%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP129-4.004 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n008.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 10:12:59 AM UTC 2026
% Result : Unsatisfiable 0.74s 0.94s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 48
% Syntax : Number of formulae : 271 ( 52 unt; 29 def)
% Number of atoms : 709 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 793 ( 355 ~; 409 |; 0 &)
% ( 29 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 33 ( 32 usr; 30 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 119 ( 0 sgn 119 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( product(e_4,X0,X1)
| ~ group_element(X1)
| product(e_1,X0,X1)
| product(e_2,X0,X1)
| product(e_3,X0,X1)
| ~ group_element(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',row_surjectivity) ).
fof(f2,axiom,
! [X0,X1] :
( product(X0,e_4,X1)
| ~ group_element(X1)
| product(X0,e_1,X1)
| product(X0,e_2,X1)
| product(X0,e_3,X1)
| ~ group_element(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',column_surjectivity) ).
fof(f3,negated_conjecture,
! [X2,X3,X0,X1] :
( product(X0,X1,X2)
| ~ product(X2,X0,X3)
| ~ product(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qg3_1) ).
fof(f4,negated_conjecture,
! [X2,X3,X0,X1] :
( product(X0,X1,X2)
| ~ product(X1,X3,X2)
| ~ product(X3,X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qg3_2) ).
fof(f5,axiom,
group_element(e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_1) ).
fof(f6,axiom,
group_element(e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_2) ).
fof(f7,axiom,
group_element(e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_3) ).
fof(f8,axiom,
group_element(e_4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_4) ).
fof(f9,axiom,
~ equalish(e_1,e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_1_is_not_e_2) ).
fof(f10,axiom,
~ equalish(e_1,e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_1_is_not_e_3) ).
fof(f11,axiom,
~ equalish(e_1,e_4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_1_is_not_e_4) ).
fof(f13,axiom,
~ equalish(e_2,e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_2_is_not_e_3) ).
fof(f14,axiom,
~ equalish(e_2,e_4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_2_is_not_e_4) ).
fof(f17,axiom,
~ equalish(e_3,e_4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_3_is_not_e_4) ).
fof(f21,axiom,
! [X0,X1] :
( product(X0,X1,e_4)
| ~ group_element(X1)
| product(X0,X1,e_1)
| product(X0,X1,e_2)
| product(X0,X1,e_3)
| ~ group_element(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_total_function1) ).
fof(f22,axiom,
! [X2,X3,X0,X1] :
( equalish(X2,X3)
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_total_function2) ).
fof(f23,axiom,
! [X2,X3,X0,X1] :
( equalish(X1,X3)
| ~ product(X0,X3,X2)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_right_cancellation) ).
fof(f24,axiom,
! [X2,X3,X0,X1] :
( equalish(X0,X3)
| ~ product(X3,X1,X2)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_left_cancellation) ).
fof(f25,negated_conjecture,
! [X2,X3,X0,X1] :
( product(X2,X0,X3)
| ~ product(X1,X2,X3)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qg3) ).
fof(f26,plain,
! [X0,X1] :
( ~ product(e_2,X0,X1)
| ~ product(e_1,X0,X1) ),
inference(resolution,[],[f9,f24]) ).
fof(f28,plain,
! [X0,X1] :
( ~ product(X0,X1,e_2)
| ~ product(X0,X1,e_1) ),
inference(resolution,[],[f9,f22]) ).
fof(f29,plain,
! [X0,X1] :
( ~ product(e_3,X0,X1)
| ~ product(e_1,X0,X1) ),
inference(resolution,[],[f10,f24]) ).
fof(f31,plain,
! [X0,X1] :
( ~ product(X0,X1,e_3)
| ~ product(X0,X1,e_1) ),
inference(resolution,[],[f10,f22]) ).
fof(f33,plain,
! [X0,X1] :
( ~ product(X0,e_1,X1)
| ~ product(X0,e_4,X1) ),
inference(resolution,[],[f11,f23]) ).
fof(f34,plain,
! [X0,X1] :
( ~ product(X0,X1,e_1)
| ~ product(X0,X1,e_4) ),
inference(resolution,[],[f11,f22]) ).
fof(f38,plain,
! [X0,X1] :
( ~ product(e_3,X0,X1)
| ~ product(e_2,X0,X1) ),
inference(resolution,[],[f13,f24]) ).
fof(f40,plain,
! [X0,X1] :
( ~ product(X0,X1,e_3)
| ~ product(X0,X1,e_2) ),
inference(resolution,[],[f13,f22]) ).
fof(f42,plain,
! [X0,X1] :
( ~ product(X0,e_4,X1)
| ~ product(X0,e_2,X1) ),
inference(resolution,[],[f14,f23]) ).
fof(f43,plain,
! [X0,X1] :
( ~ product(X0,X1,e_4)
| ~ product(X0,X1,e_2) ),
inference(resolution,[],[f14,f22]) ).
fof(f50,plain,
! [X0,X1] :
( ~ product(e_3,X0,X1)
| ~ product(e_4,X0,X1) ),
inference(resolution,[],[f17,f24]) ).
fof(f52,plain,
! [X0,X1] :
( ~ product(X0,X1,e_3)
| ~ product(X0,X1,e_4) ),
inference(resolution,[],[f17,f22]) ).
fof(f62,plain,
! [X2,X0,X1] :
( ~ product(e_1,X0,X1)
| ~ product(X2,e_2,X1)
| ~ product(X0,X2,e_2) ),
inference(resolution,[],[f26,f25]) ).
fof(f64,plain,
! [X2,X0,X1] :
( ~ product(e_1,X0,X1)
| ~ product(X1,e_2,X2)
| ~ product(X0,X1,X2) ),
inference(resolution,[],[f26,f3]) ).
fof(f74,plain,
! [X0] :
( ~ product(e_1,e_2,X0)
| ~ product(e_2,e_1,e_2) ),
inference(factoring,[],[f62]) ).
fof(f77,definition,
( spl0_1
<=> product(e_1,e_2,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f78,plain,
( product(e_1,e_2,e_2)
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f77]) ).
fof(f79,plain,
( ~ product(e_1,e_2,e_2)
| spl0_1 ),
inference(avatar_component_clause,[],[f77]) ).
fof(f81,definition,
( spl0_2
<=> product(e_1,e_1,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f82,plain,
( product(e_1,e_1,e_2)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f81]) ).
fof(f83,plain,
( ~ product(e_1,e_1,e_2)
| spl0_2 ),
inference(avatar_component_clause,[],[f81]) ).
fof(f86,definition,
( spl0_3
<=> product(e_2,e_1,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f88,plain,
( ~ product(e_2,e_1,e_2)
| spl0_3 ),
inference(avatar_component_clause,[],[f86]) ).
fof(f90,definition,
( spl0_4
<=> ! [X0] : ~ product(e_1,e_2,X0) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f91,plain,
( ! [X0] : ~ product(e_1,e_2,X0)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f90]) ).
fof(f92,plain,
( ~ spl0_3
| spl0_4 ),
inference(avatar_split_clause,[],[f74,f90,f86]) ).
fof(f102,plain,
( ! [X0] :
( ~ product(e_2,X0,e_1)
| ~ product(X0,e_1,e_2) )
| spl0_1 ),
inference(resolution,[],[f79,f25]) ).
fof(f107,plain,
! [X2,X0,X1] :
( ~ product(X1,e_2,X2)
| ~ product(e_2,X0,X2)
| ~ product(X0,X1,e_1) ),
inference(resolution,[],[f28,f3]) ).
fof(f109,plain,
! [X0] :
( ~ product(e_4,X0,e_1)
| ~ group_element(e_2)
| product(e_1,X0,e_2)
| product(e_2,X0,e_2)
| product(e_3,X0,e_2)
| ~ group_element(X0) ),
inference(resolution,[],[f28,f1]) ).
fof(f110,plain,
! [X0] :
( ~ group_element(X0)
| product(e_1,X0,e_2)
| product(e_2,X0,e_2)
| product(e_3,X0,e_2)
| ~ product(e_4,X0,e_1) ),
inference(forward_subsumption_resolution,[],[f109,f6]) ).
fof(f116,plain,
! [X2,X0,X1] :
( ~ product(e_1,X0,X1)
| ~ product(X0,X2,X1)
| ~ product(X2,e_3,X0) ),
inference(resolution,[],[f29,f4]) ).
fof(f125,plain,
( ~ product(e_4,e_1,e_2)
| ~ group_element(e_1)
| product(e_2,e_1,e_1)
| product(e_2,e_2,e_1)
| product(e_2,e_3,e_1)
| ~ group_element(e_2)
| spl0_1 ),
inference(resolution,[],[f102,f2]) ).
fof(f126,plain,
( ~ product(e_4,e_1,e_2)
| product(e_2,e_1,e_1)
| product(e_2,e_2,e_1)
| product(e_2,e_3,e_1)
| ~ group_element(e_2)
| spl0_1 ),
inference(forward_subsumption_resolution,[],[f125,f5]) ).
fof(f127,plain,
( ~ product(e_4,e_1,e_2)
| product(e_2,e_1,e_1)
| product(e_2,e_2,e_1)
| product(e_2,e_3,e_1)
| spl0_1 ),
inference(forward_subsumption_resolution,[],[f126,f6]) ).
fof(f129,definition,
( spl0_5
<=> product(e_2,e_3,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f131,plain,
( product(e_2,e_3,e_1)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f129]) ).
fof(f133,definition,
( spl0_6
<=> product(e_2,e_2,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f134,plain,
( ~ product(e_2,e_2,e_1)
| spl0_6 ),
inference(avatar_component_clause,[],[f133]) ).
fof(f137,definition,
( spl0_7
<=> product(e_2,e_1,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f139,plain,
( product(e_2,e_1,e_1)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f137]) ).
fof(f141,definition,
( spl0_8
<=> product(e_4,e_1,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f144,plain,
( spl0_5
| spl0_6
| spl0_7
| ~ spl0_8
| spl0_1 ),
inference(avatar_split_clause,[],[f127,f77,f141,f137,f133,f129]) ).
fof(f166,plain,
! [X2,X0,X1] :
( ~ product(e_3,X0,X2)
| ~ product(X0,X1,e_1)
| ~ product(X1,e_3,X2) ),
inference(resolution,[],[f31,f3]) ).
fof(f187,plain,
! [X2,X0,X1] :
( ~ product(e_1,X2,X1)
| ~ product(X0,e_4,X1)
| ~ product(X2,X0,e_1) ),
inference(resolution,[],[f33,f4]) ).
fof(f199,plain,
! [X0] :
( ~ product(X0,e_4,e_4)
| ~ group_element(e_1)
| product(X0,e_1,e_1)
| product(X0,e_2,e_1)
| product(X0,e_3,e_1)
| ~ group_element(X0) ),
inference(resolution,[],[f34,f2]) ).
fof(f202,plain,
! [X0] :
( ~ group_element(X0)
| product(X0,e_1,e_1)
| product(X0,e_2,e_1)
| product(X0,e_3,e_1)
| ~ product(X0,e_4,e_4) ),
inference(forward_subsumption_resolution,[],[f199,f5]) ).
fof(f217,definition,
( spl0_11
<=> product(e_1,e_1,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f218,plain,
( ~ product(e_1,e_1,e_1)
| spl0_11 ),
inference(avatar_component_clause,[],[f217]) ).
fof(f219,plain,
( product(e_1,e_1,e_1)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f217]) ).
fof(f223,plain,
( ~ product(e_1,e_1,e_1)
| ~ spl0_7 ),
inference(resolution,[],[f139,f26]) ).
fof(f224,plain,
( ~ spl0_11
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f223,f137,f217]) ).
fof(f246,plain,
! [X2,X0,X1] :
( ~ product(e_2,X0,X1)
| ~ product(X0,X2,X1)
| ~ product(X2,e_3,X0) ),
inference(resolution,[],[f38,f4]) ).
fof(f276,plain,
! [X2,X0,X1] :
( ~ product(e_3,X0,X2)
| ~ product(X0,X1,e_2)
| ~ product(X1,e_3,X2) ),
inference(resolution,[],[f40,f3]) ).
fof(f298,plain,
! [X2,X0,X1] :
( ~ product(X0,e_2,X1)
| ~ product(X2,X0,X1)
| ~ product(e_4,X2,X0) ),
inference(resolution,[],[f42,f25]) ).
fof(f311,plain,
! [X2,X0,X1] :
( ~ product(X1,e_4,X2)
| ~ product(e_4,X0,X2)
| ~ product(X0,X1,e_2) ),
inference(resolution,[],[f43,f3]) ).
fof(f318,plain,
( ! [X0] :
( ~ product(e_1,e_1,X0)
| ~ product(e_1,e_1,X0) )
| spl0_11 ),
inference(resolution,[],[f218,f3]) ).
fof(f319,plain,
( ! [X0] : ~ product(e_1,e_1,X0)
| spl0_11 ),
inference(duplicate_literal_removal,[],[f318]) ).
fof(f327,plain,
( ~ group_element(e_1)
| product(e_1,e_1,e_1)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_3)
| ~ group_element(e_1)
| spl0_11 ),
inference(resolution,[],[f319,f21]) ).
fof(f328,plain,
( ~ group_element(e_1)
| product(e_1,e_1,e_1)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_3)
| spl0_11 ),
inference(duplicate_literal_removal,[],[f327]) ).
fof(f329,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_3)
| spl0_11 ),
inference(forward_subsumption_resolution,[],[f328,f5]) ).
fof(f330,plain,
( product(e_1,e_1,e_2)
| product(e_1,e_1,e_3)
| spl0_11 ),
inference(forward_subsumption_resolution,[],[f329,f218]) ).
fof(f336,plain,
( product(e_1,e_1,e_2)
| spl0_11 ),
inference(forward_subsumption_resolution,[],[f330,f319]) ).
fof(f337,plain,
( $false
| spl0_11 ),
inference(forward_subsumption_resolution,[],[f336,f319]) ).
fof(f338,plain,
spl0_11,
inference(avatar_contradiction_clause,[],[f337]) ).
fof(f345,definition,
( spl0_15
<=> product(e_3,e_3,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f357,plain,
( ~ product(e_1,e_1,e_1)
| ~ spl0_2 ),
inference(resolution,[],[f82,f28]) ).
fof(f361,plain,
( ~ spl0_11
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f357,f81,f217]) ).
fof(f373,plain,
! [X2,X0,X1] :
( ~ product(X2,e_3,X0)
| ~ product(X0,X2,X1)
| ~ product(e_4,X0,X1) ),
inference(resolution,[],[f50,f4]) ).
fof(f382,plain,
( ~ group_element(e_2)
| product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_3)
| ~ group_element(e_1)
| ~ spl0_4 ),
inference(resolution,[],[f91,f21]) ).
fof(f383,plain,
( product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_3)
| ~ group_element(e_1)
| ~ spl0_4 ),
inference(forward_subsumption_resolution,[],[f382,f6]) ).
fof(f384,plain,
( product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| ~ group_element(e_1)
| ~ spl0_4 ),
inference(forward_subsumption_resolution,[],[f383,f91]) ).
fof(f385,plain,
( product(e_1,e_2,e_1)
| ~ group_element(e_1)
| ~ spl0_4 ),
inference(forward_subsumption_resolution,[],[f384,f91]) ).
fof(f386,plain,
( ~ group_element(e_1)
| ~ spl0_4 ),
inference(forward_subsumption_resolution,[],[f385,f91]) ).
fof(f387,plain,
( $false
| ~ spl0_4 ),
inference(forward_subsumption_resolution,[],[f386,f5]) ).
fof(f388,plain,
~ spl0_4,
inference(avatar_contradiction_clause,[],[f387]) ).
fof(f397,plain,
( ! [X0] :
( ~ product(e_1,X0,e_2)
| ~ product(X0,e_2,e_1) )
| spl0_3 ),
inference(resolution,[],[f88,f4]) ).
fof(f401,plain,
! [X2,X0,X1] :
( ~ product(e_3,X0,X2)
| ~ product(X0,X1,e_4)
| ~ product(X1,e_3,X2) ),
inference(resolution,[],[f52,f3]) ).
fof(f406,plain,
( ~ product(e_2,e_3,e_4)
| ~ spl0_5 ),
inference(resolution,[],[f131,f34]) ).
fof(f466,definition,
( spl0_18
<=> ! [X0] : ~ product(e_1,e_1,X0) ),
introduced(definition,[new_symbols(definition,[spl0_18])],[avatar_definition]) ).
fof(f467,plain,
( ! [X0] : ~ product(e_1,e_1,X0)
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f466]) ).
fof(f504,plain,
( ~ product(e_1,e_4,e_1)
| ~ spl0_11 ),
inference(resolution,[],[f219,f33]) ).
fof(f544,definition,
( spl0_19
<=> product(e_2,e_3,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_19])],[avatar_definition]) ).
fof(f575,plain,
( ~ product(e_2,e_2,e_1)
| ~ product(e_2,e_2,e_1) ),
inference(factoring,[],[f107]) ).
fof(f576,plain,
~ product(e_2,e_2,e_1),
inference(duplicate_literal_removal,[],[f575]) ).
fof(f612,plain,
! [X0] :
( ~ product(e_1,e_1,X0)
| ~ product(e_1,e_3,e_1) ),
inference(factoring,[],[f116]) ).
fof(f720,plain,
( ~ product(e_3,e_3,e_1)
| ~ product(e_3,e_3,e_1) ),
inference(factoring,[],[f166]) ).
fof(f722,plain,
~ product(e_3,e_3,e_1),
inference(duplicate_literal_removal,[],[f720]) ).
fof(f724,definition,
( spl0_23
<=> product(e_3,e_3,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_23])],[avatar_definition]) ).
fof(f726,plain,
( ~ product(e_3,e_3,e_1)
| spl0_23 ),
inference(avatar_component_clause,[],[f724]) ).
fof(f731,plain,
~ spl0_23,
inference(avatar_split_clause,[],[f722,f724]) ).
fof(f750,definition,
( spl0_26
<=> ! [X0] : ~ product(e_1,e_4,X0) ),
introduced(definition,[new_symbols(definition,[spl0_26])],[avatar_definition]) ).
fof(f751,plain,
( ! [X0] : ~ product(e_1,e_4,X0)
| ~ spl0_26 ),
inference(avatar_component_clause,[],[f750]) ).
fof(f817,plain,
( ~ group_element(e_4)
| product(e_1,e_4,e_1)
| product(e_1,e_4,e_2)
| product(e_1,e_4,e_3)
| ~ group_element(e_1)
| ~ spl0_26 ),
inference(resolution,[],[f751,f21]) ).
fof(f818,plain,
( product(e_1,e_4,e_1)
| product(e_1,e_4,e_2)
| product(e_1,e_4,e_3)
| ~ group_element(e_1)
| ~ spl0_26 ),
inference(forward_subsumption_resolution,[],[f817,f8]) ).
fof(f820,plain,
( product(e_1,e_4,e_2)
| product(e_1,e_4,e_3)
| ~ group_element(e_1)
| ~ spl0_11
| ~ spl0_26 ),
inference(forward_subsumption_resolution,[],[f818,f504]) ).
fof(f827,plain,
( product(e_1,e_4,e_2)
| ~ group_element(e_1)
| ~ spl0_11
| ~ spl0_26 ),
inference(forward_subsumption_resolution,[],[f820,f751]) ).
fof(f828,plain,
( ~ group_element(e_1)
| ~ spl0_11
| ~ spl0_26 ),
inference(forward_subsumption_resolution,[],[f827,f751]) ).
fof(f829,plain,
( $false
| ~ spl0_11
| ~ spl0_26 ),
inference(forward_subsumption_resolution,[],[f828,f5]) ).
fof(f830,plain,
( ~ spl0_11
| ~ spl0_26 ),
inference(avatar_contradiction_clause,[],[f829]) ).
fof(f837,plain,
! [X0] :
( ~ product(e_1,e_4,X0)
| ~ product(e_4,e_1,e_1) ),
inference(factoring,[],[f187]) ).
fof(f858,definition,
( spl0_31
<=> product(e_1,e_3,e_4) ),
introduced(definition,[new_symbols(definition,[spl0_31])],[avatar_definition]) ).
fof(f860,plain,
( product(e_1,e_3,e_4)
| ~ spl0_31 ),
inference(avatar_component_clause,[],[f858]) ).
fof(f969,plain,
! [X0] :
( ~ product(e_2,e_2,X0)
| ~ product(e_2,e_3,e_2) ),
inference(factoring,[],[f246]) ).
fof(f1018,plain,
( ~ product(e_1,e_3,e_2)
| ~ spl0_31 ),
inference(resolution,[],[f860,f43]) ).
fof(f1131,plain,
( ~ product(e_3,e_3,e_2)
| ~ product(e_3,e_3,e_2) ),
inference(factoring,[],[f276]) ).
fof(f1133,plain,
~ product(e_3,e_3,e_2),
inference(duplicate_literal_removal,[],[f1131]) ).
fof(f1135,plain,
~ spl0_15,
inference(avatar_split_clause,[],[f1133,f345]) ).
fof(f1173,definition,
( spl0_40
<=> product(e_4,e_2,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_40])],[avatar_definition]) ).
fof(f1177,definition,
( spl0_41
<=> product(e_4,e_2,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_41])],[avatar_definition]) ).
fof(f1179,plain,
( product(e_4,e_2,e_1)
| ~ spl0_41 ),
inference(avatar_component_clause,[],[f1177]) ).
fof(f1224,definition,
( spl0_45
<=> ! [X0] : ~ product(e_4,e_4,X0) ),
introduced(definition,[new_symbols(definition,[spl0_45])],[avatar_definition]) ).
fof(f1225,plain,
( ! [X0] : ~ product(e_4,e_4,X0)
| ~ spl0_45 ),
inference(avatar_component_clause,[],[f1224]) ).
fof(f1244,definition,
( spl0_46
<=> product(e_1,e_3,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_46])],[avatar_definition]) ).
fof(f1246,plain,
( ~ product(e_1,e_3,e_1)
| spl0_46 ),
inference(avatar_component_clause,[],[f1244]) ).
fof(f1247,plain,
( ~ spl0_46
| spl0_18 ),
inference(avatar_split_clause,[],[f612,f466,f1244]) ).
fof(f1273,plain,
! [X0] :
( ~ product(e_2,e_2,X0)
| ~ product(e_4,e_2,e_2) ),
inference(factoring,[],[f298]) ).
fof(f1277,definition,
( spl0_49
<=> ! [X0] : ~ product(e_2,e_2,X0) ),
introduced(definition,[new_symbols(definition,[spl0_49])],[avatar_definition]) ).
fof(f1278,plain,
( ! [X0] : ~ product(e_2,e_2,X0)
| ~ spl0_49 ),
inference(avatar_component_clause,[],[f1277]) ).
fof(f1279,plain,
( ~ spl0_40
| spl0_49 ),
inference(avatar_split_clause,[],[f1273,f1277,f1173]) ).
fof(f1291,plain,
( ! [X0] :
( ~ product(e_2,e_2,X0)
| ~ product(e_2,e_2,X0) )
| ~ spl0_1 ),
inference(resolution,[],[f78,f64]) ).
fof(f1299,plain,
( ! [X0] : ~ product(e_2,e_2,X0)
| ~ spl0_1 ),
inference(duplicate_literal_removal,[],[f1291]) ).
fof(f1300,plain,
( spl0_49
| ~ spl0_1 ),
inference(avatar_split_clause,[],[f1299,f77,f1277]) ).
fof(f1385,plain,
( ~ product(e_4,e_4,e_2)
| ~ product(e_4,e_4,e_2) ),
inference(factoring,[],[f311]) ).
fof(f1386,plain,
~ product(e_4,e_4,e_2),
inference(duplicate_literal_removal,[],[f1385]) ).
fof(f1417,plain,
( ~ group_element(e_2)
| product(e_2,e_2,e_1)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_3)
| ~ group_element(e_2)
| ~ spl0_49 ),
inference(resolution,[],[f1278,f21]) ).
fof(f1418,plain,
( ~ group_element(e_2)
| product(e_2,e_2,e_1)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_3)
| ~ spl0_49 ),
inference(duplicate_literal_removal,[],[f1417]) ).
fof(f1419,plain,
( product(e_2,e_2,e_1)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_3)
| ~ spl0_49 ),
inference(forward_subsumption_resolution,[],[f1418,f6]) ).
fof(f1420,plain,
( product(e_2,e_2,e_2)
| product(e_2,e_2,e_3)
| spl0_6
| ~ spl0_49 ),
inference(forward_subsumption_resolution,[],[f1419,f134]) ).
fof(f1421,plain,
( product(e_2,e_2,e_2)
| spl0_6
| ~ spl0_49 ),
inference(forward_subsumption_resolution,[],[f1420,f1278]) ).
fof(f1422,plain,
( $false
| spl0_6
| ~ spl0_49 ),
inference(forward_subsumption_resolution,[],[f1421,f1278]) ).
fof(f1423,plain,
( spl0_6
| ~ spl0_49 ),
inference(avatar_contradiction_clause,[],[f1422]) ).
fof(f1465,definition,
( spl0_56
<=> product(e_4,e_3,e_4) ),
introduced(definition,[new_symbols(definition,[spl0_56])],[avatar_definition]) ).
fof(f1466,plain,
( product(e_4,e_3,e_4)
| ~ spl0_56 ),
inference(avatar_component_clause,[],[f1465]) ).
fof(f1467,plain,
( ~ product(e_4,e_3,e_4)
| spl0_56 ),
inference(avatar_component_clause,[],[f1465]) ).
fof(f1476,plain,
( ~ group_element(e_4)
| product(e_4,e_4,e_1)
| product(e_4,e_4,e_2)
| product(e_4,e_4,e_3)
| ~ group_element(e_4)
| ~ spl0_45 ),
inference(resolution,[],[f1225,f21]) ).
fof(f1477,plain,
( ~ group_element(e_4)
| product(e_4,e_4,e_1)
| product(e_4,e_4,e_2)
| product(e_4,e_4,e_3)
| ~ spl0_45 ),
inference(duplicate_literal_removal,[],[f1476]) ).
fof(f1478,plain,
( product(e_4,e_4,e_1)
| product(e_4,e_4,e_2)
| product(e_4,e_4,e_3)
| ~ spl0_45 ),
inference(forward_subsumption_resolution,[],[f1477,f8]) ).
fof(f1481,plain,
( product(e_4,e_4,e_1)
| product(e_4,e_4,e_2)
| ~ spl0_45 ),
inference(forward_subsumption_resolution,[],[f1478,f1225]) ).
fof(f1482,plain,
( product(e_4,e_4,e_1)
| ~ spl0_45 ),
inference(forward_subsumption_resolution,[],[f1481,f1225]) ).
fof(f1483,plain,
( $false
| ~ spl0_45 ),
inference(forward_subsumption_resolution,[],[f1482,f1225]) ).
fof(f1484,plain,
~ spl0_45,
inference(avatar_contradiction_clause,[],[f1483]) ).
fof(f1616,plain,
( ~ product(e_3,e_3,e_4)
| ~ product(e_3,e_3,e_4) ),
inference(factoring,[],[f401]) ).
fof(f1618,plain,
~ product(e_3,e_3,e_4),
inference(duplicate_literal_removal,[],[f1616]) ).
fof(f1620,definition,
( spl0_59
<=> product(e_3,e_3,e_4) ),
introduced(definition,[new_symbols(definition,[spl0_59])],[avatar_definition]) ).
fof(f1624,plain,
~ spl0_59,
inference(avatar_split_clause,[],[f1618,f1620]) ).
fof(f1714,definition,
( spl0_63
<=> product(e_2,e_3,e_4) ),
introduced(definition,[new_symbols(definition,[spl0_63])],[avatar_definition]) ).
fof(f1719,definition,
( spl0_64
<=> product(e_4,e_3,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_64])],[avatar_definition]) ).
fof(f1721,plain,
( product(e_4,e_3,e_2)
| ~ spl0_64 ),
inference(avatar_component_clause,[],[f1719]) ).
fof(f1723,definition,
( spl0_65
<=> product(e_4,e_3,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_65])],[avatar_definition]) ).
fof(f1724,plain,
( ~ product(e_4,e_3,e_1)
| spl0_65 ),
inference(avatar_component_clause,[],[f1723]) ).
fof(f1748,plain,
( product(e_1,e_3,e_2)
| product(e_2,e_3,e_2)
| product(e_3,e_3,e_2)
| ~ product(e_4,e_3,e_1) ),
inference(resolution,[],[f110,f7]) ).
fof(f1758,definition,
( spl0_67
<=> product(e_1,e_3,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_67])],[avatar_definition]) ).
fof(f1759,plain,
( ~ product(e_1,e_3,e_2)
| spl0_67 ),
inference(avatar_component_clause,[],[f1758]) ).
fof(f1766,plain,
( ! [X0] :
( ~ product(e_4,e_4,X0)
| ~ product(e_4,e_4,X0) )
| ~ spl0_56 ),
inference(resolution,[],[f1466,f373]) ).
fof(f1773,plain,
( ! [X0] : ~ product(e_4,e_4,X0)
| ~ spl0_56 ),
inference(duplicate_literal_removal,[],[f1766]) ).
fof(f1776,plain,
( spl0_45
| ~ spl0_56 ),
inference(avatar_split_clause,[],[f1773,f1465,f1224]) ).
fof(f1778,plain,
( ~ spl0_67
| ~ spl0_31 ),
inference(avatar_split_clause,[],[f1018,f858,f1758]) ).
fof(f1836,plain,
( $false
| ~ spl0_11
| ~ spl0_18 ),
inference(resolution,[],[f467,f219]) ).
fof(f1842,plain,
( ~ spl0_11
| ~ spl0_18 ),
inference(avatar_contradiction_clause,[],[f1836]) ).
fof(f1853,plain,
( ~ spl0_19
| spl0_49 ),
inference(avatar_split_clause,[],[f969,f1277,f544]) ).
fof(f1856,plain,
( ~ spl0_65
| spl0_15
| spl0_19
| spl0_67 ),
inference(avatar_split_clause,[],[f1748,f1758,f544,f345,f1723]) ).
fof(f1882,plain,
( ~ group_element(e_4)
| product(e_1,e_3,e_4)
| product(e_2,e_3,e_4)
| product(e_3,e_3,e_4)
| ~ group_element(e_3)
| spl0_56 ),
inference(resolution,[],[f1467,f1]) ).
fof(f1888,plain,
( product(e_1,e_3,e_4)
| product(e_2,e_3,e_4)
| product(e_3,e_3,e_4)
| ~ group_element(e_3)
| spl0_56 ),
inference(forward_subsumption_resolution,[],[f1882,f8]) ).
fof(f1890,plain,
( product(e_1,e_3,e_4)
| product(e_2,e_3,e_4)
| product(e_3,e_3,e_4)
| spl0_56 ),
inference(forward_subsumption_resolution,[],[f1888,f7]) ).
fof(f1892,plain,
( spl0_59
| spl0_63
| spl0_31
| spl0_56 ),
inference(avatar_split_clause,[],[f1890,f1465,f858,f1714,f1620]) ).
fof(f1970,plain,
~ spl0_6,
inference(avatar_split_clause,[],[f576,f133]) ).
fof(f1980,plain,
( ~ spl0_63
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f406,f129,f1714]) ).
fof(f1987,definition,
( spl0_70
<=> product(e_4,e_1,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_70])],[avatar_definition]) ).
fof(f1990,plain,
( ~ spl0_70
| spl0_26 ),
inference(avatar_split_clause,[],[f837,f750,f1987]) ).
fof(f1992,definition,
( spl0_71
<=> product(e_4,e_4,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_71])],[avatar_definition]) ).
fof(f1994,plain,
( ~ product(e_4,e_4,e_2)
| spl0_71 ),
inference(avatar_component_clause,[],[f1992]) ).
fof(f2025,plain,
~ spl0_71,
inference(avatar_split_clause,[],[f1386,f1992]) ).
fof(f2034,definition,
( spl0_72
<=> product(e_4,e_4,e_4) ),
introduced(definition,[new_symbols(definition,[spl0_72])],[avatar_definition]) ).
fof(f2036,plain,
( ~ product(e_4,e_4,e_4)
| spl0_72 ),
inference(avatar_component_clause,[],[f2034]) ).
fof(f2117,plain,
( product(e_4,e_1,e_1)
| product(e_4,e_2,e_1)
| product(e_4,e_3,e_1)
| ~ product(e_4,e_4,e_4) ),
inference(resolution,[],[f202,f8]) ).
fof(f2118,plain,
( ~ spl0_72
| spl0_65
| spl0_41
| spl0_70 ),
inference(avatar_split_clause,[],[f2117,f1987,f1177,f1723,f2034]) ).
fof(f2200,plain,
( ~ group_element(e_2)
| product(e_4,e_1,e_2)
| product(e_4,e_2,e_2)
| product(e_4,e_3,e_2)
| ~ group_element(e_4)
| spl0_71 ),
inference(resolution,[],[f1994,f2]) ).
fof(f2204,plain,
( product(e_4,e_1,e_2)
| product(e_4,e_2,e_2)
| product(e_4,e_3,e_2)
| ~ group_element(e_4)
| spl0_71 ),
inference(forward_subsumption_resolution,[],[f2200,f6]) ).
fof(f2206,plain,
( product(e_4,e_1,e_2)
| product(e_4,e_2,e_2)
| product(e_4,e_3,e_2)
| spl0_71 ),
inference(forward_subsumption_resolution,[],[f2204,f8]) ).
fof(f2208,plain,
( spl0_64
| spl0_40
| spl0_8
| spl0_71 ),
inference(avatar_split_clause,[],[f2206,f1992,f141,f1173,f1719]) ).
fof(f2226,plain,
( ! [X0] :
( ~ product(e_4,e_4,X0)
| ~ product(e_4,e_4,X0) )
| spl0_72 ),
inference(resolution,[],[f2036,f3]) ).
fof(f2227,plain,
( ! [X0] : ~ product(e_4,e_4,X0)
| spl0_72 ),
inference(duplicate_literal_removal,[],[f2226]) ).
fof(f2231,plain,
( spl0_45
| spl0_72 ),
inference(avatar_split_clause,[],[f2227,f2034,f1224]) ).
fof(f2622,plain,
( ~ product(e_4,e_3,e_1)
| ~ spl0_64 ),
inference(resolution,[],[f1721,f28]) ).
fof(f2640,plain,
( ~ spl0_65
| ~ spl0_64 ),
inference(avatar_split_clause,[],[f2622,f1719,f1723]) ).
fof(f2652,plain,
( ~ group_element(e_1)
| product(e_1,e_3,e_1)
| product(e_2,e_3,e_1)
| product(e_3,e_3,e_1)
| ~ group_element(e_3)
| spl0_65 ),
inference(resolution,[],[f1724,f1]) ).
fof(f2656,plain,
( product(e_1,e_3,e_1)
| product(e_2,e_3,e_1)
| product(e_3,e_3,e_1)
| ~ group_element(e_3)
| spl0_65 ),
inference(forward_subsumption_resolution,[],[f2652,f5]) ).
fof(f2657,plain,
( product(e_2,e_3,e_1)
| product(e_3,e_3,e_1)
| ~ group_element(e_3)
| spl0_46
| spl0_65 ),
inference(forward_subsumption_resolution,[],[f2656,f1246]) ).
fof(f2658,plain,
( product(e_2,e_3,e_1)
| ~ group_element(e_3)
| spl0_23
| spl0_46
| spl0_65 ),
inference(forward_subsumption_resolution,[],[f2657,f726]) ).
fof(f2659,plain,
( product(e_2,e_3,e_1)
| spl0_23
| spl0_46
| spl0_65 ),
inference(forward_subsumption_resolution,[],[f2658,f7]) ).
fof(f2660,plain,
( spl0_5
| spl0_23
| spl0_46
| spl0_65 ),
inference(avatar_split_clause,[],[f2659,f1723,f1244,f724,f129]) ).
fof(f3088,plain,
( ~ product(e_4,e_2,e_1)
| ~ group_element(e_2)
| product(e_1,e_1,e_2)
| product(e_1,e_2,e_2)
| product(e_1,e_3,e_2)
| ~ group_element(e_1)
| spl0_3 ),
inference(resolution,[],[f397,f2]) ).
fof(f3089,plain,
( ~ group_element(e_2)
| product(e_1,e_1,e_2)
| product(e_1,e_2,e_2)
| product(e_1,e_3,e_2)
| ~ group_element(e_1)
| spl0_3
| ~ spl0_41 ),
inference(forward_subsumption_resolution,[],[f3088,f1179]) ).
fof(f3092,plain,
( product(e_1,e_1,e_2)
| product(e_1,e_2,e_2)
| product(e_1,e_3,e_2)
| ~ group_element(e_1)
| spl0_3
| ~ spl0_41 ),
inference(forward_subsumption_resolution,[],[f3089,f6]) ).
fof(f3093,plain,
( product(e_1,e_2,e_2)
| product(e_1,e_3,e_2)
| ~ group_element(e_1)
| spl0_2
| spl0_3
| ~ spl0_41 ),
inference(forward_subsumption_resolution,[],[f3092,f83]) ).
fof(f3094,plain,
( product(e_1,e_3,e_2)
| ~ group_element(e_1)
| spl0_1
| spl0_2
| spl0_3
| ~ spl0_41 ),
inference(forward_subsumption_resolution,[],[f3093,f79]) ).
fof(f3095,plain,
( ~ group_element(e_1)
| spl0_1
| spl0_2
| spl0_3
| ~ spl0_41
| spl0_67 ),
inference(forward_subsumption_resolution,[],[f3094,f1759]) ).
fof(f3096,plain,
( $false
| spl0_1
| spl0_2
| spl0_3
| ~ spl0_41
| spl0_67 ),
inference(forward_subsumption_resolution,[],[f3095,f5]) ).
fof(f3097,plain,
( spl0_1
| spl0_2
| spl0_3
| ~ spl0_41
| spl0_67 ),
inference(avatar_contradiction_clause,[],[f3096]) ).
cnf(s2,plain,
( ~ spl0_3
| spl0_4 ),
inference(sat_conversion,[],[f92]) ).
cnf(s3,plain,
( spl0_1
| spl0_5
| spl0_6
| spl0_7
| ~ spl0_8 ),
inference(sat_conversion,[],[f144]) ).
cnf(s7,plain,
( ~ spl0_7
| ~ spl0_11 ),
inference(sat_conversion,[],[f224]) ).
cnf(s14,plain,
spl0_11,
inference(sat_conversion,[],[f338]) ).
cnf(s19,plain,
( ~ spl0_2
| ~ spl0_11 ),
inference(sat_conversion,[],[f361]) ).
cnf(s23,plain,
~ spl0_4,
inference(sat_conversion,[],[f388]) ).
cnf(s40,plain,
~ spl0_23,
inference(sat_conversion,[],[f731]) ).
cnf(s49,plain,
( ~ spl0_11
| ~ spl0_26 ),
inference(sat_conversion,[],[f830]) ).
cnf(s70,plain,
~ spl0_15,
inference(sat_conversion,[],[f1135]) ).
cnf(s83,plain,
( spl0_18
| ~ spl0_46 ),
inference(sat_conversion,[],[f1247]) ).
cnf(s92,plain,
( ~ spl0_40
| spl0_49 ),
inference(sat_conversion,[],[f1279]) ).
cnf(s93,plain,
( ~ spl0_1
| spl0_49 ),
inference(sat_conversion,[],[f1300]) ).
cnf(s107,plain,
( spl0_6
| ~ spl0_49 ),
inference(sat_conversion,[],[f1423]) ).
cnf(s113,plain,
~ spl0_45,
inference(sat_conversion,[],[f1484]) ).
cnf(s127,plain,
~ spl0_59,
inference(sat_conversion,[],[f1624]) ).
cnf(s149,plain,
( spl0_45
| ~ spl0_56 ),
inference(sat_conversion,[],[f1776]) ).
cnf(s151,plain,
( ~ spl0_31
| ~ spl0_67 ),
inference(sat_conversion,[],[f1778]) ).
cnf(s163,plain,
( ~ spl0_11
| ~ spl0_18 ),
inference(sat_conversion,[],[f1842]) ).
cnf(s166,plain,
( ~ spl0_19
| spl0_49 ),
inference(sat_conversion,[],[f1853]) ).
cnf(s168,plain,
( spl0_15
| spl0_19
| ~ spl0_65
| spl0_67 ),
inference(sat_conversion,[],[f1856]) ).
cnf(s186,plain,
( spl0_31
| spl0_56
| spl0_59
| spl0_63 ),
inference(sat_conversion,[],[f1892]) ).
cnf(s206,plain,
~ spl0_6,
inference(sat_conversion,[],[f1970]) ).
cnf(s214,plain,
( ~ spl0_5
| ~ spl0_63 ),
inference(sat_conversion,[],[f1980]) ).
cnf(s232,plain,
( spl0_26
| ~ spl0_70 ),
inference(sat_conversion,[],[f1990]) ).
cnf(s247,plain,
~ spl0_71,
inference(sat_conversion,[],[f2025]) ).
cnf(s265,plain,
( spl0_41
| spl0_65
| spl0_70
| ~ spl0_72 ),
inference(sat_conversion,[],[f2118]) ).
cnf(s282,plain,
( spl0_8
| spl0_40
| spl0_64
| spl0_71 ),
inference(sat_conversion,[],[f2208]) ).
cnf(s287,plain,
( spl0_45
| spl0_72 ),
inference(sat_conversion,[],[f2231]) ).
cnf(s340,plain,
( ~ spl0_64
| ~ spl0_65 ),
inference(sat_conversion,[],[f2640]) ).
cnf(s341,plain,
( spl0_5
| spl0_23
| spl0_46
| spl0_65 ),
inference(sat_conversion,[],[f2660]) ).
cnf(s359,plain,
( spl0_1
| spl0_2
| spl0_3
| ~ spl0_41
| spl0_67 ),
inference(sat_conversion,[],[f3097]) ).
cnf(s362,plain,
spl0_72,
inference(rat,[],[s287,s113]) ).
cnf(s364,plain,
~ spl0_56,
inference(rat,[],[s149,s113]) ).
cnf(s365,plain,
~ spl0_49,
inference(rat,[],[s107,s206]) ).
cnf(s370,plain,
~ spl0_19,
inference(rat,[],[s166,s365]) ).
cnf(s374,plain,
~ spl0_1,
inference(rat,[],[s93,s365]) ).
cnf(s375,plain,
~ spl0_40,
inference(rat,[],[s92,s365]) ).
cnf(s392,plain,
~ spl0_18,
inference(rat,[],[s163,s14]) ).
cnf(s394,plain,
~ spl0_26,
inference(rat,[],[s49,s14]) ).
cnf(s395,plain,
~ spl0_2,
inference(rat,[],[s19,s14]) ).
cnf(s396,plain,
~ spl0_46,
inference(rat,[],[s83,s392]) ).
cnf(s397,plain,
~ spl0_70,
inference(rat,[],[s232,s394]) ).
cnf(s401,plain,
~ spl0_7,
inference(rat,[],[s7,s14]) ).
cnf(s403,plain,
( spl0_5
| ~ spl0_8 ),
inference(rat,[],[s3,s401,s206,s374]) ).
cnf(s404,plain,
~ spl0_3,
inference(rat,[],[s2,s23]) ).
cnf(s406,plain,
spl0_5,
inference(rat,[],[s282,s340,s403,s341,s375,s247,s40,s396]) ).
cnf(s408,plain,
~ spl0_63,
inference(rat,[],[s214,s406]) ).
cnf(s411,plain,
spl0_31,
inference(rat,[],[s186,s364,s127,s408]) ).
cnf(s416,plain,
~ spl0_67,
inference(rat,[],[s151,s411]) ).
cnf(s422,plain,
~ spl0_65,
inference(rat,[],[s168,s70,s370,s416]) ).
cnf(s423,plain,
~ spl0_41,
inference(rat,[],[s359,s404,s395,s374,s416]) ).
cnf(s430,plain,
$false,
inference(rat,[],[s265,s362,s397,s422,s423]) ).
fof(f3098,plain,
$false,
inference(avatar_sat_refutation,[],[s430]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP129-4.004 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n008.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sun Sep 27 09:28:27 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 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
% 0.74/0.94 % (970677)Input is clausal, will run a generic CNF schedule.
% 0.74/0.94 % (970687)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=671268413:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 0.74/0.94 % (970684)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2674579892:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 0.74/0.94 % (970686)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1426788959:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 0.74/0.94 % (970688)dis-21_1_sil=8000:lcm=predicate:random_seed=2952988624: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)
% 0.74/0.94 % (970682)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=2159686836:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 0.74/0.94 % (970683)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2682694042:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 0.74/0.94 % (970685)lrs+10_1_sil=8000:sp=occurrence:random_seed=943081754:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 0.74/0.94 % (970685)Refutation not found, incomplete strategy
% 0.74/0.94 % (970685)------------------------------
% 0.74/0.94 % (970685)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.74/0.94 % (970685)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.94 % (970685)CaDiCaL version: 2.1.3
% 0.74/0.94 % (970685)Termination reason: Refutation not found, incomplete strategy
% 0.74/0.94 % (970685)Time elapsed: 0.001 s
% 0.74/0.94 % (970685)Peak memory usage: 87 MB
% 0.74/0.94 % (970687)First to succeed.
% 0.74/0.94 % (970687)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-970677"
% 0.74/0.94 % (970686)Instruction limit reached!
% 0.74/0.94 % (970686)------------------------------
% 0.74/0.94 % (970686)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.74/0.94 % (970686)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.94 % (970686)CaDiCaL version: 2.1.3
% 0.74/0.94 % (970686)Termination reason: Instruction limit
% 0.74/0.94 % (970686)Termination phase: Saturation
% 0.74/0.94 % (970686)Time elapsed: 0.057 s
% 0.74/0.94 % (970686)Peak memory usage: 87 MB
% 0.74/0.94 % (970686)Instructions burned: 115 (million)
% 0.74/0.94 % (970688)Instruction limit reached!
% 0.74/0.94 % (970688)------------------------------
% 0.74/0.94 % (970688)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.74/0.94 % (970688)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.94 % (970688)CaDiCaL version: 2.1.3
% 0.74/0.94 % (970688)Termination reason: Instruction limit
% 0.74/0.94 % (970688)Termination phase: Saturation
% 0.74/0.94 % (970688)Time elapsed: 0.072 s
% 0.74/0.94 % (970688)Peak memory usage: 89 MB
% 0.74/0.94 % (970688)Instructions burned: 117 (million)
% 0.74/0.94 % (970687)Refutation found. Thanks to Tanya!
% 0.74/0.94 % SZS status Unsatisfiable for theBenchmark
% 0.74/0.94 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/1.03 % (970687)------------------------------
% 0.17/1.03 % (970687)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.17/1.03 % (970687)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/1.03 % (970687)CaDiCaL version: 2.1.3
% 0.17/1.03 % (970687)Termination reason: Refutation
% 0.17/1.03 % (970687)Time elapsed: 0.042 s
% 0.17/1.03 % (970687)Peak memory usage: 90 MB
% 0.17/1.03 % (970687)Instructions burned: 125 (million)
% 0.17/1.03 % (970687)------------------------------
% 0.17/1.03 % (970687)------------------------------
% 0.17/1.03 % (970677)Success in time 0.321 s
% 0.17/1.03 % Vampire exiting
%------------------------------------------------------------------------------