%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP133-2.003 : 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 : n002.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 10:13:02 AM UTC 2026
% Result : Unsatisfiable 2.56s 1.27s
% Output : Refutation 3.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 30
% Syntax : Number of formulae : 178 ( 28 unt; 16 def)
% Number of atoms : 455 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 522 ( 245 ~; 261 |; 0 &)
% ( 16 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 22 ( 21 usr; 17 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 76 ( 0 sgn 76 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
next(e_1,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_1_then_e_2) ).
fof(f5,axiom,
greater(e_3,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_greater_e_2) ).
fof(f6,axiom,
! [X2,X0,X1] :
( ~ greater(X1,X2)
| ~ next(X0,X2)
| ~ product(X0,e_1,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',no_redundancy) ).
fof(f7,axiom,
group_element(e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_1) ).
fof(f8,axiom,
group_element(e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_2) ).
fof(f9,axiom,
group_element(e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_3) ).
fof(f10,axiom,
~ equalish(e_1,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_1_is_not_e_2) ).
fof(f11,axiom,
~ equalish(e_1,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_1_is_not_e_3) ).
fof(f13,axiom,
~ equalish(e_2,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_2_is_not_e_3) ).
fof(f16,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/sandbox/benchmark/theBenchmark.p',product_total_function1) ).
fof(f17,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(f18,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(f19,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(f20,negated_conjecture,
! [X2,X3,X0,X1] :
( product(X2,X3,X0)
| ~ product(X1,X0,X3)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qg3) ).
fof(f23,plain,
! [X0] :
( ~ next(X0,e_2)
| ~ product(X0,e_1,e_3) ),
inference(resolution,[],[f5,f6]) ).
fof(f25,plain,
! [X0,X1] :
( ~ product(X0,e_2,X1)
| ~ product(X0,e_1,X1) ),
inference(resolution,[],[f10,f18]) ).
fof(f26,plain,
! [X0,X1] :
( ~ product(X0,X1,e_2)
| ~ product(X0,X1,e_1) ),
inference(resolution,[],[f10,f17]) ).
fof(f27,plain,
! [X0,X1] :
( ~ product(e_3,X0,X1)
| ~ product(e_1,X0,X1) ),
inference(resolution,[],[f11,f19]) ).
fof(f28,plain,
! [X0,X1] :
( ~ product(X0,e_3,X1)
| ~ product(X0,e_1,X1) ),
inference(resolution,[],[f11,f18]) ).
fof(f33,plain,
! [X0,X1] :
( ~ product(e_3,X0,X1)
| ~ product(e_2,X0,X1) ),
inference(resolution,[],[f13,f19]) ).
fof(f34,plain,
! [X0,X1] :
( ~ product(X0,e_3,X1)
| ~ product(X0,e_2,X1) ),
inference(resolution,[],[f13,f18]) ).
fof(f42,plain,
~ product(e_1,e_1,e_3),
inference(resolution,[],[f23,f1]) ).
fof(f52,plain,
! [X2,X0,X1] :
( ~ product(X0,X1,e_1)
| ~ product(X2,e_2,X1)
| ~ product(e_2,X2,X0) ),
inference(resolution,[],[f26,f20]) ).
fof(f55,plain,
! [X2,X0,X1] :
( ~ product(e_1,X0,X1)
| ~ product(X2,X1,X0)
| ~ product(X1,X2,e_3) ),
inference(resolution,[],[f27,f20]) ).
fof(f56,plain,
! [X0] :
( ~ product(e_1,X0,e_3)
| ~ group_element(X0)
| product(e_3,X0,e_1)
| product(e_3,X0,e_2)
| ~ group_element(e_3) ),
inference(resolution,[],[f27,f16]) ).
fof(f57,plain,
! [X0] :
( ~ product(e_1,X0,e_3)
| ~ group_element(X0)
| product(e_3,X0,e_1)
| product(e_3,X0,e_2) ),
inference(forward_subsumption_resolution,[],[f56,f9]) ).
fof(f59,plain,
! [X2,X0,X1] :
( ~ product(X2,X1,e_3)
| ~ product(X0,e_1,X1)
| ~ product(X1,X2,X0) ),
inference(resolution,[],[f28,f20]) ).
fof(f62,plain,
! [X2,X3,X0,X1] :
( ~ product(e_2,X0,X2)
| ~ product(X0,e_2,X1)
| ~ product(X3,e_1,X1)
| ~ product(e_1,X3,X2) ),
inference(resolution,[],[f52,f20]) ).
fof(f65,plain,
! [X0,X1] :
( ~ product(X0,e_3,X1)
| ~ product(e_3,X0,e_3)
| ~ group_element(X1)
| product(e_1,X1,e_1)
| product(e_1,X1,e_2)
| ~ group_element(e_1) ),
inference(resolution,[],[f55,f16]) ).
fof(f67,plain,
! [X0,X1] :
( ~ product(e_3,X0,e_3)
| ~ product(X0,e_3,X1)
| ~ group_element(X1)
| product(e_1,X1,e_1)
| product(e_1,X1,e_2) ),
inference(forward_subsumption_resolution,[],[f65,f7]) ).
fof(f73,plain,
! [X0] :
( ~ product(e_3,e_1,X0)
| ~ product(X0,X0,e_3) ),
inference(factoring,[],[f59]) ).
fof(f76,plain,
( ~ product(e_3,e_3,e_3)
| ~ group_element(e_1)
| product(e_3,e_1,e_1)
| product(e_3,e_1,e_2)
| ~ group_element(e_3) ),
inference(resolution,[],[f73,f16]) ).
fof(f77,plain,
( ~ product(e_3,e_3,e_3)
| product(e_3,e_1,e_1)
| product(e_3,e_1,e_2)
| ~ group_element(e_3) ),
inference(forward_subsumption_resolution,[],[f76,f7]) ).
fof(f78,plain,
( ~ product(e_3,e_3,e_3)
| product(e_3,e_1,e_1)
| product(e_3,e_1,e_2) ),
inference(forward_subsumption_resolution,[],[f77,f9]) ).
fof(f80,definition,
( spl0_1
<=> product(e_3,e_1,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f82,plain,
( product(e_3,e_1,e_2)
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f80]) ).
fof(f84,definition,
( spl0_2
<=> product(e_3,e_1,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f86,plain,
( product(e_3,e_1,e_1)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f84]) ).
fof(f88,definition,
( spl0_3
<=> product(e_3,e_3,e_3) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f90,plain,
( ~ product(e_3,e_3,e_3)
| spl0_3 ),
inference(avatar_component_clause,[],[f88]) ).
fof(f91,plain,
( spl0_1
| spl0_2
| ~ spl0_3 ),
inference(avatar_split_clause,[],[f78,f88,f84,f80]) ).
fof(f92,plain,
! [X2,X0,X1] :
( ~ product(e_2,X0,X1)
| ~ product(X2,X1,X0)
| ~ product(X1,X2,e_3) ),
inference(resolution,[],[f33,f20]) ).
fof(f93,plain,
! [X0] :
( ~ product(e_2,X0,e_3)
| ~ group_element(X0)
| product(e_3,X0,e_1)
| product(e_3,X0,e_2)
| ~ group_element(e_3) ),
inference(resolution,[],[f33,f16]) ).
fof(f94,plain,
! [X0] :
( ~ product(e_2,X0,e_3)
| ~ group_element(X0)
| product(e_3,X0,e_1)
| product(e_3,X0,e_2) ),
inference(forward_subsumption_resolution,[],[f93,f9]) ).
fof(f100,definition,
( spl0_4
<=> product(e_3,e_3,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f104,definition,
( spl0_5
<=> product(e_3,e_3,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f105,plain,
( ~ product(e_3,e_3,e_1)
| spl0_5 ),
inference(avatar_component_clause,[],[f104]) ).
fof(f108,plain,
! [X2,X0,X1] :
( ~ product(X2,X1,e_3)
| ~ product(X0,e_2,X1)
| ~ product(X1,X2,X0) ),
inference(resolution,[],[f34,f20]) ).
fof(f109,plain,
! [X0] :
( ~ product(X0,e_2,e_3)
| ~ group_element(e_3)
| product(X0,e_3,e_1)
| product(X0,e_3,e_2)
| ~ group_element(X0) ),
inference(resolution,[],[f34,f16]) ).
fof(f110,plain,
! [X0] :
( ~ product(X0,e_2,e_3)
| product(X0,e_3,e_1)
| product(X0,e_3,e_2)
| ~ group_element(X0) ),
inference(forward_subsumption_resolution,[],[f109,f9]) ).
fof(f112,plain,
( ~ product(e_2,e_1,e_2)
| ~ spl0_1 ),
inference(resolution,[],[f82,f33]) ).
fof(f113,plain,
( ~ product(e_1,e_1,e_2)
| ~ spl0_1 ),
inference(resolution,[],[f82,f27]) ).
fof(f143,plain,
( ~ product(e_1,e_1,e_3)
| ~ spl0_2 ),
inference(resolution,[],[f86,f73]) ).
fof(f145,plain,
( ~ product(e_1,e_1,e_1)
| ~ spl0_2 ),
inference(resolution,[],[f86,f27]) ).
fof(f157,definition,
( spl0_9
<=> product(e_2,e_3,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f172,plain,
! [X0] :
( ~ product(X0,e_2,e_3)
| ~ product(e_2,X0,X0) ),
inference(factoring,[],[f92]) ).
fof(f187,plain,
! [X0] :
( ~ product(e_3,e_2,X0)
| ~ product(X0,X0,e_3) ),
inference(factoring,[],[f108]) ).
fof(f191,plain,
( ~ group_element(e_1)
| product(e_1,e_1,e_1)
| product(e_1,e_1,e_2)
| ~ group_element(e_1)
| ~ spl0_2 ),
inference(resolution,[],[f143,f16]) ).
fof(f193,plain,
( ~ group_element(e_1)
| product(e_1,e_1,e_1)
| product(e_1,e_1,e_2)
| ~ spl0_2 ),
inference(duplicate_literal_removal,[],[f191]) ).
fof(f194,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_1,e_2)
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f193,f7]) ).
fof(f196,definition,
( spl0_10
<=> product(e_1,e_1,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f198,plain,
( product(e_1,e_1,e_2)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f196]) ).
fof(f200,definition,
( spl0_11
<=> product(e_1,e_1,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f203,plain,
( spl0_10
| spl0_11
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f194,f84,f200,f196]) ).
fof(f204,plain,
( ~ group_element(e_1)
| product(e_1,e_1,e_1)
| product(e_1,e_1,e_2)
| ~ group_element(e_1) ),
inference(resolution,[],[f42,f16]) ).
fof(f205,plain,
! [X0] :
( ~ product(e_3,X0,e_1)
| ~ product(X0,e_3,e_1) ),
inference(resolution,[],[f42,f20]) ).
fof(f206,plain,
( ~ group_element(e_1)
| product(e_1,e_1,e_1)
| product(e_1,e_1,e_2) ),
inference(duplicate_literal_removal,[],[f204]) ).
fof(f207,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_1,e_2) ),
inference(forward_subsumption_resolution,[],[f206,f7]) ).
fof(f208,plain,
( spl0_10
| spl0_11 ),
inference(avatar_split_clause,[],[f207,f200,f196]) ).
fof(f220,plain,
! [X0] :
( ~ group_element(X0)
| product(e_3,X0,e_1)
| product(e_3,X0,e_2)
| ~ group_element(X0)
| product(e_1,X0,e_1)
| product(e_1,X0,e_2)
| ~ group_element(e_1) ),
inference(resolution,[],[f57,f16]) ).
fof(f222,plain,
! [X0] :
( ~ group_element(X0)
| product(e_3,X0,e_1)
| product(e_3,X0,e_2)
| product(e_1,X0,e_1)
| product(e_1,X0,e_2)
| ~ group_element(e_1) ),
inference(duplicate_literal_removal,[],[f220]) ).
fof(f223,plain,
! [X0] :
( ~ group_element(X0)
| product(e_3,X0,e_1)
| product(e_3,X0,e_2)
| product(e_1,X0,e_1)
| product(e_1,X0,e_2) ),
inference(forward_subsumption_resolution,[],[f222,f7]) ).
fof(f234,definition,
( spl0_12
<=> product(e_2,e_1,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f243,plain,
! [X0,X1] :
( ~ product(e_3,X1,e_2)
| product(e_3,X0,e_1)
| product(e_3,X0,e_2)
| ~ product(X1,e_3,X0)
| ~ group_element(X0) ),
inference(resolution,[],[f94,f20]) ).
fof(f248,plain,
! [X0,X1] :
( ~ product(X1,e_3,e_2)
| product(X0,e_3,e_2)
| ~ group_element(X0)
| product(X0,e_3,e_1)
| ~ product(e_3,X1,X0) ),
inference(resolution,[],[f110,f20]) ).
fof(f277,plain,
( ~ product(e_3,e_3,e_3)
| ~ group_element(e_2)
| product(e_3,e_2,e_1)
| product(e_3,e_2,e_2)
| ~ group_element(e_3) ),
inference(resolution,[],[f187,f16]) ).
fof(f281,plain,
~ product(e_3,e_3,e_1),
inference(factoring,[],[f205]) ).
fof(f287,plain,
~ spl0_5,
inference(avatar_split_clause,[],[f281,f104]) ).
fof(f288,plain,
( ~ product(e_3,e_3,e_3)
| product(e_3,e_2,e_1)
| product(e_3,e_2,e_2)
| ~ group_element(e_3) ),
inference(forward_subsumption_resolution,[],[f277,f8]) ).
fof(f289,plain,
( ~ product(e_3,e_3,e_3)
| product(e_3,e_2,e_1)
| product(e_3,e_2,e_2) ),
inference(forward_subsumption_resolution,[],[f288,f9]) ).
fof(f291,definition,
( spl0_14
<=> product(e_3,e_2,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f293,plain,
( product(e_3,e_2,e_2)
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f291]) ).
fof(f295,definition,
( spl0_15
<=> product(e_3,e_2,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f297,plain,
( product(e_3,e_2,e_1)
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f295]) ).
fof(f298,plain,
( spl0_14
| spl0_15
| ~ spl0_3 ),
inference(avatar_split_clause,[],[f289,f88,f295,f291]) ).
fof(f301,plain,
( ~ product(e_1,e_3,e_1)
| ~ spl0_2 ),
inference(resolution,[],[f86,f205]) ).
fof(f326,plain,
! [X0] :
( ~ product(e_2,e_1,X0)
| ~ product(e_1,e_2,X0)
| ~ product(e_1,e_2,X0) ),
inference(factoring,[],[f62]) ).
fof(f327,plain,
! [X0] :
( ~ product(e_2,e_1,X0)
| ~ product(e_1,e_2,X0) ),
inference(duplicate_literal_removal,[],[f326]) ).
fof(f387,plain,
( ~ product(e_3,e_3,e_3)
| ~ group_element(e_3)
| product(e_1,e_3,e_1)
| product(e_1,e_3,e_2) ),
inference(factoring,[],[f67]) ).
fof(f394,definition,
( spl0_16
<=> product(e_1,e_2,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition]) ).
fof(f398,definition,
( spl0_17
<=> product(e_1,e_2,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition]) ).
fof(f402,plain,
( ~ product(e_3,e_3,e_3)
| product(e_1,e_3,e_1)
| product(e_1,e_3,e_2) ),
inference(forward_subsumption_resolution,[],[f387,f9]) ).
fof(f403,plain,
( ~ product(e_3,e_3,e_3)
| product(e_1,e_3,e_2)
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f402,f301]) ).
fof(f405,definition,
( spl0_18
<=> product(e_1,e_3,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_18])],[avatar_definition]) ).
fof(f407,plain,
( product(e_1,e_3,e_2)
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f405]) ).
fof(f408,plain,
( spl0_18
| ~ spl0_3
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f403,f84,f88,f405]) ).
fof(f413,plain,
( ~ group_element(e_3)
| product(e_3,e_3,e_1)
| product(e_3,e_3,e_2)
| ~ group_element(e_3)
| spl0_3 ),
inference(resolution,[],[f90,f16]) ).
fof(f415,plain,
( ~ group_element(e_3)
| product(e_3,e_3,e_1)
| product(e_3,e_3,e_2)
| spl0_3 ),
inference(duplicate_literal_removal,[],[f413]) ).
fof(f416,plain,
( product(e_3,e_3,e_1)
| product(e_3,e_3,e_2)
| spl0_3 ),
inference(forward_subsumption_resolution,[],[f415,f9]) ).
fof(f417,plain,
( product(e_3,e_3,e_2)
| spl0_3
| spl0_5 ),
inference(forward_subsumption_resolution,[],[f416,f105]) ).
fof(f418,plain,
( spl0_4
| spl0_3
| spl0_5 ),
inference(avatar_split_clause,[],[f417,f104,f88,f100]) ).
fof(f454,plain,
( ~ product(e_3,e_3,e_2)
| product(e_3,e_2,e_1)
| product(e_3,e_2,e_2)
| ~ group_element(e_2) ),
inference(factoring,[],[f243]) ).
fof(f459,plain,
( ~ product(e_3,e_3,e_2)
| product(e_3,e_2,e_1)
| ~ group_element(e_2) ),
inference(forward_subsumption_resolution,[],[f454,f34]) ).
fof(f461,plain,
( ~ product(e_3,e_3,e_2)
| product(e_3,e_2,e_1) ),
inference(forward_subsumption_resolution,[],[f459,f8]) ).
fof(f463,plain,
( spl0_15
| ~ spl0_4 ),
inference(avatar_split_clause,[],[f461,f100,f295]) ).
fof(f478,plain,
( ~ product(e_3,e_3,e_2)
| product(e_2,e_3,e_2)
| ~ group_element(e_2)
| product(e_2,e_3,e_1) ),
inference(factoring,[],[f248]) ).
fof(f479,plain,
( ~ product(e_3,e_3,e_2)
| ~ group_element(e_2)
| product(e_2,e_3,e_1) ),
inference(forward_subsumption_resolution,[],[f478,f33]) ).
fof(f480,plain,
( ~ product(e_3,e_3,e_2)
| product(e_2,e_3,e_1) ),
inference(forward_subsumption_resolution,[],[f479,f8]) ).
fof(f488,plain,
( ~ product(e_3,e_1,e_2)
| ~ spl0_14 ),
inference(resolution,[],[f293,f25]) ).
fof(f512,plain,
( ~ product(e_1,e_2,e_2)
| ~ spl0_18 ),
inference(resolution,[],[f407,f34]) ).
fof(f513,plain,
( ~ product(e_1,e_1,e_2)
| ~ spl0_18 ),
inference(resolution,[],[f407,f28]) ).
fof(f518,plain,
( $false
| ~ spl0_10
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f513,f198]) ).
fof(f519,plain,
( ~ spl0_10
| ~ spl0_18 ),
inference(avatar_contradiction_clause,[],[f518]) ).
fof(f520,plain,
( ~ spl0_16
| ~ spl0_18 ),
inference(avatar_split_clause,[],[f512,f405,f394]) ).
fof(f521,plain,
( ~ spl0_12
| ~ spl0_1 ),
inference(avatar_split_clause,[],[f112,f80,f234]) ).
fof(f526,definition,
( spl0_19
<=> product(e_1,e_3,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_19])],[avatar_definition]) ).
fof(f528,plain,
( product(e_1,e_3,e_1)
| ~ spl0_19 ),
inference(avatar_component_clause,[],[f526]) ).
fof(f530,plain,
( ~ spl0_1
| ~ spl0_14 ),
inference(avatar_split_clause,[],[f488,f291,f80]) ).
fof(f532,plain,
( ~ spl0_11
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f145,f84,f200]) ).
fof(f540,plain,
( ~ spl0_10
| ~ spl0_1 ),
inference(avatar_split_clause,[],[f113,f80,f196]) ).
fof(f557,plain,
( product(e_3,e_3,e_1)
| product(e_3,e_3,e_2)
| product(e_1,e_3,e_1)
| product(e_1,e_3,e_2) ),
inference(resolution,[],[f223,f9]) ).
fof(f558,plain,
( product(e_3,e_3,e_2)
| product(e_1,e_3,e_1)
| product(e_1,e_3,e_2)
| spl0_5 ),
inference(forward_subsumption_resolution,[],[f557,f105]) ).
fof(f560,plain,
( spl0_18
| spl0_19
| spl0_4
| spl0_5 ),
inference(avatar_split_clause,[],[f558,f104,f100,f526,f405]) ).
fof(f580,plain,
( ~ product(e_2,e_3,e_1)
| ~ spl0_15 ),
inference(resolution,[],[f297,f205]) ).
fof(f582,plain,
( ~ product(e_1,e_2,e_1)
| ~ spl0_15 ),
inference(resolution,[],[f297,f27]) ).
fof(f589,plain,
( ~ spl0_17
| ~ spl0_15 ),
inference(avatar_split_clause,[],[f582,f295,f398]) ).
fof(f610,plain,
( ~ product(e_1,e_2,e_3)
| ~ group_element(e_1)
| product(e_2,e_1,e_1)
| product(e_2,e_1,e_2)
| ~ group_element(e_2) ),
inference(resolution,[],[f327,f16]) ).
fof(f611,plain,
( ~ product(e_1,e_2,e_3)
| ~ group_element(e_1)
| product(e_2,e_1,e_2)
| ~ group_element(e_2) ),
inference(forward_subsumption_resolution,[],[f610,f172]) ).
fof(f612,plain,
( ~ product(e_1,e_2,e_3)
| product(e_2,e_1,e_2)
| ~ group_element(e_2) ),
inference(forward_subsumption_resolution,[],[f611,f7]) ).
fof(f613,plain,
( ~ product(e_1,e_2,e_3)
| product(e_2,e_1,e_2) ),
inference(forward_subsumption_resolution,[],[f612,f8]) ).
fof(f615,definition,
( spl0_20
<=> product(e_1,e_2,e_3) ),
introduced(definition,[new_symbols(definition,[spl0_20])],[avatar_definition]) ).
fof(f617,plain,
( ~ product(e_1,e_2,e_3)
| spl0_20 ),
inference(avatar_component_clause,[],[f615]) ).
fof(f618,plain,
( spl0_12
| ~ spl0_20 ),
inference(avatar_split_clause,[],[f613,f615,f234]) ).
fof(f695,plain,
( ~ group_element(e_2)
| product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| ~ group_element(e_1)
| spl0_20 ),
inference(resolution,[],[f617,f16]) ).
fof(f697,plain,
( product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| ~ group_element(e_1)
| spl0_20 ),
inference(forward_subsumption_resolution,[],[f695,f8]) ).
fof(f698,plain,
( product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| spl0_20 ),
inference(forward_subsumption_resolution,[],[f697,f7]) ).
fof(f699,plain,
( spl0_16
| spl0_17
| spl0_20 ),
inference(avatar_split_clause,[],[f698,f615,f398,f394]) ).
fof(f712,plain,
( ~ product(e_1,e_1,e_1)
| ~ spl0_19 ),
inference(resolution,[],[f528,f28]) ).
fof(f719,plain,
( ~ spl0_11
| ~ spl0_19 ),
inference(avatar_split_clause,[],[f712,f526,f200]) ).
fof(f728,plain,
( spl0_9
| ~ spl0_4 ),
inference(avatar_split_clause,[],[f480,f100,f157]) ).
fof(f732,plain,
( ~ spl0_9
| ~ spl0_15 ),
inference(avatar_split_clause,[],[f580,f295,f157]) ).
cnf(s1,plain,
( spl0_1
| spl0_2
| ~ spl0_3 ),
inference(sat_conversion,[],[f91]) ).
cnf(s10,plain,
( ~ spl0_2
| spl0_10
| spl0_11 ),
inference(sat_conversion,[],[f203]) ).
cnf(s11,plain,
( spl0_10
| spl0_11 ),
inference(sat_conversion,[],[f208]) ).
cnf(s19,plain,
~ spl0_5,
inference(sat_conversion,[],[f287]) ).
cnf(s20,plain,
( ~ spl0_3
| spl0_14
| spl0_15 ),
inference(sat_conversion,[],[f298]) ).
cnf(s31,plain,
( ~ spl0_2
| ~ spl0_3
| spl0_18 ),
inference(sat_conversion,[],[f408]) ).
cnf(s38,plain,
( spl0_3
| spl0_4
| spl0_5 ),
inference(sat_conversion,[],[f418]) ).
cnf(s43,plain,
( ~ spl0_4
| spl0_15 ),
inference(sat_conversion,[],[f463]) ).
cnf(s52,plain,
( ~ spl0_10
| ~ spl0_18 ),
inference(sat_conversion,[],[f519]) ).
cnf(s53,plain,
( ~ spl0_16
| ~ spl0_18 ),
inference(sat_conversion,[],[f520]) ).
cnf(s54,plain,
( ~ spl0_1
| ~ spl0_12 ),
inference(sat_conversion,[],[f521]) ).
cnf(s58,plain,
( ~ spl0_1
| ~ spl0_14 ),
inference(sat_conversion,[],[f530]) ).
cnf(s62,plain,
( ~ spl0_2
| ~ spl0_11 ),
inference(sat_conversion,[],[f532]) ).
cnf(s71,plain,
( ~ spl0_1
| ~ spl0_10 ),
inference(sat_conversion,[],[f540]) ).
cnf(s80,plain,
( spl0_4
| spl0_5
| spl0_18
| spl0_19 ),
inference(sat_conversion,[],[f560]) ).
cnf(s85,plain,
( ~ spl0_15
| ~ spl0_17 ),
inference(sat_conversion,[],[f589]) ).
cnf(s92,plain,
( spl0_12
| ~ spl0_20 ),
inference(sat_conversion,[],[f618]) ).
cnf(s103,plain,
( spl0_16
| spl0_17
| spl0_20 ),
inference(sat_conversion,[],[f699]) ).
cnf(s105,plain,
( ~ spl0_11
| ~ spl0_19 ),
inference(sat_conversion,[],[f719]) ).
cnf(s115,plain,
( ~ spl0_4
| spl0_9 ),
inference(sat_conversion,[],[f728]) ).
cnf(s118,plain,
( ~ spl0_9
| ~ spl0_15 ),
inference(sat_conversion,[],[f732]) ).
cnf(s127,plain,
~ spl0_4,
inference(rat,[],[s118,s43,s115]) ).
cnf(s128,plain,
spl0_3,
inference(rat,[],[s38,s19,s127]) ).
cnf(s130,plain,
~ spl0_2,
inference(rat,[],[s52,s10,s31,s62,s128]) ).
cnf(s131,plain,
spl0_1,
inference(rat,[],[s1,s128,s130]) ).
cnf(s132,plain,
~ spl0_10,
inference(rat,[],[s71,s131]) ).
cnf(s133,plain,
~ spl0_14,
inference(rat,[],[s58,s131]) ).
cnf(s134,plain,
~ spl0_12,
inference(rat,[],[s54,s131]) ).
cnf(s135,plain,
spl0_11,
inference(rat,[],[s11,s132]) ).
cnf(s136,plain,
spl0_15,
inference(rat,[],[s20,s128,s133]) ).
cnf(s137,plain,
~ spl0_20,
inference(rat,[],[s92,s134]) ).
cnf(s138,plain,
~ spl0_19,
inference(rat,[],[s105,s135]) ).
cnf(s141,plain,
~ spl0_17,
inference(rat,[],[s85,s136]) ).
cnf(s142,plain,
spl0_18,
inference(rat,[],[s80,s127,s19,s138]) ).
cnf(s145,plain,
spl0_16,
inference(rat,[],[s103,s137,s141]) ).
cnf(s146,plain,
$false,
inference(rat,[],[s53,s142,s145]) ).
fof(f742,plain,
$false,
inference(avatar_sat_refutation,[],[s146]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP133-2.003 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n002.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sun Sep 27 09:34:06 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 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
% 2.56/1.27 % (3283876)Input is clausal, will run a generic CNF schedule.
% 2.56/1.27 % (3283885)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1898528400:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.56/1.27 % (3283886)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=77449992:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.56/1.27 % (3283882)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2599704681:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.56/1.27 % (3283887)dis-21_1_sil=8000:lcm=predicate:random_seed=1410056468: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)
% 2.56/1.27 % (3283881)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=1407923693:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.56/1.27 % (3283883)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1326921293:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.56/1.27 % (3283885)Instruction limit reached!
% 2.56/1.27 % (3283885)------------------------------
% 2.56/1.27 % (3283885)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.56/1.27 % (3283885)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.56/1.27 % (3283885)CaDiCaL version: 2.1.3
% 2.56/1.27 % (3283885)Termination reason: Instruction limit
% 2.56/1.27 % (3283885)Termination phase: Saturation
% 2.56/1.27 % (3283885)Time elapsed: 0.033 s
% 2.56/1.27 % (3283885)Peak memory usage: 88 MB
% 2.56/1.27 % (3283885)Instructions burned: 122 (million)
% 2.56/1.27 % (3283884)lrs+10_1_sil=8000:sp=occurrence:random_seed=743658305:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.56/1.27 % (3283886)First to succeed.
% 2.56/1.27 % (3283886)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3283876"
% 2.56/1.27 % (3283887)Also succeeded, but the first one will report.
% 2.56/1.27 % (3283884)Instruction limit reached!
% 2.56/1.27 % (3283884)------------------------------
% 2.56/1.27 % (3283884)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.56/1.27 % (3283884)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.56/1.27 % (3283884)CaDiCaL version: 2.1.3
% 2.56/1.27 % (3283884)Termination reason: Instruction limit
% 2.56/1.27 % (3283884)Termination phase: Saturation
% 2.56/1.27 % (3283884)Time elapsed: 0.066 s
% 2.56/1.27 % (3283884)Peak memory usage: 88 MB
% 2.56/1.27 % (3283884)Instructions burned: 108 (million)
% 2.56/1.27 % (3283895)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=3284206470:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 2.56/1.27 % (3283895)Also succeeded, but the first one will report.
% 2.56/1.27 % (3283896)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=2597224926:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2997 on theBenchmark for (2997ds/189Mi)
% 2.56/1.27 % (3283896)Refutation not found, incomplete strategy
% 2.56/1.27 % (3283896)------------------------------
% 2.56/1.27 % (3283896)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.56/1.27 % (3283896)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.56/1.27 % (3283896)CaDiCaL version: 2.1.3
% 2.56/1.27 % (3283896)Termination reason: Refutation not found, incomplete strategy
% 2.56/1.27 % (3283896)Time elapsed: 0.001 s
% 2.56/1.27 % (3283896)Peak memory usage: 87 MB
% 2.56/1.27 % (3283896)Instructions burned: 1 (million)
% 2.56/1.27 % (3283886)Refutation found. Thanks to Tanya!
% 2.56/1.27 % SZS status Unsatisfiable for theBenchmark
% 2.56/1.27 % SZS output start Proof for theBenchmark
% See solution above
% 3.54/1.44 % (3283886)------------------------------
% 3.54/1.44 % (3283886)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.54/1.44 % (3283886)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.54/1.44 % (3283886)CaDiCaL version: 2.1.3
% 3.54/1.44 % (3283886)Termination reason: Refutation
% 3.54/1.44 % (3283886)Time elapsed: 0.020 s
% 3.54/1.44 % (3283886)Peak memory usage: 89 MB
% 3.54/1.44 % (3283886)Instructions burned: 29 (million)
% 3.54/1.44 % (3283886)------------------------------
% 3.54/1.44 % (3283886)------------------------------
% 3.54/1.44 % (3283876)Success in time 0.418 s
% 3.54/1.44 % Vampire exiting
%------------------------------------------------------------------------------