TSTP Solution File: SEU059+1 by iProver---3.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SEU059+1 : TPTP v8.1.2. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n010.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 : Thu Aug 31 17:03:34 EDT 2023
% Result : Theorem 10.31s 2.19s
% Output : CNFRefutation 10.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 6
% Syntax : Number of formulae : 85 ( 10 unt; 0 def)
% Number of atoms : 374 ( 46 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 482 ( 193 ~; 210 |; 65 &)
% ( 8 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-3 aty)
% Number of variables : 166 ( 3 sgn; 111 !; 17 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,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(f6,axiom,
! [X0,X1,X2] :
( set_difference(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ( ~ in(X3,X1)
& in(X3,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_xboole_0) ).
fof(f26,conjecture,
! [X0,X1,X2] :
( ( function(X2)
& relation(X2) )
=> relation_inverse_image(X2,set_difference(X0,X1)) = set_difference(relation_inverse_image(X2,X0),relation_inverse_image(X2,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t138_funct_1) ).
fof(f27,negated_conjecture,
~ ! [X0,X1,X2] :
( ( function(X2)
& relation(X2) )
=> relation_inverse_image(X2,set_difference(X0,X1)) = set_difference(relation_inverse_image(X2,X0),relation_inverse_image(X2,X1)) ),
inference(negated_conjecture,[],[f26]) ).
fof(f50,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,[],[f5]) ).
fof(f51,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,[],[f50]) ).
fof(f58,plain,
? [X0,X1,X2] :
( relation_inverse_image(X2,set_difference(X0,X1)) != set_difference(relation_inverse_image(X2,X0),relation_inverse_image(X2,X1))
& function(X2)
& relation(X2) ),
inference(ennf_transformation,[],[f27]) ).
fof(f59,plain,
? [X0,X1,X2] :
( relation_inverse_image(X2,set_difference(X0,X1)) != set_difference(relation_inverse_image(X2,X0),relation_inverse_image(X2,X1))
& function(X2)
& relation(X2) ),
inference(flattening,[],[f58]) ).
fof(f71,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,[],[f51]) ).
fof(f72,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,[],[f71]) ).
fof(f73,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,[],[f72]) ).
fof(f74,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(f75,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])],[f73,f74]) ).
fof(f76,plain,
! [X0,X1,X2] :
( ( set_difference(X0,X1) = X2
| ? [X3] :
( ( in(X3,X1)
| ~ in(X3,X0)
| ~ in(X3,X2) )
& ( ( ~ in(X3,X1)
& in(X3,X0) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| in(X3,X1)
| ~ in(X3,X0) )
& ( ( ~ in(X3,X1)
& in(X3,X0) )
| ~ in(X3,X2) ) )
| set_difference(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f6]) ).
fof(f77,plain,
! [X0,X1,X2] :
( ( set_difference(X0,X1) = X2
| ? [X3] :
( ( in(X3,X1)
| ~ in(X3,X0)
| ~ in(X3,X2) )
& ( ( ~ in(X3,X1)
& in(X3,X0) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| in(X3,X1)
| ~ in(X3,X0) )
& ( ( ~ in(X3,X1)
& in(X3,X0) )
| ~ in(X3,X2) ) )
| set_difference(X0,X1) != X2 ) ),
inference(flattening,[],[f76]) ).
fof(f78,plain,
! [X0,X1,X2] :
( ( set_difference(X0,X1) = X2
| ? [X3] :
( ( in(X3,X1)
| ~ in(X3,X0)
| ~ in(X3,X2) )
& ( ( ~ in(X3,X1)
& in(X3,X0) )
| in(X3,X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| in(X4,X1)
| ~ in(X4,X0) )
& ( ( ~ in(X4,X1)
& in(X4,X0) )
| ~ in(X4,X2) ) )
| set_difference(X0,X1) != X2 ) ),
inference(rectify,[],[f77]) ).
fof(f79,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( in(X3,X1)
| ~ in(X3,X0)
| ~ in(X3,X2) )
& ( ( ~ in(X3,X1)
& in(X3,X0) )
| in(X3,X2) ) )
=> ( ( in(sK1(X0,X1,X2),X1)
| ~ in(sK1(X0,X1,X2),X0)
| ~ in(sK1(X0,X1,X2),X2) )
& ( ( ~ in(sK1(X0,X1,X2),X1)
& in(sK1(X0,X1,X2),X0) )
| in(sK1(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f80,plain,
! [X0,X1,X2] :
( ( set_difference(X0,X1) = X2
| ( ( in(sK1(X0,X1,X2),X1)
| ~ in(sK1(X0,X1,X2),X0)
| ~ in(sK1(X0,X1,X2),X2) )
& ( ( ~ in(sK1(X0,X1,X2),X1)
& in(sK1(X0,X1,X2),X0) )
| in(sK1(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| in(X4,X1)
| ~ in(X4,X0) )
& ( ( ~ in(X4,X1)
& in(X4,X0) )
| ~ in(X4,X2) ) )
| set_difference(X0,X1) != X2 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f78,f79]) ).
fof(f103,plain,
( ? [X0,X1,X2] :
( relation_inverse_image(X2,set_difference(X0,X1)) != set_difference(relation_inverse_image(X2,X0),relation_inverse_image(X2,X1))
& function(X2)
& relation(X2) )
=> ( relation_inverse_image(sK15,set_difference(sK13,sK14)) != set_difference(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14))
& function(sK15)
& relation(sK15) ) ),
introduced(choice_axiom,[]) ).
fof(f104,plain,
( relation_inverse_image(sK15,set_difference(sK13,sK14)) != set_difference(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14))
& function(sK15)
& relation(sK15) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK13,sK14,sK15])],[f59,f103]) ).
fof(f113,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,[],[f75]) ).
fof(f114,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,[],[f75]) ).
fof(f115,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,[],[f75]) ).
fof(f119,plain,
! [X2,X0,X1,X4] :
( in(X4,X0)
| ~ in(X4,X2)
| set_difference(X0,X1) != X2 ),
inference(cnf_transformation,[],[f80]) ).
fof(f120,plain,
! [X2,X0,X1,X4] :
( ~ in(X4,X1)
| ~ in(X4,X2)
| set_difference(X0,X1) != X2 ),
inference(cnf_transformation,[],[f80]) ).
fof(f121,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| in(X4,X1)
| ~ in(X4,X0)
| set_difference(X0,X1) != X2 ),
inference(cnf_transformation,[],[f80]) ).
fof(f122,plain,
! [X2,X0,X1] :
( set_difference(X0,X1) = X2
| in(sK1(X0,X1,X2),X0)
| in(sK1(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f80]) ).
fof(f123,plain,
! [X2,X0,X1] :
( set_difference(X0,X1) = X2
| ~ in(sK1(X0,X1,X2),X1)
| in(sK1(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f80]) ).
fof(f124,plain,
! [X2,X0,X1] :
( set_difference(X0,X1) = X2
| in(sK1(X0,X1,X2),X1)
| ~ in(sK1(X0,X1,X2),X0)
| ~ in(sK1(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f80]) ).
fof(f155,plain,
relation(sK15),
inference(cnf_transformation,[],[f104]) ).
fof(f156,plain,
function(sK15),
inference(cnf_transformation,[],[f104]) ).
fof(f157,plain,
relation_inverse_image(sK15,set_difference(sK13,sK14)) != set_difference(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14)),
inference(cnf_transformation,[],[f104]) ).
fof(f170,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,[],[f115]) ).
fof(f171,plain,
! [X0,X1,X4] :
( in(apply(X0,X4),X1)
| ~ in(X4,relation_inverse_image(X0,X1))
| ~ function(X0)
| ~ relation(X0) ),
inference(equality_resolution,[],[f114]) ).
fof(f172,plain,
! [X0,X1,X4] :
( in(X4,relation_dom(X0))
| ~ in(X4,relation_inverse_image(X0,X1))
| ~ function(X0)
| ~ relation(X0) ),
inference(equality_resolution,[],[f113]) ).
fof(f173,plain,
! [X0,X1,X4] :
( in(X4,set_difference(X0,X1))
| in(X4,X1)
| ~ in(X4,X0) ),
inference(equality_resolution,[],[f121]) ).
fof(f174,plain,
! [X0,X1,X4] :
( ~ in(X4,X1)
| ~ in(X4,set_difference(X0,X1)) ),
inference(equality_resolution,[],[f120]) ).
fof(f175,plain,
! [X0,X1,X4] :
( in(X4,X0)
| ~ in(X4,set_difference(X0,X1)) ),
inference(equality_resolution,[],[f119]) ).
cnf(c_55,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,[],[f170]) ).
cnf(c_56,plain,
( ~ in(X0,relation_inverse_image(X1,X2))
| ~ function(X1)
| ~ relation(X1)
| in(apply(X1,X0),X2) ),
inference(cnf_transformation,[],[f171]) ).
cnf(c_57,plain,
( ~ in(X0,relation_inverse_image(X1,X2))
| ~ function(X1)
| ~ relation(X1)
| in(X0,relation_dom(X1)) ),
inference(cnf_transformation,[],[f172]) ).
cnf(c_58,plain,
( ~ in(sK1(X0,X1,X2),X0)
| ~ in(sK1(X0,X1,X2),X2)
| set_difference(X0,X1) = X2
| in(sK1(X0,X1,X2),X1) ),
inference(cnf_transformation,[],[f124]) ).
cnf(c_59,plain,
( ~ in(sK1(X0,X1,X2),X1)
| set_difference(X0,X1) = X2
| in(sK1(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f123]) ).
cnf(c_60,plain,
( set_difference(X0,X1) = X2
| in(sK1(X0,X1,X2),X0)
| in(sK1(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f122]) ).
cnf(c_61,plain,
( ~ in(X0,X1)
| in(X0,set_difference(X1,X2))
| in(X0,X2) ),
inference(cnf_transformation,[],[f173]) ).
cnf(c_62,plain,
( ~ in(X0,set_difference(X1,X2))
| ~ in(X0,X2) ),
inference(cnf_transformation,[],[f174]) ).
cnf(c_63,plain,
( ~ in(X0,set_difference(X1,X2))
| in(X0,X1) ),
inference(cnf_transformation,[],[f175]) ).
cnf(c_94,negated_conjecture,
set_difference(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14)) != relation_inverse_image(sK15,set_difference(sK13,sK14)),
inference(cnf_transformation,[],[f157]) ).
cnf(c_95,negated_conjecture,
function(sK15),
inference(cnf_transformation,[],[f156]) ).
cnf(c_96,negated_conjecture,
relation(sK15),
inference(cnf_transformation,[],[f155]) ).
cnf(c_2259,plain,
( set_difference(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14)) = relation_inverse_image(sK15,set_difference(sK13,sK14))
| in(sK1(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14),relation_inverse_image(sK15,set_difference(sK13,sK14))),relation_inverse_image(sK15,set_difference(sK13,sK14)))
| in(sK1(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14),relation_inverse_image(sK15,set_difference(sK13,sK14))),relation_inverse_image(sK15,sK13)) ),
inference(instantiation,[status(thm)],[c_60]) ).
cnf(c_2263,plain,
( set_difference(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14)) = relation_inverse_image(sK15,set_difference(sK13,sK14))
| in(sK1(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14),relation_inverse_image(sK15,set_difference(sK13,sK14))),relation_inverse_image(sK15,set_difference(sK13,sK14)))
| in(sK1(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14),relation_inverse_image(sK15,set_difference(sK13,sK14))),relation_inverse_image(sK15,sK13)) ),
inference(instantiation,[status(thm)],[c_60]) ).
cnf(c_2264,plain,
( in(sK1(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14),relation_inverse_image(sK15,set_difference(sK13,sK14))),relation_inverse_image(sK15,set_difference(sK13,sK14)))
| in(sK1(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14),relation_inverse_image(sK15,set_difference(sK13,sK14))),relation_inverse_image(sK15,sK13)) ),
inference(global_subsumption_just,[status(thm)],[c_2263,c_94,c_2259]) ).
cnf(c_2309,plain,
( ~ in(sK1(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14),relation_inverse_image(sK15,set_difference(sK13,sK14))),relation_inverse_image(sK15,set_difference(sK13,sK14)))
| ~ function(sK15)
| ~ relation(sK15)
| in(apply(sK15,sK1(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14),relation_inverse_image(sK15,set_difference(sK13,sK14)))),set_difference(sK13,sK14)) ),
inference(instantiation,[status(thm)],[c_56]) ).
cnf(c_2310,plain,
( ~ in(sK1(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14),relation_inverse_image(sK15,set_difference(sK13,sK14))),relation_inverse_image(sK15,set_difference(sK13,sK14)))
| ~ function(sK15)
| ~ relation(sK15)
| in(sK1(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14),relation_inverse_image(sK15,set_difference(sK13,sK14))),relation_dom(sK15)) ),
inference(instantiation,[status(thm)],[c_57]) ).
cnf(c_2311,plain,
( ~ in(sK1(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14),relation_inverse_image(sK15,set_difference(sK13,sK14))),relation_inverse_image(sK15,set_difference(sK13,sK14)))
| in(sK1(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14),relation_inverse_image(sK15,set_difference(sK13,sK14))),relation_dom(sK15)) ),
inference(global_subsumption_just,[status(thm)],[c_2310,c_96,c_95,c_2310]) ).
cnf(c_2313,plain,
( ~ in(sK1(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14),relation_inverse_image(sK15,set_difference(sK13,sK14))),relation_inverse_image(sK15,set_difference(sK13,sK14)))
| in(apply(sK15,sK1(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14),relation_inverse_image(sK15,set_difference(sK13,sK14)))),set_difference(sK13,sK14)) ),
inference(global_subsumption_just,[status(thm)],[c_2309,c_96,c_95,c_2309]) ).
cnf(c_2388,plain,
( ~ in(sK1(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14),relation_inverse_image(sK15,set_difference(sK13,sK14))),relation_inverse_image(sK15,sK13))
| ~ function(sK15)
| ~ relation(sK15)
| in(apply(sK15,sK1(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14),relation_inverse_image(sK15,set_difference(sK13,sK14)))),sK13) ),
inference(instantiation,[status(thm)],[c_56]) ).
cnf(c_2389,plain,
( ~ in(sK1(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14),relation_inverse_image(sK15,set_difference(sK13,sK14))),relation_inverse_image(sK15,sK13))
| ~ function(sK15)
| ~ relation(sK15)
| in(sK1(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14),relation_inverse_image(sK15,set_difference(sK13,sK14))),relation_dom(sK15)) ),
inference(instantiation,[status(thm)],[c_57]) ).
cnf(c_2390,plain,
in(sK1(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14),relation_inverse_image(sK15,set_difference(sK13,sK14))),relation_dom(sK15)),
inference(global_subsumption_just,[status(thm)],[c_2389,c_96,c_95,c_94,c_2259,c_2311,c_2389]) ).
cnf(c_2392,plain,
( ~ in(sK1(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14),relation_inverse_image(sK15,set_difference(sK13,sK14))),relation_inverse_image(sK15,sK13))
| in(apply(sK15,sK1(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14),relation_inverse_image(sK15,set_difference(sK13,sK14)))),sK13) ),
inference(global_subsumption_just,[status(thm)],[c_2388,c_96,c_95,c_2388]) ).
cnf(c_2394,plain,
( ~ in(sK1(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14),relation_inverse_image(sK15,set_difference(sK13,sK14))),relation_inverse_image(sK15,set_difference(sK13,sK14)))
| ~ in(sK1(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14),relation_inverse_image(sK15,set_difference(sK13,sK14))),relation_inverse_image(sK15,sK13))
| set_difference(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14)) = relation_inverse_image(sK15,set_difference(sK13,sK14))
| in(sK1(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14),relation_inverse_image(sK15,set_difference(sK13,sK14))),relation_inverse_image(sK15,sK14)) ),
inference(instantiation,[status(thm)],[c_58]) ).
cnf(c_2527,plain,
( ~ in(apply(sK15,sK1(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14),relation_inverse_image(sK15,set_difference(sK13,sK14)))),X0)
| ~ in(sK1(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14),relation_inverse_image(sK15,set_difference(sK13,sK14))),relation_dom(sK15))
| ~ function(sK15)
| ~ relation(sK15)
| in(sK1(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14),relation_inverse_image(sK15,set_difference(sK13,sK14))),relation_inverse_image(sK15,X0)) ),
inference(instantiation,[status(thm)],[c_55]) ).
cnf(c_2529,plain,
( ~ in(apply(sK15,sK1(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14),relation_inverse_image(sK15,set_difference(sK13,sK14)))),X0)
| in(sK1(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14),relation_inverse_image(sK15,set_difference(sK13,sK14))),relation_inverse_image(sK15,X0)) ),
inference(global_subsumption_just,[status(thm)],[c_2527,c_96,c_95,c_2390,c_2527]) ).
cnf(c_2813,plain,
( ~ in(apply(sK15,sK1(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14),relation_inverse_image(sK15,set_difference(sK13,sK14)))),X0)
| ~ in(sK1(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14),relation_inverse_image(sK15,set_difference(sK13,sK14))),relation_dom(sK15))
| ~ function(sK15)
| ~ relation(sK15)
| in(sK1(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14),relation_inverse_image(sK15,set_difference(sK13,sK14))),relation_inverse_image(sK15,X0)) ),
inference(instantiation,[status(thm)],[c_55]) ).
cnf(c_2814,plain,
( ~ in(apply(sK15,sK1(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14),relation_inverse_image(sK15,set_difference(sK13,sK14)))),X0)
| in(sK1(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14),relation_inverse_image(sK15,set_difference(sK13,sK14))),relation_inverse_image(sK15,X0)) ),
inference(global_subsumption_just,[status(thm)],[c_2813,c_2529]) ).
cnf(c_2824,plain,
( ~ in(apply(sK15,sK1(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14),relation_inverse_image(sK15,set_difference(sK13,sK14)))),set_difference(sK13,sK14))
| ~ in(apply(sK15,sK1(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14),relation_inverse_image(sK15,set_difference(sK13,sK14)))),sK14) ),
inference(instantiation,[status(thm)],[c_62]) ).
cnf(c_2825,plain,
( ~ in(apply(sK15,sK1(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14),relation_inverse_image(sK15,set_difference(sK13,sK14)))),set_difference(sK13,sK14))
| in(apply(sK15,sK1(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14),relation_inverse_image(sK15,set_difference(sK13,sK14)))),sK13) ),
inference(instantiation,[status(thm)],[c_63]) ).
cnf(c_2826,plain,
in(apply(sK15,sK1(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14),relation_inverse_image(sK15,set_difference(sK13,sK14)))),sK13),
inference(global_subsumption_just,[status(thm)],[c_2825,c_2264,c_2313,c_2392,c_2825]) ).
cnf(c_3527,plain,
( ~ in(apply(sK15,sK1(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14),relation_inverse_image(sK15,set_difference(sK13,sK14)))),sK13)
| in(sK1(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14),relation_inverse_image(sK15,set_difference(sK13,sK14))),relation_inverse_image(sK15,sK13)) ),
inference(instantiation,[status(thm)],[c_2814]) ).
cnf(c_3530,plain,
( ~ in(apply(sK15,sK1(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14),relation_inverse_image(sK15,set_difference(sK13,sK14)))),sK14)
| in(sK1(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14),relation_inverse_image(sK15,set_difference(sK13,sK14))),relation_inverse_image(sK15,sK14)) ),
inference(instantiation,[status(thm)],[c_2814]) ).
cnf(c_5470,plain,
( ~ in(sK1(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14),relation_inverse_image(sK15,set_difference(sK13,sK14))),relation_inverse_image(sK15,set_difference(sK13,sK14)))
| ~ in(sK1(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14),relation_inverse_image(sK15,set_difference(sK13,sK14))),relation_inverse_image(sK15,sK13))
| set_difference(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14)) = relation_inverse_image(sK15,set_difference(sK13,sK14))
| in(sK1(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14),relation_inverse_image(sK15,set_difference(sK13,sK14))),relation_inverse_image(sK15,sK14)) ),
inference(instantiation,[status(thm)],[c_58]) ).
cnf(c_5471,plain,
( ~ in(sK1(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14),relation_inverse_image(sK15,set_difference(sK13,sK14))),relation_inverse_image(sK15,set_difference(sK13,sK14)))
| in(sK1(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14),relation_inverse_image(sK15,set_difference(sK13,sK14))),relation_inverse_image(sK15,sK14)) ),
inference(global_subsumption_just,[status(thm)],[c_5470,c_94,c_2394,c_2826,c_3527]) ).
cnf(c_5640,plain,
( ~ in(apply(sK15,sK1(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14),relation_inverse_image(sK15,set_difference(sK13,sK14)))),X0)
| ~ in(sK1(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14),relation_inverse_image(sK15,set_difference(sK13,sK14))),relation_dom(sK15))
| ~ function(sK15)
| ~ relation(sK15)
| in(sK1(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14),relation_inverse_image(sK15,set_difference(sK13,sK14))),relation_inverse_image(sK15,X0)) ),
inference(instantiation,[status(thm)],[c_55]) ).
cnf(c_5641,plain,
( ~ in(apply(sK15,sK1(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14),relation_inverse_image(sK15,set_difference(sK13,sK14)))),X0)
| in(sK1(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14),relation_inverse_image(sK15,set_difference(sK13,sK14))),relation_inverse_image(sK15,X0)) ),
inference(global_subsumption_just,[status(thm)],[c_5640,c_96,c_95,c_94,c_2259,c_2311,c_2389,c_2527]) ).
cnf(c_5650,plain,
( ~ in(apply(sK15,sK1(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14),relation_inverse_image(sK15,set_difference(sK13,sK14)))),sK13)
| in(apply(sK15,sK1(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14),relation_inverse_image(sK15,set_difference(sK13,sK14)))),set_difference(sK13,X0))
| in(apply(sK15,sK1(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14),relation_inverse_image(sK15,set_difference(sK13,sK14)))),X0) ),
inference(instantiation,[status(thm)],[c_61]) ).
cnf(c_5661,plain,
( in(apply(sK15,sK1(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14),relation_inverse_image(sK15,set_difference(sK13,sK14)))),set_difference(sK13,X0))
| in(apply(sK15,sK1(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14),relation_inverse_image(sK15,set_difference(sK13,sK14)))),X0) ),
inference(global_subsumption_just,[status(thm)],[c_5650,c_2264,c_2313,c_2392,c_2825,c_5650]) ).
cnf(c_6056,plain,
( ~ in(apply(sK15,sK1(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14),relation_inverse_image(sK15,set_difference(sK13,sK14)))),set_difference(sK13,X0))
| in(sK1(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14),relation_inverse_image(sK15,set_difference(sK13,sK14))),relation_inverse_image(sK15,set_difference(sK13,X0))) ),
inference(instantiation,[status(thm)],[c_5641]) ).
cnf(c_7849,plain,
( ~ in(apply(sK15,sK1(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14),relation_inverse_image(sK15,set_difference(sK13,sK14)))),set_difference(sK13,sK14))
| in(sK1(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14),relation_inverse_image(sK15,set_difference(sK13,sK14))),relation_inverse_image(sK15,set_difference(sK13,sK14))) ),
inference(instantiation,[status(thm)],[c_6056]) ).
cnf(c_8129,plain,
( ~ in(sK1(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14),relation_inverse_image(sK15,set_difference(sK13,sK14))),relation_inverse_image(X0,X1))
| ~ function(X0)
| ~ relation(X0)
| in(apply(X0,sK1(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14),relation_inverse_image(sK15,set_difference(sK13,sK14)))),X1) ),
inference(instantiation,[status(thm)],[c_56]) ).
cnf(c_15849,plain,
( in(apply(sK15,sK1(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14),relation_inverse_image(sK15,set_difference(sK13,sK14)))),set_difference(sK13,sK14))
| in(apply(sK15,sK1(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14),relation_inverse_image(sK15,set_difference(sK13,sK14)))),sK14) ),
inference(instantiation,[status(thm)],[c_5661]) ).
cnf(c_17508,plain,
( ~ in(sK1(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14),relation_inverse_image(sK15,set_difference(sK13,sK14))),relation_inverse_image(sK15,sK14))
| ~ function(sK15)
| ~ relation(sK15)
| in(apply(sK15,sK1(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14),relation_inverse_image(sK15,set_difference(sK13,sK14)))),sK14) ),
inference(instantiation,[status(thm)],[c_8129]) ).
cnf(c_17526,plain,
in(apply(sK15,sK1(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14),relation_inverse_image(sK15,set_difference(sK13,sK14)))),sK14),
inference(global_subsumption_just,[status(thm)],[c_17508,c_96,c_95,c_5471,c_7849,c_15849,c_17508]) ).
cnf(c_17542,plain,
( ~ in(sK1(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14),relation_inverse_image(sK15,set_difference(sK13,sK14))),relation_inverse_image(sK15,sK14))
| set_difference(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14)) = relation_inverse_image(sK15,set_difference(sK13,sK14))
| in(sK1(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14),relation_inverse_image(sK15,set_difference(sK13,sK14))),relation_inverse_image(sK15,set_difference(sK13,sK14))) ),
inference(instantiation,[status(thm)],[c_59]) ).
cnf(c_17543,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_17542,c_17526,c_3530,c_2824,c_2313,c_94]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU059+1 : TPTP v8.1.2. Bugfixed v4.0.0.
% 0.00/0.13 % Command : run_iprover %s %d THM
% 0.16/0.34 % Computer : n010.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Wed Aug 23 12:51:51 EDT 2023
% 0.16/0.34 % CPUTime :
% 0.20/0.47 Running first-order theorem proving
% 0.20/0.47 Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 10.31/2.19 % SZS status Started for theBenchmark.p
% 10.31/2.19 % SZS status Theorem for theBenchmark.p
% 10.31/2.19
% 10.31/2.19 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 10.31/2.19
% 10.31/2.19 ------ iProver source info
% 10.31/2.19
% 10.31/2.19 git: date: 2023-05-31 18:12:56 +0000
% 10.31/2.19 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 10.31/2.19 git: non_committed_changes: false
% 10.31/2.19 git: last_make_outside_of_git: false
% 10.31/2.19
% 10.31/2.19 ------ Parsing...
% 10.31/2.19 ------ Clausification by vclausify_rel & Parsing by iProver...
% 10.31/2.19
% 10.31/2.19 ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e
% 10.31/2.19
% 10.31/2.19 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 10.31/2.19
% 10.31/2.19 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 10.31/2.19 ------ Proving...
% 10.31/2.19 ------ Problem Properties
% 10.31/2.19
% 10.31/2.19
% 10.31/2.19 clauses 56
% 10.31/2.19 conjectures 3
% 10.31/2.19 EPR 26
% 10.31/2.19 Horn 47
% 10.31/2.19 unary 26
% 10.31/2.19 binary 12
% 10.31/2.19 lits 116
% 10.31/2.19 lits eq 13
% 10.31/2.19 fd_pure 0
% 10.31/2.19 fd_pseudo 0
% 10.31/2.19 fd_cond 1
% 10.31/2.19 fd_pseudo_cond 9
% 10.31/2.19 AC symbols 0
% 10.31/2.19
% 10.31/2.19 ------ Input Options Time Limit: Unbounded
% 10.31/2.19
% 10.31/2.19
% 10.31/2.19 ------
% 10.31/2.19 Current options:
% 10.31/2.19 ------
% 10.31/2.19
% 10.31/2.19
% 10.31/2.19
% 10.31/2.19
% 10.31/2.19 ------ Proving...
% 10.31/2.19
% 10.31/2.19
% 10.31/2.19 % SZS status Theorem for theBenchmark.p
% 10.31/2.19
% 10.31/2.19 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 10.31/2.19
% 10.31/2.19
%------------------------------------------------------------------------------