%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP128-1.003 : 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 : n020.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 10:12:57 AM UTC 2026
% Result : Unsatisfiable 2.11s 1.17s
% Output : Refutation 2.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 27
% Syntax : Number of formulae : 198 ( 15 unt; 16 def)
% Number of atoms : 541 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 629 ( 286 ~; 327 |; 0 &)
% ( 16 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 20 ( 19 usr; 17 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 65 ( 0 sgn 65 !; 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,
~ equalish(e_1,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_1_is_not_e_2) ).
fof(f5,axiom,
~ equalish(e_1,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_1_is_not_e_3) ).
fof(f7,axiom,
~ equalish(e_2,e_3),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',product_left_cancellation) ).
fof(f14,negated_conjecture,
! [X2,X3,X0,X1] :
( product(X0,X2,X3)
| ~ product(X2,X1,X3)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox/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(f19,plain,
! [X0,X1] :
( ~ product(X0,e_3,X1)
| ~ product(X0,e_1,X1) ),
inference(resolution,[],[f5,f12]) ).
fof(f25,plain,
! [X0,X1] :
( ~ product(X0,e_3,X1)
| ~ product(X0,e_2,X1) ),
inference(resolution,[],[f7,f12]) ).
fof(f26,plain,
! [X0,X1] :
( ~ product(X0,X1,e_2)
| ~ product(X0,X1,e_3) ),
inference(resolution,[],[f7,f11]) ).
fof(f33,plain,
! [X2,X0,X1] :
( ~ product(e_2,X2,X0)
| ~ product(X0,X2,X1)
| ~ 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(X0,X2,e_2)
| ~ product(e_2,X2,X1)
| ~ product(X0,e_1,X1) ),
inference(resolution,[],[f16,f14]) ).
fof(f37,plain,
! [X0] :
( ~ product(X0,e_1,e_3)
| ~ group_element(e_2)
| product(X0,e_2,e_1)
| product(X0,e_2,e_2)
| ~ group_element(X0) ),
inference(resolution,[],[f16,f10]) ).
fof(f38,plain,
! [X0] :
( ~ product(X0,e_1,e_3)
| product(X0,e_2,e_1)
| product(X0,e_2,e_2)
| ~ group_element(X0) ),
inference(forward_subsumption_resolution,[],[f37,f2]) ).
fof(f41,plain,
! [X0] :
( ~ product(e_2,X0,e_2)
| ~ product(e_1,e_2,e_2) ),
inference(factoring,[],[f33]) ).
fof(f43,definition,
( spl0_1
<=> product(e_1,e_2,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f45,plain,
( ~ product(e_1,e_2,e_2)
| spl0_1 ),
inference(avatar_component_clause,[],[f43]) ).
fof(f47,definition,
( spl0_2
<=> ! [X0] : ~ product(e_2,X0,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f48,plain,
( ! [X0] : ~ product(e_2,X0,e_2)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f47]) ).
fof(f49,plain,
( ~ spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f41,f47,f43]) ).
fof(f51,plain,
! [X2,X0,X1] :
( ~ product(X1,X2,e_2)
| ~ product(X0,X1,e_1)
| ~ product(X0,X2,X1) ),
inference(resolution,[],[f17,f14]) ).
fof(f57,plain,
! [X0] :
( ~ product(e_2,X0,e_2)
| ~ product(e_2,e_1,e_2) ),
inference(factoring,[],[f36]) ).
fof(f60,definition,
( spl0_3
<=> product(e_2,e_1,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f61,plain,
( product(e_2,e_1,e_2)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f60]) ).
fof(f62,plain,
( ~ product(e_2,e_1,e_2)
| spl0_3 ),
inference(avatar_component_clause,[],[f60]) ).
fof(f67,plain,
( ~ spl0_3
| spl0_2 ),
inference(avatar_split_clause,[],[f57,f47,f60]) ).
fof(f69,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(f70,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,[],[f69,f3]) ).
fof(f75,plain,
! [X0] :
( ~ product(e_2,X0,e_2)
| ~ product(e_2,e_2,e_1) ),
inference(factoring,[],[f51]) ).
fof(f77,definition,
( spl0_5
<=> product(e_2,e_2,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f79,plain,
( ~ product(e_2,e_2,e_1)
| spl0_5 ),
inference(avatar_component_clause,[],[f77]) ).
fof(f80,plain,
( ~ spl0_5
| spl0_2 ),
inference(avatar_split_clause,[],[f75,f47,f77]) ).
fof(f86,definition,
( spl0_6
<=> product(e_1,e_3,e_3) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f87,plain,
( product(e_1,e_3,e_3)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f86]) ).
fof(f88,plain,
( ~ product(e_1,e_3,e_3)
| spl0_6 ),
inference(avatar_component_clause,[],[f86]) ).
fof(f102,definition,
( spl0_8
<=> product(e_1,e_3,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f104,plain,
( product(e_1,e_3,e_2)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f102]) ).
fof(f106,definition,
( spl0_9
<=> product(e_1,e_3,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f108,plain,
( product(e_1,e_3,e_1)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f106]) ).
fof(f113,plain,
( ~ product(e_1,e_2,e_3)
| ~ spl0_6 ),
inference(resolution,[],[f87,f25]) ).
fof(f115,plain,
! [X2,X0,X1] :
( ~ product(X1,X2,e_2)
| ~ product(X0,X1,e_3)
| ~ product(X0,X2,X1) ),
inference(resolution,[],[f26,f14]) ).
fof(f119,plain,
( ~ group_element(e_2)
| product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| ~ group_element(e_1)
| ~ spl0_6 ),
inference(resolution,[],[f113,f10]) ).
fof(f121,plain,
( product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| ~ group_element(e_1)
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[],[f119,f2]) ).
fof(f122,plain,
( product(e_1,e_2,e_1)
| ~ group_element(e_1)
| spl0_1
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[],[f121,f45]) ).
fof(f123,plain,
( product(e_1,e_2,e_1)
| spl0_1
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[],[f122,f1]) ).
fof(f129,definition,
( spl0_10
<=> product(e_1,e_1,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f130,plain,
( ~ product(e_1,e_1,e_2)
| spl0_10 ),
inference(avatar_component_clause,[],[f129]) ).
fof(f133,definition,
( spl0_11
<=> product(e_1,e_1,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f134,plain,
( ~ product(e_1,e_1,e_1)
| spl0_11 ),
inference(avatar_component_clause,[],[f133]) ).
fof(f146,plain,
( ~ product(e_1,e_2,e_2)
| ~ spl0_8 ),
inference(resolution,[],[f104,f25]) ).
fof(f147,plain,
( ~ product(e_1,e_1,e_2)
| ~ spl0_8 ),
inference(resolution,[],[f104,f19]) ).
fof(f148,plain,
( ~ spl0_10
| ~ spl0_8 ),
inference(avatar_split_clause,[],[f147,f102,f129]) ).
fof(f163,definition,
( spl0_12
<=> product(e_1,e_1,e_3) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f164,plain,
( product(e_1,e_1,e_3)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f163]) ).
fof(f165,plain,
( ~ product(e_1,e_1,e_3)
| spl0_12 ),
inference(avatar_component_clause,[],[f163]) ).
fof(f167,definition,
( spl0_13
<=> ! [X0] : ~ product(e_1,X0,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f168,plain,
( ! [X0] : ~ product(e_1,X0,e_1)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f167]) ).
fof(f170,plain,
( ~ group_element(e_1)
| product(e_1,e_1,e_1)
| product(e_1,e_1,e_2)
| ~ group_element(e_1)
| spl0_12 ),
inference(resolution,[],[f165,f10]) ).
fof(f172,plain,
( ~ group_element(e_1)
| product(e_1,e_1,e_1)
| product(e_1,e_1,e_2)
| spl0_12 ),
inference(duplicate_literal_removal,[],[f170]) ).
fof(f173,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_1,e_2)
| spl0_12 ),
inference(forward_subsumption_resolution,[],[f172,f1]) ).
fof(f174,plain,
( product(e_1,e_1,e_1)
| spl0_10
| spl0_12 ),
inference(forward_subsumption_resolution,[],[f173,f130]) ).
fof(f190,plain,
( ! [X0] :
( ~ product(X0,e_3,e_1)
| ~ product(X0,e_1,e_3) )
| ~ spl0_8 ),
inference(resolution,[],[f115,f104]) ).
fof(f191,plain,
! [X0] :
( ~ product(e_2,X0,e_2)
| ~ product(e_2,e_2,e_3) ),
inference(factoring,[],[f115]) ).
fof(f193,definition,
( spl0_14
<=> product(e_2,e_2,e_3) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f195,plain,
( ~ product(e_2,e_2,e_3)
| spl0_14 ),
inference(avatar_component_clause,[],[f193]) ).
fof(f196,plain,
( ~ spl0_14
| spl0_2 ),
inference(avatar_split_clause,[],[f191,f47,f193]) ).
fof(f197,plain,
( ~ group_element(e_2)
| product(e_2,e_2,e_1)
| product(e_2,e_2,e_2)
| ~ group_element(e_2)
| spl0_14 ),
inference(resolution,[],[f195,f10]) ).
fof(f199,plain,
( ~ group_element(e_2)
| product(e_2,e_2,e_1)
| product(e_2,e_2,e_2)
| spl0_14 ),
inference(duplicate_literal_removal,[],[f197]) ).
fof(f200,plain,
( product(e_2,e_2,e_1)
| product(e_2,e_2,e_2)
| spl0_14 ),
inference(forward_subsumption_resolution,[],[f199,f2]) ).
fof(f201,plain,
( product(e_2,e_2,e_2)
| spl0_5
| spl0_14 ),
inference(forward_subsumption_resolution,[],[f200,f79]) ).
fof(f215,plain,
! [X0,X1] :
( ~ product(X0,X1,e_1)
| product(X0,e_2,e_2)
| ~ group_element(X0)
| ~ product(e_1,X1,e_3)
| product(X0,e_2,e_1) ),
inference(resolution,[],[f38,f14]) ).
fof(f264,definition,
( spl0_23
<=> product(e_2,e_3,e_3) ),
introduced(definition,[new_symbols(definition,[spl0_23])],[avatar_definition]) ).
fof(f265,plain,
( product(e_2,e_3,e_3)
| ~ spl0_23 ),
inference(avatar_component_clause,[],[f264]) ).
fof(f266,plain,
( ~ product(e_2,e_3,e_3)
| spl0_23 ),
inference(avatar_component_clause,[],[f264]) ).
fof(f286,plain,
( ! [X0] :
( ~ product(X0,e_1,e_3)
| product(X0,e_3,e_2)
| ~ group_element(X0) )
| ~ spl0_8 ),
inference(forward_subsumption_resolution,[],[f70,f190]) ).
fof(f292,definition,
( spl0_26
<=> product(e_2,e_3,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_26])],[avatar_definition]) ).
fof(f294,plain,
( product(e_2,e_3,e_2)
| ~ spl0_26 ),
inference(avatar_component_clause,[],[f292]) ).
fof(f296,definition,
( spl0_27
<=> product(e_2,e_3,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_27])],[avatar_definition]) ).
fof(f298,plain,
( product(e_2,e_3,e_1)
| ~ spl0_27 ),
inference(avatar_component_clause,[],[f296]) ).
fof(f300,plain,
( ! [X0] :
( 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) )
| ~ spl0_8 ),
inference(resolution,[],[f286,f10]) ).
fof(f302,plain,
( ! [X0] :
( 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) )
| ~ spl0_8 ),
inference(duplicate_literal_removal,[],[f300]) ).
fof(f303,plain,
( ! [X0] :
( ~ group_element(X0)
| product(X0,e_3,e_2)
| product(X0,e_1,e_1)
| product(X0,e_1,e_2) )
| ~ spl0_8 ),
inference(forward_subsumption_resolution,[],[f302,f1]) ).
fof(f316,plain,
( ~ product(e_2,e_1,e_3)
| ~ spl0_23 ),
inference(resolution,[],[f265,f19]) ).
fof(f326,plain,
( ~ group_element(e_1)
| product(e_2,e_1,e_1)
| product(e_2,e_1,e_2)
| ~ group_element(e_2)
| ~ spl0_23 ),
inference(resolution,[],[f316,f10]) ).
fof(f328,plain,
( product(e_2,e_1,e_1)
| product(e_2,e_1,e_2)
| ~ group_element(e_2)
| ~ spl0_23 ),
inference(forward_subsumption_resolution,[],[f326,f1]) ).
fof(f329,plain,
( product(e_2,e_1,e_1)
| ~ group_element(e_2)
| spl0_3
| ~ spl0_23 ),
inference(forward_subsumption_resolution,[],[f328,f62]) ).
fof(f330,plain,
( product(e_2,e_1,e_1)
| spl0_3
| ~ spl0_23 ),
inference(forward_subsumption_resolution,[],[f329,f2]) ).
fof(f332,plain,
( product(e_2,e_3,e_2)
| product(e_2,e_1,e_1)
| product(e_2,e_1,e_2)
| ~ spl0_8 ),
inference(resolution,[],[f303,f2]) ).
fof(f335,plain,
( product(e_2,e_3,e_2)
| product(e_2,e_1,e_1)
| spl0_3
| ~ spl0_8 ),
inference(forward_subsumption_resolution,[],[f332,f62]) ).
fof(f337,definition,
( spl0_28
<=> product(e_2,e_1,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_28])],[avatar_definition]) ).
fof(f339,plain,
( product(e_2,e_1,e_1)
| ~ spl0_28 ),
inference(avatar_component_clause,[],[f337]) ).
fof(f340,plain,
( spl0_28
| spl0_26
| spl0_3
| ~ spl0_8 ),
inference(avatar_split_clause,[],[f335,f102,f60,f292,f337]) ).
fof(f361,plain,
( ~ group_element(e_3)
| product(e_2,e_3,e_1)
| product(e_2,e_3,e_2)
| ~ group_element(e_2)
| spl0_23 ),
inference(resolution,[],[f266,f10]) ).
fof(f363,plain,
( product(e_2,e_3,e_1)
| product(e_2,e_3,e_2)
| ~ group_element(e_2)
| spl0_23 ),
inference(forward_subsumption_resolution,[],[f361,f3]) ).
fof(f364,plain,
( product(e_2,e_3,e_1)
| product(e_2,e_3,e_2)
| spl0_23 ),
inference(forward_subsumption_resolution,[],[f363,f2]) ).
fof(f365,plain,
( spl0_26
| spl0_27
| spl0_23 ),
inference(avatar_split_clause,[],[f364,f264,f296,f292]) ).
fof(f386,plain,
( ~ product(e_1,e_3,e_2)
| ~ spl0_26 ),
inference(resolution,[],[f294,f15]) ).
fof(f387,plain,
( ~ product(e_2,e_2,e_2)
| ~ spl0_26 ),
inference(resolution,[],[f294,f25]) ).
fof(f389,plain,
( $false
| spl0_5
| spl0_14
| ~ spl0_26 ),
inference(forward_subsumption_resolution,[],[f387,f201]) ).
fof(f390,plain,
( spl0_5
| spl0_14
| ~ spl0_26 ),
inference(avatar_contradiction_clause,[],[f389]) ).
fof(f408,plain,
( ~ group_element(e_2)
| product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| ~ group_element(e_1)
| ~ spl0_6 ),
inference(resolution,[],[f113,f10]) ).
fof(f410,plain,
( product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| ~ group_element(e_1)
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[],[f408,f2]) ).
fof(f411,plain,
( product(e_1,e_2,e_1)
| ~ group_element(e_1)
| spl0_1
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[],[f410,f45]) ).
fof(f412,plain,
( product(e_1,e_2,e_1)
| spl0_1
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[],[f411,f1]) ).
fof(f427,plain,
( ~ product(e_1,e_3,e_1)
| ~ spl0_27 ),
inference(resolution,[],[f298,f15]) ).
fof(f428,plain,
( ~ product(e_2,e_2,e_1)
| ~ spl0_27 ),
inference(resolution,[],[f298,f25]) ).
fof(f429,plain,
( ~ product(e_2,e_1,e_1)
| ~ spl0_27 ),
inference(resolution,[],[f298,f19]) ).
fof(f430,plain,
( ~ spl0_28
| ~ spl0_27 ),
inference(avatar_split_clause,[],[f429,f296,f337]) ).
fof(f451,plain,
( ~ product(e_1,e_1,e_1)
| spl0_1
| ~ spl0_6 ),
inference(resolution,[],[f123,f16]) ).
fof(f456,plain,
( ~ spl0_11
| spl0_1
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f451,f86,f43,f133]) ).
fof(f481,plain,
( ! [X0] :
( ~ product(e_1,X0,e_1)
| ~ product(e_1,X0,e_1) )
| spl0_11 ),
inference(resolution,[],[f134,f14]) ).
fof(f482,plain,
( ! [X0] : ~ product(e_1,X0,e_1)
| spl0_11 ),
inference(duplicate_literal_removal,[],[f481]) ).
fof(f483,plain,
( spl0_13
| spl0_11 ),
inference(avatar_split_clause,[],[f482,f133,f167]) ).
fof(f484,plain,
( ~ spl0_9
| ~ spl0_27 ),
inference(avatar_split_clause,[],[f427,f296,f106]) ).
fof(f485,plain,
( spl0_28
| spl0_3
| ~ spl0_23 ),
inference(avatar_split_clause,[],[f330,f264,f60,f337]) ).
fof(f506,plain,
( ~ product(e_1,e_1,e_1)
| ~ spl0_9 ),
inference(resolution,[],[f108,f19]) ).
fof(f507,plain,
( ~ spl0_11
| ~ spl0_9 ),
inference(avatar_split_clause,[],[f506,f106,f133]) ).
fof(f512,plain,
( product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| ~ group_element(e_1)
| ~ spl0_12 ),
inference(resolution,[],[f164,f38]) ).
fof(f513,plain,
( product(e_1,e_2,e_1)
| ~ group_element(e_1)
| spl0_1
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f512,f45]) ).
fof(f516,plain,
( product(e_1,e_2,e_1)
| spl0_1
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f513,f1]) ).
fof(f520,plain,
( $false
| ~ spl0_9
| ~ spl0_13 ),
inference(resolution,[],[f168,f108]) ).
fof(f522,plain,
( ~ spl0_9
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f520]) ).
fof(f526,plain,
( $false
| spl0_1
| ~ spl0_6
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f412,f168]) ).
fof(f527,plain,
( spl0_1
| ~ spl0_6
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f526]) ).
fof(f535,plain,
( ~ spl0_5
| ~ spl0_27 ),
inference(avatar_split_clause,[],[f428,f296,f77]) ).
fof(f546,plain,
( $false
| spl0_10
| spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f174,f168]) ).
fof(f547,plain,
( spl0_10
| spl0_12
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f546]) ).
fof(f555,plain,
( $false
| spl0_1
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f516,f168]) ).
fof(f556,plain,
( spl0_1
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f555]) ).
fof(f557,plain,
( ~ spl0_1
| ~ spl0_8 ),
inference(avatar_split_clause,[],[f146,f102,f43]) ).
fof(f560,plain,
( $false
| ~ spl0_2
| ~ spl0_3 ),
inference(forward_subsumption_resolution,[],[f61,f48]) ).
fof(f561,plain,
( ~ spl0_2
| ~ spl0_3 ),
inference(avatar_contradiction_clause,[],[f560]) ).
fof(f576,plain,
( ~ group_element(e_3)
| product(e_1,e_3,e_1)
| product(e_1,e_3,e_2)
| ~ group_element(e_1)
| spl0_6 ),
inference(resolution,[],[f88,f10]) ).
fof(f578,plain,
( product(e_1,e_3,e_1)
| product(e_1,e_3,e_2)
| ~ group_element(e_1)
| spl0_6 ),
inference(forward_subsumption_resolution,[],[f576,f3]) ).
fof(f579,plain,
( product(e_1,e_3,e_1)
| product(e_1,e_3,e_2)
| spl0_6 ),
inference(forward_subsumption_resolution,[],[f578,f1]) ).
fof(f580,plain,
( spl0_8
| spl0_9
| spl0_6 ),
inference(avatar_split_clause,[],[f579,f86,f106,f102]) ).
fof(f662,plain,
( ~ product(e_1,e_1,e_1)
| ~ spl0_28 ),
inference(resolution,[],[f339,f15]) ).
fof(f664,plain,
( ~ spl0_11
| ~ spl0_28 ),
inference(avatar_split_clause,[],[f662,f337,f133]) ).
fof(f666,plain,
( ~ spl0_8
| ~ spl0_26 ),
inference(avatar_split_clause,[],[f386,f292,f102]) ).
fof(f687,plain,
( ~ group_element(e_3)
| product(e_2,e_3,e_1)
| product(e_2,e_3,e_2)
| ~ spl0_6 ),
inference(resolution,[],[f87,f35]) ).
fof(f691,plain,
( product(e_2,e_3,e_1)
| product(e_2,e_3,e_2)
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[],[f687,f3]) ).
fof(f697,plain,
( product(e_2,e_3,e_1)
| ~ spl0_2
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[],[f691,f48]) ).
fof(f698,plain,
( spl0_27
| ~ spl0_2
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f697,f86,f47,f296]) ).
fof(f726,plain,
( product(e_2,e_2,e_2)
| ~ group_element(e_2)
| ~ product(e_1,e_3,e_3)
| product(e_2,e_2,e_1)
| ~ spl0_27 ),
inference(resolution,[],[f298,f215]) ).
fof(f735,plain,
( ~ group_element(e_2)
| ~ product(e_1,e_3,e_3)
| product(e_2,e_2,e_1)
| ~ spl0_2
| ~ spl0_27 ),
inference(forward_subsumption_resolution,[],[f726,f48]) ).
fof(f736,plain,
( ~ product(e_1,e_3,e_3)
| product(e_2,e_2,e_1)
| ~ spl0_2
| ~ spl0_27 ),
inference(forward_subsumption_resolution,[],[f735,f2]) ).
fof(f737,plain,
( product(e_2,e_2,e_1)
| ~ spl0_2
| ~ spl0_6
| ~ spl0_27 ),
inference(forward_subsumption_resolution,[],[f736,f87]) ).
fof(f738,plain,
( $false
| ~ spl0_2
| spl0_5
| ~ spl0_6
| ~ spl0_27 ),
inference(forward_subsumption_resolution,[],[f737,f79]) ).
fof(f739,plain,
( ~ spl0_2
| spl0_5
| ~ spl0_6
| ~ spl0_27 ),
inference(avatar_contradiction_clause,[],[f738]) ).
cnf(s1,plain,
( ~ spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f49]) ).
cnf(s3,plain,
( spl0_2
| ~ spl0_3 ),
inference(sat_conversion,[],[f67]) ).
cnf(s4,plain,
( spl0_2
| ~ spl0_5 ),
inference(sat_conversion,[],[f80]) ).
cnf(s9,plain,
( ~ spl0_8
| ~ spl0_10 ),
inference(sat_conversion,[],[f148]) ).
cnf(s13,plain,
( spl0_2
| ~ spl0_14 ),
inference(sat_conversion,[],[f196]) ).
cnf(s26,plain,
( spl0_3
| ~ spl0_8
| spl0_26
| spl0_28 ),
inference(sat_conversion,[],[f340]) ).
cnf(s33,plain,
( spl0_23
| spl0_26
| spl0_27 ),
inference(sat_conversion,[],[f365]) ).
cnf(s34,plain,
( spl0_5
| spl0_14
| ~ spl0_26 ),
inference(sat_conversion,[],[f390]) ).
cnf(s39,plain,
( ~ spl0_27
| ~ spl0_28 ),
inference(sat_conversion,[],[f430]) ).
cnf(s42,plain,
( spl0_1
| ~ spl0_6
| ~ spl0_11 ),
inference(sat_conversion,[],[f456]) ).
cnf(s46,plain,
( spl0_11
| spl0_13 ),
inference(sat_conversion,[],[f483]) ).
cnf(s48,plain,
( ~ spl0_9
| ~ spl0_27 ),
inference(sat_conversion,[],[f484]) ).
cnf(s49,plain,
( spl0_3
| ~ spl0_23
| spl0_28 ),
inference(sat_conversion,[],[f485]) ).
cnf(s53,plain,
( ~ spl0_9
| ~ spl0_11 ),
inference(sat_conversion,[],[f507]) ).
cnf(s57,plain,
( ~ spl0_9
| ~ spl0_13 ),
inference(sat_conversion,[],[f522]) ).
cnf(s60,plain,
( spl0_1
| ~ spl0_6
| ~ spl0_13 ),
inference(sat_conversion,[],[f527]) ).
cnf(s66,plain,
( ~ spl0_5
| ~ spl0_27 ),
inference(sat_conversion,[],[f535]) ).
cnf(s68,plain,
( spl0_10
| spl0_12
| ~ spl0_13 ),
inference(sat_conversion,[],[f547]) ).
cnf(s78,plain,
( spl0_1
| ~ spl0_12
| ~ spl0_13 ),
inference(sat_conversion,[],[f556]) ).
cnf(s79,plain,
( ~ spl0_1
| ~ spl0_8 ),
inference(sat_conversion,[],[f557]) ).
cnf(s87,plain,
( ~ spl0_2
| ~ spl0_3 ),
inference(sat_conversion,[],[f561]) ).
cnf(s97,plain,
( spl0_6
| spl0_8
| spl0_9 ),
inference(sat_conversion,[],[f580]) ).
cnf(s110,plain,
( ~ spl0_11
| ~ spl0_28 ),
inference(sat_conversion,[],[f664]) ).
cnf(s112,plain,
( ~ spl0_8
| ~ spl0_26 ),
inference(sat_conversion,[],[f666]) ).
cnf(s122,plain,
( ~ spl0_2
| ~ spl0_6
| spl0_27 ),
inference(sat_conversion,[],[f698]) ).
cnf(s129,plain,
( ~ spl0_2
| spl0_5
| ~ spl0_6
| ~ spl0_27 ),
inference(sat_conversion,[],[f739]) ).
cnf(s130,plain,
( ~ spl0_27
| spl0_6
| spl0_2 ),
inference(rat,[],[s26,s97,s39,s48,s3,s34,s4,s13]) ).
cnf(s131,plain,
( spl0_6
| spl0_2
| spl0_1 ),
inference(rat,[],[s9,s68,s97,s78,s57,s46,s110,s49,s33,s130,s3,s34,s4,s13]) ).
cnf(s132,plain,
( ~ spl0_6
| spl0_1 ),
inference(rat,[],[s46,s42,s60]) ).
cnf(s133,plain,
( ~ spl0_13
| spl0_1 ),
inference(rat,[],[s9,s68,s97,s78,s57,s132]) ).
cnf(s134,plain,
( spl0_6
| spl0_1 ),
inference(rat,[],[s26,s112,s97,s53,s110,s46,s133,s87,s131]) ).
cnf(s135,plain,
spl0_1,
inference(rat,[],[s134,s132]) ).
cnf(s136,plain,
~ spl0_8,
inference(rat,[],[s79,s135]) ).
cnf(s138,plain,
spl0_2,
inference(rat,[],[s1,s135]) ).
cnf(s140,plain,
~ spl0_9,
inference(rat,[],[s46,s53,s57]) ).
cnf(s141,plain,
spl0_6,
inference(rat,[],[s97,s136,s140]) ).
cnf(s143,plain,
spl0_27,
inference(rat,[],[s122,s138,s141]) ).
cnf(s149,plain,
spl0_5,
inference(rat,[],[s129,s143,s138,s141]) ).
cnf(s152,plain,
$false,
inference(rat,[],[s66,s143,s149]) ).
fof(f740,plain,
$false,
inference(avatar_sat_refutation,[],[s152]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP128-1.003 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n020.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 27 09:27:19 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 2.11/1.17 % (3127278)Input is clausal, will run a generic CNF schedule.
% 2.11/1.17 % (3127286)lrs+10_1_sil=8000:sp=occurrence:random_seed=1934049975:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.11/1.17 % (3127286)Instruction limit reached!
% 2.11/1.17 % (3127286)------------------------------
% 2.11/1.17 % (3127286)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.11/1.17 % (3127286)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.11/1.17 % (3127286)CaDiCaL version: 2.1.3
% 2.11/1.17 % (3127286)Termination reason: Instruction limit
% 2.11/1.17 % (3127286)Termination phase: Saturation
% 2.11/1.17 % (3127286)Time elapsed: 0.033 s
% 2.11/1.17 % (3127286)Peak memory usage: 88 MB
% 2.11/1.17 % (3127286)Instructions burned: 109 (million)
% 2.11/1.17 % (3127288)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3666475734:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.11/1.17 % (3127289)dis-21_1_sil=8000:lcm=predicate:random_seed=2982547572: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)
% 2.11/1.17 % (3127287)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3829726145:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.11/1.17 % (3127284)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=743916262:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.11/1.17 % (3127283)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=1784882924:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.11/1.17 % (3127285)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2998715858:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.11/1.17 % (3127288)First to succeed.
% 2.11/1.17 % (3127288)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3127278"
% 2.11/1.17 % (3127287)Instruction limit reached!
% 2.11/1.17 % (3127287)------------------------------
% 2.11/1.17 % (3127287)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.11/1.17 % (3127287)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.11/1.17 % (3127287)CaDiCaL version: 2.1.3
% 2.11/1.17 % (3127287)Termination reason: Instruction limit
% 2.11/1.17 % (3127287)Termination phase: Saturation
% 2.11/1.17 % (3127287)Time elapsed: 0.064 s
% 2.11/1.17 % (3127287)Peak memory usage: 88 MB
% 2.11/1.17 % (3127287)Instructions burned: 116 (million)
% 2.11/1.17 % (3127289)Instruction limit reached!
% 2.11/1.17 % (3127289)------------------------------
% 2.11/1.17 % (3127289)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.11/1.17 % (3127289)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.11/1.17 % (3127289)CaDiCaL version: 2.1.3
% 2.11/1.17 % (3127289)Termination reason: Instruction limit
% 2.11/1.17 % (3127289)Termination phase: Saturation
% 2.11/1.17 % (3127289)Time elapsed: 0.066 s
% 2.11/1.17 % (3127289)Peak memory usage: 88 MB
% 2.11/1.17 % (3127289)Instructions burned: 118 (million)
% 2.11/1.17 % (3127291)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=1571673922:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 2.11/1.17 % (3127288)Refutation found. Thanks to Tanya!
% 2.11/1.17 % SZS status Unsatisfiable for theBenchmark
% 2.11/1.17 % SZS output start Proof for theBenchmark
% See solution above
% 2.68/1.27 % (3127288)------------------------------
% 2.68/1.27 % (3127288)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.68/1.27 % (3127288)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.68/1.27 % (3127288)CaDiCaL version: 2.1.3
% 2.68/1.27 % (3127288)Termination reason: Refutation
% 2.68/1.27 % (3127288)Time elapsed: 0.010 s
% 2.68/1.27 % (3127288)Peak memory usage: 89 MB
% 2.68/1.27 % (3127288)Instructions burned: 24 (million)
% 2.68/1.27 % (3127288)------------------------------
% 2.68/1.27 % (3127288)------------------------------
% 2.68/1.27 % (3127278)Success in time 0.314 s
% 2.68/1.27 % Vampire exiting
%------------------------------------------------------------------------------