TSTP Solution File: SEU076+1 by iProver---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : SEU076+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n004.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 03:04:28 EDT 2024
% Result : Theorem 61.61s 9.20s
% Output : CNFRefutation 61.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 13
% Syntax : Number of formulae : 92 ( 16 unt; 0 def)
% Number of atoms : 457 ( 102 equ)
% Maximal formula atoms : 20 ( 4 avg)
% Number of connectives : 609 ( 244 ~; 238 |; 102 &)
% ( 11 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 3 con; 0-3 aty)
% Number of variables : 210 ( 0 sgn 126 !; 32 ?)
% 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(f6,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(f7,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ( one_to_one(X0)
<=> ! [X1,X2] :
( ( apply(X0,X1) = apply(X0,X2)
& in(X2,relation_dom(X0))
& in(X1,relation_dom(X0)) )
=> X1 = X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_funct_1) ).
fof(f26,conjecture,
! [X0,X1,X2] :
( ( function(X2)
& relation(X2) )
=> ( ( one_to_one(X2)
& subset(X0,relation_dom(X2))
& subset(relation_image(X2,X0),relation_image(X2,X1)) )
=> subset(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t157_funct_1) ).
fof(f27,negated_conjecture,
~ ! [X0,X1,X2] :
( ( function(X2)
& relation(X2) )
=> ( ( one_to_one(X2)
& subset(X0,relation_dom(X2))
& subset(relation_image(X2,X0),relation_image(X2,X1)) )
=> subset(X0,X1) ) ),
inference(negated_conjecture,[],[f26]) ).
fof(f44,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(f45,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,[],[f44]) ).
fof(f46,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f6]) ).
fof(f47,plain,
! [X0] :
( ( one_to_one(X0)
<=> ! [X1,X2] :
( X1 = X2
| apply(X0,X1) != apply(X0,X2)
| ~ in(X2,relation_dom(X0))
| ~ in(X1,relation_dom(X0)) ) )
| ~ function(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f7]) ).
fof(f48,plain,
! [X0] :
( ( one_to_one(X0)
<=> ! [X1,X2] :
( X1 = X2
| apply(X0,X1) != apply(X0,X2)
| ~ in(X2,relation_dom(X0))
| ~ in(X1,relation_dom(X0)) ) )
| ~ function(X0)
| ~ relation(X0) ),
inference(flattening,[],[f47]) ).
fof(f53,plain,
? [X0,X1,X2] :
( ~ subset(X0,X1)
& one_to_one(X2)
& subset(X0,relation_dom(X2))
& subset(relation_image(X2,X0),relation_image(X2,X1))
& function(X2)
& relation(X2) ),
inference(ennf_transformation,[],[f27]) ).
fof(f54,plain,
? [X0,X1,X2] :
( ~ subset(X0,X1)
& one_to_one(X2)
& subset(X0,relation_dom(X2))
& subset(relation_image(X2,X0),relation_image(X2,X1))
& function(X2)
& relation(X2) ),
inference(flattening,[],[f53]) ).
fof(f64,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,[],[f45]) ).
fof(f65,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,[],[f64]) ).
fof(f66,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(f67,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(f68,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(f69,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])],[f65,f68,f67,f66]) ).
fof(f70,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) )
| ~ subset(X0,X1) ) ),
inference(nnf_transformation,[],[f46]) ).
fof(f71,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(rectify,[],[f70]) ).
fof(f72,plain,
! [X0,X1] :
( ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) )
=> ( ~ in(sK3(X0,X1),X1)
& in(sK3(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f73,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ in(sK3(X0,X1),X1)
& in(sK3(X0,X1),X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f71,f72]) ).
fof(f74,plain,
! [X0] :
( ( ( one_to_one(X0)
| ? [X1,X2] :
( X1 != X2
& apply(X0,X1) = apply(X0,X2)
& in(X2,relation_dom(X0))
& in(X1,relation_dom(X0)) ) )
& ( ! [X1,X2] :
( X1 = X2
| apply(X0,X1) != apply(X0,X2)
| ~ in(X2,relation_dom(X0))
| ~ in(X1,relation_dom(X0)) )
| ~ one_to_one(X0) ) )
| ~ function(X0)
| ~ relation(X0) ),
inference(nnf_transformation,[],[f48]) ).
fof(f75,plain,
! [X0] :
( ( ( one_to_one(X0)
| ? [X1,X2] :
( X1 != X2
& apply(X0,X1) = apply(X0,X2)
& in(X2,relation_dom(X0))
& in(X1,relation_dom(X0)) ) )
& ( ! [X3,X4] :
( X3 = X4
| apply(X0,X4) != apply(X0,X3)
| ~ in(X4,relation_dom(X0))
| ~ in(X3,relation_dom(X0)) )
| ~ one_to_one(X0) ) )
| ~ function(X0)
| ~ relation(X0) ),
inference(rectify,[],[f74]) ).
fof(f76,plain,
! [X0] :
( ? [X1,X2] :
( X1 != X2
& apply(X0,X1) = apply(X0,X2)
& in(X2,relation_dom(X0))
& in(X1,relation_dom(X0)) )
=> ( sK4(X0) != sK5(X0)
& apply(X0,sK4(X0)) = apply(X0,sK5(X0))
& in(sK5(X0),relation_dom(X0))
& in(sK4(X0),relation_dom(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f77,plain,
! [X0] :
( ( ( one_to_one(X0)
| ( sK4(X0) != sK5(X0)
& apply(X0,sK4(X0)) = apply(X0,sK5(X0))
& in(sK5(X0),relation_dom(X0))
& in(sK4(X0),relation_dom(X0)) ) )
& ( ! [X3,X4] :
( X3 = X4
| apply(X0,X4) != apply(X0,X3)
| ~ in(X4,relation_dom(X0))
| ~ in(X3,relation_dom(X0)) )
| ~ one_to_one(X0) ) )
| ~ function(X0)
| ~ relation(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5])],[f75,f76]) ).
fof(f100,plain,
( ? [X0,X1,X2] :
( ~ subset(X0,X1)
& one_to_one(X2)
& subset(X0,relation_dom(X2))
& subset(relation_image(X2,X0),relation_image(X2,X1))
& function(X2)
& relation(X2) )
=> ( ~ subset(sK17,sK18)
& one_to_one(sK19)
& subset(sK17,relation_dom(sK19))
& subset(relation_image(sK19,sK17),relation_image(sK19,sK18))
& function(sK19)
& relation(sK19) ) ),
introduced(choice_axiom,[]) ).
fof(f101,plain,
( ~ subset(sK17,sK18)
& one_to_one(sK19)
& subset(sK17,relation_dom(sK19))
& subset(relation_image(sK19,sK17),relation_image(sK19,sK18))
& function(sK19)
& relation(sK19) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK17,sK18,sK19])],[f54,f100]) ).
fof(f109,plain,
! [X2,X0,X1,X6] :
( in(sK2(X0,X1,X6),relation_dom(X0))
| ~ in(X6,X2)
| relation_image(X0,X1) != X2
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f69]) ).
fof(f110,plain,
! [X2,X0,X1,X6] :
( in(sK2(X0,X1,X6),X1)
| ~ in(X6,X2)
| relation_image(X0,X1) != X2
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f69]) ).
fof(f111,plain,
! [X2,X0,X1,X6] :
( apply(X0,sK2(X0,X1,X6)) = X6
| ~ in(X6,X2)
| relation_image(X0,X1) != X2
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f69]) ).
fof(f112,plain,
! [X2,X0,X1,X6,X7] :
( in(X6,X2)
| apply(X0,X7) != X6
| ~ in(X7,X1)
| ~ in(X7,relation_dom(X0))
| relation_image(X0,X1) != X2
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f69]) ).
fof(f117,plain,
! [X3,X0,X1] :
( in(X3,X1)
| ~ in(X3,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f73]) ).
fof(f118,plain,
! [X0,X1] :
( subset(X0,X1)
| in(sK3(X0,X1),X0) ),
inference(cnf_transformation,[],[f73]) ).
fof(f119,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ in(sK3(X0,X1),X1) ),
inference(cnf_transformation,[],[f73]) ).
fof(f120,plain,
! [X3,X0,X4] :
( X3 = X4
| apply(X0,X4) != apply(X0,X3)
| ~ in(X4,relation_dom(X0))
| ~ in(X3,relation_dom(X0))
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f77]) ).
fof(f155,plain,
relation(sK19),
inference(cnf_transformation,[],[f101]) ).
fof(f156,plain,
function(sK19),
inference(cnf_transformation,[],[f101]) ).
fof(f157,plain,
subset(relation_image(sK19,sK17),relation_image(sK19,sK18)),
inference(cnf_transformation,[],[f101]) ).
fof(f158,plain,
subset(sK17,relation_dom(sK19)),
inference(cnf_transformation,[],[f101]) ).
fof(f159,plain,
one_to_one(sK19),
inference(cnf_transformation,[],[f101]) ).
fof(f160,plain,
~ subset(sK17,sK18),
inference(cnf_transformation,[],[f101]) ).
fof(f170,plain,
! [X2,X0,X1,X7] :
( in(apply(X0,X7),X2)
| ~ in(X7,X1)
| ~ in(X7,relation_dom(X0))
| relation_image(X0,X1) != X2
| ~ function(X0)
| ~ relation(X0) ),
inference(equality_resolution,[],[f112]) ).
fof(f171,plain,
! [X0,X1,X7] :
( in(apply(X0,X7),relation_image(X0,X1))
| ~ in(X7,X1)
| ~ in(X7,relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(equality_resolution,[],[f170]) ).
fof(f172,plain,
! [X0,X1,X6] :
( apply(X0,sK2(X0,X1,X6)) = X6
| ~ in(X6,relation_image(X0,X1))
| ~ function(X0)
| ~ relation(X0) ),
inference(equality_resolution,[],[f111]) ).
fof(f173,plain,
! [X0,X1,X6] :
( in(sK2(X0,X1,X6),X1)
| ~ in(X6,relation_image(X0,X1))
| ~ function(X0)
| ~ relation(X0) ),
inference(equality_resolution,[],[f110]) ).
fof(f174,plain,
! [X0,X1,X6] :
( in(sK2(X0,X1,X6),relation_dom(X0))
| ~ in(X6,relation_image(X0,X1))
| ~ function(X0)
| ~ relation(X0) ),
inference(equality_resolution,[],[f109]) ).
cnf(c_57,plain,
( ~ in(X0,relation_dom(X1))
| ~ in(X0,X2)
| ~ function(X1)
| ~ relation(X1)
| in(apply(X1,X0),relation_image(X1,X2)) ),
inference(cnf_transformation,[],[f171]) ).
cnf(c_58,plain,
( ~ in(X0,relation_image(X1,X2))
| ~ function(X1)
| ~ relation(X1)
| apply(X1,sK2(X1,X2,X0)) = X0 ),
inference(cnf_transformation,[],[f172]) ).
cnf(c_59,plain,
( ~ in(X0,relation_image(X1,X2))
| ~ function(X1)
| ~ relation(X1)
| in(sK2(X1,X2,X0),X2) ),
inference(cnf_transformation,[],[f173]) ).
cnf(c_60,plain,
( ~ in(X0,relation_image(X1,X2))
| ~ function(X1)
| ~ relation(X1)
| in(sK2(X1,X2,X0),relation_dom(X1)) ),
inference(cnf_transformation,[],[f174]) ).
cnf(c_61,plain,
( ~ in(sK3(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f119]) ).
cnf(c_62,plain,
( in(sK3(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f118]) ).
cnf(c_63,plain,
( ~ in(X0,X1)
| ~ subset(X1,X2)
| in(X0,X2) ),
inference(cnf_transformation,[],[f117]) ).
cnf(c_68,plain,
( apply(X0,X1) != apply(X0,X2)
| ~ in(X1,relation_dom(X0))
| ~ in(X2,relation_dom(X0))
| ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| X1 = X2 ),
inference(cnf_transformation,[],[f120]) ).
cnf(c_99,negated_conjecture,
~ subset(sK17,sK18),
inference(cnf_transformation,[],[f160]) ).
cnf(c_100,negated_conjecture,
one_to_one(sK19),
inference(cnf_transformation,[],[f159]) ).
cnf(c_101,negated_conjecture,
subset(sK17,relation_dom(sK19)),
inference(cnf_transformation,[],[f158]) ).
cnf(c_102,negated_conjecture,
subset(relation_image(sK19,sK17),relation_image(sK19,sK18)),
inference(cnf_transformation,[],[f157]) ).
cnf(c_103,negated_conjecture,
function(sK19),
inference(cnf_transformation,[],[f156]) ).
cnf(c_104,negated_conjecture,
relation(sK19),
inference(cnf_transformation,[],[f155]) ).
cnf(c_168,plain,
X0 = X0,
theory(equality) ).
cnf(c_170,plain,
( X0 != X1
| X2 != X1
| X2 = X0 ),
theory(equality) ).
cnf(c_171,plain,
( X0 != X1
| X2 != X3
| ~ in(X1,X3)
| in(X0,X2) ),
theory(equality) ).
cnf(c_189,plain,
( in(sK3(sK17,sK18),sK17)
| subset(sK17,sK18) ),
inference(instantiation,[status(thm)],[c_62]) ).
cnf(c_229,plain,
( ~ in(sK3(sK17,sK18),sK17)
| ~ subset(sK17,X0)
| in(sK3(sK17,sK18),X0) ),
inference(instantiation,[status(thm)],[c_63]) ).
cnf(c_232,plain,
( ~ in(sK3(sK17,sK18),relation_dom(X0))
| ~ in(sK3(sK17,sK18),sK17)
| ~ function(X0)
| ~ relation(X0)
| in(apply(X0,sK3(sK17,sK18)),relation_image(X0,sK17)) ),
inference(instantiation,[status(thm)],[c_57]) ).
cnf(c_247,plain,
sK18 = sK18,
inference(instantiation,[status(thm)],[c_168]) ).
cnf(c_419,plain,
( ~ in(sK3(sK17,sK18),sK17)
| ~ subset(sK17,relation_dom(sK19))
| in(sK3(sK17,sK18),relation_dom(sK19)) ),
inference(instantiation,[status(thm)],[c_229]) ).
cnf(c_920,plain,
( ~ in(sK3(sK17,sK18),relation_dom(sK19))
| ~ in(sK3(sK17,sK18),sK17)
| ~ function(sK19)
| ~ relation(sK19)
| in(apply(sK19,sK3(sK17,sK18)),relation_image(sK19,sK17)) ),
inference(instantiation,[status(thm)],[c_232]) ).
cnf(c_1186,plain,
( apply(X0,X1) != apply(X0,sK3(sK17,sK18))
| ~ in(sK3(sK17,sK18),relation_dom(X0))
| ~ in(X1,relation_dom(X0))
| ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| X1 = sK3(sK17,sK18) ),
inference(instantiation,[status(thm)],[c_68]) ).
cnf(c_1307,plain,
( ~ in(X0,relation_image(X1,X2))
| ~ subset(relation_image(X1,X2),X3)
| in(X0,X3) ),
inference(instantiation,[status(thm)],[c_63]) ).
cnf(c_3108,plain,
sK3(sK17,sK18) = sK3(sK17,sK18),
inference(instantiation,[status(thm)],[c_168]) ).
cnf(c_3306,plain,
( sK3(sK17,sK18) != X0
| X1 != X0
| sK3(sK17,sK18) = X1 ),
inference(instantiation,[status(thm)],[c_170]) ).
cnf(c_3509,plain,
( ~ in(sK3(X0,sK18),sK18)
| subset(X0,sK18) ),
inference(instantiation,[status(thm)],[c_61]) ).
cnf(c_4737,plain,
( ~ in(apply(sK19,sK3(sK17,sK18)),relation_image(sK19,sK17))
| ~ subset(relation_image(sK19,sK17),X0)
| in(apply(sK19,sK3(sK17,sK18)),X0) ),
inference(instantiation,[status(thm)],[c_1307]) ).
cnf(c_4745,plain,
( apply(sK19,X0) != apply(sK19,sK3(sK17,sK18))
| ~ in(sK3(sK17,sK18),relation_dom(sK19))
| ~ in(X0,relation_dom(sK19))
| ~ function(sK19)
| ~ relation(sK19)
| ~ one_to_one(sK19)
| X0 = sK3(sK17,sK18) ),
inference(instantiation,[status(thm)],[c_1186]) ).
cnf(c_8089,plain,
( apply(sK19,sK2(sK19,X0,apply(sK19,sK3(sK17,sK18)))) != apply(sK19,sK3(sK17,sK18))
| ~ in(sK2(sK19,X0,apply(sK19,sK3(sK17,sK18))),relation_dom(sK19))
| ~ in(sK3(sK17,sK18),relation_dom(sK19))
| ~ function(sK19)
| ~ relation(sK19)
| ~ one_to_one(sK19)
| sK2(sK19,X0,apply(sK19,sK3(sK17,sK18))) = sK3(sK17,sK18) ),
inference(instantiation,[status(thm)],[c_4745]) ).
cnf(c_8090,plain,
( ~ in(apply(sK19,sK3(sK17,sK18)),relation_image(sK19,X0))
| ~ function(sK19)
| ~ relation(sK19)
| apply(sK19,sK2(sK19,X0,apply(sK19,sK3(sK17,sK18)))) = apply(sK19,sK3(sK17,sK18)) ),
inference(instantiation,[status(thm)],[c_58]) ).
cnf(c_8874,plain,
( ~ in(apply(sK19,sK3(sK17,sK18)),relation_image(sK19,sK17))
| ~ subset(relation_image(sK19,sK17),relation_image(sK19,sK18))
| in(apply(sK19,sK3(sK17,sK18)),relation_image(sK19,sK18)) ),
inference(instantiation,[status(thm)],[c_4737]) ).
cnf(c_9580,plain,
( ~ in(sK3(sK17,sK18),sK18)
| subset(sK17,sK18) ),
inference(instantiation,[status(thm)],[c_3509]) ).
cnf(c_10063,plain,
( sK3(sK17,sK18) != sK3(sK17,sK18)
| X0 != sK3(sK17,sK18)
| sK3(sK17,sK18) = X0 ),
inference(instantiation,[status(thm)],[c_3306]) ).
cnf(c_12959,plain,
( ~ in(apply(sK19,sK3(sK17,sK18)),relation_image(sK19,sK18))
| ~ function(sK19)
| ~ relation(sK19)
| in(sK2(sK19,sK18,apply(sK19,sK3(sK17,sK18))),relation_dom(sK19)) ),
inference(instantiation,[status(thm)],[c_60]) ).
cnf(c_12960,plain,
( ~ in(apply(sK19,sK3(sK17,sK18)),relation_image(sK19,sK18))
| ~ function(sK19)
| ~ relation(sK19)
| in(sK2(sK19,sK18,apply(sK19,sK3(sK17,sK18))),sK18) ),
inference(instantiation,[status(thm)],[c_59]) ).
cnf(c_13673,plain,
( ~ in(apply(sK19,sK3(sK17,sK18)),relation_image(sK19,sK18))
| ~ function(sK19)
| ~ relation(sK19)
| apply(sK19,sK2(sK19,sK18,apply(sK19,sK3(sK17,sK18)))) = apply(sK19,sK3(sK17,sK18)) ),
inference(instantiation,[status(thm)],[c_8090]) ).
cnf(c_20334,plain,
( apply(sK19,sK2(sK19,sK18,apply(sK19,sK3(sK17,sK18)))) != apply(sK19,sK3(sK17,sK18))
| ~ in(sK2(sK19,sK18,apply(sK19,sK3(sK17,sK18))),relation_dom(sK19))
| ~ in(sK3(sK17,sK18),relation_dom(sK19))
| ~ function(sK19)
| ~ relation(sK19)
| ~ one_to_one(sK19)
| sK2(sK19,sK18,apply(sK19,sK3(sK17,sK18))) = sK3(sK17,sK18) ),
inference(instantiation,[status(thm)],[c_8089]) ).
cnf(c_29943,plain,
( sK2(sK19,sK18,apply(sK19,sK3(sK17,sK18))) != sK3(sK17,sK18)
| sK3(sK17,sK18) != sK3(sK17,sK18)
| sK3(sK17,sK18) = sK2(sK19,sK18,apply(sK19,sK3(sK17,sK18))) ),
inference(instantiation,[status(thm)],[c_10063]) ).
cnf(c_42916,plain,
( X0 != X1
| X2 != sK18
| ~ in(X1,sK18)
| in(X0,X2) ),
inference(instantiation,[status(thm)],[c_171]) ).
cnf(c_52224,plain,
( X0 != X1
| sK18 != sK18
| ~ in(X1,sK18)
| in(X0,sK18) ),
inference(instantiation,[status(thm)],[c_42916]) ).
cnf(c_54024,plain,
( sK3(sK17,sK18) != X0
| sK18 != sK18
| ~ in(X0,sK18)
| in(sK3(sK17,sK18),sK18) ),
inference(instantiation,[status(thm)],[c_52224]) ).
cnf(c_59545,plain,
( sK3(sK17,sK18) != sK2(sK19,sK18,apply(sK19,sK3(sK17,sK18)))
| sK18 != sK18
| ~ in(sK2(sK19,sK18,apply(sK19,sK3(sK17,sK18))),sK18)
| in(sK3(sK17,sK18),sK18) ),
inference(instantiation,[status(thm)],[c_54024]) ).
cnf(c_59546,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_59545,c_29943,c_20334,c_13673,c_12959,c_12960,c_9580,c_8874,c_3108,c_920,c_419,c_247,c_189,c_102,c_99,c_101,c_100,c_103,c_104]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU076+1 : TPTP v8.1.2. Released v3.2.0.
% 0.11/0.12 % Command : run_iprover %s %d THM
% 0.11/0.32 % Computer : n004.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.33 % DateTime : Thu May 2 17:29:33 EDT 2024
% 0.11/0.33 % CPUTime :
% 0.18/0.44 Running first-order theorem proving
% 0.18/0.44 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
% 61.61/9.20 % SZS status Started for theBenchmark.p
% 61.61/9.20 % SZS status Theorem for theBenchmark.p
% 61.61/9.20
% 61.61/9.20 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 61.61/9.20
% 61.61/9.20 ------ iProver source info
% 61.61/9.20
% 61.61/9.20 git: date: 2024-05-02 19:28:25 +0000
% 61.61/9.20 git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 61.61/9.20 git: non_committed_changes: false
% 61.61/9.20
% 61.61/9.20 ------ Parsing...
% 61.61/9.20 ------ Clausification by vclausify_rel & Parsing by iProver...
% 61.61/9.20
% 61.61/9.20 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 1 0s sf_e
% 61.61/9.20
% 61.61/9.20 ------ Preprocessing...
% 61.61/9.20
% 61.61/9.20 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 61.61/9.20 ------ Proving...
% 61.61/9.20 ------ Problem Properties
% 61.61/9.20
% 61.61/9.20
% 61.61/9.20 clauses 62
% 61.61/9.20 conjectures 6
% 61.61/9.20 EPR 32
% 61.61/9.20 Horn 53
% 61.61/9.20 unary 28
% 61.61/9.20 binary 15
% 61.61/9.20 lits 138
% 61.61/9.20 lits eq 13
% 61.61/9.20 fd_pure 0
% 61.61/9.20 fd_pseudo 0
% 61.61/9.20 fd_cond 1
% 61.61/9.20 fd_pseudo_cond 6
% 61.61/9.20 AC symbols 0
% 61.61/9.20
% 61.61/9.20 ------ Input Options Time Limit: Unbounded
% 61.61/9.20
% 61.61/9.20
% 61.61/9.20 ------
% 61.61/9.20 Current options:
% 61.61/9.20 ------
% 61.61/9.20
% 61.61/9.20
% 61.61/9.20
% 61.61/9.20
% 61.61/9.20 ------ Proving...
% 61.61/9.20
% 61.61/9.20
% 61.61/9.20 % SZS status Theorem for theBenchmark.p
% 61.61/9.20
% 61.61/9.20 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 61.61/9.20
% 61.61/9.21
%------------------------------------------------------------------------------