
introduced(definition,[new_symbols(definition,[spl0_51])],[avatar_definition]) ).
fof(f1502,definition,
( spl0_52
<=> product(e_3,e_4,e_4) ),
introduced(definition,[new_symbols(definition,[spl0_52])],[avatar_definition]) ).
fof(f1503,plain,
( product(e_3,e_4,e_4)
| ~ spl0_52 ),
inference(avatar_component_clause,[],[f1502]) ).
fof(f1504,plain,
( ~ product(e_3,e_4,e_4)
| spl0_52 ),
inference(avatar_component_clause,[],[f1502]) ).
fof(f1698,plain,
( ~ product(e_4,e_4,e_4)
| ~ spl0_52 ),
inference(resolution,[],[f1503,f51]) ).
fof(f1709,plain,
( $false
| ~ spl0_52 ),
inference(forward_subsumption_resolution,[],[f1698,f25]) ).
fof(f1710,plain,
~ spl0_52,
inference(avatar_contradiction_clause,[],[f1709]) ).
fof(f1711,plain,
~ spl0_16,
inference(avatar_split_clause,[],[f206,f465]) ).
fof(f1746,plain,
~ spl0_45,
inference(avatar_split_clause,[],[f263,f1289]) ).
fof(f1754,plain,
( ~ group_element(e_4)
| product(e_3,e_1,e_4)
| product(e_3,e_2,e_4)
| product(e_3,e_3,e_4)
| ~ group_element(e_3)
| spl0_52 ),
inference(resolution,[],[f1504,f2]) ).
fof(f1760,plain,
( product(e_3,e_1,e_4)
| product(e_3,e_2,e_4)
| product(e_3,e_3,e_4)
| ~ group_element(e_3)
| spl0_52 ),
inference(forward_subsumption_resolution,[],[f1754,f8]) ).
fof(f1832,plain,
( ~ product(e_1,e_2,e_4)
| ~ spl0_38 ),
inference(resolution,[],[f1234,f30]) ).
fof(f1851,plain,
( ~ spl0_9
| ~ spl0_38 ),
inference(avatar_split_clause,[],[f1832,f1232,f222]) ).
fof(f1863,plain,
( ~ product(e_1,e_3,e_4)
| product(e_2,e_3,e_1)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_3) ),
inference(resolution,[],[f70,f7]) ).
fof(f1875,plain,
~ spl0_32,
inference(avatar_split_clause,[],[f252,f1010]) ).
fof(f1880,plain,
( product(e_3,e_1,e_4)
| product(e_3,e_2,e_4)
| product(e_3,e_3,e_4)
| spl0_52 ),
inference(forward_subsumption_resolution,[],[f1760,f7]) ).
fof(f1881,plain,
~ spl0_51,
inference(avatar_split_clause,[],[f403,f1468]) ).
fof(f1882,plain,
( ~ product(e_1,e_3,e_4)
| product(e_2,e_3,e_1)
| product(e_2,e_3,e_3)
| spl0_45 ),
inference(forward_subsumption_resolution,[],[f1863,f1291]) ).
fof(f1885,plain,
( spl0_51
| spl0_38
| spl0_25
| spl0_52 ),
inference(avatar_split_clause,[],[f1880,f1502,f804,f1232,f1468]) ).
fof(f1886,plain,
( spl0_32
| spl0_5
| ~ spl0_34
| spl0_45 ),
inference(avatar_split_clause,[],[f1882,f1289,f1064,f174,f1010]) ).
fof(f1889,plain,
( spl0_34
| spl0_9
| spl0_16
| spl0_28 ),
inference(avatar_split_clause,[],[f1027,f925,f465,f222,f1064]) ).
fof(f1892,plain,
( ~ product(e_4,e_1,e_2)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_3)
| spl0_11 ),
inference(forward_subsumption_resolution,[],[f1401,f5]) ).
fof(f1893,plain,
~ spl0_2,
inference(avatar_split_clause,[],[f67,f92]) ).
fof(f1894,plain,
( spl0_10
| spl0_2
| ~ spl0_19
| spl0_11 ),
inference(avatar_split_clause,[],[f1892,f237,f558,f92,f233]) ).
cnf(s7,plain,
( spl0_1
| ~ spl0_5
| ~ spl0_10 ),
inference(sat_conversion,[],[f247]) ).
cnf(s15,plain,
( spl0_2
| spl0_9
| spl0_10
| spl0_11 ),
inference(sat_conversion,[],[f399]) ).
cnf(s23,plain,
~ spl0_1,
inference(sat_conversion,[],[f538]) ).
cnf(s31,plain,
~ spl0_11,
inference(sat_conversion,[],[f631]) ).
cnf(s34,plain,
( spl0_1
| spl0_3
| spl0_19 ),
inference(sat_conversion,[],[f689]) ).
cnf(s42,plain,
( ~ spl0_3
| ~ spl0_25 ),
inference(sat_conversion,[],[f839]) ).
cnf(s48,plain,
~ spl0_28,
inference(sat_conversion,[],[f999]) ).
cnf(s84,plain,
( ~ spl0_9
| ~ spl0_10 ),
inference(sat_conversion,[],[f1398]) ).
cnf(s116,plain,
~ spl0_52,
inference(sat_conversion,[],[f1710]) ).
cnf(s117,plain,
~ spl0_16,
inference(sat_conversion,[],[f1711]) ).
cnf(s125,plain,
~ spl0_45,
inference(sat_conversion,[],[f1746]) ).
cnf(s146,plain,
( ~ spl0_9
| ~ spl0_38 ),
inference(sat_conversion,[],[f1851]) ).
cnf(s149,plain,
~ spl0_32,
inference(sat_conversion,[],[f1875]) ).
cnf(s163,plain,
~ spl0_51,
inference(sat_conversion,[],[f1881]) ).
cnf(s166,plain,
( spl0_25
| spl0_38
| spl0_51
| spl0_52 ),
inference(sat_conversion,[],[f1885]) ).
cnf(s167,plain,
( spl0_5
| spl0_32
| ~ spl0_34
| spl0_45 ),
inference(sat_conversion,[],[f1886]) ).
cnf(s176,plain,
( spl0_9
| spl0_16
| spl0_28
| spl0_34 ),
inference(sat_conversion,[],[f1889]) ).
cnf(s184,plain,
~ spl0_2,
inference(sat_conversion,[],[f1893]) ).
cnf(s185,plain,
( spl0_2
| spl0_10
| spl0_11
| ~ spl0_19 ),
inference(sat_conversion,[],[f1894]) ).
cnf(s211,plain,
( spl0_9
| spl0_10 ),
inference(rat,[],[s15,s31,s184]) ).
cnf(s214,plain,
( ~ spl0_5
| ~ spl0_10 ),
inference(rat,[],[s7,s23]) ).
cnf(s217,plain,
~ spl0_10,
inference(rat,[],[s167,s176,s214,s84,s149,s125,s117,s48]) ).
cnf(s218,plain,
~ spl0_19,
inference(rat,[],[s185,s31,s184,s217]) ).
cnf(s219,plain,
spl0_9,
inference(rat,[],[s211,s217]) ).
cnf(s220,plain,
spl0_3,
inference(rat,[],[s34,s23,s218]) ).
cnf(s221,plain,
~ spl0_38,
inference(rat,[],[s146,s219]) ).
cnf(s225,plain,
~ spl0_25,
inference(rat,[],[s42,s220]) ).
cnf(s226,plain,
$false,
inference(rat,[],[s166,s116,s163,s221,s225]) ).
fof(f1895,plain,
$false,
inference(avatar_sat_refutation,[],[s226]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP126-4.004 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.40 % Computer : n006.cluster.edu
% 0.12/0.40 % Model : x86_64 x86_64
% 0.12/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.40 % Memory : 8046.5625MB
% 0.12/0.40 % OS : Linux 6.8.0-71-generic
% 0.12/0.40 % CPULimit : 300
% 0.12/0.40 % WCLimit : 300
% 0.12/0.40 % DateTime : Sun Sep 27 09:25:41 UTC 2026
% 0.12/0.40 % CPUTime :
% 0.12/0.40 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.44 Running first-order theorem proving
% 0.12/0.44 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
% 2.72/1.36 % (2726817)Input is clausal, will run a generic CNF schedule.
% 2.72/1.36 % (2726826)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1468264190:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.72/1.36 % (2726826)Instruction limit reached!
% 2.72/1.36 % (2726826)------------------------------
% 2.72/1.36 % (2726826)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.72/1.36 % (2726826)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.72/1.36 % (2726826)CaDiCaL version: 2.1.3
% 2.72/1.36 % (2726826)Termination reason: Instruction limit
% 2.72/1.36 % (2726826)Termination phase: Saturation
% 2.72/1.36 % (2726826)Time elapsed: 0.029 s
% 2.72/1.36 % (2726826)Peak memory usage: 87 MB
% 2.72/1.36 % (2726826)Instructions burned: 115 (million)
% 2.72/1.36 % (2726823)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1420186711:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.72/1.36 % (2726825)lrs+10_1_sil=8000:sp=occurrence:random_seed=1899617779:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.72/1.36 % (2726828)dis-21_1_sil=8000:lcm=predicate:random_seed=3257371942: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)
% 2.72/1.36 % (2726822)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=4117063983:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.72/1.36 % (2726824)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=296352924:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.72/1.36 % (2726825)Refutation not found, incomplete strategy
% 2.72/1.36 % (2726825)------------------------------
% 2.72/1.36 % (2726825)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.72/1.36 % (2726825)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.72/1.36 % (2726825)CaDiCaL version: 2.1.3
% 2.72/1.36 % (2726825)Termination reason: Refutation not found, incomplete strategy
% 2.72/1.36 % (2726825)Time elapsed: 0.001 s
% 2.72/1.36 % (2726825)Peak memory usage: 87 MB
% 2.72/1.36 % (2726827)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1799747124:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.72/1.36 % (2726827)First to succeed.
% 2.72/1.36 % (2726827)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2726817"
% 2.72/1.36 % (2726828)Also succeeded, but the first one will report.
% 2.72/1.36 % (2726830)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=3830274985:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 2.72/1.36 % (2726830)Also succeeded, but the first one will report.
% 2.72/1.36 % (2726825)------------------------------
% 2.72/1.36 % (2726825)------------------------------
% 2.72/1.36 % (2726827)Refutation found. Thanks to Tanya!
% 2.72/1.36 % SZS status Unsatisfiable for theBenchmark
% 2.72/1.36 % SZS output start Proof for theBenchmark
% See solution above
% 3.91/1.46 % (2726827)------------------------------
% 3.91/1.46 % (2726827)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.91/1.46 % (2726827)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.91/1.46 % (2726827)CaDiCaL version: 2.1.3
% 3.91/1.46 % (2726827)Termination reason: Refutation
% 3.91/1.46 % (2726827)Time elapsed: 0.044 s
% 3.91/1.46 % (2726827)Peak memory usage: 89 MB
% 3.91/1.46 % (2726827)Instructions burned: 67 (million)
% 3.91/1.46 % (2726827)------------------------------
% 3.91/1.46 % (2726827)------------------------------
% 3.91/1.46 % (2726817)Success in time 0.483 s
% 3.91/1.46 % Vampire exiting
%------------------------------------------------------------------------------