TSTP Solution File: SEU081+1 by iProver---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : SEU081+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n002.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 03:04:29 EDT 2024
% Result : Theorem 61.81s 9.27s
% Output : CNFRefutation 61.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 20
% Syntax : Number of formulae : 124 ( 22 unt; 0 def)
% Number of atoms : 482 ( 159 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 619 ( 261 ~; 267 |; 69 &)
% ( 9 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 2 con; 0-3 aty)
% Number of variables : 226 ( 4 sgn 128 !; 24 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ! [X1,X2] :
( relation_image(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( apply(X0,X4) = X3
& in(X4,X1)
& in(X4,relation_dom(X0)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d12_funct_1) ).
fof(f7,axiom,
! [X0] :
? [X1] : element(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(f11,axiom,
! [X0] :
( function(identity_relation(X0))
& relation(identity_relation(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_funct_1) ).
fof(f26,conjecture,
! [X0,X1] :
( element(X1,powerset(X0))
=> relation_image(identity_relation(X0),X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t162_funct_1) ).
fof(f27,negated_conjecture,
~ ! [X0,X1] :
( element(X1,powerset(X0))
=> relation_image(identity_relation(X0),X1) = X1 ),
inference(negated_conjecture,[],[f26]) ).
fof(f29,axiom,
! [X0,X1] :
( element(X0,X1)
=> ( in(X0,X1)
| empty(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
fof(f30,axiom,
! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> ( identity_relation(X0) = X1
<=> ( ! [X2] :
( in(X2,X0)
=> apply(X1,X2) = X2 )
& relation_dom(X1) = X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_funct_1) ).
fof(f32,axiom,
! [X0,X1,X2] :
( ( element(X1,powerset(X2))
& in(X0,X1) )
=> element(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).
fof(f33,axiom,
! [X0,X1,X2] :
~ ( empty(X2)
& element(X1,powerset(X2))
& in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_subset) ).
fof(f35,axiom,
! [X0,X1] :
~ ( empty(X1)
& in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
fof(f48,plain,
! [X0] :
( ! [X1,X2] :
( relation_image(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( apply(X0,X4) = X3
& in(X4,X1)
& in(X4,relation_dom(X0)) ) ) )
| ~ function(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f49,plain,
! [X0] :
( ! [X1,X2] :
( relation_image(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( apply(X0,X4) = X3
& in(X4,X1)
& in(X4,relation_dom(X0)) ) ) )
| ~ function(X0)
| ~ relation(X0) ),
inference(flattening,[],[f48]) ).
fof(f54,plain,
? [X0,X1] :
( relation_image(identity_relation(X0),X1) != X1
& element(X1,powerset(X0)) ),
inference(ennf_transformation,[],[f27]) ).
fof(f56,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(ennf_transformation,[],[f29]) ).
fof(f57,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(flattening,[],[f56]) ).
fof(f58,plain,
! [X0,X1] :
( ( identity_relation(X0) = X1
<=> ( ! [X2] :
( apply(X1,X2) = X2
| ~ in(X2,X0) )
& relation_dom(X1) = X0 ) )
| ~ function(X1)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f30]) ).
fof(f59,plain,
! [X0,X1] :
( ( identity_relation(X0) = X1
<=> ( ! [X2] :
( apply(X1,X2) = X2
| ~ in(X2,X0) )
& relation_dom(X1) = X0 ) )
| ~ function(X1)
| ~ relation(X1) ),
inference(flattening,[],[f58]) ).
fof(f61,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f32]) ).
fof(f62,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(flattening,[],[f61]) ).
fof(f63,plain,
! [X0,X1,X2] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f33]) ).
fof(f65,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f35]) ).
fof(f67,plain,
! [X0] :
( ! [X1,X2] :
( ( relation_image(X0,X1) = X2
| ? [X3] :
( ( ! [X4] :
( apply(X0,X4) != X3
| ~ in(X4,X1)
| ~ in(X4,relation_dom(X0)) )
| ~ in(X3,X2) )
& ( ? [X4] :
( apply(X0,X4) = X3
& in(X4,X1)
& in(X4,relation_dom(X0)) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ! [X4] :
( apply(X0,X4) != X3
| ~ in(X4,X1)
| ~ in(X4,relation_dom(X0)) ) )
& ( ? [X4] :
( apply(X0,X4) = X3
& in(X4,X1)
& in(X4,relation_dom(X0)) )
| ~ in(X3,X2) ) )
| relation_image(X0,X1) != X2 ) )
| ~ function(X0)
| ~ relation(X0) ),
inference(nnf_transformation,[],[f49]) ).
fof(f68,plain,
! [X0] :
( ! [X1,X2] :
( ( relation_image(X0,X1) = X2
| ? [X3] :
( ( ! [X4] :
( apply(X0,X4) != X3
| ~ in(X4,X1)
| ~ in(X4,relation_dom(X0)) )
| ~ in(X3,X2) )
& ( ? [X5] :
( apply(X0,X5) = X3
& in(X5,X1)
& in(X5,relation_dom(X0)) )
| in(X3,X2) ) ) )
& ( ! [X6] :
( ( in(X6,X2)
| ! [X7] :
( apply(X0,X7) != X6
| ~ in(X7,X1)
| ~ in(X7,relation_dom(X0)) ) )
& ( ? [X8] :
( apply(X0,X8) = X6
& in(X8,X1)
& in(X8,relation_dom(X0)) )
| ~ in(X6,X2) ) )
| relation_image(X0,X1) != X2 ) )
| ~ function(X0)
| ~ relation(X0) ),
inference(rectify,[],[f67]) ).
fof(f69,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ! [X4] :
( apply(X0,X4) != X3
| ~ in(X4,X1)
| ~ in(X4,relation_dom(X0)) )
| ~ in(X3,X2) )
& ( ? [X5] :
( apply(X0,X5) = X3
& in(X5,X1)
& in(X5,relation_dom(X0)) )
| in(X3,X2) ) )
=> ( ( ! [X4] :
( apply(X0,X4) != sK0(X0,X1,X2)
| ~ in(X4,X1)
| ~ in(X4,relation_dom(X0)) )
| ~ in(sK0(X0,X1,X2),X2) )
& ( ? [X5] :
( apply(X0,X5) = sK0(X0,X1,X2)
& in(X5,X1)
& in(X5,relation_dom(X0)) )
| in(sK0(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f70,plain,
! [X0,X1,X2] :
( ? [X5] :
( apply(X0,X5) = sK0(X0,X1,X2)
& in(X5,X1)
& in(X5,relation_dom(X0)) )
=> ( sK0(X0,X1,X2) = apply(X0,sK1(X0,X1,X2))
& in(sK1(X0,X1,X2),X1)
& in(sK1(X0,X1,X2),relation_dom(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f71,plain,
! [X0,X1,X6] :
( ? [X8] :
( apply(X0,X8) = X6
& in(X8,X1)
& in(X8,relation_dom(X0)) )
=> ( apply(X0,sK2(X0,X1,X6)) = X6
& in(sK2(X0,X1,X6),X1)
& in(sK2(X0,X1,X6),relation_dom(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f72,plain,
! [X0] :
( ! [X1,X2] :
( ( relation_image(X0,X1) = X2
| ( ( ! [X4] :
( apply(X0,X4) != sK0(X0,X1,X2)
| ~ in(X4,X1)
| ~ in(X4,relation_dom(X0)) )
| ~ in(sK0(X0,X1,X2),X2) )
& ( ( sK0(X0,X1,X2) = apply(X0,sK1(X0,X1,X2))
& in(sK1(X0,X1,X2),X1)
& in(sK1(X0,X1,X2),relation_dom(X0)) )
| in(sK0(X0,X1,X2),X2) ) ) )
& ( ! [X6] :
( ( in(X6,X2)
| ! [X7] :
( apply(X0,X7) != X6
| ~ in(X7,X1)
| ~ in(X7,relation_dom(X0)) ) )
& ( ( apply(X0,sK2(X0,X1,X6)) = X6
& in(sK2(X0,X1,X6),X1)
& in(sK2(X0,X1,X6),relation_dom(X0)) )
| ~ in(X6,X2) ) )
| relation_image(X0,X1) != X2 ) )
| ~ function(X0)
| ~ relation(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f68,f71,f70,f69]) ).
fof(f73,plain,
! [X0] :
( ? [X1] : element(X1,X0)
=> element(sK3(X0),X0) ),
introduced(choice_axiom,[]) ).
fof(f74,plain,
! [X0] : element(sK3(X0),X0),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f7,f73]) ).
fof(f95,plain,
( ? [X0,X1] :
( relation_image(identity_relation(X0),X1) != X1
& element(X1,powerset(X0)) )
=> ( sK15 != relation_image(identity_relation(sK14),sK15)
& element(sK15,powerset(sK14)) ) ),
introduced(choice_axiom,[]) ).
fof(f96,plain,
( sK15 != relation_image(identity_relation(sK14),sK15)
& element(sK15,powerset(sK14)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK14,sK15])],[f54,f95]) ).
fof(f97,plain,
! [X0,X1] :
( ( ( identity_relation(X0) = X1
| ? [X2] :
( apply(X1,X2) != X2
& in(X2,X0) )
| relation_dom(X1) != X0 )
& ( ( ! [X2] :
( apply(X1,X2) = X2
| ~ in(X2,X0) )
& relation_dom(X1) = X0 )
| identity_relation(X0) != X1 ) )
| ~ function(X1)
| ~ relation(X1) ),
inference(nnf_transformation,[],[f59]) ).
fof(f98,plain,
! [X0,X1] :
( ( ( identity_relation(X0) = X1
| ? [X2] :
( apply(X1,X2) != X2
& in(X2,X0) )
| relation_dom(X1) != X0 )
& ( ( ! [X2] :
( apply(X1,X2) = X2
| ~ in(X2,X0) )
& relation_dom(X1) = X0 )
| identity_relation(X0) != X1 ) )
| ~ function(X1)
| ~ relation(X1) ),
inference(flattening,[],[f97]) ).
fof(f99,plain,
! [X0,X1] :
( ( ( identity_relation(X0) = X1
| ? [X2] :
( apply(X1,X2) != X2
& in(X2,X0) )
| relation_dom(X1) != X0 )
& ( ( ! [X3] :
( apply(X1,X3) = X3
| ~ in(X3,X0) )
& relation_dom(X1) = X0 )
| identity_relation(X0) != X1 ) )
| ~ function(X1)
| ~ relation(X1) ),
inference(rectify,[],[f98]) ).
fof(f100,plain,
! [X0,X1] :
( ? [X2] :
( apply(X1,X2) != X2
& in(X2,X0) )
=> ( sK16(X0,X1) != apply(X1,sK16(X0,X1))
& in(sK16(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f101,plain,
! [X0,X1] :
( ( ( identity_relation(X0) = X1
| ( sK16(X0,X1) != apply(X1,sK16(X0,X1))
& in(sK16(X0,X1),X0) )
| relation_dom(X1) != X0 )
& ( ( ! [X3] :
( apply(X1,X3) = X3
| ~ in(X3,X0) )
& relation_dom(X1) = X0 )
| identity_relation(X0) != X1 ) )
| ~ function(X1)
| ~ relation(X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK16])],[f99,f100]) ).
fof(f112,plain,
! [X2,X0,X1] :
( relation_image(X0,X1) = X2
| in(sK1(X0,X1,X2),X1)
| in(sK0(X0,X1,X2),X2)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f72]) ).
fof(f113,plain,
! [X2,X0,X1] :
( relation_image(X0,X1) = X2
| sK0(X0,X1,X2) = apply(X0,sK1(X0,X1,X2))
| in(sK0(X0,X1,X2),X2)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f72]) ).
fof(f114,plain,
! [X2,X0,X1,X4] :
( relation_image(X0,X1) = X2
| apply(X0,X4) != sK0(X0,X1,X2)
| ~ in(X4,X1)
| ~ in(X4,relation_dom(X0))
| ~ in(sK0(X0,X1,X2),X2)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f72]) ).
fof(f116,plain,
! [X0] : element(sK3(X0),X0),
inference(cnf_transformation,[],[f74]) ).
fof(f121,plain,
! [X0] : relation(identity_relation(X0)),
inference(cnf_transformation,[],[f11]) ).
fof(f122,plain,
! [X0] : function(identity_relation(X0)),
inference(cnf_transformation,[],[f11]) ).
fof(f147,plain,
element(sK15,powerset(sK14)),
inference(cnf_transformation,[],[f96]) ).
fof(f148,plain,
sK15 != relation_image(identity_relation(sK14),sK15),
inference(cnf_transformation,[],[f96]) ).
fof(f150,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[],[f57]) ).
fof(f151,plain,
! [X0,X1] :
( relation_dom(X1) = X0
| identity_relation(X0) != X1
| ~ function(X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f101]) ).
fof(f152,plain,
! [X3,X0,X1] :
( apply(X1,X3) = X3
| ~ in(X3,X0)
| identity_relation(X0) != X1
| ~ function(X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f101]) ).
fof(f156,plain,
! [X2,X0,X1] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f62]) ).
fof(f157,plain,
! [X2,X0,X1] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f63]) ).
fof(f159,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f65]) ).
fof(f168,plain,
! [X3,X0] :
( apply(identity_relation(X0),X3) = X3
| ~ in(X3,X0)
| ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0)) ),
inference(equality_resolution,[],[f152]) ).
fof(f169,plain,
! [X0] :
( relation_dom(identity_relation(X0)) = X0
| ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0)) ),
inference(equality_resolution,[],[f151]) ).
cnf(c_52,plain,
( sK0(X0,X1,X2) != apply(X0,X3)
| ~ in(sK0(X0,X1,X2),X2)
| ~ in(X3,relation_dom(X0))
| ~ in(X3,X1)
| ~ function(X0)
| ~ relation(X0)
| relation_image(X0,X1) = X2 ),
inference(cnf_transformation,[],[f114]) ).
cnf(c_53,plain,
( ~ function(X0)
| ~ relation(X0)
| apply(X0,sK1(X0,X1,X2)) = sK0(X0,X1,X2)
| relation_image(X0,X1) = X2
| in(sK0(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f113]) ).
cnf(c_54,plain,
( ~ function(X0)
| ~ relation(X0)
| relation_image(X0,X1) = X2
| in(sK0(X0,X1,X2),X2)
| in(sK1(X0,X1,X2),X1) ),
inference(cnf_transformation,[],[f112]) ).
cnf(c_61,plain,
element(sK3(X0),X0),
inference(cnf_transformation,[],[f116]) ).
cnf(c_66,plain,
function(identity_relation(X0)),
inference(cnf_transformation,[],[f122]) ).
cnf(c_67,plain,
relation(identity_relation(X0)),
inference(cnf_transformation,[],[f121]) ).
cnf(c_92,negated_conjecture,
relation_image(identity_relation(sK14),sK15) != sK15,
inference(cnf_transformation,[],[f148]) ).
cnf(c_93,negated_conjecture,
element(sK15,powerset(sK14)),
inference(cnf_transformation,[],[f147]) ).
cnf(c_95,plain,
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(cnf_transformation,[],[f150]) ).
cnf(c_98,plain,
( ~ in(X0,X1)
| ~ function(identity_relation(X1))
| ~ relation(identity_relation(X1))
| apply(identity_relation(X1),X0) = X0 ),
inference(cnf_transformation,[],[f168]) ).
cnf(c_99,plain,
( ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0))
| relation_dom(identity_relation(X0)) = X0 ),
inference(cnf_transformation,[],[f169]) ).
cnf(c_101,plain,
( ~ element(X0,powerset(X1))
| ~ in(X2,X0)
| element(X2,X1) ),
inference(cnf_transformation,[],[f156]) ).
cnf(c_102,plain,
( ~ element(X0,powerset(X1))
| ~ in(X2,X0)
| ~ empty(X1) ),
inference(cnf_transformation,[],[f157]) ).
cnf(c_104,plain,
( ~ in(X0,X1)
| ~ empty(X1) ),
inference(cnf_transformation,[],[f159]) ).
cnf(c_130,plain,
relation_dom(identity_relation(X0)) = X0,
inference(global_subsumption_just,[status(thm)],[c_99,c_67,c_66,c_99]) ).
cnf(c_161,plain,
X0 = X0,
theory(equality) ).
cnf(c_163,plain,
( X0 != X1
| X2 != X1
| X2 = X0 ),
theory(equality) ).
cnf(c_164,plain,
( X0 != X1
| X2 != X3
| ~ in(X1,X3)
| in(X0,X2) ),
theory(equality) ).
cnf(c_172,plain,
( X0 != X1
| X2 != X3
| ~ element(X1,X3)
| element(X0,X2) ),
theory(equality) ).
cnf(c_173,plain,
( X0 != X1
| powerset(X0) = powerset(X1) ),
theory(equality) ).
cnf(c_198,plain,
( X0 != sK15
| X1 != powerset(sK14)
| ~ element(sK15,powerset(sK14))
| element(X0,X1) ),
inference(instantiation,[status(thm)],[c_172]) ).
cnf(c_204,plain,
( ~ function(identity_relation(sK14))
| ~ relation(identity_relation(sK14))
| apply(identity_relation(sK14),sK1(identity_relation(sK14),sK15,sK15)) = sK0(identity_relation(sK14),sK15,sK15)
| relation_image(identity_relation(sK14),sK15) = sK15
| in(sK0(identity_relation(sK14),sK15,sK15),sK15) ),
inference(instantiation,[status(thm)],[c_53]) ).
cnf(c_223,plain,
( ~ element(X0,sK15)
| in(X0,sK15)
| empty(sK15) ),
inference(instantiation,[status(thm)],[c_95]) ).
cnf(c_233,plain,
relation(identity_relation(sK14)),
inference(instantiation,[status(thm)],[c_67]) ).
cnf(c_263,plain,
( X0 != powerset(sK14)
| sK15 != sK15
| ~ element(sK15,powerset(sK14))
| element(sK15,X0) ),
inference(instantiation,[status(thm)],[c_198]) ).
cnf(c_264,plain,
sK15 = sK15,
inference(instantiation,[status(thm)],[c_161]) ).
cnf(c_547,plain,
function(identity_relation(sK14)),
inference(instantiation,[status(thm)],[c_66]) ).
cnf(c_620,plain,
( X0 != sK14
| powerset(X0) = powerset(sK14) ),
inference(instantiation,[status(thm)],[c_173]) ).
cnf(c_1120,plain,
( ~ element(sK3(sK15),sK15)
| in(sK3(sK15),sK15)
| empty(sK15) ),
inference(instantiation,[status(thm)],[c_223]) ).
cnf(c_1121,plain,
element(sK3(sK15),sK15),
inference(instantiation,[status(thm)],[c_61]) ).
cnf(c_1669,plain,
( ~ in(sK0(identity_relation(sK14),sK15,sK15),sK15)
| ~ empty(sK15) ),
inference(instantiation,[status(thm)],[c_104]) ).
cnf(c_1673,plain,
( sK0(X0,sK15,X1) != apply(X0,sK0(identity_relation(sK14),sK15,sK15))
| ~ in(sK0(identity_relation(sK14),sK15,sK15),relation_dom(X0))
| ~ in(sK0(identity_relation(sK14),sK15,sK15),sK15)
| ~ in(sK0(X0,sK15,X1),X1)
| ~ function(X0)
| ~ relation(X0)
| relation_image(X0,sK15) = X1 ),
inference(instantiation,[status(thm)],[c_52]) ).
cnf(c_1677,plain,
( ~ in(sK0(identity_relation(sK14),sK15,sK15),sK15)
| ~ element(sK15,powerset(X0))
| element(sK0(identity_relation(sK14),sK15,sK15),X0) ),
inference(instantiation,[status(thm)],[c_101]) ).
cnf(c_1766,plain,
( relation_dom(identity_relation(sK14)) != sK14
| powerset(relation_dom(identity_relation(sK14))) = powerset(sK14) ),
inference(instantiation,[status(thm)],[c_620]) ).
cnf(c_1767,plain,
relation_dom(identity_relation(sK14)) = sK14,
inference(instantiation,[status(thm)],[c_130]) ).
cnf(c_2063,plain,
( ~ element(sK15,powerset(X0))
| ~ in(sK3(sK15),sK15)
| ~ empty(X0) ),
inference(instantiation,[status(thm)],[c_102]) ).
cnf(c_5303,plain,
( powerset(relation_dom(identity_relation(sK14))) != powerset(sK14)
| sK15 != sK15
| ~ element(sK15,powerset(sK14))
| element(sK15,powerset(relation_dom(identity_relation(sK14)))) ),
inference(instantiation,[status(thm)],[c_263]) ).
cnf(c_5572,plain,
( ~ element(X0,sK14)
| in(X0,sK14)
| empty(sK14) ),
inference(instantiation,[status(thm)],[c_95]) ).
cnf(c_6113,plain,
( ~ in(sK0(identity_relation(sK14),sK15,sK15),sK15)
| ~ element(sK15,powerset(sK14))
| element(sK0(identity_relation(sK14),sK15,sK15),sK14) ),
inference(instantiation,[status(thm)],[c_1677]) ).
cnf(c_6167,plain,
( ~ function(identity_relation(sK14))
| ~ relation(identity_relation(sK14))
| in(sK0(identity_relation(sK14),sK15,sK15),sK15)
| in(sK1(identity_relation(sK14),sK15,sK15),sK15) ),
inference(resolution,[status(thm)],[c_54,c_92]) ).
cnf(c_6216,plain,
( apply(X0,sK0(identity_relation(sK14),sK15,sK15)) != X1
| sK0(X0,sK15,X2) != X1
| sK0(X0,sK15,X2) = apply(X0,sK0(identity_relation(sK14),sK15,sK15)) ),
inference(instantiation,[status(thm)],[c_163]) ).
cnf(c_6582,plain,
( ~ in(sK3(sK15),sK15)
| ~ element(sK15,powerset(sK14))
| ~ empty(sK14) ),
inference(instantiation,[status(thm)],[c_2063]) ).
cnf(c_7192,plain,
( in(sK0(identity_relation(sK14),sK15,sK15),sK15)
| in(sK1(identity_relation(sK14),sK15,sK15),sK15) ),
inference(global_subsumption_just,[status(thm)],[c_6167,c_233,c_547,c_6167]) ).
cnf(c_7263,plain,
( ~ empty(sK15)
| in(sK0(identity_relation(sK14),sK15,sK15),sK15) ),
inference(resolution,[status(thm)],[c_7192,c_104]) ).
cnf(c_7265,plain,
~ empty(sK15),
inference(global_subsumption_just,[status(thm)],[c_7263,c_1669,c_7263]) ).
cnf(c_11625,plain,
( ~ element(X0,relation_dom(identity_relation(sK14)))
| in(X0,relation_dom(identity_relation(sK14)))
| empty(relation_dom(identity_relation(sK14))) ),
inference(instantiation,[status(thm)],[c_95]) ).
cnf(c_12153,plain,
( ~ element(sK15,powerset(relation_dom(identity_relation(sK14))))
| ~ in(sK3(sK15),sK15)
| ~ empty(relation_dom(identity_relation(sK14))) ),
inference(instantiation,[status(thm)],[c_2063]) ).
cnf(c_12156,plain,
( ~ in(sK0(identity_relation(sK14),sK15,sK15),sK15)
| ~ element(sK15,powerset(relation_dom(identity_relation(sK14))))
| element(sK0(identity_relation(sK14),sK15,sK15),relation_dom(identity_relation(sK14))) ),
inference(instantiation,[status(thm)],[c_1677]) ).
cnf(c_12471,plain,
sK0(identity_relation(sK14),sK15,sK15) = sK0(identity_relation(sK14),sK15,sK15),
inference(instantiation,[status(thm)],[c_161]) ).
cnf(c_13174,plain,
( apply(X0,sK0(identity_relation(sK14),sK15,sK15)) != sK0(X0,sK15,X1)
| sK0(X0,sK15,X1) != sK0(X0,sK15,X1)
| sK0(X0,sK15,X1) = apply(X0,sK0(identity_relation(sK14),sK15,sK15)) ),
inference(instantiation,[status(thm)],[c_6216]) ).
cnf(c_14053,plain,
( ~ element(sK0(identity_relation(sK14),sK15,sK15),sK14)
| in(sK0(identity_relation(sK14),sK15,sK15),sK14)
| empty(sK14) ),
inference(instantiation,[status(thm)],[c_5572]) ).
cnf(c_20190,plain,
( ~ in(sK0(identity_relation(sK14),sK15,sK15),sK14)
| ~ function(identity_relation(sK14))
| ~ relation(identity_relation(sK14))
| apply(identity_relation(sK14),sK0(identity_relation(sK14),sK15,sK15)) = sK0(identity_relation(sK14),sK15,sK15) ),
inference(instantiation,[status(thm)],[c_98]) ).
cnf(c_20719,plain,
( ~ element(sK0(identity_relation(sK14),sK15,sK15),relation_dom(identity_relation(sK14)))
| in(sK0(identity_relation(sK14),sK15,sK15),relation_dom(identity_relation(sK14)))
| empty(relation_dom(identity_relation(sK14))) ),
inference(instantiation,[status(thm)],[c_11625]) ).
cnf(c_26386,plain,
( apply(identity_relation(sK14),sK0(identity_relation(sK14),sK15,sK15)) != sK0(identity_relation(sK14),sK15,sK15)
| sK0(identity_relation(sK14),sK15,sK15) != sK0(identity_relation(sK14),sK15,sK15)
| sK0(identity_relation(sK14),sK15,sK15) = apply(identity_relation(sK14),sK0(identity_relation(sK14),sK15,sK15)) ),
inference(instantiation,[status(thm)],[c_13174]) ).
cnf(c_29101,plain,
( sK0(identity_relation(sK14),sK15,X0) != apply(identity_relation(sK14),sK0(identity_relation(sK14),sK15,sK15))
| ~ in(sK0(identity_relation(sK14),sK15,sK15),relation_dom(identity_relation(sK14)))
| ~ in(sK0(identity_relation(sK14),sK15,X0),X0)
| ~ in(sK0(identity_relation(sK14),sK15,sK15),sK15)
| ~ function(identity_relation(sK14))
| ~ relation(identity_relation(sK14))
| relation_image(identity_relation(sK14),sK15) = X0 ),
inference(instantiation,[status(thm)],[c_1673]) ).
cnf(c_37696,plain,
( sK0(identity_relation(sK14),sK15,sK15) != apply(identity_relation(sK14),sK0(identity_relation(sK14),sK15,sK15))
| ~ in(sK0(identity_relation(sK14),sK15,sK15),relation_dom(identity_relation(sK14)))
| ~ in(sK0(identity_relation(sK14),sK15,sK15),sK15)
| ~ function(identity_relation(sK14))
| ~ relation(identity_relation(sK14))
| relation_image(identity_relation(sK14),sK15) = sK15 ),
inference(instantiation,[status(thm)],[c_29101]) ).
cnf(c_38743,plain,
( ~ in(sK1(identity_relation(sK14),sK15,sK15),sK15)
| ~ element(sK15,powerset(X0))
| element(sK1(identity_relation(sK14),sK15,sK15),X0) ),
inference(instantiation,[status(thm)],[c_101]) ).
cnf(c_38745,plain,
( X0 != sK1(identity_relation(sK14),sK15,sK15)
| X1 != sK15
| ~ in(sK1(identity_relation(sK14),sK15,sK15),sK15)
| in(X0,X1) ),
inference(instantiation,[status(thm)],[c_164]) ).
cnf(c_39031,plain,
( ~ in(sK1(identity_relation(sK14),sK15,sK15),sK15)
| ~ element(sK15,powerset(sK14))
| element(sK1(identity_relation(sK14),sK15,sK15),sK14) ),
inference(instantiation,[status(thm)],[c_38743]) ).
cnf(c_39093,plain,
( X0 != sK1(identity_relation(sK14),sK15,sK15)
| sK15 != sK15
| ~ in(sK1(identity_relation(sK14),sK15,sK15),sK15)
| in(X0,sK15) ),
inference(instantiation,[status(thm)],[c_38745]) ).
cnf(c_39158,plain,
( apply(X0,sK1(identity_relation(sK14),sK15,sK15)) != X1
| sK0(X0,sK15,X2) != X1
| sK0(X0,sK15,X2) = apply(X0,sK1(identity_relation(sK14),sK15,sK15)) ),
inference(instantiation,[status(thm)],[c_163]) ).
cnf(c_39549,plain,
( ~ element(X0,sK14)
| in(X0,sK14)
| empty(sK14) ),
inference(instantiation,[status(thm)],[c_95]) ).
cnf(c_40091,plain,
( apply(X0,sK1(identity_relation(sK14),sK15,sK15)) != sK0(X0,sK15,X1)
| sK0(X0,sK15,X1) != sK0(X0,sK15,X1)
| sK0(X0,sK15,X1) = apply(X0,sK1(identity_relation(sK14),sK15,sK15)) ),
inference(instantiation,[status(thm)],[c_39158]) ).
cnf(c_41109,plain,
( ~ element(sK1(identity_relation(sK14),sK15,sK15),sK14)
| in(sK1(identity_relation(sK14),sK15,sK15),sK14)
| empty(sK14) ),
inference(instantiation,[status(thm)],[c_39549]) ).
cnf(c_42959,plain,
( apply(identity_relation(sK14),sK1(identity_relation(sK14),sK15,sK15)) != sK0(identity_relation(sK14),sK15,sK15)
| sK0(identity_relation(sK14),sK15,sK15) != sK0(identity_relation(sK14),sK15,sK15)
| sK0(identity_relation(sK14),sK15,sK15) = apply(identity_relation(sK14),sK1(identity_relation(sK14),sK15,sK15)) ),
inference(instantiation,[status(thm)],[c_40091]) ).
cnf(c_45409,plain,
( ~ in(sK1(identity_relation(sK14),sK15,sK15),sK14)
| ~ function(identity_relation(sK14))
| ~ relation(identity_relation(sK14))
| apply(identity_relation(sK14),sK1(identity_relation(sK14),sK15,sK15)) = sK1(identity_relation(sK14),sK15,sK15) ),
inference(instantiation,[status(thm)],[c_98]) ).
cnf(c_45611,plain,
( X0 != X1
| X2 != sK15
| ~ in(X1,sK15)
| in(X0,X2) ),
inference(instantiation,[status(thm)],[c_164]) ).
cnf(c_50090,plain,
( apply(identity_relation(sK14),sK1(identity_relation(sK14),sK15,sK15)) != sK1(identity_relation(sK14),sK15,sK15)
| sK15 != sK15
| ~ in(sK1(identity_relation(sK14),sK15,sK15),sK15)
| in(apply(identity_relation(sK14),sK1(identity_relation(sK14),sK15,sK15)),sK15) ),
inference(instantiation,[status(thm)],[c_39093]) ).
cnf(c_51188,plain,
( X0 != X1
| sK15 != sK15
| ~ in(X1,sK15)
| in(X0,sK15) ),
inference(instantiation,[status(thm)],[c_45611]) ).
cnf(c_55060,plain,
( X0 != apply(identity_relation(sK14),sK1(identity_relation(sK14),sK15,sK15))
| sK15 != sK15
| ~ in(apply(identity_relation(sK14),sK1(identity_relation(sK14),sK15,sK15)),sK15)
| in(X0,sK15) ),
inference(instantiation,[status(thm)],[c_51188]) ).
cnf(c_63512,plain,
( sK0(identity_relation(sK14),sK15,sK15) != apply(identity_relation(sK14),sK1(identity_relation(sK14),sK15,sK15))
| sK15 != sK15
| ~ in(apply(identity_relation(sK14),sK1(identity_relation(sK14),sK15,sK15)),sK15)
| in(sK0(identity_relation(sK14),sK15,sK15),sK15) ),
inference(instantiation,[status(thm)],[c_55060]) ).
cnf(c_63513,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_63512,c_50090,c_45409,c_42959,c_41109,c_39031,c_37696,c_26386,c_20719,c_20190,c_14053,c_12471,c_12153,c_12156,c_7265,c_7192,c_6582,c_6113,c_5303,c_1767,c_1766,c_1121,c_1120,c_547,c_264,c_233,c_204,c_92,c_93]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SEU081+1 : TPTP v8.1.2. Released v3.2.0.
% 0.03/0.14 % Command : run_iprover %s %d THM
% 0.13/0.35 % Computer : n002.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Thu May 2 17:53:42 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.19/0.48 Running first-order theorem proving
% 0.19/0.48 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
% 61.81/9.27 % SZS status Started for theBenchmark.p
% 61.81/9.27 % SZS status Theorem for theBenchmark.p
% 61.81/9.27
% 61.81/9.27 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 61.81/9.27
% 61.81/9.27 ------ iProver source info
% 61.81/9.27
% 61.81/9.27 git: date: 2024-05-02 19:28:25 +0000
% 61.81/9.27 git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 61.81/9.27 git: non_committed_changes: false
% 61.81/9.27
% 61.81/9.27 ------ Parsing...
% 61.81/9.27 ------ Clausification by vclausify_rel & Parsing by iProver...
% 61.81/9.27
% 61.81/9.27 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 1 0s sf_e
% 61.81/9.27
% 61.81/9.27 ------ Preprocessing...
% 61.81/9.27
% 61.81/9.27 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 61.81/9.27 ------ Proving...
% 61.81/9.27 ------ Problem Properties
% 61.81/9.27
% 61.81/9.27
% 61.81/9.27 clauses 53
% 61.81/9.27 conjectures 2
% 61.81/9.27 EPR 25
% 61.81/9.27 Horn 47
% 61.81/9.27 unary 26
% 61.81/9.27 binary 11
% 61.81/9.27 lits 114
% 61.81/9.27 lits eq 15
% 61.81/9.27 fd_pure 0
% 61.81/9.27 fd_pseudo 0
% 61.81/9.27 fd_cond 1
% 61.81/9.27 fd_pseudo_cond 5
% 61.81/9.27 AC symbols 0
% 61.81/9.27
% 61.81/9.27 ------ Input Options Time Limit: Unbounded
% 61.81/9.27
% 61.81/9.27
% 61.81/9.27 ------
% 61.81/9.27 Current options:
% 61.81/9.27 ------
% 61.81/9.27
% 61.81/9.27
% 61.81/9.27
% 61.81/9.27
% 61.81/9.27 ------ Proving...
% 61.81/9.27
% 61.81/9.27
% 61.81/9.27 % SZS status Theorem for theBenchmark.p
% 61.81/9.27
% 61.81/9.27 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 61.81/9.27
% 61.81/9.27
%------------------------------------------------------------------------------