TSTP Solution File: SEU342+1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SEU342+1 : TPTP v8.2.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n006.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 May 21 04:00:10 EDT 2024
% Result : Theorem 32.06s 4.94s
% Output : Refutation 32.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 136
% Syntax : Number of formulae : 828 ( 78 unt; 0 def)
% Number of atoms : 2743 ( 259 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 2987 (1072 ~;1621 |; 158 &)
% ( 94 <=>; 39 =>; 0 <=; 3 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 107 ( 105 usr; 87 prp; 0-3 aty)
% Number of functors : 23 ( 23 usr; 11 con; 0-4 aty)
% Number of variables : 608 ( 554 !; 54 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f32550,plain,
$false,
inference(avatar_sat_refutation,[],[f208,f216,f268,f301,f306,f317,f339,f344,f610,f631,f639,f673,f690,f699,f708,f731,f736,f760,f765,f770,f775,f784,f786,f787,f788,f858,f900,f917,f923,f1106,f1147,f1249,f1563,f1739,f1742,f2001,f2009,f2069,f2077,f5445,f5713,f5734,f6019,f6043,f9928,f10859,f14618,f14637,f14910,f14929,f15092,f15111,f30264,f30268,f30445,f30449,f30626,f30630,f30807,f30811,f30988,f30992,f32263,f32267,f32545,f32549]) ).
fof(f32549,plain,
( spl17_2
| spl17_4
| ~ spl17_20
| ~ spl17_85 ),
inference(avatar_contradiction_clause,[],[f32548]) ).
fof(f32548,plain,
( $false
| spl17_2
| spl17_4
| ~ spl17_20
| ~ spl17_85 ),
inference(subsumption_resolution,[],[f32547,f266]) ).
fof(f266,plain,
( ~ below_refl(sK3,sK4,sK5)
| spl17_4 ),
inference(avatar_component_clause,[],[f265]) ).
fof(f265,plain,
( spl17_4
<=> below_refl(sK3,sK4,sK5) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_4])]) ).
fof(f32547,plain,
( below_refl(sK3,sK4,sK5)
| spl17_2
| ~ spl17_20
| ~ spl17_85 ),
inference(forward_demodulation,[],[f32546,f32424]) ).
fof(f32424,plain,
( sK4 = sK7(sK3,ordered_pair(sK4,sK5))
| spl17_2
| ~ spl17_20
| ~ spl17_85 ),
inference(equality_resolution,[],[f32364]) ).
fof(f32364,plain,
( ! [X0,X1] :
( ordered_pair(X0,X1) != ordered_pair(sK4,sK5)
| sK7(sK3,ordered_pair(sK4,sK5)) = X0 )
| spl17_2
| ~ spl17_20
| ~ spl17_85 ),
inference(superposition,[],[f167,f32352]) ).
fof(f32352,plain,
( ordered_pair(sK4,sK5) = ordered_pair(sK7(sK3,ordered_pair(sK4,sK5)),sK8(sK3,ordered_pair(sK4,sK5)))
| spl17_2
| ~ spl17_20
| ~ spl17_85 ),
inference(forward_demodulation,[],[f32339,f740]) ).
fof(f740,plain,
( ordered_pair(sK4,sK5) = ordered_pair_as_product_element(the_carrier(sK3),the_carrier(sK3),sK7(sK3,ordered_pair(sK4,sK5)),sK8(sK3,ordered_pair(sK4,sK5)))
| ~ spl17_20 ),
inference(resolution,[],[f730,f155]) ).
fof(f155,plain,
! [X0,X1] :
( ~ sP1(X0,X1)
| ordered_pair_as_product_element(the_carrier(X0),the_carrier(X0),sK7(X0,X1),sK8(X0,X1)) = X1 ),
inference(cnf_transformation,[],[f99]) ).
fof(f99,plain,
! [X0,X1] :
( ( sP1(X0,X1)
| ! [X2,X3] :
( ~ below_refl(X0,X2,X3)
| ordered_pair_as_product_element(the_carrier(X0),the_carrier(X0),X2,X3) != X1
| ~ element(X3,the_carrier(X0))
| ~ element(X2,the_carrier(X0)) ) )
& ( ( below_refl(X0,sK7(X0,X1),sK8(X0,X1))
& ordered_pair_as_product_element(the_carrier(X0),the_carrier(X0),sK7(X0,X1),sK8(X0,X1)) = X1
& element(sK8(X0,X1),the_carrier(X0))
& element(sK7(X0,X1),the_carrier(X0)) )
| ~ sP1(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8])],[f97,f98]) ).
fof(f98,plain,
! [X0,X1] :
( ? [X4,X5] :
( below_refl(X0,X4,X5)
& ordered_pair_as_product_element(the_carrier(X0),the_carrier(X0),X4,X5) = X1
& element(X5,the_carrier(X0))
& element(X4,the_carrier(X0)) )
=> ( below_refl(X0,sK7(X0,X1),sK8(X0,X1))
& ordered_pair_as_product_element(the_carrier(X0),the_carrier(X0),sK7(X0,X1),sK8(X0,X1)) = X1
& element(sK8(X0,X1),the_carrier(X0))
& element(sK7(X0,X1),the_carrier(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f97,plain,
! [X0,X1] :
( ( sP1(X0,X1)
| ! [X2,X3] :
( ~ below_refl(X0,X2,X3)
| ordered_pair_as_product_element(the_carrier(X0),the_carrier(X0),X2,X3) != X1
| ~ element(X3,the_carrier(X0))
| ~ element(X2,the_carrier(X0)) ) )
& ( ? [X4,X5] :
( below_refl(X0,X4,X5)
& ordered_pair_as_product_element(the_carrier(X0),the_carrier(X0),X4,X5) = X1
& element(X5,the_carrier(X0))
& element(X4,the_carrier(X0)) )
| ~ sP1(X0,X1) ) ),
inference(rectify,[],[f96]) ).
fof(f96,plain,
! [X1,X0] :
( ( sP1(X1,X0)
| ! [X2,X3] :
( ~ below_refl(X1,X2,X3)
| ordered_pair_as_product_element(the_carrier(X1),the_carrier(X1),X2,X3) != X0
| ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1)) ) )
& ( ? [X2,X3] :
( below_refl(X1,X2,X3)
& ordered_pair_as_product_element(the_carrier(X1),the_carrier(X1),X2,X3) = X0
& element(X3,the_carrier(X1))
& element(X2,the_carrier(X1)) )
| ~ sP1(X1,X0) ) ),
inference(nnf_transformation,[],[f83]) ).
fof(f83,plain,
! [X1,X0] :
( sP1(X1,X0)
<=> ? [X2,X3] :
( below_refl(X1,X2,X3)
& ordered_pair_as_product_element(the_carrier(X1),the_carrier(X1),X2,X3) = X0
& element(X3,the_carrier(X1))
& element(X2,the_carrier(X1)) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f730,plain,
( sP1(sK3,ordered_pair(sK4,sK5))
| ~ spl17_20 ),
inference(avatar_component_clause,[],[f728]) ).
fof(f728,plain,
( spl17_20
<=> sP1(sK3,ordered_pair(sK4,sK5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_20])]) ).
fof(f32339,plain,
( ordered_pair_as_product_element(the_carrier(sK3),the_carrier(sK3),sK7(sK3,ordered_pair(sK4,sK5)),sK8(sK3,ordered_pair(sK4,sK5))) = ordered_pair(sK7(sK3,ordered_pair(sK4,sK5)),sK8(sK3,ordered_pair(sK4,sK5)))
| spl17_2
| ~ spl17_20
| ~ spl17_85 ),
inference(resolution,[],[f32295,f6833]) ).
fof(f6833,plain,
( ! [X0,X1] :
( ~ in(X0,X1)
| ordered_pair_as_product_element(the_carrier(sK3),X1,sK7(sK3,ordered_pair(sK4,sK5)),X0) = ordered_pair(sK7(sK3,ordered_pair(sK4,sK5)),X0) )
| spl17_2
| ~ spl17_20 ),
inference(subsumption_resolution,[],[f6822,f206]) ).
fof(f206,plain,
( ~ empty(the_carrier(sK3))
| spl17_2 ),
inference(avatar_component_clause,[],[f205]) ).
fof(f205,plain,
( spl17_2
<=> empty(the_carrier(sK3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_2])]) ).
fof(f6822,plain,
( ! [X0,X1] :
( empty(the_carrier(sK3))
| ~ in(X0,X1)
| ordered_pair_as_product_element(the_carrier(sK3),X1,sK7(sK3,ordered_pair(sK4,sK5)),X0) = ordered_pair(sK7(sK3,ordered_pair(sK4,sK5)),X0) )
| ~ spl17_20 ),
inference(resolution,[],[f1000,f730]) ).
fof(f1000,plain,
! [X2,X3,X0,X1] :
( ~ sP1(X0,X2)
| empty(the_carrier(X0))
| ~ in(X3,X1)
| ordered_pair_as_product_element(the_carrier(X0),X1,sK7(X0,X2),X3) = ordered_pair(sK7(X0,X2),X3) ),
inference(resolution,[],[f477,f153]) ).
fof(f153,plain,
! [X0,X1] :
( element(sK7(X0,X1),the_carrier(X0))
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f99]) ).
fof(f477,plain,
! [X2,X3,X0,X1] :
( ~ element(X2,X0)
| ordered_pair_as_product_element(X0,X1,X2,X3) = ordered_pair(X2,X3)
| empty(X0)
| ~ in(X3,X1) ),
inference(subsumption_resolution,[],[f474,f163]) ).
fof(f163,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ empty(X1) ),
inference(cnf_transformation,[],[f71]) ).
fof(f71,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f44]) ).
fof(f44,axiom,
! [X0,X1] :
~ ( empty(X1)
& in(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
fof(f474,plain,
! [X2,X3,X0,X1] :
( ordered_pair_as_product_element(X0,X1,X2,X3) = ordered_pair(X2,X3)
| ~ element(X2,X0)
| empty(X1)
| empty(X0)
| ~ in(X3,X1) ),
inference(resolution,[],[f169,f149]) ).
fof(f149,plain,
! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f62]) ).
fof(f62,plain,
! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f37]) ).
fof(f37,axiom,
! [X0,X1] :
( in(X0,X1)
=> element(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
fof(f169,plain,
! [X2,X3,X0,X1] :
( ~ element(X3,X1)
| ordered_pair_as_product_element(X0,X1,X2,X3) = ordered_pair(X2,X3)
| ~ element(X2,X0)
| empty(X1)
| empty(X0) ),
inference(cnf_transformation,[],[f78]) ).
fof(f78,plain,
! [X0,X1,X2,X3] :
( ordered_pair_as_product_element(X0,X1,X2,X3) = ordered_pair(X2,X3)
| ~ element(X3,X1)
| ~ element(X2,X0)
| empty(X1)
| empty(X0) ),
inference(flattening,[],[f77]) ).
fof(f77,plain,
! [X0,X1,X2,X3] :
( ordered_pair_as_product_element(X0,X1,X2,X3) = ordered_pair(X2,X3)
| ~ element(X3,X1)
| ~ element(X2,X0)
| empty(X1)
| empty(X0) ),
inference(ennf_transformation,[],[f34]) ).
fof(f34,axiom,
! [X0,X1,X2,X3] :
( ( element(X3,X1)
& element(X2,X0)
& ~ empty(X1)
& ~ empty(X0) )
=> ordered_pair_as_product_element(X0,X1,X2,X3) = ordered_pair(X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k1_domain_1) ).
fof(f32295,plain,
( in(sK8(sK3,ordered_pair(sK4,sK5)),the_carrier(sK3))
| spl17_2
| ~ spl17_85 ),
inference(subsumption_resolution,[],[f32271,f206]) ).
fof(f32271,plain,
( empty(the_carrier(sK3))
| in(sK8(sK3,ordered_pair(sK4,sK5)),the_carrier(sK3))
| ~ spl17_85 ),
inference(resolution,[],[f32257,f150]) ).
fof(f150,plain,
! [X0,X1] :
( ~ element(X0,X1)
| empty(X1)
| in(X0,X1) ),
inference(cnf_transformation,[],[f64]) ).
fof(f64,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(flattening,[],[f63]) ).
fof(f63,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(ennf_transformation,[],[f38]) ).
fof(f38,axiom,
! [X0,X1] :
( element(X0,X1)
=> ( in(X0,X1)
| empty(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
fof(f32257,plain,
( element(sK8(sK3,ordered_pair(sK4,sK5)),the_carrier(sK3))
| ~ spl17_85 ),
inference(avatar_component_clause,[],[f32256]) ).
fof(f32256,plain,
( spl17_85
<=> element(sK8(sK3,ordered_pair(sK4,sK5)),the_carrier(sK3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_85])]) ).
fof(f167,plain,
! [X2,X3,X0,X1] :
( ordered_pair(X0,X1) != ordered_pair(X2,X3)
| X0 = X2 ),
inference(cnf_transformation,[],[f76]) ).
fof(f76,plain,
! [X0,X1,X2,X3] :
( ( X1 = X3
& X0 = X2 )
| ordered_pair(X0,X1) != ordered_pair(X2,X3) ),
inference(ennf_transformation,[],[f42]) ).
fof(f42,axiom,
! [X0,X1,X2,X3] :
( ordered_pair(X0,X1) = ordered_pair(X2,X3)
=> ( X1 = X3
& X0 = X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t33_zfmisc_1) ).
fof(f32546,plain,
( below_refl(sK3,sK7(sK3,ordered_pair(sK4,sK5)),sK5)
| spl17_2
| ~ spl17_20
| ~ spl17_85 ),
inference(subsumption_resolution,[],[f32541,f730]) ).
fof(f32541,plain,
( below_refl(sK3,sK7(sK3,ordered_pair(sK4,sK5)),sK5)
| ~ sP1(sK3,ordered_pair(sK4,sK5))
| spl17_2
| ~ spl17_20
| ~ spl17_85 ),
inference(superposition,[],[f156,f32524]) ).
fof(f32524,plain,
( sK5 = sK8(sK3,ordered_pair(sK4,sK5))
| spl17_2
| ~ spl17_20
| ~ spl17_85 ),
inference(equality_resolution,[],[f32366]) ).
fof(f32366,plain,
( ! [X0,X1] :
( ordered_pair(X0,X1) != ordered_pair(sK4,sK5)
| sK8(sK3,ordered_pair(sK4,sK5)) = X1 )
| spl17_2
| ~ spl17_20
| ~ spl17_85 ),
inference(superposition,[],[f168,f32352]) ).
fof(f168,plain,
! [X2,X3,X0,X1] :
( ordered_pair(X0,X1) != ordered_pair(X2,X3)
| X1 = X3 ),
inference(cnf_transformation,[],[f76]) ).
fof(f156,plain,
! [X0,X1] :
( below_refl(X0,sK7(X0,X1),sK8(X0,X1))
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f99]) ).
fof(f32545,plain,
( spl17_2
| spl17_4
| ~ spl17_20
| ~ spl17_85 ),
inference(avatar_contradiction_clause,[],[f32544]) ).
fof(f32544,plain,
( $false
| spl17_2
| spl17_4
| ~ spl17_20
| ~ spl17_85 ),
inference(subsumption_resolution,[],[f32536,f266]) ).
fof(f32536,plain,
( below_refl(sK3,sK4,sK5)
| spl17_2
| ~ spl17_20
| ~ spl17_85 ),
inference(superposition,[],[f32444,f32524]) ).
fof(f32444,plain,
( below_refl(sK3,sK4,sK8(sK3,ordered_pair(sK4,sK5)))
| spl17_2
| ~ spl17_20
| ~ spl17_85 ),
inference(subsumption_resolution,[],[f32442,f730]) ).
fof(f32442,plain,
( below_refl(sK3,sK4,sK8(sK3,ordered_pair(sK4,sK5)))
| ~ sP1(sK3,ordered_pair(sK4,sK5))
| spl17_2
| ~ spl17_20
| ~ spl17_85 ),
inference(superposition,[],[f156,f32424]) ).
fof(f32267,plain,
( ~ spl17_20
| spl17_85 ),
inference(avatar_contradiction_clause,[],[f32266]) ).
fof(f32266,plain,
( $false
| ~ spl17_20
| spl17_85 ),
inference(subsumption_resolution,[],[f32264,f730]) ).
fof(f32264,plain,
( ~ sP1(sK3,ordered_pair(sK4,sK5))
| spl17_85 ),
inference(resolution,[],[f32258,f154]) ).
fof(f154,plain,
! [X0,X1] :
( element(sK8(X0,X1),the_carrier(X0))
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f99]) ).
fof(f32258,plain,
( ~ element(sK8(sK3,ordered_pair(sK4,sK5)),the_carrier(sK3))
| spl17_85 ),
inference(avatar_component_clause,[],[f32256]) ).
fof(f32263,plain,
( ~ spl17_85
| ~ spl17_86
| spl17_2
| ~ spl17_20 ),
inference(avatar_split_clause,[],[f9529,f728,f205,f32260,f32256]) ).
fof(f32260,plain,
( spl17_86
<=> in(cartesian_product2(the_carrier(sK3),the_carrier(sK3)),ordered_pair(sK8(sK3,ordered_pair(sK4,sK5)),sK4)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_86])]) ).
fof(f9529,plain,
( ~ in(cartesian_product2(the_carrier(sK3),the_carrier(sK3)),ordered_pair(sK8(sK3,ordered_pair(sK4,sK5)),sK4))
| ~ element(sK8(sK3,ordered_pair(sK4,sK5)),the_carrier(sK3))
| spl17_2
| ~ spl17_20 ),
inference(subsumption_resolution,[],[f9528,f121]) ).
fof(f121,plain,
element(sK4,the_carrier(sK3)),
inference(cnf_transformation,[],[f91]) ).
fof(f91,plain,
( ( ~ below_refl(sK3,sK4,sK5)
| ~ in(ordered_pair_as_product_element(the_carrier(sK3),the_carrier(sK3),sK4,sK5),relation_of_lattice(sK3)) )
& ( below_refl(sK3,sK4,sK5)
| in(ordered_pair_as_product_element(the_carrier(sK3),the_carrier(sK3),sK4,sK5),relation_of_lattice(sK3)) )
& element(sK5,the_carrier(sK3))
& element(sK4,the_carrier(sK3))
& latt_str(sK3)
& lattice(sK3)
& ~ empty_carrier(sK3) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5])],[f87,f90,f89,f88]) ).
fof(f88,plain,
( ? [X0] :
( ? [X1] :
( ? [X2] :
( ( ~ below_refl(X0,X1,X2)
| ~ in(ordered_pair_as_product_element(the_carrier(X0),the_carrier(X0),X1,X2),relation_of_lattice(X0)) )
& ( below_refl(X0,X1,X2)
| in(ordered_pair_as_product_element(the_carrier(X0),the_carrier(X0),X1,X2),relation_of_lattice(X0)) )
& element(X2,the_carrier(X0)) )
& element(X1,the_carrier(X0)) )
& latt_str(X0)
& lattice(X0)
& ~ empty_carrier(X0) )
=> ( ? [X1] :
( ? [X2] :
( ( ~ below_refl(sK3,X1,X2)
| ~ in(ordered_pair_as_product_element(the_carrier(sK3),the_carrier(sK3),X1,X2),relation_of_lattice(sK3)) )
& ( below_refl(sK3,X1,X2)
| in(ordered_pair_as_product_element(the_carrier(sK3),the_carrier(sK3),X1,X2),relation_of_lattice(sK3)) )
& element(X2,the_carrier(sK3)) )
& element(X1,the_carrier(sK3)) )
& latt_str(sK3)
& lattice(sK3)
& ~ empty_carrier(sK3) ) ),
introduced(choice_axiom,[]) ).
fof(f89,plain,
( ? [X1] :
( ? [X2] :
( ( ~ below_refl(sK3,X1,X2)
| ~ in(ordered_pair_as_product_element(the_carrier(sK3),the_carrier(sK3),X1,X2),relation_of_lattice(sK3)) )
& ( below_refl(sK3,X1,X2)
| in(ordered_pair_as_product_element(the_carrier(sK3),the_carrier(sK3),X1,X2),relation_of_lattice(sK3)) )
& element(X2,the_carrier(sK3)) )
& element(X1,the_carrier(sK3)) )
=> ( ? [X2] :
( ( ~ below_refl(sK3,sK4,X2)
| ~ in(ordered_pair_as_product_element(the_carrier(sK3),the_carrier(sK3),sK4,X2),relation_of_lattice(sK3)) )
& ( below_refl(sK3,sK4,X2)
| in(ordered_pair_as_product_element(the_carrier(sK3),the_carrier(sK3),sK4,X2),relation_of_lattice(sK3)) )
& element(X2,the_carrier(sK3)) )
& element(sK4,the_carrier(sK3)) ) ),
introduced(choice_axiom,[]) ).
fof(f90,plain,
( ? [X2] :
( ( ~ below_refl(sK3,sK4,X2)
| ~ in(ordered_pair_as_product_element(the_carrier(sK3),the_carrier(sK3),sK4,X2),relation_of_lattice(sK3)) )
& ( below_refl(sK3,sK4,X2)
| in(ordered_pair_as_product_element(the_carrier(sK3),the_carrier(sK3),sK4,X2),relation_of_lattice(sK3)) )
& element(X2,the_carrier(sK3)) )
=> ( ( ~ below_refl(sK3,sK4,sK5)
| ~ in(ordered_pair_as_product_element(the_carrier(sK3),the_carrier(sK3),sK4,sK5),relation_of_lattice(sK3)) )
& ( below_refl(sK3,sK4,sK5)
| in(ordered_pair_as_product_element(the_carrier(sK3),the_carrier(sK3),sK4,sK5),relation_of_lattice(sK3)) )
& element(sK5,the_carrier(sK3)) ) ),
introduced(choice_axiom,[]) ).
fof(f87,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ( ~ below_refl(X0,X1,X2)
| ~ in(ordered_pair_as_product_element(the_carrier(X0),the_carrier(X0),X1,X2),relation_of_lattice(X0)) )
& ( below_refl(X0,X1,X2)
| in(ordered_pair_as_product_element(the_carrier(X0),the_carrier(X0),X1,X2),relation_of_lattice(X0)) )
& element(X2,the_carrier(X0)) )
& element(X1,the_carrier(X0)) )
& latt_str(X0)
& lattice(X0)
& ~ empty_carrier(X0) ),
inference(flattening,[],[f86]) ).
fof(f86,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ( ~ below_refl(X0,X1,X2)
| ~ in(ordered_pair_as_product_element(the_carrier(X0),the_carrier(X0),X1,X2),relation_of_lattice(X0)) )
& ( below_refl(X0,X1,X2)
| in(ordered_pair_as_product_element(the_carrier(X0),the_carrier(X0),X1,X2),relation_of_lattice(X0)) )
& element(X2,the_carrier(X0)) )
& element(X1,the_carrier(X0)) )
& latt_str(X0)
& lattice(X0)
& ~ empty_carrier(X0) ),
inference(nnf_transformation,[],[f48]) ).
fof(f48,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ( in(ordered_pair_as_product_element(the_carrier(X0),the_carrier(X0),X1,X2),relation_of_lattice(X0))
<~> below_refl(X0,X1,X2) )
& element(X2,the_carrier(X0)) )
& element(X1,the_carrier(X0)) )
& latt_str(X0)
& lattice(X0)
& ~ empty_carrier(X0) ),
inference(flattening,[],[f47]) ).
fof(f47,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ( in(ordered_pair_as_product_element(the_carrier(X0),the_carrier(X0),X1,X2),relation_of_lattice(X0))
<~> below_refl(X0,X1,X2) )
& element(X2,the_carrier(X0)) )
& element(X1,the_carrier(X0)) )
& latt_str(X0)
& lattice(X0)
& ~ empty_carrier(X0) ),
inference(ennf_transformation,[],[f41]) ).
fof(f41,negated_conjecture,
~ ! [X0] :
( ( latt_str(X0)
& lattice(X0)
& ~ empty_carrier(X0) )
=> ! [X1] :
( element(X1,the_carrier(X0))
=> ! [X2] :
( element(X2,the_carrier(X0))
=> ( in(ordered_pair_as_product_element(the_carrier(X0),the_carrier(X0),X1,X2),relation_of_lattice(X0))
<=> below_refl(X0,X1,X2) ) ) ) ),
inference(negated_conjecture,[],[f40]) ).
fof(f40,conjecture,
! [X0] :
( ( latt_str(X0)
& lattice(X0)
& ~ empty_carrier(X0) )
=> ! [X1] :
( element(X1,the_carrier(X0))
=> ! [X2] :
( element(X2,the_carrier(X0))
=> ( in(ordered_pair_as_product_element(the_carrier(X0),the_carrier(X0),X1,X2),relation_of_lattice(X0))
<=> below_refl(X0,X1,X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_filter_1) ).
fof(f9528,plain,
( ~ in(cartesian_product2(the_carrier(sK3),the_carrier(sK3)),ordered_pair(sK8(sK3,ordered_pair(sK4,sK5)),sK4))
| ~ element(sK4,the_carrier(sK3))
| ~ element(sK8(sK3,ordered_pair(sK4,sK5)),the_carrier(sK3))
| spl17_2
| ~ spl17_20 ),
inference(subsumption_resolution,[],[f9526,f206]) ).
fof(f9526,plain,
( ~ in(cartesian_product2(the_carrier(sK3),the_carrier(sK3)),ordered_pair(sK8(sK3,ordered_pair(sK4,sK5)),sK4))
| empty(the_carrier(sK3))
| ~ element(sK4,the_carrier(sK3))
| ~ element(sK8(sK3,ordered_pair(sK4,sK5)),the_carrier(sK3))
| spl17_2
| ~ spl17_20 ),
inference(duplicate_literal_removal,[],[f9521]) ).
fof(f9521,plain,
( ~ in(cartesian_product2(the_carrier(sK3),the_carrier(sK3)),ordered_pair(sK8(sK3,ordered_pair(sK4,sK5)),sK4))
| empty(the_carrier(sK3))
| empty(the_carrier(sK3))
| ~ element(sK4,the_carrier(sK3))
| ~ element(sK8(sK3,ordered_pair(sK4,sK5)),the_carrier(sK3))
| spl17_2
| ~ spl17_20 ),
inference(superposition,[],[f1254,f3564]) ).
fof(f3564,plain,
( ordered_pair_as_product_element(the_carrier(sK3),the_carrier(sK3),sK8(sK3,ordered_pair(sK4,sK5)),sK4) = ordered_pair(sK8(sK3,ordered_pair(sK4,sK5)),sK4)
| spl17_2
| ~ spl17_20 ),
inference(subsumption_resolution,[],[f3558,f206]) ).
fof(f3558,plain,
( empty(the_carrier(sK3))
| ordered_pair_as_product_element(the_carrier(sK3),the_carrier(sK3),sK8(sK3,ordered_pair(sK4,sK5)),sK4) = ordered_pair(sK8(sK3,ordered_pair(sK4,sK5)),sK4)
| spl17_2
| ~ spl17_20 ),
inference(resolution,[],[f481,f730]) ).
fof(f481,plain,
( ! [X0,X1] :
( ~ sP1(X0,X1)
| empty(the_carrier(X0))
| ordered_pair_as_product_element(the_carrier(X0),the_carrier(sK3),sK8(X0,X1),sK4) = ordered_pair(sK8(X0,X1),sK4) )
| spl17_2 ),
inference(resolution,[],[f475,f154]) ).
fof(f475,plain,
( ! [X0,X1] :
( ~ element(X1,X0)
| ordered_pair_as_product_element(X0,the_carrier(sK3),X1,sK4) = ordered_pair(X1,sK4)
| empty(X0) )
| spl17_2 ),
inference(subsumption_resolution,[],[f469,f206]) ).
fof(f469,plain,
! [X0,X1] :
( ordered_pair_as_product_element(X0,the_carrier(sK3),X1,sK4) = ordered_pair(X1,sK4)
| ~ element(X1,X0)
| empty(the_carrier(sK3))
| empty(X0) ),
inference(resolution,[],[f169,f121]) ).
fof(f1254,plain,
! [X2,X3,X0,X1] :
( ~ in(cartesian_product2(X1,X2),ordered_pair_as_product_element(X1,X2,X0,X3))
| empty(X2)
| empty(X1)
| ~ element(X3,X2)
| ~ element(X0,X1) ),
inference(resolution,[],[f549,f148]) ).
fof(f148,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f61]) ).
fof(f61,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(f549,plain,
! [X2,X3,X0,X1] :
( in(ordered_pair_as_product_element(X3,X1,X2,X0),cartesian_product2(X3,X1))
| ~ element(X2,X3)
| empty(X1)
| empty(X3)
| ~ element(X0,X1) ),
inference(subsumption_resolution,[],[f536,f159]) ).
fof(f159,plain,
! [X0,X1] :
( ~ empty(cartesian_product2(X0,X1))
| empty(X1)
| empty(X0) ),
inference(cnf_transformation,[],[f68]) ).
fof(f68,plain,
! [X0,X1] :
( ~ empty(cartesian_product2(X0,X1))
| empty(X1)
| empty(X0) ),
inference(flattening,[],[f67]) ).
fof(f67,plain,
! [X0,X1] :
( ~ empty(cartesian_product2(X0,X1))
| empty(X1)
| empty(X0) ),
inference(ennf_transformation,[],[f29]) ).
fof(f29,axiom,
! [X0,X1] :
( ( ~ empty(X1)
& ~ empty(X0) )
=> ~ empty(cartesian_product2(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_subset_1) ).
fof(f536,plain,
! [X2,X3,X0,X1] :
( ~ element(X0,X1)
| ~ element(X2,X3)
| empty(X1)
| empty(X3)
| empty(cartesian_product2(X3,X1))
| in(ordered_pair_as_product_element(X3,X1,X2,X0),cartesian_product2(X3,X1)) ),
inference(resolution,[],[f170,f150]) ).
fof(f170,plain,
! [X2,X3,X0,X1] :
( element(ordered_pair_as_product_element(X0,X1,X2,X3),cartesian_product2(X0,X1))
| ~ element(X3,X1)
| ~ element(X2,X0)
| empty(X1)
| empty(X0) ),
inference(cnf_transformation,[],[f80]) ).
fof(f80,plain,
! [X0,X1,X2,X3] :
( element(ordered_pair_as_product_element(X0,X1,X2,X3),cartesian_product2(X0,X1))
| ~ element(X3,X1)
| ~ element(X2,X0)
| empty(X1)
| empty(X0) ),
inference(flattening,[],[f79]) ).
fof(f79,plain,
! [X0,X1,X2,X3] :
( element(ordered_pair_as_product_element(X0,X1,X2,X3),cartesian_product2(X0,X1))
| ~ element(X3,X1)
| ~ element(X2,X0)
| empty(X1)
| empty(X0) ),
inference(ennf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X0,X1,X2,X3] :
( ( element(X3,X1)
& element(X2,X0)
& ~ empty(X1)
& ~ empty(X0) )
=> element(ordered_pair_as_product_element(X0,X1,X2,X3),cartesian_product2(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_domain_1) ).
fof(f30992,plain,
( ~ spl17_10
| spl17_83 ),
inference(avatar_contradiction_clause,[],[f30991]) ).
fof(f30991,plain,
( $false
| ~ spl17_10
| spl17_83 ),
inference(subsumption_resolution,[],[f30989,f338]) ).
fof(f338,plain,
( sP1(sK3,sK6(relation_of_lattice(sK3)))
| ~ spl17_10 ),
inference(avatar_component_clause,[],[f336]) ).
fof(f336,plain,
( spl17_10
<=> sP1(sK3,sK6(relation_of_lattice(sK3))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_10])]) ).
fof(f30989,plain,
( ~ sP1(sK3,sK6(relation_of_lattice(sK3)))
| spl17_83 ),
inference(resolution,[],[f30983,f154]) ).
fof(f30983,plain,
( ~ element(sK8(sK3,sK6(relation_of_lattice(sK3))),the_carrier(sK3))
| spl17_83 ),
inference(avatar_component_clause,[],[f30981]) ).
fof(f30981,plain,
( spl17_83
<=> element(sK8(sK3,sK6(relation_of_lattice(sK3))),the_carrier(sK3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_83])]) ).
fof(f30988,plain,
( ~ spl17_83
| ~ spl17_84
| spl17_2
| ~ spl17_10 ),
inference(avatar_split_clause,[],[f9515,f336,f205,f30985,f30981]) ).
fof(f30985,plain,
( spl17_84
<=> in(cartesian_product2(the_carrier(sK3),the_carrier(sK3)),ordered_pair(sK8(sK3,sK6(relation_of_lattice(sK3))),sK4)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_84])]) ).
fof(f9515,plain,
( ~ in(cartesian_product2(the_carrier(sK3),the_carrier(sK3)),ordered_pair(sK8(sK3,sK6(relation_of_lattice(sK3))),sK4))
| ~ element(sK8(sK3,sK6(relation_of_lattice(sK3))),the_carrier(sK3))
| spl17_2
| ~ spl17_10 ),
inference(subsumption_resolution,[],[f9514,f121]) ).
fof(f9514,plain,
( ~ in(cartesian_product2(the_carrier(sK3),the_carrier(sK3)),ordered_pair(sK8(sK3,sK6(relation_of_lattice(sK3))),sK4))
| ~ element(sK4,the_carrier(sK3))
| ~ element(sK8(sK3,sK6(relation_of_lattice(sK3))),the_carrier(sK3))
| spl17_2
| ~ spl17_10 ),
inference(subsumption_resolution,[],[f9512,f206]) ).
fof(f9512,plain,
( ~ in(cartesian_product2(the_carrier(sK3),the_carrier(sK3)),ordered_pair(sK8(sK3,sK6(relation_of_lattice(sK3))),sK4))
| empty(the_carrier(sK3))
| ~ element(sK4,the_carrier(sK3))
| ~ element(sK8(sK3,sK6(relation_of_lattice(sK3))),the_carrier(sK3))
| spl17_2
| ~ spl17_10 ),
inference(duplicate_literal_removal,[],[f9507]) ).
fof(f9507,plain,
( ~ in(cartesian_product2(the_carrier(sK3),the_carrier(sK3)),ordered_pair(sK8(sK3,sK6(relation_of_lattice(sK3))),sK4))
| empty(the_carrier(sK3))
| empty(the_carrier(sK3))
| ~ element(sK4,the_carrier(sK3))
| ~ element(sK8(sK3,sK6(relation_of_lattice(sK3))),the_carrier(sK3))
| spl17_2
| ~ spl17_10 ),
inference(superposition,[],[f1254,f3563]) ).
fof(f3563,plain,
( ordered_pair_as_product_element(the_carrier(sK3),the_carrier(sK3),sK8(sK3,sK6(relation_of_lattice(sK3))),sK4) = ordered_pair(sK8(sK3,sK6(relation_of_lattice(sK3))),sK4)
| spl17_2
| ~ spl17_10 ),
inference(subsumption_resolution,[],[f3557,f206]) ).
fof(f3557,plain,
( empty(the_carrier(sK3))
| ordered_pair_as_product_element(the_carrier(sK3),the_carrier(sK3),sK8(sK3,sK6(relation_of_lattice(sK3))),sK4) = ordered_pair(sK8(sK3,sK6(relation_of_lattice(sK3))),sK4)
| spl17_2
| ~ spl17_10 ),
inference(resolution,[],[f481,f338]) ).
fof(f30811,plain,
( ~ spl17_18
| spl17_81 ),
inference(avatar_contradiction_clause,[],[f30810]) ).
fof(f30810,plain,
( $false
| ~ spl17_18
| spl17_81 ),
inference(subsumption_resolution,[],[f30808,f707]) ).
fof(f707,plain,
( sP1(sK3,ordered_pair(sK4,sK4))
| ~ spl17_18 ),
inference(avatar_component_clause,[],[f705]) ).
fof(f705,plain,
( spl17_18
<=> sP1(sK3,ordered_pair(sK4,sK4)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_18])]) ).
fof(f30808,plain,
( ~ sP1(sK3,ordered_pair(sK4,sK4))
| spl17_81 ),
inference(resolution,[],[f30802,f153]) ).
fof(f30802,plain,
( ~ element(sK7(sK3,ordered_pair(sK4,sK4)),the_carrier(sK3))
| spl17_81 ),
inference(avatar_component_clause,[],[f30800]) ).
fof(f30800,plain,
( spl17_81
<=> element(sK7(sK3,ordered_pair(sK4,sK4)),the_carrier(sK3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_81])]) ).
fof(f30807,plain,
( ~ spl17_81
| ~ spl17_82
| spl17_2
| ~ spl17_18 ),
inference(avatar_split_clause,[],[f9022,f705,f205,f30804,f30800]) ).
fof(f30804,plain,
( spl17_82
<=> in(cartesian_product2(the_carrier(sK3),the_carrier(sK3)),ordered_pair(sK7(sK3,ordered_pair(sK4,sK4)),sK4)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_82])]) ).
fof(f9022,plain,
( ~ in(cartesian_product2(the_carrier(sK3),the_carrier(sK3)),ordered_pair(sK7(sK3,ordered_pair(sK4,sK4)),sK4))
| ~ element(sK7(sK3,ordered_pair(sK4,sK4)),the_carrier(sK3))
| spl17_2
| ~ spl17_18 ),
inference(subsumption_resolution,[],[f9021,f121]) ).
fof(f9021,plain,
( ~ in(cartesian_product2(the_carrier(sK3),the_carrier(sK3)),ordered_pair(sK7(sK3,ordered_pair(sK4,sK4)),sK4))
| ~ element(sK4,the_carrier(sK3))
| ~ element(sK7(sK3,ordered_pair(sK4,sK4)),the_carrier(sK3))
| spl17_2
| ~ spl17_18 ),
inference(subsumption_resolution,[],[f9019,f206]) ).
fof(f9019,plain,
( ~ in(cartesian_product2(the_carrier(sK3),the_carrier(sK3)),ordered_pair(sK7(sK3,ordered_pair(sK4,sK4)),sK4))
| empty(the_carrier(sK3))
| ~ element(sK4,the_carrier(sK3))
| ~ element(sK7(sK3,ordered_pair(sK4,sK4)),the_carrier(sK3))
| spl17_2
| ~ spl17_18 ),
inference(duplicate_literal_removal,[],[f9014]) ).
fof(f9014,plain,
( ~ in(cartesian_product2(the_carrier(sK3),the_carrier(sK3)),ordered_pair(sK7(sK3,ordered_pair(sK4,sK4)),sK4))
| empty(the_carrier(sK3))
| empty(the_carrier(sK3))
| ~ element(sK4,the_carrier(sK3))
| ~ element(sK7(sK3,ordered_pair(sK4,sK4)),the_carrier(sK3))
| spl17_2
| ~ spl17_18 ),
inference(superposition,[],[f1254,f3477]) ).
fof(f3477,plain,
( ordered_pair_as_product_element(the_carrier(sK3),the_carrier(sK3),sK7(sK3,ordered_pair(sK4,sK4)),sK4) = ordered_pair(sK7(sK3,ordered_pair(sK4,sK4)),sK4)
| spl17_2
| ~ spl17_18 ),
inference(subsumption_resolution,[],[f3471,f206]) ).
fof(f3471,plain,
( empty(the_carrier(sK3))
| ordered_pair_as_product_element(the_carrier(sK3),the_carrier(sK3),sK7(sK3,ordered_pair(sK4,sK4)),sK4) = ordered_pair(sK7(sK3,ordered_pair(sK4,sK4)),sK4)
| spl17_2
| ~ spl17_18 ),
inference(resolution,[],[f480,f707]) ).
fof(f480,plain,
( ! [X0,X1] :
( ~ sP1(X0,X1)
| empty(the_carrier(X0))
| ordered_pair_as_product_element(the_carrier(X0),the_carrier(sK3),sK7(X0,X1),sK4) = ordered_pair(sK7(X0,X1),sK4) )
| spl17_2 ),
inference(resolution,[],[f475,f153]) ).
fof(f30630,plain,
( ~ spl17_14
| spl17_79 ),
inference(avatar_contradiction_clause,[],[f30629]) ).
fof(f30629,plain,
( $false
| ~ spl17_14
| spl17_79 ),
inference(subsumption_resolution,[],[f30627,f689]) ).
fof(f689,plain,
( sP1(sK3,ordered_pair(sK5,sK5))
| ~ spl17_14 ),
inference(avatar_component_clause,[],[f687]) ).
fof(f687,plain,
( spl17_14
<=> sP1(sK3,ordered_pair(sK5,sK5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_14])]) ).
fof(f30627,plain,
( ~ sP1(sK3,ordered_pair(sK5,sK5))
| spl17_79 ),
inference(resolution,[],[f30621,f153]) ).
fof(f30621,plain,
( ~ element(sK7(sK3,ordered_pair(sK5,sK5)),the_carrier(sK3))
| spl17_79 ),
inference(avatar_component_clause,[],[f30619]) ).
fof(f30619,plain,
( spl17_79
<=> element(sK7(sK3,ordered_pair(sK5,sK5)),the_carrier(sK3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_79])]) ).
fof(f30626,plain,
( ~ spl17_79
| ~ spl17_80
| spl17_2
| ~ spl17_14 ),
inference(avatar_split_clause,[],[f8946,f687,f205,f30623,f30619]) ).
fof(f30623,plain,
( spl17_80
<=> in(cartesian_product2(the_carrier(sK3),the_carrier(sK3)),ordered_pair(sK7(sK3,ordered_pair(sK5,sK5)),sK4)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_80])]) ).
fof(f8946,plain,
( ~ in(cartesian_product2(the_carrier(sK3),the_carrier(sK3)),ordered_pair(sK7(sK3,ordered_pair(sK5,sK5)),sK4))
| ~ element(sK7(sK3,ordered_pair(sK5,sK5)),the_carrier(sK3))
| spl17_2
| ~ spl17_14 ),
inference(subsumption_resolution,[],[f8945,f121]) ).
fof(f8945,plain,
( ~ in(cartesian_product2(the_carrier(sK3),the_carrier(sK3)),ordered_pair(sK7(sK3,ordered_pair(sK5,sK5)),sK4))
| ~ element(sK4,the_carrier(sK3))
| ~ element(sK7(sK3,ordered_pair(sK5,sK5)),the_carrier(sK3))
| spl17_2
| ~ spl17_14 ),
inference(subsumption_resolution,[],[f8943,f206]) ).
fof(f8943,plain,
( ~ in(cartesian_product2(the_carrier(sK3),the_carrier(sK3)),ordered_pair(sK7(sK3,ordered_pair(sK5,sK5)),sK4))
| empty(the_carrier(sK3))
| ~ element(sK4,the_carrier(sK3))
| ~ element(sK7(sK3,ordered_pair(sK5,sK5)),the_carrier(sK3))
| spl17_2
| ~ spl17_14 ),
inference(duplicate_literal_removal,[],[f8938]) ).
fof(f8938,plain,
( ~ in(cartesian_product2(the_carrier(sK3),the_carrier(sK3)),ordered_pair(sK7(sK3,ordered_pair(sK5,sK5)),sK4))
| empty(the_carrier(sK3))
| empty(the_carrier(sK3))
| ~ element(sK4,the_carrier(sK3))
| ~ element(sK7(sK3,ordered_pair(sK5,sK5)),the_carrier(sK3))
| spl17_2
| ~ spl17_14 ),
inference(superposition,[],[f1254,f3476]) ).
fof(f3476,plain,
( ordered_pair_as_product_element(the_carrier(sK3),the_carrier(sK3),sK7(sK3,ordered_pair(sK5,sK5)),sK4) = ordered_pair(sK7(sK3,ordered_pair(sK5,sK5)),sK4)
| spl17_2
| ~ spl17_14 ),
inference(subsumption_resolution,[],[f3470,f206]) ).
fof(f3470,plain,
( empty(the_carrier(sK3))
| ordered_pair_as_product_element(the_carrier(sK3),the_carrier(sK3),sK7(sK3,ordered_pair(sK5,sK5)),sK4) = ordered_pair(sK7(sK3,ordered_pair(sK5,sK5)),sK4)
| spl17_2
| ~ spl17_14 ),
inference(resolution,[],[f480,f689]) ).
fof(f30449,plain,
( ~ spl17_20
| spl17_77 ),
inference(avatar_contradiction_clause,[],[f30448]) ).
fof(f30448,plain,
( $false
| ~ spl17_20
| spl17_77 ),
inference(subsumption_resolution,[],[f30446,f730]) ).
fof(f30446,plain,
( ~ sP1(sK3,ordered_pair(sK4,sK5))
| spl17_77 ),
inference(resolution,[],[f30440,f153]) ).
fof(f30440,plain,
( ~ element(sK7(sK3,ordered_pair(sK4,sK5)),the_carrier(sK3))
| spl17_77 ),
inference(avatar_component_clause,[],[f30438]) ).
fof(f30438,plain,
( spl17_77
<=> element(sK7(sK3,ordered_pair(sK4,sK5)),the_carrier(sK3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_77])]) ).
fof(f30445,plain,
( ~ spl17_77
| ~ spl17_78
| spl17_2
| ~ spl17_20 ),
inference(avatar_split_clause,[],[f8932,f728,f205,f30442,f30438]) ).
fof(f30442,plain,
( spl17_78
<=> in(cartesian_product2(the_carrier(sK3),the_carrier(sK3)),ordered_pair(sK7(sK3,ordered_pair(sK4,sK5)),sK4)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_78])]) ).
fof(f8932,plain,
( ~ in(cartesian_product2(the_carrier(sK3),the_carrier(sK3)),ordered_pair(sK7(sK3,ordered_pair(sK4,sK5)),sK4))
| ~ element(sK7(sK3,ordered_pair(sK4,sK5)),the_carrier(sK3))
| spl17_2
| ~ spl17_20 ),
inference(subsumption_resolution,[],[f8931,f121]) ).
fof(f8931,plain,
( ~ in(cartesian_product2(the_carrier(sK3),the_carrier(sK3)),ordered_pair(sK7(sK3,ordered_pair(sK4,sK5)),sK4))
| ~ element(sK4,the_carrier(sK3))
| ~ element(sK7(sK3,ordered_pair(sK4,sK5)),the_carrier(sK3))
| spl17_2
| ~ spl17_20 ),
inference(subsumption_resolution,[],[f8929,f206]) ).
fof(f8929,plain,
( ~ in(cartesian_product2(the_carrier(sK3),the_carrier(sK3)),ordered_pair(sK7(sK3,ordered_pair(sK4,sK5)),sK4))
| empty(the_carrier(sK3))
| ~ element(sK4,the_carrier(sK3))
| ~ element(sK7(sK3,ordered_pair(sK4,sK5)),the_carrier(sK3))
| spl17_2
| ~ spl17_20 ),
inference(duplicate_literal_removal,[],[f8924]) ).
fof(f8924,plain,
( ~ in(cartesian_product2(the_carrier(sK3),the_carrier(sK3)),ordered_pair(sK7(sK3,ordered_pair(sK4,sK5)),sK4))
| empty(the_carrier(sK3))
| empty(the_carrier(sK3))
| ~ element(sK4,the_carrier(sK3))
| ~ element(sK7(sK3,ordered_pair(sK4,sK5)),the_carrier(sK3))
| spl17_2
| ~ spl17_20 ),
inference(superposition,[],[f1254,f3475]) ).
fof(f3475,plain,
( ordered_pair_as_product_element(the_carrier(sK3),the_carrier(sK3),sK7(sK3,ordered_pair(sK4,sK5)),sK4) = ordered_pair(sK7(sK3,ordered_pair(sK4,sK5)),sK4)
| spl17_2
| ~ spl17_20 ),
inference(subsumption_resolution,[],[f3469,f206]) ).
fof(f3469,plain,
( empty(the_carrier(sK3))
| ordered_pair_as_product_element(the_carrier(sK3),the_carrier(sK3),sK7(sK3,ordered_pair(sK4,sK5)),sK4) = ordered_pair(sK7(sK3,ordered_pair(sK4,sK5)),sK4)
| spl17_2
| ~ spl17_20 ),
inference(resolution,[],[f480,f730]) ).
fof(f30268,plain,
( ~ spl17_10
| spl17_75 ),
inference(avatar_contradiction_clause,[],[f30267]) ).
fof(f30267,plain,
( $false
| ~ spl17_10
| spl17_75 ),
inference(subsumption_resolution,[],[f30265,f338]) ).
fof(f30265,plain,
( ~ sP1(sK3,sK6(relation_of_lattice(sK3)))
| spl17_75 ),
inference(resolution,[],[f30259,f153]) ).
fof(f30259,plain,
( ~ element(sK7(sK3,sK6(relation_of_lattice(sK3))),the_carrier(sK3))
| spl17_75 ),
inference(avatar_component_clause,[],[f30257]) ).
fof(f30257,plain,
( spl17_75
<=> element(sK7(sK3,sK6(relation_of_lattice(sK3))),the_carrier(sK3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_75])]) ).
fof(f30264,plain,
( ~ spl17_75
| ~ spl17_76
| spl17_2
| ~ spl17_10 ),
inference(avatar_split_clause,[],[f8918,f336,f205,f30261,f30257]) ).
fof(f30261,plain,
( spl17_76
<=> in(cartesian_product2(the_carrier(sK3),the_carrier(sK3)),ordered_pair(sK7(sK3,sK6(relation_of_lattice(sK3))),sK4)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_76])]) ).
fof(f8918,plain,
( ~ in(cartesian_product2(the_carrier(sK3),the_carrier(sK3)),ordered_pair(sK7(sK3,sK6(relation_of_lattice(sK3))),sK4))
| ~ element(sK7(sK3,sK6(relation_of_lattice(sK3))),the_carrier(sK3))
| spl17_2
| ~ spl17_10 ),
inference(subsumption_resolution,[],[f8917,f121]) ).
fof(f8917,plain,
( ~ in(cartesian_product2(the_carrier(sK3),the_carrier(sK3)),ordered_pair(sK7(sK3,sK6(relation_of_lattice(sK3))),sK4))
| ~ element(sK4,the_carrier(sK3))
| ~ element(sK7(sK3,sK6(relation_of_lattice(sK3))),the_carrier(sK3))
| spl17_2
| ~ spl17_10 ),
inference(subsumption_resolution,[],[f8915,f206]) ).
fof(f8915,plain,
( ~ in(cartesian_product2(the_carrier(sK3),the_carrier(sK3)),ordered_pair(sK7(sK3,sK6(relation_of_lattice(sK3))),sK4))
| empty(the_carrier(sK3))
| ~ element(sK4,the_carrier(sK3))
| ~ element(sK7(sK3,sK6(relation_of_lattice(sK3))),the_carrier(sK3))
| spl17_2
| ~ spl17_10 ),
inference(duplicate_literal_removal,[],[f8910]) ).
fof(f8910,plain,
( ~ in(cartesian_product2(the_carrier(sK3),the_carrier(sK3)),ordered_pair(sK7(sK3,sK6(relation_of_lattice(sK3))),sK4))
| empty(the_carrier(sK3))
| empty(the_carrier(sK3))
| ~ element(sK4,the_carrier(sK3))
| ~ element(sK7(sK3,sK6(relation_of_lattice(sK3))),the_carrier(sK3))
| spl17_2
| ~ spl17_10 ),
inference(superposition,[],[f1254,f3474]) ).
fof(f3474,plain,
( ordered_pair_as_product_element(the_carrier(sK3),the_carrier(sK3),sK7(sK3,sK6(relation_of_lattice(sK3))),sK4) = ordered_pair(sK7(sK3,sK6(relation_of_lattice(sK3))),sK4)
| spl17_2
| ~ spl17_10 ),
inference(subsumption_resolution,[],[f3468,f206]) ).
fof(f3468,plain,
( empty(the_carrier(sK3))
| ordered_pair_as_product_element(the_carrier(sK3),the_carrier(sK3),sK7(sK3,sK6(relation_of_lattice(sK3))),sK4) = ordered_pair(sK7(sK3,sK6(relation_of_lattice(sK3))),sK4)
| spl17_2
| ~ spl17_10 ),
inference(resolution,[],[f480,f338]) ).
fof(f15111,plain,
( ~ spl17_71
| ~ spl17_72
| ~ spl17_73
| ~ spl17_74
| spl17_69 ),
inference(avatar_split_clause,[],[f15094,f15085,f15108,f15104,f15100,f15096]) ).
fof(f15096,plain,
( spl17_71
<=> meet_commutative(sK16) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_71])]) ).
fof(f15100,plain,
( spl17_72
<=> meet_absorbing(sK16) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_72])]) ).
fof(f15104,plain,
( spl17_73
<=> join_absorbing(sK16) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_73])]) ).
fof(f15108,plain,
( spl17_74
<=> latt_str(sK16) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_74])]) ).
fof(f15085,plain,
( spl17_69
<=> below_refl(sK16,sK6(the_carrier(sK16)),sK6(the_carrier(sK16))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_69])]) ).
fof(f15094,plain,
( ~ latt_str(sK16)
| ~ join_absorbing(sK16)
| ~ meet_absorbing(sK16)
| ~ meet_commutative(sK16)
| spl17_69 ),
inference(subsumption_resolution,[],[f15093,f178]) ).
fof(f178,plain,
~ empty_carrier(sK16),
inference(cnf_transformation,[],[f117]) ).
fof(f117,plain,
( ~ empty_carrier(sK16)
& one_sorted_str(sK16) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK16])],[f33,f116]) ).
fof(f116,plain,
( ? [X0] :
( ~ empty_carrier(X0)
& one_sorted_str(X0) )
=> ( ~ empty_carrier(sK16)
& one_sorted_str(sK16) ) ),
introduced(choice_axiom,[]) ).
fof(f33,axiom,
? [X0] :
( ~ empty_carrier(X0)
& one_sorted_str(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_struct_0) ).
fof(f15093,plain,
( ~ latt_str(sK16)
| ~ join_absorbing(sK16)
| ~ meet_absorbing(sK16)
| ~ meet_commutative(sK16)
| empty_carrier(sK16)
| spl17_69 ),
inference(resolution,[],[f15087,f1191]) ).
fof(f1191,plain,
! [X0] :
( below_refl(X0,sK6(the_carrier(X0)),sK6(the_carrier(X0)))
| ~ latt_str(X0)
| ~ join_absorbing(X0)
| ~ meet_absorbing(X0)
| ~ meet_commutative(X0)
| empty_carrier(X0) ),
inference(resolution,[],[f717,f144]) ).
fof(f144,plain,
! [X0] : element(sK6(X0),X0),
inference(cnf_transformation,[],[f94]) ).
fof(f94,plain,
! [X0] : element(sK6(X0),X0),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f24,f93]) ).
fof(f93,plain,
! [X0] :
( ? [X1] : element(X1,X0)
=> element(sK6(X0),X0) ),
introduced(choice_axiom,[]) ).
fof(f24,axiom,
! [X0] :
? [X1] : element(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(f717,plain,
! [X0,X1] :
( ~ element(X1,the_carrier(X0))
| below_refl(X0,X1,X1)
| ~ latt_str(X0)
| ~ join_absorbing(X0)
| ~ meet_absorbing(X0)
| ~ meet_commutative(X0)
| empty_carrier(X0) ),
inference(resolution,[],[f164,f144]) ).
fof(f164,plain,
! [X2,X0,X1] :
( ~ element(X2,the_carrier(X0))
| below_refl(X0,X1,X1)
| ~ element(X1,the_carrier(X0))
| ~ latt_str(X0)
| ~ join_absorbing(X0)
| ~ meet_absorbing(X0)
| ~ meet_commutative(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f73]) ).
fof(f73,plain,
! [X0,X1,X2] :
( below_refl(X0,X1,X1)
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ latt_str(X0)
| ~ join_absorbing(X0)
| ~ meet_absorbing(X0)
| ~ meet_commutative(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f72]) ).
fof(f72,plain,
! [X0,X1,X2] :
( below_refl(X0,X1,X1)
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ latt_str(X0)
| ~ join_absorbing(X0)
| ~ meet_absorbing(X0)
| ~ meet_commutative(X0)
| empty_carrier(X0) ),
inference(ennf_transformation,[],[f36]) ).
fof(f36,axiom,
! [X0,X1,X2] :
( ( element(X2,the_carrier(X0))
& element(X1,the_carrier(X0))
& latt_str(X0)
& join_absorbing(X0)
& meet_absorbing(X0)
& meet_commutative(X0)
& ~ empty_carrier(X0) )
=> below_refl(X0,X1,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r3_lattices) ).
fof(f15087,plain,
( ~ below_refl(sK16,sK6(the_carrier(sK16)),sK6(the_carrier(sK16)))
| spl17_69 ),
inference(avatar_component_clause,[],[f15085]) ).
fof(f15092,plain,
( ~ spl17_69
| spl17_70
| spl17_43 ),
inference(avatar_split_clause,[],[f15003,f5438,f15089,f15085]) ).
fof(f15089,plain,
( spl17_70
<=> sP1(sK16,ordered_pair(sK6(the_carrier(sK16)),sK6(the_carrier(sK16)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_70])]) ).
fof(f5438,plain,
( spl17_43
<=> empty(the_carrier(sK16)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_43])]) ).
fof(f15003,plain,
( sP1(sK16,ordered_pair(sK6(the_carrier(sK16)),sK6(the_carrier(sK16))))
| ~ below_refl(sK16,sK6(the_carrier(sK16)),sK6(the_carrier(sK16)))
| spl17_43 ),
inference(subsumption_resolution,[],[f15002,f144]) ).
fof(f15002,plain,
( sP1(sK16,ordered_pair(sK6(the_carrier(sK16)),sK6(the_carrier(sK16))))
| ~ below_refl(sK16,sK6(the_carrier(sK16)),sK6(the_carrier(sK16)))
| ~ element(sK6(the_carrier(sK16)),the_carrier(sK16))
| spl17_43 ),
inference(duplicate_literal_removal,[],[f14995]) ).
fof(f14995,plain,
( sP1(sK16,ordered_pair(sK6(the_carrier(sK16)),sK6(the_carrier(sK16))))
| ~ below_refl(sK16,sK6(the_carrier(sK16)),sK6(the_carrier(sK16)))
| ~ element(sK6(the_carrier(sK16)),the_carrier(sK16))
| ~ element(sK6(the_carrier(sK16)),the_carrier(sK16))
| spl17_43 ),
inference(superposition,[],[f179,f12986]) ).
fof(f12986,plain,
( ordered_pair_as_product_element(the_carrier(sK16),the_carrier(sK16),sK6(the_carrier(sK16)),sK6(the_carrier(sK16))) = ordered_pair(sK6(the_carrier(sK16)),sK6(the_carrier(sK16)))
| spl17_43 ),
inference(resolution,[],[f4282,f5439]) ).
fof(f5439,plain,
( ~ empty(the_carrier(sK16))
| spl17_43 ),
inference(avatar_component_clause,[],[f5438]) ).
fof(f4282,plain,
! [X0] :
( empty(X0)
| ordered_pair_as_product_element(X0,X0,sK6(X0),sK6(X0)) = ordered_pair(sK6(X0),sK6(X0)) ),
inference(factoring,[],[f1107]) ).
fof(f1107,plain,
! [X0,X1] :
( empty(X1)
| empty(X0)
| ordered_pair_as_product_element(X0,X1,sK6(X0),sK6(X1)) = ordered_pair(sK6(X0),sK6(X1)) ),
inference(resolution,[],[f473,f144]) ).
fof(f473,plain,
! [X2,X0,X1] :
( ~ element(X2,X0)
| ordered_pair_as_product_element(X0,X1,X2,sK6(X1)) = ordered_pair(X2,sK6(X1))
| empty(X1)
| empty(X0) ),
inference(resolution,[],[f169,f144]) ).
fof(f179,plain,
! [X2,X3,X0] :
( sP1(X0,ordered_pair_as_product_element(the_carrier(X0),the_carrier(X0),X2,X3))
| ~ below_refl(X0,X2,X3)
| ~ element(X3,the_carrier(X0))
| ~ element(X2,the_carrier(X0)) ),
inference(equality_resolution,[],[f157]) ).
fof(f157,plain,
! [X2,X3,X0,X1] :
( sP1(X0,X1)
| ~ below_refl(X0,X2,X3)
| ordered_pair_as_product_element(the_carrier(X0),the_carrier(X0),X2,X3) != X1
| ~ element(X3,the_carrier(X0))
| ~ element(X2,the_carrier(X0)) ),
inference(cnf_transformation,[],[f99]) ).
fof(f14929,plain,
( ~ spl17_65
| ~ spl17_66
| ~ spl17_67
| ~ spl17_68
| spl17_49
| spl17_63 ),
inference(avatar_split_clause,[],[f14912,f14903,f6012,f14926,f14922,f14918,f14914]) ).
fof(f14914,plain,
( spl17_65
<=> meet_commutative(sK14) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_65])]) ).
fof(f14918,plain,
( spl17_66
<=> meet_absorbing(sK14) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_66])]) ).
fof(f14922,plain,
( spl17_67
<=> join_absorbing(sK14) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_67])]) ).
fof(f14926,plain,
( spl17_68
<=> latt_str(sK14) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_68])]) ).
fof(f6012,plain,
( spl17_49
<=> empty_carrier(sK14) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_49])]) ).
fof(f14903,plain,
( spl17_63
<=> below_refl(sK14,sK6(the_carrier(sK14)),sK6(the_carrier(sK14))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_63])]) ).
fof(f14912,plain,
( ~ latt_str(sK14)
| ~ join_absorbing(sK14)
| ~ meet_absorbing(sK14)
| ~ meet_commutative(sK14)
| spl17_49
| spl17_63 ),
inference(subsumption_resolution,[],[f14911,f6013]) ).
fof(f6013,plain,
( ~ empty_carrier(sK14)
| spl17_49 ),
inference(avatar_component_clause,[],[f6012]) ).
fof(f14911,plain,
( ~ latt_str(sK14)
| ~ join_absorbing(sK14)
| ~ meet_absorbing(sK14)
| ~ meet_commutative(sK14)
| empty_carrier(sK14)
| spl17_63 ),
inference(resolution,[],[f14905,f1191]) ).
fof(f14905,plain,
( ~ below_refl(sK14,sK6(the_carrier(sK14)),sK6(the_carrier(sK14)))
| spl17_63 ),
inference(avatar_component_clause,[],[f14903]) ).
fof(f14910,plain,
( ~ spl17_63
| spl17_64
| spl17_51 ),
inference(avatar_split_clause,[],[f14794,f6036,f14907,f14903]) ).
fof(f14907,plain,
( spl17_64
<=> sP1(sK14,ordered_pair(sK6(the_carrier(sK14)),sK6(the_carrier(sK14)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_64])]) ).
fof(f6036,plain,
( spl17_51
<=> empty(the_carrier(sK14)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_51])]) ).
fof(f14794,plain,
( sP1(sK14,ordered_pair(sK6(the_carrier(sK14)),sK6(the_carrier(sK14))))
| ~ below_refl(sK14,sK6(the_carrier(sK14)),sK6(the_carrier(sK14)))
| spl17_51 ),
inference(subsumption_resolution,[],[f14793,f144]) ).
fof(f14793,plain,
( sP1(sK14,ordered_pair(sK6(the_carrier(sK14)),sK6(the_carrier(sK14))))
| ~ below_refl(sK14,sK6(the_carrier(sK14)),sK6(the_carrier(sK14)))
| ~ element(sK6(the_carrier(sK14)),the_carrier(sK14))
| spl17_51 ),
inference(duplicate_literal_removal,[],[f14786]) ).
fof(f14786,plain,
( sP1(sK14,ordered_pair(sK6(the_carrier(sK14)),sK6(the_carrier(sK14))))
| ~ below_refl(sK14,sK6(the_carrier(sK14)),sK6(the_carrier(sK14)))
| ~ element(sK6(the_carrier(sK14)),the_carrier(sK14))
| ~ element(sK6(the_carrier(sK14)),the_carrier(sK14))
| spl17_51 ),
inference(superposition,[],[f179,f12985]) ).
fof(f12985,plain,
( ordered_pair_as_product_element(the_carrier(sK14),the_carrier(sK14),sK6(the_carrier(sK14)),sK6(the_carrier(sK14))) = ordered_pair(sK6(the_carrier(sK14)),sK6(the_carrier(sK14)))
| spl17_51 ),
inference(resolution,[],[f4282,f6037]) ).
fof(f6037,plain,
( ~ empty(the_carrier(sK14))
| spl17_51 ),
inference(avatar_component_clause,[],[f6036]) ).
fof(f14637,plain,
( ~ spl17_59
| ~ spl17_60
| ~ spl17_61
| ~ spl17_62
| spl17_45
| spl17_57 ),
inference(avatar_split_clause,[],[f14620,f14611,f5706,f14634,f14630,f14626,f14622]) ).
fof(f14622,plain,
( spl17_59
<=> meet_commutative(sK12) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_59])]) ).
fof(f14626,plain,
( spl17_60
<=> meet_absorbing(sK12) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_60])]) ).
fof(f14630,plain,
( spl17_61
<=> join_absorbing(sK12) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_61])]) ).
fof(f14634,plain,
( spl17_62
<=> latt_str(sK12) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_62])]) ).
fof(f5706,plain,
( spl17_45
<=> empty_carrier(sK12) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_45])]) ).
fof(f14611,plain,
( spl17_57
<=> below_refl(sK12,sK6(the_carrier(sK12)),sK6(the_carrier(sK12))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_57])]) ).
fof(f14620,plain,
( ~ latt_str(sK12)
| ~ join_absorbing(sK12)
| ~ meet_absorbing(sK12)
| ~ meet_commutative(sK12)
| spl17_45
| spl17_57 ),
inference(subsumption_resolution,[],[f14619,f5707]) ).
fof(f5707,plain,
( ~ empty_carrier(sK12)
| spl17_45 ),
inference(avatar_component_clause,[],[f5706]) ).
fof(f14619,plain,
( ~ latt_str(sK12)
| ~ join_absorbing(sK12)
| ~ meet_absorbing(sK12)
| ~ meet_commutative(sK12)
| empty_carrier(sK12)
| spl17_57 ),
inference(resolution,[],[f14613,f1191]) ).
fof(f14613,plain,
( ~ below_refl(sK12,sK6(the_carrier(sK12)),sK6(the_carrier(sK12)))
| spl17_57 ),
inference(avatar_component_clause,[],[f14611]) ).
fof(f14618,plain,
( ~ spl17_57
| spl17_58
| spl17_47 ),
inference(avatar_split_clause,[],[f14502,f5727,f14615,f14611]) ).
fof(f14615,plain,
( spl17_58
<=> sP1(sK12,ordered_pair(sK6(the_carrier(sK12)),sK6(the_carrier(sK12)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_58])]) ).
fof(f5727,plain,
( spl17_47
<=> empty(the_carrier(sK12)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_47])]) ).
fof(f14502,plain,
( sP1(sK12,ordered_pair(sK6(the_carrier(sK12)),sK6(the_carrier(sK12))))
| ~ below_refl(sK12,sK6(the_carrier(sK12)),sK6(the_carrier(sK12)))
| spl17_47 ),
inference(subsumption_resolution,[],[f14501,f144]) ).
fof(f14501,plain,
( sP1(sK12,ordered_pair(sK6(the_carrier(sK12)),sK6(the_carrier(sK12))))
| ~ below_refl(sK12,sK6(the_carrier(sK12)),sK6(the_carrier(sK12)))
| ~ element(sK6(the_carrier(sK12)),the_carrier(sK12))
| spl17_47 ),
inference(duplicate_literal_removal,[],[f14494]) ).
fof(f14494,plain,
( sP1(sK12,ordered_pair(sK6(the_carrier(sK12)),sK6(the_carrier(sK12))))
| ~ below_refl(sK12,sK6(the_carrier(sK12)),sK6(the_carrier(sK12)))
| ~ element(sK6(the_carrier(sK12)),the_carrier(sK12))
| ~ element(sK6(the_carrier(sK12)),the_carrier(sK12))
| spl17_47 ),
inference(superposition,[],[f179,f12984]) ).
fof(f12984,plain,
( ordered_pair_as_product_element(the_carrier(sK12),the_carrier(sK12),sK6(the_carrier(sK12)),sK6(the_carrier(sK12))) = ordered_pair(sK6(the_carrier(sK12)),sK6(the_carrier(sK12)))
| spl17_47 ),
inference(resolution,[],[f4282,f5728]) ).
fof(f5728,plain,
( ~ empty(the_carrier(sK12))
| spl17_47 ),
inference(avatar_component_clause,[],[f5727]) ).
fof(f10859,plain,
( spl17_55
| spl17_56
| spl17_2 ),
inference(avatar_split_clause,[],[f10849,f205,f10856,f10852]) ).
fof(f10852,plain,
( spl17_55
<=> ordered_pair_as_product_element(the_carrier(sK11),the_carrier(sK3),sK6(the_carrier(sK11)),sK4) = ordered_pair(sK6(the_carrier(sK11)),sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_55])]) ).
fof(f10856,plain,
( spl17_56
<=> empty_carrier(sK11) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_56])]) ).
fof(f10849,plain,
( empty_carrier(sK11)
| ordered_pair_as_product_element(the_carrier(sK11),the_carrier(sK3),sK6(the_carrier(sK11)),sK4) = ordered_pair(sK6(the_carrier(sK11)),sK4)
| spl17_2 ),
inference(resolution,[],[f5420,f172]) ).
fof(f172,plain,
meet_semilatt_str(sK11),
inference(cnf_transformation,[],[f107]) ).
fof(f107,plain,
meet_semilatt_str(sK11),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK11])],[f20,f106]) ).
fof(f106,plain,
( ? [X0] : meet_semilatt_str(X0)
=> meet_semilatt_str(sK11) ),
introduced(choice_axiom,[]) ).
fof(f20,axiom,
? [X0] : meet_semilatt_str(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l1_lattices) ).
fof(f5420,plain,
( ! [X0] :
( ~ meet_semilatt_str(X0)
| empty_carrier(X0)
| ordered_pair_as_product_element(the_carrier(X0),the_carrier(sK3),sK6(the_carrier(X0)),sK4) = ordered_pair(sK6(the_carrier(X0)),sK4) )
| spl17_2 ),
inference(resolution,[],[f506,f127]) ).
fof(f127,plain,
! [X0] :
( one_sorted_str(X0)
| ~ meet_semilatt_str(X0) ),
inference(cnf_transformation,[],[f49]) ).
fof(f49,plain,
! [X0] :
( one_sorted_str(X0)
| ~ meet_semilatt_str(X0) ),
inference(ennf_transformation,[],[f14]) ).
fof(f14,axiom,
! [X0] :
( meet_semilatt_str(X0)
=> one_sorted_str(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_lattices) ).
fof(f506,plain,
( ! [X0] :
( ~ one_sorted_str(X0)
| ordered_pair_as_product_element(the_carrier(X0),the_carrier(sK3),sK6(the_carrier(X0)),sK4) = ordered_pair(sK6(the_carrier(X0)),sK4)
| empty_carrier(X0) )
| spl17_2 ),
inference(resolution,[],[f482,f143]) ).
fof(f143,plain,
! [X0] :
( ~ empty(the_carrier(X0))
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f60]) ).
fof(f60,plain,
! [X0] :
( ~ empty(the_carrier(X0))
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f59]) ).
fof(f59,plain,
! [X0] :
( ~ empty(the_carrier(X0))
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(ennf_transformation,[],[f25]) ).
fof(f25,axiom,
! [X0] :
( ( one_sorted_str(X0)
& ~ empty_carrier(X0) )
=> ~ empty(the_carrier(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_struct_0) ).
fof(f482,plain,
( ! [X0] :
( empty(X0)
| ordered_pair_as_product_element(X0,the_carrier(sK3),sK6(X0),sK4) = ordered_pair(sK6(X0),sK4) )
| spl17_2 ),
inference(resolution,[],[f475,f144]) ).
fof(f9928,plain,
( spl17_53
| spl17_54
| spl17_2
| ~ spl17_24 ),
inference(avatar_split_clause,[],[f9907,f758,f205,f9925,f9921]) ).
fof(f9921,plain,
( spl17_53
<=> empty_set = the_carrier(sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_53])]) ).
fof(f9925,plain,
( spl17_54
<=> sP1(sK3,ordered_pair(sK6(the_carrier(sK3)),sK6(the_carrier(sK3)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_54])]) ).
fof(f758,plain,
( spl17_24
<=> ! [X0] :
( below_refl(sK3,X0,X0)
| ~ element(X0,the_carrier(sK3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_24])]) ).
fof(f9907,plain,
( sP1(sK3,ordered_pair(sK6(the_carrier(sK3)),sK6(the_carrier(sK3))))
| empty_set = the_carrier(sK3)
| spl17_2
| ~ spl17_24 ),
inference(subsumption_resolution,[],[f9906,f144]) ).
fof(f9906,plain,
( sP1(sK3,ordered_pair(sK6(the_carrier(sK3)),sK6(the_carrier(sK3))))
| ~ element(sK6(the_carrier(sK3)),the_carrier(sK3))
| empty_set = the_carrier(sK3)
| spl17_2
| ~ spl17_24 ),
inference(subsumption_resolution,[],[f9905,f781]) ).
fof(f781,plain,
( below_refl(sK3,sK6(the_carrier(sK3)),sK6(the_carrier(sK3)))
| ~ spl17_24 ),
inference(resolution,[],[f759,f144]) ).
fof(f759,plain,
( ! [X0] :
( ~ element(X0,the_carrier(sK3))
| below_refl(sK3,X0,X0) )
| ~ spl17_24 ),
inference(avatar_component_clause,[],[f758]) ).
fof(f9905,plain,
( sP1(sK3,ordered_pair(sK6(the_carrier(sK3)),sK6(the_carrier(sK3))))
| ~ below_refl(sK3,sK6(the_carrier(sK3)),sK6(the_carrier(sK3)))
| ~ element(sK6(the_carrier(sK3)),the_carrier(sK3))
| empty_set = the_carrier(sK3)
| spl17_2 ),
inference(duplicate_literal_removal,[],[f9901]) ).
fof(f9901,plain,
( sP1(sK3,ordered_pair(sK6(the_carrier(sK3)),sK6(the_carrier(sK3))))
| ~ below_refl(sK3,sK6(the_carrier(sK3)),sK6(the_carrier(sK3)))
| ~ element(sK6(the_carrier(sK3)),the_carrier(sK3))
| ~ element(sK6(the_carrier(sK3)),the_carrier(sK3))
| empty_set = the_carrier(sK3)
| spl17_2 ),
inference(superposition,[],[f179,f4288]) ).
fof(f4288,plain,
( ! [X0] :
( ordered_pair_as_product_element(X0,the_carrier(sK3),sK6(X0),sK6(the_carrier(sK3))) = ordered_pair(sK6(X0),sK6(the_carrier(sK3)))
| empty_set = X0 )
| spl17_2 ),
inference(resolution,[],[f4249,f141]) ).
fof(f141,plain,
! [X0] :
( ~ empty(X0)
| empty_set = X0 ),
inference(cnf_transformation,[],[f56]) ).
fof(f56,plain,
! [X0] :
( empty_set = X0
| ~ empty(X0) ),
inference(ennf_transformation,[],[f43]) ).
fof(f43,axiom,
! [X0] :
( empty(X0)
=> empty_set = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
fof(f4249,plain,
( ! [X0] :
( empty(X0)
| ordered_pair_as_product_element(X0,the_carrier(sK3),sK6(X0),sK6(the_carrier(sK3))) = ordered_pair(sK6(X0),sK6(the_carrier(sK3))) )
| spl17_2 ),
inference(resolution,[],[f1107,f206]) ).
fof(f6043,plain,
( spl17_51
| ~ spl17_52
| spl17_2
| ~ spl17_50 ),
inference(avatar_split_clause,[],[f6025,f6016,f205,f6040,f6036]) ).
fof(f6040,plain,
( spl17_52
<=> in(cartesian_product2(the_carrier(sK14),the_carrier(sK3)),ordered_pair(sK6(the_carrier(sK14)),sK4)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_52])]) ).
fof(f6016,plain,
( spl17_50
<=> ordered_pair_as_product_element(the_carrier(sK14),the_carrier(sK3),sK6(the_carrier(sK14)),sK4) = ordered_pair(sK6(the_carrier(sK14)),sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_50])]) ).
fof(f6025,plain,
( ~ in(cartesian_product2(the_carrier(sK14),the_carrier(sK3)),ordered_pair(sK6(the_carrier(sK14)),sK4))
| empty(the_carrier(sK14))
| spl17_2
| ~ spl17_50 ),
inference(subsumption_resolution,[],[f6024,f144]) ).
fof(f6024,plain,
( ~ in(cartesian_product2(the_carrier(sK14),the_carrier(sK3)),ordered_pair(sK6(the_carrier(sK14)),sK4))
| empty(the_carrier(sK14))
| ~ element(sK6(the_carrier(sK14)),the_carrier(sK14))
| spl17_2
| ~ spl17_50 ),
inference(subsumption_resolution,[],[f6023,f121]) ).
fof(f6023,plain,
( ~ in(cartesian_product2(the_carrier(sK14),the_carrier(sK3)),ordered_pair(sK6(the_carrier(sK14)),sK4))
| empty(the_carrier(sK14))
| ~ element(sK4,the_carrier(sK3))
| ~ element(sK6(the_carrier(sK14)),the_carrier(sK14))
| spl17_2
| ~ spl17_50 ),
inference(subsumption_resolution,[],[f6020,f206]) ).
fof(f6020,plain,
( ~ in(cartesian_product2(the_carrier(sK14),the_carrier(sK3)),ordered_pair(sK6(the_carrier(sK14)),sK4))
| empty(the_carrier(sK3))
| empty(the_carrier(sK14))
| ~ element(sK4,the_carrier(sK3))
| ~ element(sK6(the_carrier(sK14)),the_carrier(sK14))
| ~ spl17_50 ),
inference(superposition,[],[f1254,f6018]) ).
fof(f6018,plain,
( ordered_pair_as_product_element(the_carrier(sK14),the_carrier(sK3),sK6(the_carrier(sK14)),sK4) = ordered_pair(sK6(the_carrier(sK14)),sK4)
| ~ spl17_50 ),
inference(avatar_component_clause,[],[f6016]) ).
fof(f6019,plain,
( spl17_49
| spl17_50
| spl17_2 ),
inference(avatar_split_clause,[],[f5422,f205,f6016,f6012]) ).
fof(f5422,plain,
( ordered_pair_as_product_element(the_carrier(sK14),the_carrier(sK3),sK6(the_carrier(sK14)),sK4) = ordered_pair(sK6(the_carrier(sK14)),sK4)
| empty_carrier(sK14)
| spl17_2 ),
inference(resolution,[],[f506,f175]) ).
fof(f175,plain,
one_sorted_str(sK14),
inference(cnf_transformation,[],[f113]) ).
fof(f113,plain,
one_sorted_str(sK14),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK14])],[f21,f112]) ).
fof(f112,plain,
( ? [X0] : one_sorted_str(X0)
=> one_sorted_str(sK14) ),
introduced(choice_axiom,[]) ).
fof(f21,axiom,
? [X0] : one_sorted_str(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l1_struct_0) ).
fof(f5734,plain,
( spl17_47
| ~ spl17_48
| spl17_2
| ~ spl17_46 ),
inference(avatar_split_clause,[],[f5719,f5710,f205,f5731,f5727]) ).
fof(f5731,plain,
( spl17_48
<=> in(cartesian_product2(the_carrier(sK12),the_carrier(sK3)),ordered_pair(sK6(the_carrier(sK12)),sK4)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_48])]) ).
fof(f5710,plain,
( spl17_46
<=> ordered_pair_as_product_element(the_carrier(sK12),the_carrier(sK3),sK6(the_carrier(sK12)),sK4) = ordered_pair(sK6(the_carrier(sK12)),sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_46])]) ).
fof(f5719,plain,
( ~ in(cartesian_product2(the_carrier(sK12),the_carrier(sK3)),ordered_pair(sK6(the_carrier(sK12)),sK4))
| empty(the_carrier(sK12))
| spl17_2
| ~ spl17_46 ),
inference(subsumption_resolution,[],[f5718,f144]) ).
fof(f5718,plain,
( ~ in(cartesian_product2(the_carrier(sK12),the_carrier(sK3)),ordered_pair(sK6(the_carrier(sK12)),sK4))
| empty(the_carrier(sK12))
| ~ element(sK6(the_carrier(sK12)),the_carrier(sK12))
| spl17_2
| ~ spl17_46 ),
inference(subsumption_resolution,[],[f5717,f121]) ).
fof(f5717,plain,
( ~ in(cartesian_product2(the_carrier(sK12),the_carrier(sK3)),ordered_pair(sK6(the_carrier(sK12)),sK4))
| empty(the_carrier(sK12))
| ~ element(sK4,the_carrier(sK3))
| ~ element(sK6(the_carrier(sK12)),the_carrier(sK12))
| spl17_2
| ~ spl17_46 ),
inference(subsumption_resolution,[],[f5714,f206]) ).
fof(f5714,plain,
( ~ in(cartesian_product2(the_carrier(sK12),the_carrier(sK3)),ordered_pair(sK6(the_carrier(sK12)),sK4))
| empty(the_carrier(sK3))
| empty(the_carrier(sK12))
| ~ element(sK4,the_carrier(sK3))
| ~ element(sK6(the_carrier(sK12)),the_carrier(sK12))
| ~ spl17_46 ),
inference(superposition,[],[f1254,f5712]) ).
fof(f5712,plain,
( ordered_pair_as_product_element(the_carrier(sK12),the_carrier(sK3),sK6(the_carrier(sK12)),sK4) = ordered_pair(sK6(the_carrier(sK12)),sK4)
| ~ spl17_46 ),
inference(avatar_component_clause,[],[f5710]) ).
fof(f5713,plain,
( spl17_45
| spl17_46
| spl17_2 ),
inference(avatar_split_clause,[],[f5421,f205,f5710,f5706]) ).
fof(f5421,plain,
( ordered_pair_as_product_element(the_carrier(sK12),the_carrier(sK3),sK6(the_carrier(sK12)),sK4) = ordered_pair(sK6(the_carrier(sK12)),sK4)
| empty_carrier(sK12)
| spl17_2 ),
inference(resolution,[],[f506,f180]) ).
fof(f180,plain,
one_sorted_str(sK12),
inference(resolution,[],[f128,f173]) ).
fof(f173,plain,
join_semilatt_str(sK12),
inference(cnf_transformation,[],[f109]) ).
fof(f109,plain,
join_semilatt_str(sK12),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK12])],[f22,f108]) ).
fof(f108,plain,
( ? [X0] : join_semilatt_str(X0)
=> join_semilatt_str(sK12) ),
introduced(choice_axiom,[]) ).
fof(f22,axiom,
? [X0] : join_semilatt_str(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l2_lattices) ).
fof(f128,plain,
! [X0] :
( ~ join_semilatt_str(X0)
| one_sorted_str(X0) ),
inference(cnf_transformation,[],[f50]) ).
fof(f50,plain,
! [X0] :
( one_sorted_str(X0)
| ~ join_semilatt_str(X0) ),
inference(ennf_transformation,[],[f16]) ).
fof(f16,axiom,
! [X0] :
( join_semilatt_str(X0)
=> one_sorted_str(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l2_lattices) ).
fof(f5445,plain,
( spl17_43
| ~ spl17_44
| spl17_2 ),
inference(avatar_split_clause,[],[f5430,f205,f5442,f5438]) ).
fof(f5442,plain,
( spl17_44
<=> in(cartesian_product2(the_carrier(sK16),the_carrier(sK3)),ordered_pair(sK6(the_carrier(sK16)),sK4)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_44])]) ).
fof(f5430,plain,
( ~ in(cartesian_product2(the_carrier(sK16),the_carrier(sK3)),ordered_pair(sK6(the_carrier(sK16)),sK4))
| empty(the_carrier(sK16))
| spl17_2 ),
inference(subsumption_resolution,[],[f5429,f144]) ).
fof(f5429,plain,
( ~ in(cartesian_product2(the_carrier(sK16),the_carrier(sK3)),ordered_pair(sK6(the_carrier(sK16)),sK4))
| empty(the_carrier(sK16))
| ~ element(sK6(the_carrier(sK16)),the_carrier(sK16))
| spl17_2 ),
inference(subsumption_resolution,[],[f5428,f121]) ).
fof(f5428,plain,
( ~ in(cartesian_product2(the_carrier(sK16),the_carrier(sK3)),ordered_pair(sK6(the_carrier(sK16)),sK4))
| empty(the_carrier(sK16))
| ~ element(sK4,the_carrier(sK3))
| ~ element(sK6(the_carrier(sK16)),the_carrier(sK16))
| spl17_2 ),
inference(subsumption_resolution,[],[f5425,f206]) ).
fof(f5425,plain,
( ~ in(cartesian_product2(the_carrier(sK16),the_carrier(sK3)),ordered_pair(sK6(the_carrier(sK16)),sK4))
| empty(the_carrier(sK3))
| empty(the_carrier(sK16))
| ~ element(sK4,the_carrier(sK3))
| ~ element(sK6(the_carrier(sK16)),the_carrier(sK16))
| spl17_2 ),
inference(superposition,[],[f1254,f5424]) ).
fof(f5424,plain,
( ordered_pair_as_product_element(the_carrier(sK16),the_carrier(sK3),sK6(the_carrier(sK16)),sK4) = ordered_pair(sK6(the_carrier(sK16)),sK4)
| spl17_2 ),
inference(subsumption_resolution,[],[f5423,f178]) ).
fof(f5423,plain,
( ordered_pair_as_product_element(the_carrier(sK16),the_carrier(sK3),sK6(the_carrier(sK16)),sK4) = ordered_pair(sK6(the_carrier(sK16)),sK4)
| empty_carrier(sK16)
| spl17_2 ),
inference(resolution,[],[f506,f177]) ).
fof(f177,plain,
one_sorted_str(sK16),
inference(cnf_transformation,[],[f117]) ).
fof(f2077,plain,
( ~ spl17_18
| spl17_41 ),
inference(avatar_contradiction_clause,[],[f2076]) ).
fof(f2076,plain,
( $false
| ~ spl17_18
| spl17_41 ),
inference(subsumption_resolution,[],[f2075,f118]) ).
fof(f118,plain,
~ empty_carrier(sK3),
inference(cnf_transformation,[],[f91]) ).
fof(f2075,plain,
( empty_carrier(sK3)
| ~ spl17_18
| spl17_41 ),
inference(subsumption_resolution,[],[f2074,f119]) ).
fof(f119,plain,
lattice(sK3),
inference(cnf_transformation,[],[f91]) ).
fof(f2074,plain,
( ~ lattice(sK3)
| empty_carrier(sK3)
| ~ spl17_18
| spl17_41 ),
inference(subsumption_resolution,[],[f2073,f120]) ).
fof(f120,plain,
latt_str(sK3),
inference(cnf_transformation,[],[f91]) ).
fof(f2073,plain,
( ~ latt_str(sK3)
| ~ lattice(sK3)
| empty_carrier(sK3)
| ~ spl17_18
| spl17_41 ),
inference(resolution,[],[f2072,f158]) ).
fof(f158,plain,
! [X0,X1] :
( sP2(X0,X1)
| ~ latt_str(X1)
| ~ lattice(X1)
| empty_carrier(X1) ),
inference(cnf_transformation,[],[f85]) ).
fof(f85,plain,
! [X0,X1] :
( sP2(X0,X1)
| ~ latt_str(X1)
| ~ lattice(X1)
| empty_carrier(X1) ),
inference(definition_folding,[],[f66,f84,f83]) ).
fof(f84,plain,
! [X0,X1] :
( ( in(X0,a_1_0_filter_1(X1))
<=> sP1(X1,X0) )
| ~ sP2(X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).
fof(f66,plain,
! [X0,X1] :
( ( in(X0,a_1_0_filter_1(X1))
<=> ? [X2,X3] :
( below_refl(X1,X2,X3)
& ordered_pair_as_product_element(the_carrier(X1),the_carrier(X1),X2,X3) = X0
& element(X3,the_carrier(X1))
& element(X2,the_carrier(X1)) ) )
| ~ latt_str(X1)
| ~ lattice(X1)
| empty_carrier(X1) ),
inference(flattening,[],[f65]) ).
fof(f65,plain,
! [X0,X1] :
( ( in(X0,a_1_0_filter_1(X1))
<=> ? [X2,X3] :
( below_refl(X1,X2,X3)
& ordered_pair_as_product_element(the_carrier(X1),the_carrier(X1),X2,X3) = X0
& element(X3,the_carrier(X1))
& element(X2,the_carrier(X1)) ) )
| ~ latt_str(X1)
| ~ lattice(X1)
| empty_carrier(X1) ),
inference(ennf_transformation,[],[f30]) ).
fof(f30,axiom,
! [X0,X1] :
( ( latt_str(X1)
& lattice(X1)
& ~ empty_carrier(X1) )
=> ( in(X0,a_1_0_filter_1(X1))
<=> ? [X2,X3] :
( below_refl(X1,X2,X3)
& ordered_pair_as_product_element(the_carrier(X1),the_carrier(X1),X2,X3) = X0
& element(X3,the_carrier(X1))
& element(X2,the_carrier(X1)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_1_0_filter_1) ).
fof(f2072,plain,
( ~ sP2(ordered_pair(sK4,sK4),sK3)
| ~ spl17_18
| spl17_41 ),
inference(subsumption_resolution,[],[f2071,f707]) ).
fof(f2071,plain,
( ~ sP1(sK3,ordered_pair(sK4,sK4))
| ~ sP2(ordered_pair(sK4,sK4),sK3)
| spl17_41 ),
inference(resolution,[],[f2070,f284]) ).
fof(f284,plain,
! [X0] :
( in(X0,relation_of_lattice(sK3))
| ~ sP1(sK3,X0)
| ~ sP2(X0,sK3) ),
inference(superposition,[],[f152,f282]) ).
fof(f282,plain,
relation_of_lattice(sK3) = a_1_0_filter_1(sK3),
inference(subsumption_resolution,[],[f281,f118]) ).
fof(f281,plain,
( relation_of_lattice(sK3) = a_1_0_filter_1(sK3)
| empty_carrier(sK3) ),
inference(subsumption_resolution,[],[f280,f120]) ).
fof(f280,plain,
( ~ latt_str(sK3)
| relation_of_lattice(sK3) = a_1_0_filter_1(sK3)
| empty_carrier(sK3) ),
inference(resolution,[],[f142,f119]) ).
fof(f142,plain,
! [X0] :
( ~ lattice(X0)
| ~ latt_str(X0)
| relation_of_lattice(X0) = a_1_0_filter_1(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f58]) ).
fof(f58,plain,
! [X0] :
( relation_of_lattice(X0) = a_1_0_filter_1(X0)
| ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f57]) ).
fof(f57,plain,
! [X0] :
( relation_of_lattice(X0) = a_1_0_filter_1(X0)
| ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0] :
( ( latt_str(X0)
& lattice(X0)
& ~ empty_carrier(X0) )
=> relation_of_lattice(X0) = a_1_0_filter_1(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_filter_1) ).
fof(f152,plain,
! [X0,X1] :
( in(X0,a_1_0_filter_1(X1))
| ~ sP1(X1,X0)
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f95]) ).
fof(f95,plain,
! [X0,X1] :
( ( ( in(X0,a_1_0_filter_1(X1))
| ~ sP1(X1,X0) )
& ( sP1(X1,X0)
| ~ in(X0,a_1_0_filter_1(X1)) ) )
| ~ sP2(X0,X1) ),
inference(nnf_transformation,[],[f84]) ).
fof(f2070,plain,
( ~ in(ordered_pair(sK4,sK4),relation_of_lattice(sK3))
| spl17_41 ),
inference(resolution,[],[f2064,f149]) ).
fof(f2064,plain,
( ~ element(ordered_pair(sK4,sK4),relation_of_lattice(sK3))
| spl17_41 ),
inference(avatar_component_clause,[],[f2062]) ).
fof(f2062,plain,
( spl17_41
<=> element(ordered_pair(sK4,sK4),relation_of_lattice(sK3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_41])]) ).
fof(f2069,plain,
( ~ spl17_41
| spl17_42
| spl17_2
| spl17_7
| ~ spl17_18 ),
inference(avatar_split_clause,[],[f1592,f705,f311,f205,f2066,f2062]) ).
fof(f2066,plain,
( spl17_42
<=> in(ordered_pair(ordered_pair(sK4,sK4),sK4),cartesian_product2(relation_of_lattice(sK3),the_carrier(sK3))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_42])]) ).
fof(f311,plain,
( spl17_7
<=> empty(relation_of_lattice(sK3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_7])]) ).
fof(f1592,plain,
( in(ordered_pair(ordered_pair(sK4,sK4),sK4),cartesian_product2(relation_of_lattice(sK3),the_carrier(sK3)))
| ~ element(ordered_pair(sK4,sK4),relation_of_lattice(sK3))
| spl17_2
| spl17_7
| ~ spl17_18 ),
inference(subsumption_resolution,[],[f1591,f121]) ).
fof(f1591,plain,
( in(ordered_pair(ordered_pair(sK4,sK4),sK4),cartesian_product2(relation_of_lattice(sK3),the_carrier(sK3)))
| ~ element(ordered_pair(sK4,sK4),relation_of_lattice(sK3))
| ~ element(sK4,the_carrier(sK3))
| spl17_2
| spl17_7
| ~ spl17_18 ),
inference(subsumption_resolution,[],[f1590,f313]) ).
fof(f313,plain,
( ~ empty(relation_of_lattice(sK3))
| spl17_7 ),
inference(avatar_component_clause,[],[f311]) ).
fof(f1590,plain,
( in(ordered_pair(ordered_pair(sK4,sK4),sK4),cartesian_product2(relation_of_lattice(sK3),the_carrier(sK3)))
| ~ element(ordered_pair(sK4,sK4),relation_of_lattice(sK3))
| empty(relation_of_lattice(sK3))
| ~ element(sK4,the_carrier(sK3))
| spl17_2
| ~ spl17_18 ),
inference(subsumption_resolution,[],[f1588,f206]) ).
fof(f1588,plain,
( in(ordered_pair(ordered_pair(sK4,sK4),sK4),cartesian_product2(relation_of_lattice(sK3),the_carrier(sK3)))
| ~ element(ordered_pair(sK4,sK4),relation_of_lattice(sK3))
| empty(the_carrier(sK3))
| empty(relation_of_lattice(sK3))
| ~ element(sK4,the_carrier(sK3))
| spl17_2
| ~ spl17_18 ),
inference(superposition,[],[f549,f1578]) ).
fof(f1578,plain,
( ordered_pair(ordered_pair(sK4,sK4),sK4) = ordered_pair_as_product_element(relation_of_lattice(sK3),the_carrier(sK3),ordered_pair(sK4,sK4),sK4)
| spl17_2
| ~ spl17_18 ),
inference(resolution,[],[f1574,f707]) ).
fof(f1574,plain,
( ! [X0] :
( ~ sP1(sK3,X0)
| ordered_pair(X0,sK4) = ordered_pair_as_product_element(relation_of_lattice(sK3),the_carrier(sK3),X0,sK4) )
| spl17_2 ),
inference(subsumption_resolution,[],[f1573,f118]) ).
fof(f1573,plain,
( ! [X0] :
( ~ sP1(sK3,X0)
| ordered_pair(X0,sK4) = ordered_pair_as_product_element(relation_of_lattice(sK3),the_carrier(sK3),X0,sK4)
| empty_carrier(sK3) )
| spl17_2 ),
inference(subsumption_resolution,[],[f1572,f119]) ).
fof(f1572,plain,
( ! [X0] :
( ~ sP1(sK3,X0)
| ordered_pair(X0,sK4) = ordered_pair_as_product_element(relation_of_lattice(sK3),the_carrier(sK3),X0,sK4)
| ~ lattice(sK3)
| empty_carrier(sK3) )
| spl17_2 ),
inference(subsumption_resolution,[],[f1568,f120]) ).
fof(f1568,plain,
( ! [X0] :
( ~ sP1(sK3,X0)
| ordered_pair(X0,sK4) = ordered_pair_as_product_element(relation_of_lattice(sK3),the_carrier(sK3),X0,sK4)
| ~ latt_str(sK3)
| ~ lattice(sK3)
| empty_carrier(sK3) )
| spl17_2 ),
inference(resolution,[],[f494,f158]) ).
fof(f494,plain,
( ! [X0] :
( ~ sP2(X0,sK3)
| ~ sP1(sK3,X0)
| ordered_pair(X0,sK4) = ordered_pair_as_product_element(relation_of_lattice(sK3),the_carrier(sK3),X0,sK4) )
| spl17_2 ),
inference(resolution,[],[f486,f284]) ).
fof(f486,plain,
( ! [X0,X1] :
( ~ in(X1,X0)
| ordered_pair_as_product_element(X0,the_carrier(sK3),X1,sK4) = ordered_pair(X1,sK4) )
| spl17_2 ),
inference(subsumption_resolution,[],[f483,f163]) ).
fof(f483,plain,
( ! [X0,X1] :
( ordered_pair_as_product_element(X0,the_carrier(sK3),X1,sK4) = ordered_pair(X1,sK4)
| empty(X0)
| ~ in(X1,X0) )
| spl17_2 ),
inference(resolution,[],[f475,f149]) ).
fof(f2009,plain,
( ~ spl17_14
| spl17_39 ),
inference(avatar_contradiction_clause,[],[f2008]) ).
fof(f2008,plain,
( $false
| ~ spl17_14
| spl17_39 ),
inference(subsumption_resolution,[],[f2007,f118]) ).
fof(f2007,plain,
( empty_carrier(sK3)
| ~ spl17_14
| spl17_39 ),
inference(subsumption_resolution,[],[f2006,f119]) ).
fof(f2006,plain,
( ~ lattice(sK3)
| empty_carrier(sK3)
| ~ spl17_14
| spl17_39 ),
inference(subsumption_resolution,[],[f2005,f120]) ).
fof(f2005,plain,
( ~ latt_str(sK3)
| ~ lattice(sK3)
| empty_carrier(sK3)
| ~ spl17_14
| spl17_39 ),
inference(resolution,[],[f2004,f158]) ).
fof(f2004,plain,
( ~ sP2(ordered_pair(sK5,sK5),sK3)
| ~ spl17_14
| spl17_39 ),
inference(subsumption_resolution,[],[f2003,f689]) ).
fof(f2003,plain,
( ~ sP1(sK3,ordered_pair(sK5,sK5))
| ~ sP2(ordered_pair(sK5,sK5),sK3)
| spl17_39 ),
inference(resolution,[],[f2002,f284]) ).
fof(f2002,plain,
( ~ in(ordered_pair(sK5,sK5),relation_of_lattice(sK3))
| spl17_39 ),
inference(resolution,[],[f1996,f149]) ).
fof(f1996,plain,
( ~ element(ordered_pair(sK5,sK5),relation_of_lattice(sK3))
| spl17_39 ),
inference(avatar_component_clause,[],[f1994]) ).
fof(f1994,plain,
( spl17_39
<=> element(ordered_pair(sK5,sK5),relation_of_lattice(sK3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_39])]) ).
fof(f2001,plain,
( ~ spl17_39
| spl17_40
| spl17_2
| spl17_7
| ~ spl17_14 ),
inference(avatar_split_clause,[],[f1584,f687,f311,f205,f1998,f1994]) ).
fof(f1998,plain,
( spl17_40
<=> in(ordered_pair(ordered_pair(sK5,sK5),sK4),cartesian_product2(relation_of_lattice(sK3),the_carrier(sK3))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_40])]) ).
fof(f1584,plain,
( in(ordered_pair(ordered_pair(sK5,sK5),sK4),cartesian_product2(relation_of_lattice(sK3),the_carrier(sK3)))
| ~ element(ordered_pair(sK5,sK5),relation_of_lattice(sK3))
| spl17_2
| spl17_7
| ~ spl17_14 ),
inference(subsumption_resolution,[],[f1583,f121]) ).
fof(f1583,plain,
( in(ordered_pair(ordered_pair(sK5,sK5),sK4),cartesian_product2(relation_of_lattice(sK3),the_carrier(sK3)))
| ~ element(ordered_pair(sK5,sK5),relation_of_lattice(sK3))
| ~ element(sK4,the_carrier(sK3))
| spl17_2
| spl17_7
| ~ spl17_14 ),
inference(subsumption_resolution,[],[f1582,f313]) ).
fof(f1582,plain,
( in(ordered_pair(ordered_pair(sK5,sK5),sK4),cartesian_product2(relation_of_lattice(sK3),the_carrier(sK3)))
| ~ element(ordered_pair(sK5,sK5),relation_of_lattice(sK3))
| empty(relation_of_lattice(sK3))
| ~ element(sK4,the_carrier(sK3))
| spl17_2
| ~ spl17_14 ),
inference(subsumption_resolution,[],[f1580,f206]) ).
fof(f1580,plain,
( in(ordered_pair(ordered_pair(sK5,sK5),sK4),cartesian_product2(relation_of_lattice(sK3),the_carrier(sK3)))
| ~ element(ordered_pair(sK5,sK5),relation_of_lattice(sK3))
| empty(the_carrier(sK3))
| empty(relation_of_lattice(sK3))
| ~ element(sK4,the_carrier(sK3))
| spl17_2
| ~ spl17_14 ),
inference(superposition,[],[f549,f1577]) ).
fof(f1577,plain,
( ordered_pair(ordered_pair(sK5,sK5),sK4) = ordered_pair_as_product_element(relation_of_lattice(sK3),the_carrier(sK3),ordered_pair(sK5,sK5),sK4)
| spl17_2
| ~ spl17_14 ),
inference(resolution,[],[f1574,f689]) ).
fof(f1742,plain,
( spl17_2
| ~ spl17_3
| spl17_37 ),
inference(avatar_contradiction_clause,[],[f1741]) ).
fof(f1741,plain,
( $false
| spl17_2
| ~ spl17_3
| spl17_37 ),
inference(subsumption_resolution,[],[f1740,f676]) ).
fof(f676,plain,
( in(ordered_pair(sK4,sK5),relation_of_lattice(sK3))
| spl17_2
| ~ spl17_3 ),
inference(forward_demodulation,[],[f263,f515]) ).
fof(f515,plain,
( ordered_pair_as_product_element(the_carrier(sK3),the_carrier(sK3),sK4,sK5) = ordered_pair(sK4,sK5)
| spl17_2 ),
inference(subsumption_resolution,[],[f509,f206]) ).
fof(f509,plain,
( ordered_pair_as_product_element(the_carrier(sK3),the_carrier(sK3),sK4,sK5) = ordered_pair(sK4,sK5)
| empty(the_carrier(sK3))
| spl17_2 ),
inference(resolution,[],[f476,f121]) ).
fof(f476,plain,
( ! [X0,X1] :
( ~ element(X1,X0)
| ordered_pair_as_product_element(X0,the_carrier(sK3),X1,sK5) = ordered_pair(X1,sK5)
| empty(X0) )
| spl17_2 ),
inference(subsumption_resolution,[],[f470,f206]) ).
fof(f470,plain,
! [X0,X1] :
( ordered_pair_as_product_element(X0,the_carrier(sK3),X1,sK5) = ordered_pair(X1,sK5)
| ~ element(X1,X0)
| empty(the_carrier(sK3))
| empty(X0) ),
inference(resolution,[],[f169,f122]) ).
fof(f122,plain,
element(sK5,the_carrier(sK3)),
inference(cnf_transformation,[],[f91]) ).
fof(f263,plain,
( in(ordered_pair_as_product_element(the_carrier(sK3),the_carrier(sK3),sK4,sK5),relation_of_lattice(sK3))
| ~ spl17_3 ),
inference(avatar_component_clause,[],[f261]) ).
fof(f261,plain,
( spl17_3
<=> in(ordered_pair_as_product_element(the_carrier(sK3),the_carrier(sK3),sK4,sK5),relation_of_lattice(sK3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_3])]) ).
fof(f1740,plain,
( ~ in(ordered_pair(sK4,sK5),relation_of_lattice(sK3))
| spl17_37 ),
inference(resolution,[],[f1734,f149]) ).
fof(f1734,plain,
( ~ element(ordered_pair(sK4,sK5),relation_of_lattice(sK3))
| spl17_37 ),
inference(avatar_component_clause,[],[f1732]) ).
fof(f1732,plain,
( spl17_37
<=> element(ordered_pair(sK4,sK5),relation_of_lattice(sK3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_37])]) ).
fof(f1739,plain,
( ~ spl17_37
| spl17_38
| spl17_2
| ~ spl17_3
| spl17_7 ),
inference(avatar_split_clause,[],[f904,f311,f261,f205,f1736,f1732]) ).
fof(f1736,plain,
( spl17_38
<=> element(ordered_pair(ordered_pair(sK4,sK5),sK5),cartesian_product2(relation_of_lattice(sK3),the_carrier(sK3))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_38])]) ).
fof(f904,plain,
( element(ordered_pair(ordered_pair(sK4,sK5),sK5),cartesian_product2(relation_of_lattice(sK3),the_carrier(sK3)))
| ~ element(ordered_pair(sK4,sK5),relation_of_lattice(sK3))
| spl17_2
| ~ spl17_3
| spl17_7 ),
inference(subsumption_resolution,[],[f903,f313]) ).
fof(f903,plain,
( element(ordered_pair(ordered_pair(sK4,sK5),sK5),cartesian_product2(relation_of_lattice(sK3),the_carrier(sK3)))
| ~ element(ordered_pair(sK4,sK5),relation_of_lattice(sK3))
| empty(relation_of_lattice(sK3))
| spl17_2
| ~ spl17_3 ),
inference(subsumption_resolution,[],[f902,f206]) ).
fof(f902,plain,
( element(ordered_pair(ordered_pair(sK4,sK5),sK5),cartesian_product2(relation_of_lattice(sK3),the_carrier(sK3)))
| ~ element(ordered_pair(sK4,sK5),relation_of_lattice(sK3))
| empty(the_carrier(sK3))
| empty(relation_of_lattice(sK3))
| spl17_2
| ~ spl17_3 ),
inference(subsumption_resolution,[],[f901,f122]) ).
fof(f901,plain,
( element(ordered_pair(ordered_pair(sK4,sK5),sK5),cartesian_product2(relation_of_lattice(sK3),the_carrier(sK3)))
| ~ element(sK5,the_carrier(sK3))
| ~ element(ordered_pair(sK4,sK5),relation_of_lattice(sK3))
| empty(the_carrier(sK3))
| empty(relation_of_lattice(sK3))
| spl17_2
| ~ spl17_3 ),
inference(superposition,[],[f170,f678]) ).
fof(f678,plain,
( ordered_pair(ordered_pair(sK4,sK5),sK5) = ordered_pair_as_product_element(relation_of_lattice(sK3),the_carrier(sK3),ordered_pair(sK4,sK5),sK5)
| spl17_2
| ~ spl17_3 ),
inference(resolution,[],[f676,f517]) ).
fof(f517,plain,
( ! [X0,X1] :
( ~ in(X1,X0)
| ordered_pair_as_product_element(X0,the_carrier(sK3),X1,sK5) = ordered_pair(X1,sK5) )
| spl17_2 ),
inference(subsumption_resolution,[],[f514,f163]) ).
fof(f514,plain,
( ! [X0,X1] :
( ordered_pair_as_product_element(X0,the_carrier(sK3),X1,sK5) = ordered_pair(X1,sK5)
| empty(X0)
| ~ in(X1,X0) )
| spl17_2 ),
inference(resolution,[],[f476,f149]) ).
fof(f1563,plain,
( ~ spl17_35
| spl17_36
| spl17_2 ),
inference(avatar_split_clause,[],[f1526,f205,f1560,f1556]) ).
fof(f1556,plain,
( spl17_35
<=> below_refl(sK3,sK5,sK6(the_carrier(sK3))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_35])]) ).
fof(f1560,plain,
( spl17_36
<=> sP1(sK3,ordered_pair(sK5,sK6(the_carrier(sK3)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_36])]) ).
fof(f1526,plain,
( sP1(sK3,ordered_pair(sK5,sK6(the_carrier(sK3))))
| ~ below_refl(sK3,sK5,sK6(the_carrier(sK3)))
| spl17_2 ),
inference(subsumption_resolution,[],[f1525,f122]) ).
fof(f1525,plain,
( sP1(sK3,ordered_pair(sK5,sK6(the_carrier(sK3))))
| ~ below_refl(sK3,sK5,sK6(the_carrier(sK3)))
| ~ element(sK5,the_carrier(sK3))
| spl17_2 ),
inference(subsumption_resolution,[],[f1520,f144]) ).
fof(f1520,plain,
( sP1(sK3,ordered_pair(sK5,sK6(the_carrier(sK3))))
| ~ below_refl(sK3,sK5,sK6(the_carrier(sK3)))
| ~ element(sK6(the_carrier(sK3)),the_carrier(sK3))
| ~ element(sK5,the_carrier(sK3))
| spl17_2 ),
inference(superposition,[],[f179,f1084]) ).
fof(f1084,plain,
( ordered_pair_as_product_element(the_carrier(sK3),the_carrier(sK3),sK5,sK6(the_carrier(sK3))) = ordered_pair(sK5,sK6(the_carrier(sK3)))
| spl17_2 ),
inference(resolution,[],[f1034,f206]) ).
fof(f1034,plain,
( ! [X0] :
( empty(X0)
| ordered_pair_as_product_element(the_carrier(sK3),X0,sK5,sK6(X0)) = ordered_pair(sK5,sK6(X0)) )
| spl17_2 ),
inference(resolution,[],[f1013,f198]) ).
fof(f198,plain,
! [X0] :
( in(sK6(X0),X0)
| empty(X0) ),
inference(resolution,[],[f150,f144]) ).
fof(f1013,plain,
( ! [X0,X1] :
( ~ in(X1,X0)
| ordered_pair_as_product_element(the_carrier(sK3),X0,sK5,X1) = ordered_pair(sK5,X1) )
| spl17_2 ),
inference(subsumption_resolution,[],[f999,f206]) ).
fof(f999,plain,
! [X0,X1] :
( ordered_pair_as_product_element(the_carrier(sK3),X0,sK5,X1) = ordered_pair(sK5,X1)
| empty(the_carrier(sK3))
| ~ in(X1,X0) ),
inference(resolution,[],[f477,f122]) ).
fof(f1249,plain,
( ~ spl17_33
| spl17_34
| spl17_2 ),
inference(avatar_split_clause,[],[f1219,f205,f1246,f1242]) ).
fof(f1242,plain,
( spl17_33
<=> below_refl(sK3,sK4,sK6(the_carrier(sK3))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_33])]) ).
fof(f1246,plain,
( spl17_34
<=> sP1(sK3,ordered_pair(sK4,sK6(the_carrier(sK3)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_34])]) ).
fof(f1219,plain,
( sP1(sK3,ordered_pair(sK4,sK6(the_carrier(sK3))))
| ~ below_refl(sK3,sK4,sK6(the_carrier(sK3)))
| spl17_2 ),
inference(subsumption_resolution,[],[f1218,f121]) ).
fof(f1218,plain,
( sP1(sK3,ordered_pair(sK4,sK6(the_carrier(sK3))))
| ~ below_refl(sK3,sK4,sK6(the_carrier(sK3)))
| ~ element(sK4,the_carrier(sK3))
| spl17_2 ),
inference(subsumption_resolution,[],[f1215,f144]) ).
fof(f1215,plain,
( sP1(sK3,ordered_pair(sK4,sK6(the_carrier(sK3))))
| ~ below_refl(sK3,sK4,sK6(the_carrier(sK3)))
| ~ element(sK6(the_carrier(sK3)),the_carrier(sK3))
| ~ element(sK4,the_carrier(sK3))
| spl17_2 ),
inference(superposition,[],[f179,f1062]) ).
fof(f1062,plain,
( ordered_pair_as_product_element(the_carrier(sK3),the_carrier(sK3),sK4,sK6(the_carrier(sK3))) = ordered_pair(sK4,sK6(the_carrier(sK3)))
| spl17_2 ),
inference(resolution,[],[f1016,f206]) ).
fof(f1016,plain,
( ! [X0] :
( empty(X0)
| ordered_pair_as_product_element(the_carrier(sK3),X0,sK4,sK6(X0)) = ordered_pair(sK4,sK6(X0)) )
| spl17_2 ),
inference(resolution,[],[f1012,f198]) ).
fof(f1012,plain,
( ! [X0,X1] :
( ~ in(X1,X0)
| ordered_pair_as_product_element(the_carrier(sK3),X0,sK4,X1) = ordered_pair(sK4,X1) )
| spl17_2 ),
inference(subsumption_resolution,[],[f998,f206]) ).
fof(f998,plain,
! [X0,X1] :
( ordered_pair_as_product_element(the_carrier(sK3),X0,sK4,X1) = ordered_pair(sK4,X1)
| empty(the_carrier(sK3))
| ~ in(X1,X0) ),
inference(resolution,[],[f477,f121]) ).
fof(f1147,plain,
( spl17_2
| ~ spl17_32 ),
inference(avatar_contradiction_clause,[],[f1146]) ).
fof(f1146,plain,
( $false
| spl17_2
| ~ spl17_32 ),
inference(subsumption_resolution,[],[f1145,f206]) ).
fof(f1145,plain,
( empty(the_carrier(sK3))
| ~ spl17_32 ),
inference(subsumption_resolution,[],[f1142,f171]) ).
fof(f171,plain,
~ empty(sK10),
inference(cnf_transformation,[],[f105]) ).
fof(f105,plain,
~ empty(sK10),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10])],[f32,f104]) ).
fof(f104,plain,
( ? [X0] : ~ empty(X0)
=> ~ empty(sK10) ),
introduced(choice_axiom,[]) ).
fof(f32,axiom,
? [X0] : ~ empty(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
fof(f1142,plain,
( empty(sK10)
| empty(the_carrier(sK3))
| ~ spl17_32 ),
inference(resolution,[],[f1105,f159]) ).
fof(f1105,plain,
( empty(cartesian_product2(the_carrier(sK3),sK10))
| ~ spl17_32 ),
inference(avatar_component_clause,[],[f1103]) ).
fof(f1103,plain,
( spl17_32
<=> empty(cartesian_product2(the_carrier(sK3),sK10)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_32])]) ).
fof(f1106,plain,
( spl17_31
| spl17_32
| spl17_2 ),
inference(avatar_split_clause,[],[f1073,f205,f1103,f1099]) ).
fof(f1099,plain,
( spl17_31
<=> in(ordered_pair(sK4,sK6(sK10)),cartesian_product2(the_carrier(sK3),sK10)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_31])]) ).
fof(f1073,plain,
( empty(cartesian_product2(the_carrier(sK3),sK10))
| in(ordered_pair(sK4,sK6(sK10)),cartesian_product2(the_carrier(sK3),sK10))
| spl17_2 ),
inference(resolution,[],[f1068,f150]) ).
fof(f1068,plain,
( element(ordered_pair(sK4,sK6(sK10)),cartesian_product2(the_carrier(sK3),sK10))
| spl17_2 ),
inference(subsumption_resolution,[],[f1067,f206]) ).
fof(f1067,plain,
( element(ordered_pair(sK4,sK6(sK10)),cartesian_product2(the_carrier(sK3),sK10))
| empty(the_carrier(sK3))
| spl17_2 ),
inference(subsumption_resolution,[],[f1066,f171]) ).
fof(f1066,plain,
( element(ordered_pair(sK4,sK6(sK10)),cartesian_product2(the_carrier(sK3),sK10))
| empty(sK10)
| empty(the_carrier(sK3))
| spl17_2 ),
inference(subsumption_resolution,[],[f1065,f121]) ).
fof(f1065,plain,
( element(ordered_pair(sK4,sK6(sK10)),cartesian_product2(the_carrier(sK3),sK10))
| ~ element(sK4,the_carrier(sK3))
| empty(sK10)
| empty(the_carrier(sK3))
| spl17_2 ),
inference(subsumption_resolution,[],[f1064,f144]) ).
fof(f1064,plain,
( element(ordered_pair(sK4,sK6(sK10)),cartesian_product2(the_carrier(sK3),sK10))
| ~ element(sK6(sK10),sK10)
| ~ element(sK4,the_carrier(sK3))
| empty(sK10)
| empty(the_carrier(sK3))
| spl17_2 ),
inference(superposition,[],[f170,f1063]) ).
fof(f1063,plain,
( ordered_pair_as_product_element(the_carrier(sK3),sK10,sK4,sK6(sK10)) = ordered_pair(sK4,sK6(sK10))
| spl17_2 ),
inference(resolution,[],[f1016,f171]) ).
fof(f923,plain,
( spl17_2
| ~ spl17_30 ),
inference(avatar_contradiction_clause,[],[f922]) ).
fof(f922,plain,
( $false
| spl17_2
| ~ spl17_30 ),
inference(subsumption_resolution,[],[f921,f206]) ).
fof(f921,plain,
( empty(the_carrier(sK3))
| ~ spl17_30 ),
inference(duplicate_literal_removal,[],[f918]) ).
fof(f918,plain,
( empty(the_carrier(sK3))
| empty(the_carrier(sK3))
| ~ spl17_30 ),
inference(resolution,[],[f916,f159]) ).
fof(f916,plain,
( empty(cartesian_product2(the_carrier(sK3),the_carrier(sK3)))
| ~ spl17_30 ),
inference(avatar_component_clause,[],[f914]) ).
fof(f914,plain,
( spl17_30
<=> empty(cartesian_product2(the_carrier(sK3),the_carrier(sK3))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_30])]) ).
fof(f917,plain,
( spl17_29
| spl17_30
| spl17_2 ),
inference(avatar_split_clause,[],[f567,f205,f914,f910]) ).
fof(f910,plain,
( spl17_29
<=> in(ordered_pair(sK4,sK4),cartesian_product2(the_carrier(sK3),the_carrier(sK3))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_29])]) ).
fof(f567,plain,
( empty(cartesian_product2(the_carrier(sK3),the_carrier(sK3)))
| in(ordered_pair(sK4,sK4),cartesian_product2(the_carrier(sK3),the_carrier(sK3)))
| spl17_2 ),
inference(resolution,[],[f551,f150]) ).
fof(f551,plain,
( element(ordered_pair(sK4,sK4),cartesian_product2(the_carrier(sK3),the_carrier(sK3)))
| spl17_2 ),
inference(subsumption_resolution,[],[f550,f206]) ).
fof(f550,plain,
( element(ordered_pair(sK4,sK4),cartesian_product2(the_carrier(sK3),the_carrier(sK3)))
| empty(the_carrier(sK3))
| spl17_2 ),
inference(subsumption_resolution,[],[f545,f121]) ).
fof(f545,plain,
( element(ordered_pair(sK4,sK4),cartesian_product2(the_carrier(sK3),the_carrier(sK3)))
| ~ element(sK4,the_carrier(sK3))
| empty(the_carrier(sK3))
| spl17_2 ),
inference(duplicate_literal_removal,[],[f537]) ).
fof(f537,plain,
( element(ordered_pair(sK4,sK4),cartesian_product2(the_carrier(sK3),the_carrier(sK3)))
| ~ element(sK4,the_carrier(sK3))
| ~ element(sK4,the_carrier(sK3))
| empty(the_carrier(sK3))
| empty(the_carrier(sK3))
| spl17_2 ),
inference(superposition,[],[f170,f484]) ).
fof(f484,plain,
( ordered_pair_as_product_element(the_carrier(sK3),the_carrier(sK3),sK4,sK4) = ordered_pair(sK4,sK4)
| spl17_2 ),
inference(subsumption_resolution,[],[f478,f206]) ).
fof(f478,plain,
( ordered_pair_as_product_element(the_carrier(sK3),the_carrier(sK3),sK4,sK4) = ordered_pair(sK4,sK4)
| empty(the_carrier(sK3))
| spl17_2 ),
inference(resolution,[],[f475,f121]) ).
fof(f900,plain,
( ~ spl17_27
| spl17_28
| spl17_2 ),
inference(avatar_split_clause,[],[f884,f205,f897,f893]) ).
fof(f893,plain,
( spl17_27
<=> below_refl(sK3,sK6(the_carrier(sK3)),sK5) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_27])]) ).
fof(f897,plain,
( spl17_28
<=> sP1(sK3,ordered_pair(sK6(the_carrier(sK3)),sK5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_28])]) ).
fof(f884,plain,
( sP1(sK3,ordered_pair(sK6(the_carrier(sK3)),sK5))
| ~ below_refl(sK3,sK6(the_carrier(sK3)),sK5)
| spl17_2 ),
inference(subsumption_resolution,[],[f883,f144]) ).
fof(f883,plain,
( sP1(sK3,ordered_pair(sK6(the_carrier(sK3)),sK5))
| ~ below_refl(sK3,sK6(the_carrier(sK3)),sK5)
| ~ element(sK6(the_carrier(sK3)),the_carrier(sK3))
| spl17_2 ),
inference(subsumption_resolution,[],[f880,f122]) ).
fof(f880,plain,
( sP1(sK3,ordered_pair(sK6(the_carrier(sK3)),sK5))
| ~ below_refl(sK3,sK6(the_carrier(sK3)),sK5)
| ~ element(sK5,the_carrier(sK3))
| ~ element(sK6(the_carrier(sK3)),the_carrier(sK3))
| spl17_2 ),
inference(superposition,[],[f179,f591]) ).
fof(f591,plain,
( ordered_pair_as_product_element(the_carrier(sK3),the_carrier(sK3),sK6(the_carrier(sK3)),sK5) = ordered_pair(sK6(the_carrier(sK3)),sK5)
| spl17_2 ),
inference(resolution,[],[f513,f206]) ).
fof(f513,plain,
( ! [X0] :
( empty(X0)
| ordered_pair_as_product_element(X0,the_carrier(sK3),sK6(X0),sK5) = ordered_pair(sK6(X0),sK5) )
| spl17_2 ),
inference(resolution,[],[f476,f144]) ).
fof(f858,plain,
( ~ spl17_25
| spl17_26
| spl17_2 ),
inference(avatar_split_clause,[],[f842,f205,f855,f851]) ).
fof(f851,plain,
( spl17_25
<=> below_refl(sK3,sK6(the_carrier(sK3)),sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_25])]) ).
fof(f855,plain,
( spl17_26
<=> sP1(sK3,ordered_pair(sK6(the_carrier(sK3)),sK4)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_26])]) ).
fof(f842,plain,
( sP1(sK3,ordered_pair(sK6(the_carrier(sK3)),sK4))
| ~ below_refl(sK3,sK6(the_carrier(sK3)),sK4)
| spl17_2 ),
inference(subsumption_resolution,[],[f841,f144]) ).
fof(f841,plain,
( sP1(sK3,ordered_pair(sK6(the_carrier(sK3)),sK4))
| ~ below_refl(sK3,sK6(the_carrier(sK3)),sK4)
| ~ element(sK6(the_carrier(sK3)),the_carrier(sK3))
| spl17_2 ),
inference(subsumption_resolution,[],[f838,f121]) ).
fof(f838,plain,
( sP1(sK3,ordered_pair(sK6(the_carrier(sK3)),sK4))
| ~ below_refl(sK3,sK6(the_carrier(sK3)),sK4)
| ~ element(sK4,the_carrier(sK3))
| ~ element(sK6(the_carrier(sK3)),the_carrier(sK3))
| spl17_2 ),
inference(superposition,[],[f179,f507]) ).
fof(f507,plain,
( ordered_pair_as_product_element(the_carrier(sK3),the_carrier(sK3),sK6(the_carrier(sK3)),sK4) = ordered_pair(sK6(the_carrier(sK3)),sK4)
| spl17_2 ),
inference(resolution,[],[f482,f206]) ).
fof(f788,plain,
( spl17_13
| ~ spl17_24 ),
inference(avatar_split_clause,[],[f778,f758,f683]) ).
fof(f683,plain,
( spl17_13
<=> below_refl(sK3,sK5,sK5) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_13])]) ).
fof(f778,plain,
( below_refl(sK3,sK5,sK5)
| ~ spl17_24 ),
inference(resolution,[],[f759,f122]) ).
fof(f787,plain,
( spl17_17
| ~ spl17_24 ),
inference(avatar_split_clause,[],[f777,f758,f701]) ).
fof(f701,plain,
( spl17_17
<=> below_refl(sK3,sK4,sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_17])]) ).
fof(f777,plain,
( below_refl(sK3,sK4,sK4)
| ~ spl17_24 ),
inference(resolution,[],[f759,f121]) ).
fof(f786,plain,
( spl17_13
| ~ spl17_24 ),
inference(avatar_contradiction_clause,[],[f785]) ).
fof(f785,plain,
( $false
| spl17_13
| ~ spl17_24 ),
inference(subsumption_resolution,[],[f778,f685]) ).
fof(f685,plain,
( ~ below_refl(sK3,sK5,sK5)
| spl17_13 ),
inference(avatar_component_clause,[],[f683]) ).
fof(f784,plain,
( spl17_17
| ~ spl17_24 ),
inference(avatar_contradiction_clause,[],[f783]) ).
fof(f783,plain,
( $false
| spl17_17
| ~ spl17_24 ),
inference(subsumption_resolution,[],[f777,f703]) ).
fof(f703,plain,
( ~ below_refl(sK3,sK4,sK4)
| spl17_17 ),
inference(avatar_component_clause,[],[f701]) ).
fof(f775,plain,
spl17_23,
inference(avatar_contradiction_clause,[],[f774]) ).
fof(f774,plain,
( $false
| spl17_23 ),
inference(subsumption_resolution,[],[f773,f119]) ).
fof(f773,plain,
( ~ lattice(sK3)
| spl17_23 ),
inference(subsumption_resolution,[],[f772,f120]) ).
fof(f772,plain,
( ~ latt_str(sK3)
| ~ lattice(sK3)
| spl17_23 ),
inference(subsumption_resolution,[],[f771,f118]) ).
fof(f771,plain,
( empty_carrier(sK3)
| ~ latt_str(sK3)
| ~ lattice(sK3)
| spl17_23 ),
inference(resolution,[],[f756,f190]) ).
fof(f190,plain,
! [X0] :
( join_absorbing(X0)
| empty_carrier(X0)
| ~ latt_str(X0)
| ~ lattice(X0) ),
inference(resolution,[],[f140,f139]) ).
fof(f139,plain,
! [X0] :
( ~ sP0(X0)
| join_absorbing(X0) ),
inference(cnf_transformation,[],[f92]) ).
fof(f92,plain,
! [X0] :
( ( join_absorbing(X0)
& meet_absorbing(X0)
& meet_associative(X0)
& meet_commutative(X0)
& join_associative(X0)
& join_commutative(X0)
& ~ empty_carrier(X0) )
| ~ sP0(X0) ),
inference(nnf_transformation,[],[f81]) ).
fof(f81,plain,
! [X0] :
( ( join_absorbing(X0)
& meet_absorbing(X0)
& meet_associative(X0)
& meet_commutative(X0)
& join_associative(X0)
& join_commutative(X0)
& ~ empty_carrier(X0) )
| ~ sP0(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f140,plain,
! [X0] :
( sP0(X0)
| ~ lattice(X0)
| empty_carrier(X0)
| ~ latt_str(X0) ),
inference(cnf_transformation,[],[f82]) ).
fof(f82,plain,
! [X0] :
( sP0(X0)
| ~ lattice(X0)
| empty_carrier(X0)
| ~ latt_str(X0) ),
inference(definition_folding,[],[f55,f81]) ).
fof(f55,plain,
! [X0] :
( ( join_absorbing(X0)
& meet_absorbing(X0)
& meet_associative(X0)
& meet_commutative(X0)
& join_associative(X0)
& join_commutative(X0)
& ~ empty_carrier(X0) )
| ~ lattice(X0)
| empty_carrier(X0)
| ~ latt_str(X0) ),
inference(flattening,[],[f54]) ).
fof(f54,plain,
! [X0] :
( ( join_absorbing(X0)
& meet_absorbing(X0)
& meet_associative(X0)
& meet_commutative(X0)
& join_associative(X0)
& join_commutative(X0)
& ~ empty_carrier(X0) )
| ~ lattice(X0)
| empty_carrier(X0)
| ~ latt_str(X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f2,axiom,
! [X0] :
( latt_str(X0)
=> ( ( lattice(X0)
& ~ empty_carrier(X0) )
=> ( join_absorbing(X0)
& meet_absorbing(X0)
& meet_associative(X0)
& meet_commutative(X0)
& join_associative(X0)
& join_commutative(X0)
& ~ empty_carrier(X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_lattices) ).
fof(f756,plain,
( ~ join_absorbing(sK3)
| spl17_23 ),
inference(avatar_component_clause,[],[f754]) ).
fof(f754,plain,
( spl17_23
<=> join_absorbing(sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_23])]) ).
fof(f770,plain,
spl17_22,
inference(avatar_contradiction_clause,[],[f769]) ).
fof(f769,plain,
( $false
| spl17_22 ),
inference(subsumption_resolution,[],[f768,f119]) ).
fof(f768,plain,
( ~ lattice(sK3)
| spl17_22 ),
inference(subsumption_resolution,[],[f767,f120]) ).
fof(f767,plain,
( ~ latt_str(sK3)
| ~ lattice(sK3)
| spl17_22 ),
inference(subsumption_resolution,[],[f766,f118]) ).
fof(f766,plain,
( empty_carrier(sK3)
| ~ latt_str(sK3)
| ~ lattice(sK3)
| spl17_22 ),
inference(resolution,[],[f752,f191]) ).
fof(f191,plain,
! [X0] :
( meet_absorbing(X0)
| empty_carrier(X0)
| ~ latt_str(X0)
| ~ lattice(X0) ),
inference(resolution,[],[f140,f138]) ).
fof(f138,plain,
! [X0] :
( ~ sP0(X0)
| meet_absorbing(X0) ),
inference(cnf_transformation,[],[f92]) ).
fof(f752,plain,
( ~ meet_absorbing(sK3)
| spl17_22 ),
inference(avatar_component_clause,[],[f750]) ).
fof(f750,plain,
( spl17_22
<=> meet_absorbing(sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_22])]) ).
fof(f765,plain,
spl17_21,
inference(avatar_contradiction_clause,[],[f764]) ).
fof(f764,plain,
( $false
| spl17_21 ),
inference(subsumption_resolution,[],[f763,f119]) ).
fof(f763,plain,
( ~ lattice(sK3)
| spl17_21 ),
inference(subsumption_resolution,[],[f762,f120]) ).
fof(f762,plain,
( ~ latt_str(sK3)
| ~ lattice(sK3)
| spl17_21 ),
inference(subsumption_resolution,[],[f761,f118]) ).
fof(f761,plain,
( empty_carrier(sK3)
| ~ latt_str(sK3)
| ~ lattice(sK3)
| spl17_21 ),
inference(resolution,[],[f748,f193]) ).
fof(f193,plain,
! [X0] :
( meet_commutative(X0)
| empty_carrier(X0)
| ~ latt_str(X0)
| ~ lattice(X0) ),
inference(resolution,[],[f140,f136]) ).
fof(f136,plain,
! [X0] :
( ~ sP0(X0)
| meet_commutative(X0) ),
inference(cnf_transformation,[],[f92]) ).
fof(f748,plain,
( ~ meet_commutative(sK3)
| spl17_21 ),
inference(avatar_component_clause,[],[f746]) ).
fof(f746,plain,
( spl17_21
<=> meet_commutative(sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_21])]) ).
fof(f760,plain,
( ~ spl17_21
| ~ spl17_22
| ~ spl17_23
| spl17_24 ),
inference(avatar_split_clause,[],[f720,f758,f754,f750,f746]) ).
fof(f720,plain,
! [X0] :
( below_refl(sK3,X0,X0)
| ~ element(X0,the_carrier(sK3))
| ~ join_absorbing(sK3)
| ~ meet_absorbing(sK3)
| ~ meet_commutative(sK3) ),
inference(subsumption_resolution,[],[f719,f118]) ).
fof(f719,plain,
! [X0] :
( below_refl(sK3,X0,X0)
| ~ element(X0,the_carrier(sK3))
| ~ join_absorbing(sK3)
| ~ meet_absorbing(sK3)
| ~ meet_commutative(sK3)
| empty_carrier(sK3) ),
inference(subsumption_resolution,[],[f713,f120]) ).
fof(f713,plain,
! [X0] :
( below_refl(sK3,X0,X0)
| ~ element(X0,the_carrier(sK3))
| ~ latt_str(sK3)
| ~ join_absorbing(sK3)
| ~ meet_absorbing(sK3)
| ~ meet_commutative(sK3)
| empty_carrier(sK3) ),
inference(resolution,[],[f164,f121]) ).
fof(f736,plain,
spl17_19,
inference(avatar_contradiction_clause,[],[f735]) ).
fof(f735,plain,
( $false
| spl17_19 ),
inference(subsumption_resolution,[],[f734,f118]) ).
fof(f734,plain,
( empty_carrier(sK3)
| spl17_19 ),
inference(subsumption_resolution,[],[f733,f119]) ).
fof(f733,plain,
( ~ lattice(sK3)
| empty_carrier(sK3)
| spl17_19 ),
inference(subsumption_resolution,[],[f732,f120]) ).
fof(f732,plain,
( ~ latt_str(sK3)
| ~ lattice(sK3)
| empty_carrier(sK3)
| spl17_19 ),
inference(resolution,[],[f726,f158]) ).
fof(f726,plain,
( ~ sP2(ordered_pair(sK4,sK5),sK3)
| spl17_19 ),
inference(avatar_component_clause,[],[f724]) ).
fof(f724,plain,
( spl17_19
<=> sP2(ordered_pair(sK4,sK5),sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_19])]) ).
fof(f731,plain,
( ~ spl17_19
| spl17_20
| spl17_2
| ~ spl17_3 ),
inference(avatar_split_clause,[],[f677,f261,f205,f728,f724]) ).
fof(f677,plain,
( sP1(sK3,ordered_pair(sK4,sK5))
| ~ sP2(ordered_pair(sK4,sK5),sK3)
| spl17_2
| ~ spl17_3 ),
inference(resolution,[],[f676,f285]) ).
fof(f285,plain,
! [X0] :
( ~ in(X0,relation_of_lattice(sK3))
| sP1(sK3,X0)
| ~ sP2(X0,sK3) ),
inference(superposition,[],[f151,f282]) ).
fof(f151,plain,
! [X0,X1] :
( ~ in(X0,a_1_0_filter_1(X1))
| sP1(X1,X0)
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f95]) ).
fof(f708,plain,
( ~ spl17_17
| spl17_18
| spl17_2 ),
inference(avatar_split_clause,[],[f648,f205,f705,f701]) ).
fof(f648,plain,
( sP1(sK3,ordered_pair(sK4,sK4))
| ~ below_refl(sK3,sK4,sK4)
| spl17_2 ),
inference(subsumption_resolution,[],[f621,f121]) ).
fof(f621,plain,
( sP1(sK3,ordered_pair(sK4,sK4))
| ~ below_refl(sK3,sK4,sK4)
| ~ element(sK4,the_carrier(sK3))
| spl17_2 ),
inference(duplicate_literal_removal,[],[f616]) ).
fof(f616,plain,
( sP1(sK3,ordered_pair(sK4,sK4))
| ~ below_refl(sK3,sK4,sK4)
| ~ element(sK4,the_carrier(sK3))
| ~ element(sK4,the_carrier(sK3))
| spl17_2 ),
inference(superposition,[],[f179,f484]) ).
fof(f699,plain,
( ~ spl17_15
| spl17_16
| spl17_2 ),
inference(avatar_split_clause,[],[f647,f205,f696,f692]) ).
fof(f692,plain,
( spl17_15
<=> below_refl(sK3,sK5,sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_15])]) ).
fof(f696,plain,
( spl17_16
<=> sP1(sK3,ordered_pair(sK5,sK4)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_16])]) ).
fof(f647,plain,
( sP1(sK3,ordered_pair(sK5,sK4))
| ~ below_refl(sK3,sK5,sK4)
| spl17_2 ),
inference(subsumption_resolution,[],[f646,f122]) ).
fof(f646,plain,
( sP1(sK3,ordered_pair(sK5,sK4))
| ~ below_refl(sK3,sK5,sK4)
| ~ element(sK5,the_carrier(sK3))
| spl17_2 ),
inference(subsumption_resolution,[],[f617,f121]) ).
fof(f617,plain,
( sP1(sK3,ordered_pair(sK5,sK4))
| ~ below_refl(sK3,sK5,sK4)
| ~ element(sK4,the_carrier(sK3))
| ~ element(sK5,the_carrier(sK3))
| spl17_2 ),
inference(superposition,[],[f179,f485]) ).
fof(f485,plain,
( ordered_pair_as_product_element(the_carrier(sK3),the_carrier(sK3),sK5,sK4) = ordered_pair(sK5,sK4)
| spl17_2 ),
inference(subsumption_resolution,[],[f479,f206]) ).
fof(f479,plain,
( ordered_pair_as_product_element(the_carrier(sK3),the_carrier(sK3),sK5,sK4) = ordered_pair(sK5,sK4)
| empty(the_carrier(sK3))
| spl17_2 ),
inference(resolution,[],[f475,f122]) ).
fof(f690,plain,
( ~ spl17_13
| spl17_14
| spl17_2 ),
inference(avatar_split_clause,[],[f642,f205,f687,f683]) ).
fof(f642,plain,
( sP1(sK3,ordered_pair(sK5,sK5))
| ~ below_refl(sK3,sK5,sK5)
| spl17_2 ),
inference(subsumption_resolution,[],[f620,f122]) ).
fof(f620,plain,
( sP1(sK3,ordered_pair(sK5,sK5))
| ~ below_refl(sK3,sK5,sK5)
| ~ element(sK5,the_carrier(sK3))
| spl17_2 ),
inference(duplicate_literal_removal,[],[f619]) ).
fof(f619,plain,
( sP1(sK3,ordered_pair(sK5,sK5))
| ~ below_refl(sK3,sK5,sK5)
| ~ element(sK5,the_carrier(sK3))
| ~ element(sK5,the_carrier(sK3))
| spl17_2 ),
inference(superposition,[],[f179,f516]) ).
fof(f516,plain,
( ordered_pair_as_product_element(the_carrier(sK3),the_carrier(sK3),sK5,sK5) = ordered_pair(sK5,sK5)
| spl17_2 ),
inference(subsumption_resolution,[],[f510,f206]) ).
fof(f510,plain,
( ordered_pair_as_product_element(the_carrier(sK3),the_carrier(sK3),sK5,sK5) = ordered_pair(sK5,sK5)
| empty(the_carrier(sK3))
| spl17_2 ),
inference(resolution,[],[f476,f122]) ).
fof(f673,plain,
( spl17_2
| ~ spl17_4 ),
inference(avatar_contradiction_clause,[],[f672]) ).
fof(f672,plain,
( $false
| spl17_2
| ~ spl17_4 ),
inference(subsumption_resolution,[],[f671,f118]) ).
fof(f671,plain,
( empty_carrier(sK3)
| spl17_2
| ~ spl17_4 ),
inference(subsumption_resolution,[],[f670,f119]) ).
fof(f670,plain,
( ~ lattice(sK3)
| empty_carrier(sK3)
| spl17_2
| ~ spl17_4 ),
inference(subsumption_resolution,[],[f669,f120]) ).
fof(f669,plain,
( ~ latt_str(sK3)
| ~ lattice(sK3)
| empty_carrier(sK3)
| spl17_2
| ~ spl17_4 ),
inference(resolution,[],[f668,f158]) ).
fof(f668,plain,
( ~ sP2(ordered_pair(sK4,sK5),sK3)
| spl17_2
| ~ spl17_4 ),
inference(subsumption_resolution,[],[f667,f645]) ).
fof(f645,plain,
( sP1(sK3,ordered_pair(sK4,sK5))
| spl17_2
| ~ spl17_4 ),
inference(global_subsumption,[],[f124,f164,f118,f119,f120,f125,f171,f172,f173,f174,f175,f176,f177,f178,f126,f121,f122,f127,f128,f180,f129,f130,f134,f135,f136,f137,f138,f139,f144,f145,f181,f141,f183,f163,f148,f149,f143,f146,f162,f140,f150,f197,f196,f206,f219,f220,f198,f159,f222,f190,f191,f192,f193,f194,f195,f153,f154,f158,f147,f227,f228,f230,f231,f232,f151,f234,f233,f152,f237,f167,f168,f226,f244,f245,f247,f248,f249,f250,f229,f252,f253,f254,f255,f256,f257,f258,f123,f267,f236,f269,f246,f272,f273,f274,f275,f277,f278,f279,f142,f156,f282,f283,f286,f284,f290,f292,f288,f285,f160,f322,f324,f325,f326,f328,f329,f319,f161,f369,f155,f323,f413,f327,f422,f410,f419,f224,f225,f132,f239,f427,f429,f169,f471,f472,f473,f477,f475,f480,f481,f484,f485,f486,f487,f488,f489,f492,f493,f495,f498,f499,f482,f500,f501,f502,f503,f504,f505,f506,f507,f508,f476,f511,f512,f515,f516,f517,f520,f521,f522,f525,f526,f528,f531,f532,f170,f546,f547,f548,f549,f551,f564,f565,f566,f567,f554,f568,f569,f570,f571,f561,f572,f573,f574,f575,f563,f576,f577,f578,f579,f558,f580,f581,f582,f513,f584,f585,f586,f587,f588,f589,f590,f591,f592,f597,f598,f599,f600,f601,f583,f179,f614,f615,f640,f641,f368,f642,f644]) ).
fof(f644,plain,
( sP1(sK3,ordered_pair(sK4,sK5))
| ~ below_refl(sK3,sK4,sK5)
| spl17_2 ),
inference(subsumption_resolution,[],[f643,f121]) ).
fof(f643,plain,
( sP1(sK3,ordered_pair(sK4,sK5))
| ~ below_refl(sK3,sK4,sK5)
| ~ element(sK4,the_carrier(sK3))
| spl17_2 ),
inference(subsumption_resolution,[],[f618,f122]) ).
fof(f618,plain,
( sP1(sK3,ordered_pair(sK4,sK5))
| ~ below_refl(sK3,sK4,sK5)
| ~ element(sK5,the_carrier(sK3))
| ~ element(sK4,the_carrier(sK3))
| spl17_2 ),
inference(superposition,[],[f179,f515]) ).
fof(f368,plain,
! [X0] :
( relation_of_lattice(sK3) = X0
| ~ in(sK9(X0,relation_of_lattice(sK3)),X0)
| ~ sP1(sK3,sK9(X0,relation_of_lattice(sK3)))
| ~ sP2(sK9(X0,relation_of_lattice(sK3)),sK3) ),
inference(resolution,[],[f161,f284]) ).
fof(f641,plain,
( ~ in(ordered_pair(sK4,sK5),relation_of_lattice(sK3))
| spl17_2
| ~ spl17_4 ),
inference(global_subsumption,[],[f124,f164,f118,f119,f120,f125,f171,f172,f173,f174,f175,f176,f177,f178,f126,f121,f122,f127,f128,f180,f129,f130,f134,f135,f136,f137,f138,f139,f144,f145,f181,f141,f183,f163,f148,f149,f143,f146,f162,f140,f150,f197,f196,f206,f219,f220,f198,f159,f222,f190,f191,f192,f193,f194,f195,f153,f154,f158,f147,f227,f228,f230,f231,f232,f151,f234,f233,f152,f237,f167,f168,f226,f244,f245,f247,f248,f249,f250,f229,f252,f253,f254,f255,f256,f257,f258,f123,f267,f236,f269,f246,f272,f273,f274,f275,f277,f278,f279,f142,f156,f282,f283,f286,f284,f290,f292,f288,f285,f160,f322,f324,f325,f326,f328,f329,f319,f161,f369,f155,f323,f413,f327,f422,f410,f419,f224,f225,f132,f239,f427,f429,f169,f471,f472,f473,f477,f475,f480,f481,f484,f485,f486,f487,f488,f489,f492,f493,f495,f498,f499,f482,f500,f501,f502,f503,f504,f505,f506,f507,f508,f476,f511,f512,f515,f516,f517,f520,f521,f522,f525,f526,f528,f531,f532,f170,f546,f547,f548,f549,f551,f564,f565,f566,f567,f554,f568,f569,f570,f571,f561,f572,f573,f574,f575,f563,f576,f577,f578,f579,f558,f580,f581,f582,f513,f584,f585,f586,f587,f588,f589,f590,f591,f592,f597,f598,f599,f600,f601,f583,f179,f614,f615,f640]) ).
fof(f640,plain,
( ~ in(ordered_pair(sK4,sK5),relation_of_lattice(sK3))
| ~ below_refl(sK3,sK4,sK5)
| spl17_2 ),
inference(forward_demodulation,[],[f124,f515]) ).
fof(f615,plain,
! [X2,X0,X1] :
( ~ below_refl(X0,X1,X2)
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ordered_pair_as_product_element(the_carrier(X0),the_carrier(X0),X1,X2) = ordered_pair_as_product_element(the_carrier(X0),the_carrier(X0),sK7(X0,ordered_pair_as_product_element(the_carrier(X0),the_carrier(X0),X1,X2)),sK8(X0,ordered_pair_as_product_element(the_carrier(X0),the_carrier(X0),X1,X2))) ),
inference(resolution,[],[f179,f155]) ).
fof(f614,plain,
! [X2,X0,X1] :
( ~ below_refl(X0,X1,X2)
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ empty(a_1_0_filter_1(X0))
| ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) ),
inference(resolution,[],[f179,f239]) ).
fof(f583,plain,
( empty(cartesian_product2(sK10,the_carrier(sK3)))
| in(ordered_pair(sK6(sK10),sK4),cartesian_product2(sK10,the_carrier(sK3)))
| spl17_2 ),
inference(resolution,[],[f558,f150]) ).
fof(f601,plain,
( empty(cartesian_product2(sK10,the_carrier(sK3)))
| in(ordered_pair(sK6(sK10),sK5),cartesian_product2(sK10,the_carrier(sK3)))
| spl17_2 ),
inference(resolution,[],[f597,f150]) ).
fof(f600,plain,
( ! [X0,X1] :
( ordered_pair_as_product_element(X0,cartesian_product2(sK10,the_carrier(sK3)),X1,ordered_pair(sK6(sK10),sK5)) = ordered_pair(X1,ordered_pair(sK6(sK10),sK5))
| ~ element(X1,X0)
| empty(cartesian_product2(sK10,the_carrier(sK3)))
| empty(X0) )
| spl17_2 ),
inference(resolution,[],[f597,f169]) ).
fof(f599,plain,
( ordered_pair_as_product_element(cartesian_product2(sK10,the_carrier(sK3)),the_carrier(sK3),ordered_pair(sK6(sK10),sK5),sK4) = ordered_pair(ordered_pair(sK6(sK10),sK5),sK4)
| empty(cartesian_product2(sK10,the_carrier(sK3)))
| spl17_2 ),
inference(resolution,[],[f597,f475]) ).
fof(f598,plain,
( ordered_pair_as_product_element(cartesian_product2(sK10,the_carrier(sK3)),the_carrier(sK3),ordered_pair(sK6(sK10),sK5),sK5) = ordered_pair(ordered_pair(sK6(sK10),sK5),sK5)
| empty(cartesian_product2(sK10,the_carrier(sK3)))
| spl17_2 ),
inference(resolution,[],[f597,f476]) ).
fof(f597,plain,
( element(ordered_pair(sK6(sK10),sK5),cartesian_product2(sK10,the_carrier(sK3)))
| spl17_2 ),
inference(subsumption_resolution,[],[f596,f171]) ).
fof(f596,plain,
( element(ordered_pair(sK6(sK10),sK5),cartesian_product2(sK10,the_carrier(sK3)))
| empty(sK10)
| spl17_2 ),
inference(subsumption_resolution,[],[f595,f206]) ).
fof(f595,plain,
( element(ordered_pair(sK6(sK10),sK5),cartesian_product2(sK10,the_carrier(sK3)))
| empty(the_carrier(sK3))
| empty(sK10)
| spl17_2 ),
inference(subsumption_resolution,[],[f594,f144]) ).
fof(f594,plain,
( element(ordered_pair(sK6(sK10),sK5),cartesian_product2(sK10,the_carrier(sK3)))
| ~ element(sK6(sK10),sK10)
| empty(the_carrier(sK3))
| empty(sK10)
| spl17_2 ),
inference(subsumption_resolution,[],[f593,f122]) ).
fof(f593,plain,
( element(ordered_pair(sK6(sK10),sK5),cartesian_product2(sK10,the_carrier(sK3)))
| ~ element(sK5,the_carrier(sK3))
| ~ element(sK6(sK10),sK10)
| empty(the_carrier(sK3))
| empty(sK10)
| spl17_2 ),
inference(superposition,[],[f170,f592]) ).
fof(f592,plain,
( ordered_pair_as_product_element(sK10,the_carrier(sK3),sK6(sK10),sK5) = ordered_pair(sK6(sK10),sK5)
| spl17_2 ),
inference(resolution,[],[f513,f171]) ).
fof(f590,plain,
( ! [X0] :
( ~ one_sorted_str(X0)
| ordered_pair_as_product_element(the_carrier(X0),the_carrier(sK3),sK6(the_carrier(X0)),sK5) = ordered_pair(sK6(the_carrier(X0)),sK5)
| empty_carrier(X0) )
| spl17_2 ),
inference(resolution,[],[f513,f143]) ).
fof(f589,plain,
( ! [X0,X1] :
( empty(X1)
| empty(X0)
| ordered_pair_as_product_element(cartesian_product2(X0,X1),the_carrier(sK3),sK6(cartesian_product2(X0,X1)),sK5) = ordered_pair(sK6(cartesian_product2(X0,X1)),sK5) )
| spl17_2 ),
inference(resolution,[],[f513,f159]) ).
fof(f588,plain,
( ! [X0] : ordered_pair_as_product_element(singleton(X0),the_carrier(sK3),sK6(singleton(X0)),sK5) = ordered_pair(sK6(singleton(X0)),sK5)
| spl17_2 ),
inference(resolution,[],[f513,f126]) ).
fof(f587,plain,
( ! [X0,X1] : ordered_pair_as_product_element(ordered_pair(X0,X1),the_carrier(sK3),sK6(ordered_pair(X0,X1)),sK5) = ordered_pair(sK6(ordered_pair(X0,X1)),sK5)
| spl17_2 ),
inference(resolution,[],[f513,f233]) ).
fof(f586,plain,
( ! [X0,X1] : ordered_pair_as_product_element(unordered_pair(X0,X1),the_carrier(sK3),sK6(unordered_pair(X0,X1)),sK5) = ordered_pair(sK6(unordered_pair(X0,X1)),sK5)
| spl17_2 ),
inference(resolution,[],[f513,f145]) ).
fof(f585,plain,
( ! [X0] :
( ordered_pair_as_product_element(X0,the_carrier(sK3),sK6(X0),sK5) = ordered_pair(sK6(X0),sK5)
| empty_set = X0 )
| spl17_2 ),
inference(resolution,[],[f513,f141]) ).
fof(f584,plain,
( ! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ordered_pair_as_product_element(X0,the_carrier(sK3),sK6(X0),sK5) = ordered_pair(sK6(X0),sK5) )
| spl17_2 ),
inference(resolution,[],[f513,f162]) ).
fof(f582,plain,
( ! [X0,X1] :
( ordered_pair_as_product_element(X0,cartesian_product2(sK10,the_carrier(sK3)),X1,ordered_pair(sK6(sK10),sK4)) = ordered_pair(X1,ordered_pair(sK6(sK10),sK4))
| ~ element(X1,X0)
| empty(cartesian_product2(sK10,the_carrier(sK3)))
| empty(X0) )
| spl17_2 ),
inference(resolution,[],[f558,f169]) ).
fof(f581,plain,
( ordered_pair_as_product_element(cartesian_product2(sK10,the_carrier(sK3)),the_carrier(sK3),ordered_pair(sK6(sK10),sK4),sK4) = ordered_pair(ordered_pair(sK6(sK10),sK4),sK4)
| empty(cartesian_product2(sK10,the_carrier(sK3)))
| spl17_2 ),
inference(resolution,[],[f558,f475]) ).
fof(f580,plain,
( ordered_pair_as_product_element(cartesian_product2(sK10,the_carrier(sK3)),the_carrier(sK3),ordered_pair(sK6(sK10),sK4),sK5) = ordered_pair(ordered_pair(sK6(sK10),sK4),sK5)
| empty(cartesian_product2(sK10,the_carrier(sK3)))
| spl17_2 ),
inference(resolution,[],[f558,f476]) ).
fof(f558,plain,
( element(ordered_pair(sK6(sK10),sK4),cartesian_product2(sK10,the_carrier(sK3)))
| spl17_2 ),
inference(subsumption_resolution,[],[f557,f171]) ).
fof(f557,plain,
( element(ordered_pair(sK6(sK10),sK4),cartesian_product2(sK10,the_carrier(sK3)))
| empty(sK10)
| spl17_2 ),
inference(subsumption_resolution,[],[f556,f206]) ).
fof(f556,plain,
( element(ordered_pair(sK6(sK10),sK4),cartesian_product2(sK10,the_carrier(sK3)))
| empty(the_carrier(sK3))
| empty(sK10)
| spl17_2 ),
inference(subsumption_resolution,[],[f555,f144]) ).
fof(f555,plain,
( element(ordered_pair(sK6(sK10),sK4),cartesian_product2(sK10,the_carrier(sK3)))
| ~ element(sK6(sK10),sK10)
| empty(the_carrier(sK3))
| empty(sK10)
| spl17_2 ),
inference(subsumption_resolution,[],[f539,f121]) ).
fof(f539,plain,
( element(ordered_pair(sK6(sK10),sK4),cartesian_product2(sK10,the_carrier(sK3)))
| ~ element(sK4,the_carrier(sK3))
| ~ element(sK6(sK10),sK10)
| empty(the_carrier(sK3))
| empty(sK10)
| spl17_2 ),
inference(superposition,[],[f170,f508]) ).
fof(f579,plain,
( empty(cartesian_product2(the_carrier(sK3),the_carrier(sK3)))
| in(ordered_pair(sK5,sK5),cartesian_product2(the_carrier(sK3),the_carrier(sK3)))
| spl17_2 ),
inference(resolution,[],[f563,f150]) ).
fof(f578,plain,
( ! [X0,X1] :
( ordered_pair_as_product_element(X0,cartesian_product2(the_carrier(sK3),the_carrier(sK3)),X1,ordered_pair(sK5,sK5)) = ordered_pair(X1,ordered_pair(sK5,sK5))
| ~ element(X1,X0)
| empty(cartesian_product2(the_carrier(sK3),the_carrier(sK3)))
| empty(X0) )
| spl17_2 ),
inference(resolution,[],[f563,f169]) ).
fof(f577,plain,
( ordered_pair_as_product_element(cartesian_product2(the_carrier(sK3),the_carrier(sK3)),the_carrier(sK3),ordered_pair(sK5,sK5),sK4) = ordered_pair(ordered_pair(sK5,sK5),sK4)
| empty(cartesian_product2(the_carrier(sK3),the_carrier(sK3)))
| spl17_2 ),
inference(resolution,[],[f563,f475]) ).
fof(f576,plain,
( ordered_pair_as_product_element(cartesian_product2(the_carrier(sK3),the_carrier(sK3)),the_carrier(sK3),ordered_pair(sK5,sK5),sK5) = ordered_pair(ordered_pair(sK5,sK5),sK5)
| empty(cartesian_product2(the_carrier(sK3),the_carrier(sK3)))
| spl17_2 ),
inference(resolution,[],[f563,f476]) ).
fof(f563,plain,
( element(ordered_pair(sK5,sK5),cartesian_product2(the_carrier(sK3),the_carrier(sK3)))
| spl17_2 ),
inference(subsumption_resolution,[],[f562,f206]) ).
fof(f562,plain,
( element(ordered_pair(sK5,sK5),cartesian_product2(the_carrier(sK3),the_carrier(sK3)))
| empty(the_carrier(sK3))
| spl17_2 ),
inference(subsumption_resolution,[],[f542,f122]) ).
fof(f542,plain,
( element(ordered_pair(sK5,sK5),cartesian_product2(the_carrier(sK3),the_carrier(sK3)))
| ~ element(sK5,the_carrier(sK3))
| empty(the_carrier(sK3))
| spl17_2 ),
inference(duplicate_literal_removal,[],[f541]) ).
fof(f541,plain,
( element(ordered_pair(sK5,sK5),cartesian_product2(the_carrier(sK3),the_carrier(sK3)))
| ~ element(sK5,the_carrier(sK3))
| ~ element(sK5,the_carrier(sK3))
| empty(the_carrier(sK3))
| empty(the_carrier(sK3))
| spl17_2 ),
inference(superposition,[],[f170,f516]) ).
fof(f575,plain,
( empty(cartesian_product2(the_carrier(sK3),the_carrier(sK3)))
| in(ordered_pair(sK4,sK5),cartesian_product2(the_carrier(sK3),the_carrier(sK3)))
| spl17_2 ),
inference(resolution,[],[f561,f150]) ).
fof(f574,plain,
( ! [X0,X1] :
( ordered_pair_as_product_element(X0,cartesian_product2(the_carrier(sK3),the_carrier(sK3)),X1,ordered_pair(sK4,sK5)) = ordered_pair(X1,ordered_pair(sK4,sK5))
| ~ element(X1,X0)
| empty(cartesian_product2(the_carrier(sK3),the_carrier(sK3)))
| empty(X0) )
| spl17_2 ),
inference(resolution,[],[f561,f169]) ).
fof(f573,plain,
( ordered_pair_as_product_element(cartesian_product2(the_carrier(sK3),the_carrier(sK3)),the_carrier(sK3),ordered_pair(sK4,sK5),sK4) = ordered_pair(ordered_pair(sK4,sK5),sK4)
| empty(cartesian_product2(the_carrier(sK3),the_carrier(sK3)))
| spl17_2 ),
inference(resolution,[],[f561,f475]) ).
fof(f572,plain,
( ordered_pair_as_product_element(cartesian_product2(the_carrier(sK3),the_carrier(sK3)),the_carrier(sK3),ordered_pair(sK4,sK5),sK5) = ordered_pair(ordered_pair(sK4,sK5),sK5)
| empty(cartesian_product2(the_carrier(sK3),the_carrier(sK3)))
| spl17_2 ),
inference(resolution,[],[f561,f476]) ).
fof(f561,plain,
( element(ordered_pair(sK4,sK5),cartesian_product2(the_carrier(sK3),the_carrier(sK3)))
| spl17_2 ),
inference(subsumption_resolution,[],[f560,f206]) ).
fof(f560,plain,
( element(ordered_pair(sK4,sK5),cartesian_product2(the_carrier(sK3),the_carrier(sK3)))
| empty(the_carrier(sK3))
| spl17_2 ),
inference(subsumption_resolution,[],[f559,f121]) ).
fof(f559,plain,
( element(ordered_pair(sK4,sK5),cartesian_product2(the_carrier(sK3),the_carrier(sK3)))
| ~ element(sK4,the_carrier(sK3))
| empty(the_carrier(sK3))
| spl17_2 ),
inference(subsumption_resolution,[],[f543,f122]) ).
fof(f543,plain,
( element(ordered_pair(sK4,sK5),cartesian_product2(the_carrier(sK3),the_carrier(sK3)))
| ~ element(sK5,the_carrier(sK3))
| ~ element(sK4,the_carrier(sK3))
| empty(the_carrier(sK3))
| spl17_2 ),
inference(duplicate_literal_removal,[],[f540]) ).
fof(f540,plain,
( element(ordered_pair(sK4,sK5),cartesian_product2(the_carrier(sK3),the_carrier(sK3)))
| ~ element(sK5,the_carrier(sK3))
| ~ element(sK4,the_carrier(sK3))
| empty(the_carrier(sK3))
| empty(the_carrier(sK3))
| spl17_2 ),
inference(superposition,[],[f170,f515]) ).
fof(f571,plain,
( empty(cartesian_product2(the_carrier(sK3),the_carrier(sK3)))
| in(ordered_pair(sK5,sK4),cartesian_product2(the_carrier(sK3),the_carrier(sK3)))
| spl17_2 ),
inference(resolution,[],[f554,f150]) ).
fof(f570,plain,
( ! [X0,X1] :
( ordered_pair_as_product_element(X0,cartesian_product2(the_carrier(sK3),the_carrier(sK3)),X1,ordered_pair(sK5,sK4)) = ordered_pair(X1,ordered_pair(sK5,sK4))
| ~ element(X1,X0)
| empty(cartesian_product2(the_carrier(sK3),the_carrier(sK3)))
| empty(X0) )
| spl17_2 ),
inference(resolution,[],[f554,f169]) ).
fof(f569,plain,
( ordered_pair_as_product_element(cartesian_product2(the_carrier(sK3),the_carrier(sK3)),the_carrier(sK3),ordered_pair(sK5,sK4),sK4) = ordered_pair(ordered_pair(sK5,sK4),sK4)
| empty(cartesian_product2(the_carrier(sK3),the_carrier(sK3)))
| spl17_2 ),
inference(resolution,[],[f554,f475]) ).
fof(f568,plain,
( ordered_pair_as_product_element(cartesian_product2(the_carrier(sK3),the_carrier(sK3)),the_carrier(sK3),ordered_pair(sK5,sK4),sK5) = ordered_pair(ordered_pair(sK5,sK4),sK5)
| empty(cartesian_product2(the_carrier(sK3),the_carrier(sK3)))
| spl17_2 ),
inference(resolution,[],[f554,f476]) ).
fof(f554,plain,
( element(ordered_pair(sK5,sK4),cartesian_product2(the_carrier(sK3),the_carrier(sK3)))
| spl17_2 ),
inference(subsumption_resolution,[],[f553,f206]) ).
fof(f553,plain,
( element(ordered_pair(sK5,sK4),cartesian_product2(the_carrier(sK3),the_carrier(sK3)))
| empty(the_carrier(sK3))
| spl17_2 ),
inference(subsumption_resolution,[],[f552,f122]) ).
fof(f552,plain,
( element(ordered_pair(sK5,sK4),cartesian_product2(the_carrier(sK3),the_carrier(sK3)))
| ~ element(sK5,the_carrier(sK3))
| empty(the_carrier(sK3))
| spl17_2 ),
inference(subsumption_resolution,[],[f544,f121]) ).
fof(f544,plain,
( element(ordered_pair(sK5,sK4),cartesian_product2(the_carrier(sK3),the_carrier(sK3)))
| ~ element(sK4,the_carrier(sK3))
| ~ element(sK5,the_carrier(sK3))
| empty(the_carrier(sK3))
| spl17_2 ),
inference(duplicate_literal_removal,[],[f538]) ).
fof(f538,plain,
( element(ordered_pair(sK5,sK4),cartesian_product2(the_carrier(sK3),the_carrier(sK3)))
| ~ element(sK4,the_carrier(sK3))
| ~ element(sK5,the_carrier(sK3))
| empty(the_carrier(sK3))
| empty(the_carrier(sK3))
| spl17_2 ),
inference(superposition,[],[f170,f485]) ).
fof(f566,plain,
( ! [X0,X1] :
( ordered_pair_as_product_element(X0,cartesian_product2(the_carrier(sK3),the_carrier(sK3)),X1,ordered_pair(sK4,sK4)) = ordered_pair(X1,ordered_pair(sK4,sK4))
| ~ element(X1,X0)
| empty(cartesian_product2(the_carrier(sK3),the_carrier(sK3)))
| empty(X0) )
| spl17_2 ),
inference(resolution,[],[f551,f169]) ).
fof(f565,plain,
( ordered_pair_as_product_element(cartesian_product2(the_carrier(sK3),the_carrier(sK3)),the_carrier(sK3),ordered_pair(sK4,sK4),sK4) = ordered_pair(ordered_pair(sK4,sK4),sK4)
| empty(cartesian_product2(the_carrier(sK3),the_carrier(sK3)))
| spl17_2 ),
inference(resolution,[],[f551,f475]) ).
fof(f564,plain,
( ordered_pair_as_product_element(cartesian_product2(the_carrier(sK3),the_carrier(sK3)),the_carrier(sK3),ordered_pair(sK4,sK4),sK5) = ordered_pair(ordered_pair(sK4,sK4),sK5)
| empty(cartesian_product2(the_carrier(sK3),the_carrier(sK3)))
| spl17_2 ),
inference(resolution,[],[f551,f476]) ).
fof(f548,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ element(X5,X4)
| ~ element(X2,X3)
| empty(X1)
| empty(X3)
| ordered_pair_as_product_element(X4,cartesian_product2(X3,X1),X5,ordered_pair_as_product_element(X3,X1,X2,X0)) = ordered_pair(X5,ordered_pair_as_product_element(X3,X1,X2,X0))
| ~ element(X0,X1)
| empty(X4) ),
inference(subsumption_resolution,[],[f535,f159]) ).
fof(f535,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ element(X0,X1)
| ~ element(X2,X3)
| empty(X1)
| empty(X3)
| ordered_pair_as_product_element(X4,cartesian_product2(X3,X1),X5,ordered_pair_as_product_element(X3,X1,X2,X0)) = ordered_pair(X5,ordered_pair_as_product_element(X3,X1,X2,X0))
| ~ element(X5,X4)
| empty(cartesian_product2(X3,X1))
| empty(X4) ),
inference(resolution,[],[f170,f169]) ).
fof(f547,plain,
( ! [X2,X3,X0,X1] :
( ~ element(X2,X3)
| ~ element(X0,X1)
| empty(X1)
| empty(X3)
| ordered_pair_as_product_element(cartesian_product2(X3,X1),the_carrier(sK3),ordered_pair_as_product_element(X3,X1,X2,X0),sK4) = ordered_pair(ordered_pair_as_product_element(X3,X1,X2,X0),sK4) )
| spl17_2 ),
inference(subsumption_resolution,[],[f534,f159]) ).
fof(f534,plain,
( ! [X2,X3,X0,X1] :
( ~ element(X0,X1)
| ~ element(X2,X3)
| empty(X1)
| empty(X3)
| ordered_pair_as_product_element(cartesian_product2(X3,X1),the_carrier(sK3),ordered_pair_as_product_element(X3,X1,X2,X0),sK4) = ordered_pair(ordered_pair_as_product_element(X3,X1,X2,X0),sK4)
| empty(cartesian_product2(X3,X1)) )
| spl17_2 ),
inference(resolution,[],[f170,f475]) ).
fof(f546,plain,
( ! [X2,X3,X0,X1] :
( ~ element(X2,X3)
| ~ element(X0,X1)
| empty(X1)
| empty(X3)
| ordered_pair_as_product_element(cartesian_product2(X3,X1),the_carrier(sK3),ordered_pair_as_product_element(X3,X1,X2,X0),sK5) = ordered_pair(ordered_pair_as_product_element(X3,X1,X2,X0),sK5) )
| spl17_2 ),
inference(subsumption_resolution,[],[f533,f159]) ).
fof(f533,plain,
( ! [X2,X3,X0,X1] :
( ~ element(X0,X1)
| ~ element(X2,X3)
| empty(X1)
| empty(X3)
| ordered_pair_as_product_element(cartesian_product2(X3,X1),the_carrier(sK3),ordered_pair_as_product_element(X3,X1,X2,X0),sK5) = ordered_pair(ordered_pair_as_product_element(X3,X1,X2,X0),sK5)
| empty(cartesian_product2(X3,X1)) )
| spl17_2 ),
inference(resolution,[],[f170,f476]) ).
fof(f532,plain,
( ! [X0,X1] :
( ordered_pair_as_product_element(the_carrier(X0),the_carrier(sK3),sK8(X0,X1),sK5) = ordered_pair(sK8(X0,X1),sK5)
| empty(the_carrier(X0))
| ~ sP1(X0,X1) )
| spl17_2 ),
inference(resolution,[],[f517,f225]) ).
fof(f531,plain,
( ! [X0,X1] :
( ordered_pair_as_product_element(the_carrier(X0),the_carrier(sK3),sK7(X0,X1),sK5) = ordered_pair(sK7(X0,X1),sK5)
| empty(the_carrier(X0))
| ~ sP1(X0,X1) )
| spl17_2 ),
inference(resolution,[],[f517,f224]) ).
fof(f528,plain,
( ! [X0,X1] :
( ~ sP2(X1,X0)
| ~ sP1(X0,X1)
| ordered_pair(X1,sK5) = ordered_pair_as_product_element(a_1_0_filter_1(X0),the_carrier(sK3),X1,sK5) )
| spl17_2 ),
inference(resolution,[],[f517,f152]) ).
fof(f526,plain,
( ! [X0,X1] :
( in(sK9(X1,X0),X1)
| ordered_pair_as_product_element(X0,the_carrier(sK3),sK9(X1,X0),sK5) = ordered_pair(sK9(X1,X0),sK5)
| X0 = X1 )
| spl17_2 ),
inference(resolution,[],[f517,f160]) ).
fof(f525,plain,
( ! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ordered_pair_as_product_element(X0,the_carrier(sK3),sK9(X1,X0),sK5) = ordered_pair(sK9(X1,X0),sK5) )
| spl17_2 ),
inference(resolution,[],[f517,f327]) ).
fof(f522,plain,
( ! [X0,X1] :
( in(sK9(X0,X1),X1)
| ordered_pair_as_product_element(X0,the_carrier(sK3),sK9(X0,X1),sK5) = ordered_pair(sK9(X0,X1),sK5)
| X0 = X1 )
| spl17_2 ),
inference(resolution,[],[f517,f160]) ).
fof(f521,plain,
( ! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ordered_pair_as_product_element(X0,the_carrier(sK3),sK9(X0,X1),sK5) = ordered_pair(sK9(X0,X1),sK5) )
| spl17_2 ),
inference(resolution,[],[f517,f323]) ).
fof(f520,plain,
( ! [X0] :
( ordered_pair_as_product_element(X0,the_carrier(sK3),sK6(X0),sK5) = ordered_pair(sK6(X0),sK5)
| empty(X0) )
| spl17_2 ),
inference(resolution,[],[f517,f198]) ).
fof(f512,plain,
( ! [X0,X1] :
( ~ sP1(X0,X1)
| empty(the_carrier(X0))
| ordered_pair_as_product_element(the_carrier(X0),the_carrier(sK3),sK8(X0,X1),sK5) = ordered_pair(sK8(X0,X1),sK5) )
| spl17_2 ),
inference(resolution,[],[f476,f154]) ).
fof(f511,plain,
( ! [X0,X1] :
( ~ sP1(X0,X1)
| empty(the_carrier(X0))
| ordered_pair_as_product_element(the_carrier(X0),the_carrier(sK3),sK7(X0,X1),sK5) = ordered_pair(sK7(X0,X1),sK5) )
| spl17_2 ),
inference(resolution,[],[f476,f153]) ).
fof(f508,plain,
( ordered_pair_as_product_element(sK10,the_carrier(sK3),sK6(sK10),sK4) = ordered_pair(sK6(sK10),sK4)
| spl17_2 ),
inference(resolution,[],[f482,f171]) ).
fof(f505,plain,
( ! [X0,X1] :
( empty(X1)
| empty(X0)
| ordered_pair_as_product_element(cartesian_product2(X0,X1),the_carrier(sK3),sK6(cartesian_product2(X0,X1)),sK4) = ordered_pair(sK6(cartesian_product2(X0,X1)),sK4) )
| spl17_2 ),
inference(resolution,[],[f482,f159]) ).
fof(f504,plain,
( ! [X0] : ordered_pair_as_product_element(singleton(X0),the_carrier(sK3),sK6(singleton(X0)),sK4) = ordered_pair(sK6(singleton(X0)),sK4)
| spl17_2 ),
inference(resolution,[],[f482,f126]) ).
fof(f503,plain,
( ! [X0,X1] : ordered_pair_as_product_element(ordered_pair(X0,X1),the_carrier(sK3),sK6(ordered_pair(X0,X1)),sK4) = ordered_pair(sK6(ordered_pair(X0,X1)),sK4)
| spl17_2 ),
inference(resolution,[],[f482,f233]) ).
fof(f502,plain,
( ! [X0,X1] : ordered_pair_as_product_element(unordered_pair(X0,X1),the_carrier(sK3),sK6(unordered_pair(X0,X1)),sK4) = ordered_pair(sK6(unordered_pair(X0,X1)),sK4)
| spl17_2 ),
inference(resolution,[],[f482,f145]) ).
fof(f501,plain,
( ! [X0] :
( ordered_pair_as_product_element(X0,the_carrier(sK3),sK6(X0),sK4) = ordered_pair(sK6(X0),sK4)
| empty_set = X0 )
| spl17_2 ),
inference(resolution,[],[f482,f141]) ).
fof(f500,plain,
( ! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ordered_pair_as_product_element(X0,the_carrier(sK3),sK6(X0),sK4) = ordered_pair(sK6(X0),sK4) )
| spl17_2 ),
inference(resolution,[],[f482,f162]) ).
fof(f499,plain,
( ! [X0,X1] :
( ordered_pair_as_product_element(the_carrier(X0),the_carrier(sK3),sK8(X0,X1),sK4) = ordered_pair(sK8(X0,X1),sK4)
| empty(the_carrier(X0))
| ~ sP1(X0,X1) )
| spl17_2 ),
inference(resolution,[],[f486,f225]) ).
fof(f498,plain,
( ! [X0,X1] :
( ordered_pair_as_product_element(the_carrier(X0),the_carrier(sK3),sK7(X0,X1),sK4) = ordered_pair(sK7(X0,X1),sK4)
| empty(the_carrier(X0))
| ~ sP1(X0,X1) )
| spl17_2 ),
inference(resolution,[],[f486,f224]) ).
fof(f495,plain,
( ! [X0,X1] :
( ~ sP2(X1,X0)
| ~ sP1(X0,X1)
| ordered_pair(X1,sK4) = ordered_pair_as_product_element(a_1_0_filter_1(X0),the_carrier(sK3),X1,sK4) )
| spl17_2 ),
inference(resolution,[],[f486,f152]) ).
fof(f493,plain,
( ! [X0,X1] :
( in(sK9(X1,X0),X1)
| ordered_pair_as_product_element(X0,the_carrier(sK3),sK9(X1,X0),sK4) = ordered_pair(sK9(X1,X0),sK4)
| X0 = X1 )
| spl17_2 ),
inference(resolution,[],[f486,f160]) ).
fof(f492,plain,
( ! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ordered_pair_as_product_element(X0,the_carrier(sK3),sK9(X1,X0),sK4) = ordered_pair(sK9(X1,X0),sK4) )
| spl17_2 ),
inference(resolution,[],[f486,f327]) ).
fof(f489,plain,
( ! [X0,X1] :
( in(sK9(X0,X1),X1)
| ordered_pair_as_product_element(X0,the_carrier(sK3),sK9(X0,X1),sK4) = ordered_pair(sK9(X0,X1),sK4)
| X0 = X1 )
| spl17_2 ),
inference(resolution,[],[f486,f160]) ).
fof(f488,plain,
( ! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ordered_pair_as_product_element(X0,the_carrier(sK3),sK9(X0,X1),sK4) = ordered_pair(sK9(X0,X1),sK4) )
| spl17_2 ),
inference(resolution,[],[f486,f323]) ).
fof(f487,plain,
( ! [X0] :
( ordered_pair_as_product_element(X0,the_carrier(sK3),sK6(X0),sK4) = ordered_pair(sK6(X0),sK4)
| empty(X0) )
| spl17_2 ),
inference(resolution,[],[f486,f198]) ).
fof(f472,plain,
! [X2,X3,X0,X1] :
( ~ sP1(X1,X3)
| ~ element(X2,X0)
| empty(the_carrier(X1))
| empty(X0)
| ordered_pair_as_product_element(X0,the_carrier(X1),X2,sK8(X1,X3)) = ordered_pair(X2,sK8(X1,X3)) ),
inference(resolution,[],[f169,f154]) ).
fof(f471,plain,
! [X2,X3,X0,X1] :
( ~ sP1(X1,X3)
| ~ element(X2,X0)
| empty(the_carrier(X1))
| empty(X0)
| ordered_pair_as_product_element(X0,the_carrier(X1),X2,sK7(X1,X3)) = ordered_pair(X2,sK7(X1,X3)) ),
inference(resolution,[],[f169,f153]) ).
fof(f429,plain,
! [X0,X1] :
( ~ in(the_carrier(X0),sK8(X0,X1))
| ~ sP1(X0,X1)
| empty(the_carrier(X0)) ),
inference(resolution,[],[f225,f148]) ).
fof(f427,plain,
! [X0,X1] :
( ~ in(the_carrier(X0),sK7(X0,X1))
| ~ sP1(X0,X1)
| empty(the_carrier(X0)) ),
inference(resolution,[],[f224,f148]) ).
fof(f239,plain,
! [X0,X1] :
( ~ sP1(X0,X1)
| ~ empty(a_1_0_filter_1(X0))
| ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) ),
inference(resolution,[],[f237,f158]) ).
fof(f132,plain,
! [X0] :
( ~ join_absorbing(X0)
| lattice(X0)
| ~ meet_absorbing(X0)
| ~ meet_associative(X0)
| ~ meet_commutative(X0)
| ~ join_associative(X0)
| ~ join_commutative(X0)
| empty_carrier(X0)
| ~ latt_str(X0) ),
inference(cnf_transformation,[],[f53]) ).
fof(f53,plain,
! [X0] :
( ( lattice(X0)
& ~ empty_carrier(X0) )
| ~ join_absorbing(X0)
| ~ meet_absorbing(X0)
| ~ meet_associative(X0)
| ~ meet_commutative(X0)
| ~ join_associative(X0)
| ~ join_commutative(X0)
| empty_carrier(X0)
| ~ latt_str(X0) ),
inference(flattening,[],[f52]) ).
fof(f52,plain,
! [X0] :
( ( lattice(X0)
& ~ empty_carrier(X0) )
| ~ join_absorbing(X0)
| ~ meet_absorbing(X0)
| ~ meet_associative(X0)
| ~ meet_commutative(X0)
| ~ join_associative(X0)
| ~ join_commutative(X0)
| empty_carrier(X0)
| ~ latt_str(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0] :
( latt_str(X0)
=> ( ( join_absorbing(X0)
& meet_absorbing(X0)
& meet_associative(X0)
& meet_commutative(X0)
& join_associative(X0)
& join_commutative(X0)
& ~ empty_carrier(X0) )
=> ( lattice(X0)
& ~ empty_carrier(X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_lattices) ).
fof(f225,plain,
! [X0,X1] :
( in(sK8(X0,X1),the_carrier(X0))
| empty(the_carrier(X0))
| ~ sP1(X0,X1) ),
inference(resolution,[],[f154,f150]) ).
fof(f224,plain,
! [X0,X1] :
( in(sK7(X0,X1),the_carrier(X0))
| empty(the_carrier(X0))
| ~ sP1(X0,X1) ),
inference(resolution,[],[f153,f150]) ).
fof(f419,plain,
! [X0,X1] :
( ~ in(X1,sK9(X0,X1))
| ~ empty(X0)
| X0 = X1 ),
inference(resolution,[],[f327,f148]) ).
fof(f410,plain,
! [X0,X1] :
( ~ in(X0,sK9(X0,X1))
| ~ empty(X1)
| X0 = X1 ),
inference(resolution,[],[f323,f148]) ).
fof(f422,plain,
! [X0,X1] :
( ~ sP2(sK9(X0,a_1_0_filter_1(X1)),X1)
| ~ empty(X0)
| sP1(X1,sK9(X0,a_1_0_filter_1(X1)))
| a_1_0_filter_1(X1) = X0 ),
inference(resolution,[],[f327,f151]) ).
fof(f327,plain,
! [X0,X1] :
( in(sK9(X0,X1),X1)
| X0 = X1
| ~ empty(X0) ),
inference(resolution,[],[f160,f163]) ).
fof(f413,plain,
! [X0,X1] :
( ~ sP2(sK9(a_1_0_filter_1(X0),X1),X0)
| ~ empty(X1)
| sP1(X0,sK9(a_1_0_filter_1(X0),X1))
| a_1_0_filter_1(X0) = X1 ),
inference(resolution,[],[f323,f151]) ).
fof(f323,plain,
! [X0,X1] :
( in(sK9(X0,X1),X0)
| X0 = X1
| ~ empty(X1) ),
inference(resolution,[],[f160,f163]) ).
fof(f369,plain,
! [X0,X1] :
( ~ sP2(sK9(X0,a_1_0_filter_1(X1)),X1)
| ~ in(sK9(X0,a_1_0_filter_1(X1)),X0)
| ~ sP1(X1,sK9(X0,a_1_0_filter_1(X1)))
| a_1_0_filter_1(X1) = X0 ),
inference(resolution,[],[f161,f152]) ).
fof(f161,plain,
! [X0,X1] :
( ~ in(sK9(X0,X1),X1)
| X0 = X1
| ~ in(sK9(X0,X1),X0) ),
inference(cnf_transformation,[],[f102]) ).
fof(f102,plain,
! [X0,X1] :
( X0 = X1
| ( ( ~ in(sK9(X0,X1),X1)
| ~ in(sK9(X0,X1),X0) )
& ( in(sK9(X0,X1),X1)
| in(sK9(X0,X1),X0) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9])],[f100,f101]) ).
fof(f101,plain,
! [X0,X1] :
( ? [X2] :
( ( ~ in(X2,X1)
| ~ in(X2,X0) )
& ( in(X2,X1)
| in(X2,X0) ) )
=> ( ( ~ in(sK9(X0,X1),X1)
| ~ in(sK9(X0,X1),X0) )
& ( in(sK9(X0,X1),X1)
| in(sK9(X0,X1),X0) ) ) ),
introduced(choice_axiom,[]) ).
fof(f100,plain,
! [X0,X1] :
( X0 = X1
| ? [X2] :
( ( ~ in(X2,X1)
| ~ in(X2,X0) )
& ( in(X2,X1)
| in(X2,X0) ) ) ),
inference(nnf_transformation,[],[f69]) ).
fof(f69,plain,
! [X0,X1] :
( X0 = X1
| ? [X2] :
( in(X2,X0)
<~> in(X2,X1) ) ),
inference(ennf_transformation,[],[f39]) ).
fof(f39,axiom,
! [X0,X1] :
( ! [X2] :
( in(X2,X0)
<=> in(X2,X1) )
=> X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_tarski) ).
fof(f319,plain,
( sP1(sK3,sK6(relation_of_lattice(sK3)))
| ~ sP2(sK6(relation_of_lattice(sK3)),sK3)
| empty(relation_of_lattice(sK3)) ),
inference(resolution,[],[f285,f198]) ).
fof(f329,plain,
! [X0,X1] :
( ~ sP2(sK9(a_1_0_filter_1(X0),X1),X0)
| a_1_0_filter_1(X0) = X1
| sP1(X0,sK9(a_1_0_filter_1(X0),X1))
| in(sK9(a_1_0_filter_1(X0),X1),X1) ),
inference(resolution,[],[f160,f151]) ).
fof(f328,plain,
! [X0] :
( in(sK9(relation_of_lattice(sK3),X0),X0)
| relation_of_lattice(sK3) = X0
| sP1(sK3,sK9(relation_of_lattice(sK3),X0))
| ~ sP2(sK9(relation_of_lattice(sK3),X0),sK3) ),
inference(resolution,[],[f160,f285]) ).
fof(f326,plain,
! [X0,X1] :
( ~ in(X0,sK9(X0,X1))
| X0 = X1
| in(sK9(X0,X1),X1) ),
inference(resolution,[],[f160,f148]) ).
fof(f325,plain,
! [X0,X1] :
( ~ sP2(sK9(X0,a_1_0_filter_1(X1)),X1)
| a_1_0_filter_1(X1) = X0
| sP1(X1,sK9(X0,a_1_0_filter_1(X1)))
| in(sK9(X0,a_1_0_filter_1(X1)),X0) ),
inference(resolution,[],[f160,f151]) ).
fof(f324,plain,
! [X0] :
( in(sK9(X0,relation_of_lattice(sK3)),X0)
| relation_of_lattice(sK3) = X0
| sP1(sK3,sK9(X0,relation_of_lattice(sK3)))
| ~ sP2(sK9(X0,relation_of_lattice(sK3)),sK3) ),
inference(resolution,[],[f160,f285]) ).
fof(f322,plain,
! [X0,X1] :
( ~ in(X1,sK9(X0,X1))
| X0 = X1
| in(sK9(X0,X1),X0) ),
inference(resolution,[],[f160,f148]) ).
fof(f160,plain,
! [X0,X1] :
( in(sK9(X0,X1),X1)
| in(sK9(X0,X1),X0)
| X0 = X1 ),
inference(cnf_transformation,[],[f102]) ).
fof(f288,plain,
! [X0] :
( ~ sP1(sK3,X0)
| ~ sP2(X0,sK3)
| ~ empty(relation_of_lattice(sK3)) ),
inference(resolution,[],[f284,f163]) ).
fof(f292,plain,
( ~ sP1(sK3,relation_of_lattice(sK3))
| ~ sP2(relation_of_lattice(sK3),sK3) ),
inference(duplicate_literal_removal,[],[f289]) ).
fof(f289,plain,
( ~ sP1(sK3,relation_of_lattice(sK3))
| ~ sP2(relation_of_lattice(sK3),sK3)
| ~ sP2(relation_of_lattice(sK3),sK3)
| ~ sP1(sK3,relation_of_lattice(sK3)) ),
inference(resolution,[],[f284,f283]) ).
fof(f290,plain,
! [X0] :
( ~ sP1(sK3,a_1_0_filter_1(X0))
| ~ sP2(a_1_0_filter_1(X0),sK3)
| ~ sP2(relation_of_lattice(sK3),X0)
| ~ sP1(X0,relation_of_lattice(sK3)) ),
inference(resolution,[],[f284,f236]) ).
fof(f286,plain,
! [X0] :
( ~ sP2(a_1_0_filter_1(X0),sK3)
| ~ sP1(sK3,a_1_0_filter_1(X0))
| ~ sP1(X0,relation_of_lattice(sK3))
| ~ sP2(relation_of_lattice(sK3),X0) ),
inference(resolution,[],[f283,f152]) ).
fof(f283,plain,
! [X0] :
( ~ in(relation_of_lattice(sK3),X0)
| ~ sP2(X0,sK3)
| ~ sP1(sK3,X0) ),
inference(superposition,[],[f236,f282]) ).
fof(f279,plain,
! [X0,X1] : unordered_pair(singleton(singleton(X0)),ordered_pair(X0,X1)) = ordered_pair(singleton(X0),unordered_pair(X1,X0)),
inference(superposition,[],[f229,f246]) ).
fof(f278,plain,
! [X0,X1] : ordered_pair(unordered_pair(X1,X0),singleton(X0)) = unordered_pair(ordered_pair(X0,X1),singleton(unordered_pair(X1,X0))),
inference(superposition,[],[f226,f246]) ).
fof(f277,plain,
! [X0,X1] : unordered_pair(ordered_pair(X0,X1),singleton(singleton(X0))) = ordered_pair(singleton(X0),unordered_pair(X1,X0)),
inference(superposition,[],[f147,f246]) ).
fof(f275,plain,
! [X0,X1] : ordered_pair(unordered_pair(X1,X0),singleton(X0)) = unordered_pair(singleton(unordered_pair(X1,X0)),ordered_pair(X0,X1)),
inference(superposition,[],[f246,f246]) ).
fof(f274,plain,
! [X0,X1] : ordered_pair(unordered_pair(X0,X1),singleton(X0)) = unordered_pair(singleton(unordered_pair(X0,X1)),ordered_pair(X0,X1)),
inference(superposition,[],[f246,f229]) ).
fof(f273,plain,
! [X0,X1] : ordered_pair(singleton(X1),unordered_pair(X0,X1)) = unordered_pair(singleton(singleton(X1)),ordered_pair(X1,X0)),
inference(superposition,[],[f246,f226]) ).
fof(f272,plain,
! [X0,X1] : ordered_pair(singleton(X0),unordered_pair(X0,X1)) = unordered_pair(singleton(singleton(X0)),ordered_pair(X0,X1)),
inference(superposition,[],[f246,f147]) ).
fof(f246,plain,
! [X0,X1] : ordered_pair(X1,X0) = unordered_pair(singleton(X1),unordered_pair(X0,X1)),
inference(superposition,[],[f226,f146]) ).
fof(f269,plain,
! [X0,X1] :
( ~ sP2(a_1_0_filter_1(X1),X0)
| ~ sP1(X1,a_1_0_filter_1(X0))
| ~ sP1(X0,a_1_0_filter_1(X1))
| ~ sP2(a_1_0_filter_1(X0),X1) ),
inference(resolution,[],[f236,f152]) ).
fof(f236,plain,
! [X0,X1] :
( ~ in(a_1_0_filter_1(X0),X1)
| ~ sP2(X1,X0)
| ~ sP1(X0,X1) ),
inference(resolution,[],[f152,f148]) ).
fof(f267,plain,
( below_refl(sK3,sK4,sK5)
| ~ spl17_4 ),
inference(avatar_component_clause,[],[f265]) ).
fof(f123,plain,
( below_refl(sK3,sK4,sK5)
| in(ordered_pair_as_product_element(the_carrier(sK3),the_carrier(sK3),sK4,sK5),relation_of_lattice(sK3)) ),
inference(cnf_transformation,[],[f91]) ).
fof(f258,plain,
! [X0,X1] : ordered_pair(singleton(X0),unordered_pair(X0,X1)) = unordered_pair(ordered_pair(X0,X1),singleton(singleton(X0))),
inference(superposition,[],[f147,f229]) ).
fof(f257,plain,
! [X0,X1] : ordered_pair(unordered_pair(X0,X1),singleton(X0)) = unordered_pair(ordered_pair(X0,X1),singleton(unordered_pair(X0,X1))),
inference(superposition,[],[f226,f229]) ).
fof(f256,plain,
! [X0,X1] : ordered_pair(singleton(X0),unordered_pair(X0,X1)) = unordered_pair(singleton(singleton(X0)),ordered_pair(X0,X1)),
inference(superposition,[],[f229,f229]) ).
fof(f255,plain,
! [X0,X1] : ordered_pair(unordered_pair(X0,X1),singleton(X1)) = unordered_pair(singleton(unordered_pair(X0,X1)),ordered_pair(X1,X0)),
inference(superposition,[],[f229,f226]) ).
fof(f254,plain,
! [X0,X1] : ordered_pair(unordered_pair(X0,X1),singleton(X0)) = unordered_pair(singleton(unordered_pair(X0,X1)),ordered_pair(X0,X1)),
inference(superposition,[],[f229,f147]) ).
fof(f253,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(singleton(X0),unordered_pair(X1,X0)),
inference(superposition,[],[f229,f146]) ).
fof(f252,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(singleton(X0),unordered_pair(X1,X0)),
inference(superposition,[],[f229,f146]) ).
fof(f229,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(singleton(X0),unordered_pair(X0,X1)),
inference(superposition,[],[f147,f146]) ).
fof(f250,plain,
! [X0,X1] : ordered_pair(X1,X0) = unordered_pair(singleton(X1),unordered_pair(X0,X1)),
inference(superposition,[],[f146,f226]) ).
fof(f249,plain,
! [X0,X1] : ordered_pair(X1,X0) = unordered_pair(singleton(X1),unordered_pair(X0,X1)),
inference(superposition,[],[f146,f226]) ).
fof(f248,plain,
! [X0,X1] : ordered_pair(unordered_pair(X0,X1),singleton(X1)) = unordered_pair(ordered_pair(X1,X0),singleton(unordered_pair(X0,X1))),
inference(superposition,[],[f147,f226]) ).
fof(f247,plain,
! [X0,X1] : ordered_pair(X1,X0) = unordered_pair(singleton(X1),unordered_pair(X0,X1)),
inference(superposition,[],[f226,f146]) ).
fof(f245,plain,
! [X0,X1] : ordered_pair(singleton(X1),unordered_pair(X0,X1)) = unordered_pair(ordered_pair(X1,X0),singleton(singleton(X1))),
inference(superposition,[],[f226,f226]) ).
fof(f244,plain,
! [X0,X1] : ordered_pair(singleton(X0),unordered_pair(X0,X1)) = unordered_pair(ordered_pair(X0,X1),singleton(singleton(X0))),
inference(superposition,[],[f226,f147]) ).
fof(f226,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X1,X0),singleton(X0)),
inference(superposition,[],[f147,f146]) ).
fof(f237,plain,
! [X0,X1] :
( ~ sP2(X1,X0)
| ~ sP1(X0,X1)
| ~ empty(a_1_0_filter_1(X0)) ),
inference(resolution,[],[f152,f163]) ).
fof(f233,plain,
! [X0,X1] : ~ empty(ordered_pair(X0,X1)),
inference(superposition,[],[f145,f147]) ).
fof(f234,plain,
! [X0] :
( ~ sP2(sK6(a_1_0_filter_1(X0)),X0)
| sP1(X0,sK6(a_1_0_filter_1(X0)))
| empty(a_1_0_filter_1(X0)) ),
inference(resolution,[],[f151,f198]) ).
fof(f232,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(singleton(X0),unordered_pair(X0,X1)),
inference(superposition,[],[f146,f147]) ).
fof(f231,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(singleton(X0),unordered_pair(X0,X1)),
inference(superposition,[],[f146,f147]) ).
fof(f230,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(singleton(X0),unordered_pair(X0,X1)),
inference(superposition,[],[f147,f146]) ).
fof(f228,plain,
! [X0,X1] : ordered_pair(unordered_pair(X0,X1),singleton(X0)) = unordered_pair(ordered_pair(X0,X1),singleton(unordered_pair(X0,X1))),
inference(superposition,[],[f147,f147]) ).
fof(f227,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X1,X0),singleton(X0)),
inference(superposition,[],[f147,f146]) ).
fof(f147,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f5]) ).
fof(f5,axiom,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_tarski) ).
fof(f195,plain,
! [X0] :
( join_commutative(X0)
| empty_carrier(X0)
| ~ latt_str(X0)
| ~ lattice(X0) ),
inference(resolution,[],[f140,f134]) ).
fof(f194,plain,
! [X0] :
( join_associative(X0)
| empty_carrier(X0)
| ~ latt_str(X0)
| ~ lattice(X0) ),
inference(resolution,[],[f140,f135]) ).
fof(f192,plain,
! [X0] :
( meet_associative(X0)
| empty_carrier(X0)
| ~ latt_str(X0)
| ~ lattice(X0) ),
inference(resolution,[],[f140,f137]) ).
fof(f222,plain,
! [X0] :
( ~ in(X0,sK6(X0))
| empty(X0) ),
inference(resolution,[],[f198,f148]) ).
fof(f220,plain,
( ~ in(the_carrier(sK3),sK5)
| spl17_2 ),
inference(resolution,[],[f219,f148]) ).
fof(f219,plain,
( in(sK5,the_carrier(sK3))
| spl17_2 ),
inference(subsumption_resolution,[],[f197,f206]) ).
fof(f196,plain,
( empty(the_carrier(sK3))
| in(sK4,the_carrier(sK3)) ),
inference(resolution,[],[f150,f121]) ).
fof(f197,plain,
( empty(the_carrier(sK3))
| in(sK5,the_carrier(sK3)) ),
inference(resolution,[],[f150,f122]) ).
fof(f162,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(cnf_transformation,[],[f70]) ).
fof(f70,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(ennf_transformation,[],[f45]) ).
fof(f45,axiom,
! [X0,X1] :
~ ( empty(X1)
& X0 != X1
& empty(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_boole) ).
fof(f146,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f183,plain,
empty_set = sK15,
inference(resolution,[],[f141,f176]) ).
fof(f181,plain,
! [X0] :
( one_sorted_str(X0)
| ~ latt_str(X0) ),
inference(resolution,[],[f130,f128]) ).
fof(f145,plain,
! [X0,X1] : ~ empty(unordered_pair(X0,X1)),
inference(cnf_transformation,[],[f28]) ).
fof(f28,axiom,
! [X0,X1] : ~ empty(unordered_pair(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_subset_1) ).
fof(f137,plain,
! [X0] :
( ~ sP0(X0)
| meet_associative(X0) ),
inference(cnf_transformation,[],[f92]) ).
fof(f135,plain,
! [X0] :
( ~ sP0(X0)
| join_associative(X0) ),
inference(cnf_transformation,[],[f92]) ).
fof(f134,plain,
! [X0] :
( ~ sP0(X0)
| join_commutative(X0) ),
inference(cnf_transformation,[],[f92]) ).
fof(f130,plain,
! [X0] :
( join_semilatt_str(X0)
| ~ latt_str(X0) ),
inference(cnf_transformation,[],[f51]) ).
fof(f51,plain,
! [X0] :
( ( join_semilatt_str(X0)
& meet_semilatt_str(X0) )
| ~ latt_str(X0) ),
inference(ennf_transformation,[],[f17]) ).
fof(f17,axiom,
! [X0] :
( latt_str(X0)
=> ( join_semilatt_str(X0)
& meet_semilatt_str(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l3_lattices) ).
fof(f129,plain,
! [X0] :
( meet_semilatt_str(X0)
| ~ latt_str(X0) ),
inference(cnf_transformation,[],[f51]) ).
fof(f126,plain,
! [X0] : ~ empty(singleton(X0)),
inference(cnf_transformation,[],[f27]) ).
fof(f27,axiom,
! [X0] : ~ empty(singleton(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_subset_1) ).
fof(f176,plain,
empty(sK15),
inference(cnf_transformation,[],[f115]) ).
fof(f115,plain,
empty(sK15),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK15])],[f31,f114]) ).
fof(f114,plain,
( ? [X0] : empty(X0)
=> empty(sK15) ),
introduced(choice_axiom,[]) ).
fof(f31,axiom,
? [X0] : empty(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
fof(f174,plain,
latt_str(sK13),
inference(cnf_transformation,[],[f111]) ).
fof(f111,plain,
latt_str(sK13),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK13])],[f23,f110]) ).
fof(f110,plain,
( ? [X0] : latt_str(X0)
=> latt_str(sK13) ),
introduced(choice_axiom,[]) ).
fof(f23,axiom,
? [X0] : latt_str(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l3_lattices) ).
fof(f125,plain,
empty(empty_set),
inference(cnf_transformation,[],[f26]) ).
fof(f26,axiom,
empty(empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
fof(f124,plain,
( ~ below_refl(sK3,sK4,sK5)
| ~ in(ordered_pair_as_product_element(the_carrier(sK3),the_carrier(sK3),sK4,sK5),relation_of_lattice(sK3)) ),
inference(cnf_transformation,[],[f91]) ).
fof(f667,plain,
( ~ sP1(sK3,ordered_pair(sK4,sK5))
| ~ sP2(ordered_pair(sK4,sK5),sK3)
| spl17_2
| ~ spl17_4 ),
inference(resolution,[],[f641,f284]) ).
fof(f639,plain,
( ~ spl17_3
| ~ spl17_7
| ~ spl17_9
| spl17_10 ),
inference(avatar_contradiction_clause,[],[f638]) ).
fof(f638,plain,
( $false
| ~ spl17_3
| ~ spl17_7
| ~ spl17_9
| spl17_10 ),
inference(subsumption_resolution,[],[f637,f390]) ).
fof(f390,plain,
( ! [X0] : ~ in(X0,empty_set)
| ~ spl17_7
| ~ spl17_9
| spl17_10 ),
inference(subsumption_resolution,[],[f389,f118]) ).
fof(f389,plain,
( ! [X0] :
( ~ in(X0,empty_set)
| empty_carrier(sK3) )
| ~ spl17_7
| ~ spl17_9
| spl17_10 ),
inference(subsumption_resolution,[],[f388,f119]) ).
fof(f388,plain,
( ! [X0] :
( ~ in(X0,empty_set)
| ~ lattice(sK3)
| empty_carrier(sK3) )
| ~ spl17_7
| ~ spl17_9
| spl17_10 ),
inference(subsumption_resolution,[],[f384,f120]) ).
fof(f384,plain,
( ! [X0] :
( ~ in(X0,empty_set)
| ~ latt_str(sK3)
| ~ lattice(sK3)
| empty_carrier(sK3) )
| ~ spl17_7
| ~ spl17_9
| spl17_10 ),
inference(resolution,[],[f357,f158]) ).
fof(f357,plain,
( ! [X0] :
( ~ sP2(X0,sK3)
| ~ in(X0,empty_set) )
| ~ spl17_7
| ~ spl17_9
| spl17_10 ),
inference(global_subsumption,[],[f124,f132,f179,f155,f161,f164,f169,f170,f118,f119,f120,f125,f171,f172,f173,f174,f175,f176,f177,f178,f126,f121,f122,f127,f128,f180,f129,f130,f134,f135,f136,f137,f138,f139,f144,f145,f181,f141,f183,f163,f148,f149,f143,f146,f162,f140,f150,f197,f196,f198,f159,f222,f190,f191,f192,f193,f194,f195,f153,f224,f154,f225,f158,f147,f227,f228,f230,f231,f232,f151,f234,f233,f152,f237,f239,f167,f168,f226,f244,f245,f247,f248,f249,f250,f229,f252,f253,f254,f255,f256,f257,f258,f123,f236,f269,f246,f272,f273,f274,f275,f277,f278,f279,f142,f156,f282,f283,f286,f284,f290,f292,f288,f285,f160,f322,f323,f324,f325,f326,f327,f328,f329,f337,f319,f345,f333,f312,f346,f347,f349,f355,f350,f356,f351]) ).
fof(f351,plain,
( ! [X0] :
( ~ in(X0,empty_set)
| sP1(sK3,X0)
| ~ sP2(X0,sK3) )
| ~ spl17_7 ),
inference(superposition,[],[f285,f347]) ).
fof(f356,plain,
( ! [X0] :
( ~ sP1(sK3,X0)
| ~ sP2(X0,sK3) )
| ~ spl17_7
| ~ spl17_9
| spl17_10 ),
inference(global_subsumption,[],[f350,f124,f132,f179,f155,f161,f164,f169,f170,f118,f119,f120,f125,f171,f172,f173,f174,f175,f176,f177,f178,f126,f121,f122,f127,f128,f180,f129,f130,f134,f135,f136,f137,f138,f139,f144,f145,f181,f141,f183,f163,f148,f149,f143,f146,f162,f140,f150,f197,f196,f198,f159,f222,f190,f191,f192,f193,f194,f195,f153,f224,f154,f225,f158,f147,f227,f228,f230,f231,f232,f151,f234,f233,f152,f237,f239,f167,f168,f226,f244,f245,f247,f248,f249,f250,f229,f252,f253,f254,f255,f256,f257,f258,f123,f236,f269,f246,f272,f273,f274,f275,f277,f278,f279,f142,f156,f282,f283,f286,f284,f290,f292,f288,f285,f160,f322,f323,f324,f325,f326,f327,f328,f329,f337,f319,f345,f333]) ).
fof(f350,plain,
( ! [X0] :
( in(X0,empty_set)
| ~ sP1(sK3,X0)
| ~ sP2(X0,sK3) )
| ~ spl17_7 ),
inference(superposition,[],[f284,f347]) ).
fof(f355,plain,
( ! [X0] :
( ~ sP2(X0,sK3)
| ~ sP1(sK3,X0) )
| ~ spl17_7
| ~ spl17_9
| spl17_10 ),
inference(global_subsumption,[],[f349,f124,f132,f179,f155,f161,f164,f169,f170,f118,f119,f120,f125,f171,f172,f173,f174,f175,f176,f177,f178,f126,f121,f122,f127,f128,f180,f129,f130,f134,f135,f136,f137,f138,f139,f144,f145,f181,f141,f183,f163,f148,f149,f143,f146,f162,f140,f150,f197,f196,f198,f159,f222,f190,f191,f192,f193,f194,f195,f153,f224,f154,f225,f158,f147,f227,f228,f230,f231,f232,f151,f234,f233,f152,f237,f239,f167,f168,f226,f244,f245,f247,f248,f249,f250,f229,f252,f253,f254,f255,f256,f257,f258,f123,f236,f269,f246,f272,f273,f274,f275,f277,f278,f279,f142,f156,f282,f283,f286,f284,f290,f292,f288,f285,f160,f322,f323,f324,f325,f326,f327,f328,f329,f337,f319,f345,f333]) ).
fof(f349,plain,
( ! [X0] :
( ~ in(empty_set,X0)
| ~ sP2(X0,sK3)
| ~ sP1(sK3,X0) )
| ~ spl17_7 ),
inference(superposition,[],[f283,f347]) ).
fof(f347,plain,
( empty_set = relation_of_lattice(sK3)
| ~ spl17_7 ),
inference(resolution,[],[f312,f141]) ).
fof(f346,plain,
( ! [X0] :
( relation_of_lattice(sK3) = X0
| ~ empty(X0) )
| ~ spl17_7 ),
inference(resolution,[],[f312,f162]) ).
fof(f312,plain,
( empty(relation_of_lattice(sK3))
| ~ spl17_7 ),
inference(avatar_component_clause,[],[f311]) ).
fof(f333,plain,
( sP2(sK6(relation_of_lattice(sK3)),sK3)
| ~ spl17_9 ),
inference(avatar_component_clause,[],[f332]) ).
fof(f332,plain,
( spl17_9
<=> sP2(sK6(relation_of_lattice(sK3)),sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_9])]) ).
fof(f345,plain,
( ~ sP2(sK6(relation_of_lattice(sK3)),sK3)
| empty(relation_of_lattice(sK3))
| spl17_10 ),
inference(global_subsumption,[],[f124,f132,f179,f155,f161,f164,f169,f170,f118,f119,f120,f125,f171,f172,f173,f174,f175,f176,f177,f178,f126,f121,f122,f127,f128,f180,f129,f130,f134,f135,f136,f137,f138,f139,f144,f145,f181,f141,f183,f163,f148,f149,f143,f146,f162,f140,f150,f197,f196,f198,f159,f222,f190,f191,f192,f193,f194,f195,f153,f224,f154,f225,f158,f147,f227,f228,f230,f231,f232,f151,f234,f233,f152,f237,f239,f167,f168,f226,f244,f245,f247,f248,f249,f250,f229,f252,f253,f254,f255,f256,f257,f258,f123,f236,f269,f246,f272,f273,f274,f275,f277,f278,f279,f142,f156,f282,f283,f286,f284,f290,f292,f288,f285,f160,f322,f323,f324,f325,f326,f327,f328,f329,f337,f319]) ).
fof(f337,plain,
( ~ sP1(sK3,sK6(relation_of_lattice(sK3)))
| spl17_10 ),
inference(avatar_component_clause,[],[f336]) ).
fof(f637,plain,
( in(ordered_pair_as_product_element(the_carrier(sK3),the_carrier(sK3),sK4,sK5),empty_set)
| ~ spl17_3
| ~ spl17_7 ),
inference(forward_demodulation,[],[f263,f347]) ).
fof(f631,plain,
( spl17_2
| ~ spl17_4
| ~ spl17_8 ),
inference(avatar_contradiction_clause,[],[f630]) ).
fof(f630,plain,
( $false
| spl17_2
| ~ spl17_4
| ~ spl17_8 ),
inference(subsumption_resolution,[],[f629,f121]) ).
fof(f629,plain,
( ~ element(sK4,the_carrier(sK3))
| spl17_2
| ~ spl17_4
| ~ spl17_8 ),
inference(subsumption_resolution,[],[f628,f122]) ).
fof(f628,plain,
( ~ element(sK5,the_carrier(sK3))
| ~ element(sK4,the_carrier(sK3))
| spl17_2
| ~ spl17_4
| ~ spl17_8 ),
inference(subsumption_resolution,[],[f627,f267]) ).
fof(f627,plain,
( ~ below_refl(sK3,sK4,sK5)
| ~ element(sK5,the_carrier(sK3))
| ~ element(sK4,the_carrier(sK3))
| spl17_2
| ~ spl17_8 ),
inference(subsumption_resolution,[],[f618,f382]) ).
fof(f382,plain,
( ! [X0] : ~ sP1(sK3,X0)
| ~ spl17_8 ),
inference(subsumption_resolution,[],[f381,f118]) ).
fof(f381,plain,
( ! [X0] :
( ~ sP1(sK3,X0)
| empty_carrier(sK3) )
| ~ spl17_8 ),
inference(subsumption_resolution,[],[f380,f119]) ).
fof(f380,plain,
( ! [X0] :
( ~ sP1(sK3,X0)
| ~ lattice(sK3)
| empty_carrier(sK3) )
| ~ spl17_8 ),
inference(subsumption_resolution,[],[f376,f120]) ).
fof(f376,plain,
( ! [X0] :
( ~ sP1(sK3,X0)
| ~ latt_str(sK3)
| ~ lattice(sK3)
| empty_carrier(sK3) )
| ~ spl17_8 ),
inference(resolution,[],[f316,f158]) ).
fof(f316,plain,
( ! [X0] :
( ~ sP2(X0,sK3)
| ~ sP1(sK3,X0) )
| ~ spl17_8 ),
inference(avatar_component_clause,[],[f315]) ).
fof(f315,plain,
( spl17_8
<=> ! [X0] :
( ~ sP1(sK3,X0)
| ~ sP2(X0,sK3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_8])]) ).
fof(f610,plain,
( spl17_11
| spl17_12
| spl17_2 ),
inference(avatar_split_clause,[],[f583,f205,f607,f603]) ).
fof(f603,plain,
( spl17_11
<=> in(ordered_pair(sK6(sK10),sK4),cartesian_product2(sK10,the_carrier(sK3))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_11])]) ).
fof(f607,plain,
( spl17_12
<=> empty(cartesian_product2(sK10,the_carrier(sK3))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_12])]) ).
fof(f344,plain,
spl17_9,
inference(avatar_contradiction_clause,[],[f343]) ).
fof(f343,plain,
( $false
| spl17_9 ),
inference(subsumption_resolution,[],[f342,f118]) ).
fof(f342,plain,
( empty_carrier(sK3)
| spl17_9 ),
inference(subsumption_resolution,[],[f341,f119]) ).
fof(f341,plain,
( ~ lattice(sK3)
| empty_carrier(sK3)
| spl17_9 ),
inference(subsumption_resolution,[],[f340,f120]) ).
fof(f340,plain,
( ~ latt_str(sK3)
| ~ lattice(sK3)
| empty_carrier(sK3)
| spl17_9 ),
inference(resolution,[],[f334,f158]) ).
fof(f334,plain,
( ~ sP2(sK6(relation_of_lattice(sK3)),sK3)
| spl17_9 ),
inference(avatar_component_clause,[],[f332]) ).
fof(f339,plain,
( ~ spl17_9
| spl17_10
| spl17_7 ),
inference(avatar_split_clause,[],[f321,f311,f336,f332]) ).
fof(f321,plain,
( sP1(sK3,sK6(relation_of_lattice(sK3)))
| ~ sP2(sK6(relation_of_lattice(sK3)),sK3)
| spl17_7 ),
inference(subsumption_resolution,[],[f319,f313]) ).
fof(f317,plain,
( ~ spl17_7
| spl17_8 ),
inference(avatar_split_clause,[],[f288,f315,f311]) ).
fof(f306,plain,
spl17_5,
inference(avatar_contradiction_clause,[],[f305]) ).
fof(f305,plain,
( $false
| spl17_5 ),
inference(subsumption_resolution,[],[f304,f118]) ).
fof(f304,plain,
( empty_carrier(sK3)
| spl17_5 ),
inference(subsumption_resolution,[],[f303,f119]) ).
fof(f303,plain,
( ~ lattice(sK3)
| empty_carrier(sK3)
| spl17_5 ),
inference(subsumption_resolution,[],[f302,f120]) ).
fof(f302,plain,
( ~ latt_str(sK3)
| ~ lattice(sK3)
| empty_carrier(sK3)
| spl17_5 ),
inference(resolution,[],[f296,f158]) ).
fof(f296,plain,
( ~ sP2(relation_of_lattice(sK3),sK3)
| spl17_5 ),
inference(avatar_component_clause,[],[f294]) ).
fof(f294,plain,
( spl17_5
<=> sP2(relation_of_lattice(sK3),sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_5])]) ).
fof(f301,plain,
( ~ spl17_5
| ~ spl17_6 ),
inference(avatar_split_clause,[],[f292,f298,f294]) ).
fof(f298,plain,
( spl17_6
<=> sP1(sK3,relation_of_lattice(sK3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_6])]) ).
fof(f268,plain,
( spl17_3
| spl17_4 ),
inference(avatar_split_clause,[],[f123,f265,f261]) ).
fof(f216,plain,
~ spl17_2,
inference(avatar_contradiction_clause,[],[f215]) ).
fof(f215,plain,
( $false
| ~ spl17_2 ),
inference(subsumption_resolution,[],[f213,f120]) ).
fof(f213,plain,
( ~ latt_str(sK3)
| ~ spl17_2 ),
inference(resolution,[],[f212,f181]) ).
fof(f212,plain,
( ~ one_sorted_str(sK3)
| ~ spl17_2 ),
inference(subsumption_resolution,[],[f209,f118]) ).
fof(f209,plain,
( ~ one_sorted_str(sK3)
| empty_carrier(sK3)
| ~ spl17_2 ),
inference(resolution,[],[f207,f143]) ).
fof(f207,plain,
( empty(the_carrier(sK3))
| ~ spl17_2 ),
inference(avatar_component_clause,[],[f205]) ).
fof(f208,plain,
( spl17_1
| spl17_2 ),
inference(avatar_split_clause,[],[f196,f205,f201]) ).
fof(f201,plain,
( spl17_1
<=> in(sK4,the_carrier(sK3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1])]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SEU342+1 : TPTP v8.2.0. Released v3.3.0.
% 0.07/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.36 % Computer : n006.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Sun May 19 17:40:38 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.14/0.36 % (4888)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.38 % (4891)WARNING: value z3 for option sas not known
% 0.14/0.38 % (4889)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.38 % (4890)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.38 % (4892)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.38 % (4891)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)
% 0.14/0.38 % (4893)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)
% 0.14/0.38 % (4894)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)
% 0.14/0.38 % (4895)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)
% 0.14/0.38 TRYING [1]
% 0.14/0.38 TRYING [2]
% 0.14/0.39 TRYING [3]
% 0.14/0.39 TRYING [1]
% 0.14/0.39 TRYING [2]
% 0.21/0.40 TRYING [4]
% 0.21/0.41 TRYING [3]
% 0.21/0.46 TRYING [5]
% 0.21/0.48 TRYING [4]
% 1.79/0.62 TRYING [6]
% 1.95/0.65 TRYING [5]
% 7.28/1.42 TRYING [7]
% 7.81/1.47 TRYING [6]
% 7.85/1.48 TRYING [1]
% 7.85/1.48 TRYING [2]
% 7.85/1.48 TRYING [3]
% 7.85/1.49 TRYING [4]
% 8.09/1.52 TRYING [5]
% 8.30/1.60 TRYING [6]
% 10.41/1.87 TRYING [7]
% 15.59/2.60 TRYING [8]
% 28.87/4.57 TRYING [7]
% 31.80/4.92 % (4891)First to succeed.
% 32.06/4.93 % (4891)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-4888"
% 32.06/4.94 % (4891)Refutation found. Thanks to Tanya!
% 32.06/4.94 % SZS status Theorem for theBenchmark
% 32.06/4.94 % SZS output start Proof for theBenchmark
% See solution above
% 32.06/4.94 % (4891)------------------------------
% 32.06/4.94 % (4891)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 32.06/4.94 % (4891)Termination reason: Refutation
% 32.06/4.94
% 32.06/4.94 % (4891)Memory used [KB]: 17870
% 32.06/4.94 % (4891)Time elapsed: 4.542 s
% 32.06/4.94 % (4891)Instructions burned: 21794 (million)
% 32.06/4.94 % (4888)Success in time 4.548 s
%------------------------------------------------------------------------------