TSTP Solution File: SEU293+1 by iProver---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : SEU293+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n005.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 : Fri May 3 03:05:21 EDT 2024
% Result : Theorem 6.79s 1.66s
% Output : CNFRefutation 6.79s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named definition)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0,X1,X2] :
( element(X2,powerset(cartesian_product2(X0,X1)))
=> relation(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relset_1) ).
fof(f6,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ! [X1,X2] :
( relation_inverse_image(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ( in(apply(X0,X3),X1)
& in(X3,relation_dom(X0)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d13_funct_1) ).
fof(f7,axiom,
! [X0,X1,X2] :
( relation_of2_as_subset(X2,X0,X1)
=> ( ( empty_set = X1
=> ( ( quasi_total(X2,X0,X1)
<=> empty_set = X2 )
| empty_set = X0 ) )
& ( ( empty_set = X1
=> empty_set = X0 )
=> ( quasi_total(X2,X0,X1)
<=> relation_dom_as_subset(X0,X1,X2) = X0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_funct_2) ).
fof(f17,axiom,
! [X0,X1,X2] :
( relation_of2_as_subset(X2,X0,X1)
=> element(X2,powerset(cartesian_product2(X0,X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m2_relset_1) ).
fof(f42,axiom,
! [X0,X1,X2] :
( relation_of2(X2,X0,X1)
=> relation_dom_as_subset(X0,X1,X2) = relation_dom(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k4_relset_1) ).
fof(f43,axiom,
! [X0,X1,X2] :
( relation_of2_as_subset(X2,X0,X1)
<=> relation_of2(X2,X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
fof(f45,axiom,
! [X0,X1] :
( in(X0,X1)
=> element(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
fof(f48,conjecture,
! [X0,X1,X2,X3] :
( ( relation_of2_as_subset(X3,X0,X1)
& quasi_total(X3,X0,X1)
& function(X3) )
=> ( empty_set != X1
=> ! [X4] :
( in(X4,relation_inverse_image(X3,X2))
<=> ( in(apply(X3,X4),X2)
& in(X4,X0) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_funct_2) ).
fof(f49,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( ( relation_of2_as_subset(X3,X0,X1)
& quasi_total(X3,X0,X1)
& function(X3) )
=> ( empty_set != X1
=> ! [X4] :
( in(X4,relation_inverse_image(X3,X2))
<=> ( in(apply(X3,X4),X2)
& in(X4,X0) ) ) ) ),
inference(negated_conjecture,[],[f48]) ).
fof(f66,plain,
! [X0,X1,X2] :
( relation(X2)
| ~ element(X2,powerset(cartesian_product2(X0,X1))) ),
inference(ennf_transformation,[],[f4]) ).
fof(f69,plain,
! [X0] :
( ! [X1,X2] :
( relation_inverse_image(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ( in(apply(X0,X3),X1)
& in(X3,relation_dom(X0)) ) ) )
| ~ function(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f70,plain,
! [X0] :
( ! [X1,X2] :
( relation_inverse_image(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ( in(apply(X0,X3),X1)
& in(X3,relation_dom(X0)) ) ) )
| ~ function(X0)
| ~ relation(X0) ),
inference(flattening,[],[f69]) ).
fof(f71,plain,
! [X0,X1,X2] :
( ( ( ( quasi_total(X2,X0,X1)
<=> empty_set = X2 )
| empty_set = X0
| empty_set != X1 )
& ( ( quasi_total(X2,X0,X1)
<=> relation_dom_as_subset(X0,X1,X2) = X0 )
| ( empty_set != X0
& empty_set = X1 ) ) )
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(ennf_transformation,[],[f7]) ).
fof(f72,plain,
! [X0,X1,X2] :
( ( ( ( quasi_total(X2,X0,X1)
<=> empty_set = X2 )
| empty_set = X0
| empty_set != X1 )
& ( ( quasi_total(X2,X0,X1)
<=> relation_dom_as_subset(X0,X1,X2) = X0 )
| ( empty_set != X0
& empty_set = X1 ) ) )
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(flattening,[],[f71]) ).
fof(f74,plain,
! [X0,X1,X2] :
( element(X2,powerset(cartesian_product2(X0,X1)))
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(ennf_transformation,[],[f17]) ).
fof(f81,plain,
! [X0,X1,X2] :
( relation_dom_as_subset(X0,X1,X2) = relation_dom(X2)
| ~ relation_of2(X2,X0,X1) ),
inference(ennf_transformation,[],[f42]) ).
fof(f82,plain,
! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f45]) ).
fof(f86,plain,
? [X0,X1,X2,X3] :
( ? [X4] :
( in(X4,relation_inverse_image(X3,X2))
<~> ( in(apply(X3,X4),X2)
& in(X4,X0) ) )
& empty_set != X1
& relation_of2_as_subset(X3,X0,X1)
& quasi_total(X3,X0,X1)
& function(X3) ),
inference(ennf_transformation,[],[f49]) ).
fof(f87,plain,
? [X0,X1,X2,X3] :
( ? [X4] :
( in(X4,relation_inverse_image(X3,X2))
<~> ( in(apply(X3,X4),X2)
& in(X4,X0) ) )
& empty_set != X1
& relation_of2_as_subset(X3,X0,X1)
& quasi_total(X3,X0,X1)
& function(X3) ),
inference(flattening,[],[f86]) ).
fof(f94,plain,
! [X0] :
( ! [X1,X2] :
( ( relation_inverse_image(X0,X1) = X2
| ? [X3] :
( ( ~ in(apply(X0,X3),X1)
| ~ in(X3,relation_dom(X0))
| ~ in(X3,X2) )
& ( ( in(apply(X0,X3),X1)
& in(X3,relation_dom(X0)) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ~ in(apply(X0,X3),X1)
| ~ in(X3,relation_dom(X0)) )
& ( ( in(apply(X0,X3),X1)
& in(X3,relation_dom(X0)) )
| ~ in(X3,X2) ) )
| relation_inverse_image(X0,X1) != X2 ) )
| ~ function(X0)
| ~ relation(X0) ),
inference(nnf_transformation,[],[f70]) ).
fof(f95,plain,
! [X0] :
( ! [X1,X2] :
( ( relation_inverse_image(X0,X1) = X2
| ? [X3] :
( ( ~ in(apply(X0,X3),X1)
| ~ in(X3,relation_dom(X0))
| ~ in(X3,X2) )
& ( ( in(apply(X0,X3),X1)
& in(X3,relation_dom(X0)) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ~ in(apply(X0,X3),X1)
| ~ in(X3,relation_dom(X0)) )
& ( ( in(apply(X0,X3),X1)
& in(X3,relation_dom(X0)) )
| ~ in(X3,X2) ) )
| relation_inverse_image(X0,X1) != X2 ) )
| ~ function(X0)
| ~ relation(X0) ),
inference(flattening,[],[f94]) ).
fof(f96,plain,
! [X0] :
( ! [X1,X2] :
( ( relation_inverse_image(X0,X1) = X2
| ? [X3] :
( ( ~ in(apply(X0,X3),X1)
| ~ in(X3,relation_dom(X0))
| ~ in(X3,X2) )
& ( ( in(apply(X0,X3),X1)
& in(X3,relation_dom(X0)) )
| in(X3,X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ in(apply(X0,X4),X1)
| ~ in(X4,relation_dom(X0)) )
& ( ( in(apply(X0,X4),X1)
& in(X4,relation_dom(X0)) )
| ~ in(X4,X2) ) )
| relation_inverse_image(X0,X1) != X2 ) )
| ~ function(X0)
| ~ relation(X0) ),
inference(rectify,[],[f95]) ).
fof(f97,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ~ in(apply(X0,X3),X1)
| ~ in(X3,relation_dom(X0))
| ~ in(X3,X2) )
& ( ( in(apply(X0,X3),X1)
& in(X3,relation_dom(X0)) )
| in(X3,X2) ) )
=> ( ( ~ in(apply(X0,sK0(X0,X1,X2)),X1)
| ~ in(sK0(X0,X1,X2),relation_dom(X0))
| ~ in(sK0(X0,X1,X2),X2) )
& ( ( in(apply(X0,sK0(X0,X1,X2)),X1)
& in(sK0(X0,X1,X2),relation_dom(X0)) )
| in(sK0(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f98,plain,
! [X0] :
( ! [X1,X2] :
( ( relation_inverse_image(X0,X1) = X2
| ( ( ~ in(apply(X0,sK0(X0,X1,X2)),X1)
| ~ in(sK0(X0,X1,X2),relation_dom(X0))
| ~ in(sK0(X0,X1,X2),X2) )
& ( ( in(apply(X0,sK0(X0,X1,X2)),X1)
& in(sK0(X0,X1,X2),relation_dom(X0)) )
| in(sK0(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ in(apply(X0,X4),X1)
| ~ in(X4,relation_dom(X0)) )
& ( ( in(apply(X0,X4),X1)
& in(X4,relation_dom(X0)) )
| ~ in(X4,X2) ) )
| relation_inverse_image(X0,X1) != X2 ) )
| ~ function(X0)
| ~ relation(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f96,f97]) ).
fof(f99,plain,
! [X0,X1,X2] :
( ( ( ( ( quasi_total(X2,X0,X1)
| empty_set != X2 )
& ( empty_set = X2
| ~ quasi_total(X2,X0,X1) ) )
| empty_set = X0
| empty_set != X1 )
& ( ( ( quasi_total(X2,X0,X1)
| relation_dom_as_subset(X0,X1,X2) != X0 )
& ( relation_dom_as_subset(X0,X1,X2) = X0
| ~ quasi_total(X2,X0,X1) ) )
| ( empty_set != X0
& empty_set = X1 ) ) )
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(nnf_transformation,[],[f72]) ).
fof(f134,plain,
! [X0,X1,X2] :
( ( relation_of2_as_subset(X2,X0,X1)
| ~ relation_of2(X2,X0,X1) )
& ( relation_of2(X2,X0,X1)
| ~ relation_of2_as_subset(X2,X0,X1) ) ),
inference(nnf_transformation,[],[f43]) ).
fof(f135,plain,
? [X0,X1,X2,X3] :
( ? [X4] :
( ( ~ in(apply(X3,X4),X2)
| ~ in(X4,X0)
| ~ in(X4,relation_inverse_image(X3,X2)) )
& ( ( in(apply(X3,X4),X2)
& in(X4,X0) )
| in(X4,relation_inverse_image(X3,X2)) ) )
& empty_set != X1
& relation_of2_as_subset(X3,X0,X1)
& quasi_total(X3,X0,X1)
& function(X3) ),
inference(nnf_transformation,[],[f87]) ).
fof(f136,plain,
? [X0,X1,X2,X3] :
( ? [X4] :
( ( ~ in(apply(X3,X4),X2)
| ~ in(X4,X0)
| ~ in(X4,relation_inverse_image(X3,X2)) )
& ( ( in(apply(X3,X4),X2)
& in(X4,X0) )
| in(X4,relation_inverse_image(X3,X2)) ) )
& empty_set != X1
& relation_of2_as_subset(X3,X0,X1)
& quasi_total(X3,X0,X1)
& function(X3) ),
inference(flattening,[],[f135]) ).
fof(f137,plain,
( ? [X0,X1,X2,X3] :
( ? [X4] :
( ( ~ in(apply(X3,X4),X2)
| ~ in(X4,X0)
| ~ in(X4,relation_inverse_image(X3,X2)) )
& ( ( in(apply(X3,X4),X2)
& in(X4,X0) )
| in(X4,relation_inverse_image(X3,X2)) ) )
& empty_set != X1
& relation_of2_as_subset(X3,X0,X1)
& quasi_total(X3,X0,X1)
& function(X3) )
=> ( ? [X4] :
( ( ~ in(apply(sK21,X4),sK20)
| ~ in(X4,sK18)
| ~ in(X4,relation_inverse_image(sK21,sK20)) )
& ( ( in(apply(sK21,X4),sK20)
& in(X4,sK18) )
| in(X4,relation_inverse_image(sK21,sK20)) ) )
& empty_set != sK19
& relation_of2_as_subset(sK21,sK18,sK19)
& quasi_total(sK21,sK18,sK19)
& function(sK21) ) ),
introduced(choice_axiom,[]) ).
fof(f138,plain,
( ? [X4] :
( ( ~ in(apply(sK21,X4),sK20)
| ~ in(X4,sK18)
| ~ in(X4,relation_inverse_image(sK21,sK20)) )
& ( ( in(apply(sK21,X4),sK20)
& in(X4,sK18) )
| in(X4,relation_inverse_image(sK21,sK20)) ) )
=> ( ( ~ in(apply(sK21,sK22),sK20)
| ~ in(sK22,sK18)
| ~ in(sK22,relation_inverse_image(sK21,sK20)) )
& ( ( in(apply(sK21,sK22),sK20)
& in(sK22,sK18) )
| in(sK22,relation_inverse_image(sK21,sK20)) ) ) ),
introduced(choice_axiom,[]) ).
fof(f139,plain,
( ( ~ in(apply(sK21,sK22),sK20)
| ~ in(sK22,sK18)
| ~ in(sK22,relation_inverse_image(sK21,sK20)) )
& ( ( in(apply(sK21,sK22),sK20)
& in(sK22,sK18) )
| in(sK22,relation_inverse_image(sK21,sK20)) )
& empty_set != sK19
& relation_of2_as_subset(sK21,sK18,sK19)
& quasi_total(sK21,sK18,sK19)
& function(sK21) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK18,sK19,sK20,sK21,sK22])],[f136,f138,f137]) ).
fof(f143,plain,
! [X2,X0,X1] :
( relation(X2)
| ~ element(X2,powerset(cartesian_product2(X0,X1))) ),
inference(cnf_transformation,[],[f66]) ).
fof(f146,plain,
! [X2,X0,X1,X4] :
( in(X4,relation_dom(X0))
| ~ in(X4,X2)
| relation_inverse_image(X0,X1) != X2
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f98]) ).
fof(f147,plain,
! [X2,X0,X1,X4] :
( in(apply(X0,X4),X1)
| ~ in(X4,X2)
| relation_inverse_image(X0,X1) != X2
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f98]) ).
fof(f148,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(apply(X0,X4),X1)
| ~ in(X4,relation_dom(X0))
| relation_inverse_image(X0,X1) != X2
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f98]) ).
fof(f152,plain,
! [X2,X0,X1] :
( relation_dom_as_subset(X0,X1,X2) = X0
| ~ quasi_total(X2,X0,X1)
| empty_set = X1
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(cnf_transformation,[],[f99]) ).
fof(f159,plain,
! [X2,X0,X1] :
( element(X2,powerset(cartesian_product2(X0,X1)))
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(cnf_transformation,[],[f74]) ).
fof(f203,plain,
! [X2,X0,X1] :
( relation_dom_as_subset(X0,X1,X2) = relation_dom(X2)
| ~ relation_of2(X2,X0,X1) ),
inference(cnf_transformation,[],[f81]) ).
fof(f204,plain,
! [X2,X0,X1] :
( relation_of2(X2,X0,X1)
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(cnf_transformation,[],[f134]) ).
fof(f205,plain,
! [X2,X0,X1] :
( relation_of2_as_subset(X2,X0,X1)
| ~ relation_of2(X2,X0,X1) ),
inference(cnf_transformation,[],[f134]) ).
fof(f207,plain,
! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f82]) ).
fof(f210,plain,
function(sK21),
inference(cnf_transformation,[],[f139]) ).
fof(f211,plain,
quasi_total(sK21,sK18,sK19),
inference(cnf_transformation,[],[f139]) ).
fof(f212,plain,
relation_of2_as_subset(sK21,sK18,sK19),
inference(cnf_transformation,[],[f139]) ).
fof(f213,plain,
empty_set != sK19,
inference(cnf_transformation,[],[f139]) ).
fof(f214,plain,
( in(sK22,sK18)
| in(sK22,relation_inverse_image(sK21,sK20)) ),
inference(cnf_transformation,[],[f139]) ).
fof(f215,plain,
( in(apply(sK21,sK22),sK20)
| in(sK22,relation_inverse_image(sK21,sK20)) ),
inference(cnf_transformation,[],[f139]) ).
fof(f216,plain,
( ~ in(apply(sK21,sK22),sK20)
| ~ in(sK22,sK18)
| ~ in(sK22,relation_inverse_image(sK21,sK20)) ),
inference(cnf_transformation,[],[f139]) ).
fof(f222,plain,
! [X0,X1,X4] :
( in(X4,relation_inverse_image(X0,X1))
| ~ in(apply(X0,X4),X1)
| ~ in(X4,relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(equality_resolution,[],[f148]) ).
fof(f223,plain,
! [X0,X1,X4] :
( in(apply(X0,X4),X1)
| ~ in(X4,relation_inverse_image(X0,X1))
| ~ function(X0)
| ~ relation(X0) ),
inference(equality_resolution,[],[f147]) ).
fof(f224,plain,
! [X0,X1,X4] :
( in(X4,relation_dom(X0))
| ~ in(X4,relation_inverse_image(X0,X1))
| ~ function(X0)
| ~ relation(X0) ),
inference(equality_resolution,[],[f146]) ).
cnf(c_52,plain,
( ~ element(X0,powerset(cartesian_product2(X1,X2)))
| relation(X0) ),
inference(cnf_transformation,[],[f143]) ).
cnf(c_56,plain,
( ~ in(apply(X0,X1),X2)
| ~ in(X1,relation_dom(X0))
| ~ function(X0)
| ~ relation(X0)
| in(X1,relation_inverse_image(X0,X2)) ),
inference(cnf_transformation,[],[f222]) ).
cnf(c_57,plain,
( ~ in(X0,relation_inverse_image(X1,X2))
| ~ function(X1)
| ~ relation(X1)
| in(apply(X1,X0),X2) ),
inference(cnf_transformation,[],[f223]) ).
cnf(c_58,plain,
( ~ in(X0,relation_inverse_image(X1,X2))
| ~ function(X1)
| ~ relation(X1)
| in(X0,relation_dom(X1)) ),
inference(cnf_transformation,[],[f224]) ).
cnf(c_64,plain,
( ~ quasi_total(X0,X1,X2)
| ~ relation_of2_as_subset(X0,X1,X2)
| relation_dom_as_subset(X1,X2,X0) = X1
| X2 = empty_set ),
inference(cnf_transformation,[],[f152]) ).
cnf(c_66,plain,
( ~ relation_of2_as_subset(X0,X1,X2)
| element(X0,powerset(cartesian_product2(X1,X2))) ),
inference(cnf_transformation,[],[f159]) ).
cnf(c_110,plain,
( ~ relation_of2(X0,X1,X2)
| relation_dom_as_subset(X1,X2,X0) = relation_dom(X0) ),
inference(cnf_transformation,[],[f203]) ).
cnf(c_111,plain,
( ~ relation_of2(X0,X1,X2)
| relation_of2_as_subset(X0,X1,X2) ),
inference(cnf_transformation,[],[f205]) ).
cnf(c_112,plain,
( ~ relation_of2_as_subset(X0,X1,X2)
| relation_of2(X0,X1,X2) ),
inference(cnf_transformation,[],[f204]) ).
cnf(c_114,plain,
( ~ in(X0,X1)
| element(X0,X1) ),
inference(cnf_transformation,[],[f207]) ).
cnf(c_117,negated_conjecture,
( ~ in(apply(sK21,sK22),sK20)
| ~ in(sK22,relation_inverse_image(sK21,sK20))
| ~ in(sK22,sK18) ),
inference(cnf_transformation,[],[f216]) ).
cnf(c_118,negated_conjecture,
( in(apply(sK21,sK22),sK20)
| in(sK22,relation_inverse_image(sK21,sK20)) ),
inference(cnf_transformation,[],[f215]) ).
cnf(c_119,negated_conjecture,
( in(sK22,relation_inverse_image(sK21,sK20))
| in(sK22,sK18) ),
inference(cnf_transformation,[],[f214]) ).
cnf(c_120,negated_conjecture,
empty_set != sK19,
inference(cnf_transformation,[],[f213]) ).
cnf(c_121,negated_conjecture,
relation_of2_as_subset(sK21,sK18,sK19),
inference(cnf_transformation,[],[f212]) ).
cnf(c_122,negated_conjecture,
quasi_total(sK21,sK18,sK19),
inference(cnf_transformation,[],[f211]) ).
cnf(c_123,negated_conjecture,
function(sK21),
inference(cnf_transformation,[],[f210]) ).
cnf(c_166,plain,
( relation_of2(X0,X1,X2)
| ~ relation_of2_as_subset(X0,X1,X2) ),
inference(prop_impl_just,[status(thm)],[c_112]) ).
cnf(c_167,plain,
( ~ relation_of2_as_subset(X0,X1,X2)
| relation_of2(X0,X1,X2) ),
inference(renaming,[status(thm)],[c_166]) ).
cnf(c_168,plain,
( ~ relation_of2(X0,X1,X2)
| relation_of2_as_subset(X0,X1,X2) ),
inference(prop_impl_just,[status(thm)],[c_111]) ).
cnf(c_196,plain,
( element(X0,powerset(cartesian_product2(X1,X2)))
| ~ relation_of2(X0,X1,X2) ),
inference(prop_impl_just,[status(thm)],[c_111,c_66]) ).
cnf(c_197,plain,
( ~ relation_of2(X0,X1,X2)
| element(X0,powerset(cartesian_product2(X1,X2))) ),
inference(renaming,[status(thm)],[c_196]) ).
cnf(c_351,plain,
( ~ quasi_total(X0,X1,X2)
| ~ relation_of2(X0,X1,X2)
| relation_dom_as_subset(X1,X2,X0) = X1
| X2 = empty_set ),
inference(bin_hyper_res,[status(thm)],[c_64,c_168]) ).
cnf(c_1222,plain,
( X0 != sK21
| X1 != sK18
| X2 != sK19
| relation_of2(X0,X1,X2) ),
inference(resolution_lifted,[status(thm)],[c_167,c_121]) ).
cnf(c_1223,plain,
relation_of2(sK21,sK18,sK19),
inference(unflattening,[status(thm)],[c_1222]) ).
cnf(c_1327,plain,
( X0 != sK21
| X1 != sK18
| X2 != sK19
| ~ relation_of2(X0,X1,X2)
| relation_dom_as_subset(X1,X2,X0) = X1
| X2 = empty_set ),
inference(resolution_lifted,[status(thm)],[c_351,c_122]) ).
cnf(c_1328,plain,
( ~ relation_of2(sK21,sK18,sK19)
| relation_dom_as_subset(sK18,sK19,sK21) = sK18
| sK19 = empty_set ),
inference(unflattening,[status(thm)],[c_1327]) ).
cnf(c_1329,plain,
( relation_dom_as_subset(sK18,sK19,sK21) = sK18
| sK19 = empty_set ),
inference(global_subsumption_just,[status(thm)],[c_1328,c_1223,c_1328]) ).
cnf(c_1464,plain,
( X0 != sK21
| X1 != sK18
| X2 != sK19
| relation_of2(X0,X1,X2) ),
inference(resolution_lifted,[status(thm)],[c_167,c_121]) ).
cnf(c_1465,plain,
relation_of2(sK21,sK18,sK19),
inference(unflattening,[status(thm)],[c_1464]) ).
cnf(c_10027,plain,
relation_inverse_image(sK21,sK20) = sP0_iProver_def,
definition ).
cnf(c_10028,plain,
apply(sK21,sK22) = sP1_iProver_def,
definition ).
cnf(c_10029,negated_conjecture,
function(sK21),
inference(demodulation,[status(thm)],[c_123]) ).
cnf(c_10030,negated_conjecture,
empty_set != sK19,
inference(demodulation,[status(thm)],[c_120]) ).
cnf(c_10031,negated_conjecture,
( in(sK22,sK18)
| in(sK22,sP0_iProver_def) ),
inference(demodulation,[status(thm)],[c_119,c_10027]) ).
cnf(c_10032,negated_conjecture,
( in(sK22,sP0_iProver_def)
| in(sP1_iProver_def,sK20) ),
inference(demodulation,[status(thm)],[c_118,c_10028]) ).
cnf(c_10033,negated_conjecture,
( ~ in(sK22,sK18)
| ~ in(sK22,sP0_iProver_def)
| ~ in(sP1_iProver_def,sK20) ),
inference(demodulation,[status(thm)],[c_117]) ).
cnf(c_11279,plain,
relation_dom_as_subset(sK18,sK19,sK21) = relation_dom(sK21),
inference(superposition,[status(thm)],[c_1465,c_110]) ).
cnf(c_11287,plain,
( relation_dom(sK21) = sK18
| empty_set = sK19 ),
inference(demodulation,[status(thm)],[c_1329,c_11279]) ).
cnf(c_11288,plain,
relation_dom(sK21) = sK18,
inference(forward_subsumption_resolution,[status(thm)],[c_11287,c_10030]) ).
cnf(c_11301,plain,
( ~ in(X0,sP0_iProver_def)
| ~ function(sK21)
| ~ relation(sK21)
| in(X0,relation_dom(sK21)) ),
inference(superposition,[status(thm)],[c_10027,c_58]) ).
cnf(c_11302,plain,
( ~ in(X0,sP0_iProver_def)
| ~ function(sK21)
| ~ relation(sK21)
| in(X0,sK18) ),
inference(light_normalisation,[status(thm)],[c_11301,c_11288]) ).
cnf(c_11303,plain,
( ~ in(X0,sP0_iProver_def)
| ~ relation(sK21)
| in(X0,sK18) ),
inference(forward_subsumption_resolution,[status(thm)],[c_11302,c_10029]) ).
cnf(c_11340,plain,
( ~ in(X0,sP0_iProver_def)
| ~ function(sK21)
| ~ relation(sK21)
| in(apply(sK21,X0),sK20) ),
inference(superposition,[status(thm)],[c_10027,c_57]) ).
cnf(c_11341,plain,
( ~ in(X0,sP0_iProver_def)
| ~ relation(sK21)
| in(apply(sK21,X0),sK20) ),
inference(forward_subsumption_resolution,[status(thm)],[c_11340,c_10029]) ).
cnf(c_11379,plain,
( ~ in(sK22,relation_dom(sK21))
| ~ in(sP1_iProver_def,X0)
| ~ function(sK21)
| ~ relation(sK21)
| in(sK22,relation_inverse_image(sK21,X0)) ),
inference(superposition,[status(thm)],[c_10028,c_56]) ).
cnf(c_11384,plain,
( ~ in(sP1_iProver_def,X0)
| ~ in(sK22,sK18)
| ~ function(sK21)
| ~ relation(sK21)
| in(sK22,relation_inverse_image(sK21,X0)) ),
inference(light_normalisation,[status(thm)],[c_11379,c_11288]) ).
cnf(c_11385,plain,
( ~ in(sP1_iProver_def,X0)
| ~ in(sK22,sK18)
| ~ relation(sK21)
| in(sK22,relation_inverse_image(sK21,X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_11384,c_10029]) ).
cnf(c_11433,plain,
( ~ relation(sK21)
| in(sK22,sK18)
| in(sP1_iProver_def,sK20) ),
inference(superposition,[status(thm)],[c_10032,c_11303]) ).
cnf(c_11467,plain,
( ~ relation(sK21)
| in(sP1_iProver_def,sK20)
| element(sK22,sK18) ),
inference(superposition,[status(thm)],[c_11433,c_114]) ).
cnf(c_11488,plain,
( ~ in(sK22,sP0_iProver_def)
| ~ relation(sK21)
| in(sP1_iProver_def,sK20) ),
inference(superposition,[status(thm)],[c_10028,c_11341]) ).
cnf(c_11534,plain,
( ~ in(sK22,sK18)
| ~ in(sP1_iProver_def,sK20)
| ~ relation(sK21)
| in(sK22,sP0_iProver_def) ),
inference(superposition,[status(thm)],[c_10027,c_11385]) ).
cnf(c_11908,plain,
( in(sP1_iProver_def,sK20)
| ~ relation(sK21) ),
inference(global_subsumption_just,[status(thm)],[c_11467,c_10032,c_11488]) ).
cnf(c_11909,plain,
( ~ relation(sK21)
| in(sP1_iProver_def,sK20) ),
inference(renaming,[status(thm)],[c_11908]) ).
cnf(c_12023,plain,
( ~ relation(sK21)
| in(sK22,sP0_iProver_def) ),
inference(global_subsumption_just,[status(thm)],[c_11534,c_10031,c_11534,c_11909]) ).
cnf(c_12032,plain,
( ~ relation(sK21)
| in(sK22,sK18) ),
inference(superposition,[status(thm)],[c_12023,c_11303]) ).
cnf(c_12041,plain,
~ relation(sK21),
inference(global_subsumption_just,[status(thm)],[c_12032,c_10033,c_11909,c_12023,c_12032]) ).
cnf(c_14489,plain,
( ~ relation_of2(X0,X1,X2)
| relation(X0) ),
inference(superposition,[status(thm)],[c_197,c_52]) ).
cnf(c_14535,plain,
relation(sK21),
inference(superposition,[status(thm)],[c_1465,c_14489]) ).
cnf(c_14537,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_14535,c_12041]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU293+1 : TPTP v8.1.2. Released v3.3.0.
% 0.07/0.13 % Command : run_iprover %s %d THM
% 0.12/0.33 % Computer : n005.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu May 2 17:51:41 EDT 2024
% 0.12/0.34 % CPUTime :
% 0.18/0.46 Running first-order theorem proving
% 0.18/0.46 Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 6.79/1.66 % SZS status Started for theBenchmark.p
% 6.79/1.66 % SZS status Theorem for theBenchmark.p
% 6.79/1.66
% 6.79/1.66 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 6.79/1.66
% 6.79/1.66 ------ iProver source info
% 6.79/1.66
% 6.79/1.66 git: date: 2024-05-02 19:28:25 +0000
% 6.79/1.66 git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 6.79/1.66 git: non_committed_changes: false
% 6.79/1.66
% 6.79/1.66 ------ Parsing...
% 6.79/1.66 ------ Clausification by vclausify_rel & Parsing by iProver...
% 6.79/1.66
% 6.79/1.66 ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sup_sim: 0 sf_s rm: 3 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 3 0s sf_e pe_s pe_e
% 6.79/1.66
% 6.79/1.66 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 6.79/1.66
% 6.79/1.66 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 6.79/1.66 ------ Proving...
% 6.79/1.66 ------ Problem Properties
% 6.79/1.66
% 6.79/1.66
% 6.79/1.66 clauses 73
% 6.79/1.66 conjectures 5
% 6.79/1.66 EPR 35
% 6.79/1.66 Horn 63
% 6.79/1.66 unary 40
% 6.79/1.66 binary 20
% 6.79/1.66 lits 130
% 6.79/1.66 lits eq 18
% 6.79/1.66 fd_pure 0
% 6.79/1.66 fd_pseudo 0
% 6.79/1.66 fd_cond 2
% 6.79/1.66 fd_pseudo_cond 4
% 6.79/1.66 AC symbols 0
% 6.79/1.66
% 6.79/1.66 ------ Schedule dynamic 5 is on
% 6.79/1.66
% 6.79/1.66 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 6.79/1.66
% 6.79/1.66
% 6.79/1.66 ------
% 6.79/1.66 Current options:
% 6.79/1.66 ------
% 6.79/1.66
% 6.79/1.66
% 6.79/1.66
% 6.79/1.66
% 6.79/1.66 ------ Proving...
% 6.79/1.66
% 6.79/1.66
% 6.79/1.66 % SZS status Theorem for theBenchmark.p
% 6.79/1.66
% 6.79/1.66 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 6.79/1.66
% 6.79/1.66
%------------------------------------------------------------------------------