%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP130-1.003 : 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 : n011.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 10:13:00 AM UTC 2026
% Result : Unsatisfiable 2.72s 1.28s
% Output : Refutation 3.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 33
% Syntax : Number of formulae : 279 ( 22 unt; 22 def)
% Number of atoms : 814 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 918 ( 383 ~; 513 |; 0 &)
% ( 22 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 26 ( 25 usr; 23 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 94 ( 0 sgn 94 !; 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(X3,X1,X0)
| ~ product(X0,X2,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(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(f20,plain,
! [X0,X1] :
( ~ product(X0,X1,e_1)
| ~ product(X0,X1,e_3) ),
inference(resolution,[],[f5,f11]) ).
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(f26,plain,
! [X0,X1] :
( ~ product(X0,X1,e_2)
| ~ product(X0,X1,e_3) ),
inference(resolution,[],[f7,f11]) ).
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(X1,e_2,X2)
| ~ product(X1,X2,X0)
| ~ 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(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,
! [X0] :
( ~ product(X0,e_2,e_2)
| ~ product(e_2,e_1,X0) ),
inference(factoring,[],[f36]) ).
fof(f51,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(f52,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,[],[f51,f3]) ).
fof(f54,plain,
! [X2,X0,X1] :
( ~ product(X0,X1,e_3)
| ~ product(e_1,X2,X0)
| ~ product(e_1,X1,X2) ),
inference(resolution,[],[f20,f14]) ).
fof(f58,definition,
( spl0_1
<=> product(e_2,e_1,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f60,plain,
( ~ product(e_2,e_1,e_2)
| spl0_1 ),
inference(avatar_component_clause,[],[f58]) ).
fof(f71,definition,
( spl0_3
<=> product(e_1,e_1,e_3) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f72,plain,
( product(e_1,e_1,e_3)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f71]) ).
fof(f73,plain,
( ~ product(e_1,e_1,e_3)
| spl0_3 ),
inference(avatar_component_clause,[],[f71]) ).
fof(f79,plain,
! [X2,X0,X1] :
( ~ product(e_2,X0,X1)
| ~ product(X1,X2,e_3)
| ~ product(X1,X0,X2) ),
inference(resolution,[],[f24,f14]) ).
fof(f80,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(f81,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,[],[f80,f3]) ).
fof(f83,plain,
( ! [X0] :
( ~ product(e_3,X0,e_1)
| ~ product(e_3,e_1,X0) )
| spl0_3 ),
inference(resolution,[],[f73,f14]) ).
fof(f87,definition,
( spl0_5
<=> product(e_1,e_1,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f88,plain,
( ~ product(e_1,e_1,e_2)
| spl0_5 ),
inference(avatar_component_clause,[],[f87]) ).
fof(f91,definition,
( spl0_6
<=> product(e_1,e_1,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f96,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(f97,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,[],[f96,f3]) ).
fof(f104,plain,
! [X2,X0,X1] :
( ~ product(e_2,X2,X0)
| ~ product(X0,X1,e_3)
| ~ product(e_2,X1,X2) ),
inference(resolution,[],[f26,f14]) ).
fof(f105,plain,
( ! [X0] :
( ~ product(e_2,X0,e_1)
| ~ product(e_2,e_1,X0) )
| spl0_5 ),
inference(resolution,[],[f88,f14]) ).
fof(f110,plain,
( ~ product(e_3,e_1,e_1)
| spl0_3 ),
inference(factoring,[],[f83]) ).
fof(f113,plain,
( ~ product(e_2,e_1,e_1)
| spl0_5 ),
inference(factoring,[],[f105]) ).
fof(f125,definition,
( spl0_7
<=> product(e_3,e_1,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f126,plain,
( ~ product(e_3,e_1,e_2)
| spl0_7 ),
inference(avatar_component_clause,[],[f125]) ).
fof(f127,plain,
( product(e_3,e_1,e_2)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f125]) ).
fof(f135,plain,
! [X0] :
( ~ product(e_1,X0,e_3)
| ~ product(e_1,e_3,e_1) ),
inference(factoring,[],[f54]) ).
fof(f137,definition,
( spl0_9
<=> product(e_1,e_3,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f139,plain,
( ~ product(e_1,e_3,e_1)
| spl0_9 ),
inference(avatar_component_clause,[],[f137]) ).
fof(f141,definition,
( spl0_10
<=> ! [X0] : ~ product(e_1,X0,e_3) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f142,plain,
( ! [X0] : ~ product(e_1,X0,e_3)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f141]) ).
fof(f143,plain,
( ~ spl0_9
| spl0_10 ),
inference(avatar_split_clause,[],[f135,f141,f137]) ).
fof(f147,plain,
! [X0] :
( ~ product(e_2,X0,e_2)
| ~ product(e_2,e_2,e_3) ),
inference(factoring,[],[f79]) ).
fof(f149,definition,
( spl0_11
<=> product(e_2,e_2,e_3) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f150,plain,
( product(e_2,e_2,e_3)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f149]) ).
fof(f151,plain,
( ~ product(e_2,e_2,e_3)
| spl0_11 ),
inference(avatar_component_clause,[],[f149]) ).
fof(f153,definition,
( spl0_12
<=> ! [X0] : ~ product(e_2,X0,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f154,plain,
( ! [X0] : ~ product(e_2,X0,e_2)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f153]) ).
fof(f155,plain,
( ~ spl0_11
| spl0_12 ),
inference(avatar_split_clause,[],[f147,f153,f149]) ).
fof(f162,definition,
( spl0_13
<=> product(e_2,e_2,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f164,plain,
( product(e_2,e_2,e_2)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f162]) ).
fof(f166,definition,
( spl0_14
<=> product(e_2,e_2,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f176,plain,
( ~ product(e_1,e_2,e_3)
| ~ spl0_11 ),
inference(resolution,[],[f150,f15]) ).
fof(f178,plain,
( ~ product(e_2,e_1,e_3)
| ~ spl0_11 ),
inference(resolution,[],[f150,f16]) ).
fof(f182,plain,
! [X0] :
( ~ product(X0,X0,e_3)
| ~ product(e_2,X0,X0) ),
inference(factoring,[],[f104]) ).
fof(f191,definition,
( spl0_15
<=> product(e_3,e_3,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f193,plain,
( product(e_3,e_3,e_2)
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f191]) ).
fof(f195,definition,
( spl0_16
<=> product(e_3,e_3,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition]) ).
fof(f197,plain,
( product(e_3,e_3,e_1)
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f195]) ).
fof(f207,plain,
( ~ product(e_2,e_1,e_2)
| ~ spl0_7 ),
inference(resolution,[],[f127,f24]) ).
fof(f208,plain,
( ~ product(e_1,e_1,e_2)
| ~ spl0_7 ),
inference(resolution,[],[f127,f18]) ).
fof(f209,plain,
! [X0] :
( product(X0,e_2,e_1)
| product(X0,e_2,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,[],[f38,f10]) ).
fof(f211,plain,
! [X0] :
( product(X0,e_2,e_1)
| product(X0,e_2,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,[],[f209]) ).
fof(f212,plain,
! [X0] :
( ~ group_element(X0)
| product(X0,e_2,e_2)
| product(X0,e_2,e_1)
| product(X0,e_1,e_1)
| product(X0,e_1,e_2) ),
inference(forward_subsumption_resolution,[],[f211,f1]) ).
fof(f229,definition,
( spl0_17
<=> product(e_1,e_2,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition]) ).
fof(f231,plain,
( product(e_1,e_2,e_2)
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f229]) ).
fof(f233,definition,
( spl0_18
<=> product(e_1,e_2,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_18])],[avatar_definition]) ).
fof(f239,plain,
! [X0] :
( ~ group_element(X0)
| product(e_2,X0,e_1)
| product(e_2,X0,e_2)
| ~ group_element(X0)
| product(e_1,X0,e_1)
| product(e_1,X0,e_2)
| ~ group_element(e_1) ),
inference(resolution,[],[f35,f10]) ).
fof(f240,plain,
! [X0,X1] :
( ~ product(e_3,X1,e_1)
| product(e_2,X0,e_1)
| product(e_2,X0,e_2)
| ~ group_element(X0)
| ~ product(e_3,X0,X1) ),
inference(resolution,[],[f35,f14]) ).
fof(f241,plain,
! [X0] :
( ~ group_element(X0)
| product(e_2,X0,e_1)
| product(e_2,X0,e_2)
| product(e_1,X0,e_1)
| product(e_1,X0,e_2)
| ~ group_element(e_1) ),
inference(duplicate_literal_removal,[],[f239]) ).
fof(f242,plain,
! [X0] :
( ~ group_element(X0)
| product(e_2,X0,e_1)
| product(e_2,X0,e_2)
| product(e_1,X0,e_1)
| product(e_1,X0,e_2) ),
inference(forward_subsumption_resolution,[],[f241,f1]) ).
fof(f244,plain,
( ! [X0] :
( ~ product(e_3,e_2,X0)
| ~ product(e_3,X0,e_2) )
| spl0_11 ),
inference(resolution,[],[f151,f14]) ).
fof(f248,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,[],[f52,f10]) ).
fof(f249,plain,
! [X0,X1] :
( ~ product(e_3,e_1,X1)
| product(X0,e_3,e_2)
| ~ group_element(X0)
| ~ product(e_3,X1,X0)
| product(X0,e_3,e_1) ),
inference(resolution,[],[f52,f14]) ).
fof(f250,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,[],[f248]) ).
fof(f251,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,[],[f250,f1]) ).
fof(f253,plain,
( ~ product(e_2,e_1,e_2)
| ~ spl0_13 ),
inference(resolution,[],[f164,f48]) ).
fof(f265,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,[],[f81,f10]) ).
fof(f267,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,[],[f265]) ).
fof(f268,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,[],[f267,f2]) ).
fof(f270,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,[],[f97,f10]) ).
fof(f272,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,[],[f270]) ).
fof(f273,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,[],[f272,f2]) ).
fof(f282,definition,
( spl0_19
<=> product(e_3,e_2,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_19])],[avatar_definition]) ).
fof(f283,plain,
( ~ product(e_3,e_2,e_2)
| spl0_19 ),
inference(avatar_component_clause,[],[f282]) ).
fof(f286,definition,
( spl0_20
<=> product(e_3,e_2,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_20])],[avatar_definition]) ).
fof(f288,plain,
( product(e_3,e_2,e_1)
| ~ spl0_20 ),
inference(avatar_component_clause,[],[f286]) ).
fof(f305,plain,
( ~ product(e_1,e_3,e_2)
| ~ spl0_15 ),
inference(resolution,[],[f193,f18]) ).
fof(f308,plain,
( ~ product(e_3,e_2,e_2)
| ~ spl0_15 ),
inference(resolution,[],[f193,f25]) ).
fof(f309,plain,
( ~ product(e_3,e_1,e_2)
| ~ spl0_15 ),
inference(resolution,[],[f193,f19]) ).
fof(f312,plain,
( ~ spl0_19
| ~ spl0_15 ),
inference(avatar_split_clause,[],[f308,f191,f282]) ).
fof(f314,plain,
( ~ spl0_7
| ~ spl0_15 ),
inference(avatar_split_clause,[],[f309,f191,f125]) ).
fof(f367,plain,
( ~ product(e_3,e_2,e_2)
| spl0_11 ),
inference(factoring,[],[f244]) ).
fof(f384,plain,
( ~ product(e_3,e_1,e_2)
| spl0_3
| ~ spl0_20 ),
inference(resolution,[],[f288,f83]) ).
fof(f391,plain,
( ~ product(e_2,e_2,e_1)
| ~ spl0_20 ),
inference(resolution,[],[f288,f24]) ).
fof(f392,plain,
( ~ product(e_1,e_2,e_1)
| ~ spl0_20 ),
inference(resolution,[],[f288,f18]) ).
fof(f396,plain,
( ~ spl0_18
| ~ spl0_20 ),
inference(avatar_split_clause,[],[f392,f286,f233]) ).
fof(f406,plain,
( ~ spl0_14
| ~ spl0_20 ),
inference(avatar_split_clause,[],[f391,f286,f166]) ).
fof(f437,definition,
( spl0_26
<=> product(e_2,e_3,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_26])],[avatar_definition]) ).
fof(f441,definition,
( spl0_27
<=> product(e_2,e_3,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_27])],[avatar_definition]) ).
fof(f446,plain,
( ~ spl0_19
| spl0_11 ),
inference(avatar_split_clause,[],[f367,f149,f282]) ).
fof(f487,plain,
( ~ product(e_3,e_1,e_3)
| spl0_3
| ~ spl0_16 ),
inference(resolution,[],[f197,f83]) ).
fof(f492,plain,
( ~ product(e_2,e_3,e_1)
| ~ spl0_16 ),
inference(resolution,[],[f197,f24]) ).
fof(f499,plain,
( ~ product(e_3,e_1,e_1)
| ~ spl0_16 ),
inference(resolution,[],[f197,f19]) ).
fof(f500,plain,
( ~ spl0_27
| ~ spl0_16 ),
inference(avatar_split_clause,[],[f492,f195,f441]) ).
fof(f521,plain,
( ~ product(e_1,e_1,e_2)
| ~ spl0_17 ),
inference(resolution,[],[f231,f16]) ).
fof(f529,plain,
( ! [X0,X1] :
( ~ product(e_3,X1,e_1)
| product(e_2,X0,e_1)
| ~ group_element(X0)
| ~ product(e_3,X0,X1) )
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f240,f154]) ).
fof(f530,plain,
( ~ group_element(e_1)
| product(e_3,e_1,e_1)
| product(e_3,e_1,e_2)
| ~ group_element(e_3)
| spl0_3
| ~ spl0_16 ),
inference(resolution,[],[f487,f10]) ).
fof(f532,plain,
( product(e_3,e_1,e_1)
| product(e_3,e_1,e_2)
| ~ group_element(e_3)
| spl0_3
| ~ spl0_16 ),
inference(forward_subsumption_resolution,[],[f530,f1]) ).
fof(f533,plain,
( product(e_3,e_1,e_2)
| ~ group_element(e_3)
| spl0_3
| ~ spl0_16 ),
inference(forward_subsumption_resolution,[],[f532,f110]) ).
fof(f534,plain,
( ~ group_element(e_3)
| spl0_3
| spl0_7
| ~ spl0_16 ),
inference(forward_subsumption_resolution,[],[f533,f126]) ).
fof(f535,plain,
( $false
| spl0_3
| spl0_7
| ~ spl0_16 ),
inference(forward_subsumption_resolution,[],[f534,f3]) ).
fof(f536,plain,
( spl0_3
| spl0_7
| ~ spl0_16 ),
inference(avatar_contradiction_clause,[],[f535]) ).
fof(f561,plain,
( ~ product(e_3,e_1,e_1)
| product(e_2,e_1,e_1)
| ~ group_element(e_1)
| ~ spl0_12 ),
inference(factoring,[],[f529]) ).
fof(f562,plain,
( ~ group_element(e_2)
| product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| ~ group_element(e_1)
| ~ spl0_11 ),
inference(resolution,[],[f176,f10]) ).
fof(f566,plain,
( ~ product(e_3,e_1,e_1)
| product(e_1,e_3,e_2)
| ~ group_element(e_1)
| product(e_1,e_3,e_1) ),
inference(factoring,[],[f249]) ).
fof(f571,plain,
( ~ group_element(e_1)
| product(e_2,e_1,e_1)
| product(e_2,e_1,e_2)
| ~ group_element(e_2)
| ~ spl0_11 ),
inference(resolution,[],[f178,f10]) ).
fof(f573,plain,
( product(e_2,e_1,e_1)
| product(e_2,e_1,e_2)
| ~ group_element(e_2)
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f571,f1]) ).
fof(f574,plain,
( product(e_2,e_1,e_2)
| ~ group_element(e_2)
| spl0_5
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f573,f113]) ).
fof(f575,plain,
( ~ group_element(e_2)
| spl0_5
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f574,f154]) ).
fof(f576,plain,
( $false
| spl0_5
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f575,f2]) ).
fof(f577,plain,
( spl0_5
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f576]) ).
fof(f578,plain,
( ~ spl0_5
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f521,f229,f87]) ).
fof(f582,plain,
( product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| ~ group_element(e_1)
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f562,f2]) ).
fof(f588,plain,
( ~ product(e_3,e_1,e_1)
| ~ group_element(e_1)
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f561,f24]) ).
fof(f589,plain,
( ~ product(e_3,e_1,e_1)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1) ),
inference(forward_subsumption_resolution,[],[f566,f1]) ).
fof(f591,plain,
( product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f582,f1]) ).
fof(f596,definition,
( spl0_28
<=> product(e_3,e_1,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_28])],[avatar_definition]) ).
fof(f598,plain,
( ~ product(e_3,e_1,e_1)
| spl0_28 ),
inference(avatar_component_clause,[],[f596]) ).
fof(f601,plain,
( ~ product(e_3,e_1,e_1)
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f588,f1]) ).
fof(f604,plain,
( spl0_17
| spl0_18
| ~ spl0_11 ),
inference(avatar_split_clause,[],[f591,f149,f233,f229]) ).
fof(f606,definition,
( spl0_29
<=> product(e_1,e_3,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_29])],[avatar_definition]) ).
fof(f608,plain,
( product(e_1,e_3,e_2)
| ~ spl0_29 ),
inference(avatar_component_clause,[],[f606]) ).
fof(f615,plain,
( ~ spl0_28
| ~ spl0_12 ),
inference(avatar_split_clause,[],[f601,f153,f596]) ).
fof(f622,plain,
( ~ spl0_5
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f208,f125,f87]) ).
fof(f624,plain,
( spl0_9
| spl0_29
| ~ spl0_28 ),
inference(avatar_split_clause,[],[f589,f596,f606,f137]) ).
fof(f633,plain,
( ~ spl0_28
| ~ spl0_16 ),
inference(avatar_split_clause,[],[f499,f195,f596]) ).
fof(f635,plain,
( ~ group_element(e_1)
| product(e_2,e_1,e_1)
| product(e_2,e_1,e_2)
| ~ spl0_3 ),
inference(resolution,[],[f72,f35]) ).
fof(f636,plain,
( ~ group_element(e_1)
| product(e_3,e_1,e_1)
| product(e_3,e_1,e_2)
| ~ spl0_3 ),
inference(resolution,[],[f72,f45]) ).
fof(f639,plain,
( ~ product(e_2,e_1,e_1)
| ~ spl0_3 ),
inference(resolution,[],[f72,f182]) ).
fof(f648,plain,
( product(e_3,e_1,e_1)
| product(e_3,e_1,e_2)
| ~ spl0_3 ),
inference(forward_subsumption_resolution,[],[f636,f1]) ).
fof(f649,plain,
( product(e_2,e_1,e_1)
| product(e_2,e_1,e_2)
| ~ spl0_3 ),
inference(forward_subsumption_resolution,[],[f635,f1]) ).
fof(f652,plain,
( spl0_7
| spl0_28
| ~ spl0_3 ),
inference(avatar_split_clause,[],[f648,f71,f596,f125]) ).
fof(f653,plain,
( product(e_2,e_1,e_1)
| spl0_1
| ~ spl0_3 ),
inference(forward_subsumption_resolution,[],[f649,f60]) ).
fof(f654,plain,
( ~ spl0_28
| spl0_3 ),
inference(avatar_split_clause,[],[f110,f71,f596]) ).
fof(f656,plain,
( ~ group_element(e_1)
| product(e_1,e_1,e_1)
| product(e_1,e_1,e_2)
| ~ group_element(e_1)
| spl0_3 ),
inference(resolution,[],[f73,f10]) ).
fof(f658,plain,
( ~ group_element(e_1)
| product(e_1,e_1,e_1)
| product(e_1,e_1,e_2)
| spl0_3 ),
inference(duplicate_literal_removal,[],[f656]) ).
fof(f659,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_1,e_2)
| spl0_3 ),
inference(forward_subsumption_resolution,[],[f658,f1]) ).
fof(f660,plain,
( spl0_5
| spl0_6
| spl0_3 ),
inference(avatar_split_clause,[],[f659,f71,f91,f87]) ).
fof(f663,plain,
( ! [X0,X1] :
( ~ product(e_3,X0,e_1)
| ~ product(e_3,X1,X0) )
| ~ spl0_10 ),
inference(resolution,[],[f142,f14]) ).
fof(f666,plain,
( ~ group_element(e_2)
| product(e_2,e_2,e_1)
| product(e_2,e_2,e_2)
| ~ group_element(e_2)
| spl0_11 ),
inference(resolution,[],[f151,f10]) ).
fof(f667,plain,
( ! [X0] :
( ~ product(e_3,e_2,X0)
| ~ product(e_3,X0,e_2) )
| spl0_11 ),
inference(resolution,[],[f151,f14]) ).
fof(f668,plain,
( ~ group_element(e_2)
| product(e_2,e_2,e_1)
| product(e_2,e_2,e_2)
| spl0_11 ),
inference(duplicate_literal_removal,[],[f666]) ).
fof(f669,plain,
( product(e_2,e_2,e_1)
| product(e_2,e_2,e_2)
| spl0_11 ),
inference(forward_subsumption_resolution,[],[f668,f2]) ).
fof(f692,plain,
( ~ product(e_3,e_1,e_1)
| product(e_2,e_1,e_1)
| product(e_2,e_1,e_2)
| ~ group_element(e_1) ),
inference(factoring,[],[f240]) ).
fof(f693,plain,
( ~ product(e_3,e_1,e_1)
| product(e_2,e_1,e_2)
| ~ group_element(e_1) ),
inference(forward_subsumption_resolution,[],[f692,f24]) ).
fof(f740,plain,
( product(e_3,e_2,e_2)
| product(e_3,e_2,e_1)
| product(e_3,e_1,e_1)
| product(e_3,e_1,e_2) ),
inference(resolution,[],[f212,f3]) ).
fof(f751,plain,
( product(e_2,e_2,e_1)
| product(e_2,e_2,e_2)
| product(e_1,e_2,e_1)
| product(e_1,e_2,e_2) ),
inference(resolution,[],[f242,f2]) ).
fof(f758,plain,
( product(e_2,e_3,e_2)
| product(e_2,e_3,e_1)
| product(e_2,e_1,e_1)
| product(e_2,e_1,e_2) ),
inference(resolution,[],[f251,f2]) ).
fof(f759,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,[],[f251,f3]) ).
fof(f763,definition,
( spl0_32
<=> product(e_2,e_1,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_32])],[avatar_definition]) ).
fof(f765,plain,
( product(e_2,e_1,e_1)
| ~ spl0_32 ),
inference(avatar_component_clause,[],[f763]) ).
fof(f767,plain,
( ~ spl0_1
| ~ spl0_13 ),
inference(avatar_split_clause,[],[f253,f162,f58]) ).
fof(f768,plain,
( ~ spl0_1
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f207,f125,f58]) ).
fof(f769,plain,
( ~ product(e_3,e_1,e_1)
| product(e_2,e_1,e_2) ),
inference(forward_subsumption_resolution,[],[f693,f1]) ).
fof(f771,plain,
( spl0_1
| ~ spl0_28 ),
inference(avatar_split_clause,[],[f769,f596,f58]) ).
fof(f772,plain,
( spl0_1
| spl0_32
| spl0_27
| spl0_26 ),
inference(avatar_split_clause,[],[f758,f437,f441,f763,f58]) ).
fof(f773,plain,
( ! [X0] :
( ~ product(e_2,e_1,X0)
| ~ product(e_2,X0,e_2) )
| spl0_1 ),
inference(resolution,[],[f60,f14]) ).
fof(f802,plain,
( product(e_3,e_1,e_1)
| product(e_3,e_1,e_2)
| product(e_2,e_1,e_1)
| product(e_2,e_1,e_2) ),
inference(resolution,[],[f268,f1]) ).
fof(f807,plain,
( product(e_1,e_3,e_2)
| product(e_1,e_3,e_1)
| product(e_1,e_2,e_1)
| product(e_1,e_2,e_2) ),
inference(resolution,[],[f273,f1]) ).
fof(f809,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,[],[f273,f3]) ).
fof(f811,plain,
( product(e_1,e_3,e_2)
| product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| spl0_9 ),
inference(forward_subsumption_resolution,[],[f807,f139]) ).
fof(f813,plain,
( spl0_17
| spl0_18
| spl0_29
| spl0_9 ),
inference(avatar_split_clause,[],[f811,f137,f606,f233,f229]) ).
fof(f826,plain,
( ~ product(e_1,e_1,e_2)
| ~ spl0_29 ),
inference(resolution,[],[f608,f19]) ).
fof(f835,plain,
( ~ product(e_1,e_1,e_1)
| ~ spl0_32 ),
inference(resolution,[],[f765,f15]) ).
fof(f843,plain,
( spl0_13
| spl0_14
| spl0_11 ),
inference(avatar_split_clause,[],[f669,f149,f166,f162]) ).
fof(f845,plain,
( spl0_17
| spl0_18
| spl0_13
| spl0_14 ),
inference(avatar_split_clause,[],[f751,f166,f162,f233,f229]) ).
fof(f930,plain,
( ~ product(e_3,e_3,e_2)
| ~ group_element(e_2)
| product(e_3,e_2,e_1)
| product(e_3,e_2,e_2)
| ~ group_element(e_3)
| spl0_11 ),
inference(resolution,[],[f667,f10]) ).
fof(f935,plain,
( ~ product(e_2,e_3,e_2)
| ~ group_element(e_1)
| product(e_2,e_1,e_1)
| product(e_2,e_1,e_2)
| ~ group_element(e_2)
| spl0_1 ),
inference(resolution,[],[f773,f10]) ).
fof(f948,plain,
( $false
| ~ spl0_3
| ~ spl0_10 ),
inference(forward_subsumption_resolution,[],[f72,f142]) ).
fof(f949,plain,
( ~ spl0_3
| ~ spl0_10 ),
inference(avatar_contradiction_clause,[],[f948]) ).
fof(f950,plain,
( ~ spl0_32
| ~ spl0_3 ),
inference(avatar_split_clause,[],[f639,f71,f763]) ).
fof(f951,plain,
( spl0_32
| spl0_1
| ~ spl0_3 ),
inference(avatar_split_clause,[],[f653,f71,f58,f763]) ).
fof(f952,plain,
( ~ spl0_6
| ~ spl0_32 ),
inference(avatar_split_clause,[],[f835,f763,f91]) ).
fof(f953,plain,
( ~ product(e_2,e_3,e_2)
| product(e_2,e_1,e_1)
| product(e_2,e_1,e_2)
| ~ group_element(e_2)
| spl0_1 ),
inference(forward_subsumption_resolution,[],[f935,f1]) ).
fof(f957,plain,
( ~ product(e_2,e_3,e_2)
| product(e_2,e_1,e_1)
| ~ group_element(e_2)
| spl0_1 ),
inference(forward_subsumption_resolution,[],[f953,f19]) ).
fof(f961,plain,
( ~ product(e_2,e_3,e_2)
| product(e_2,e_1,e_1)
| spl0_1 ),
inference(forward_subsumption_resolution,[],[f957,f2]) ).
fof(f964,plain,
( spl0_32
| ~ spl0_26
| spl0_1 ),
inference(avatar_split_clause,[],[f961,f58,f437,f763]) ).
fof(f965,plain,
( ~ spl0_7
| spl0_3
| ~ spl0_20 ),
inference(avatar_split_clause,[],[f384,f286,f71,f125]) ).
fof(f967,plain,
( ~ spl0_29
| ~ spl0_15 ),
inference(avatar_split_clause,[],[f305,f191,f606]) ).
fof(f969,plain,
( product(e_3,e_3,e_2)
| product(e_3,e_3,e_1)
| product(e_3,e_2,e_1)
| spl0_19 ),
inference(forward_subsumption_resolution,[],[f809,f283]) ).
fof(f971,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_3)
| spl0_11 ),
inference(forward_subsumption_resolution,[],[f930,f2]) ).
fof(f972,plain,
( product(e_3,e_2,e_1)
| product(e_3,e_1,e_1)
| product(e_3,e_1,e_2)
| spl0_19 ),
inference(forward_subsumption_resolution,[],[f740,f283]) ).
fof(f974,plain,
( product(e_3,e_3,e_2)
| product(e_3,e_3,e_1)
| product(e_3,e_1,e_2)
| spl0_28 ),
inference(forward_subsumption_resolution,[],[f759,f598]) ).
fof(f975,plain,
( product(e_3,e_1,e_2)
| product(e_2,e_1,e_1)
| product(e_2,e_1,e_2)
| spl0_28 ),
inference(forward_subsumption_resolution,[],[f802,f598]) ).
fof(f976,plain,
( ~ spl0_5
| ~ spl0_29 ),
inference(avatar_split_clause,[],[f826,f606,f87]) ).
fof(f980,plain,
( spl0_20
| spl0_16
| spl0_15
| spl0_19 ),
inference(avatar_split_clause,[],[f969,f282,f191,f195,f286]) ).
fof(f982,plain,
( ~ product(e_3,e_3,e_2)
| product(e_3,e_2,e_1)
| ~ group_element(e_3)
| spl0_11 ),
inference(forward_subsumption_resolution,[],[f971,f25]) ).
fof(f983,plain,
( product(e_3,e_2,e_1)
| product(e_3,e_1,e_2)
| spl0_19
| spl0_28 ),
inference(forward_subsumption_resolution,[],[f972,f598]) ).
fof(f985,plain,
( spl0_7
| spl0_16
| spl0_15
| spl0_28 ),
inference(avatar_split_clause,[],[f974,f596,f191,f195,f125]) ).
fof(f986,plain,
( product(e_3,e_1,e_2)
| product(e_2,e_1,e_1)
| spl0_1
| spl0_28 ),
inference(forward_subsumption_resolution,[],[f975,f60]) ).
fof(f987,plain,
( ~ product(e_3,e_3,e_2)
| ~ group_element(e_3)
| ~ spl0_10
| spl0_11 ),
inference(forward_subsumption_resolution,[],[f982,f663]) ).
fof(f988,plain,
( spl0_7
| spl0_20
| spl0_19
| spl0_28 ),
inference(avatar_split_clause,[],[f983,f596,f282,f286,f125]) ).
fof(f989,plain,
( spl0_32
| spl0_7
| spl0_1
| spl0_28 ),
inference(avatar_split_clause,[],[f986,f596,f58,f125,f763]) ).
fof(f990,plain,
( ~ product(e_3,e_3,e_2)
| ~ spl0_10
| spl0_11 ),
inference(forward_subsumption_resolution,[],[f987,f3]) ).
fof(f991,plain,
( ~ spl0_15
| ~ spl0_10
| spl0_11 ),
inference(avatar_split_clause,[],[f990,f149,f141,f191]) ).
cnf(s7,plain,
( ~ spl0_9
| spl0_10 ),
inference(sat_conversion,[],[f143]) ).
cnf(s8,plain,
( ~ spl0_11
| spl0_12 ),
inference(sat_conversion,[],[f155]) ).
cnf(s21,plain,
( ~ spl0_15
| ~ spl0_19 ),
inference(sat_conversion,[],[f312]) ).
cnf(s23,plain,
( ~ spl0_7
| ~ spl0_15 ),
inference(sat_conversion,[],[f314]) ).
cnf(s26,plain,
( ~ spl0_18
| ~ spl0_20 ),
inference(sat_conversion,[],[f396]) ).
cnf(s29,plain,
( ~ spl0_14
| ~ spl0_20 ),
inference(sat_conversion,[],[f406]) ).
cnf(s37,plain,
( spl0_11
| ~ spl0_19 ),
inference(sat_conversion,[],[f446]) ).
cnf(s40,plain,
( ~ spl0_16
| ~ spl0_27 ),
inference(sat_conversion,[],[f500]) ).
cnf(s43,plain,
( spl0_3
| spl0_7
| ~ spl0_16 ),
inference(sat_conversion,[],[f536]) ).
cnf(s50,plain,
( spl0_5
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f577]) ).
cnf(s53,plain,
( ~ spl0_5
| ~ spl0_17 ),
inference(sat_conversion,[],[f578]) ).
cnf(s57,plain,
( ~ spl0_11
| spl0_17
| spl0_18 ),
inference(sat_conversion,[],[f604]) ).
cnf(s61,plain,
( ~ spl0_12
| ~ spl0_28 ),
inference(sat_conversion,[],[f615]) ).
cnf(s65,plain,
( ~ spl0_5
| ~ spl0_7 ),
inference(sat_conversion,[],[f622]) ).
cnf(s67,plain,
( spl0_9
| ~ spl0_28
| spl0_29 ),
inference(sat_conversion,[],[f624]) ).
cnf(s77,plain,
( ~ spl0_16
| ~ spl0_28 ),
inference(sat_conversion,[],[f633]) ).
cnf(s82,plain,
( ~ spl0_3
| spl0_7
| spl0_28 ),
inference(sat_conversion,[],[f652]) ).
cnf(s83,plain,
( spl0_3
| ~ spl0_28 ),
inference(sat_conversion,[],[f654]) ).
cnf(s87,plain,
( spl0_3
| spl0_5
| spl0_6 ),
inference(sat_conversion,[],[f660]) ).
cnf(s103,plain,
( ~ spl0_1
| ~ spl0_13 ),
inference(sat_conversion,[],[f767]) ).
cnf(s105,plain,
( ~ spl0_1
| ~ spl0_7 ),
inference(sat_conversion,[],[f768]) ).
cnf(s110,plain,
( spl0_1
| ~ spl0_28 ),
inference(sat_conversion,[],[f771]) ).
cnf(s112,plain,
( spl0_1
| spl0_26
| spl0_27
| spl0_32 ),
inference(sat_conversion,[],[f772]) ).
cnf(s120,plain,
( spl0_9
| spl0_17
| spl0_18
| spl0_29 ),
inference(sat_conversion,[],[f813]) ).
cnf(s132,plain,
( spl0_11
| spl0_13
| spl0_14 ),
inference(sat_conversion,[],[f843]) ).
cnf(s133,plain,
( spl0_13
| spl0_14
| spl0_17
| spl0_18 ),
inference(sat_conversion,[],[f845]) ).
cnf(s144,plain,
( ~ spl0_3
| ~ spl0_10 ),
inference(sat_conversion,[],[f949]) ).
cnf(s145,plain,
( ~ spl0_3
| ~ spl0_32 ),
inference(sat_conversion,[],[f950]) ).
cnf(s146,plain,
( spl0_1
| ~ spl0_3
| spl0_32 ),
inference(sat_conversion,[],[f951]) ).
cnf(s155,plain,
( ~ spl0_6
| ~ spl0_32 ),
inference(sat_conversion,[],[f952]) ).
cnf(s159,plain,
( spl0_1
| ~ spl0_26
| spl0_32 ),
inference(sat_conversion,[],[f964]) ).
cnf(s160,plain,
( spl0_3
| ~ spl0_7
| ~ spl0_20 ),
inference(sat_conversion,[],[f965]) ).
cnf(s166,plain,
( ~ spl0_15
| ~ spl0_29 ),
inference(sat_conversion,[],[f967]) ).
cnf(s171,plain,
( ~ spl0_5
| ~ spl0_29 ),
inference(sat_conversion,[],[f976]) ).
cnf(s175,plain,
( spl0_15
| spl0_16
| spl0_19
| spl0_20 ),
inference(sat_conversion,[],[f980]) ).
cnf(s178,plain,
( spl0_7
| spl0_15
| spl0_16
| spl0_28 ),
inference(sat_conversion,[],[f985]) ).
cnf(s179,plain,
( spl0_7
| spl0_19
| spl0_20
| spl0_28 ),
inference(sat_conversion,[],[f988]) ).
cnf(s180,plain,
( spl0_1
| spl0_7
| spl0_28
| spl0_32 ),
inference(sat_conversion,[],[f989]) ).
cnf(s181,plain,
( ~ spl0_10
| spl0_11
| ~ spl0_15 ),
inference(sat_conversion,[],[f991]) ).
cnf(s182,plain,
( spl0_5
| spl0_3
| spl0_1 ),
inference(rat,[],[s50,s8,s37,s175,s40,s112,s160,s23,s159,s180,s155,s87,s110]) ).
cnf(s183,plain,
( spl0_3
| spl0_1 ),
inference(rat,[],[s181,s7,s57,s120,s26,s179,s21,s178,s43,s53,s65,s171,s182,s110]) ).
cnf(s184,plain,
( ~ spl0_3
| spl0_1 ),
inference(rat,[],[s145,s146]) ).
cnf(s185,plain,
spl0_1,
inference(rat,[],[s184,s183]) ).
cnf(s186,plain,
~ spl0_7,
inference(rat,[],[s105,s185]) ).
cnf(s187,plain,
~ spl0_13,
inference(rat,[],[s103,s185]) ).
cnf(s190,plain,
~ spl0_20,
inference(rat,[],[s50,s53,s8,s133,s132,s26,s29,s187]) ).
cnf(s191,plain,
spl0_3,
inference(rat,[],[s21,s178,s179,s43,s83,s186,s190]) ).
cnf(s192,plain,
~ spl0_10,
inference(rat,[],[s144,s191]) ).
cnf(s194,plain,
spl0_28,
inference(rat,[],[s82,s186,s191]) ).
cnf(s196,plain,
~ spl0_9,
inference(rat,[],[s7,s192]) ).
cnf(s197,plain,
~ spl0_16,
inference(rat,[],[s77,s194]) ).
cnf(s198,plain,
~ spl0_12,
inference(rat,[],[s61,s194]) ).
cnf(s199,plain,
spl0_29,
inference(rat,[],[s67,s196,s194]) ).
cnf(s200,plain,
~ spl0_11,
inference(rat,[],[s8,s198]) ).
cnf(s202,plain,
~ spl0_15,
inference(rat,[],[s166,s199]) ).
cnf(s206,plain,
~ spl0_19,
inference(rat,[],[s37,s200]) ).
cnf(s208,plain,
$false,
inference(rat,[],[s175,s197,s190,s202,s206]) ).
fof(f992,plain,
$false,
inference(avatar_sat_refutation,[],[s208]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP130-1.003 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n011.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
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 27 09:27:47 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 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
% 2.72/1.28 % (2144828)Input is clausal, will run a generic CNF schedule.
% 2.72/1.28 % (2144912)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=2184057313:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.72/1.28 % (2144917)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3712635620:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.72/1.28 % (2144913)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3024393326:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.72/1.28 % (2144916)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2433957552:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.72/1.28 % (2144915)lrs+10_1_sil=8000:sp=occurrence:random_seed=3699385545:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.72/1.28 % (2144918)dis-21_1_sil=8000:lcm=predicate:random_seed=2433019236: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)
% 2.72/1.28 % (2144914)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1535752341:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.72/1.28 % (2144917)First to succeed.
% 2.72/1.28 % (2144917)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2144828"
% 2.72/1.28 % (2144918)Also succeeded, but the first one will report.
% 2.72/1.28 % (2144916)Instruction limit reached!
% 2.72/1.28 % (2144916)------------------------------
% 2.72/1.28 % (2144916)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.72/1.28 % (2144916)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.72/1.28 % (2144916)CaDiCaL version: 2.1.3
% 2.72/1.28 % (2144916)Termination reason: Instruction limit
% 2.72/1.28 % (2144916)Termination phase: Saturation
% 2.72/1.28 % (2144916)Time elapsed: 0.059 s
% 2.72/1.28 % (2144916)Peak memory usage: 88 MB
% 2.72/1.28 % (2144916)Instructions burned: 114 (million)
% 2.72/1.28 % (2144915)Instruction limit reached!
% 2.72/1.28 % (2144915)------------------------------
% 2.72/1.28 % (2144915)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.72/1.28 % (2144915)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.72/1.28 % (2144915)CaDiCaL version: 2.1.3
% 2.72/1.28 % (2144915)Termination reason: Instruction limit
% 2.72/1.28 % (2144915)Termination phase: Saturation
% 2.72/1.28 % (2144915)Time elapsed: 0.062 s
% 2.72/1.28 % (2144915)Peak memory usage: 88 MB
% 2.72/1.28 % (2144915)Instructions burned: 108 (million)
% 2.72/1.28 % (2144926)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=2862609086:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 2.72/1.28 % (2144927)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=2267048090: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)
% 2.72/1.28 % (2144927)Refutation not found, incomplete strategy
% 2.72/1.28 % (2144927)------------------------------
% 2.72/1.28 % (2144927)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.72/1.28 % (2144927)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.72/1.28 % (2144927)CaDiCaL version: 2.1.3
% 2.72/1.28 % (2144927)Termination reason: Refutation not found, incomplete strategy
% 2.72/1.28 % (2144927)Time elapsed: 0.001 s
% 2.72/1.28 % (2144927)Peak memory usage: 87 MB
% 2.72/1.28 % (2144926)Also succeeded, but the first one will report.
% 2.72/1.28 % (2144917)Refutation found. Thanks to Tanya!
% 2.72/1.28 % SZS status Unsatisfiable for theBenchmark
% 2.72/1.28 % SZS output start Proof for theBenchmark
% See solution above
% 3.69/1.47 % (2144917)------------------------------
% 3.69/1.47 % (2144917)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.69/1.47 % (2144917)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.69/1.47 % (2144917)CaDiCaL version: 2.1.3
% 3.69/1.47 % (2144917)Termination reason: Refutation
% 3.69/1.47 % (2144917)Time elapsed: 0.029 s
% 3.69/1.47 % (2144917)Peak memory usage: 89 MB
% 3.69/1.47 % (2144917)Instructions burned: 37 (million)
% 3.69/1.47 % (2144917)------------------------------
% 3.69/1.47 % (2144917)------------------------------
% 3.69/1.47 % (2144828)Success in time 0.436 s
% 3.69/1.47 % Vampire exiting
%------------------------------------------------------------------------------