TSTP Solution File: HAL002+1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : HAL002+1 : TPTP v8.1.2. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n027.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun May 5 06:11:12 EDT 2024
% Result : Theorem 0.23s 0.46s
% Output : Refutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 37
% Syntax : Number of formulae : 360 ( 6 unt; 0 def)
% Number of atoms : 1498 ( 359 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 1890 ( 752 ~; 916 |; 147 &)
% ( 20 <=>; 52 =>; 0 <=; 3 <~>)
% Maximal formula depth : 17 ( 7 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 21 ( 19 usr; 13 prp; 0-4 aty)
% Number of functors : 15 ( 15 usr; 3 con; 0-5 aty)
% Number of variables : 958 ( 912 !; 46 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1243,plain,
$false,
inference(avatar_sat_refutation,[],[f126,f145,f153,f156,f159,f160,f188,f518,f522,f1046,f1054,f1093,f1169,f1209,f1211,f1227,f1232,f1234,f1236,f1242]) ).
fof(f1242,plain,
( ~ spl9_1
| spl9_2
| spl9_3 ),
inference(avatar_contradiction_clause,[],[f1241]) ).
fof(f1241,plain,
( $false
| ~ spl9_1
| spl9_2
| spl9_3 ),
inference(subsumption_resolution,[],[f1240,f84]) ).
fof(f84,plain,
morphism(x,any1,any2),
inference(cnf_transformation,[],[f16]) ).
fof(f16,axiom,
morphism(x,any1,any2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_morphism) ).
fof(f1240,plain,
( ~ morphism(x,any1,any2)
| ~ spl9_1
| spl9_2
| spl9_3 ),
inference(subsumption_resolution,[],[f1239,f124]) ).
fof(f124,plain,
( ~ injection_2(x)
| spl9_2 ),
inference(avatar_component_clause,[],[f123]) ).
fof(f123,plain,
( spl9_2
<=> injection_2(x) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_2])]) ).
fof(f1239,plain,
( injection_2(x)
| ~ morphism(x,any1,any2)
| ~ spl9_1
| spl9_3 ),
inference(resolution,[],[f1229,f97]) ).
fof(f97,plain,
! [X2,X0,X1] :
( element(sK2(X0,X1,X2),X1)
| injection_2(X0)
| ~ morphism(X0,X1,X2) ),
inference(cnf_transformation,[],[f66]) ).
fof(f66,plain,
! [X0,X1,X2] :
( injection_2(X0)
| ( zero(X1) != sK2(X0,X1,X2)
& zero(X2) = apply(X0,sK2(X0,X1,X2))
& element(sK2(X0,X1,X2),X1) )
| ~ morphism(X0,X1,X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f49,f65]) ).
fof(f65,plain,
! [X0,X1,X2] :
( ? [X3] :
( zero(X1) != X3
& apply(X0,X3) = zero(X2)
& element(X3,X1) )
=> ( zero(X1) != sK2(X0,X1,X2)
& zero(X2) = apply(X0,sK2(X0,X1,X2))
& element(sK2(X0,X1,X2),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f49,plain,
! [X0,X1,X2] :
( injection_2(X0)
| ? [X3] :
( zero(X1) != X3
& apply(X0,X3) = zero(X2)
& element(X3,X1) )
| ~ morphism(X0,X1,X2) ),
inference(flattening,[],[f48]) ).
fof(f48,plain,
! [X0,X1,X2] :
( injection_2(X0)
| ? [X3] :
( zero(X1) != X3
& apply(X0,X3) = zero(X2)
& element(X3,X1) )
| ~ morphism(X0,X1,X2) ),
inference(ennf_transformation,[],[f15]) ).
fof(f15,axiom,
! [X0,X1,X2] :
( ( ! [X3] :
( ( apply(X0,X3) = zero(X2)
& element(X3,X1) )
=> zero(X1) = X3 )
& morphism(X0,X1,X2) )
=> injection_2(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',properties_for_injection_2) ).
fof(f1229,plain,
( ~ element(sK2(x,any1,any2),any1)
| ~ spl9_1
| spl9_3 ),
inference(global_subsumption,[],[f117,f82,f84,f85,f87,f127,f100,f101,f86,f134,f136,f140,f93,f95,f97,f99,f103,f135,f89,f180,f94,f189,f190,f191,f98,f90,f96,f102,f91,f146,f282,f283,f284,f92,f165,f168,f195,f353,f354,f355,f116,f375,f88,f416,f433,f434,f435,f104,f460,f108,f566,f567,f568,f569,f573,f587,f595,f596,f597,f598,f602,f616,f105,f655,f113,f747,f109,f778,f779,f780,f781,f785,f803,f288,f826,f827,f828,f829,f830,f831,f172,f839,f840,f841,f842,f843,f844,f173,f174,f110,f912,f913,f914,f915,f916,f920,f929,f940,f115,f111,f1094,f114,f1123,f83,f1170,f128,f1171,f131,f1172,f236,f1173,f320,f1174,f322,f1175,f889,f1177,f349,f276,f1179,f197,f121,f1180,f1182,f1183,f1189,f1178,f112,f1188,f1192]) ).
fof(f1192,plain,
( element(zero(any1),any1)
| ~ element(sK2(x,any1,any2),any1)
| ~ spl9_1 ),
inference(duplicate_literal_removal,[],[f1191]) ).
fof(f1191,plain,
( element(zero(any1),any1)
| ~ element(sK2(x,any1,any2),any1)
| ~ element(sK2(x,any1,any2),any1)
| ~ spl9_1 ),
inference(superposition,[],[f93,f1178]) ).
fof(f1188,plain,
( ! [X2,X0,X1] :
( ~ element(sK2(x,any1,any2),X1)
| sK2(x,any1,any2) = X0
| apply(x,X0) != zero(any2)
| ~ element(X0,X1)
| ~ morphism(x,X1,X2) )
| ~ spl9_1 ),
inference(subsumption_resolution,[],[f1184,f121]) ).
fof(f1184,plain,
( ! [X2,X0,X1] :
( apply(x,X0) != zero(any2)
| sK2(x,any1,any2) = X0
| ~ element(sK2(x,any1,any2),X1)
| ~ element(X0,X1)
| ~ morphism(x,X1,X2)
| ~ injection(x) )
| ~ spl9_1 ),
inference(superposition,[],[f92,f1180]) ).
fof(f112,plain,
! [X2,X3,X0,X1,X6,X4] :
( zero(X4) != apply(X1,sK6(X0,X1,X2,X3,X4))
| apply(X0,X6) != sK6(X0,X1,X2,X3,X4)
| ~ element(X6,X2)
| exact(X0,X1)
| ~ element(sK6(X0,X1,X2,X3,X4),X3)
| ~ morphism(X1,X3,X4)
| ~ morphism(X0,X2,X3) ),
inference(cnf_transformation,[],[f79]) ).
fof(f79,plain,
! [X0,X1,X2,X3,X4] :
( exact(X0,X1)
| ( ( ! [X6] :
( apply(X0,X6) != sK6(X0,X1,X2,X3,X4)
| ~ element(X6,X2) )
| zero(X4) != apply(X1,sK6(X0,X1,X2,X3,X4))
| ~ element(sK6(X0,X1,X2,X3,X4),X3) )
& ( ( sK6(X0,X1,X2,X3,X4) = apply(X0,sK7(X0,X1,X2,X3,X4))
& element(sK7(X0,X1,X2,X3,X4),X2) )
| ( zero(X4) = apply(X1,sK6(X0,X1,X2,X3,X4))
& element(sK6(X0,X1,X2,X3,X4),X3) ) ) )
| ~ morphism(X1,X3,X4)
| ~ morphism(X0,X2,X3) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7])],[f76,f78,f77]) ).
fof(f77,plain,
! [X0,X1,X2,X3,X4] :
( ? [X5] :
( ( ! [X6] :
( apply(X0,X6) != X5
| ~ element(X6,X2) )
| zero(X4) != apply(X1,X5)
| ~ element(X5,X3) )
& ( ? [X7] :
( apply(X0,X7) = X5
& element(X7,X2) )
| ( zero(X4) = apply(X1,X5)
& element(X5,X3) ) ) )
=> ( ( ! [X6] :
( apply(X0,X6) != sK6(X0,X1,X2,X3,X4)
| ~ element(X6,X2) )
| zero(X4) != apply(X1,sK6(X0,X1,X2,X3,X4))
| ~ element(sK6(X0,X1,X2,X3,X4),X3) )
& ( ? [X7] :
( apply(X0,X7) = sK6(X0,X1,X2,X3,X4)
& element(X7,X2) )
| ( zero(X4) = apply(X1,sK6(X0,X1,X2,X3,X4))
& element(sK6(X0,X1,X2,X3,X4),X3) ) ) ) ),
introduced(choice_axiom,[]) ).
fof(f78,plain,
! [X0,X1,X2,X3,X4] :
( ? [X7] :
( apply(X0,X7) = sK6(X0,X1,X2,X3,X4)
& element(X7,X2) )
=> ( sK6(X0,X1,X2,X3,X4) = apply(X0,sK7(X0,X1,X2,X3,X4))
& element(sK7(X0,X1,X2,X3,X4),X2) ) ),
introduced(choice_axiom,[]) ).
fof(f76,plain,
! [X0,X1,X2,X3,X4] :
( exact(X0,X1)
| ? [X5] :
( ( ! [X6] :
( apply(X0,X6) != X5
| ~ element(X6,X2) )
| zero(X4) != apply(X1,X5)
| ~ element(X5,X3) )
& ( ? [X7] :
( apply(X0,X7) = X5
& element(X7,X2) )
| ( zero(X4) = apply(X1,X5)
& element(X5,X3) ) ) )
| ~ morphism(X1,X3,X4)
| ~ morphism(X0,X2,X3) ),
inference(rectify,[],[f75]) ).
fof(f75,plain,
! [X0,X1,X2,X3,X4] :
( exact(X0,X1)
| ? [X5] :
( ( ! [X6] :
( apply(X0,X6) != X5
| ~ element(X6,X2) )
| zero(X4) != apply(X1,X5)
| ~ element(X5,X3) )
& ( ? [X6] :
( apply(X0,X6) = X5
& element(X6,X2) )
| ( zero(X4) = apply(X1,X5)
& element(X5,X3) ) ) )
| ~ morphism(X1,X3,X4)
| ~ morphism(X0,X2,X3) ),
inference(flattening,[],[f74]) ).
fof(f74,plain,
! [X0,X1,X2,X3,X4] :
( exact(X0,X1)
| ? [X5] :
( ( ! [X6] :
( apply(X0,X6) != X5
| ~ element(X6,X2) )
| zero(X4) != apply(X1,X5)
| ~ element(X5,X3) )
& ( ? [X6] :
( apply(X0,X6) = X5
& element(X6,X2) )
| ( zero(X4) = apply(X1,X5)
& element(X5,X3) ) ) )
| ~ morphism(X1,X3,X4)
| ~ morphism(X0,X2,X3) ),
inference(nnf_transformation,[],[f55]) ).
fof(f55,plain,
! [X0,X1,X2,X3,X4] :
( exact(X0,X1)
| ? [X5] :
( ( zero(X4) = apply(X1,X5)
& element(X5,X3) )
<~> ? [X6] :
( apply(X0,X6) = X5
& element(X6,X2) ) )
| ~ morphism(X1,X3,X4)
| ~ morphism(X0,X2,X3) ),
inference(flattening,[],[f54]) ).
fof(f54,plain,
! [X0,X1,X2,X3,X4] :
( exact(X0,X1)
| ? [X5] :
( ( zero(X4) = apply(X1,X5)
& element(X5,X3) )
<~> ? [X6] :
( apply(X0,X6) = X5
& element(X6,X2) ) )
| ~ morphism(X1,X3,X4)
| ~ morphism(X0,X2,X3) ),
inference(ennf_transformation,[],[f28]) ).
fof(f28,plain,
! [X0,X1,X2,X3,X4] :
( ( ! [X5] :
( ( zero(X4) = apply(X1,X5)
& element(X5,X3) )
<=> ? [X6] :
( apply(X0,X6) = X5
& element(X6,X2) ) )
& morphism(X1,X3,X4)
& morphism(X0,X2,X3) )
=> exact(X0,X1) ),
inference(rectify,[],[f7]) ).
fof(f7,axiom,
! [X8,X9,X1,X10,X2] :
( ( ! [X11] :
( ( zero(X2) = apply(X9,X11)
& element(X11,X10) )
<=> ? [X7] :
( apply(X8,X7) = X11
& element(X7,X1) ) )
& morphism(X9,X10,X2)
& morphism(X8,X1,X10) )
=> exact(X8,X9) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',properties_for_exact) ).
fof(f1178,plain,
( zero(any1) = subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))
| ~ spl9_1 ),
inference(global_subsumption,[],[f117,f112,f82,f84,f85,f87,f127,f100,f101,f86,f134,f136,f93,f95,f97,f99,f103,f135,f89,f180,f94,f189,f190,f191,f98,f90,f96,f102,f91,f146,f282,f283,f284,f92,f165,f168,f195,f353,f354,f355,f116,f375,f88,f416,f433,f434,f435,f104,f460,f108,f566,f567,f568,f569,f573,f587,f595,f596,f597,f598,f602,f616,f105,f655,f113,f747,f109,f778,f779,f780,f781,f785,f803,f288,f826,f827,f828,f829,f830,f831,f172,f839,f840,f841,f842,f843,f844,f173,f174,f110,f912,f913,f914,f915,f916,f920,f929,f940,f115,f121,f111,f1094,f114,f1123,f83,f1170,f128,f1171,f131,f1172,f236,f1173,f320,f1174,f322,f1175,f889,f1177,f349]) ).
fof(f1189,plain,
( ! [X2,X0,X1] :
( apply(x,X0) != zero(any2)
| sK2(x,any1,any2) = X0
| ~ element(X0,X1)
| ~ element(sK2(x,any1,any2),X1)
| ~ morphism(x,X1,X2) )
| ~ spl9_1 ),
inference(subsumption_resolution,[],[f1185,f121]) ).
fof(f1185,plain,
( ! [X2,X0,X1] :
( apply(x,X0) != zero(any2)
| sK2(x,any1,any2) = X0
| ~ element(X0,X1)
| ~ element(sK2(x,any1,any2),X1)
| ~ morphism(x,X1,X2)
| ~ injection(x) )
| ~ spl9_1 ),
inference(superposition,[],[f92,f1180]) ).
fof(f1183,plain,
( ! [X2,X3,X0,X1] :
( zero(X0) != zero(any2)
| element(sK5(X1,X2,sK2(x,any1,any2)),X2)
| ~ element(sK2(x,any1,any2),X3)
| ~ morphism(x,X3,X0)
| ~ morphism(X1,X2,X3)
| ~ exact(X1,x) )
| ~ spl9_1 ),
inference(superposition,[],[f104,f1180]) ).
fof(f1182,plain,
( ! [X2,X3,X0,X1] :
( zero(X0) != zero(any2)
| sK2(x,any1,any2) = apply(X1,sK5(X1,X2,sK2(x,any1,any2)))
| ~ element(sK2(x,any1,any2),X3)
| ~ morphism(x,X3,X0)
| ~ morphism(X1,X2,X3)
| ~ exact(X1,x) )
| ~ spl9_1 ),
inference(superposition,[],[f105,f1180]) ).
fof(f1180,plain,
( zero(any2) = apply(x,sK2(x,any1,any2))
| ~ spl9_1 ),
inference(global_subsumption,[],[f117,f112,f82,f84,f85,f87,f127,f100,f101,f86,f134,f136,f93,f95,f97,f99,f103,f135,f89,f180,f94,f189,f190,f191,f98,f90,f96,f102,f91,f146,f282,f283,f284,f92,f165,f168,f195,f353,f354,f355,f116,f375,f88,f416,f433,f434,f435,f104,f460,f108,f566,f567,f568,f569,f573,f587,f595,f596,f597,f598,f602,f616,f105,f655,f113,f747,f109,f778,f779,f780,f781,f785,f803,f288,f826,f827,f828,f829,f830,f831,f172,f839,f840,f841,f842,f843,f844,f173,f174,f110,f912,f913,f914,f915,f916,f920,f929,f940,f115,f121,f111,f1094,f114,f1123,f83,f1170,f128,f1171,f131,f1172,f236,f1173,f320,f1174,f322,f1175,f889,f1177,f349,f1178,f276,f1179,f197]) ).
fof(f121,plain,
( injection(x)
| ~ spl9_1 ),
inference(avatar_component_clause,[],[f119]) ).
fof(f119,plain,
( spl9_1
<=> injection(x) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_1])]) ).
fof(f197,plain,
( zero(any2) = apply(x,sK2(x,any1,any2))
| injection_2(x) ),
inference(resolution,[],[f98,f84]) ).
fof(f1179,plain,
( ~ injection_2(x)
| ~ spl9_1 ),
inference(global_subsumption,[],[f117,f112,f82,f84,f85,f87,f127,f100,f101,f86,f134,f136,f93,f95,f97,f99,f103,f135,f89,f180,f94,f189,f190,f191,f98,f90,f96,f102,f91,f146,f282,f283,f284,f92,f165,f168,f195,f353,f354,f355,f116,f375,f88,f416,f433,f434,f435,f104,f460,f108,f566,f567,f568,f569,f573,f587,f595,f596,f597,f598,f602,f616,f105,f655,f113,f747,f109,f778,f779,f780,f781,f785,f803,f288,f826,f827,f828,f829,f830,f831,f172,f839,f840,f841,f842,f843,f844,f173,f174,f110,f912,f913,f914,f915,f916,f920,f929,f940,f115,f121,f111,f1094,f114,f1123,f83,f1170,f128,f1171,f131,f1172,f236,f1173,f320,f1174,f322,f1175,f889,f1177,f349,f1178,f276]) ).
fof(f276,plain,
! [X0,X1] :
( zero(X0) != zero(any2)
| zero(X1) = zero(any1)
| ~ element(zero(any1),X1)
| ~ morphism(x,X1,X0)
| ~ injection_2(x) ),
inference(superposition,[],[f91,f127]) ).
fof(f349,plain,
( injection_2(x)
| zero(any1) = subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)) ),
inference(resolution,[],[f168,f84]) ).
fof(f1177,plain,
( zero(any2) = subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,sK2(x,any1,any2)))
| ~ spl9_1 ),
inference(global_subsumption,[],[f117,f112,f82,f84,f85,f87,f127,f100,f101,f86,f134,f136,f93,f95,f97,f99,f103,f135,f89,f180,f94,f189,f190,f191,f98,f90,f96,f102,f91,f146,f282,f283,f284,f92,f165,f168,f195,f353,f354,f355,f116,f375,f88,f416,f433,f434,f435,f104,f460,f108,f566,f567,f568,f569,f573,f587,f595,f596,f597,f598,f602,f616,f105,f655,f113,f747,f109,f778,f779,f780,f781,f785,f803,f288,f826,f827,f828,f829,f830,f831,f172,f839,f840,f841,f842,f843,f844,f173,f174,f110,f912,f913,f914,f915,f916,f920,f929,f940,f115,f121,f111,f1094,f114,f1123,f83,f1170,f128,f1171,f131,f1172,f236,f1173,f320,f1174,f322,f1175,f889]) ).
fof(f889,plain,
( injection_2(x)
| zero(any2) = subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,sK2(x,any1,any2))) ),
inference(resolution,[],[f173,f84]) ).
fof(f1175,plain,
( ! [X2,X0,X1] :
( apply(x,X0) != zero(any2)
| zero(any1) = X0
| ~ element(zero(any1),X1)
| ~ element(X0,X1)
| ~ morphism(x,X1,X2) )
| ~ spl9_1 ),
inference(global_subsumption,[],[f117,f112,f82,f84,f85,f87,f127,f100,f101,f86,f134,f136,f93,f95,f97,f99,f103,f135,f89,f180,f94,f189,f190,f191,f98,f90,f96,f102,f91,f146,f282,f283,f284,f92,f165,f168,f195,f353,f354,f355,f116,f375,f88,f416,f433,f434,f435,f104,f460,f108,f566,f567,f568,f569,f573,f587,f595,f596,f597,f598,f602,f616,f105,f655,f113,f747,f109,f778,f779,f780,f781,f785,f803,f288,f826,f827,f828,f829,f830,f831,f172,f839,f840,f841,f842,f843,f844,f173,f174,f110,f912,f913,f914,f915,f916,f920,f929,f940,f115,f121,f111,f1094,f114,f1123,f83,f1170,f128,f1171,f131,f1172,f236,f1173,f320,f1174,f322]) ).
fof(f322,plain,
! [X2,X0,X1] :
( apply(x,X0) != zero(any2)
| zero(any1) = X0
| ~ element(zero(any1),X1)
| ~ element(X0,X1)
| ~ morphism(x,X1,X2)
| ~ injection(x) ),
inference(superposition,[],[f92,f127]) ).
fof(f1174,plain,
( ! [X2,X0,X1] :
( apply(x,X0) != zero(any2)
| zero(any1) = X0
| ~ element(X0,X1)
| ~ element(zero(any1),X1)
| ~ morphism(x,X1,X2) )
| ~ spl9_1 ),
inference(global_subsumption,[],[f117,f112,f82,f84,f85,f87,f127,f100,f101,f86,f134,f136,f93,f95,f97,f99,f103,f135,f89,f180,f94,f189,f190,f191,f98,f90,f96,f102,f91,f146,f282,f283,f284,f92,f165,f168,f195,f353,f354,f355,f116,f375,f88,f416,f433,f434,f435,f104,f460,f108,f566,f567,f568,f569,f573,f587,f595,f596,f597,f598,f602,f616,f105,f655,f113,f747,f109,f778,f779,f780,f781,f785,f803,f288,f826,f827,f828,f829,f830,f831,f172,f839,f840,f841,f842,f843,f844,f173,f174,f110,f912,f913,f914,f915,f916,f920,f929,f940,f115,f322,f121,f111,f1094,f114,f1123,f83,f1170,f128,f1171,f131,f1172,f236,f1173,f320]) ).
fof(f320,plain,
! [X2,X0,X1] :
( apply(x,X0) != zero(any2)
| zero(any1) = X0
| ~ element(X0,X1)
| ~ element(zero(any1),X1)
| ~ morphism(x,X1,X2)
| ~ injection(x) ),
inference(superposition,[],[f92,f127]) ).
fof(f1173,plain,
( injection(x)
| ~ spl9_1 ),
inference(global_subsumption,[],[f117,f112,f82,f84,f85,f87,f127,f100,f101,f86,f134,f136,f93,f95,f97,f99,f103,f135,f89,f180,f94,f189,f190,f191,f98,f90,f96,f102,f91,f146,f282,f283,f284,f92,f165,f168,f195,f353,f354,f355,f116,f375,f88,f416,f433,f434,f435,f104,f460,f108,f566,f567,f568,f569,f573,f587,f595,f596,f597,f598,f602,f616,f105,f655,f113,f747,f109,f778,f779,f780,f781,f785,f803,f288,f826,f827,f828,f829,f830,f831,f172,f839,f840,f841,f842,f843,f844,f173,f174,f110,f912,f913,f914,f915,f916,f920,f929,f940,f115,f322,f320,f121,f111,f1094,f114,f1123,f83,f1170,f128,f1171,f131,f1172,f236]) ).
fof(f236,plain,
( apply(x,sK3(x,any1)) = apply(x,sK4(x,any1))
| injection(x) ),
inference(resolution,[],[f102,f84]) ).
fof(f1172,plain,
( injection(x)
| ~ spl9_1 ),
inference(global_subsumption,[],[f117,f112,f82,f84,f85,f87,f127,f100,f101,f86,f134,f136,f93,f95,f97,f99,f103,f135,f89,f180,f94,f189,f190,f191,f98,f90,f96,f102,f91,f146,f282,f283,f284,f92,f165,f168,f195,f353,f354,f355,f116,f375,f88,f416,f433,f434,f435,f104,f460,f108,f566,f567,f568,f569,f573,f587,f595,f596,f597,f598,f602,f616,f105,f655,f113,f747,f109,f778,f779,f780,f781,f785,f803,f288,f826,f827,f828,f829,f830,f831,f172,f839,f840,f841,f842,f843,f844,f173,f174,f110,f912,f913,f914,f915,f916,f920,f929,f940,f115,f322,f320,f236,f121,f111,f1094,f114,f1123,f83,f1170,f128,f1171,f131]) ).
fof(f131,plain,
( element(sK4(x,any1),any1)
| injection(x) ),
inference(resolution,[],[f101,f84]) ).
fof(f1171,plain,
( injection(x)
| ~ spl9_1 ),
inference(global_subsumption,[],[f117,f112,f82,f84,f85,f87,f127,f100,f101,f86,f134,f136,f93,f95,f97,f99,f103,f135,f89,f180,f94,f189,f190,f191,f98,f90,f96,f102,f91,f146,f282,f283,f284,f92,f165,f168,f195,f353,f354,f355,f116,f375,f88,f416,f433,f434,f435,f104,f460,f108,f566,f567,f568,f569,f573,f587,f595,f596,f597,f598,f602,f616,f105,f655,f113,f747,f109,f778,f779,f780,f781,f785,f803,f288,f826,f827,f828,f829,f830,f831,f172,f839,f840,f841,f842,f843,f844,f173,f174,f110,f912,f913,f914,f915,f916,f920,f929,f940,f115,f322,f320,f236,f131,f121,f111,f1094,f114,f1123,f83,f1170,f128]) ).
fof(f128,plain,
( element(sK3(x,any1),any1)
| injection(x) ),
inference(resolution,[],[f100,f84]) ).
fof(f1170,plain,
( ~ injection_2(x)
| ~ spl9_1 ),
inference(global_subsumption,[],[f117,f112,f82,f84,f85,f87,f127,f100,f101,f86,f134,f136,f93,f95,f97,f99,f103,f135,f89,f180,f94,f189,f190,f191,f98,f90,f96,f102,f91,f146,f282,f283,f284,f92,f165,f168,f195,f353,f354,f355,f116,f375,f88,f416,f433,f434,f435,f104,f460,f108,f566,f567,f568,f569,f573,f587,f595,f596,f597,f598,f602,f616,f105,f655,f113,f747,f109,f778,f779,f780,f781,f785,f803,f288,f826,f827,f828,f829,f830,f831,f172,f839,f840,f841,f842,f843,f844,f173,f174,f110,f912,f913,f914,f915,f916,f920,f929,f940,f115,f322,f320,f236,f131,f128,f121,f111,f1094,f114,f1123,f83]) ).
fof(f83,plain,
( ~ injection_2(x)
| ~ injection(x) ),
inference(cnf_transformation,[],[f60]) ).
fof(f60,plain,
( ( ~ injection_2(x)
| ~ injection(x) )
& ( injection_2(x)
| injection(x) ) ),
inference(nnf_transformation,[],[f31]) ).
fof(f31,plain,
( injection(x)
<~> injection_2(x) ),
inference(ennf_transformation,[],[f18]) ).
fof(f18,negated_conjecture,
~ ( injection(x)
<=> injection_2(x) ),
inference(negated_conjecture,[],[f17]) ).
fof(f17,conjecture,
( injection(x)
<=> injection_2(x) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',my) ).
fof(f1123,plain,
! [X2,X3,X0,X1,X4,X5] :
( commute(X0,X1,X0,X1)
| ~ morphism(X1,X2,X3)
| ~ morphism(X0,X4,X2)
| ~ morphism(X1,X5,X3)
| ~ morphism(X0,X4,X5) ),
inference(equality_resolution,[],[f114]) ).
fof(f114,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( apply(X1,apply(X0,sK8(X0,X1,X2,X3,X4))) != apply(X3,apply(X2,sK8(X0,X1,X2,X3,X4)))
| commute(X0,X1,X2,X3)
| ~ morphism(X3,X6,X7)
| ~ morphism(X2,X4,X6)
| ~ morphism(X1,X5,X7)
| ~ morphism(X0,X4,X5) ),
inference(cnf_transformation,[],[f81]) ).
fof(f81,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( commute(X0,X1,X2,X3)
| ( apply(X1,apply(X0,sK8(X0,X1,X2,X3,X4))) != apply(X3,apply(X2,sK8(X0,X1,X2,X3,X4)))
& element(sK8(X0,X1,X2,X3,X4),X4) )
| ~ morphism(X3,X6,X7)
| ~ morphism(X2,X4,X6)
| ~ morphism(X1,X5,X7)
| ~ morphism(X0,X4,X5) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f57,f80]) ).
fof(f80,plain,
! [X0,X1,X2,X3,X4] :
( ? [X8] :
( apply(X1,apply(X0,X8)) != apply(X3,apply(X2,X8))
& element(X8,X4) )
=> ( apply(X1,apply(X0,sK8(X0,X1,X2,X3,X4))) != apply(X3,apply(X2,sK8(X0,X1,X2,X3,X4)))
& element(sK8(X0,X1,X2,X3,X4),X4) ) ),
introduced(choice_axiom,[]) ).
fof(f57,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( commute(X0,X1,X2,X3)
| ? [X8] :
( apply(X1,apply(X0,X8)) != apply(X3,apply(X2,X8))
& element(X8,X4) )
| ~ morphism(X3,X6,X7)
| ~ morphism(X2,X4,X6)
| ~ morphism(X1,X5,X7)
| ~ morphism(X0,X4,X5) ),
inference(flattening,[],[f56]) ).
fof(f56,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( commute(X0,X1,X2,X3)
| ? [X8] :
( apply(X1,apply(X0,X8)) != apply(X3,apply(X2,X8))
& element(X8,X4) )
| ~ morphism(X3,X6,X7)
| ~ morphism(X2,X4,X6)
| ~ morphism(X1,X5,X7)
| ~ morphism(X0,X4,X5) ),
inference(ennf_transformation,[],[f29]) ).
fof(f29,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ( ! [X8] :
( element(X8,X4)
=> apply(X1,apply(X0,X8)) = apply(X3,apply(X2,X8)) )
& morphism(X3,X6,X7)
& morphism(X2,X4,X6)
& morphism(X1,X5,X7)
& morphism(X0,X4,X5) )
=> commute(X0,X1,X2,X3) ),
inference(rectify,[],[f9]) ).
fof(f9,axiom,
! [X12,X13,X14,X15,X1,X16,X17,X2] :
( ( ! [X7] :
( element(X7,X1)
=> apply(X13,apply(X12,X7)) = apply(X15,apply(X14,X7)) )
& morphism(X15,X17,X2)
& morphism(X14,X1,X17)
& morphism(X13,X16,X2)
& morphism(X12,X1,X16) )
=> commute(X12,X13,X14,X15) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',properties_for_commute) ).
fof(f1094,plain,
! [X0,X1] :
( sK6(X0,x,X1,any1,any2) = apply(X0,sK7(X0,x,X1,any1,any2))
| zero(any2) = apply(x,sK6(X0,x,X1,any1,any2))
| exact(X0,x)
| ~ morphism(X0,X1,any1) ),
inference(resolution,[],[f111,f84]) ).
fof(f111,plain,
! [X2,X3,X0,X1,X4] :
( ~ morphism(X1,X3,X4)
| sK6(X0,X1,X2,X3,X4) = apply(X0,sK7(X0,X1,X2,X3,X4))
| zero(X4) = apply(X1,sK6(X0,X1,X2,X3,X4))
| exact(X0,X1)
| ~ morphism(X0,X2,X3) ),
inference(cnf_transformation,[],[f79]) ).
fof(f115,plain,
! [X2,X3,X0,X1,X8,X6,X7,X4,X5] :
( ~ commute(X0,X1,X2,X3)
| ~ element(X8,X4)
| ~ morphism(X3,X6,X7)
| ~ morphism(X2,X4,X6)
| ~ morphism(X1,X5,X7)
| ~ morphism(X0,X4,X5)
| apply(X1,apply(X0,X8)) = apply(X3,apply(X2,X8)) ),
inference(cnf_transformation,[],[f59]) ).
fof(f59,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ! [X8] :
( apply(X1,apply(X0,X8)) = apply(X3,apply(X2,X8))
| ~ element(X8,X4) )
| ~ morphism(X3,X6,X7)
| ~ morphism(X2,X4,X6)
| ~ morphism(X1,X5,X7)
| ~ morphism(X0,X4,X5)
| ~ commute(X0,X1,X2,X3) ),
inference(flattening,[],[f58]) ).
fof(f58,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ! [X8] :
( apply(X1,apply(X0,X8)) = apply(X3,apply(X2,X8))
| ~ element(X8,X4) )
| ~ morphism(X3,X6,X7)
| ~ morphism(X2,X4,X6)
| ~ morphism(X1,X5,X7)
| ~ morphism(X0,X4,X5)
| ~ commute(X0,X1,X2,X3) ),
inference(ennf_transformation,[],[f30]) ).
fof(f30,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ( morphism(X3,X6,X7)
& morphism(X2,X4,X6)
& morphism(X1,X5,X7)
& morphism(X0,X4,X5)
& commute(X0,X1,X2,X3) )
=> ! [X8] :
( element(X8,X4)
=> apply(X1,apply(X0,X8)) = apply(X3,apply(X2,X8)) ) ),
inference(rectify,[],[f8]) ).
fof(f8,axiom,
! [X12,X13,X14,X15,X1,X16,X17,X2] :
( ( morphism(X15,X17,X2)
& morphism(X14,X1,X17)
& morphism(X13,X16,X2)
& morphism(X12,X1,X16)
& commute(X12,X13,X14,X15) )
=> ! [X7] :
( element(X7,X1)
=> apply(X13,apply(X12,X7)) = apply(X15,apply(X14,X7)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commute_properties) ).
fof(f940,plain,
! [X2,X3,X0,X1,X4] :
( sK6(X0,X1,X2,any1,X3) = apply(X0,sK7(X0,X1,X2,any1,X3))
| exact(X0,X1)
| ~ morphism(X1,any1,X3)
| ~ morphism(X0,X2,any1)
| ~ element(X4,any1)
| apply(x,subtract(any1,sK6(X0,X1,X2,any1,X3),X4)) = subtract(any2,apply(x,sK6(X0,X1,X2,any1,X3)),apply(x,X4)) ),
inference(resolution,[],[f110,f416]) ).
fof(f929,plain,
! [X2,X3,X0,X1,X4] :
( sK6(X0,X1,X2,any1,X3) = apply(X0,sK7(X0,X1,X2,any1,X3))
| exact(X0,X1)
| ~ morphism(X1,any1,X3)
| ~ morphism(X0,X2,any1)
| zero(any2) = subtract(any2,subtract(any2,apply(x,sK6(X0,X1,X2,any1,X3)),X4),subtract(any2,apply(x,sK6(X0,X1,X2,any1,X3)),X4))
| ~ element(X4,any2) ),
inference(resolution,[],[f110,f288]) ).
fof(f920,plain,
! [X2,X3,X0,X1,X4] :
( sK6(X0,X1,X2,any1,X3) = apply(X0,sK7(X0,X1,X2,any1,X3))
| exact(X0,X1)
| ~ morphism(X1,any1,X3)
| ~ morphism(X0,X2,any1)
| ~ element(X4,any2)
| apply(x,sK6(X0,X1,X2,any1,X3)) = subtract(any2,X4,subtract(any2,X4,apply(x,sK6(X0,X1,X2,any1,X3)))) ),
inference(resolution,[],[f110,f195]) ).
fof(f916,plain,
! [X2,X3,X0,X1,X4] :
( sK6(X0,X1,X2,any1,X3) = apply(X0,sK7(X0,X1,X2,any1,X3))
| exact(X0,X1)
| ~ morphism(X1,any1,X3)
| ~ morphism(X0,X2,any1)
| zero(any2) = subtract(any2,apply(x,subtract(any1,X4,sK6(X0,X1,X2,any1,X3))),apply(x,subtract(any1,X4,sK6(X0,X1,X2,any1,X3))))
| ~ element(X4,any1) ),
inference(resolution,[],[f110,f172]) ).
fof(f915,plain,
! [X2,X3,X0,X1] :
( sK6(X0,X1,X2,any1,X3) = apply(X0,sK7(X0,X1,X2,any1,X3))
| exact(X0,X1)
| ~ morphism(X1,any1,X3)
| ~ morphism(X0,X2,any1)
| zero(any2) = subtract(any2,apply(x,sK6(X0,X1,X2,any1,X3)),apply(x,sK6(X0,X1,X2,any1,X3))) ),
inference(resolution,[],[f110,f135]) ).
fof(f914,plain,
! [X2,X3,X0,X1,X4] :
( sK6(X0,X1,X2,X3,X4) = apply(X0,sK7(X0,X1,X2,X3,X4))
| exact(X0,X1)
| ~ morphism(X1,X3,X4)
| ~ morphism(X0,X2,X3)
| zero(X3) = subtract(X3,sK6(X0,X1,X2,X3,X4),sK6(X0,X1,X2,X3,X4)) ),
inference(resolution,[],[f110,f85]) ).
fof(f913,plain,
! [X2,X3,X0,X1,X4,X5] :
( sK6(X0,X1,X2,X3,X4) = apply(X0,sK7(X0,X1,X2,X3,X4))
| exact(X0,X1)
| ~ morphism(X1,X3,X4)
| ~ morphism(X0,X2,X3)
| sK6(X0,X1,X2,X3,X4) = subtract(X3,X5,subtract(X3,X5,sK6(X0,X1,X2,X3,X4)))
| ~ element(X5,X3) ),
inference(resolution,[],[f110,f94]) ).
fof(f912,plain,
! [X2,X3,X0,X1,X4,X5] :
( sK6(X0,X1,X2,X3,X4) = apply(X0,sK7(X0,X1,X2,X3,X4))
| exact(X0,X1)
| ~ morphism(X1,X3,X4)
| ~ morphism(X0,X2,X3)
| ~ element(X5,X3)
| zero(X3) = subtract(X3,subtract(X3,sK6(X0,X1,X2,X3,X4),X5),subtract(X3,sK6(X0,X1,X2,X3,X4),X5)) ),
inference(resolution,[],[f110,f146]) ).
fof(f110,plain,
! [X2,X3,X0,X1,X4] :
( element(sK6(X0,X1,X2,X3,X4),X3)
| sK6(X0,X1,X2,X3,X4) = apply(X0,sK7(X0,X1,X2,X3,X4))
| exact(X0,X1)
| ~ morphism(X1,X3,X4)
| ~ morphism(X0,X2,X3) ),
inference(cnf_transformation,[],[f79]) ).
fof(f174,plain,
! [X0,X1] :
( ~ morphism(X0,X1,any1)
| surjection(X0)
| zero(any2) = subtract(any2,apply(x,sK1(X0,X1,any1)),apply(x,sK1(X0,X1,any1))) ),
inference(resolution,[],[f135,f95]) ).
fof(f173,plain,
! [X0,X1] :
( ~ morphism(X0,any1,X1)
| injection_2(X0)
| zero(any2) = subtract(any2,apply(x,sK2(X0,any1,X1)),apply(x,sK2(X0,any1,X1))) ),
inference(resolution,[],[f135,f97]) ).
fof(f844,plain,
! [X2,X3,X0,X1,X4] :
( zero(any2) = subtract(any2,apply(x,subtract(any1,X0,sK6(X1,X2,X3,any1,X4))),apply(x,subtract(any1,X0,sK6(X1,X2,X3,any1,X4))))
| ~ element(X0,any1)
| element(sK7(X1,X2,X3,any1,X4),X3)
| exact(X1,X2)
| ~ morphism(X2,any1,X4)
| ~ morphism(X1,X3,any1) ),
inference(resolution,[],[f172,f108]) ).
fof(f843,plain,
! [X2,X3,X0,X1,X4] :
( zero(any2) = subtract(any2,apply(x,subtract(any1,X0,sK7(X1,X2,any1,X3,X4))),apply(x,subtract(any1,X0,sK7(X1,X2,any1,X3,X4))))
| ~ element(X0,any1)
| element(sK6(X1,X2,any1,X3,X4),X3)
| exact(X1,X2)
| ~ morphism(X2,X3,X4)
| ~ morphism(X1,any1,X3) ),
inference(resolution,[],[f172,f108]) ).
fof(f842,plain,
! [X2,X3,X0,X1,X4] :
( zero(any2) = subtract(any2,apply(x,subtract(any1,X0,sK7(X1,X2,any1,X3,X4))),apply(x,subtract(any1,X0,sK7(X1,X2,any1,X3,X4))))
| ~ element(X0,any1)
| exact(X1,X2)
| zero(X4) = apply(X2,sK6(X1,X2,any1,X3,X4))
| ~ morphism(X2,X3,X4)
| ~ morphism(X1,any1,X3) ),
inference(resolution,[],[f172,f109]) ).
fof(f841,plain,
! [X2,X0,X1] :
( zero(any2) = subtract(any2,apply(x,subtract(any1,X0,sK1(X1,X2,any1))),apply(x,subtract(any1,X0,sK1(X1,X2,any1))))
| ~ element(X0,any1)
| surjection(X1)
| ~ morphism(X1,X2,any1) ),
inference(resolution,[],[f172,f95]) ).
fof(f840,plain,
! [X2,X0,X1] :
( zero(any2) = subtract(any2,apply(x,subtract(any1,X0,sK2(X1,any1,X2))),apply(x,subtract(any1,X0,sK2(X1,any1,X2))))
| ~ element(X0,any1)
| injection_2(X1)
| ~ morphism(X1,any1,X2) ),
inference(resolution,[],[f172,f97]) ).
fof(f839,plain,
! [X2,X0,X1] :
( zero(any2) = subtract(any2,apply(x,subtract(any1,X0,subtract(any1,X1,X2))),apply(x,subtract(any1,X0,subtract(any1,X1,X2))))
| ~ element(X0,any1)
| ~ element(X2,any1)
| ~ element(X1,any1) ),
inference(resolution,[],[f172,f93]) ).
fof(f172,plain,
! [X0,X1] :
( ~ element(X1,any1)
| zero(any2) = subtract(any2,apply(x,subtract(any1,X0,X1)),apply(x,subtract(any1,X0,X1)))
| ~ element(X0,any1) ),
inference(resolution,[],[f135,f93]) ).
fof(f831,plain,
! [X2,X3,X0,X1,X4] :
( zero(any2) = subtract(any2,subtract(any2,apply(x,sK6(X0,X1,X2,any1,X3)),X4),subtract(any2,apply(x,sK6(X0,X1,X2,any1,X3)),X4))
| ~ element(X4,any2)
| element(sK7(X0,X1,X2,any1,X3),X2)
| exact(X0,X1)
| ~ morphism(X1,any1,X3)
| ~ morphism(X0,X2,any1) ),
inference(resolution,[],[f288,f108]) ).
fof(f830,plain,
! [X2,X3,X0,X1,X4] :
( zero(any2) = subtract(any2,subtract(any2,apply(x,sK7(X0,X1,any1,X2,X3)),X4),subtract(any2,apply(x,sK7(X0,X1,any1,X2,X3)),X4))
| ~ element(X4,any2)
| element(sK6(X0,X1,any1,X2,X3),X2)
| exact(X0,X1)
| ~ morphism(X1,X2,X3)
| ~ morphism(X0,any1,X2) ),
inference(resolution,[],[f288,f108]) ).
fof(f829,plain,
! [X2,X3,X0,X1,X4] :
( zero(any2) = subtract(any2,subtract(any2,apply(x,sK7(X0,X1,any1,X2,X3)),X4),subtract(any2,apply(x,sK7(X0,X1,any1,X2,X3)),X4))
| ~ element(X4,any2)
| exact(X0,X1)
| zero(X3) = apply(X1,sK6(X0,X1,any1,X2,X3))
| ~ morphism(X1,X2,X3)
| ~ morphism(X0,any1,X2) ),
inference(resolution,[],[f288,f109]) ).
fof(f828,plain,
! [X2,X0,X1] :
( zero(any2) = subtract(any2,subtract(any2,apply(x,sK1(X0,X1,any1)),X2),subtract(any2,apply(x,sK1(X0,X1,any1)),X2))
| ~ element(X2,any2)
| surjection(X0)
| ~ morphism(X0,X1,any1) ),
inference(resolution,[],[f288,f95]) ).
fof(f827,plain,
! [X2,X0,X1] :
( zero(any2) = subtract(any2,subtract(any2,apply(x,sK2(X0,any1,X1)),X2),subtract(any2,apply(x,sK2(X0,any1,X1)),X2))
| ~ element(X2,any2)
| injection_2(X0)
| ~ morphism(X0,any1,X1) ),
inference(resolution,[],[f288,f97]) ).
fof(f826,plain,
! [X2,X0,X1] :
( zero(any2) = subtract(any2,subtract(any2,apply(x,subtract(any1,X0,X1)),X2),subtract(any2,apply(x,subtract(any1,X0,X1)),X2))
| ~ element(X2,any2)
| ~ element(X1,any1)
| ~ element(X0,any1) ),
inference(resolution,[],[f288,f93]) ).
fof(f288,plain,
! [X0,X1] :
( ~ element(X1,any1)
| zero(any2) = subtract(any2,subtract(any2,apply(x,X1),X0),subtract(any2,apply(x,X1),X0))
| ~ element(X0,any2) ),
inference(resolution,[],[f146,f134]) ).
fof(f803,plain,
! [X2,X3,X0,X1,X4] :
( exact(X0,X1)
| zero(X2) = apply(X1,sK6(X0,X1,any1,X3,X2))
| ~ morphism(X1,X3,X2)
| ~ morphism(X0,any1,X3)
| ~ element(X4,any1)
| apply(x,subtract(any1,sK7(X0,X1,any1,X3,X2),X4)) = subtract(any2,apply(x,sK7(X0,X1,any1,X3,X2)),apply(x,X4)) ),
inference(resolution,[],[f109,f416]) ).
fof(f785,plain,
! [X2,X3,X0,X1,X4] :
( exact(X0,X1)
| zero(X2) = apply(X1,sK6(X0,X1,any1,X3,X2))
| ~ morphism(X1,X3,X2)
| ~ morphism(X0,any1,X3)
| ~ element(X4,any2)
| apply(x,sK7(X0,X1,any1,X3,X2)) = subtract(any2,X4,subtract(any2,X4,apply(x,sK7(X0,X1,any1,X3,X2)))) ),
inference(resolution,[],[f109,f195]) ).
fof(f781,plain,
! [X2,X3,X0,X1] :
( exact(X0,X1)
| zero(X2) = apply(X1,sK6(X0,X1,any1,X3,X2))
| ~ morphism(X1,X3,X2)
| ~ morphism(X0,any1,X3)
| zero(any2) = subtract(any2,apply(x,sK7(X0,X1,any1,X3,X2)),apply(x,sK7(X0,X1,any1,X3,X2))) ),
inference(resolution,[],[f109,f135]) ).
fof(f780,plain,
! [X2,X3,X0,X1,X4] :
( exact(X0,X1)
| zero(X2) = apply(X1,sK6(X0,X1,X3,X4,X2))
| ~ morphism(X1,X4,X2)
| ~ morphism(X0,X3,X4)
| zero(X3) = subtract(X3,sK7(X0,X1,X3,X4,X2),sK7(X0,X1,X3,X4,X2)) ),
inference(resolution,[],[f109,f85]) ).
fof(f779,plain,
! [X2,X3,X0,X1,X4,X5] :
( exact(X0,X1)
| zero(X2) = apply(X1,sK6(X0,X1,X3,X4,X2))
| ~ morphism(X1,X4,X2)
| ~ morphism(X0,X3,X4)
| sK7(X0,X1,X3,X4,X2) = subtract(X3,X5,subtract(X3,X5,sK7(X0,X1,X3,X4,X2)))
| ~ element(X5,X3) ),
inference(resolution,[],[f109,f94]) ).
fof(f778,plain,
! [X2,X3,X0,X1,X4,X5] :
( exact(X0,X1)
| zero(X2) = apply(X1,sK6(X0,X1,X3,X4,X2))
| ~ morphism(X1,X4,X2)
| ~ morphism(X0,X3,X4)
| ~ element(X5,X3)
| zero(X3) = subtract(X3,subtract(X3,sK7(X0,X1,X3,X4,X2),X5),subtract(X3,sK7(X0,X1,X3,X4,X2),X5)) ),
inference(resolution,[],[f109,f146]) ).
fof(f109,plain,
! [X2,X3,X0,X1,X4] :
( element(sK7(X0,X1,X2,X3,X4),X2)
| exact(X0,X1)
| zero(X4) = apply(X1,sK6(X0,X1,X2,X3,X4))
| ~ morphism(X1,X3,X4)
| ~ morphism(X0,X2,X3) ),
inference(cnf_transformation,[],[f79]) ).
fof(f747,plain,
! [X2,X3,X0,X1,X4] :
( element(sK8(X0,X1,X2,x,X3),X3)
| commute(X0,X1,X2,x)
| ~ morphism(X2,X3,any1)
| ~ morphism(X1,X4,any2)
| ~ morphism(X0,X3,X4) ),
inference(resolution,[],[f113,f84]) ).
fof(f113,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( ~ morphism(X3,X6,X7)
| element(sK8(X0,X1,X2,X3,X4),X4)
| commute(X0,X1,X2,X3)
| ~ morphism(X2,X4,X6)
| ~ morphism(X1,X5,X7)
| ~ morphism(X0,X4,X5) ),
inference(cnf_transformation,[],[f81]) ).
fof(f655,plain,
! [X2,X3,X0,X1] :
( zero(X0) != zero(any2)
| zero(any1) = apply(X1,sK5(X1,X2,zero(any1)))
| ~ element(zero(any1),X3)
| ~ morphism(x,X3,X0)
| ~ morphism(X1,X2,X3)
| ~ exact(X1,x) ),
inference(superposition,[],[f105,f127]) ).
fof(f105,plain,
! [X2,X3,X0,X1,X4,X5] :
( zero(X4) != apply(X1,X5)
| apply(X0,sK5(X0,X2,X5)) = X5
| ~ element(X5,X3)
| ~ morphism(X1,X3,X4)
| ~ morphism(X0,X2,X3)
| ~ exact(X0,X1) ),
inference(cnf_transformation,[],[f73]) ).
fof(f73,plain,
! [X0,X1,X2,X3,X4] :
( ! [X5] :
( ( ( zero(X4) = apply(X1,X5)
& element(X5,X3) )
| ! [X6] :
( apply(X0,X6) != X5
| ~ element(X6,X2) ) )
& ( ( apply(X0,sK5(X0,X2,X5)) = X5
& element(sK5(X0,X2,X5),X2) )
| zero(X4) != apply(X1,X5)
| ~ element(X5,X3) ) )
| ~ morphism(X1,X3,X4)
| ~ morphism(X0,X2,X3)
| ~ exact(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f71,f72]) ).
fof(f72,plain,
! [X0,X2,X5] :
( ? [X7] :
( apply(X0,X7) = X5
& element(X7,X2) )
=> ( apply(X0,sK5(X0,X2,X5)) = X5
& element(sK5(X0,X2,X5),X2) ) ),
introduced(choice_axiom,[]) ).
fof(f71,plain,
! [X0,X1,X2,X3,X4] :
( ! [X5] :
( ( ( zero(X4) = apply(X1,X5)
& element(X5,X3) )
| ! [X6] :
( apply(X0,X6) != X5
| ~ element(X6,X2) ) )
& ( ? [X7] :
( apply(X0,X7) = X5
& element(X7,X2) )
| zero(X4) != apply(X1,X5)
| ~ element(X5,X3) ) )
| ~ morphism(X1,X3,X4)
| ~ morphism(X0,X2,X3)
| ~ exact(X0,X1) ),
inference(rectify,[],[f70]) ).
fof(f70,plain,
! [X0,X1,X2,X3,X4] :
( ! [X5] :
( ( ( zero(X4) = apply(X1,X5)
& element(X5,X3) )
| ! [X6] :
( apply(X0,X6) != X5
| ~ element(X6,X2) ) )
& ( ? [X6] :
( apply(X0,X6) = X5
& element(X6,X2) )
| zero(X4) != apply(X1,X5)
| ~ element(X5,X3) ) )
| ~ morphism(X1,X3,X4)
| ~ morphism(X0,X2,X3)
| ~ exact(X0,X1) ),
inference(flattening,[],[f69]) ).
fof(f69,plain,
! [X0,X1,X2,X3,X4] :
( ! [X5] :
( ( ( zero(X4) = apply(X1,X5)
& element(X5,X3) )
| ! [X6] :
( apply(X0,X6) != X5
| ~ element(X6,X2) ) )
& ( ? [X6] :
( apply(X0,X6) = X5
& element(X6,X2) )
| zero(X4) != apply(X1,X5)
| ~ element(X5,X3) ) )
| ~ morphism(X1,X3,X4)
| ~ morphism(X0,X2,X3)
| ~ exact(X0,X1) ),
inference(nnf_transformation,[],[f53]) ).
fof(f53,plain,
! [X0,X1,X2,X3,X4] :
( ! [X5] :
( ( zero(X4) = apply(X1,X5)
& element(X5,X3) )
<=> ? [X6] :
( apply(X0,X6) = X5
& element(X6,X2) ) )
| ~ morphism(X1,X3,X4)
| ~ morphism(X0,X2,X3)
| ~ exact(X0,X1) ),
inference(flattening,[],[f52]) ).
fof(f52,plain,
! [X0,X1,X2,X3,X4] :
( ! [X5] :
( ( zero(X4) = apply(X1,X5)
& element(X5,X3) )
<=> ? [X6] :
( apply(X0,X6) = X5
& element(X6,X2) ) )
| ~ morphism(X1,X3,X4)
| ~ morphism(X0,X2,X3)
| ~ exact(X0,X1) ),
inference(ennf_transformation,[],[f27]) ).
fof(f27,plain,
! [X0,X1,X2,X3,X4] :
( ( morphism(X1,X3,X4)
& morphism(X0,X2,X3)
& exact(X0,X1) )
=> ! [X5] :
( ( zero(X4) = apply(X1,X5)
& element(X5,X3) )
<=> ? [X6] :
( apply(X0,X6) = X5
& element(X6,X2) ) ) ),
inference(rectify,[],[f6]) ).
fof(f6,axiom,
! [X8,X9,X1,X10,X2] :
( ( morphism(X9,X10,X2)
& morphism(X8,X1,X10)
& exact(X8,X9) )
=> ! [X11] :
( ( zero(X2) = apply(X9,X11)
& element(X11,X10) )
<=> ? [X7] :
( apply(X8,X7) = X11
& element(X7,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exact_properties) ).
fof(f616,plain,
! [X2,X3,X0,X1,X4] :
( element(sK7(X0,X1,X2,any1,X3),X2)
| exact(X0,X1)
| ~ morphism(X1,any1,X3)
| ~ morphism(X0,X2,any1)
| ~ element(X4,any1)
| apply(x,subtract(any1,sK6(X0,X1,X2,any1,X3),X4)) = subtract(any2,apply(x,sK6(X0,X1,X2,any1,X3)),apply(x,X4)) ),
inference(resolution,[],[f108,f416]) ).
fof(f602,plain,
! [X2,X3,X0,X1,X4] :
( element(sK7(X0,X1,X2,any1,X3),X2)
| exact(X0,X1)
| ~ morphism(X1,any1,X3)
| ~ morphism(X0,X2,any1)
| ~ element(X4,any2)
| apply(x,sK6(X0,X1,X2,any1,X3)) = subtract(any2,X4,subtract(any2,X4,apply(x,sK6(X0,X1,X2,any1,X3)))) ),
inference(resolution,[],[f108,f195]) ).
fof(f598,plain,
! [X2,X3,X0,X1] :
( element(sK7(X0,X1,X2,any1,X3),X2)
| exact(X0,X1)
| ~ morphism(X1,any1,X3)
| ~ morphism(X0,X2,any1)
| zero(any2) = subtract(any2,apply(x,sK6(X0,X1,X2,any1,X3)),apply(x,sK6(X0,X1,X2,any1,X3))) ),
inference(resolution,[],[f108,f135]) ).
fof(f597,plain,
! [X2,X3,X0,X1,X4] :
( element(sK7(X0,X1,X2,X3,X4),X2)
| exact(X0,X1)
| ~ morphism(X1,X3,X4)
| ~ morphism(X0,X2,X3)
| zero(X3) = subtract(X3,sK6(X0,X1,X2,X3,X4),sK6(X0,X1,X2,X3,X4)) ),
inference(resolution,[],[f108,f85]) ).
fof(f596,plain,
! [X2,X3,X0,X1,X4,X5] :
( element(sK7(X0,X1,X2,X3,X4),X2)
| exact(X0,X1)
| ~ morphism(X1,X3,X4)
| ~ morphism(X0,X2,X3)
| sK6(X0,X1,X2,X3,X4) = subtract(X3,X5,subtract(X3,X5,sK6(X0,X1,X2,X3,X4)))
| ~ element(X5,X3) ),
inference(resolution,[],[f108,f94]) ).
fof(f595,plain,
! [X2,X3,X0,X1,X4,X5] :
( element(sK7(X0,X1,X2,X3,X4),X2)
| exact(X0,X1)
| ~ morphism(X1,X3,X4)
| ~ morphism(X0,X2,X3)
| ~ element(X5,X3)
| zero(X3) = subtract(X3,subtract(X3,sK6(X0,X1,X2,X3,X4),X5),subtract(X3,sK6(X0,X1,X2,X3,X4),X5)) ),
inference(resolution,[],[f108,f146]) ).
fof(f587,plain,
! [X2,X3,X0,X1,X4] :
( element(sK6(X0,X1,any1,X2,X3),X2)
| exact(X0,X1)
| ~ morphism(X1,X2,X3)
| ~ morphism(X0,any1,X2)
| ~ element(X4,any1)
| apply(x,subtract(any1,sK7(X0,X1,any1,X2,X3),X4)) = subtract(any2,apply(x,sK7(X0,X1,any1,X2,X3)),apply(x,X4)) ),
inference(resolution,[],[f108,f416]) ).
fof(f573,plain,
! [X2,X3,X0,X1,X4] :
( element(sK6(X0,X1,any1,X2,X3),X2)
| exact(X0,X1)
| ~ morphism(X1,X2,X3)
| ~ morphism(X0,any1,X2)
| ~ element(X4,any2)
| apply(x,sK7(X0,X1,any1,X2,X3)) = subtract(any2,X4,subtract(any2,X4,apply(x,sK7(X0,X1,any1,X2,X3)))) ),
inference(resolution,[],[f108,f195]) ).
fof(f569,plain,
! [X2,X3,X0,X1] :
( element(sK6(X0,X1,any1,X2,X3),X2)
| exact(X0,X1)
| ~ morphism(X1,X2,X3)
| ~ morphism(X0,any1,X2)
| zero(any2) = subtract(any2,apply(x,sK7(X0,X1,any1,X2,X3)),apply(x,sK7(X0,X1,any1,X2,X3))) ),
inference(resolution,[],[f108,f135]) ).
fof(f568,plain,
! [X2,X3,X0,X1,X4] :
( element(sK6(X0,X1,X2,X3,X4),X3)
| exact(X0,X1)
| ~ morphism(X1,X3,X4)
| ~ morphism(X0,X2,X3)
| zero(X2) = subtract(X2,sK7(X0,X1,X2,X3,X4),sK7(X0,X1,X2,X3,X4)) ),
inference(resolution,[],[f108,f85]) ).
fof(f567,plain,
! [X2,X3,X0,X1,X4,X5] :
( element(sK6(X0,X1,X2,X3,X4),X3)
| exact(X0,X1)
| ~ morphism(X1,X3,X4)
| ~ morphism(X0,X2,X3)
| sK7(X0,X1,X2,X3,X4) = subtract(X2,X5,subtract(X2,X5,sK7(X0,X1,X2,X3,X4)))
| ~ element(X5,X2) ),
inference(resolution,[],[f108,f94]) ).
fof(f566,plain,
! [X2,X3,X0,X1,X4,X5] :
( element(sK6(X0,X1,X2,X3,X4),X3)
| exact(X0,X1)
| ~ morphism(X1,X3,X4)
| ~ morphism(X0,X2,X3)
| ~ element(X5,X2)
| zero(X2) = subtract(X2,subtract(X2,sK7(X0,X1,X2,X3,X4),X5),subtract(X2,sK7(X0,X1,X2,X3,X4),X5)) ),
inference(resolution,[],[f108,f146]) ).
fof(f108,plain,
! [X2,X3,X0,X1,X4] :
( element(sK7(X0,X1,X2,X3,X4),X2)
| element(sK6(X0,X1,X2,X3,X4),X3)
| exact(X0,X1)
| ~ morphism(X1,X3,X4)
| ~ morphism(X0,X2,X3) ),
inference(cnf_transformation,[],[f79]) ).
fof(f460,plain,
! [X2,X3,X0,X1] :
( zero(X0) != zero(any2)
| element(sK5(X1,X2,zero(any1)),X2)
| ~ element(zero(any1),X3)
| ~ morphism(x,X3,X0)
| ~ morphism(X1,X2,X3)
| ~ exact(X1,x) ),
inference(superposition,[],[f104,f127]) ).
fof(f104,plain,
! [X2,X3,X0,X1,X4,X5] :
( zero(X4) != apply(X1,X5)
| element(sK5(X0,X2,X5),X2)
| ~ element(X5,X3)
| ~ morphism(X1,X3,X4)
| ~ morphism(X0,X2,X3)
| ~ exact(X0,X1) ),
inference(cnf_transformation,[],[f73]) ).
fof(f435,plain,
! [X2,X0,X1] :
( ~ element(X0,any1)
| apply(x,subtract(any1,sK1(X1,X2,any1),X0)) = subtract(any2,apply(x,sK1(X1,X2,any1)),apply(x,X0))
| surjection(X1)
| ~ morphism(X1,X2,any1) ),
inference(resolution,[],[f416,f95]) ).
fof(f434,plain,
! [X2,X0,X1] :
( ~ element(X0,any1)
| apply(x,subtract(any1,sK2(X1,any1,X2),X0)) = subtract(any2,apply(x,sK2(X1,any1,X2)),apply(x,X0))
| injection_2(X1)
| ~ morphism(X1,any1,X2) ),
inference(resolution,[],[f416,f97]) ).
fof(f433,plain,
! [X2,X0,X1] :
( ~ element(X0,any1)
| apply(x,subtract(any1,subtract(any1,X1,X2),X0)) = subtract(any2,apply(x,subtract(any1,X1,X2)),apply(x,X0))
| ~ element(X2,any1)
| ~ element(X1,any1) ),
inference(resolution,[],[f416,f93]) ).
fof(f416,plain,
! [X0,X1] :
( ~ element(X1,any1)
| ~ element(X0,any1)
| apply(x,subtract(any1,X1,X0)) = subtract(any2,apply(x,X1),apply(x,X0)) ),
inference(resolution,[],[f88,f84]) ).
fof(f88,plain,
! [X2,X3,X0,X1,X4] :
( ~ morphism(X0,X1,X2)
| ~ element(X4,X1)
| ~ element(X3,X1)
| apply(X0,subtract(X1,X3,X4)) = subtract(X2,apply(X0,X3),apply(X0,X4)) ),
inference(cnf_transformation,[],[f35]) ).
fof(f35,plain,
! [X0,X1,X2] :
( ! [X3,X4] :
( apply(X0,subtract(X1,X3,X4)) = subtract(X2,apply(X0,X3),apply(X0,X4))
| ~ element(X4,X1)
| ~ element(X3,X1) )
| ~ morphism(X0,X1,X2) ),
inference(flattening,[],[f34]) ).
fof(f34,plain,
! [X0,X1,X2] :
( ! [X3,X4] :
( apply(X0,subtract(X1,X3,X4)) = subtract(X2,apply(X0,X3),apply(X0,X4))
| ~ element(X4,X1)
| ~ element(X3,X1) )
| ~ morphism(X0,X1,X2) ),
inference(ennf_transformation,[],[f20]) ).
fof(f20,plain,
! [X0,X1,X2] :
( morphism(X0,X1,X2)
=> ! [X3,X4] :
( ( element(X4,X1)
& element(X3,X1) )
=> apply(X0,subtract(X1,X3,X4)) = subtract(X2,apply(X0,X3),apply(X0,X4)) ) ),
inference(rectify,[],[f13]) ).
fof(f13,axiom,
! [X0,X1,X2] :
( morphism(X0,X1,X2)
=> ! [X4,X5] :
( ( element(X5,X1)
& element(X4,X1) )
=> apply(X0,subtract(X1,X4,X5)) = subtract(X2,apply(X0,X4),apply(X0,X5)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subtract_distribution) ).
fof(f375,plain,
! [X2,X0,X1] :
( ~ morphism(X2,X1,any1)
| zero(any2) = apply(x,apply(X2,X0))
| ~ element(X0,X1)
| ~ exact(X2,x) ),
inference(resolution,[],[f116,f84]) ).
fof(f116,plain,
! [X2,X3,X0,X1,X6,X4] :
( ~ morphism(X1,X3,X4)
| ~ element(X6,X2)
| zero(X4) = apply(X1,apply(X0,X6))
| ~ morphism(X0,X2,X3)
| ~ exact(X0,X1) ),
inference(equality_resolution,[],[f107]) ).
fof(f107,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( zero(X4) = apply(X1,X5)
| apply(X0,X6) != X5
| ~ element(X6,X2)
| ~ morphism(X1,X3,X4)
| ~ morphism(X0,X2,X3)
| ~ exact(X0,X1) ),
inference(cnf_transformation,[],[f73]) ).
fof(f355,plain,
! [X2,X0,X1] :
( ~ element(X0,any2)
| apply(x,sK1(X1,X2,any1)) = subtract(any2,X0,subtract(any2,X0,apply(x,sK1(X1,X2,any1))))
| surjection(X1)
| ~ morphism(X1,X2,any1) ),
inference(resolution,[],[f195,f95]) ).
fof(f354,plain,
! [X2,X0,X1] :
( ~ element(X0,any2)
| apply(x,sK2(X1,any1,X2)) = subtract(any2,X0,subtract(any2,X0,apply(x,sK2(X1,any1,X2))))
| injection_2(X1)
| ~ morphism(X1,any1,X2) ),
inference(resolution,[],[f195,f97]) ).
fof(f353,plain,
! [X2,X0,X1] :
( ~ element(X0,any2)
| apply(x,subtract(any1,X1,X2)) = subtract(any2,X0,subtract(any2,X0,apply(x,subtract(any1,X1,X2))))
| ~ element(X2,any1)
| ~ element(X1,any1) ),
inference(resolution,[],[f195,f93]) ).
fof(f195,plain,
! [X0,X1] :
( ~ element(X1,any1)
| ~ element(X0,any2)
| apply(x,X1) = subtract(any2,X0,subtract(any2,X0,apply(x,X1))) ),
inference(resolution,[],[f94,f134]) ).
fof(f168,plain,
! [X2,X0,X1] :
( ~ morphism(X0,X1,X2)
| injection_2(X0)
| zero(X1) = subtract(X1,sK2(X0,X1,X2),sK2(X0,X1,X2)) ),
inference(resolution,[],[f97,f85]) ).
fof(f165,plain,
! [X2,X0,X1] :
( ~ morphism(X0,X1,X2)
| surjection(X0)
| zero(X2) = subtract(X2,sK1(X0,X1,X2),sK1(X0,X1,X2)) ),
inference(resolution,[],[f95,f85]) ).
fof(f92,plain,
! [X2,X3,X0,X1,X4] :
( apply(X0,X3) != apply(X0,X4)
| X3 = X4
| ~ element(X4,X1)
| ~ element(X3,X1)
| ~ morphism(X0,X1,X2)
| ~ injection(X0) ),
inference(cnf_transformation,[],[f41]) ).
fof(f41,plain,
! [X0,X1,X2] :
( ! [X3,X4] :
( X3 = X4
| apply(X0,X3) != apply(X0,X4)
| ~ element(X4,X1)
| ~ element(X3,X1) )
| ~ morphism(X0,X1,X2)
| ~ injection(X0) ),
inference(flattening,[],[f40]) ).
fof(f40,plain,
! [X0,X1,X2] :
( ! [X3,X4] :
( X3 = X4
| apply(X0,X3) != apply(X0,X4)
| ~ element(X4,X1)
| ~ element(X3,X1) )
| ~ morphism(X0,X1,X2)
| ~ injection(X0) ),
inference(ennf_transformation,[],[f22]) ).
fof(f22,plain,
! [X0,X1,X2] :
( ( morphism(X0,X1,X2)
& injection(X0) )
=> ! [X3,X4] :
( ( apply(X0,X3) = apply(X0,X4)
& element(X4,X1)
& element(X3,X1) )
=> X3 = X4 ) ),
inference(rectify,[],[f2]) ).
fof(f2,axiom,
! [X0,X1,X2] :
( ( morphism(X0,X1,X2)
& injection(X0) )
=> ! [X4,X5] :
( ( apply(X0,X4) = apply(X0,X5)
& element(X5,X1)
& element(X4,X1) )
=> X4 = X5 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',injection_properties) ).
fof(f284,plain,
! [X2,X3,X0,X1] :
( ~ element(X0,X1)
| zero(X1) = subtract(X1,subtract(X1,sK1(X2,X3,X1),X0),subtract(X1,sK1(X2,X3,X1),X0))
| surjection(X2)
| ~ morphism(X2,X3,X1) ),
inference(resolution,[],[f146,f95]) ).
fof(f283,plain,
! [X2,X3,X0,X1] :
( ~ element(X0,X1)
| zero(X1) = subtract(X1,subtract(X1,sK2(X2,X1,X3),X0),subtract(X1,sK2(X2,X1,X3),X0))
| injection_2(X2)
| ~ morphism(X2,X1,X3) ),
inference(resolution,[],[f146,f97]) ).
fof(f282,plain,
! [X2,X3,X0,X1] :
( ~ element(X0,X1)
| zero(X1) = subtract(X1,subtract(X1,subtract(X1,X2,X3),X0),subtract(X1,subtract(X1,X2,X3),X0))
| ~ element(X3,X1)
| ~ element(X2,X1) ),
inference(resolution,[],[f146,f93]) ).
fof(f146,plain,
! [X2,X0,X1] :
( ~ element(X2,X1)
| ~ element(X0,X1)
| zero(X1) = subtract(X1,subtract(X1,X2,X0),subtract(X1,X2,X0)) ),
inference(resolution,[],[f93,f85]) ).
fof(f91,plain,
! [X2,X3,X0,X1] :
( apply(X0,X3) != zero(X2)
| zero(X1) = X3
| ~ element(X3,X1)
| ~ morphism(X0,X1,X2)
| ~ injection_2(X0) ),
inference(cnf_transformation,[],[f39]) ).
fof(f39,plain,
! [X0,X1,X2] :
( ! [X3] :
( zero(X1) = X3
| apply(X0,X3) != zero(X2)
| ~ element(X3,X1) )
| ~ morphism(X0,X1,X2)
| ~ injection_2(X0) ),
inference(flattening,[],[f38]) ).
fof(f38,plain,
! [X0,X1,X2] :
( ! [X3] :
( zero(X1) = X3
| apply(X0,X3) != zero(X2)
| ~ element(X3,X1) )
| ~ morphism(X0,X1,X2)
| ~ injection_2(X0) ),
inference(ennf_transformation,[],[f14]) ).
fof(f14,axiom,
! [X0,X1,X2] :
( ( morphism(X0,X1,X2)
& injection_2(X0) )
=> ! [X3] :
( ( apply(X0,X3) = zero(X2)
& element(X3,X1) )
=> zero(X1) = X3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',injection_properties_2) ).
fof(f102,plain,
! [X2,X0,X1] :
( ~ morphism(X0,X1,X2)
| apply(X0,sK3(X0,X1)) = apply(X0,sK4(X0,X1))
| injection(X0) ),
inference(cnf_transformation,[],[f68]) ).
fof(f68,plain,
! [X0,X1,X2] :
( injection(X0)
| ( sK3(X0,X1) != sK4(X0,X1)
& apply(X0,sK3(X0,X1)) = apply(X0,sK4(X0,X1))
& element(sK4(X0,X1),X1)
& element(sK3(X0,X1),X1) )
| ~ morphism(X0,X1,X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4])],[f51,f67]) ).
fof(f67,plain,
! [X0,X1] :
( ? [X3,X4] :
( X3 != X4
& apply(X0,X3) = apply(X0,X4)
& element(X4,X1)
& element(X3,X1) )
=> ( sK3(X0,X1) != sK4(X0,X1)
& apply(X0,sK3(X0,X1)) = apply(X0,sK4(X0,X1))
& element(sK4(X0,X1),X1)
& element(sK3(X0,X1),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f51,plain,
! [X0,X1,X2] :
( injection(X0)
| ? [X3,X4] :
( X3 != X4
& apply(X0,X3) = apply(X0,X4)
& element(X4,X1)
& element(X3,X1) )
| ~ morphism(X0,X1,X2) ),
inference(flattening,[],[f50]) ).
fof(f50,plain,
! [X0,X1,X2] :
( injection(X0)
| ? [X3,X4] :
( X3 != X4
& apply(X0,X3) = apply(X0,X4)
& element(X4,X1)
& element(X3,X1) )
| ~ morphism(X0,X1,X2) ),
inference(ennf_transformation,[],[f26]) ).
fof(f26,plain,
! [X0,X1,X2] :
( ( ! [X3,X4] :
( ( apply(X0,X3) = apply(X0,X4)
& element(X4,X1)
& element(X3,X1) )
=> X3 = X4 )
& morphism(X0,X1,X2) )
=> injection(X0) ),
inference(rectify,[],[f3]) ).
fof(f3,axiom,
! [X0,X1,X2] :
( ( ! [X4,X5] :
( ( apply(X0,X4) = apply(X0,X5)
& element(X5,X1)
& element(X4,X1) )
=> X4 = X5 )
& morphism(X0,X1,X2) )
=> injection(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',properties_for_injection) ).
fof(f96,plain,
! [X2,X0,X1,X4] :
( apply(X0,X4) != sK1(X0,X1,X2)
| surjection(X0)
| ~ element(X4,X1)
| ~ morphism(X0,X1,X2) ),
inference(cnf_transformation,[],[f64]) ).
fof(f64,plain,
! [X0,X1,X2] :
( surjection(X0)
| ( ! [X4] :
( apply(X0,X4) != sK1(X0,X1,X2)
| ~ element(X4,X1) )
& element(sK1(X0,X1,X2),X2) )
| ~ morphism(X0,X1,X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f47,f63]) ).
fof(f63,plain,
! [X0,X1,X2] :
( ? [X3] :
( ! [X4] :
( apply(X0,X4) != X3
| ~ element(X4,X1) )
& element(X3,X2) )
=> ( ! [X4] :
( apply(X0,X4) != sK1(X0,X1,X2)
| ~ element(X4,X1) )
& element(sK1(X0,X1,X2),X2) ) ),
introduced(choice_axiom,[]) ).
fof(f47,plain,
! [X0,X1,X2] :
( surjection(X0)
| ? [X3] :
( ! [X4] :
( apply(X0,X4) != X3
| ~ element(X4,X1) )
& element(X3,X2) )
| ~ morphism(X0,X1,X2) ),
inference(flattening,[],[f46]) ).
fof(f46,plain,
! [X0,X1,X2] :
( surjection(X0)
| ? [X3] :
( ! [X4] :
( apply(X0,X4) != X3
| ~ element(X4,X1) )
& element(X3,X2) )
| ~ morphism(X0,X1,X2) ),
inference(ennf_transformation,[],[f25]) ).
fof(f25,plain,
! [X0,X1,X2] :
( ( ! [X3] :
( element(X3,X2)
=> ? [X4] :
( apply(X0,X4) = X3
& element(X4,X1) ) )
& morphism(X0,X1,X2) )
=> surjection(X0) ),
inference(rectify,[],[f5]) ).
fof(f5,axiom,
! [X0,X1,X2] :
( ( ! [X6] :
( element(X6,X2)
=> ? [X7] :
( apply(X0,X7) = X6
& element(X7,X1) ) )
& morphism(X0,X1,X2) )
=> surjection(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',properties_for_surjection) ).
fof(f90,plain,
! [X2,X3,X0,X1] :
( ~ morphism(X0,X1,X2)
| ~ element(X3,X2)
| apply(X0,sK0(X0,X1,X3)) = X3
| ~ surjection(X0) ),
inference(cnf_transformation,[],[f62]) ).
fof(f62,plain,
! [X0,X1,X2] :
( ! [X3] :
( ( apply(X0,sK0(X0,X1,X3)) = X3
& element(sK0(X0,X1,X3),X1) )
| ~ element(X3,X2) )
| ~ morphism(X0,X1,X2)
| ~ surjection(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f37,f61]) ).
fof(f61,plain,
! [X0,X1,X3] :
( ? [X4] :
( apply(X0,X4) = X3
& element(X4,X1) )
=> ( apply(X0,sK0(X0,X1,X3)) = X3
& element(sK0(X0,X1,X3),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f37,plain,
! [X0,X1,X2] :
( ! [X3] :
( ? [X4] :
( apply(X0,X4) = X3
& element(X4,X1) )
| ~ element(X3,X2) )
| ~ morphism(X0,X1,X2)
| ~ surjection(X0) ),
inference(flattening,[],[f36]) ).
fof(f36,plain,
! [X0,X1,X2] :
( ! [X3] :
( ? [X4] :
( apply(X0,X4) = X3
& element(X4,X1) )
| ~ element(X3,X2) )
| ~ morphism(X0,X1,X2)
| ~ surjection(X0) ),
inference(ennf_transformation,[],[f21]) ).
fof(f21,plain,
! [X0,X1,X2] :
( ( morphism(X0,X1,X2)
& surjection(X0) )
=> ! [X3] :
( element(X3,X2)
=> ? [X4] :
( apply(X0,X4) = X3
& element(X4,X1) ) ) ),
inference(rectify,[],[f4]) ).
fof(f4,axiom,
! [X0,X1,X2] :
( ( morphism(X0,X1,X2)
& surjection(X0) )
=> ! [X6] :
( element(X6,X2)
=> ? [X7] :
( apply(X0,X7) = X6
& element(X7,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',surjection_properties) ).
fof(f98,plain,
! [X2,X0,X1] :
( ~ morphism(X0,X1,X2)
| zero(X2) = apply(X0,sK2(X0,X1,X2))
| injection_2(X0) ),
inference(cnf_transformation,[],[f66]) ).
fof(f191,plain,
! [X2,X3,X0,X1] :
( sK1(X2,X3,X0) = subtract(X0,X1,subtract(X0,X1,sK1(X2,X3,X0)))
| ~ element(X1,X0)
| surjection(X2)
| ~ morphism(X2,X3,X0) ),
inference(resolution,[],[f94,f95]) ).
fof(f190,plain,
! [X2,X3,X0,X1] :
( sK2(X2,X0,X3) = subtract(X0,X1,subtract(X0,X1,sK2(X2,X0,X3)))
| ~ element(X1,X0)
| injection_2(X2)
| ~ morphism(X2,X0,X3) ),
inference(resolution,[],[f94,f97]) ).
fof(f189,plain,
! [X2,X3,X0,X1] :
( subtract(X0,X2,X3) = subtract(X0,X1,subtract(X0,X1,subtract(X0,X2,X3)))
| ~ element(X1,X0)
| ~ element(X3,X0)
| ~ element(X2,X0) ),
inference(resolution,[],[f94,f93]) ).
fof(f94,plain,
! [X2,X0,X1] :
( ~ element(X2,X0)
| subtract(X0,X1,subtract(X0,X1,X2)) = X2
| ~ element(X1,X0) ),
inference(cnf_transformation,[],[f45]) ).
fof(f45,plain,
! [X0,X1,X2] :
( subtract(X0,X1,subtract(X0,X1,X2)) = X2
| ~ element(X2,X0)
| ~ element(X1,X0) ),
inference(flattening,[],[f44]) ).
fof(f44,plain,
! [X0,X1,X2] :
( subtract(X0,X1,subtract(X0,X1,X2)) = X2
| ~ element(X2,X0)
| ~ element(X1,X0) ),
inference(ennf_transformation,[],[f24]) ).
fof(f24,plain,
! [X0,X1,X2] :
( ( element(X2,X0)
& element(X1,X0) )
=> subtract(X0,X1,subtract(X0,X1,X2)) = X2 ),
inference(rectify,[],[f12]) ).
fof(f12,axiom,
! [X1,X4,X5] :
( ( element(X5,X1)
& element(X4,X1) )
=> subtract(X1,X4,subtract(X1,X4,X5)) = X5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subtract_cancellation) ).
fof(f180,plain,
! [X0] :
( ~ element(X0,any2)
| element(sK0(x,any1,X0),any1)
| ~ surjection(x) ),
inference(resolution,[],[f89,f84]) ).
fof(f89,plain,
! [X2,X3,X0,X1] :
( ~ morphism(X0,X1,X2)
| ~ element(X3,X2)
| element(sK0(X0,X1,X3),X1)
| ~ surjection(X0) ),
inference(cnf_transformation,[],[f62]) ).
fof(f135,plain,
! [X0] :
( ~ element(X0,any1)
| zero(any2) = subtract(any2,apply(x,X0),apply(x,X0)) ),
inference(resolution,[],[f134,f85]) ).
fof(f103,plain,
! [X2,X0,X1] :
( sK3(X0,X1) != sK4(X0,X1)
| injection(X0)
| ~ morphism(X0,X1,X2) ),
inference(cnf_transformation,[],[f68]) ).
fof(f99,plain,
! [X2,X0,X1] :
( zero(X1) != sK2(X0,X1,X2)
| injection_2(X0)
| ~ morphism(X0,X1,X2) ),
inference(cnf_transformation,[],[f66]) ).
fof(f95,plain,
! [X2,X0,X1] :
( element(sK1(X0,X1,X2),X2)
| surjection(X0)
| ~ morphism(X0,X1,X2) ),
inference(cnf_transformation,[],[f64]) ).
fof(f93,plain,
! [X2,X0,X1] :
( element(subtract(X0,X1,X2),X0)
| ~ element(X2,X0)
| ~ element(X1,X0) ),
inference(cnf_transformation,[],[f43]) ).
fof(f43,plain,
! [X0,X1,X2] :
( element(subtract(X0,X1,X2),X0)
| ~ element(X2,X0)
| ~ element(X1,X0) ),
inference(flattening,[],[f42]) ).
fof(f42,plain,
! [X0,X1,X2] :
( element(subtract(X0,X1,X2),X0)
| ~ element(X2,X0)
| ~ element(X1,X0) ),
inference(ennf_transformation,[],[f23]) ).
fof(f23,plain,
! [X0,X1,X2] :
( ( element(X2,X0)
& element(X1,X0) )
=> element(subtract(X0,X1,X2),X0) ),
inference(rectify,[],[f10]) ).
fof(f10,axiom,
! [X1,X4,X5] :
( ( element(X5,X1)
& element(X4,X1) )
=> element(subtract(X1,X4,X5),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subtract_in_domain) ).
fof(f140,plain,
( ~ element(zero(any1),any1)
| spl9_3 ),
inference(avatar_component_clause,[],[f138]) ).
fof(f138,plain,
( spl9_3
<=> element(zero(any1),any1) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_3])]) ).
fof(f136,plain,
( element(zero(any2),any2)
| ~ element(zero(any1),any1) ),
inference(superposition,[],[f134,f127]) ).
fof(f134,plain,
! [X0] :
( element(apply(x,X0),any2)
| ~ element(X0,any1) ),
inference(resolution,[],[f86,f84]) ).
fof(f86,plain,
! [X2,X3,X0,X1] :
( ~ morphism(X0,X1,X2)
| ~ element(X3,X1)
| element(apply(X0,X3),X2) ),
inference(cnf_transformation,[],[f33]) ).
fof(f33,plain,
! [X0,X1,X2] :
( ( apply(X0,zero(X1)) = zero(X2)
& ! [X3] :
( element(apply(X0,X3),X2)
| ~ element(X3,X1) ) )
| ~ morphism(X0,X1,X2) ),
inference(ennf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0,X1,X2] :
( morphism(X0,X1,X2)
=> ( apply(X0,zero(X1)) = zero(X2)
& ! [X3] :
( element(X3,X1)
=> element(apply(X0,X3),X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',morphism) ).
fof(f101,plain,
! [X2,X0,X1] :
( ~ morphism(X0,X1,X2)
| element(sK4(X0,X1),X1)
| injection(X0) ),
inference(cnf_transformation,[],[f68]) ).
fof(f100,plain,
! [X2,X0,X1] :
( ~ morphism(X0,X1,X2)
| element(sK3(X0,X1),X1)
| injection(X0) ),
inference(cnf_transformation,[],[f68]) ).
fof(f127,plain,
apply(x,zero(any1)) = zero(any2),
inference(resolution,[],[f87,f84]) ).
fof(f87,plain,
! [X2,X0,X1] :
( ~ morphism(X0,X1,X2)
| apply(X0,zero(X1)) = zero(X2) ),
inference(cnf_transformation,[],[f33]) ).
fof(f85,plain,
! [X0,X1] :
( ~ element(X1,X0)
| zero(X0) = subtract(X0,X1,X1) ),
inference(cnf_transformation,[],[f32]) ).
fof(f32,plain,
! [X0,X1] :
( zero(X0) = subtract(X0,X1,X1)
| ~ element(X1,X0) ),
inference(ennf_transformation,[],[f19]) ).
fof(f19,plain,
! [X0,X1] :
( element(X1,X0)
=> zero(X0) = subtract(X0,X1,X1) ),
inference(rectify,[],[f11]) ).
fof(f11,axiom,
! [X1,X3] :
( element(X3,X1)
=> zero(X1) = subtract(X1,X3,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subtract_to_0) ).
fof(f82,plain,
( injection_2(x)
| injection(x) ),
inference(cnf_transformation,[],[f60]) ).
fof(f117,plain,
! [X2,X3,X0,X1,X6,X4] :
( element(apply(X0,X6),X3)
| ~ element(X6,X2)
| ~ morphism(X1,X3,X4)
| ~ morphism(X0,X2,X3)
| ~ exact(X0,X1) ),
inference(equality_resolution,[],[f106]) ).
fof(f106,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( element(X5,X3)
| apply(X0,X6) != X5
| ~ element(X6,X2)
| ~ morphism(X1,X3,X4)
| ~ morphism(X0,X2,X3)
| ~ exact(X0,X1) ),
inference(cnf_transformation,[],[f73]) ).
fof(f1236,plain,
( spl9_3
| ~ spl9_7 ),
inference(avatar_contradiction_clause,[],[f1235]) ).
fof(f1235,plain,
( $false
| spl9_3
| ~ spl9_7 ),
inference(global_subsumption,[],[f117,f82,f84,f85,f87,f127,f100,f101,f86,f134,f136,f93,f95,f97,f99,f103,f135,f89,f180,f94,f189,f190,f191,f98,f90,f96,f102,f91,f146,f282,f283,f284,f92,f165,f168,f195,f353,f354,f355,f116,f375,f88,f416,f433,f434,f435,f104,f460,f512,f108,f566,f567,f568,f569,f573,f587,f595,f596,f597,f598,f602,f616,f546,f629,f630,f631,f632,f633,f105,f655,f545,f665,f666,f667,f668,f669,f113,f747,f109,f778,f779,f780,f781,f785,f803,f807,f808,f288,f826,f827,f828,f829,f830,f831,f172,f836,f839,f840,f841,f842,f843,f844,f173,f174,f110,f912,f913,f914,f915,f916,f920,f929,f940,f944,f945,f115,f823,f662,f626,f541,f527,f111,f1094,f547,f114,f1123,f83,f128,f131,f236,f320,f322,f889,f349,f276,f197,f523,f112,f1230,f140]) ).
fof(f1230,plain,
( element(zero(any1),any1)
| ~ spl9_7 ),
inference(subsumption_resolution,[],[f1118,f512]) ).
fof(f1118,plain,
( element(zero(any1),any1)
| ~ element(subtract(any1,zero(any1),sK3(x,any1)),any1)
| ~ spl9_7 ),
inference(duplicate_literal_removal,[],[f1117]) ).
fof(f1117,plain,
( element(zero(any1),any1)
| ~ element(subtract(any1,zero(any1),sK3(x,any1)),any1)
| ~ element(subtract(any1,zero(any1),sK3(x,any1)),any1)
| ~ spl9_7 ),
inference(superposition,[],[f93,f547]) ).
fof(f523,plain,
( zero(any2) = subtract(any2,apply(x,subtract(any1,zero(any1),sK3(x,any1))),apply(x,subtract(any1,zero(any1),sK3(x,any1))))
| ~ spl9_7 ),
inference(resolution,[],[f512,f135]) ).
fof(f547,plain,
( zero(any1) = subtract(any1,subtract(any1,zero(any1),sK3(x,any1)),subtract(any1,zero(any1),sK3(x,any1)))
| ~ spl9_7 ),
inference(resolution,[],[f512,f85]) ).
fof(f527,plain,
( ! [X0] :
( ~ element(X0,any2)
| apply(x,subtract(any1,zero(any1),sK3(x,any1))) = subtract(any2,X0,subtract(any2,X0,apply(x,subtract(any1,zero(any1),sK3(x,any1))))) )
| ~ spl9_7 ),
inference(resolution,[],[f512,f195]) ).
fof(f541,plain,
( ! [X0] :
( ~ element(X0,any1)
| apply(x,subtract(any1,subtract(any1,zero(any1),sK3(x,any1)),X0)) = subtract(any2,apply(x,subtract(any1,zero(any1),sK3(x,any1))),apply(x,X0)) )
| ~ spl9_7 ),
inference(resolution,[],[f512,f416]) ).
fof(f626,plain,
( subtract(any1,zero(any1),sK3(x,any1)) = subtract(any1,subtract(any1,zero(any1),sK3(x,any1)),subtract(any1,subtract(any1,zero(any1),sK3(x,any1)),subtract(any1,zero(any1),sK3(x,any1))))
| ~ spl9_7 ),
inference(resolution,[],[f546,f512]) ).
fof(f662,plain,
( zero(any1) = subtract(any1,subtract(any1,subtract(any1,zero(any1),sK3(x,any1)),subtract(any1,zero(any1),sK3(x,any1))),subtract(any1,subtract(any1,zero(any1),sK3(x,any1)),subtract(any1,zero(any1),sK3(x,any1))))
| ~ spl9_7 ),
inference(resolution,[],[f545,f512]) ).
fof(f823,plain,
( ! [X0] :
( zero(any2) = subtract(any2,subtract(any2,apply(x,subtract(any1,zero(any1),sK3(x,any1))),X0),subtract(any2,apply(x,subtract(any1,zero(any1),sK3(x,any1))),X0))
| ~ element(X0,any2) )
| ~ spl9_7 ),
inference(resolution,[],[f288,f512]) ).
fof(f945,plain,
( ! [X2,X3,X0,X1] :
( sK6(X0,X1,X2,any1,X3) = apply(X0,sK7(X0,X1,X2,any1,X3))
| exact(X0,X1)
| ~ morphism(X1,any1,X3)
| ~ morphism(X0,X2,any1)
| subtract(any1,zero(any1),sK3(x,any1)) = subtract(any1,sK6(X0,X1,X2,any1,X3),subtract(any1,sK6(X0,X1,X2,any1,X3),subtract(any1,zero(any1),sK3(x,any1)))) )
| ~ spl9_7 ),
inference(resolution,[],[f110,f546]) ).
fof(f944,plain,
( ! [X2,X3,X0,X1] :
( sK6(X0,X1,X2,any1,X3) = apply(X0,sK7(X0,X1,X2,any1,X3))
| exact(X0,X1)
| ~ morphism(X1,any1,X3)
| ~ morphism(X0,X2,any1)
| zero(any1) = subtract(any1,subtract(any1,subtract(any1,zero(any1),sK3(x,any1)),sK6(X0,X1,X2,any1,X3)),subtract(any1,subtract(any1,zero(any1),sK3(x,any1)),sK6(X0,X1,X2,any1,X3))) )
| ~ spl9_7 ),
inference(resolution,[],[f110,f545]) ).
fof(f836,plain,
( ! [X0] :
( zero(any2) = subtract(any2,apply(x,subtract(any1,X0,subtract(any1,zero(any1),sK3(x,any1)))),apply(x,subtract(any1,X0,subtract(any1,zero(any1),sK3(x,any1)))))
| ~ element(X0,any1) )
| ~ spl9_7 ),
inference(resolution,[],[f172,f512]) ).
fof(f808,plain,
( ! [X2,X3,X0,X1] :
( exact(X0,X1)
| zero(X2) = apply(X1,sK6(X0,X1,any1,X3,X2))
| ~ morphism(X1,X3,X2)
| ~ morphism(X0,any1,X3)
| subtract(any1,zero(any1),sK3(x,any1)) = subtract(any1,sK7(X0,X1,any1,X3,X2),subtract(any1,sK7(X0,X1,any1,X3,X2),subtract(any1,zero(any1),sK3(x,any1)))) )
| ~ spl9_7 ),
inference(resolution,[],[f109,f546]) ).
fof(f807,plain,
( ! [X2,X3,X0,X1] :
( exact(X0,X1)
| zero(X2) = apply(X1,sK6(X0,X1,any1,X3,X2))
| ~ morphism(X1,X3,X2)
| ~ morphism(X0,any1,X3)
| zero(any1) = subtract(any1,subtract(any1,subtract(any1,zero(any1),sK3(x,any1)),sK7(X0,X1,any1,X3,X2)),subtract(any1,subtract(any1,zero(any1),sK3(x,any1)),sK7(X0,X1,any1,X3,X2))) )
| ~ spl9_7 ),
inference(resolution,[],[f109,f545]) ).
fof(f669,plain,
( ! [X2,X3,X0,X1] :
( zero(any1) = subtract(any1,subtract(any1,subtract(any1,zero(any1),sK3(x,any1)),sK6(X0,X1,X2,any1,X3)),subtract(any1,subtract(any1,zero(any1),sK3(x,any1)),sK6(X0,X1,X2,any1,X3)))
| element(sK7(X0,X1,X2,any1,X3),X2)
| exact(X0,X1)
| ~ morphism(X1,any1,X3)
| ~ morphism(X0,X2,any1) )
| ~ spl9_7 ),
inference(resolution,[],[f545,f108]) ).
fof(f668,plain,
( ! [X2,X3,X0,X1] :
( zero(any1) = subtract(any1,subtract(any1,subtract(any1,zero(any1),sK3(x,any1)),sK7(X0,X1,any1,X2,X3)),subtract(any1,subtract(any1,zero(any1),sK3(x,any1)),sK7(X0,X1,any1,X2,X3)))
| element(sK6(X0,X1,any1,X2,X3),X2)
| exact(X0,X1)
| ~ morphism(X1,X2,X3)
| ~ morphism(X0,any1,X2) )
| ~ spl9_7 ),
inference(resolution,[],[f545,f108]) ).
fof(f667,plain,
( ! [X0,X1] :
( zero(any1) = subtract(any1,subtract(any1,subtract(any1,zero(any1),sK3(x,any1)),sK1(X0,X1,any1)),subtract(any1,subtract(any1,zero(any1),sK3(x,any1)),sK1(X0,X1,any1)))
| surjection(X0)
| ~ morphism(X0,X1,any1) )
| ~ spl9_7 ),
inference(resolution,[],[f545,f95]) ).
fof(f666,plain,
( ! [X0,X1] :
( zero(any1) = subtract(any1,subtract(any1,subtract(any1,zero(any1),sK3(x,any1)),sK2(X0,any1,X1)),subtract(any1,subtract(any1,zero(any1),sK3(x,any1)),sK2(X0,any1,X1)))
| injection_2(X0)
| ~ morphism(X0,any1,X1) )
| ~ spl9_7 ),
inference(resolution,[],[f545,f97]) ).
fof(f665,plain,
( ! [X0,X1] :
( zero(any1) = subtract(any1,subtract(any1,subtract(any1,zero(any1),sK3(x,any1)),subtract(any1,X0,X1)),subtract(any1,subtract(any1,zero(any1),sK3(x,any1)),subtract(any1,X0,X1)))
| ~ element(X1,any1)
| ~ element(X0,any1) )
| ~ spl9_7 ),
inference(resolution,[],[f545,f93]) ).
fof(f545,plain,
( ! [X0] :
( ~ element(X0,any1)
| zero(any1) = subtract(any1,subtract(any1,subtract(any1,zero(any1),sK3(x,any1)),X0),subtract(any1,subtract(any1,zero(any1),sK3(x,any1)),X0)) )
| ~ spl9_7 ),
inference(resolution,[],[f512,f146]) ).
fof(f633,plain,
( ! [X2,X3,X0,X1] :
( subtract(any1,zero(any1),sK3(x,any1)) = subtract(any1,sK6(X0,X1,X2,any1,X3),subtract(any1,sK6(X0,X1,X2,any1,X3),subtract(any1,zero(any1),sK3(x,any1))))
| element(sK7(X0,X1,X2,any1,X3),X2)
| exact(X0,X1)
| ~ morphism(X1,any1,X3)
| ~ morphism(X0,X2,any1) )
| ~ spl9_7 ),
inference(resolution,[],[f546,f108]) ).
fof(f632,plain,
( ! [X2,X3,X0,X1] :
( subtract(any1,zero(any1),sK3(x,any1)) = subtract(any1,sK7(X0,X1,any1,X2,X3),subtract(any1,sK7(X0,X1,any1,X2,X3),subtract(any1,zero(any1),sK3(x,any1))))
| element(sK6(X0,X1,any1,X2,X3),X2)
| exact(X0,X1)
| ~ morphism(X1,X2,X3)
| ~ morphism(X0,any1,X2) )
| ~ spl9_7 ),
inference(resolution,[],[f546,f108]) ).
fof(f631,plain,
( ! [X0,X1] :
( subtract(any1,zero(any1),sK3(x,any1)) = subtract(any1,sK1(X0,X1,any1),subtract(any1,sK1(X0,X1,any1),subtract(any1,zero(any1),sK3(x,any1))))
| surjection(X0)
| ~ morphism(X0,X1,any1) )
| ~ spl9_7 ),
inference(resolution,[],[f546,f95]) ).
fof(f630,plain,
( ! [X0,X1] :
( subtract(any1,zero(any1),sK3(x,any1)) = subtract(any1,sK2(X0,any1,X1),subtract(any1,sK2(X0,any1,X1),subtract(any1,zero(any1),sK3(x,any1))))
| injection_2(X0)
| ~ morphism(X0,any1,X1) )
| ~ spl9_7 ),
inference(resolution,[],[f546,f97]) ).
fof(f629,plain,
( ! [X0,X1] :
( subtract(any1,zero(any1),sK3(x,any1)) = subtract(any1,subtract(any1,X0,X1),subtract(any1,subtract(any1,X0,X1),subtract(any1,zero(any1),sK3(x,any1))))
| ~ element(X1,any1)
| ~ element(X0,any1) )
| ~ spl9_7 ),
inference(resolution,[],[f546,f93]) ).
fof(f546,plain,
( ! [X0] :
( ~ element(X0,any1)
| subtract(any1,zero(any1),sK3(x,any1)) = subtract(any1,X0,subtract(any1,X0,subtract(any1,zero(any1),sK3(x,any1)))) )
| ~ spl9_7 ),
inference(resolution,[],[f512,f94]) ).
fof(f512,plain,
( element(subtract(any1,zero(any1),sK3(x,any1)),any1)
| ~ spl9_7 ),
inference(avatar_component_clause,[],[f511]) ).
fof(f511,plain,
( spl9_7
<=> element(subtract(any1,zero(any1),sK3(x,any1)),any1) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_7])]) ).
fof(f1234,plain,
( spl9_3
| ~ spl9_7
| ~ spl9_10 ),
inference(avatar_contradiction_clause,[],[f1233]) ).
fof(f1233,plain,
( $false
| spl9_3
| ~ spl9_7
| ~ spl9_10 ),
inference(global_subsumption,[],[f1095,f117,f82,f84,f85,f87,f127,f100,f101,f86,f134,f136,f140,f93,f95,f97,f99,f103,f135,f89,f180,f94,f189,f190,f191,f98,f90,f96,f102,f91,f146,f282,f283,f284,f92,f165,f168,f195,f353,f354,f355,f116,f375,f88,f416,f433,f434,f435,f104,f460,f512,f108,f566,f567,f568,f569,f573,f587,f595,f596,f597,f598,f602,f616,f546,f629,f630,f631,f632,f633,f105,f655,f545,f665,f666,f667,f668,f669,f113,f747,f109,f778,f779,f780,f781,f785,f803,f807,f808,f288,f826,f827,f828,f829,f830,f831,f172,f836,f839,f840,f841,f842,f843,f844,f173,f174,f110,f912,f913,f914,f915,f916,f920,f929,f940,f944,f945,f115,f823,f662,f626,f541,f527,f111,f1094,f547,f114,f1123,f83,f128,f131,f236,f320,f322,f889,f349,f276,f197,f523,f112,f1230]) ).
fof(f1095,plain,
( element(zero(any1),any1)
| ~ element(sK4(x,any1),any1)
| ~ element(sK3(x,any1),any1)
| ~ spl9_10 ),
inference(superposition,[],[f93,f1045]) ).
fof(f1045,plain,
( zero(any1) = subtract(any1,sK3(x,any1),sK4(x,any1))
| ~ spl9_10 ),
inference(avatar_component_clause,[],[f1043]) ).
fof(f1043,plain,
( spl9_10
<=> zero(any1) = subtract(any1,sK3(x,any1),sK4(x,any1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_10])]) ).
fof(f1232,plain,
( spl9_3
| ~ spl9_7 ),
inference(avatar_contradiction_clause,[],[f1231]) ).
fof(f1231,plain,
( $false
| spl9_3
| ~ spl9_7 ),
inference(global_subsumption,[],[f117,f82,f84,f85,f87,f127,f100,f101,f86,f134,f136,f140,f93,f95,f97,f99,f103,f135,f89,f180,f94,f189,f190,f191,f98,f90,f96,f102,f91,f146,f282,f283,f284,f92,f165,f168,f195,f353,f354,f355,f116,f375,f88,f416,f433,f434,f435,f104,f460,f512,f108,f566,f567,f568,f569,f573,f587,f595,f596,f597,f598,f602,f616,f546,f629,f630,f631,f632,f633,f105,f655,f545,f665,f666,f667,f668,f669,f113,f747,f109,f778,f779,f780,f781,f785,f803,f807,f808,f288,f826,f827,f828,f829,f830,f831,f172,f836,f839,f840,f841,f842,f843,f844,f173,f174,f110,f912,f913,f914,f915,f916,f920,f929,f940,f944,f945,f115,f823,f662,f626,f541,f527,f111,f1094,f547,f114,f1123,f83,f128,f131,f236,f320,f322,f889,f349,f276,f197,f523,f112,f1230]) ).
fof(f1227,plain,
( spl9_2
| ~ spl9_3
| ~ spl9_12 ),
inference(avatar_contradiction_clause,[],[f1226]) ).
fof(f1226,plain,
( $false
| spl9_2
| ~ spl9_3
| ~ spl9_12 ),
inference(subsumption_resolution,[],[f1225,f84]) ).
fof(f1225,plain,
( ~ morphism(x,any1,any2)
| spl9_2
| ~ spl9_3
| ~ spl9_12 ),
inference(subsumption_resolution,[],[f1222,f124]) ).
fof(f1222,plain,
( injection_2(x)
| ~ morphism(x,any1,any2)
| ~ spl9_3
| ~ spl9_12 ),
inference(trivial_inequality_removal,[],[f1220]) ).
fof(f1220,plain,
( zero(any1) != zero(any1)
| injection_2(x)
| ~ morphism(x,any1,any2)
| ~ spl9_3
| ~ spl9_12 ),
inference(superposition,[],[f99,f1215]) ).
fof(f1215,plain,
( zero(any1) = sK2(x,any1,any2)
| ~ spl9_3
| ~ spl9_12 ),
inference(subsumption_resolution,[],[f1214,f139]) ).
fof(f139,plain,
( element(zero(any1),any1)
| ~ spl9_3 ),
inference(avatar_component_clause,[],[f138]) ).
fof(f1214,plain,
( ~ element(zero(any1),any1)
| zero(any1) = sK2(x,any1,any2)
| ~ spl9_12 ),
inference(trivial_inequality_removal,[],[f1212]) ).
fof(f1212,plain,
( zero(any2) != zero(any2)
| ~ element(zero(any1),any1)
| zero(any1) = sK2(x,any1,any2)
| ~ spl9_12 ),
inference(superposition,[],[f1208,f127]) ).
fof(f1208,plain,
( ! [X0] :
( apply(x,X0) != zero(any2)
| ~ element(X0,any1)
| sK2(x,any1,any2) = X0 )
| ~ spl9_12 ),
inference(avatar_component_clause,[],[f1207]) ).
fof(f1207,plain,
( spl9_12
<=> ! [X0] :
( sK2(x,any1,any2) = X0
| ~ element(X0,any1)
| apply(x,X0) != zero(any2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_12])]) ).
fof(f1211,plain,
~ spl9_11,
inference(avatar_contradiction_clause,[],[f1210]) ).
fof(f1210,plain,
( $false
| ~ spl9_11 ),
inference(resolution,[],[f1205,f84]) ).
fof(f1205,plain,
( ! [X1] : ~ morphism(x,any1,X1)
| ~ spl9_11 ),
inference(avatar_component_clause,[],[f1204]) ).
fof(f1204,plain,
( spl9_11
<=> ! [X1] : ~ morphism(x,any1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_11])]) ).
fof(f1209,plain,
( spl9_11
| spl9_12
| ~ spl9_1
| spl9_2 ),
inference(avatar_split_clause,[],[f1202,f123,f119,f1207,f1204]) ).
fof(f1202,plain,
( ! [X0,X1] :
( sK2(x,any1,any2) = X0
| apply(x,X0) != zero(any2)
| ~ element(X0,any1)
| ~ morphism(x,any1,X1) )
| ~ spl9_1
| spl9_2 ),
inference(subsumption_resolution,[],[f1201,f84]) ).
fof(f1201,plain,
( ! [X0,X1] :
( sK2(x,any1,any2) = X0
| apply(x,X0) != zero(any2)
| ~ element(X0,any1)
| ~ morphism(x,any1,X1)
| ~ morphism(x,any1,any2) )
| ~ spl9_1
| spl9_2 ),
inference(subsumption_resolution,[],[f1200,f124]) ).
fof(f1200,plain,
( ! [X0,X1] :
( sK2(x,any1,any2) = X0
| apply(x,X0) != zero(any2)
| ~ element(X0,any1)
| ~ morphism(x,any1,X1)
| injection_2(x)
| ~ morphism(x,any1,any2) )
| ~ spl9_1 ),
inference(resolution,[],[f1188,f97]) ).
fof(f1169,plain,
( spl9_1
| ~ spl9_2
| ~ spl9_10 ),
inference(avatar_contradiction_clause,[],[f1168]) ).
fof(f1168,plain,
( $false
| spl9_1
| ~ spl9_2
| ~ spl9_10 ),
inference(resolution,[],[f1167,f84]) ).
fof(f1167,plain,
( ! [X0] : ~ morphism(x,any1,X0)
| spl9_1
| ~ spl9_2
| ~ spl9_10 ),
inference(subsumption_resolution,[],[f1166,f120]) ).
fof(f120,plain,
( ~ injection(x)
| spl9_1 ),
inference(avatar_component_clause,[],[f119]) ).
fof(f1166,plain,
( ! [X0] :
( injection(x)
| ~ morphism(x,any1,X0) )
| ~ spl9_2
| ~ spl9_10 ),
inference(trivial_inequality_removal,[],[f1165]) ).
fof(f1165,plain,
( ! [X0] :
( sK3(x,any1) != sK3(x,any1)
| injection(x)
| ~ morphism(x,any1,X0) )
| ~ spl9_2
| ~ spl9_10 ),
inference(superposition,[],[f103,f1155]) ).
fof(f1155,plain,
( sK3(x,any1) = sK4(x,any1)
| ~ spl9_2
| ~ spl9_10 ),
inference(superposition,[],[f1154,f1136]) ).
fof(f1136,plain,
( sK4(x,any1) = subtract(any1,sK3(x,any1),zero(any1))
| ~ spl9_2
| ~ spl9_10 ),
inference(forward_demodulation,[],[f1127,f1045]) ).
fof(f1127,plain,
( sK4(x,any1) = subtract(any1,sK3(x,any1),subtract(any1,sK3(x,any1),sK4(x,any1)))
| ~ spl9_2 ),
inference(resolution,[],[f1071,f1051]) ).
fof(f1051,plain,
( element(sK3(x,any1),any1)
| ~ spl9_2 ),
inference(global_subsumption,[],[f83,f117,f112,f111,f114,f82,f125,f84,f85,f87,f127,f100,f101,f86,f134,f136,f93,f95,f97,f99,f103,f135,f89,f180,f94,f189,f190,f191,f98,f90,f96,f102,f91,f278,f280,f146,f282,f283,f284,f92,f165,f168,f195,f353,f354,f355,f116,f375,f88,f416,f433,f434,f435,f104,f460,f108,f566,f567,f568,f569,f573,f587,f595,f596,f597,f598,f602,f616,f105,f655,f113,f747,f109,f778,f779,f780,f781,f785,f803,f288,f826,f827,f828,f829,f830,f831,f172,f839,f840,f841,f842,f843,f844,f173,f174,f110,f912,f913,f914,f915,f916,f920,f929,f940,f115,f322,f1047,f320,f1048,f236,f1049,f131,f1050,f128]) ).
fof(f1050,plain,
( element(sK4(x,any1),any1)
| ~ spl9_2 ),
inference(global_subsumption,[],[f83,f117,f112,f111,f114,f82,f125,f84,f85,f87,f127,f100,f101,f86,f134,f136,f93,f95,f97,f99,f103,f135,f89,f180,f94,f189,f190,f191,f98,f90,f96,f102,f91,f278,f280,f146,f282,f283,f284,f92,f165,f168,f195,f353,f354,f355,f116,f375,f88,f416,f433,f434,f435,f104,f460,f108,f566,f567,f568,f569,f573,f587,f595,f596,f597,f598,f602,f616,f105,f655,f113,f747,f109,f778,f779,f780,f781,f785,f803,f288,f826,f827,f828,f829,f830,f831,f172,f839,f840,f841,f842,f843,f844,f173,f174,f110,f912,f913,f914,f915,f916,f920,f929,f940,f115,f322,f1047,f320,f1048,f236,f1049,f131]) ).
fof(f1049,plain,
( apply(x,sK3(x,any1)) = apply(x,sK4(x,any1))
| ~ spl9_2 ),
inference(global_subsumption,[],[f83,f117,f112,f111,f114,f82,f125,f84,f85,f87,f127,f100,f101,f86,f134,f136,f93,f95,f97,f99,f103,f135,f89,f180,f94,f189,f190,f191,f98,f90,f96,f102,f91,f278,f280,f146,f282,f283,f284,f92,f165,f168,f195,f353,f354,f355,f116,f375,f88,f416,f433,f434,f435,f104,f460,f108,f566,f567,f568,f569,f573,f587,f595,f596,f597,f598,f602,f616,f105,f655,f113,f747,f109,f778,f779,f780,f781,f785,f803,f288,f826,f827,f828,f829,f830,f831,f172,f839,f840,f841,f842,f843,f844,f173,f174,f110,f912,f913,f914,f915,f916,f920,f929,f940,f115,f322,f1047,f320,f1048,f236]) ).
fof(f1048,plain,
( ~ injection(x)
| ~ spl9_2 ),
inference(global_subsumption,[],[f83,f117,f112,f111,f114,f82,f125,f84,f85,f87,f127,f100,f101,f86,f134,f136,f93,f95,f97,f99,f103,f135,f89,f180,f94,f189,f190,f191,f98,f90,f96,f102,f91,f278,f280,f146,f282,f283,f284,f92,f165,f168,f195,f353,f354,f355,f116,f375,f88,f416,f433,f434,f435,f104,f460,f108,f566,f567,f568,f569,f573,f587,f595,f596,f597,f598,f602,f616,f105,f655,f113,f747,f109,f778,f779,f780,f781,f785,f803,f288,f826,f827,f828,f829,f830,f831,f172,f839,f840,f841,f842,f843,f844,f173,f174,f110,f912,f913,f914,f915,f916,f920,f929,f940,f115,f322,f1047,f320]) ).
fof(f1047,plain,
( ~ injection(x)
| ~ spl9_2 ),
inference(global_subsumption,[],[f83,f117,f112,f111,f114,f82,f125,f84,f85,f87,f127,f100,f101,f86,f134,f136,f93,f95,f97,f99,f103,f135,f89,f180,f94,f189,f190,f191,f98,f90,f96,f102,f91,f278,f280,f146,f282,f283,f284,f92,f165,f168,f195,f353,f354,f355,f116,f375,f88,f416,f433,f434,f435,f104,f460,f108,f566,f567,f568,f569,f573,f587,f595,f596,f597,f598,f602,f616,f105,f655,f113,f747,f109,f778,f779,f780,f781,f785,f803,f288,f826,f827,f828,f829,f830,f831,f172,f839,f840,f841,f842,f843,f844,f173,f174,f110,f912,f913,f914,f915,f916,f920,f929,f940,f115,f322]) ).
fof(f280,plain,
( ! [X0] :
( ~ element(zero(any1),X0)
| zero(X0) = zero(any1)
| ~ morphism(x,X0,any2) )
| ~ spl9_2 ),
inference(equality_resolution,[],[f278]) ).
fof(f278,plain,
( ! [X0,X1] :
( zero(X0) != zero(any2)
| zero(X1) = zero(any1)
| ~ element(zero(any1),X1)
| ~ morphism(x,X1,X0) )
| ~ spl9_2 ),
inference(subsumption_resolution,[],[f276,f125]) ).
fof(f125,plain,
( injection_2(x)
| ~ spl9_2 ),
inference(avatar_component_clause,[],[f123]) ).
fof(f1071,plain,
( ! [X0] :
( ~ element(X0,any1)
| sK4(x,any1) = subtract(any1,X0,subtract(any1,X0,sK4(x,any1))) )
| ~ spl9_2 ),
inference(resolution,[],[f1050,f94]) ).
fof(f1154,plain,
( sK3(x,any1) = subtract(any1,sK3(x,any1),zero(any1))
| ~ spl9_2 ),
inference(forward_demodulation,[],[f1145,f1090]) ).
fof(f1090,plain,
( zero(any1) = subtract(any1,sK3(x,any1),sK3(x,any1))
| ~ spl9_2 ),
inference(resolution,[],[f1051,f85]) ).
fof(f1145,plain,
( sK3(x,any1) = subtract(any1,sK3(x,any1),subtract(any1,sK3(x,any1),sK3(x,any1)))
| ~ spl9_2 ),
inference(resolution,[],[f1089,f1051]) ).
fof(f1089,plain,
( ! [X0] :
( ~ element(X0,any1)
| sK3(x,any1) = subtract(any1,X0,subtract(any1,X0,sK3(x,any1))) )
| ~ spl9_2 ),
inference(resolution,[],[f1051,f94]) ).
fof(f1093,plain,
~ spl9_9,
inference(avatar_contradiction_clause,[],[f1092]) ).
fof(f1092,plain,
( $false
| ~ spl9_9 ),
inference(subsumption_resolution,[],[f1091,f84]) ).
fof(f1091,plain,
( ~ morphism(x,any1,any2)
| ~ spl9_9 ),
inference(equality_resolution,[],[f1041]) ).
fof(f1041,plain,
( ! [X0] :
( zero(X0) != zero(any2)
| ~ morphism(x,any1,X0) )
| ~ spl9_9 ),
inference(avatar_component_clause,[],[f1040]) ).
fof(f1040,plain,
( spl9_9
<=> ! [X0] :
( zero(X0) != zero(any2)
| ~ morphism(x,any1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_9])]) ).
fof(f1054,plain,
( ~ spl9_1
| ~ spl9_2 ),
inference(avatar_contradiction_clause,[],[f1053]) ).
fof(f1053,plain,
( $false
| ~ spl9_1
| ~ spl9_2 ),
inference(global_subsumption,[],[f83,f117,f112,f111,f114,f82,f125,f84,f85,f87,f127,f100,f101,f86,f134,f136,f93,f95,f97,f99,f103,f135,f89,f180,f94,f189,f190,f191,f98,f90,f96,f102,f91,f278,f280,f146,f282,f283,f284,f92,f165,f168,f195,f353,f354,f355,f116,f375,f88,f416,f433,f434,f435,f104,f460,f108,f566,f567,f568,f569,f573,f587,f595,f596,f597,f598,f602,f616,f105,f655,f113,f747,f109,f778,f779,f780,f781,f785,f803,f288,f826,f827,f828,f829,f830,f831,f172,f839,f840,f841,f842,f843,f844,f173,f174,f110,f912,f913,f914,f915,f916,f920,f929,f940,f115,f322,f1047,f320,f1048,f236,f1049,f131,f1050,f128,f1051,f1052,f121]) ).
fof(f1052,plain,
( ~ injection(x)
| ~ spl9_2 ),
inference(subsumption_resolution,[],[f83,f125]) ).
fof(f1046,plain,
( spl9_9
| spl9_10
| spl9_1
| ~ spl9_2 ),
inference(avatar_split_clause,[],[f1038,f123,f119,f1043,f1040]) ).
fof(f1038,plain,
( ! [X0] :
( zero(any1) = subtract(any1,sK3(x,any1),sK4(x,any1))
| zero(X0) != zero(any2)
| ~ morphism(x,any1,X0) )
| spl9_1
| ~ spl9_2 ),
inference(subsumption_resolution,[],[f1037,f129]) ).
fof(f129,plain,
( element(sK3(x,any1),any1)
| spl9_1 ),
inference(subsumption_resolution,[],[f128,f120]) ).
fof(f1037,plain,
( ! [X0] :
( zero(any1) = subtract(any1,sK3(x,any1),sK4(x,any1))
| zero(X0) != zero(any2)
| ~ morphism(x,any1,X0)
| ~ element(sK3(x,any1),any1) )
| spl9_1
| ~ spl9_2 ),
inference(subsumption_resolution,[],[f1036,f132]) ).
fof(f132,plain,
( element(sK4(x,any1),any1)
| spl9_1 ),
inference(subsumption_resolution,[],[f131,f120]) ).
fof(f1036,plain,
( ! [X0] :
( zero(any1) = subtract(any1,sK3(x,any1),sK4(x,any1))
| zero(X0) != zero(any2)
| ~ morphism(x,any1,X0)
| ~ element(sK4(x,any1),any1)
| ~ element(sK3(x,any1),any1) )
| spl9_1
| ~ spl9_2 ),
inference(resolution,[],[f455,f93]) ).
fof(f455,plain,
( ! [X0,X1] :
( ~ element(subtract(any1,sK3(x,any1),sK4(x,any1)),X1)
| zero(X1) = subtract(any1,sK3(x,any1),sK4(x,any1))
| zero(X0) != zero(any2)
| ~ morphism(x,X1,X0) )
| spl9_1
| ~ spl9_2 ),
inference(subsumption_resolution,[],[f453,f125]) ).
fof(f453,plain,
( ! [X0,X1] :
( zero(X0) != zero(any2)
| zero(X1) = subtract(any1,sK3(x,any1),sK4(x,any1))
| ~ element(subtract(any1,sK3(x,any1),sK4(x,any1)),X1)
| ~ morphism(x,X1,X0)
| ~ injection_2(x) )
| spl9_1 ),
inference(superposition,[],[f91,f447]) ).
fof(f447,plain,
( zero(any2) = apply(x,subtract(any1,sK3(x,any1),sK4(x,any1)))
| spl9_1 ),
inference(forward_demodulation,[],[f446,f169]) ).
fof(f169,plain,
( zero(any2) = subtract(any2,apply(x,sK3(x,any1)),apply(x,sK3(x,any1)))
| spl9_1 ),
inference(resolution,[],[f135,f129]) ).
fof(f446,plain,
( subtract(any2,apply(x,sK3(x,any1)),apply(x,sK3(x,any1))) = apply(x,subtract(any1,sK3(x,any1),sK4(x,any1)))
| spl9_1 ),
inference(forward_demodulation,[],[f439,f237]) ).
fof(f237,plain,
( apply(x,sK3(x,any1)) = apply(x,sK4(x,any1))
| spl9_1 ),
inference(subsumption_resolution,[],[f236,f120]) ).
fof(f439,plain,
( subtract(any2,apply(x,sK3(x,any1)),apply(x,sK4(x,any1))) = apply(x,subtract(any1,sK3(x,any1),sK4(x,any1)))
| spl9_1 ),
inference(resolution,[],[f430,f132]) ).
fof(f430,plain,
( ! [X0] :
( ~ element(X0,any1)
| subtract(any2,apply(x,sK3(x,any1)),apply(x,X0)) = apply(x,subtract(any1,sK3(x,any1),X0)) )
| spl9_1 ),
inference(resolution,[],[f416,f129]) ).
fof(f522,plain,
( spl9_1
| ~ spl9_3
| spl9_7 ),
inference(avatar_contradiction_clause,[],[f521]) ).
fof(f521,plain,
( $false
| spl9_1
| ~ spl9_3
| spl9_7 ),
inference(subsumption_resolution,[],[f520,f139]) ).
fof(f520,plain,
( ~ element(zero(any1),any1)
| spl9_1
| spl9_7 ),
inference(subsumption_resolution,[],[f519,f129]) ).
fof(f519,plain,
( ~ element(sK3(x,any1),any1)
| ~ element(zero(any1),any1)
| spl9_7 ),
inference(resolution,[],[f513,f93]) ).
fof(f513,plain,
( ~ element(subtract(any1,zero(any1),sK3(x,any1)),any1)
| spl9_7 ),
inference(avatar_component_clause,[],[f511]) ).
fof(f518,plain,
( ~ spl9_7
| spl9_8
| spl9_1
| ~ spl9_3 ),
inference(avatar_split_clause,[],[f494,f138,f119,f515,f511]) ).
fof(f515,plain,
( spl9_8
<=> element(subtract(any2,zero(any2),apply(x,sK3(x,any1))),any2) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_8])]) ).
fof(f494,plain,
( element(subtract(any2,zero(any2),apply(x,sK3(x,any1))),any2)
| ~ element(subtract(any1,zero(any1),sK3(x,any1)),any1)
| spl9_1
| ~ spl9_3 ),
inference(superposition,[],[f134,f485]) ).
fof(f485,plain,
( subtract(any2,zero(any2),apply(x,sK3(x,any1))) = apply(x,subtract(any1,zero(any1),sK3(x,any1)))
| spl9_1
| ~ spl9_3 ),
inference(resolution,[],[f437,f129]) ).
fof(f437,plain,
( ! [X0] :
( ~ element(X0,any1)
| subtract(any2,zero(any2),apply(x,X0)) = apply(x,subtract(any1,zero(any1),X0)) )
| ~ spl9_3 ),
inference(forward_demodulation,[],[f432,f127]) ).
fof(f432,plain,
( ! [X0] :
( ~ element(X0,any1)
| apply(x,subtract(any1,zero(any1),X0)) = subtract(any2,apply(x,zero(any1)),apply(x,X0)) )
| ~ spl9_3 ),
inference(resolution,[],[f416,f139]) ).
fof(f188,plain,
( ~ spl9_5
| spl9_6 ),
inference(avatar_split_clause,[],[f180,f186,f182]) ).
fof(f182,plain,
( spl9_5
<=> surjection(x) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_5])]) ).
fof(f186,plain,
( spl9_6
<=> ! [X0] :
( ~ element(X0,any2)
| element(sK0(x,any1,X0),any1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_6])]) ).
fof(f160,plain,
( spl9_3
| spl9_1 ),
inference(avatar_split_clause,[],[f158,f119,f138]) ).
fof(f158,plain,
( element(zero(any1),any1)
| spl9_1 ),
inference(subsumption_resolution,[],[f150,f129]) ).
fof(f150,plain,
( element(zero(any1),any1)
| ~ element(sK3(x,any1),any1)
| spl9_1 ),
inference(duplicate_literal_removal,[],[f147]) ).
fof(f147,plain,
( element(zero(any1),any1)
| ~ element(sK3(x,any1),any1)
| ~ element(sK3(x,any1),any1)
| spl9_1 ),
inference(superposition,[],[f93,f130]) ).
fof(f130,plain,
( zero(any1) = subtract(any1,sK3(x,any1),sK3(x,any1))
| spl9_1 ),
inference(resolution,[],[f129,f85]) ).
fof(f159,plain,
( spl9_3
| spl9_1 ),
inference(avatar_split_clause,[],[f157,f119,f138]) ).
fof(f157,plain,
( element(zero(any1),any1)
| spl9_1 ),
inference(subsumption_resolution,[],[f149,f132]) ).
fof(f149,plain,
( element(zero(any1),any1)
| ~ element(sK4(x,any1),any1)
| spl9_1 ),
inference(duplicate_literal_removal,[],[f148]) ).
fof(f148,plain,
( element(zero(any1),any1)
| ~ element(sK4(x,any1),any1)
| ~ element(sK4(x,any1),any1)
| spl9_1 ),
inference(superposition,[],[f93,f133]) ).
fof(f133,plain,
( zero(any1) = subtract(any1,sK4(x,any1),sK4(x,any1))
| spl9_1 ),
inference(resolution,[],[f132,f85]) ).
fof(f156,plain,
( spl9_1
| spl9_3 ),
inference(avatar_contradiction_clause,[],[f155]) ).
fof(f155,plain,
( $false
| spl9_1
| spl9_3 ),
inference(subsumption_resolution,[],[f154,f132]) ).
fof(f154,plain,
( ~ element(sK4(x,any1),any1)
| spl9_1
| spl9_3 ),
inference(subsumption_resolution,[],[f149,f140]) ).
fof(f153,plain,
( spl9_1
| spl9_3 ),
inference(avatar_contradiction_clause,[],[f152]) ).
fof(f152,plain,
( $false
| spl9_1
| spl9_3 ),
inference(subsumption_resolution,[],[f151,f129]) ).
fof(f151,plain,
( ~ element(sK3(x,any1),any1)
| spl9_1
| spl9_3 ),
inference(subsumption_resolution,[],[f150,f140]) ).
fof(f145,plain,
( ~ spl9_3
| spl9_4 ),
inference(avatar_split_clause,[],[f136,f142,f138]) ).
fof(f142,plain,
( spl9_4
<=> element(zero(any2),any2) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_4])]) ).
fof(f126,plain,
( spl9_1
| spl9_2 ),
inference(avatar_split_clause,[],[f82,f123,f119]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : HAL002+1 : TPTP v8.1.2. Released v2.6.0.
% 0.08/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.16/0.36 % Computer : n027.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Fri May 3 19:54:53 EDT 2024
% 0.16/0.36 % CPUTime :
% 0.16/0.37 % (2430)Running in auto input_syntax mode. Trying TPTP
% 0.16/0.38 % (2433)WARNING: value z3 for option sas not known
% 0.16/0.39 % (2431)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.16/0.39 % (2432)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.16/0.39 % (2434)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.16/0.39 % (2433)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.16/0.39 % (2437)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.16/0.39 % (2436)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.16/0.39 TRYING [1]
% 0.16/0.39 TRYING [1]
% 0.16/0.39 TRYING [2]
% 0.16/0.39 TRYING [2]
% 0.16/0.39 % (2435)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.23/0.40 TRYING [3]
% 0.23/0.40 TRYING [3]
% 0.23/0.43 TRYING [4]
% 0.23/0.43 TRYING [4]
% 0.23/0.45 % (2433)First to succeed.
% 0.23/0.46 % (2433)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2430"
% 0.23/0.46 % (2433)Refutation found. Thanks to Tanya!
% 0.23/0.46 % SZS status Theorem for theBenchmark
% 0.23/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.23/0.46 % (2433)------------------------------
% 0.23/0.46 % (2433)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.23/0.46 % (2433)Termination reason: Refutation
% 0.23/0.46
% 0.23/0.46 % (2433)Memory used [KB]: 1477
% 0.23/0.46 % (2433)Time elapsed: 0.076 s
% 0.23/0.46 % (2433)Instructions burned: 131 (million)
% 0.23/0.46 % (2430)Success in time 0.093 s
%------------------------------------------------------------------------------