%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP133-1.003 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n001.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 3.12s 1.30s
% Output : Refutation 3.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 29
% Syntax : Number of formulae : 214 ( 20 unt; 18 def)
% Number of atoms : 601 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 697 ( 310 ~; 369 |; 0 &)
% ( 18 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 22 ( 21 usr; 19 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 97 ( 0 sgn 97 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
group_element(e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_1) ).
fof(f2,axiom,
group_element(e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_2) ).
fof(f3,axiom,
group_element(e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_3) ).
fof(f4,axiom,
~ equalish(e_1,e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_1_is_not_e_2) ).
fof(f5,axiom,
~ equalish(e_1,e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_1_is_not_e_3) ).
fof(f7,axiom,
~ equalish(e_2,e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_2_is_not_e_3) ).
fof(f10,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(f11,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(f12,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(f13,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(f14,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(f15,plain,
! [X0,X1] :
( ~ product(e_2,X0,X1)
| ~ product(e_1,X0,X1) ),
inference(resolution,[],[f4,f13]) ).
fof(f16,plain,
! [X0,X1] :
( ~ product(X0,e_2,X1)
| ~ product(X0,e_1,X1) ),
inference(resolution,[],[f4,f12]) ).
fof(f17,plain,
! [X0,X1] :
( ~ product(X0,X1,e_2)
| ~ product(X0,X1,e_1) ),
inference(resolution,[],[f4,f11]) ).
fof(f18,plain,
! [X0,X1] :
( ~ product(e_3,X0,X1)
| ~ product(e_1,X0,X1) ),
inference(resolution,[],[f5,f13]) ).
fof(f19,plain,
! [X0,X1] :
( ~ product(X0,e_3,X1)
| ~ product(X0,e_1,X1) ),
inference(resolution,[],[f5,f12]) ).
fof(f24,plain,
! [X0,X1] :
( ~ product(e_3,X0,X1)
| ~ product(e_2,X0,X1) ),
inference(resolution,[],[f7,f13]) ).
fof(f25,plain,
! [X0,X1] :
( ~ product(X0,e_3,X1)
| ~ product(X0,e_2,X1) ),
inference(resolution,[],[f7,f12]) ).
fof(f33,plain,
! [X2,X0,X1] :
( ~ product(X1,X2,e_2)
| ~ product(X2,X1,X0)
| ~ product(e_1,X0,X1) ),
inference(resolution,[],[f15,f14]) ).
fof(f34,plain,
! [X0] :
( ~ product(e_1,X0,e_3)
| ~ group_element(X0)
| product(e_2,X0,e_1)
| product(e_2,X0,e_2)
| ~ group_element(e_2) ),
inference(resolution,[],[f15,f10]) ).
fof(f35,plain,
! [X0] :
( ~ product(e_1,X0,e_3)
| ~ group_element(X0)
| product(e_2,X0,e_1)
| product(e_2,X0,e_2) ),
inference(forward_subsumption_resolution,[],[f34,f2]) ).
fof(f36,plain,
! [X2,X0,X1] :
( ~ product(X2,X1,e_2)
| ~ product(X0,e_1,X1)
| ~ product(X1,X2,X0) ),
inference(resolution,[],[f16,f14]) ).
fof(f40,plain,
! [X0] :
( ~ product(X0,X0,e_2)
| ~ product(e_1,e_2,X0) ),
inference(factoring,[],[f33]) ).
fof(f41,plain,
! [X2,X0,X1] :
( ~ product(X0,X1,e_1)
| ~ product(X2,e_2,X1)
| ~ product(e_2,X2,X0) ),
inference(resolution,[],[f17,f14]) ).
fof(f44,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,[],[f18,f10]) ).
fof(f45,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,[],[f44,f3]) ).
fof(f48,plain,
! [X2,X0,X1] :
( ~ product(X2,X1,e_3)
| ~ product(X0,e_1,X1)
| ~ product(X1,X2,X0) ),
inference(resolution,[],[f19,f14]) ).
fof(f49,plain,
! [X0] :
( ~ product(X0,e_1,e_3)
| ~ group_element(e_3)
| product(X0,e_3,e_1)
| product(X0,e_3,e_2)
| ~ group_element(X0) ),
inference(resolution,[],[f19,f10]) ).
fof(f50,plain,
! [X0] :
( ~ product(X0,e_1,e_3)
| product(X0,e_3,e_1)
| product(X0,e_3,e_2)
| ~ group_element(X0) ),
inference(forward_subsumption_resolution,[],[f49,f3]) ).
fof(f53,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,[],[f41,f14]) ).
fof(f61,plain,
! [X2,X0,X1] :
( ~ product(X0,e_1,X1)
| ~ product(X1,X2,X0)
| ~ group_element(X1)
| product(X2,X1,e_1)
| product(X2,X1,e_2)
| ~ group_element(X2) ),
inference(resolution,[],[f48,f10]) ).
fof(f63,plain,
! [X0] :
( ~ product(e_3,e_1,X0)
| ~ product(X0,X0,e_3) ),
inference(factoring,[],[f48]) ).
fof(f64,plain,
! [X2,X0,X1] :
( ~ product(X0,e_1,X1)
| ~ product(X1,X2,X0)
| ~ group_element(X1)
| product(X2,X1,e_1)
| ~ group_element(X2) ),
inference(forward_subsumption_resolution,[],[f61,f36]) ).
fof(f65,plain,
! [X2,X0,X1] :
( ~ product(e_2,X0,X1)
| ~ product(X2,X1,X0)
| ~ product(X1,X2,e_3) ),
inference(resolution,[],[f24,f14]) ).
fof(f66,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,[],[f24,f10]) ).
fof(f67,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,[],[f66,f3]) ).
fof(f73,definition,
( spl0_1
<=> product(e_3,e_1,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f75,plain,
( product(e_3,e_1,e_2)
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f73]) ).
fof(f77,definition,
( spl0_2
<=> product(e_3,e_1,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f79,plain,
( product(e_3,e_1,e_1)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f77]) ).
fof(f85,plain,
! [X2,X0,X1] :
( ~ product(X2,X1,e_3)
| ~ product(X0,e_2,X1)
| ~ product(X1,X2,X0) ),
inference(resolution,[],[f25,f14]) ).
fof(f86,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,[],[f25,f10]) ).
fof(f87,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,[],[f86,f3]) ).
fof(f93,definition,
( spl0_4
<=> product(e_3,e_3,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f94,plain,
( ~ product(e_3,e_3,e_2)
| spl0_4 ),
inference(avatar_component_clause,[],[f93]) ).
fof(f95,plain,
( product(e_3,e_3,e_2)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f93]) ).
fof(f97,definition,
( spl0_5
<=> product(e_3,e_3,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f106,plain,
( ~ product(e_2,e_2,e_3)
| ~ spl0_1 ),
inference(resolution,[],[f75,f63]) ).
fof(f107,plain,
( ~ product(e_2,e_1,e_2)
| ~ spl0_1 ),
inference(resolution,[],[f75,f24]) ).
fof(f123,definition,
( spl0_6
<=> product(e_2,e_2,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f125,plain,
( product(e_2,e_2,e_2)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f123]) ).
fof(f127,definition,
( spl0_7
<=> product(e_2,e_2,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f128,plain,
( ~ product(e_2,e_2,e_1)
| spl0_7 ),
inference(avatar_component_clause,[],[f127]) ).
fof(f129,plain,
( product(e_2,e_2,e_1)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f127]) ).
fof(f134,plain,
( ~ product(e_1,e_1,e_3)
| ~ spl0_2 ),
inference(resolution,[],[f79,f63]) ).
fof(f136,plain,
( ~ product(e_1,e_1,e_1)
| ~ spl0_2 ),
inference(resolution,[],[f79,f18]) ).
fof(f146,definition,
( spl0_8
<=> product(e_2,e_3,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f148,plain,
( product(e_2,e_3,e_2)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f146]) ).
fof(f150,definition,
( spl0_9
<=> product(e_2,e_3,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f152,plain,
( product(e_2,e_3,e_1)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f150]) ).
fof(f156,plain,
! [X0] :
( ~ product(X0,e_2,e_3)
| ~ product(e_2,X0,X0) ),
inference(factoring,[],[f65]) ).
fof(f163,plain,
! [X2,X0,X1] :
( ~ group_element(X1)
| ~ product(X1,X2,X0)
| ~ product(X0,e_2,X1)
| product(X2,X1,e_1)
| product(X2,X1,e_2)
| ~ group_element(X2) ),
inference(resolution,[],[f85,f10]) ).
fof(f186,plain,
! [X0,X1] :
( ~ product(e_3,X1,e_1)
| product(e_2,X0,e_1)
| product(e_2,X0,e_2)
| ~ product(X1,e_3,X0)
| ~ group_element(X0) ),
inference(resolution,[],[f35,f14]) ).
fof(f200,plain,
! [X0,X1] :
( ~ product(e_3,X1,e_1)
| product(e_3,X0,e_1)
| product(e_3,X0,e_2)
| ~ product(X1,e_3,X0)
| ~ group_element(X0) ),
inference(resolution,[],[f45,f14]) ).
fof(f212,definition,
( spl0_11
<=> product(e_1,e_3,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f216,plain,
! [X0] :
( product(X0,e_3,e_1)
| product(X0,e_3,e_2)
| ~ group_element(X0)
| ~ group_element(e_1)
| product(X0,e_1,e_1)
| product(X0,e_1,e_2)
| ~ group_element(X0) ),
inference(resolution,[],[f50,f10]) ).
fof(f218,plain,
! [X0] :
( product(X0,e_3,e_1)
| product(X0,e_3,e_2)
| ~ group_element(X0)
| ~ group_element(e_1)
| product(X0,e_1,e_1)
| product(X0,e_1,e_2) ),
inference(duplicate_literal_removal,[],[f216]) ).
fof(f219,plain,
! [X0] :
( ~ group_element(X0)
| product(X0,e_3,e_2)
| product(X0,e_3,e_1)
| product(X0,e_1,e_1)
| product(X0,e_1,e_2) ),
inference(forward_subsumption_resolution,[],[f218,f1]) ).
fof(f226,plain,
! [X0] :
( ~ group_element(X0)
| product(e_3,X0,e_1)
| product(e_3,X0,e_2)
| ~ group_element(X0)
| product(e_2,X0,e_1)
| product(e_2,X0,e_2)
| ~ group_element(e_2) ),
inference(resolution,[],[f67,f10]) ).
fof(f228,plain,
! [X0] :
( ~ group_element(X0)
| product(e_3,X0,e_1)
| product(e_3,X0,e_2)
| product(e_2,X0,e_1)
| product(e_2,X0,e_2)
| ~ group_element(e_2) ),
inference(duplicate_literal_removal,[],[f226]) ).
fof(f229,plain,
! [X0] :
( ~ group_element(X0)
| product(e_3,X0,e_1)
| product(e_3,X0,e_2)
| product(e_2,X0,e_1)
| product(e_2,X0,e_2) ),
inference(forward_subsumption_resolution,[],[f228,f2]) ).
fof(f239,plain,
( ~ product(e_3,e_1,e_2)
| ~ spl0_4 ),
inference(resolution,[],[f95,f19]) ).
fof(f242,plain,
! [X0] :
( product(X0,e_3,e_1)
| product(X0,e_3,e_2)
| ~ group_element(X0)
| ~ group_element(e_2)
| product(X0,e_2,e_1)
| product(X0,e_2,e_2)
| ~ group_element(X0) ),
inference(resolution,[],[f87,f10]) ).
fof(f243,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,[],[f87,f14]) ).
fof(f244,plain,
! [X0] :
( product(X0,e_3,e_1)
| product(X0,e_3,e_2)
| ~ group_element(X0)
| ~ group_element(e_2)
| product(X0,e_2,e_1)
| product(X0,e_2,e_2) ),
inference(duplicate_literal_removal,[],[f242]) ).
fof(f245,plain,
! [X0] :
( ~ group_element(X0)
| product(X0,e_3,e_2)
| product(X0,e_3,e_1)
| product(X0,e_2,e_1)
| product(X0,e_2,e_2) ),
inference(forward_subsumption_resolution,[],[f244,f2]) ).
fof(f251,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,[],[f134,f10]) ).
fof(f253,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,[],[f251]) ).
fof(f254,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_1,e_2)
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f253,f1]) ).
fof(f256,definition,
( spl0_12
<=> product(e_1,e_1,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f258,plain,
( product(e_1,e_1,e_2)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f256]) ).
fof(f260,definition,
( spl0_13
<=> product(e_1,e_1,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f263,plain,
( spl0_12
| spl0_13
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f254,f77,f260,f256]) ).
fof(f285,definition,
( spl0_14
<=> product(e_2,e_1,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f289,definition,
( spl0_15
<=> product(e_2,e_1,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f294,plain,
( ~ spl0_13
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f136,f77,f260]) ).
fof(f302,definition,
( spl0_16
<=> product(e_3,e_2,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition]) ).
fof(f304,plain,
( product(e_3,e_2,e_2)
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f302]) ).
fof(f306,definition,
( spl0_17
<=> product(e_3,e_2,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition]) ).
fof(f308,plain,
( product(e_3,e_2,e_1)
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f306]) ).
fof(f324,plain,
! [X0] :
( ~ product(e_2,e_1,X0)
| ~ product(e_1,e_2,X0)
| ~ product(e_1,e_2,X0) ),
inference(factoring,[],[f53]) ).
fof(f325,plain,
! [X0] :
( ~ product(e_2,e_1,X0)
| ~ product(e_1,e_2,X0) ),
inference(duplicate_literal_removal,[],[f324]) ).
fof(f346,plain,
! [X0] :
( ~ product(X0,e_1,X0)
| ~ group_element(X0)
| product(e_1,X0,e_1)
| ~ group_element(e_1) ),
inference(factoring,[],[f64]) ).
fof(f347,plain,
! [X0] :
( ~ product(X0,e_1,X0)
| ~ group_element(X0)
| product(e_1,X0,e_1) ),
inference(forward_subsumption_resolution,[],[f346,f1]) ).
fof(f379,plain,
( ~ product(e_1,e_2,e_1)
| ~ spl0_12 ),
inference(resolution,[],[f258,f40]) ).
fof(f418,plain,
( ~ product(e_3,e_3,e_1)
| product(e_2,e_1,e_1)
| product(e_2,e_1,e_2)
| ~ group_element(e_1) ),
inference(factoring,[],[f186]) ).
fof(f434,definition,
( spl0_18
<=> product(e_1,e_2,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_18])],[avatar_definition]) ).
fof(f435,plain,
( ~ product(e_1,e_2,e_2)
| spl0_18 ),
inference(avatar_component_clause,[],[f434]) ).
fof(f436,plain,
( product(e_1,e_2,e_2)
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f434]) ).
fof(f452,plain,
( ~ product(e_3,e_3,e_1)
| product(e_3,e_1,e_1)
| product(e_3,e_1,e_2)
| ~ group_element(e_1) ),
inference(factoring,[],[f200]) ).
fof(f453,plain,
( ~ product(e_3,e_3,e_1)
| product(e_3,e_1,e_2)
| ~ group_element(e_1) ),
inference(forward_subsumption_resolution,[],[f452,f19]) ).
fof(f474,plain,
( ~ product(e_1,e_2,e_2)
| ~ spl0_6 ),
inference(resolution,[],[f125,f15]) ).
fof(f476,plain,
( ~ product(e_2,e_1,e_2)
| ~ spl0_6 ),
inference(resolution,[],[f125,f16]) ).
fof(f477,plain,
( ~ spl0_14
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f476,f123,f285]) ).
fof(f478,plain,
( ~ spl0_18
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f474,f123,f434]) ).
fof(f499,plain,
( ~ product(e_2,e_2,e_1)
| ~ spl0_17 ),
inference(resolution,[],[f308,f24]) ).
fof(f503,plain,
( ~ spl0_7
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f499,f306,f127]) ).
fof(f506,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,[],[f243]) ).
fof(f515,plain,
! [X0,X1] :
( ~ product(X1,e_2,e_1)
| ~ product(e_1,X0,X1)
| product(X0,e_1,e_1)
| product(X0,e_1,e_2)
| ~ group_element(X0) ),
inference(resolution,[],[f163,f1]) ).
fof(f531,definition,
( spl0_19
<=> product(e_1,e_2,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_19])],[avatar_definition]) ).
fof(f556,plain,
( ~ product(e_1,e_1,e_2)
| ~ spl0_18 ),
inference(resolution,[],[f436,f16]) ).
fof(f557,plain,
( ~ spl0_12
| ~ spl0_18 ),
inference(avatar_split_clause,[],[f556,f434,f256]) ).
fof(f569,plain,
( product(e_3,e_3,e_2)
| product(e_3,e_3,e_1)
| product(e_3,e_1,e_1)
| product(e_3,e_1,e_2) ),
inference(resolution,[],[f219,f3]) ).
fof(f579,plain,
( product(e_3,e_3,e_1)
| product(e_3,e_3,e_2)
| product(e_2,e_3,e_1)
| product(e_2,e_3,e_2) ),
inference(resolution,[],[f229,f3]) ).
fof(f587,plain,
( product(e_3,e_3,e_2)
| product(e_3,e_3,e_1)
| product(e_3,e_2,e_1)
| product(e_3,e_2,e_2) ),
inference(resolution,[],[f245,f3]) ).
fof(f603,plain,
( ~ product(e_1,e_3,e_1)
| ~ spl0_9 ),
inference(resolution,[],[f152,f15]) ).
fof(f604,plain,
( ~ product(e_2,e_2,e_1)
| ~ spl0_9 ),
inference(resolution,[],[f152,f25]) ).
fof(f607,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,[],[f325,f10]) ).
fof(f608,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,[],[f607,f156]) ).
fof(f616,plain,
( ~ group_element(e_3)
| product(e_1,e_3,e_1)
| ~ group_element(e_1)
| product(e_3,e_1,e_1)
| product(e_3,e_1,e_2)
| ~ group_element(e_3) ),
inference(resolution,[],[f347,f10]) ).
fof(f617,plain,
( ~ group_element(e_3)
| product(e_1,e_3,e_1)
| ~ group_element(e_1)
| product(e_3,e_1,e_1)
| product(e_3,e_1,e_2) ),
inference(duplicate_literal_removal,[],[f616]) ).
fof(f618,plain,
( product(e_1,e_3,e_1)
| ~ group_element(e_1)
| product(e_3,e_1,e_1)
| product(e_3,e_1,e_2) ),
inference(forward_subsumption_resolution,[],[f617,f3]) ).
fof(f625,plain,
( ~ spl0_11
| ~ spl0_9 ),
inference(avatar_split_clause,[],[f603,f150,f212]) ).
fof(f626,plain,
( product(e_1,e_3,e_1)
| product(e_3,e_1,e_1)
| product(e_3,e_1,e_2) ),
inference(forward_subsumption_resolution,[],[f618,f1]) ).
fof(f630,plain,
( ~ spl0_14
| ~ spl0_1 ),
inference(avatar_split_clause,[],[f107,f73,f285]) ).
fof(f633,plain,
( ~ product(e_1,e_2,e_3)
| product(e_2,e_1,e_2)
| ~ group_element(e_2) ),
inference(forward_subsumption_resolution,[],[f608,f1]) ).
fof(f638,plain,
( ~ spl0_1
| ~ spl0_4 ),
inference(avatar_split_clause,[],[f239,f93,f73]) ).
fof(f643,plain,
( ~ product(e_1,e_2,e_3)
| product(e_2,e_1,e_2) ),
inference(forward_subsumption_resolution,[],[f633,f2]) ).
fof(f647,definition,
( spl0_20
<=> product(e_1,e_2,e_3) ),
introduced(definition,[new_symbols(definition,[spl0_20])],[avatar_definition]) ).
fof(f648,plain,
( product(e_1,e_2,e_3)
| ~ spl0_20 ),
inference(avatar_component_clause,[],[f647]) ).
fof(f649,plain,
( ~ product(e_1,e_2,e_3)
| spl0_20 ),
inference(avatar_component_clause,[],[f647]) ).
fof(f650,plain,
( spl0_14
| ~ spl0_20 ),
inference(avatar_split_clause,[],[f643,f647,f285]) ).
fof(f656,plain,
( ~ product(e_3,e_3,e_2)
| ~ group_element(e_2)
| product(e_2,e_3,e_1) ),
inference(forward_subsumption_resolution,[],[f506,f24]) ).
fof(f663,plain,
( ~ product(e_3,e_3,e_2)
| product(e_2,e_3,e_1) ),
inference(forward_subsumption_resolution,[],[f656,f2]) ).
fof(f669,plain,
( spl0_9
| ~ spl0_4 ),
inference(avatar_split_clause,[],[f663,f93,f150]) ).
fof(f718,plain,
( ~ group_element(e_2)
| product(e_2,e_2,e_1)
| product(e_2,e_2,e_2)
| ~ group_element(e_2)
| ~ spl0_1 ),
inference(resolution,[],[f106,f10]) ).
fof(f720,plain,
( ~ group_element(e_2)
| product(e_2,e_2,e_1)
| product(e_2,e_2,e_2)
| ~ spl0_1 ),
inference(duplicate_literal_removal,[],[f718]) ).
fof(f721,plain,
( product(e_2,e_2,e_1)
| product(e_2,e_2,e_2)
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[],[f720,f2]) ).
fof(f722,plain,
( product(e_2,e_2,e_2)
| ~ spl0_1
| spl0_7 ),
inference(forward_subsumption_resolution,[],[f721,f128]) ).
fof(f723,plain,
( spl0_6
| ~ spl0_1
| spl0_7 ),
inference(avatar_split_clause,[],[f722,f127,f73,f123]) ).
fof(f766,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,[],[f649,f10]) ).
fof(f768,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,[],[f766,f2]) ).
fof(f769,plain,
( product(e_1,e_2,e_1)
| ~ group_element(e_1)
| spl0_18
| spl0_20 ),
inference(forward_subsumption_resolution,[],[f768,f435]) ).
fof(f770,plain,
( product(e_1,e_2,e_1)
| spl0_18
| spl0_20 ),
inference(forward_subsumption_resolution,[],[f769,f1]) ).
fof(f771,plain,
( spl0_19
| spl0_18
| spl0_20 ),
inference(avatar_split_clause,[],[f770,f647,f434,f531]) ).
fof(f774,plain,
( product(e_3,e_3,e_1)
| product(e_3,e_2,e_1)
| product(e_3,e_2,e_2)
| spl0_4 ),
inference(forward_subsumption_resolution,[],[f587,f94]) ).
fof(f798,plain,
( ~ product(e_3,e_1,e_2)
| ~ spl0_16 ),
inference(resolution,[],[f304,f16]) ).
fof(f805,plain,
( ~ product(e_3,e_3,e_1)
| product(e_2,e_1,e_1)
| product(e_2,e_1,e_2) ),
inference(forward_subsumption_resolution,[],[f418,f1]) ).
fof(f807,plain,
( product(e_3,e_3,e_1)
| product(e_2,e_3,e_1)
| product(e_2,e_3,e_2)
| spl0_4 ),
inference(forward_subsumption_resolution,[],[f579,f94]) ).
fof(f809,plain,
( spl0_16
| spl0_17
| spl0_5
| spl0_4 ),
inference(avatar_split_clause,[],[f774,f93,f97,f306,f302]) ).
fof(f812,plain,
( spl0_14
| spl0_15
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f805,f97,f289,f285]) ).
fof(f814,plain,
( spl0_8
| spl0_9
| spl0_5
| spl0_4 ),
inference(avatar_split_clause,[],[f807,f93,f97,f150,f146]) ).
fof(f818,plain,
( ~ spl0_19
| ~ spl0_12 ),
inference(avatar_split_clause,[],[f379,f256,f531]) ).
fof(f819,plain,
( ~ spl0_1
| ~ spl0_16 ),
inference(avatar_split_clause,[],[f798,f302,f73]) ).
fof(f827,plain,
( spl0_1
| spl0_2
| spl0_11 ),
inference(avatar_split_clause,[],[f626,f212,f77,f73]) ).
fof(f829,plain,
( ~ product(e_3,e_3,e_1)
| product(e_3,e_1,e_2) ),
inference(forward_subsumption_resolution,[],[f453,f1]) ).
fof(f830,plain,
( product(e_3,e_3,e_1)
| product(e_3,e_1,e_1)
| product(e_3,e_1,e_2)
| spl0_4 ),
inference(forward_subsumption_resolution,[],[f569,f94]) ).
fof(f831,plain,
( spl0_1
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f829,f97,f73]) ).
fof(f832,plain,
( spl0_1
| spl0_2
| spl0_5
| spl0_4 ),
inference(avatar_split_clause,[],[f830,f93,f97,f77,f73]) ).
fof(f933,plain,
( ~ group_element(e_2)
| product(e_2,e_2,e_1)
| product(e_2,e_2,e_2)
| ~ spl0_20 ),
inference(resolution,[],[f648,f35]) ).
fof(f947,plain,
( product(e_2,e_2,e_1)
| product(e_2,e_2,e_2)
| ~ spl0_20 ),
inference(forward_subsumption_resolution,[],[f933,f2]) ).
fof(f949,plain,
( spl0_6
| spl0_7
| ~ spl0_20 ),
inference(avatar_split_clause,[],[f947,f647,f127,f123]) ).
fof(f951,plain,
( ~ product(e_1,e_2,e_1)
| product(e_2,e_1,e_1)
| product(e_2,e_1,e_2)
| ~ group_element(e_2) ),
inference(factoring,[],[f515]) ).
fof(f952,plain,
( ~ product(e_1,e_2,e_1)
| product(e_2,e_1,e_2)
| ~ group_element(e_2) ),
inference(forward_subsumption_resolution,[],[f951,f325]) ).
fof(f953,plain,
( ~ product(e_1,e_2,e_1)
| product(e_2,e_1,e_2) ),
inference(forward_subsumption_resolution,[],[f952,f2]) ).
fof(f954,plain,
( spl0_14
| ~ spl0_19 ),
inference(avatar_split_clause,[],[f953,f531,f285]) ).
fof(f1109,plain,
( ~ product(e_2,e_1,e_1)
| ~ spl0_7 ),
inference(resolution,[],[f129,f16]) ).
fof(f1111,plain,
( ~ spl0_15
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f1109,f127,f289]) ).
fof(f1145,plain,
( ~ product(e_2,e_1,e_2)
| ~ spl0_8 ),
inference(resolution,[],[f148,f19]) ).
fof(f1146,plain,
( ~ spl0_14
| ~ spl0_8 ),
inference(avatar_split_clause,[],[f1145,f146,f285]) ).
fof(f1153,plain,
( $false
| ~ spl0_7
| ~ spl0_9 ),
inference(forward_subsumption_resolution,[],[f604,f129]) ).
fof(f1154,plain,
( ~ spl0_7
| ~ spl0_9 ),
inference(avatar_contradiction_clause,[],[f1153]) ).
cnf(s14,plain,
( ~ spl0_2
| spl0_12
| spl0_13 ),
inference(sat_conversion,[],[f263]) ).
cnf(s17,plain,
( ~ spl0_2
| ~ spl0_13 ),
inference(sat_conversion,[],[f294]) ).
cnf(s40,plain,
( ~ spl0_6
| ~ spl0_14 ),
inference(sat_conversion,[],[f477]) ).
cnf(s41,plain,
( ~ spl0_6
| ~ spl0_18 ),
inference(sat_conversion,[],[f478]) ).
cnf(s47,plain,
( ~ spl0_7
| ~ spl0_17 ),
inference(sat_conversion,[],[f503]) ).
cnf(s58,plain,
( ~ spl0_12
| ~ spl0_18 ),
inference(sat_conversion,[],[f557]) ).
cnf(s68,plain,
( ~ spl0_9
| ~ spl0_11 ),
inference(sat_conversion,[],[f625]) ).
cnf(s70,plain,
( ~ spl0_1
| ~ spl0_14 ),
inference(sat_conversion,[],[f630]) ).
cnf(s79,plain,
( ~ spl0_1
| ~ spl0_4 ),
inference(sat_conversion,[],[f638]) ).
cnf(s87,plain,
( spl0_14
| ~ spl0_20 ),
inference(sat_conversion,[],[f650]) ).
cnf(s97,plain,
( ~ spl0_4
| spl0_9 ),
inference(sat_conversion,[],[f669]) ).
cnf(s104,plain,
( ~ spl0_1
| spl0_6
| spl0_7 ),
inference(sat_conversion,[],[f723]) ).
cnf(s109,plain,
( spl0_18
| spl0_19
| spl0_20 ),
inference(sat_conversion,[],[f771]) ).
cnf(s126,plain,
( spl0_4
| spl0_5
| spl0_16
| spl0_17 ),
inference(sat_conversion,[],[f809]) ).
cnf(s128,plain,
( ~ spl0_5
| spl0_14
| spl0_15 ),
inference(sat_conversion,[],[f812]) ).
cnf(s130,plain,
( spl0_4
| spl0_5
| spl0_8
| spl0_9 ),
inference(sat_conversion,[],[f814]) ).
cnf(s138,plain,
( ~ spl0_12
| ~ spl0_19 ),
inference(sat_conversion,[],[f818]) ).
cnf(s141,plain,
( ~ spl0_1
| ~ spl0_16 ),
inference(sat_conversion,[],[f819]) ).
cnf(s150,plain,
( spl0_1
| spl0_2
| spl0_11 ),
inference(sat_conversion,[],[f827]) ).
cnf(s152,plain,
( spl0_1
| ~ spl0_5 ),
inference(sat_conversion,[],[f831]) ).
cnf(s153,plain,
( spl0_1
| spl0_2
| spl0_4
| spl0_5 ),
inference(sat_conversion,[],[f832]) ).
cnf(s172,plain,
( spl0_6
| spl0_7
| ~ spl0_20 ),
inference(sat_conversion,[],[f949]) ).
cnf(s173,plain,
( spl0_14
| ~ spl0_19 ),
inference(sat_conversion,[],[f954]) ).
cnf(s185,plain,
( ~ spl0_7
| ~ spl0_15 ),
inference(sat_conversion,[],[f1111]) ).
cnf(s187,plain,
( ~ spl0_8
| ~ spl0_14 ),
inference(sat_conversion,[],[f1146]) ).
cnf(s193,plain,
( ~ spl0_7
| ~ spl0_9 ),
inference(sat_conversion,[],[f1154]) ).
cnf(s195,plain,
( spl0_2
| spl0_5
| spl0_1 ),
inference(rat,[],[s68,s97,s150,s153]) ).
cnf(s196,plain,
( spl0_5
| spl0_1 ),
inference(rat,[],[s130,s97,s193,s172,s40,s187,s87,s109,s58,s138,s14,s17,s195]) ).
cnf(s197,plain,
spl0_1,
inference(rat,[],[s196,s152]) ).
cnf(s198,plain,
~ spl0_16,
inference(rat,[],[s141,s197]) ).
cnf(s199,plain,
~ spl0_4,
inference(rat,[],[s79,s197]) ).
cnf(s201,plain,
~ spl0_14,
inference(rat,[],[s70,s197]) ).
cnf(s204,plain,
~ spl0_19,
inference(rat,[],[s173,s201]) ).
cnf(s205,plain,
~ spl0_20,
inference(rat,[],[s87,s201]) ).
cnf(s206,plain,
spl0_18,
inference(rat,[],[s109,s204,s205]) ).
cnf(s207,plain,
~ spl0_6,
inference(rat,[],[s41,s206]) ).
cnf(s208,plain,
spl0_7,
inference(rat,[],[s104,s197,s207]) ).
cnf(s210,plain,
~ spl0_15,
inference(rat,[],[s185,s208]) ).
cnf(s211,plain,
~ spl0_17,
inference(rat,[],[s47,s208]) ).
cnf(s215,plain,
~ spl0_5,
inference(rat,[],[s128,s201,s210]) ).
cnf(s218,plain,
$false,
inference(rat,[],[s126,s199,s198,s215,s211]) ).
fof(f1155,plain,
$false,
inference(avatar_sat_refutation,[],[s218]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP133-1.003 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.39 % Computer : n001.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 09:36:30 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
% 3.12/1.30 % (3294338)Input is clausal, will run a generic CNF schedule.
% 3.12/1.30 % (3294347)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=163640298:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.12/1.30 % (3294347)Instruction limit reached!
% 3.12/1.30 % (3294347)------------------------------
% 3.12/1.30 % (3294347)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.12/1.30 % (3294347)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.12/1.30 % (3294347)CaDiCaL version: 2.1.3
% 3.12/1.30 % (3294347)Termination reason: Instruction limit
% 3.12/1.30 % (3294347)Termination phase: Saturation
% 3.12/1.30 % (3294347)Time elapsed: 0.034 s
% 3.12/1.30 % (3294347)Peak memory usage: 88 MB
% 3.12/1.30 % (3294347)Instructions burned: 126 (million)
% 3.12/1.30 % (3294346)lrs+10_1_sil=8000:sp=occurrence:random_seed=3606255888:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.12/1.30 % (3294344)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3042170509:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.12/1.30 % (3294349)dis-21_1_sil=8000:lcm=predicate:random_seed=1733870503: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)
% 3.12/1.30 % (3294343)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=2190334154:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.12/1.30 % (3294345)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=211181118:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.12/1.30 % (3294348)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1547220220:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.12/1.30 % (3294348)First to succeed.
% 3.12/1.30 % (3294348)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3294338"
% 3.12/1.30 % (3294349)Also succeeded, but the first one will report.
% 3.12/1.30 % (3294346)Instruction limit reached!
% 3.12/1.30 % (3294346)------------------------------
% 3.12/1.30 % (3294346)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.12/1.30 % (3294346)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.12/1.30 % (3294346)CaDiCaL version: 2.1.3
% 3.12/1.30 % (3294346)Termination reason: Instruction limit
% 3.12/1.30 % (3294346)Termination phase: Saturation
% 3.12/1.30 % (3294346)Time elapsed: 0.063 s
% 3.12/1.30 % (3294346)Peak memory usage: 88 MB
% 3.12/1.30 % (3294346)Instructions burned: 108 (million)
% 3.12/1.30 % (3294351)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=2149410483:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 3.12/1.30 % (3294351)Also succeeded, but the first one will report.
% 3.12/1.30 % (3294358)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=2056276997: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)
% 3.12/1.30 % (3294358)Refutation not found, incomplete strategy
% 3.12/1.30 % (3294358)------------------------------
% 3.12/1.30 % (3294358)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.12/1.30 % (3294358)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.12/1.30 % (3294358)CaDiCaL version: 2.1.3
% 3.12/1.30 % (3294358)Termination reason: Refutation not found, incomplete strategy
% 3.12/1.30 % (3294358)Time elapsed: 0.001 s
% 3.12/1.30 % (3294358)Peak memory usage: 87 MB
% 3.12/1.30 % (3294348)Refutation found. Thanks to Tanya!
% 3.12/1.30 % SZS status Unsatisfiable for theBenchmark
% 3.12/1.30 % SZS output start Proof for theBenchmark
% See solution above
% 3.12/1.39 % (3294348)------------------------------
% 3.12/1.39 % (3294348)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.12/1.39 % (3294348)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.12/1.39 % (3294348)CaDiCaL version: 2.1.3
% 3.12/1.39 % (3294348)Termination reason: Refutation
% 3.12/1.39 % (3294348)Time elapsed: 0.033 s
% 3.12/1.39 % (3294348)Peak memory usage: 89 MB
% 3.12/1.39 % (3294348)Instructions burned: 47 (million)
% 3.12/1.39 % (3294348)------------------------------
% 3.12/1.39 % (3294348)------------------------------
% 3.12/1.39 % (3294338)Success in time 0.436 s
% 3.12/1.39 % Vampire exiting
%------------------------------------------------------------------------------