TSTP Solution File: SEU089+1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SEU089+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n018.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 : Tue Apr 30 15:22:06 EDT 2024
% Result : Theorem 0.22s 0.40s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 200
% Syntax : Number of formulae : 532 ( 208 unt; 0 def)
% Number of atoms : 1195 ( 10 equ)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 915 ( 252 ~; 196 |; 296 &)
% ( 120 <=>; 51 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 139 ( 137 usr; 120 prp; 0-2 aty)
% Number of functors : 34 ( 34 usr; 26 con; 0-3 aty)
% Number of variables : 340 ( 263 !; 77 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1033,plain,
$false,
inference(avatar_sat_refutation,[],[f309,f314,f319,f324,f329,f334,f339,f344,f349,f354,f359,f364,f369,f374,f379,f384,f389,f394,f399,f404,f409,f414,f419,f424,f429,f434,f439,f444,f449,f454,f459,f464,f469,f474,f479,f484,f489,f494,f499,f504,f509,f514,f519,f524,f529,f534,f539,f544,f549,f554,f559,f564,f569,f574,f579,f584,f589,f594,f599,f604,f609,f614,f619,f624,f629,f633,f637,f641,f645,f649,f653,f657,f661,f665,f669,f674,f679,f683,f687,f691,f695,f699,f703,f707,f711,f715,f746,f790,f794,f798,f802,f807,f811,f815,f819,f836,f841,f845,f849,f862,f866,f870,f874,f879,f884,f888,f892,f935,f940,f944,f948,f952,f956,f987,f991,f1005,f1019,f1025,f1031,f1032]) ).
fof(f1032,plain,
( ~ spl29_1
| ~ spl29_2
| ~ spl29_112
| spl29_114 ),
inference(avatar_split_clause,[],[f1020,f984,f950,f311,f306]) ).
fof(f306,plain,
( spl29_1
<=> finite(sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_1])]) ).
fof(f311,plain,
( spl29_2
<=> finite(sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_2])]) ).
fof(f950,plain,
( spl29_112
<=> ! [X0,X1] :
( finite(cartesian_product2(X0,X1))
| ~ finite(X1)
| ~ finite(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_112])]) ).
fof(f984,plain,
( spl29_114
<=> finite(cartesian_product2(sK0,sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_114])]) ).
fof(f1020,plain,
( ~ finite(sK1)
| ~ finite(sK0)
| ~ spl29_112
| spl29_114 ),
inference(resolution,[],[f986,f951]) ).
fof(f951,plain,
( ! [X0,X1] :
( finite(cartesian_product2(X0,X1))
| ~ finite(X1)
| ~ finite(X0) )
| ~ spl29_112 ),
inference(avatar_component_clause,[],[f950]) ).
fof(f986,plain,
( ~ finite(cartesian_product2(sK0,sK1))
| spl29_114 ),
inference(avatar_component_clause,[],[f984]) ).
fof(f1031,plain,
( spl29_119
| ~ spl29_13
| ~ spl29_81 ),
inference(avatar_split_clause,[],[f750,f693,f366,f1028]) ).
fof(f1028,plain,
( spl29_119
<=> function(sK9) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_119])]) ).
fof(f366,plain,
( spl29_13
<=> empty(sK9) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_13])]) ).
fof(f693,plain,
( spl29_81
<=> ! [X0] :
( function(X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_81])]) ).
fof(f750,plain,
( function(sK9)
| ~ spl29_13
| ~ spl29_81 ),
inference(resolution,[],[f694,f368]) ).
fof(f368,plain,
( empty(sK9)
| ~ spl29_13 ),
inference(avatar_component_clause,[],[f366]) ).
fof(f694,plain,
( ! [X0] :
( ~ empty(X0)
| function(X0) )
| ~ spl29_81 ),
inference(avatar_component_clause,[],[f693]) ).
fof(f1025,plain,
( spl29_118
| ~ spl29_62
| ~ spl29_80 ),
inference(avatar_split_clause,[],[f741,f689,f611,f1022]) ).
fof(f1022,plain,
( spl29_118
<=> finite(sK28) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_118])]) ).
fof(f611,plain,
( spl29_62
<=> empty(sK28) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_62])]) ).
fof(f689,plain,
( spl29_80
<=> ! [X0] :
( finite(X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_80])]) ).
fof(f741,plain,
( finite(sK28)
| ~ spl29_62
| ~ spl29_80 ),
inference(resolution,[],[f690,f613]) ).
fof(f613,plain,
( empty(sK28)
| ~ spl29_62 ),
inference(avatar_component_clause,[],[f611]) ).
fof(f690,plain,
( ! [X0] :
( ~ empty(X0)
| finite(X0) )
| ~ spl29_80 ),
inference(avatar_component_clause,[],[f689]) ).
fof(f1019,plain,
spl29_117,
inference(avatar_split_clause,[],[f304,f1017]) ).
fof(f1017,plain,
( spl29_117
<=> ! [X2,X0,X1] :
( ~ empty(cartesian_product2(cartesian_product2(X0,X1),X2))
| empty(X2)
| empty(X1)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_117])]) ).
fof(f304,plain,
! [X2,X0,X1] :
( ~ empty(cartesian_product2(cartesian_product2(X0,X1),X2))
| empty(X2)
| empty(X1)
| empty(X0) ),
inference(definition_unfolding,[],[f244,f242]) ).
fof(f242,plain,
! [X2,X0,X1] : cartesian_product3(X0,X1,X2) = cartesian_product2(cartesian_product2(X0,X1),X2),
inference(cnf_transformation,[],[f14]) ).
fof(f14,axiom,
! [X0,X1,X2] : cartesian_product3(X0,X1,X2) = cartesian_product2(cartesian_product2(X0,X1),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_zfmisc_1) ).
fof(f244,plain,
! [X2,X0,X1] :
( ~ empty(cartesian_product3(X0,X1,X2))
| empty(X2)
| empty(X1)
| empty(X0) ),
inference(cnf_transformation,[],[f119]) ).
fof(f119,plain,
! [X0,X1,X2] :
( ~ empty(cartesian_product3(X0,X1,X2))
| empty(X2)
| empty(X1)
| empty(X0) ),
inference(flattening,[],[f118]) ).
fof(f118,plain,
! [X0,X1,X2] :
( ~ empty(cartesian_product3(X0,X1,X2))
| empty(X2)
| empty(X1)
| empty(X0) ),
inference(ennf_transformation,[],[f23]) ).
fof(f23,axiom,
! [X0,X1,X2] :
( ( ~ empty(X2)
& ~ empty(X1)
& ~ empty(X0) )
=> ~ empty(cartesian_product3(X0,X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc5_subset_1) ).
fof(f1005,plain,
spl29_116,
inference(avatar_split_clause,[],[f245,f1003]) ).
fof(f1003,plain,
( spl29_116
<=> ! [X2,X0,X1] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_116])]) ).
fof(f245,plain,
! [X2,X0,X1] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f121]) ).
fof(f121,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(flattening,[],[f120]) ).
fof(f120,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f57]) ).
fof(f57,axiom,
! [X0,X1,X2] :
( ( element(X1,powerset(X2))
& in(X0,X1) )
=> element(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_subset) ).
fof(f991,plain,
spl29_115,
inference(avatar_split_clause,[],[f246,f989]) ).
fof(f989,plain,
( spl29_115
<=> ! [X2,X0,X1] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_115])]) ).
fof(f246,plain,
! [X2,X0,X1] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f122]) ).
fof(f122,plain,
! [X0,X1,X2] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f58]) ).
fof(f58,axiom,
! [X0,X1,X2] :
~ ( empty(X2)
& element(X1,powerset(X2))
& in(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_subset) ).
fof(f987,plain,
( ~ spl29_114
| ~ spl29_3
| spl29_4
| ~ spl29_112 ),
inference(avatar_split_clause,[],[f976,f950,f321,f316,f984]) ).
fof(f316,plain,
( spl29_3
<=> finite(sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_3])]) ).
fof(f321,plain,
( spl29_4
<=> finite(cartesian_product2(cartesian_product2(sK0,sK1),sK2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_4])]) ).
fof(f976,plain,
( ~ finite(sK2)
| ~ finite(cartesian_product2(sK0,sK1))
| spl29_4
| ~ spl29_112 ),
inference(resolution,[],[f951,f323]) ).
fof(f323,plain,
( ~ finite(cartesian_product2(cartesian_product2(sK0,sK1),sK2))
| spl29_4 ),
inference(avatar_component_clause,[],[f321]) ).
fof(f956,plain,
spl29_113,
inference(avatar_split_clause,[],[f243,f954]) ).
fof(f954,plain,
( spl29_113
<=> ! [X2,X0,X1] :
( relation(X2)
| ~ element(X2,powerset(cartesian_product2(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_113])]) ).
fof(f243,plain,
! [X2,X0,X1] :
( relation(X2)
| ~ element(X2,powerset(cartesian_product2(X0,X1))) ),
inference(cnf_transformation,[],[f117]) ).
fof(f117,plain,
! [X0,X1,X2] :
( relation(X2)
| ~ element(X2,powerset(cartesian_product2(X0,X1))) ),
inference(ennf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X0,X1,X2] :
( element(X2,powerset(cartesian_product2(X0,X1)))
=> relation(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_relset_1) ).
fof(f952,plain,
spl29_112,
inference(avatar_split_clause,[],[f237,f950]) ).
fof(f237,plain,
! [X0,X1] :
( finite(cartesian_product2(X0,X1))
| ~ finite(X1)
| ~ finite(X0) ),
inference(cnf_transformation,[],[f111]) ).
fof(f111,plain,
! [X0,X1] :
( finite(cartesian_product2(X0,X1))
| ~ finite(X1)
| ~ finite(X0) ),
inference(flattening,[],[f110]) ).
fof(f110,plain,
! [X0,X1] :
( finite(cartesian_product2(X0,X1))
| ~ finite(X1)
| ~ finite(X0) ),
inference(ennf_transformation,[],[f51]) ).
fof(f51,axiom,
! [X0,X1] :
( ( finite(X1)
& finite(X0) )
=> finite(cartesian_product2(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_finset_1) ).
fof(f948,plain,
spl29_111,
inference(avatar_split_clause,[],[f236,f946]) ).
fof(f946,plain,
( spl29_111
<=> ! [X0,X1] :
( ~ empty(cartesian_product2(X0,X1))
| empty(X1)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_111])]) ).
fof(f236,plain,
! [X0,X1] :
( ~ empty(cartesian_product2(X0,X1))
| empty(X1)
| empty(X0) ),
inference(cnf_transformation,[],[f109]) ).
fof(f109,plain,
! [X0,X1] :
( ~ empty(cartesian_product2(X0,X1))
| empty(X1)
| empty(X0) ),
inference(flattening,[],[f108]) ).
fof(f108,plain,
! [X0,X1] :
( ~ empty(cartesian_product2(X0,X1))
| empty(X1)
| empty(X0) ),
inference(ennf_transformation,[],[f22]) ).
fof(f22,axiom,
! [X0,X1] :
( ( ~ empty(X1)
& ~ empty(X0) )
=> ~ empty(cartesian_product2(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_subset_1) ).
fof(f944,plain,
spl29_110,
inference(avatar_split_clause,[],[f235,f942]) ).
fof(f942,plain,
( spl29_110
<=> ! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_110])]) ).
fof(f235,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[],[f107]) ).
fof(f107,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(flattening,[],[f106]) ).
fof(f106,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(ennf_transformation,[],[f55]) ).
fof(f55,axiom,
! [X0,X1] :
( element(X0,X1)
=> ( in(X0,X1)
| empty(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
fof(f940,plain,
spl29_109,
inference(avatar_split_clause,[],[f199,f938]) ).
fof(f938,plain,
( spl29_109
<=> ! [X0,X1] :
( finite(X1)
| ~ element(X1,powerset(X0))
| ~ finite(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_109])]) ).
fof(f199,plain,
! [X0,X1] :
( finite(X1)
| ~ element(X1,powerset(X0))
| ~ finite(X0) ),
inference(cnf_transformation,[],[f88]) ).
fof(f88,plain,
! [X0] :
( ! [X1] :
( finite(X1)
| ~ element(X1,powerset(X0)) )
| ~ finite(X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f9,axiom,
! [X0] :
( finite(X0)
=> ! [X1] :
( element(X1,powerset(X0))
=> finite(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_finset_1) ).
fof(f935,plain,
( spl29_108
| ~ spl29_56
| ~ spl29_80 ),
inference(avatar_split_clause,[],[f740,f689,f581,f932]) ).
fof(f932,plain,
( spl29_108
<=> finite(sK26) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_108])]) ).
fof(f581,plain,
( spl29_56
<=> empty(sK26) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_56])]) ).
fof(f740,plain,
( finite(sK26)
| ~ spl29_56
| ~ spl29_80 ),
inference(resolution,[],[f690,f583]) ).
fof(f583,plain,
( empty(sK26)
| ~ spl29_56 ),
inference(avatar_component_clause,[],[f581]) ).
fof(f892,plain,
spl29_107,
inference(avatar_split_clause,[],[f240,f890]) ).
fof(f890,plain,
( spl29_107
<=> ! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_107])]) ).
fof(f240,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(cnf_transformation,[],[f115]) ).
fof(f115,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(ennf_transformation,[],[f61]) ).
fof(f61,axiom,
! [X0,X1] :
~ ( empty(X1)
& X0 != X1
& empty(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_boole) ).
fof(f888,plain,
spl29_106,
inference(avatar_split_clause,[],[f239,f886]) ).
fof(f886,plain,
( spl29_106
<=> ! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_106])]) ).
fof(f239,plain,
! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f114]) ).
fof(f114,plain,
! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f63]) ).
fof(f63,plain,
! [X0,X1] :
( subset(X0,X1)
=> element(X0,powerset(X1)) ),
inference(unused_predicate_definition_removal,[],[f56]) ).
fof(f56,axiom,
! [X0,X1] :
( element(X0,powerset(X1))
<=> subset(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
fof(f884,plain,
spl29_105,
inference(avatar_split_clause,[],[f204,f882]) ).
fof(f882,plain,
( spl29_105
<=> ! [X0,X1] :
( ordinal(X1)
| ~ element(X1,X0)
| ~ ordinal(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_105])]) ).
fof(f204,plain,
! [X0,X1] :
( ordinal(X1)
| ~ element(X1,X0)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f90]) ).
fof(f90,plain,
! [X0] :
( ! [X1] :
( ( ordinal(X1)
& epsilon_connected(X1)
& epsilon_transitive(X1) )
| ~ element(X1,X0) )
| ~ ordinal(X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f2,axiom,
! [X0] :
( ordinal(X0)
=> ! [X1] :
( element(X1,X0)
=> ( ordinal(X1)
& epsilon_connected(X1)
& epsilon_transitive(X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_arytm_3) ).
fof(f879,plain,
( spl29_104
| ~ spl29_54
| ~ spl29_80 ),
inference(avatar_split_clause,[],[f739,f689,f571,f876]) ).
fof(f876,plain,
( spl29_104
<=> finite(sK25) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_104])]) ).
fof(f571,plain,
( spl29_54
<=> empty(sK25) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_54])]) ).
fof(f739,plain,
( finite(sK25)
| ~ spl29_54
| ~ spl29_80 ),
inference(resolution,[],[f690,f573]) ).
fof(f573,plain,
( empty(sK25)
| ~ spl29_54 ),
inference(avatar_component_clause,[],[f571]) ).
fof(f874,plain,
spl29_103,
inference(avatar_split_clause,[],[f203,f872]) ).
fof(f872,plain,
( spl29_103
<=> ! [X0,X1] :
( epsilon_connected(X1)
| ~ element(X1,X0)
| ~ ordinal(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_103])]) ).
fof(f203,plain,
! [X0,X1] :
( epsilon_connected(X1)
| ~ element(X1,X0)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f90]) ).
fof(f870,plain,
spl29_102,
inference(avatar_split_clause,[],[f202,f868]) ).
fof(f868,plain,
( spl29_102
<=> ! [X0,X1] :
( epsilon_transitive(X1)
| ~ element(X1,X0)
| ~ ordinal(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_102])]) ).
fof(f202,plain,
! [X0,X1] :
( epsilon_transitive(X1)
| ~ element(X1,X0)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f90]) ).
fof(f866,plain,
spl29_101,
inference(avatar_split_clause,[],[f196,f864]) ).
fof(f864,plain,
( spl29_101
<=> ! [X0] :
( element(sK4(X0),powerset(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_101])]) ).
fof(f196,plain,
! [X0] :
( element(sK4(X0),powerset(X0))
| empty(X0) ),
inference(cnf_transformation,[],[f128]) ).
fof(f128,plain,
! [X0] :
( ( finite(sK4(X0))
& ~ empty(sK4(X0))
& element(sK4(X0),powerset(X0)) )
| empty(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f87,f127]) ).
fof(f127,plain,
! [X0] :
( ? [X1] :
( finite(X1)
& ~ empty(X1)
& element(X1,powerset(X0)) )
=> ( finite(sK4(X0))
& ~ empty(sK4(X0))
& element(sK4(X0),powerset(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f87,plain,
! [X0] :
( ? [X1] :
( finite(X1)
& ~ empty(X1)
& element(X1,powerset(X0)) )
| empty(X0) ),
inference(ennf_transformation,[],[f43]) ).
fof(f43,axiom,
! [X0] :
( ~ empty(X0)
=> ? [X1] :
( finite(X1)
& ~ empty(X1)
& element(X1,powerset(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_finset_1) ).
fof(f862,plain,
spl29_100,
inference(avatar_split_clause,[],[f194,f860]) ).
fof(f860,plain,
( spl29_100
<=> ! [X0] :
( element(sK3(X0),powerset(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_100])]) ).
fof(f194,plain,
! [X0] :
( element(sK3(X0),powerset(X0))
| empty(X0) ),
inference(cnf_transformation,[],[f126]) ).
fof(f126,plain,
! [X0] :
( ( ~ empty(sK3(X0))
& element(sK3(X0),powerset(X0)) )
| empty(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f86,f125]) ).
fof(f125,plain,
! [X0] :
( ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) )
=> ( ~ empty(sK3(X0))
& element(sK3(X0),powerset(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f86,plain,
! [X0] :
( ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) )
| empty(X0) ),
inference(ennf_transformation,[],[f32]) ).
fof(f32,axiom,
! [X0] :
( ~ empty(X0)
=> ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_subset_1) ).
fof(f849,plain,
spl29_99,
inference(avatar_split_clause,[],[f234,f847]) ).
fof(f847,plain,
( spl29_99
<=> ! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_99])]) ).
fof(f234,plain,
! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f105]) ).
fof(f105,plain,
! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f52]) ).
fof(f52,axiom,
! [X0,X1] :
( in(X0,X1)
=> element(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
fof(f845,plain,
spl29_98,
inference(avatar_split_clause,[],[f233,f843]) ).
fof(f843,plain,
( spl29_98
<=> ! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_98])]) ).
fof(f233,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f104]) ).
fof(f104,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0,X1] :
( in(X0,X1)
=> ~ in(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(f841,plain,
spl29_97,
inference(avatar_split_clause,[],[f215,f839]) ).
fof(f839,plain,
( spl29_97
<=> ! [X0] :
( ordinal(X0)
| ~ epsilon_connected(X0)
| ~ epsilon_transitive(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_97])]) ).
fof(f215,plain,
! [X0] :
( ordinal(X0)
| ~ epsilon_connected(X0)
| ~ epsilon_transitive(X0) ),
inference(cnf_transformation,[],[f99]) ).
fof(f99,plain,
! [X0] :
( ordinal(X0)
| ~ epsilon_connected(X0)
| ~ epsilon_transitive(X0) ),
inference(flattening,[],[f98]) ).
fof(f98,plain,
! [X0] :
( ordinal(X0)
| ~ epsilon_connected(X0)
| ~ epsilon_transitive(X0) ),
inference(ennf_transformation,[],[f11]) ).
fof(f11,axiom,
! [X0] :
( ( epsilon_connected(X0)
& epsilon_transitive(X0) )
=> ordinal(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_ordinal1) ).
fof(f836,plain,
( spl29_96
| ~ spl29_49
| ~ spl29_80 ),
inference(avatar_split_clause,[],[f738,f689,f546,f833]) ).
fof(f833,plain,
( spl29_96
<=> finite(sK24) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_96])]) ).
fof(f546,plain,
( spl29_49
<=> empty(sK24) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_49])]) ).
fof(f738,plain,
( finite(sK24)
| ~ spl29_49
| ~ spl29_80 ),
inference(resolution,[],[f690,f548]) ).
fof(f548,plain,
( empty(sK24)
| ~ spl29_49 ),
inference(avatar_component_clause,[],[f546]) ).
fof(f819,plain,
spl29_95,
inference(avatar_split_clause,[],[f241,f817]) ).
fof(f817,plain,
( spl29_95
<=> ! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_95])]) ).
fof(f241,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f116]) ).
fof(f116,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f60]) ).
fof(f60,axiom,
! [X0,X1] :
~ ( empty(X1)
& in(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
fof(f815,plain,
spl29_94,
inference(avatar_split_clause,[],[f224,f813]) ).
fof(f813,plain,
( spl29_94
<=> ! [X0] : element(sK7(X0),powerset(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_94])]) ).
fof(f224,plain,
! [X0] : element(sK7(X0),powerset(X0)),
inference(cnf_transformation,[],[f134]) ).
fof(f134,plain,
! [X0] :
( finite(sK7(X0))
& ordinal(sK7(X0))
& epsilon_connected(sK7(X0))
& epsilon_transitive(sK7(X0))
& function(sK7(X0))
& relation(sK7(X0))
& empty(sK7(X0))
& element(sK7(X0),powerset(X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f79,f133]) ).
fof(f133,plain,
! [X0] :
( ? [X1] :
( finite(X1)
& ordinal(X1)
& epsilon_connected(X1)
& epsilon_transitive(X1)
& function(X1)
& relation(X1)
& empty(X1)
& element(X1,powerset(X0)) )
=> ( finite(sK7(X0))
& ordinal(sK7(X0))
& epsilon_connected(sK7(X0))
& epsilon_transitive(sK7(X0))
& function(sK7(X0))
& relation(sK7(X0))
& empty(sK7(X0))
& element(sK7(X0),powerset(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f79,plain,
! [X0] :
? [X1] :
( finite(X1)
& ordinal(X1)
& epsilon_connected(X1)
& epsilon_transitive(X1)
& function(X1)
& relation(X1)
& empty(X1)
& element(X1,powerset(X0)) ),
inference(pure_predicate_removal,[],[f78]) ).
fof(f78,plain,
! [X0] :
? [X1] :
( finite(X1)
& natural(X1)
& ordinal(X1)
& epsilon_connected(X1)
& epsilon_transitive(X1)
& function(X1)
& relation(X1)
& empty(X1)
& element(X1,powerset(X0)) ),
inference(pure_predicate_removal,[],[f35]) ).
fof(f35,axiom,
! [X0] :
? [X1] :
( finite(X1)
& natural(X1)
& ordinal(X1)
& epsilon_connected(X1)
& epsilon_transitive(X1)
& one_to_one(X1)
& function(X1)
& relation(X1)
& empty(X1)
& element(X1,powerset(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_finset_1) ).
fof(f811,plain,
spl29_93,
inference(avatar_split_clause,[],[f222,f809]) ).
fof(f809,plain,
( spl29_93
<=> ! [X0] : element(sK6(X0),powerset(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_93])]) ).
fof(f222,plain,
! [X0] : element(sK6(X0),powerset(X0)),
inference(cnf_transformation,[],[f132]) ).
fof(f132,plain,
! [X0] :
( empty(sK6(X0))
& element(sK6(X0),powerset(X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f40,f131]) ).
fof(f131,plain,
! [X0] :
( ? [X1] :
( empty(X1)
& element(X1,powerset(X0)) )
=> ( empty(sK6(X0))
& element(sK6(X0),powerset(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f40,axiom,
! [X0] :
? [X1] :
( empty(X1)
& element(X1,powerset(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_subset_1) ).
fof(f807,plain,
( spl29_92
| ~ spl29_13
| ~ spl29_80 ),
inference(avatar_split_clause,[],[f737,f689,f366,f804]) ).
fof(f804,plain,
( spl29_92
<=> finite(sK9) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_92])]) ).
fof(f737,plain,
( finite(sK9)
| ~ spl29_13
| ~ spl29_80 ),
inference(resolution,[],[f690,f368]) ).
fof(f802,plain,
spl29_91,
inference(avatar_split_clause,[],[f208,f800]) ).
fof(f800,plain,
( spl29_91
<=> ! [X0] :
( empty_set = X0
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_91])]) ).
fof(f208,plain,
! [X0] :
( empty_set = X0
| ~ empty(X0) ),
inference(cnf_transformation,[],[f94]) ).
fof(f94,plain,
! [X0] :
( empty_set = X0
| ~ empty(X0) ),
inference(ennf_transformation,[],[f59]) ).
fof(f59,axiom,
! [X0] :
( empty(X0)
=> empty_set = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
fof(f798,plain,
spl29_90,
inference(avatar_split_clause,[],[f198,f796]) ).
fof(f796,plain,
( spl29_90
<=> ! [X0] :
( finite(sK4(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_90])]) ).
fof(f198,plain,
! [X0] :
( finite(sK4(X0))
| empty(X0) ),
inference(cnf_transformation,[],[f128]) ).
fof(f794,plain,
spl29_89,
inference(avatar_split_clause,[],[f197,f792]) ).
fof(f792,plain,
( spl29_89
<=> ! [X0] :
( ~ empty(sK4(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_89])]) ).
fof(f197,plain,
! [X0] :
( ~ empty(sK4(X0))
| empty(X0) ),
inference(cnf_transformation,[],[f128]) ).
fof(f790,plain,
spl29_88,
inference(avatar_split_clause,[],[f195,f788]) ).
fof(f788,plain,
( spl29_88
<=> ! [X0] :
( ~ empty(sK3(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_88])]) ).
fof(f195,plain,
! [X0] :
( ~ empty(sK3(X0))
| empty(X0) ),
inference(cnf_transformation,[],[f126]) ).
fof(f746,plain,
( spl29_87
| ~ spl29_6
| ~ spl29_80 ),
inference(avatar_split_clause,[],[f734,f689,f331,f743]) ).
fof(f743,plain,
( spl29_87
<=> finite(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_87])]) ).
fof(f331,plain,
( spl29_6
<=> empty(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_6])]) ).
fof(f734,plain,
( finite(empty_set)
| ~ spl29_6
| ~ spl29_80 ),
inference(resolution,[],[f690,f333]) ).
fof(f333,plain,
( empty(empty_set)
| ~ spl29_6 ),
inference(avatar_component_clause,[],[f331]) ).
fof(f715,plain,
spl29_86,
inference(avatar_split_clause,[],[f221,f713]) ).
fof(f713,plain,
( spl29_86
<=> ! [X0] : element(sK5(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_86])]) ).
fof(f221,plain,
! [X0] : element(sK5(X0),X0),
inference(cnf_transformation,[],[f130]) ).
fof(f130,plain,
! [X0] : element(sK5(X0),X0),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f15,f129]) ).
fof(f129,plain,
! [X0] :
( ? [X1] : element(X1,X0)
=> element(sK5(X0),X0) ),
introduced(choice_axiom,[]) ).
fof(f15,axiom,
! [X0] :
? [X1] : element(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(f711,plain,
spl29_85,
inference(avatar_split_clause,[],[f211,f709]) ).
fof(f709,plain,
( spl29_85
<=> ! [X0] :
( ordinal(X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_85])]) ).
fof(f211,plain,
! [X0] :
( ordinal(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f95]) ).
fof(f95,plain,
! [X0] :
( ( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0) )
| ~ empty(X0) ),
inference(ennf_transformation,[],[f12]) ).
fof(f12,axiom,
! [X0] :
( empty(X0)
=> ( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc3_ordinal1) ).
fof(f707,plain,
spl29_84,
inference(avatar_split_clause,[],[f210,f705]) ).
fof(f705,plain,
( spl29_84
<=> ! [X0] :
( epsilon_connected(X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_84])]) ).
fof(f210,plain,
! [X0] :
( epsilon_connected(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f95]) ).
fof(f703,plain,
spl29_83,
inference(avatar_split_clause,[],[f209,f701]) ).
fof(f701,plain,
( spl29_83
<=> ! [X0] :
( epsilon_transitive(X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_83])]) ).
fof(f209,plain,
! [X0] :
( epsilon_transitive(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f95]) ).
fof(f699,plain,
spl29_82,
inference(avatar_split_clause,[],[f207,f697]) ).
fof(f697,plain,
( spl29_82
<=> ! [X0] :
( relation(X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_82])]) ).
fof(f207,plain,
! [X0] :
( relation(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f93]) ).
fof(f93,plain,
! [X0] :
( relation(X0)
| ~ empty(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0] :
( empty(X0)
=> relation(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_relat_1) ).
fof(f695,plain,
spl29_81,
inference(avatar_split_clause,[],[f206,f693]) ).
fof(f206,plain,
! [X0] :
( function(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f92]) ).
fof(f92,plain,
! [X0] :
( function(X0)
| ~ empty(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0] :
( empty(X0)
=> function(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_funct_1) ).
fof(f691,plain,
spl29_80,
inference(avatar_split_clause,[],[f205,f689]) ).
fof(f205,plain,
! [X0] :
( finite(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f91]) ).
fof(f91,plain,
! [X0] :
( finite(X0)
| ~ empty(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0] :
( empty(X0)
=> finite(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_finset_1) ).
fof(f687,plain,
spl29_79,
inference(avatar_split_clause,[],[f201,f685]) ).
fof(f685,plain,
( spl29_79
<=> ! [X0] :
( epsilon_connected(X0)
| ~ ordinal(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_79])]) ).
fof(f201,plain,
! [X0] :
( epsilon_connected(X0)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f89]) ).
fof(f89,plain,
! [X0] :
( ( epsilon_connected(X0)
& epsilon_transitive(X0) )
| ~ ordinal(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f5,axiom,
! [X0] :
( ordinal(X0)
=> ( epsilon_connected(X0)
& epsilon_transitive(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_ordinal1) ).
fof(f683,plain,
spl29_78,
inference(avatar_split_clause,[],[f200,f681]) ).
fof(f681,plain,
( spl29_78
<=> ! [X0] :
( epsilon_transitive(X0)
| ~ ordinal(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_78])]) ).
fof(f200,plain,
! [X0] :
( epsilon_transitive(X0)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f89]) ).
fof(f679,plain,
spl29_77,
inference(avatar_split_clause,[],[f298,f676]) ).
fof(f676,plain,
( spl29_77
<=> element(sK28,positive_rationals) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_77])]) ).
fof(f298,plain,
element(sK28,positive_rationals),
inference(cnf_transformation,[],[f176]) ).
fof(f176,plain,
( ordinal(sK28)
& epsilon_connected(sK28)
& epsilon_transitive(sK28)
& empty(sK28)
& element(sK28,positive_rationals) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK28])],[f82,f175]) ).
fof(f175,plain,
( ? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0)
& empty(X0)
& element(X0,positive_rationals) )
=> ( ordinal(sK28)
& epsilon_connected(sK28)
& epsilon_transitive(sK28)
& empty(sK28)
& element(sK28,positive_rationals) ) ),
introduced(choice_axiom,[]) ).
fof(f82,plain,
? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0)
& empty(X0)
& element(X0,positive_rationals) ),
inference(pure_predicate_removal,[],[f42]) ).
fof(f42,axiom,
? [X0] :
( natural(X0)
& ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0)
& empty(X0)
& element(X0,positive_rationals) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_arytm_3) ).
fof(f674,plain,
spl29_76,
inference(avatar_split_clause,[],[f293,f671]) ).
fof(f671,plain,
( spl29_76
<=> element(sK27,positive_rationals) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_76])]) ).
fof(f293,plain,
element(sK27,positive_rationals),
inference(cnf_transformation,[],[f174]) ).
fof(f174,plain,
( ordinal(sK27)
& epsilon_connected(sK27)
& epsilon_transitive(sK27)
& ~ empty(sK27)
& element(sK27,positive_rationals) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK27])],[f34,f173]) ).
fof(f173,plain,
( ? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0)
& ~ empty(X0)
& element(X0,positive_rationals) )
=> ( ordinal(sK27)
& epsilon_connected(sK27)
& epsilon_transitive(sK27)
& ~ empty(sK27)
& element(sK27,positive_rationals) ) ),
introduced(choice_axiom,[]) ).
fof(f34,axiom,
? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0)
& ~ empty(X0)
& element(X0,positive_rationals) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_arytm_3) ).
fof(f669,plain,
spl29_75,
inference(avatar_split_clause,[],[f232,f667]) ).
fof(f667,plain,
( spl29_75
<=> ! [X0] : subset(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_75])]) ).
fof(f232,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f62]) ).
fof(f62,plain,
! [X0] : subset(X0,X0),
inference(rectify,[],[f50]) ).
fof(f50,axiom,
! [X0,X1] : subset(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f665,plain,
spl29_74,
inference(avatar_split_clause,[],[f231,f663]) ).
fof(f663,plain,
( spl29_74
<=> ! [X0] : finite(sK7(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_74])]) ).
fof(f231,plain,
! [X0] : finite(sK7(X0)),
inference(cnf_transformation,[],[f134]) ).
fof(f661,plain,
spl29_73,
inference(avatar_split_clause,[],[f230,f659]) ).
fof(f659,plain,
( spl29_73
<=> ! [X0] : ordinal(sK7(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_73])]) ).
fof(f230,plain,
! [X0] : ordinal(sK7(X0)),
inference(cnf_transformation,[],[f134]) ).
fof(f657,plain,
spl29_72,
inference(avatar_split_clause,[],[f229,f655]) ).
fof(f655,plain,
( spl29_72
<=> ! [X0] : epsilon_connected(sK7(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_72])]) ).
fof(f229,plain,
! [X0] : epsilon_connected(sK7(X0)),
inference(cnf_transformation,[],[f134]) ).
fof(f653,plain,
spl29_71,
inference(avatar_split_clause,[],[f228,f651]) ).
fof(f651,plain,
( spl29_71
<=> ! [X0] : epsilon_transitive(sK7(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_71])]) ).
fof(f228,plain,
! [X0] : epsilon_transitive(sK7(X0)),
inference(cnf_transformation,[],[f134]) ).
fof(f649,plain,
spl29_70,
inference(avatar_split_clause,[],[f227,f647]) ).
fof(f647,plain,
( spl29_70
<=> ! [X0] : function(sK7(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_70])]) ).
fof(f227,plain,
! [X0] : function(sK7(X0)),
inference(cnf_transformation,[],[f134]) ).
fof(f645,plain,
spl29_69,
inference(avatar_split_clause,[],[f226,f643]) ).
fof(f643,plain,
( spl29_69
<=> ! [X0] : relation(sK7(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_69])]) ).
fof(f226,plain,
! [X0] : relation(sK7(X0)),
inference(cnf_transformation,[],[f134]) ).
fof(f641,plain,
spl29_68,
inference(avatar_split_clause,[],[f225,f639]) ).
fof(f639,plain,
( spl29_68
<=> ! [X0] : empty(sK7(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_68])]) ).
fof(f225,plain,
! [X0] : empty(sK7(X0)),
inference(cnf_transformation,[],[f134]) ).
fof(f637,plain,
spl29_67,
inference(avatar_split_clause,[],[f223,f635]) ).
fof(f635,plain,
( spl29_67
<=> ! [X0] : empty(sK6(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_67])]) ).
fof(f223,plain,
! [X0] : empty(sK6(X0)),
inference(cnf_transformation,[],[f132]) ).
fof(f633,plain,
spl29_66,
inference(avatar_split_clause,[],[f193,f631]) ).
fof(f631,plain,
( spl29_66
<=> ! [X0] : ~ empty(powerset(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_66])]) ).
fof(f193,plain,
! [X0] : ~ empty(powerset(X0)),
inference(cnf_transformation,[],[f18]) ).
fof(f18,axiom,
! [X0] : ~ empty(powerset(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_subset_1) ).
fof(f629,plain,
spl29_65,
inference(avatar_split_clause,[],[f302,f626]) ).
fof(f626,plain,
( spl29_65
<=> ordinal(sK28) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_65])]) ).
fof(f302,plain,
ordinal(sK28),
inference(cnf_transformation,[],[f176]) ).
fof(f624,plain,
spl29_64,
inference(avatar_split_clause,[],[f301,f621]) ).
fof(f621,plain,
( spl29_64
<=> epsilon_connected(sK28) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_64])]) ).
fof(f301,plain,
epsilon_connected(sK28),
inference(cnf_transformation,[],[f176]) ).
fof(f619,plain,
spl29_63,
inference(avatar_split_clause,[],[f300,f616]) ).
fof(f616,plain,
( spl29_63
<=> epsilon_transitive(sK28) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_63])]) ).
fof(f300,plain,
epsilon_transitive(sK28),
inference(cnf_transformation,[],[f176]) ).
fof(f614,plain,
spl29_62,
inference(avatar_split_clause,[],[f299,f611]) ).
fof(f299,plain,
empty(sK28),
inference(cnf_transformation,[],[f176]) ).
fof(f609,plain,
spl29_61,
inference(avatar_split_clause,[],[f297,f606]) ).
fof(f606,plain,
( spl29_61
<=> ordinal(sK27) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_61])]) ).
fof(f297,plain,
ordinal(sK27),
inference(cnf_transformation,[],[f174]) ).
fof(f604,plain,
spl29_60,
inference(avatar_split_clause,[],[f296,f601]) ).
fof(f601,plain,
( spl29_60
<=> epsilon_connected(sK27) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_60])]) ).
fof(f296,plain,
epsilon_connected(sK27),
inference(cnf_transformation,[],[f174]) ).
fof(f599,plain,
spl29_59,
inference(avatar_split_clause,[],[f295,f596]) ).
fof(f596,plain,
( spl29_59
<=> epsilon_transitive(sK27) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_59])]) ).
fof(f295,plain,
epsilon_transitive(sK27),
inference(cnf_transformation,[],[f174]) ).
fof(f594,plain,
~ spl29_58,
inference(avatar_split_clause,[],[f294,f591]) ).
fof(f591,plain,
( spl29_58
<=> empty(sK27) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_58])]) ).
fof(f294,plain,
~ empty(sK27),
inference(cnf_transformation,[],[f174]) ).
fof(f589,plain,
spl29_57,
inference(avatar_split_clause,[],[f292,f586]) ).
fof(f586,plain,
( spl29_57
<=> relation(sK26) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_57])]) ).
fof(f292,plain,
relation(sK26),
inference(cnf_transformation,[],[f172]) ).
fof(f172,plain,
( relation(sK26)
& empty(sK26) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK26])],[f31,f171]) ).
fof(f171,plain,
( ? [X0] :
( relation(X0)
& empty(X0) )
=> ( relation(sK26)
& empty(sK26) ) ),
introduced(choice_axiom,[]) ).
fof(f31,axiom,
? [X0] :
( relation(X0)
& empty(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_relat_1) ).
fof(f584,plain,
spl29_56,
inference(avatar_split_clause,[],[f291,f581]) ).
fof(f291,plain,
empty(sK26),
inference(cnf_transformation,[],[f172]) ).
fof(f579,plain,
spl29_55,
inference(avatar_split_clause,[],[f290,f576]) ).
fof(f576,plain,
( spl29_55
<=> function(sK25) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_55])]) ).
fof(f290,plain,
function(sK25),
inference(cnf_transformation,[],[f170]) ).
fof(f170,plain,
( function(sK25)
& empty(sK25)
& relation(sK25) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK25])],[f36,f169]) ).
fof(f169,plain,
( ? [X0] :
( function(X0)
& empty(X0)
& relation(X0) )
=> ( function(sK25)
& empty(sK25)
& relation(sK25) ) ),
introduced(choice_axiom,[]) ).
fof(f36,axiom,
? [X0] :
( function(X0)
& empty(X0)
& relation(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_funct_1) ).
fof(f574,plain,
spl29_54,
inference(avatar_split_clause,[],[f289,f571]) ).
fof(f289,plain,
empty(sK25),
inference(cnf_transformation,[],[f170]) ).
fof(f569,plain,
spl29_53,
inference(avatar_split_clause,[],[f288,f566]) ).
fof(f566,plain,
( spl29_53
<=> relation(sK25) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_53])]) ).
fof(f288,plain,
relation(sK25),
inference(cnf_transformation,[],[f170]) ).
fof(f564,plain,
spl29_52,
inference(avatar_split_clause,[],[f287,f561]) ).
fof(f561,plain,
( spl29_52
<=> ordinal(sK24) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_52])]) ).
fof(f287,plain,
ordinal(sK24),
inference(cnf_transformation,[],[f168]) ).
fof(f168,plain,
( ordinal(sK24)
& epsilon_connected(sK24)
& epsilon_transitive(sK24)
& empty(sK24)
& function(sK24)
& relation(sK24) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK24])],[f76,f167]) ).
fof(f167,plain,
( ? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0)
& empty(X0)
& function(X0)
& relation(X0) )
=> ( ordinal(sK24)
& epsilon_connected(sK24)
& epsilon_transitive(sK24)
& empty(sK24)
& function(sK24)
& relation(sK24) ) ),
introduced(choice_axiom,[]) ).
fof(f76,plain,
? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0)
& empty(X0)
& function(X0)
& relation(X0) ),
inference(pure_predicate_removal,[],[f37]) ).
fof(f37,axiom,
? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0)
& empty(X0)
& one_to_one(X0)
& function(X0)
& relation(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_ordinal1) ).
fof(f559,plain,
spl29_51,
inference(avatar_split_clause,[],[f286,f556]) ).
fof(f556,plain,
( spl29_51
<=> epsilon_connected(sK24) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_51])]) ).
fof(f286,plain,
epsilon_connected(sK24),
inference(cnf_transformation,[],[f168]) ).
fof(f554,plain,
spl29_50,
inference(avatar_split_clause,[],[f285,f551]) ).
fof(f551,plain,
( spl29_50
<=> epsilon_transitive(sK24) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_50])]) ).
fof(f285,plain,
epsilon_transitive(sK24),
inference(cnf_transformation,[],[f168]) ).
fof(f549,plain,
spl29_49,
inference(avatar_split_clause,[],[f284,f546]) ).
fof(f284,plain,
empty(sK24),
inference(cnf_transformation,[],[f168]) ).
fof(f544,plain,
spl29_48,
inference(avatar_split_clause,[],[f283,f541]) ).
fof(f541,plain,
( spl29_48
<=> function(sK24) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_48])]) ).
fof(f283,plain,
function(sK24),
inference(cnf_transformation,[],[f168]) ).
fof(f539,plain,
spl29_47,
inference(avatar_split_clause,[],[f282,f536]) ).
fof(f536,plain,
( spl29_47
<=> relation(sK24) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_47])]) ).
fof(f282,plain,
relation(sK24),
inference(cnf_transformation,[],[f168]) ).
fof(f534,plain,
spl29_46,
inference(avatar_split_clause,[],[f281,f531]) ).
fof(f531,plain,
( spl29_46
<=> function(sK23) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_46])]) ).
fof(f281,plain,
function(sK23),
inference(cnf_transformation,[],[f166]) ).
fof(f166,plain,
( function(sK23)
& relation(sK23) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK23])],[f77,f165]) ).
fof(f165,plain,
( ? [X0] :
( function(X0)
& relation(X0) )
=> ( function(sK23)
& relation(sK23) ) ),
introduced(choice_axiom,[]) ).
fof(f77,plain,
? [X0] :
( function(X0)
& relation(X0) ),
inference(pure_predicate_removal,[],[f44]) ).
fof(f44,axiom,
? [X0] :
( one_to_one(X0)
& function(X0)
& relation(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_funct_1) ).
fof(f529,plain,
spl29_45,
inference(avatar_split_clause,[],[f280,f526]) ).
fof(f526,plain,
( spl29_45
<=> relation(sK23) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_45])]) ).
fof(f280,plain,
relation(sK23),
inference(cnf_transformation,[],[f166]) ).
fof(f524,plain,
spl29_44,
inference(avatar_split_clause,[],[f279,f521]) ).
fof(f521,plain,
( spl29_44
<=> function(sK22) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_44])]) ).
fof(f279,plain,
function(sK22),
inference(cnf_transformation,[],[f164]) ).
fof(f164,plain,
( function(sK22)
& relation(sK22) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK22])],[f66,f163]) ).
fof(f163,plain,
( ? [X0] :
( function(X0)
& relation(X0) )
=> ( function(sK22)
& relation(sK22) ) ),
introduced(choice_axiom,[]) ).
fof(f66,plain,
? [X0] :
( function(X0)
& relation(X0) ),
inference(pure_predicate_removal,[],[f65]) ).
fof(f65,plain,
? [X0] :
( transfinite_sequence(X0)
& function(X0)
& relation(X0) ),
inference(pure_predicate_removal,[],[f38]) ).
fof(f38,axiom,
? [X0] :
( ordinal_yielding(X0)
& transfinite_sequence(X0)
& function(X0)
& relation(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_ordinal2) ).
fof(f519,plain,
spl29_43,
inference(avatar_split_clause,[],[f278,f516]) ).
fof(f516,plain,
( spl29_43
<=> relation(sK22) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_43])]) ).
fof(f278,plain,
relation(sK22),
inference(cnf_transformation,[],[f164]) ).
fof(f514,plain,
spl29_42,
inference(avatar_split_clause,[],[f277,f511]) ).
fof(f511,plain,
( spl29_42
<=> function(sK21) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_42])]) ).
fof(f277,plain,
function(sK21),
inference(cnf_transformation,[],[f162]) ).
fof(f162,plain,
( function(sK21)
& relation(sK21) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK21])],[f67,f161]) ).
fof(f161,plain,
( ? [X0] :
( function(X0)
& relation(X0) )
=> ( function(sK21)
& relation(sK21) ) ),
introduced(choice_axiom,[]) ).
fof(f67,plain,
? [X0] :
( function(X0)
& relation(X0) ),
inference(pure_predicate_removal,[],[f48]) ).
fof(f48,axiom,
? [X0] :
( transfinite_sequence(X0)
& function(X0)
& relation(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc4_ordinal1) ).
fof(f509,plain,
spl29_41,
inference(avatar_split_clause,[],[f276,f506]) ).
fof(f506,plain,
( spl29_41
<=> relation(sK21) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_41])]) ).
fof(f276,plain,
relation(sK21),
inference(cnf_transformation,[],[f162]) ).
fof(f504,plain,
spl29_40,
inference(avatar_split_clause,[],[f275,f501]) ).
fof(f501,plain,
( spl29_40
<=> function(sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_40])]) ).
fof(f275,plain,
function(sK20),
inference(cnf_transformation,[],[f160]) ).
fof(f160,plain,
( function(sK20)
& relation(sK20) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK20])],[f69,f159]) ).
fof(f159,plain,
( ? [X0] :
( function(X0)
& relation(X0) )
=> ( function(sK20)
& relation(sK20) ) ),
introduced(choice_axiom,[]) ).
fof(f69,plain,
? [X0] :
( function(X0)
& relation(X0) ),
inference(pure_predicate_removal,[],[f27]) ).
fof(f27,axiom,
? [X0] :
( function_yielding(X0)
& function(X0)
& relation(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_funcop_1) ).
fof(f499,plain,
spl29_39,
inference(avatar_split_clause,[],[f274,f496]) ).
fof(f496,plain,
( spl29_39
<=> relation(sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_39])]) ).
fof(f274,plain,
relation(sK20),
inference(cnf_transformation,[],[f160]) ).
fof(f494,plain,
spl29_38,
inference(avatar_split_clause,[],[f273,f491]) ).
fof(f491,plain,
( spl29_38
<=> function(sK19) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_38])]) ).
fof(f273,plain,
function(sK19),
inference(cnf_transformation,[],[f158]) ).
fof(f158,plain,
( function(sK19)
& relation(sK19) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK19])],[f28,f157]) ).
fof(f157,plain,
( ? [X0] :
( function(X0)
& relation(X0) )
=> ( function(sK19)
& relation(sK19) ) ),
introduced(choice_axiom,[]) ).
fof(f28,axiom,
? [X0] :
( function(X0)
& relation(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_funct_1) ).
fof(f489,plain,
spl29_37,
inference(avatar_split_clause,[],[f272,f486]) ).
fof(f486,plain,
( spl29_37
<=> relation(sK19) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_37])]) ).
fof(f272,plain,
relation(sK19),
inference(cnf_transformation,[],[f158]) ).
fof(f484,plain,
spl29_36,
inference(avatar_split_clause,[],[f271,f481]) ).
fof(f481,plain,
( spl29_36
<=> function(sK18) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_36])]) ).
fof(f271,plain,
function(sK18),
inference(cnf_transformation,[],[f156]) ).
fof(f156,plain,
( function(sK18)
& relation(sK18) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK18])],[f71,f155]) ).
fof(f155,plain,
( ? [X0] :
( function(X0)
& relation(X0) )
=> ( function(sK18)
& relation(sK18) ) ),
introduced(choice_axiom,[]) ).
fof(f71,plain,
? [X0] :
( function(X0)
& relation(X0) ),
inference(pure_predicate_removal,[],[f47]) ).
fof(f47,axiom,
? [X0] :
( function(X0)
& relation_empty_yielding(X0)
& relation(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc4_funct_1) ).
fof(f479,plain,
spl29_35,
inference(avatar_split_clause,[],[f270,f476]) ).
fof(f476,plain,
( spl29_35
<=> relation(sK18) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_35])]) ).
fof(f270,plain,
relation(sK18),
inference(cnf_transformation,[],[f156]) ).
fof(f474,plain,
spl29_34,
inference(avatar_split_clause,[],[f269,f471]) ).
fof(f471,plain,
( spl29_34
<=> relation(sK17) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_34])]) ).
fof(f269,plain,
relation(sK17),
inference(cnf_transformation,[],[f154]) ).
fof(f154,plain,
relation(sK17),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK17])],[f70,f153]) ).
fof(f153,plain,
( ? [X0] : relation(X0)
=> relation(sK17) ),
introduced(choice_axiom,[]) ).
fof(f70,plain,
? [X0] : relation(X0),
inference(pure_predicate_removal,[],[f46]) ).
fof(f46,axiom,
? [X0] :
( relation_empty_yielding(X0)
& relation(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_relat_1) ).
fof(f469,plain,
spl29_33,
inference(avatar_split_clause,[],[f268,f466]) ).
fof(f466,plain,
( spl29_33
<=> function(sK16) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_33])]) ).
fof(f268,plain,
function(sK16),
inference(cnf_transformation,[],[f152]) ).
fof(f152,plain,
( function(sK16)
& relation(sK16) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK16])],[f64,f151]) ).
fof(f151,plain,
( ? [X0] :
( function(X0)
& relation(X0) )
=> ( function(sK16)
& relation(sK16) ) ),
introduced(choice_axiom,[]) ).
fof(f64,plain,
? [X0] :
( function(X0)
& relation(X0) ),
inference(pure_predicate_removal,[],[f49]) ).
fof(f49,axiom,
? [X0] :
( function(X0)
& relation_non_empty(X0)
& relation(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc5_funct_1) ).
fof(f464,plain,
spl29_32,
inference(avatar_split_clause,[],[f267,f461]) ).
fof(f461,plain,
( spl29_32
<=> relation(sK16) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_32])]) ).
fof(f267,plain,
relation(sK16),
inference(cnf_transformation,[],[f152]) ).
fof(f459,plain,
spl29_31,
inference(avatar_split_clause,[],[f266,f456]) ).
fof(f456,plain,
( spl29_31
<=> ordinal(sK15) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_31])]) ).
fof(f266,plain,
ordinal(sK15),
inference(cnf_transformation,[],[f150]) ).
fof(f150,plain,
( ordinal(sK15)
& epsilon_connected(sK15)
& epsilon_transitive(sK15) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK15])],[f68,f149]) ).
fof(f149,plain,
( ? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0) )
=> ( ordinal(sK15)
& epsilon_connected(sK15)
& epsilon_transitive(sK15) ) ),
introduced(choice_axiom,[]) ).
fof(f68,plain,
? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0) ),
inference(pure_predicate_removal,[],[f30]) ).
fof(f30,axiom,
? [X0] :
( being_limit_ordinal(X0)
& ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_ordinal2) ).
fof(f454,plain,
spl29_30,
inference(avatar_split_clause,[],[f265,f451]) ).
fof(f451,plain,
( spl29_30
<=> epsilon_connected(sK15) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_30])]) ).
fof(f265,plain,
epsilon_connected(sK15),
inference(cnf_transformation,[],[f150]) ).
fof(f449,plain,
spl29_29,
inference(avatar_split_clause,[],[f264,f446]) ).
fof(f446,plain,
( spl29_29
<=> epsilon_transitive(sK15) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_29])]) ).
fof(f264,plain,
epsilon_transitive(sK15),
inference(cnf_transformation,[],[f150]) ).
fof(f444,plain,
spl29_28,
inference(avatar_split_clause,[],[f263,f441]) ).
fof(f441,plain,
( spl29_28
<=> ordinal(sK14) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_28])]) ).
fof(f263,plain,
ordinal(sK14),
inference(cnf_transformation,[],[f148]) ).
fof(f148,plain,
( ordinal(sK14)
& epsilon_connected(sK14)
& epsilon_transitive(sK14) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK14])],[f29,f147]) ).
fof(f147,plain,
( ? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0) )
=> ( ordinal(sK14)
& epsilon_connected(sK14)
& epsilon_transitive(sK14) ) ),
introduced(choice_axiom,[]) ).
fof(f29,axiom,
? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_ordinal1) ).
fof(f439,plain,
spl29_27,
inference(avatar_split_clause,[],[f262,f436]) ).
fof(f436,plain,
( spl29_27
<=> epsilon_connected(sK14) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_27])]) ).
fof(f262,plain,
epsilon_connected(sK14),
inference(cnf_transformation,[],[f148]) ).
fof(f434,plain,
spl29_26,
inference(avatar_split_clause,[],[f261,f431]) ).
fof(f431,plain,
( spl29_26
<=> epsilon_transitive(sK14) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_26])]) ).
fof(f261,plain,
epsilon_transitive(sK14),
inference(cnf_transformation,[],[f148]) ).
fof(f429,plain,
spl29_25,
inference(avatar_split_clause,[],[f260,f426]) ).
fof(f426,plain,
( spl29_25
<=> relation(sK13) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_25])]) ).
fof(f260,plain,
relation(sK13),
inference(cnf_transformation,[],[f146]) ).
fof(f146,plain,
( relation(sK13)
& ~ empty(sK13) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK13])],[f39,f145]) ).
fof(f145,plain,
( ? [X0] :
( relation(X0)
& ~ empty(X0) )
=> ( relation(sK13)
& ~ empty(sK13) ) ),
introduced(choice_axiom,[]) ).
fof(f39,axiom,
? [X0] :
( relation(X0)
& ~ empty(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_relat_1) ).
fof(f424,plain,
~ spl29_24,
inference(avatar_split_clause,[],[f259,f421]) ).
fof(f421,plain,
( spl29_24
<=> empty(sK13) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_24])]) ).
fof(f259,plain,
~ empty(sK13),
inference(cnf_transformation,[],[f146]) ).
fof(f419,plain,
spl29_23,
inference(avatar_split_clause,[],[f258,f416]) ).
fof(f416,plain,
( spl29_23
<=> ordinal(sK12) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_23])]) ).
fof(f258,plain,
ordinal(sK12),
inference(cnf_transformation,[],[f144]) ).
fof(f144,plain,
( ordinal(sK12)
& epsilon_connected(sK12)
& epsilon_transitive(sK12)
& ~ empty(sK12) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK12])],[f81,f143]) ).
fof(f143,plain,
( ? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0)
& ~ empty(X0) )
=> ( ordinal(sK12)
& epsilon_connected(sK12)
& epsilon_transitive(sK12)
& ~ empty(sK12) ) ),
introduced(choice_axiom,[]) ).
fof(f81,plain,
? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0)
& ~ empty(X0) ),
inference(pure_predicate_removal,[],[f25]) ).
fof(f25,axiom,
? [X0] :
( natural(X0)
& ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0)
& ~ empty(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_arytm_3) ).
fof(f414,plain,
spl29_22,
inference(avatar_split_clause,[],[f257,f411]) ).
fof(f411,plain,
( spl29_22
<=> epsilon_connected(sK12) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_22])]) ).
fof(f257,plain,
epsilon_connected(sK12),
inference(cnf_transformation,[],[f144]) ).
fof(f409,plain,
spl29_21,
inference(avatar_split_clause,[],[f256,f406]) ).
fof(f406,plain,
( spl29_21
<=> epsilon_transitive(sK12) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_21])]) ).
fof(f256,plain,
epsilon_transitive(sK12),
inference(cnf_transformation,[],[f144]) ).
fof(f404,plain,
~ spl29_20,
inference(avatar_split_clause,[],[f255,f401]) ).
fof(f401,plain,
( spl29_20
<=> empty(sK12) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_20])]) ).
fof(f255,plain,
~ empty(sK12),
inference(cnf_transformation,[],[f144]) ).
fof(f399,plain,
spl29_19,
inference(avatar_split_clause,[],[f254,f396]) ).
fof(f396,plain,
( spl29_19
<=> ordinal(sK11) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_19])]) ).
fof(f254,plain,
ordinal(sK11),
inference(cnf_transformation,[],[f142]) ).
fof(f142,plain,
( ordinal(sK11)
& epsilon_connected(sK11)
& epsilon_transitive(sK11)
& ~ empty(sK11) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK11])],[f45,f141]) ).
fof(f141,plain,
( ? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0)
& ~ empty(X0) )
=> ( ordinal(sK11)
& epsilon_connected(sK11)
& epsilon_transitive(sK11)
& ~ empty(sK11) ) ),
introduced(choice_axiom,[]) ).
fof(f45,axiom,
? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0)
& ~ empty(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_ordinal1) ).
fof(f394,plain,
spl29_18,
inference(avatar_split_clause,[],[f253,f391]) ).
fof(f391,plain,
( spl29_18
<=> epsilon_connected(sK11) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_18])]) ).
fof(f253,plain,
epsilon_connected(sK11),
inference(cnf_transformation,[],[f142]) ).
fof(f389,plain,
spl29_17,
inference(avatar_split_clause,[],[f252,f386]) ).
fof(f386,plain,
( spl29_17
<=> epsilon_transitive(sK11) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_17])]) ).
fof(f252,plain,
epsilon_transitive(sK11),
inference(cnf_transformation,[],[f142]) ).
fof(f384,plain,
~ spl29_16,
inference(avatar_split_clause,[],[f251,f381]) ).
fof(f381,plain,
( spl29_16
<=> empty(sK11) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_16])]) ).
fof(f251,plain,
~ empty(sK11),
inference(cnf_transformation,[],[f142]) ).
fof(f379,plain,
spl29_15,
inference(avatar_split_clause,[],[f250,f376]) ).
fof(f376,plain,
( spl29_15
<=> finite(sK10) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_15])]) ).
fof(f250,plain,
finite(sK10),
inference(cnf_transformation,[],[f140]) ).
fof(f140,plain,
( finite(sK10)
& ~ empty(sK10) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10])],[f26,f139]) ).
fof(f139,plain,
( ? [X0] :
( finite(X0)
& ~ empty(X0) )
=> ( finite(sK10)
& ~ empty(sK10) ) ),
introduced(choice_axiom,[]) ).
fof(f26,axiom,
? [X0] :
( finite(X0)
& ~ empty(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_finset_1) ).
fof(f374,plain,
~ spl29_14,
inference(avatar_split_clause,[],[f249,f371]) ).
fof(f371,plain,
( spl29_14
<=> empty(sK10) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_14])]) ).
fof(f249,plain,
~ empty(sK10),
inference(cnf_transformation,[],[f140]) ).
fof(f369,plain,
spl29_13,
inference(avatar_split_clause,[],[f248,f366]) ).
fof(f248,plain,
empty(sK9),
inference(cnf_transformation,[],[f138]) ).
fof(f138,plain,
empty(sK9),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9])],[f33,f137]) ).
fof(f137,plain,
( ? [X0] : empty(X0)
=> empty(sK9) ),
introduced(choice_axiom,[]) ).
fof(f33,axiom,
? [X0] : empty(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
fof(f364,plain,
~ spl29_12,
inference(avatar_split_clause,[],[f247,f361]) ).
fof(f361,plain,
( spl29_12
<=> empty(sK8) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_12])]) ).
fof(f247,plain,
~ empty(sK8),
inference(cnf_transformation,[],[f136]) ).
fof(f136,plain,
~ empty(sK8),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f41,f135]) ).
fof(f135,plain,
( ? [X0] : ~ empty(X0)
=> ~ empty(sK8) ),
introduced(choice_axiom,[]) ).
fof(f41,axiom,
? [X0] : ~ empty(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
fof(f359,plain,
spl29_11,
inference(avatar_split_clause,[],[f188,f356]) ).
fof(f356,plain,
( spl29_11
<=> ordinal(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_11])]) ).
fof(f188,plain,
ordinal(empty_set),
inference(cnf_transformation,[],[f75]) ).
fof(f75,plain,
( ordinal(empty_set)
& epsilon_connected(empty_set)
& epsilon_transitive(empty_set)
& empty(empty_set)
& function(empty_set)
& relation(empty_set) ),
inference(pure_predicate_removal,[],[f73]) ).
fof(f73,plain,
( ordinal(empty_set)
& epsilon_connected(empty_set)
& epsilon_transitive(empty_set)
& empty(empty_set)
& one_to_one(empty_set)
& function(empty_set)
& relation(empty_set) ),
inference(pure_predicate_removal,[],[f20]) ).
fof(f20,axiom,
( ordinal(empty_set)
& epsilon_connected(empty_set)
& epsilon_transitive(empty_set)
& empty(empty_set)
& one_to_one(empty_set)
& function(empty_set)
& relation_empty_yielding(empty_set)
& relation(empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_ordinal1) ).
fof(f354,plain,
spl29_10,
inference(avatar_split_clause,[],[f187,f351]) ).
fof(f351,plain,
( spl29_10
<=> epsilon_connected(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_10])]) ).
fof(f187,plain,
epsilon_connected(empty_set),
inference(cnf_transformation,[],[f75]) ).
fof(f349,plain,
spl29_9,
inference(avatar_split_clause,[],[f186,f346]) ).
fof(f346,plain,
( spl29_9
<=> epsilon_transitive(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_9])]) ).
fof(f186,plain,
epsilon_transitive(empty_set),
inference(cnf_transformation,[],[f75]) ).
fof(f344,plain,
spl29_8,
inference(avatar_split_clause,[],[f184,f341]) ).
fof(f341,plain,
( spl29_8
<=> function(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_8])]) ).
fof(f184,plain,
function(empty_set),
inference(cnf_transformation,[],[f75]) ).
fof(f339,plain,
spl29_7,
inference(avatar_split_clause,[],[f183,f336]) ).
fof(f336,plain,
( spl29_7
<=> relation(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_7])]) ).
fof(f183,plain,
relation(empty_set),
inference(cnf_transformation,[],[f75]) ).
fof(f334,plain,
spl29_6,
inference(avatar_split_clause,[],[f182,f331]) ).
fof(f182,plain,
empty(empty_set),
inference(cnf_transformation,[],[f19]) ).
fof(f19,axiom,
empty(empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
fof(f329,plain,
~ spl29_5,
inference(avatar_split_clause,[],[f181,f326]) ).
fof(f326,plain,
( spl29_5
<=> empty(positive_rationals) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_5])]) ).
fof(f181,plain,
~ empty(positive_rationals),
inference(cnf_transformation,[],[f24]) ).
fof(f24,axiom,
~ empty(positive_rationals),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc8_arytm_3) ).
fof(f324,plain,
~ spl29_4,
inference(avatar_split_clause,[],[f303,f321]) ).
fof(f303,plain,
~ finite(cartesian_product2(cartesian_product2(sK0,sK1),sK2)),
inference(definition_unfolding,[],[f180,f242]) ).
fof(f180,plain,
~ finite(cartesian_product3(sK0,sK1,sK2)),
inference(cnf_transformation,[],[f124]) ).
fof(f124,plain,
( ~ finite(cartesian_product3(sK0,sK1,sK2))
& finite(sK2)
& finite(sK1)
& finite(sK0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f85,f123]) ).
fof(f123,plain,
( ? [X0,X1,X2] :
( ~ finite(cartesian_product3(X0,X1,X2))
& finite(X2)
& finite(X1)
& finite(X0) )
=> ( ~ finite(cartesian_product3(sK0,sK1,sK2))
& finite(sK2)
& finite(sK1)
& finite(sK0) ) ),
introduced(choice_axiom,[]) ).
fof(f85,plain,
? [X0,X1,X2] :
( ~ finite(cartesian_product3(X0,X1,X2))
& finite(X2)
& finite(X1)
& finite(X0) ),
inference(flattening,[],[f84]) ).
fof(f84,plain,
? [X0,X1,X2] :
( ~ finite(cartesian_product3(X0,X1,X2))
& finite(X2)
& finite(X1)
& finite(X0) ),
inference(ennf_transformation,[],[f54]) ).
fof(f54,negated_conjecture,
~ ! [X0,X1,X2] :
( ( finite(X2)
& finite(X1)
& finite(X0) )
=> finite(cartesian_product3(X0,X1,X2)) ),
inference(negated_conjecture,[],[f53]) ).
fof(f53,conjecture,
! [X0,X1,X2] :
( ( finite(X2)
& finite(X1)
& finite(X0) )
=> finite(cartesian_product3(X0,X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_finset_1) ).
fof(f319,plain,
spl29_3,
inference(avatar_split_clause,[],[f179,f316]) ).
fof(f179,plain,
finite(sK2),
inference(cnf_transformation,[],[f124]) ).
fof(f314,plain,
spl29_2,
inference(avatar_split_clause,[],[f178,f311]) ).
fof(f178,plain,
finite(sK1),
inference(cnf_transformation,[],[f124]) ).
fof(f309,plain,
spl29_1,
inference(avatar_split_clause,[],[f177,f306]) ).
fof(f177,plain,
finite(sK0),
inference(cnf_transformation,[],[f124]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SEU089+1 : TPTP v8.1.2. Released v3.2.0.
% 0.07/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.16/0.36 % Computer : n018.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 : Mon Apr 29 20:41:13 EDT 2024
% 0.16/0.36 % CPUTime :
% 0.16/0.36 % (5265)Running in auto input_syntax mode. Trying TPTP
% 0.16/0.38 % (5268)WARNING: value z3 for option sas not known
% 0.16/0.38 % (5266)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.16/0.38 % (5269)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.16/0.38 % (5267)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.16/0.38 % (5268)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)
% 0.16/0.38 % (5270)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)
% 0.16/0.38 % (5272)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)
% 0.16/0.38 % (5271)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 [2]
% 0.16/0.39 TRYING [3]
% 0.16/0.39 TRYING [1]
% 0.16/0.39 TRYING [4]
% 0.16/0.39 TRYING [2]
% 0.16/0.39 % (5270)First to succeed.
% 0.16/0.39 TRYING [1]
% 0.16/0.39 TRYING [2]
% 0.16/0.39 TRYING [3]
% 0.16/0.40 TRYING [5]
% 0.16/0.40 TRYING [4]
% 0.16/0.40 % (5268)Also succeeded, but the first one will report.
% 0.22/0.40 TRYING [3]
% 0.22/0.40 % (5270)Refutation found. Thanks to Tanya!
% 0.22/0.40 % SZS status Theorem for theBenchmark
% 0.22/0.40 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.40 % (5270)------------------------------
% 0.22/0.40 % (5270)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.22/0.40 % (5270)Termination reason: Refutation
% 0.22/0.40
% 0.22/0.40 % (5270)Memory used [KB]: 1167
% 0.22/0.40 % (5270)Time elapsed: 0.016 s
% 0.22/0.40 % (5270)Instructions burned: 24 (million)
% 0.22/0.40 % (5270)------------------------------
% 0.22/0.40 % (5270)------------------------------
% 0.22/0.40 % (5265)Success in time 0.034 s
%------------------------------------------------------------------------------