%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP130-3.003 : 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 : n016.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 1.86s 1.30s
% Output : Refutation 3.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 32
% Syntax : Number of formulae : 281 ( 22 unt; 21 def)
% Number of atoms : 809 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 912 ( 384 ~; 507 |; 0 &)
% ( 21 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 25 ( 24 usr; 22 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 102 ( 0 sgn 102 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f17,axiom,
group_element(e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_1) ).
fof(f18,axiom,
group_element(e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_2) ).
fof(f19,axiom,
group_element(e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_3) ).
fof(f20,axiom,
~ equalish(e_1,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_1_is_not_e_2) ).
fof(f21,axiom,
~ equalish(e_1,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_1_is_not_e_3) ).
fof(f23,axiom,
~ equalish(e_2,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_2_is_not_e_3) ).
fof(f26,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(f27,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(f28,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(f29,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(f30,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(f35,plain,
! [X0,X1] :
( ~ product(e_2,X0,X1)
| ~ product(e_1,X0,X1) ),
inference(resolution,[],[f20,f29]) ).
fof(f36,plain,
! [X0,X1] :
( ~ product(X0,e_2,X1)
| ~ product(X0,e_1,X1) ),
inference(resolution,[],[f20,f28]) ).
fof(f38,plain,
! [X0,X1] :
( ~ product(e_3,X0,X1)
| ~ product(e_1,X0,X1) ),
inference(resolution,[],[f21,f29]) ).
fof(f39,plain,
! [X0,X1] :
( ~ product(X0,e_3,X1)
| ~ product(X0,e_1,X1) ),
inference(resolution,[],[f21,f28]) ).
fof(f44,plain,
! [X0,X1] :
( ~ product(e_3,X0,X1)
| ~ product(e_2,X0,X1) ),
inference(resolution,[],[f23,f29]) ).
fof(f45,plain,
! [X0,X1] :
( ~ product(X0,e_3,X1)
| ~ product(X0,e_2,X1) ),
inference(resolution,[],[f23,f28]) ).
fof(f46,plain,
! [X0,X1] :
( ~ product(X0,X1,e_2)
| ~ product(X0,X1,e_3) ),
inference(resolution,[],[f23,f27]) ).
fof(f71,plain,
! [X2,X0,X1] :
( ~ product(X1,X2,e_2)
| ~ product(e_1,X0,X1)
| ~ product(X1,X0,X2) ),
inference(resolution,[],[f35,f30]) ).
fof(f72,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,[],[f35,f26]) ).
fof(f73,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,[],[f72,f18]) ).
fof(f74,plain,
! [X2,X0,X1] :
( ~ product(X1,e_2,X2)
| ~ product(X1,X2,X0)
| ~ product(X0,e_1,X1) ),
inference(resolution,[],[f36,f30]) ).
fof(f75,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,[],[f36,f26]) ).
fof(f76,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,[],[f75,f18]) ).
fof(f81,plain,
! [X2,X0,X1] :
( ~ product(e_1,X0,X1)
| ~ product(X1,X2,e_3)
| ~ product(X1,X0,X2) ),
inference(resolution,[],[f38,f30]) ).
fof(f82,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,[],[f38,f26]) ).
fof(f83,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,[],[f82,f19]) ).
fof(f86,plain,
! [X0] :
( ~ product(X0,e_2,e_2)
| ~ product(e_2,e_1,X0) ),
inference(factoring,[],[f74]) ).
fof(f89,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,[],[f39,f26]) ).
fof(f90,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,[],[f89,f19]) ).
fof(f91,plain,
! [X0,X1] :
( ~ product(e_2,e_1,X0)
| ~ product(e_2,X1,X0)
| ~ product(e_2,e_2,X1) ),
inference(resolution,[],[f86,f30]) ).
fof(f96,definition,
( spl0_3
<=> product(e_2,e_1,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f98,plain,
( ~ product(e_2,e_1,e_2)
| spl0_3 ),
inference(avatar_component_clause,[],[f96]) ).
fof(f107,plain,
! [X0] :
( ~ product(e_1,X0,e_1)
| ~ product(e_1,e_1,e_3) ),
inference(factoring,[],[f81]) ).
fof(f109,definition,
( spl0_5
<=> product(e_1,e_1,e_3) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f110,plain,
( product(e_1,e_1,e_3)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f109]) ).
fof(f111,plain,
( ~ product(e_1,e_1,e_3)
| spl0_5 ),
inference(avatar_component_clause,[],[f109]) ).
fof(f113,definition,
( spl0_6
<=> ! [X0] : ~ product(e_1,X0,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f114,plain,
( ! [X0] : ~ product(e_1,X0,e_1)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f113]) ).
fof(f115,plain,
( ~ spl0_5
| spl0_6 ),
inference(avatar_split_clause,[],[f107,f113,f109]) ).
fof(f117,plain,
! [X2,X0,X1] :
( ~ product(e_2,X0,X1)
| ~ product(X1,X2,e_3)
| ~ product(X1,X0,X2) ),
inference(resolution,[],[f44,f30]) ).
fof(f118,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,[],[f44,f26]) ).
fof(f119,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,[],[f118,f19]) ).
fof(f125,definition,
( spl0_7
<=> product(e_1,e_1,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f127,plain,
( product(e_1,e_1,e_2)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f125]) ).
fof(f129,definition,
( spl0_8
<=> product(e_1,e_1,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f133,plain,
! [X2,X0,X1] :
( ~ product(X0,e_2,X1)
| ~ product(X1,X2,X0)
| ~ product(X1,e_3,X2) ),
inference(resolution,[],[f45,f30]) ).
fof(f134,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,[],[f45,f26]) ).
fof(f135,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,[],[f134,f19]) ).
fof(f137,plain,
! [X2,X0,X1] :
( ~ product(e_2,X2,X0)
| ~ product(X0,X1,e_3)
| ~ product(e_2,X1,X2) ),
inference(resolution,[],[f46,f30]) ).
fof(f144,definition,
( spl0_9
<=> product(e_3,e_1,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f146,plain,
( product(e_3,e_1,e_2)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f144]) ).
fof(f148,definition,
( spl0_10
<=> product(e_3,e_1,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f149,plain,
( ~ product(e_3,e_1,e_1)
| spl0_10 ),
inference(avatar_component_clause,[],[f148]) ).
fof(f161,definition,
( spl0_12
<=> product(e_3,e_3,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f162,plain,
( ~ product(e_3,e_3,e_2)
| spl0_12 ),
inference(avatar_component_clause,[],[f161]) ).
fof(f163,plain,
( product(e_3,e_3,e_2)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f161]) ).
fof(f165,definition,
( spl0_13
<=> product(e_3,e_3,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f167,plain,
( product(e_3,e_3,e_1)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f165]) ).
fof(f170,plain,
( ! [X0] :
( ~ product(e_3,X0,e_1)
| ~ product(e_3,e_1,X0) )
| spl0_5 ),
inference(resolution,[],[f111,f30]) ).
fof(f177,plain,
( ! [X0] :
( ~ product(e_1,X0,e_1)
| ~ product(e_1,X0,e_1) )
| ~ spl0_7 ),
inference(resolution,[],[f127,f71]) ).
fof(f179,plain,
( ! [X0] : ~ product(e_1,X0,e_1)
| ~ spl0_7 ),
inference(duplicate_literal_removal,[],[f177]) ).
fof(f189,definition,
( spl0_14
<=> product(e_2,e_3,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f191,plain,
( product(e_2,e_3,e_2)
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f189]) ).
fof(f193,definition,
( spl0_15
<=> product(e_2,e_3,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f195,plain,
( product(e_2,e_3,e_1)
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f193]) ).
fof(f210,plain,
( ~ product(e_3,e_1,e_2)
| ~ spl0_12 ),
inference(resolution,[],[f163,f39]) ).
fof(f211,plain,
( ~ spl0_9
| ~ spl0_12 ),
inference(avatar_split_clause,[],[f210,f161,f144]) ).
fof(f224,plain,
( ~ product(e_3,e_1,e_1)
| spl0_5 ),
inference(factoring,[],[f170]) ).
fof(f225,plain,
( ~ spl0_10
| spl0_5 ),
inference(avatar_split_clause,[],[f224,f109,f148]) ).
fof(f245,definition,
( spl0_16
<=> product(e_2,e_1,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition]) ).
fof(f246,plain,
( ~ product(e_2,e_1,e_1)
| spl0_16 ),
inference(avatar_component_clause,[],[f245]) ).
fof(f247,plain,
( product(e_2,e_1,e_1)
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f245]) ).
fof(f255,plain,
! [X0] :
( ~ product(e_2,X0,e_2)
| ~ product(e_2,e_2,e_3) ),
inference(factoring,[],[f117]) ).
fof(f257,definition,
( spl0_18
<=> product(e_2,e_2,e_3) ),
introduced(definition,[new_symbols(definition,[spl0_18])],[avatar_definition]) ).
fof(f258,plain,
( product(e_2,e_2,e_3)
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f257]) ).
fof(f259,plain,
( ~ product(e_2,e_2,e_3)
| spl0_18 ),
inference(avatar_component_clause,[],[f257]) ).
fof(f261,definition,
( spl0_19
<=> ! [X0] : ~ product(e_2,X0,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_19])],[avatar_definition]) ).
fof(f262,plain,
( ! [X0] : ~ product(e_2,X0,e_2)
| ~ spl0_19 ),
inference(avatar_component_clause,[],[f261]) ).
fof(f263,plain,
( ~ spl0_18
| spl0_19 ),
inference(avatar_split_clause,[],[f255,f261,f257]) ).
fof(f270,definition,
( spl0_20
<=> product(e_2,e_2,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_20])],[avatar_definition]) ).
fof(f272,plain,
( product(e_2,e_2,e_2)
| ~ spl0_20 ),
inference(avatar_component_clause,[],[f270]) ).
fof(f274,definition,
( spl0_21
<=> product(e_2,e_2,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_21])],[avatar_definition]) ).
fof(f276,plain,
( product(e_2,e_2,e_1)
| ~ spl0_21 ),
inference(avatar_component_clause,[],[f274]) ).
fof(f280,plain,
! [X0] :
( ~ product(X0,e_3,e_2)
| ~ product(X0,e_2,X0) ),
inference(factoring,[],[f133]) ).
fof(f284,plain,
( ~ product(e_1,e_2,e_3)
| ~ spl0_18 ),
inference(resolution,[],[f258,f35]) ).
fof(f287,plain,
( ~ product(e_2,e_1,e_3)
| ~ spl0_18 ),
inference(resolution,[],[f258,f36]) ).
fof(f291,plain,
! [X0] :
( ~ product(X0,X0,e_3)
| ~ product(e_2,X0,X0) ),
inference(factoring,[],[f137]) ).
fof(f294,plain,
( ~ group_element(e_2)
| product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| ~ group_element(e_1)
| ~ spl0_18 ),
inference(resolution,[],[f284,f26]) ).
fof(f296,plain,
( product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| ~ group_element(e_1)
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f294,f18]) ).
fof(f297,plain,
( product(e_1,e_2,e_2)
| ~ group_element(e_1)
| ~ spl0_6
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f296,f114]) ).
fof(f298,plain,
( product(e_1,e_2,e_2)
| ~ spl0_6
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f297,f17]) ).
fof(f300,plain,
( ~ group_element(e_1)
| product(e_2,e_1,e_1)
| product(e_2,e_1,e_2)
| ~ group_element(e_2)
| ~ spl0_18 ),
inference(resolution,[],[f287,f26]) ).
fof(f302,plain,
( product(e_2,e_1,e_1)
| product(e_2,e_1,e_2)
| ~ group_element(e_2)
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f300,f17]) ).
fof(f303,plain,
( product(e_2,e_1,e_1)
| ~ group_element(e_2)
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_subsumption_resolution,[],[f302,f262]) ).
fof(f304,plain,
( product(e_2,e_1,e_1)
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_subsumption_resolution,[],[f303,f18]) ).
fof(f305,plain,
( spl0_16
| ~ spl0_18
| ~ spl0_19 ),
inference(avatar_split_clause,[],[f304,f261,f257,f245]) ).
fof(f311,plain,
( ~ product(e_2,e_1,e_1)
| ~ spl0_6
| ~ spl0_18 ),
inference(resolution,[],[f298,f86]) ).
fof(f322,plain,
( ~ spl0_16
| ~ spl0_6
| ~ spl0_18 ),
inference(avatar_split_clause,[],[f311,f257,f113,f245]) ).
fof(f323,plain,
( spl0_6
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f179,f125,f113]) ).
fof(f335,definition,
( spl0_24
<=> product(e_1,e_2,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_24])],[avatar_definition]) ).
fof(f339,definition,
( spl0_25
<=> product(e_1,e_2,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_25])],[avatar_definition]) ).
fof(f340,plain,
( ~ product(e_1,e_2,e_1)
| spl0_25 ),
inference(avatar_component_clause,[],[f339]) ).
fof(f346,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,[],[f73,f26]) ).
fof(f347,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,[],[f73,f30]) ).
fof(f348,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,[],[f346]) ).
fof(f349,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,[],[f348,f17]) ).
fof(f350,plain,
( ~ group_element(e_2)
| product(e_2,e_2,e_1)
| product(e_2,e_2,e_2)
| ~ group_element(e_2)
| spl0_18 ),
inference(resolution,[],[f259,f26]) ).
fof(f352,plain,
( ~ group_element(e_2)
| product(e_2,e_2,e_1)
| product(e_2,e_2,e_2)
| spl0_18 ),
inference(duplicate_literal_removal,[],[f350]) ).
fof(f353,plain,
( product(e_2,e_2,e_1)
| product(e_2,e_2,e_2)
| spl0_18 ),
inference(forward_subsumption_resolution,[],[f352,f18]) ).
fof(f354,plain,
( spl0_20
| spl0_21
| spl0_18 ),
inference(avatar_split_clause,[],[f353,f257,f274,f270]) ).
fof(f355,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,[],[f76,f26]) ).
fof(f357,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,[],[f355]) ).
fof(f358,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,[],[f357,f17]) ).
fof(f360,plain,
! [X0] :
( ~ group_element(X0)
| product(e_3,X0,e_1)
| product(e_3,X0,e_2)
| ~ group_element(X0)
| product(e_1,X0,e_1)
| product(e_1,X0,e_2)
| ~ group_element(e_1) ),
inference(resolution,[],[f83,f26]) ).
fof(f362,plain,
! [X0] :
( ~ group_element(X0)
| product(e_3,X0,e_1)
| product(e_3,X0,e_2)
| product(e_1,X0,e_1)
| product(e_1,X0,e_2)
| ~ group_element(e_1) ),
inference(duplicate_literal_removal,[],[f360]) ).
fof(f363,plain,
! [X0] :
( ~ group_element(X0)
| product(e_3,X0,e_1)
| product(e_3,X0,e_2)
| product(e_1,X0,e_1)
| product(e_1,X0,e_2) ),
inference(forward_subsumption_resolution,[],[f362,f17]) ).
fof(f365,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,[],[f90,f26]) ).
fof(f367,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,[],[f365]) ).
fof(f368,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,[],[f367,f17]) ).
fof(f372,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,[],[f119,f26]) ).
fof(f374,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,[],[f372]) ).
fof(f375,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,[],[f374,f18]) ).
fof(f377,plain,
( ~ product(e_2,e_1,e_2)
| ~ spl0_20 ),
inference(resolution,[],[f272,f86]) ).
fof(f390,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,[],[f135,f26]) ).
fof(f391,plain,
! [X0,X1] :
( ~ product(e_3,e_2,X1)
| product(X0,e_3,e_2)
| ~ group_element(X0)
| ~ product(e_3,X1,X0)
| product(X0,e_3,e_1) ),
inference(resolution,[],[f135,f30]) ).
fof(f392,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,[],[f390]) ).
fof(f393,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,[],[f392,f18]) ).
fof(f421,plain,
( ~ product(e_1,e_1,e_1)
| ~ spl0_16 ),
inference(resolution,[],[f247,f35]) ).
fof(f450,plain,
( ~ product(e_2,e_3,e_1)
| ~ spl0_13 ),
inference(resolution,[],[f167,f44]) ).
fof(f455,plain,
( ~ spl0_15
| ~ spl0_13 ),
inference(avatar_split_clause,[],[f450,f165,f193]) ).
fof(f463,plain,
( ~ product(e_2,e_2,e_2)
| ~ spl0_14 ),
inference(resolution,[],[f191,f280]) ).
fof(f472,plain,
( ~ product(e_2,e_2,e_2)
| ~ spl0_14 ),
inference(resolution,[],[f191,f45]) ).
fof(f473,plain,
( ~ product(e_2,e_1,e_2)
| ~ spl0_14 ),
inference(resolution,[],[f191,f39]) ).
fof(f475,plain,
( $false
| ~ spl0_14
| ~ spl0_20 ),
inference(forward_subsumption_resolution,[],[f472,f272]) ).
fof(f476,plain,
( ~ spl0_14
| ~ spl0_20 ),
inference(avatar_contradiction_clause,[],[f475]) ).
fof(f535,plain,
( ~ product(e_2,e_2,e_1)
| ~ spl0_15 ),
inference(resolution,[],[f195,f45]) ).
fof(f536,plain,
( ~ product(e_2,e_1,e_1)
| ~ spl0_15 ),
inference(resolution,[],[f195,f39]) ).
fof(f562,definition,
( spl0_32
<=> product(e_3,e_2,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_32])],[avatar_definition]) ).
fof(f564,plain,
( product(e_3,e_2,e_1)
| ~ spl0_32 ),
inference(avatar_component_clause,[],[f562]) ).
fof(f575,definition,
( spl0_35
<=> product(e_3,e_2,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_35])],[avatar_definition]) ).
fof(f576,plain,
( ~ product(e_3,e_2,e_2)
| spl0_35 ),
inference(avatar_component_clause,[],[f575]) ).
fof(f577,plain,
( product(e_3,e_2,e_2)
| ~ spl0_35 ),
inference(avatar_component_clause,[],[f575]) ).
fof(f586,plain,
( ~ group_element(e_1)
| product(e_2,e_1,e_1)
| product(e_2,e_1,e_2)
| ~ spl0_5 ),
inference(resolution,[],[f110,f73]) ).
fof(f589,plain,
( ~ product(e_2,e_1,e_1)
| ~ spl0_5 ),
inference(resolution,[],[f110,f291]) ).
fof(f598,plain,
( product(e_2,e_1,e_1)
| product(e_2,e_1,e_2)
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[],[f586,f17]) ).
fof(f608,plain,
( ~ spl0_8
| ~ spl0_16 ),
inference(avatar_split_clause,[],[f421,f245,f129]) ).
fof(f609,plain,
( ~ spl0_16
| ~ spl0_15 ),
inference(avatar_split_clause,[],[f536,f193,f245]) ).
fof(f610,plain,
( ~ spl0_16
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f589,f109,f245]) ).
fof(f611,plain,
( product(e_2,e_1,e_1)
| spl0_3
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[],[f598,f98]) ).
fof(f612,plain,
( spl0_16
| spl0_3
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f611,f109,f96,f245]) ).
fof(f614,plain,
( ~ spl0_20
| ~ spl0_14 ),
inference(avatar_split_clause,[],[f463,f189,f270]) ).
fof(f623,plain,
( ~ group_element(e_1)
| product(e_1,e_1,e_1)
| product(e_1,e_1,e_2)
| ~ group_element(e_1)
| spl0_5 ),
inference(resolution,[],[f111,f26]) ).
fof(f624,plain,
( ! [X0] :
( ~ product(e_3,X0,e_1)
| ~ product(e_3,e_1,X0) )
| spl0_5 ),
inference(resolution,[],[f111,f30]) ).
fof(f625,plain,
( ~ group_element(e_1)
| product(e_1,e_1,e_1)
| product(e_1,e_1,e_2)
| spl0_5 ),
inference(duplicate_literal_removal,[],[f623]) ).
fof(f626,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_1,e_2)
| spl0_5 ),
inference(forward_subsumption_resolution,[],[f625,f17]) ).
fof(f627,plain,
( spl0_7
| spl0_8
| spl0_5 ),
inference(avatar_split_clause,[],[f626,f109,f129,f125]) ).
fof(f643,definition,
( spl0_37
<=> product(e_1,e_3,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_37])],[avatar_definition]) ).
fof(f644,plain,
( ~ product(e_1,e_3,e_2)
| spl0_37 ),
inference(avatar_component_clause,[],[f643]) ).
fof(f645,plain,
( product(e_1,e_3,e_2)
| ~ spl0_37 ),
inference(avatar_component_clause,[],[f643]) ).
fof(f665,plain,
( ~ product(e_1,e_2,e_1)
| ~ spl0_21 ),
inference(resolution,[],[f276,f35]) ).
fof(f669,plain,
( ~ product(e_2,e_1,e_1)
| ~ spl0_21 ),
inference(resolution,[],[f276,f36]) ).
fof(f670,plain,
( ~ spl0_16
| ~ spl0_21 ),
inference(avatar_split_clause,[],[f669,f274,f245]) ).
fof(f705,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,[],[f347]) ).
fof(f706,plain,
( ~ product(e_3,e_1,e_1)
| product(e_2,e_1,e_2)
| ~ group_element(e_1) ),
inference(forward_subsumption_resolution,[],[f705,f44]) ).
fof(f707,plain,
( ~ product(e_3,e_1,e_1)
| ~ group_element(e_1)
| spl0_3 ),
inference(forward_subsumption_resolution,[],[f706,f98]) ).
fof(f708,plain,
( ~ product(e_3,e_1,e_1)
| spl0_3 ),
inference(forward_subsumption_resolution,[],[f707,f17]) ).
fof(f709,plain,
( ~ spl0_10
| spl0_3 ),
inference(avatar_split_clause,[],[f708,f96,f148]) ).
fof(f737,plain,
( ~ product(e_3,e_1,e_2)
| ~ spl0_35 ),
inference(resolution,[],[f577,f36]) ).
fof(f738,plain,
( ~ spl0_9
| ~ spl0_35 ),
inference(avatar_split_clause,[],[f737,f575,f144]) ).
fof(f763,plain,
( ~ product(e_1,e_2,e_2)
| ~ spl0_37 ),
inference(resolution,[],[f645,f45]) ).
fof(f764,plain,
( ~ product(e_1,e_1,e_2)
| ~ spl0_37 ),
inference(resolution,[],[f645,f39]) ).
fof(f765,plain,
( $false
| ~ spl0_7
| ~ spl0_37 ),
inference(forward_subsumption_resolution,[],[f764,f127]) ).
fof(f766,plain,
( ~ spl0_7
| ~ spl0_37 ),
inference(avatar_contradiction_clause,[],[f765]) ).
fof(f769,plain,
( ~ product(e_3,e_2,e_2)
| product(e_2,e_3,e_2)
| ~ group_element(e_2)
| product(e_2,e_3,e_1) ),
inference(factoring,[],[f391]) ).
fof(f788,plain,
( ~ product(e_2,e_1,e_2)
| ~ spl0_9 ),
inference(resolution,[],[f146,f44]) ).
fof(f830,plain,
( ! [X0] :
( ~ group_element(X0)
| product(e_2,X0,e_1)
| product(e_2,X0,e_2)
| product(e_1,X0,e_2) )
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[],[f349,f114]) ).
fof(f849,plain,
( product(e_2,e_3,e_1)
| product(e_2,e_3,e_2)
| product(e_1,e_3,e_2)
| ~ spl0_6 ),
inference(resolution,[],[f830,f19]) ).
fof(f850,plain,
( product(e_2,e_3,e_1)
| product(e_2,e_3,e_2)
| ~ spl0_6
| spl0_37 ),
inference(forward_subsumption_resolution,[],[f849,f644]) ).
fof(f851,plain,
( spl0_14
| spl0_15
| ~ spl0_6
| spl0_37 ),
inference(avatar_split_clause,[],[f850,f643,f113,f193,f189]) ).
fof(f868,plain,
( product(e_2,e_2,e_2)
| product(e_2,e_2,e_1)
| product(e_2,e_1,e_1)
| product(e_2,e_1,e_2) ),
inference(resolution,[],[f358,f18]) ).
fof(f869,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,[],[f358,f19]) ).
fof(f888,plain,
( ~ product(e_2,e_2,e_1)
| ~ spl0_32 ),
inference(resolution,[],[f564,f44]) ).
fof(f903,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,[],[f368,f18]) ).
fof(f908,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,[],[f375,f17]) ).
fof(f911,plain,
( product(e_3,e_1,e_2)
| product(e_2,e_1,e_1)
| product(e_2,e_1,e_2)
| spl0_10 ),
inference(forward_subsumption_resolution,[],[f908,f149]) ).
fof(f916,plain,
( ~ spl0_3
| ~ spl0_20 ),
inference(avatar_split_clause,[],[f377,f270,f96]) ).
fof(f917,plain,
( product(e_2,e_3,e_2)
| product(e_2,e_3,e_1)
| product(e_2,e_1,e_2)
| spl0_16 ),
inference(forward_subsumption_resolution,[],[f903,f246]) ).
fof(f919,plain,
( spl0_3
| spl0_15
| spl0_14
| spl0_16 ),
inference(avatar_split_clause,[],[f917,f245,f189,f193,f96]) ).
fof(f920,plain,
( ~ spl0_21
| ~ spl0_15 ),
inference(avatar_split_clause,[],[f535,f193,f274]) ).
fof(f921,plain,
( ~ spl0_21
| ~ spl0_32 ),
inference(avatar_split_clause,[],[f888,f562,f274]) ).
fof(f923,plain,
( product(e_2,e_2,e_2)
| product(e_2,e_2,e_1)
| product(e_2,e_1,e_2)
| spl0_16 ),
inference(forward_subsumption_resolution,[],[f868,f246]) ).
fof(f925,plain,
( spl0_3
| spl0_21
| spl0_20
| spl0_16 ),
inference(avatar_split_clause,[],[f923,f245,f270,f274,f96]) ).
fof(f926,plain,
( ~ spl0_3
| ~ spl0_14 ),
inference(avatar_split_clause,[],[f473,f189,f96]) ).
fof(f929,plain,
( ~ product(e_3,e_2,e_2)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1) ),
inference(forward_subsumption_resolution,[],[f769,f18]) ).
fof(f930,plain,
( product(e_3,e_2,e_2)
| product(e_3,e_2,e_1)
| product(e_3,e_1,e_2)
| spl0_10 ),
inference(forward_subsumption_resolution,[],[f869,f149]) ).
fof(f937,plain,
( spl0_15
| spl0_14
| ~ spl0_35 ),
inference(avatar_split_clause,[],[f929,f575,f189,f193]) ).
fof(f945,plain,
( ~ spl0_3
| ~ spl0_9 ),
inference(avatar_split_clause,[],[f788,f144,f96]) ).
fof(f947,plain,
( product(e_3,e_1,e_2)
| product(e_2,e_1,e_2)
| spl0_10
| spl0_16 ),
inference(forward_subsumption_resolution,[],[f911,f246]) ).
fof(f948,plain,
( spl0_9
| spl0_32
| spl0_35
| spl0_10 ),
inference(avatar_split_clause,[],[f930,f148,f575,f562,f144]) ).
fof(f952,plain,
( ~ spl0_25
| ~ spl0_21 ),
inference(avatar_split_clause,[],[f665,f274,f339]) ).
fof(f953,plain,
( spl0_3
| spl0_9
| spl0_10
| spl0_16 ),
inference(avatar_split_clause,[],[f947,f245,f148,f144,f96]) ).
fof(f1001,plain,
( product(e_3,e_2,e_1)
| product(e_3,e_2,e_2)
| product(e_1,e_2,e_1)
| product(e_1,e_2,e_2) ),
inference(resolution,[],[f363,f18]) ).
fof(f1013,plain,
( product(e_2,e_3,e_2)
| product(e_2,e_3,e_1)
| product(e_2,e_2,e_1)
| product(e_2,e_2,e_2) ),
inference(resolution,[],[f393,f18]) ).
fof(f1014,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,[],[f393,f19]) ).
fof(f1113,plain,
! [X0] :
( ~ product(e_2,e_1,X0)
| ~ product(e_2,e_2,e_1) ),
inference(factoring,[],[f91]) ).
fof(f1114,plain,
( ! [X0] : ~ product(e_2,e_1,X0)
| ~ spl0_21 ),
inference(forward_subsumption_resolution,[],[f1113,f276]) ).
fof(f1116,plain,
( ~ group_element(e_1)
| product(e_2,e_1,e_1)
| product(e_2,e_1,e_2)
| ~ group_element(e_2)
| ~ spl0_21 ),
inference(resolution,[],[f1114,f26]) ).
fof(f1117,plain,
( product(e_2,e_1,e_1)
| product(e_2,e_1,e_2)
| ~ group_element(e_2)
| ~ spl0_21 ),
inference(forward_subsumption_resolution,[],[f1116,f17]) ).
fof(f1118,plain,
( product(e_2,e_1,e_2)
| ~ group_element(e_2)
| spl0_16
| ~ spl0_21 ),
inference(forward_subsumption_resolution,[],[f1117,f246]) ).
fof(f1119,plain,
( ~ group_element(e_2)
| spl0_3
| spl0_16
| ~ spl0_21 ),
inference(forward_subsumption_resolution,[],[f1118,f98]) ).
fof(f1120,plain,
( $false
| spl0_3
| spl0_16
| ~ spl0_21 ),
inference(forward_subsumption_resolution,[],[f1119,f18]) ).
fof(f1121,plain,
( spl0_3
| spl0_16
| ~ spl0_21 ),
inference(avatar_contradiction_clause,[],[f1120]) ).
fof(f1123,plain,
( product(e_3,e_2,e_1)
| product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| spl0_35 ),
inference(forward_subsumption_resolution,[],[f1001,f576]) ).
fof(f1124,plain,
( product(e_3,e_3,e_1)
| product(e_3,e_2,e_1)
| product(e_3,e_2,e_2)
| spl0_12 ),
inference(forward_subsumption_resolution,[],[f1014,f162]) ).
fof(f1129,plain,
( spl0_20
| spl0_21
| spl0_15
| spl0_14 ),
inference(avatar_split_clause,[],[f1013,f189,f193,f274,f270]) ).
fof(f1136,plain,
( product(e_3,e_2,e_1)
| product(e_1,e_2,e_2)
| spl0_25
| spl0_35 ),
inference(forward_subsumption_resolution,[],[f1123,f340]) ).
fof(f1137,plain,
( product(e_3,e_3,e_1)
| product(e_3,e_2,e_1)
| spl0_12
| spl0_35 ),
inference(forward_subsumption_resolution,[],[f1124,f576]) ).
fof(f1147,plain,
( spl0_24
| spl0_32
| spl0_25
| spl0_35 ),
inference(avatar_split_clause,[],[f1136,f575,f339,f562,f335]) ).
fof(f1148,plain,
( spl0_32
| spl0_13
| spl0_12
| spl0_35 ),
inference(avatar_split_clause,[],[f1137,f575,f161,f165,f562]) ).
fof(f1152,plain,
( ~ spl0_24
| ~ spl0_37 ),
inference(avatar_split_clause,[],[f763,f643,f335]) ).
fof(f1181,plain,
( ~ product(e_3,e_1,e_2)
| spl0_5
| ~ spl0_32 ),
inference(resolution,[],[f564,f624]) ).
fof(f1199,plain,
( $false
| spl0_5
| ~ spl0_9
| ~ spl0_32 ),
inference(forward_subsumption_resolution,[],[f1181,f146]) ).
fof(f1200,plain,
( spl0_5
| ~ spl0_9
| ~ spl0_32 ),
inference(avatar_contradiction_clause,[],[f1199]) ).
cnf(s3,plain,
( ~ spl0_5
| spl0_6 ),
inference(sat_conversion,[],[f115]) ).
cnf(s10,plain,
( ~ spl0_9
| ~ spl0_12 ),
inference(sat_conversion,[],[f211]) ).
cnf(s13,plain,
( spl0_5
| ~ spl0_10 ),
inference(sat_conversion,[],[f225]) ).
cnf(s15,plain,
( ~ spl0_18
| spl0_19 ),
inference(sat_conversion,[],[f263]) ).
cnf(s17,plain,
( spl0_16
| ~ spl0_18
| ~ spl0_19 ),
inference(sat_conversion,[],[f305]) ).
cnf(s19,plain,
( ~ spl0_6
| ~ spl0_16
| ~ spl0_18 ),
inference(sat_conversion,[],[f322]) ).
cnf(s20,plain,
( spl0_6
| ~ spl0_7 ),
inference(sat_conversion,[],[f323]) ).
cnf(s26,plain,
( spl0_18
| spl0_20
| spl0_21 ),
inference(sat_conversion,[],[f354]) ).
cnf(s35,plain,
( ~ spl0_13
| ~ spl0_15 ),
inference(sat_conversion,[],[f455]) ).
cnf(s36,plain,
( ~ spl0_14
| ~ spl0_20 ),
inference(sat_conversion,[],[f476]) ).
cnf(s61,plain,
( ~ spl0_8
| ~ spl0_16 ),
inference(sat_conversion,[],[f608]) ).
cnf(s62,plain,
( ~ spl0_15
| ~ spl0_16 ),
inference(sat_conversion,[],[f609]) ).
cnf(s63,plain,
( ~ spl0_5
| ~ spl0_16 ),
inference(sat_conversion,[],[f610]) ).
cnf(s64,plain,
( spl0_3
| ~ spl0_5
| spl0_16 ),
inference(sat_conversion,[],[f612]) ).
cnf(s70,plain,
( ~ spl0_14
| ~ spl0_20 ),
inference(sat_conversion,[],[f614]) ).
cnf(s77,plain,
( spl0_5
| spl0_7
| spl0_8 ),
inference(sat_conversion,[],[f627]) ).
cnf(s80,plain,
( ~ spl0_16
| ~ spl0_21 ),
inference(sat_conversion,[],[f670]) ).
cnf(s90,plain,
( spl0_3
| ~ spl0_10 ),
inference(sat_conversion,[],[f709]) ).
cnf(s93,plain,
( ~ spl0_9
| ~ spl0_35 ),
inference(sat_conversion,[],[f738]) ).
cnf(s97,plain,
( ~ spl0_7
| ~ spl0_37 ),
inference(sat_conversion,[],[f766]) ).
cnf(s106,plain,
( ~ spl0_6
| spl0_14
| spl0_15
| spl0_37 ),
inference(sat_conversion,[],[f851]) ).
cnf(s120,plain,
( ~ spl0_3
| ~ spl0_20 ),
inference(sat_conversion,[],[f916]) ).
cnf(s125,plain,
( spl0_3
| spl0_14
| spl0_15
| spl0_16 ),
inference(sat_conversion,[],[f919]) ).
cnf(s126,plain,
( ~ spl0_15
| ~ spl0_21 ),
inference(sat_conversion,[],[f920]) ).
cnf(s127,plain,
( ~ spl0_21
| ~ spl0_32 ),
inference(sat_conversion,[],[f921]) ).
cnf(s129,plain,
( spl0_3
| spl0_16
| spl0_20
| spl0_21 ),
inference(sat_conversion,[],[f925]) ).
cnf(s137,plain,
( ~ spl0_3
| ~ spl0_14 ),
inference(sat_conversion,[],[f926]) ).
cnf(s142,plain,
( spl0_14
| spl0_15
| ~ spl0_35 ),
inference(sat_conversion,[],[f937]) ).
cnf(s148,plain,
( ~ spl0_3
| ~ spl0_9 ),
inference(sat_conversion,[],[f945]) ).
cnf(s151,plain,
( spl0_9
| spl0_10
| spl0_32
| spl0_35 ),
inference(sat_conversion,[],[f948]) ).
cnf(s153,plain,
( ~ spl0_21
| ~ spl0_25 ),
inference(sat_conversion,[],[f952]) ).
cnf(s154,plain,
( spl0_3
| spl0_9
| spl0_10
| spl0_16 ),
inference(sat_conversion,[],[f953]) ).
cnf(s172,plain,
( spl0_3
| spl0_16
| ~ spl0_21 ),
inference(sat_conversion,[],[f1121]) ).
cnf(s183,plain,
( spl0_14
| spl0_15
| spl0_20
| spl0_21 ),
inference(sat_conversion,[],[f1129]) ).
cnf(s189,plain,
( spl0_24
| spl0_25
| spl0_32
| spl0_35 ),
inference(sat_conversion,[],[f1147]) ).
cnf(s190,plain,
( spl0_12
| spl0_13
| spl0_32
| spl0_35 ),
inference(sat_conversion,[],[f1148]) ).
cnf(s194,plain,
( ~ spl0_24
| ~ spl0_37 ),
inference(sat_conversion,[],[f1152]) ).
cnf(s204,plain,
( spl0_5
| ~ spl0_9
| ~ spl0_32 ),
inference(sat_conversion,[],[f1200]) ).
cnf(s205,plain,
( spl0_16
| spl0_5
| spl0_3 ),
inference(rat,[],[s125,s35,s70,s190,s129,s204,s10,s93,s172,s154,s90]) ).
cnf(s206,plain,
( spl0_5
| spl0_3 ),
inference(rat,[],[s36,s26,s106,s19,s20,s97,s77,s61,s62,s80,s205]) ).
cnf(s207,plain,
spl0_3,
inference(rat,[],[s64,s63,s206]) ).
cnf(s208,plain,
~ spl0_9,
inference(rat,[],[s148,s207]) ).
cnf(s209,plain,
~ spl0_14,
inference(rat,[],[s137,s207]) ).
cnf(s210,plain,
~ spl0_20,
inference(rat,[],[s120,s207]) ).
cnf(s212,plain,
( spl0_15
| spl0_10 ),
inference(rat,[],[s151,s127,s142,s183,s208,s209,s210]) ).
cnf(s213,plain,
~ spl0_15,
inference(rat,[],[s62,s17,s15,s26,s126,s210]) ).
cnf(s214,plain,
spl0_21,
inference(rat,[],[s183,s210,s209,s213]) ).
cnf(s215,plain,
~ spl0_35,
inference(rat,[],[s142,s209,s213]) ).
cnf(s218,plain,
spl0_10,
inference(rat,[],[s212,s213]) ).
cnf(s220,plain,
~ spl0_25,
inference(rat,[],[s153,s214]) ).
cnf(s221,plain,
~ spl0_32,
inference(rat,[],[s127,s214]) ).
cnf(s225,plain,
spl0_24,
inference(rat,[],[s189,s221,s220,s215]) ).
cnf(s227,plain,
spl0_5,
inference(rat,[],[s13,s218]) ).
cnf(s229,plain,
~ spl0_37,
inference(rat,[],[s194,s225]) ).
cnf(s232,plain,
spl0_6,
inference(rat,[],[s3,s227]) ).
cnf(s235,plain,
$false,
inference(rat,[],[s106,s213,s209,s229,s232]) ).
fof(f1201,plain,
$false,
inference(avatar_sat_refutation,[],[s235]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP130-3.003 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.35 % Computer : n016.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sun Sep 27 09:34:33 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 Running first-order theorem proving
% 0.12/0.38 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
% 1.86/1.30 % (2364093)Input is clausal, will run a generic CNF schedule.
% 1.86/1.30 % (2364101)lrs+10_1_sil=8000:sp=occurrence:random_seed=3433102801:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 1.86/1.30 % (2364101)Instruction limit reached!
% 1.86/1.30 % (2364101)------------------------------
% 1.86/1.30 % (2364101)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.86/1.30 % (2364101)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.86/1.30 % (2364101)CaDiCaL version: 2.1.3
% 1.86/1.30 % (2364101)Termination reason: Instruction limit
% 1.86/1.30 % (2364101)Termination phase: Saturation
% 1.86/1.30 % (2364101)Time elapsed: 0.036 s
% 1.86/1.30 % (2364101)Peak memory usage: 88 MB
% 1.86/1.30 % (2364101)Instructions burned: 109 (million)
% 1.86/1.30 % (2364102)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1888961350:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 1.86/1.30 % (2364098)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=497383480:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 1.86/1.30 % (2364100)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2923098102:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 1.86/1.30 % (2364099)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1641486193:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 1.86/1.30 % (2364104)dis-21_1_sil=8000:lcm=predicate:random_seed=399411693: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)
% 1.86/1.30 % (2364103)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2371880599:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 1.86/1.30 % (2364103)First to succeed.
% 1.86/1.30 % (2364103)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2364093"
% 1.86/1.30 % (2364104)Also succeeded, but the first one will report.
% 1.86/1.30 % (2364102)Instruction limit reached!
% 1.86/1.30 % (2364102)------------------------------
% 1.86/1.30 % (2364102)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.86/1.30 % (2364102)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.86/1.30 % (2364102)CaDiCaL version: 2.1.3
% 1.86/1.30 % (2364102)Termination reason: Instruction limit
% 1.86/1.30 % (2364102)Termination phase: Saturation
% 1.86/1.30 % (2364102)Time elapsed: 0.062 s
% 1.86/1.30 % (2364102)Peak memory usage: 88 MB
% 1.86/1.30 % (2364102)Instructions burned: 114 (million)
% 1.86/1.30 % (2364111)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=3363851676:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 1.86/1.30 % (2364111)Also succeeded, but the first one will report.
% 1.86/1.30 % (2364113)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=1310468000: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)
% 1.86/1.30 % (2364113)Refutation not found, incomplete strategy
% 1.86/1.30 % (2364113)------------------------------
% 1.86/1.30 % (2364113)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.86/1.30 % (2364113)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.86/1.30 % (2364113)CaDiCaL version: 2.1.3
% 1.86/1.30 % (2364113)Termination reason: Refutation not found, incomplete strategy
% 1.86/1.30 % (2364113)Time elapsed: 0.002 s
% 1.86/1.30 % (2364113)Peak memory usage: 87 MB
% 1.86/1.30 % (2364113)Instructions burned: 1 (million)
% 1.86/1.30 % (2364103)Refutation found. Thanks to Tanya!
% 1.86/1.30 % SZS status Unsatisfiable for theBenchmark
% 1.86/1.30 % SZS output start Proof for theBenchmark
% See solution above
% 3.99/1.50 % (2364103)------------------------------
% 3.99/1.50 % (2364103)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.99/1.50 % (2364103)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.99/1.50 % (2364103)CaDiCaL version: 2.1.3
% 3.99/1.50 % (2364103)Termination reason: Refutation
% 3.99/1.50 % (2364103)Time elapsed: 0.030 s
% 3.99/1.50 % (2364103)Peak memory usage: 90 MB
% 3.99/1.50 % (2364103)Instructions burned: 43 (million)
% 3.99/1.50 % (2364103)------------------------------
% 3.99/1.50 % (2364103)------------------------------
% 3.99/1.50 % (2364093)Success in time 0.473 s
% 3.99/1.50 % Vampire exiting
%------------------------------------------------------------------------------