%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU058+1 : TPTP v9.3.1. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 02:55:10 PM UTC 2026
% Result : Theorem 7.28s 6.95s
% Output : CNFRefutation 7.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 3
% Syntax : Number of formulae : 65 ( 7 unt; 0 def)
% Number of atoms : 312 ( 42 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 415 ( 168 ~; 183 |; 53 &)
% ( 8 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 7 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% 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 : 146 ( 0 sgn 134 !; 12 ?; 29 :)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ! [X1,X2] :
( X2 = relation_inverse_image(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(apply(X0,X3),X1)
& in(X3,relation_dom(X0)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d13_funct_1) ).
fof(f7,axiom,
! [X0,X1,X2] :
( X2 = set_intersection2(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X1)
& in(X3,X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_xboole_0) ).
fof(f28,conjecture,
! [X0,X1,X2] :
( ( function(X2)
& relation(X2) )
=> relation_inverse_image(X2,set_intersection2(X0,X1)) = set_intersection2(relation_inverse_image(X2,X0),relation_inverse_image(X2,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t137_funct_1) ).
fof(f29,negated_conjecture,
~ ! [X0,X1,X2] :
( ( function(X2)
& relation(X2) )
=> relation_inverse_image(X2,set_intersection2(X0,X1)) = set_intersection2(relation_inverse_image(X2,X0),relation_inverse_image(X2,X1)) ),
inference(negated_conjecture,[status(cth)],[f28]) ).
fof(f52,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1,X2] :
( X2 = relation_inverse_image(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(apply(X0,X3),X1)
& in(X3,relation_dom(X0)) ) ) ) ),
inference(ennf_transformation,[],[f6]) ).
fof(f53,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1,X2] :
( X2 = relation_inverse_image(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(apply(X0,X3),X1)
& in(X3,relation_dom(X0)) ) ) ) ),
inference(flattening,[],[f52]) ).
fof(f60,plain,
? [X0,X1,X2] :
( function(X2)
& relation(X2)
& relation_inverse_image(X2,set_intersection2(X0,X1)) != set_intersection2(relation_inverse_image(X2,X0),relation_inverse_image(X2,X1)) ),
inference(ennf_transformation,[],[f29]) ).
fof(f61,plain,
? [X0,X1,X2] :
( function(X2)
& relation(X2)
& relation_inverse_image(X2,set_intersection2(X0,X1)) != set_intersection2(relation_inverse_image(X2,X0),relation_inverse_image(X2,X1)) ),
inference(flattening,[],[f60]) ).
fof(f73,plain,
! [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)) ) )
& ( ~ 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(X3,X2)
| ~ in(apply(X0,X3),X1)
| ~ in(X3,relation_dom(X0)) ) )
| X2 = relation_inverse_image(X0,X1) ) ) ),
inference(nnf_transformation,[],[f53]) ).
fof(f74,plain,
! [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)) ) )
& ( ~ 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(X3,X2)
| ~ in(apply(X0,X3),X1)
| ~ in(X3,relation_dom(X0)) ) )
| X2 = relation_inverse_image(X0,X1) ) ) ),
inference(flattening,[],[f73]) ).
fof(f75,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1,X2] :
( ( relation_inverse_image(X0,X1) != 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) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| ( in(apply(X0,X3),X1)
& in(X3,relation_dom(X0)) ) )
& ( ~ in(X3,X2)
| ~ in(apply(X0,X3),X1)
| ~ in(X3,relation_dom(X0)) ) )
| X2 = relation_inverse_image(X0,X1) ) ) ),
inference(rectify,[],[f74]) ).
fof(f76,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1,X2] :
( ( relation_inverse_image(X0,X1) != 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) ) ) )
& ( ( ( 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)
| ~ in(apply(X0,sK0(X0,X1,X2)),X1)
| ~ in(sK0(X0,X1,X2),relation_dom(X0)) ) )
| X2 = relation_inverse_image(X0,X1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X3,sK0(X0,X1,X2))],[f75]) ).
fof(f77,plain,
! [X0,X1,X2] :
( ( set_intersection2(X0,X1) != X2
| ! [X3] :
( ( ~ in(X3,X2)
| ( in(X3,X1)
& in(X3,X0) ) )
& ( ~ in(X3,X1)
| ~ in(X3,X0)
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| ( in(X3,X1)
& in(X3,X0) ) )
& ( ~ in(X3,X2)
| ~ in(X3,X1)
| ~ in(X3,X0) ) )
| X2 = set_intersection2(X0,X1) ) ),
inference(nnf_transformation,[],[f7]) ).
fof(f78,plain,
! [X0,X1,X2] :
( ( set_intersection2(X0,X1) != X2
| ! [X3] :
( ( ~ in(X3,X2)
| ( in(X3,X1)
& in(X3,X0) ) )
& ( ~ in(X3,X1)
| ~ in(X3,X0)
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| ( in(X3,X1)
& in(X3,X0) ) )
& ( ~ in(X3,X2)
| ~ in(X3,X1)
| ~ in(X3,X0) ) )
| X2 = set_intersection2(X0,X1) ) ),
inference(flattening,[],[f77]) ).
fof(f79,plain,
! [X0,X1,X2] :
( ( set_intersection2(X0,X1) != X2
| ! [X4] :
( ( ~ in(X4,X2)
| ( in(X4,X1)
& in(X4,X0) ) )
& ( ~ in(X4,X1)
| ~ in(X4,X0)
| in(X4,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| ( in(X3,X1)
& in(X3,X0) ) )
& ( ~ in(X3,X2)
| ~ in(X3,X1)
| ~ in(X3,X0) ) )
| X2 = set_intersection2(X0,X1) ) ),
inference(rectify,[],[f78]) ).
fof(f80,plain,
! [X0,X1,X2] :
( ( set_intersection2(X0,X1) != X2
| ! [X4] :
( ( ~ in(X4,X2)
| ( in(X4,X1)
& in(X4,X0) ) )
& ( ~ in(X4,X1)
| ~ in(X4,X0)
| in(X4,X2) ) ) )
& ( ( ( in(sK1(X0,X1,X2),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) ) )
| X2 = set_intersection2(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X3,sK1(X0,X1,X2))],[f79]) ).
fof(f92,plain,
( function(sK15)
& relation(sK15)
& relation_inverse_image(sK15,set_intersection2(sK13,sK14)) != set_intersection2(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13,sK14,sK15]),skolemize(X0,sK13),skolemize(X1,sK14),skolemize(X2,sK15)],[f61]) ).
fof(f101,plain,
! [X2,X0,X1,X4] :
( ~ function(X0)
| ~ relation(X0)
| relation_inverse_image(X0,X1) != X2
| ~ in(X4,X2)
| in(apply(X0,X4),X1) ),
inference(cnf_transformation,[],[f76]) ).
fof(f102,plain,
! [X2,X0,X1,X4] :
( ~ function(X0)
| ~ relation(X0)
| relation_inverse_image(X0,X1) != X2
| ~ in(X4,X2)
| in(X4,relation_dom(X0)) ),
inference(cnf_transformation,[],[f76]) ).
fof(f103,plain,
! [X2,X0,X1,X4] :
( ~ function(X0)
| ~ relation(X0)
| relation_inverse_image(X0,X1) != X2
| ~ in(apply(X0,X4),X1)
| ~ in(X4,relation_dom(X0))
| in(X4,X2) ),
inference(cnf_transformation,[],[f76]) ).
fof(f107,plain,
! [X2,X0,X1,X4] :
( set_intersection2(X0,X1) != X2
| ~ in(X4,X2)
| in(X4,X1) ),
inference(cnf_transformation,[],[f80]) ).
fof(f108,plain,
! [X2,X0,X1,X4] :
( set_intersection2(X0,X1) != X2
| ~ in(X4,X2)
| in(X4,X0) ),
inference(cnf_transformation,[],[f80]) ).
fof(f109,plain,
! [X2,X0,X1,X4] :
( set_intersection2(X0,X1) != X2
| ~ in(X4,X1)
| ~ in(X4,X0)
| in(X4,X2) ),
inference(cnf_transformation,[],[f80]) ).
fof(f110,plain,
! [X2,X0,X1] :
( in(sK1(X0,X1,X2),X2)
| in(sK1(X0,X1,X2),X1)
| set_intersection2(X0,X1) = X2 ),
inference(cnf_transformation,[],[f80]) ).
fof(f111,plain,
! [X2,X0,X1] :
( in(sK1(X0,X1,X2),X2)
| in(sK1(X0,X1,X2),X0)
| set_intersection2(X0,X1) = X2 ),
inference(cnf_transformation,[],[f80]) ).
fof(f112,plain,
! [X2,X0,X1] :
( ~ in(sK1(X0,X1,X2),X2)
| ~ in(sK1(X0,X1,X2),X1)
| ~ in(sK1(X0,X1,X2),X0)
| set_intersection2(X0,X1) = X2 ),
inference(cnf_transformation,[],[f80]) ).
fof(f144,plain,
function(sK15),
inference(cnf_transformation,[],[f92]) ).
fof(f145,plain,
relation(sK15),
inference(cnf_transformation,[],[f92]) ).
fof(f146,plain,
relation_inverse_image(sK15,set_intersection2(sK13,sK14)) != set_intersection2(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14)),
inference(cnf_transformation,[],[f92]) ).
fof(f158,plain,
! [X0,X1,X4] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(apply(X0,X4),X1)
| ~ in(X4,relation_dom(X0))
| in(X4,relation_inverse_image(X0,X1)) ),
inference(equality_resolution,[],[f103]) ).
fof(f159,plain,
! [X0,X1,X4] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(X4,relation_inverse_image(X0,X1))
| in(X4,relation_dom(X0)) ),
inference(equality_resolution,[],[f102]) ).
fof(f160,plain,
! [X0,X1,X4] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(X4,relation_inverse_image(X0,X1))
| in(apply(X0,X4),X1) ),
inference(equality_resolution,[],[f101]) ).
fof(f161,plain,
! [X0,X1,X4] :
( ~ in(X4,X1)
| ~ in(X4,X0)
| in(X4,set_intersection2(X0,X1)) ),
inference(equality_resolution,[],[f109]) ).
fof(f162,plain,
! [X0,X1,X4] :
( ~ in(X4,set_intersection2(X0,X1))
| in(X4,X0) ),
inference(equality_resolution,[],[f108]) ).
fof(f163,plain,
! [X0,X1,X4] :
( ~ in(X4,set_intersection2(X0,X1))
| in(X4,X1) ),
inference(equality_resolution,[],[f107]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X1,relation_inverse_image(X0,X2))
| ~ relation(X0)
| ~ function(X0)
| ~ in(X1,relation_dom(X0))
| ~ in(apply(X0,X1),X2) ),
inference(cnf_transformation,[],[f158]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,relation_dom(X1))
| ~ relation(X1)
| ~ function(X1)
| ~ in(X0,relation_inverse_image(X1,X2)) ),
inference(cnf_transformation,[],[f159]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(X1,X0),X2)
| ~ relation(X1)
| ~ function(X1)
| ~ in(X0,relation_inverse_image(X1,X2)) ),
inference(cnf_transformation,[],[f160]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X0,X1) = X2 )
| ~ in(sK1(X0,X1,X2),X2)
| ~ in(sK1(X0,X1,X2),X1)
| ~ in(sK1(X0,X1,X2),X0) ),
inference(cnf_transformation,[],[f112]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK1(X0,X1,X2),X2)
| in(sK1(X0,X1,X2),X0)
| ( set_intersection2(X0,X1) = X2 ) ),
inference(cnf_transformation,[],[f111]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK1(X0,X1,X2),X2)
| in(sK1(X0,X1,X2),X1)
| ( set_intersection2(X0,X1) = X2 ) ),
inference(cnf_transformation,[],[f110]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,set_intersection2(X2,X1))
| ~ in(X0,X2)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f161]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X1)
| ~ in(X0,set_intersection2(X1,X2)) ),
inference(cnf_transformation,[],[f162]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| ~ in(X0,set_intersection2(X1,X2)) ),
inference(cnf_transformation,[],[f163]) ).
tcf(c_96,negated_conjecture,
set_intersection2(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14)) != relation_inverse_image(sK15,set_intersection2(sK13,sK14)),
inference(cnf_transformation,[],[f146]) ).
tcf(c_97,negated_conjecture,
relation(sK15),
inference(cnf_transformation,[],[f145]) ).
tcf(c_98,negated_conjecture,
function(sK15),
inference(cnf_transformation,[],[f144]) ).
tcf(c_2283,plain,
( in(sK1(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14),relation_inverse_image(sK15,set_intersection2(sK13,sK14))),relation_inverse_image(sK15,sK14))
| in(sK1(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14),relation_inverse_image(sK15,set_intersection2(sK13,sK14))),relation_inverse_image(sK15,set_intersection2(sK13,sK14)))
| ( set_intersection2(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14)) = relation_inverse_image(sK15,set_intersection2(sK13,sK14)) ) ),
inference(instantiation,[status(thm)],[c_61]) ).
tcf(c_2284,plain,
( in(sK1(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14),relation_inverse_image(sK15,set_intersection2(sK13,sK14))),relation_inverse_image(sK15,sK13))
| in(sK1(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14),relation_inverse_image(sK15,set_intersection2(sK13,sK14))),relation_inverse_image(sK15,set_intersection2(sK13,sK14)))
| ( set_intersection2(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14)) = relation_inverse_image(sK15,set_intersection2(sK13,sK14)) ) ),
inference(instantiation,[status(thm)],[c_60]) ).
tcf(c_2285,plain,
( ( set_intersection2(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14)) = relation_inverse_image(sK15,set_intersection2(sK13,sK14)) )
| ~ in(sK1(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14),relation_inverse_image(sK15,set_intersection2(sK13,sK14))),relation_inverse_image(sK15,sK14))
| ~ in(sK1(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14),relation_inverse_image(sK15,set_intersection2(sK13,sK14))),relation_inverse_image(sK15,sK13))
| ~ in(sK1(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14),relation_inverse_image(sK15,set_intersection2(sK13,sK14))),relation_inverse_image(sK15,set_intersection2(sK13,sK14))) ),
inference(instantiation,[status(thm)],[c_59]) ).
tcf(c_2415,plain,
( in(apply(sK15,sK1(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14),relation_inverse_image(sK15,set_intersection2(sK13,sK14)))),set_intersection2(sK13,sK14))
| ~ relation(sK15)
| ~ function(sK15)
| ~ in(sK1(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14),relation_inverse_image(sK15,set_intersection2(sK13,sK14))),relation_inverse_image(sK15,set_intersection2(sK13,sK14))) ),
inference(instantiation,[status(thm)],[c_58]) ).
tcf(c_2416,plain,
( in(sK1(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14),relation_inverse_image(sK15,set_intersection2(sK13,sK14))),relation_dom(sK15))
| ~ relation(sK15)
| ~ function(sK15)
| ~ in(sK1(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14),relation_inverse_image(sK15,set_intersection2(sK13,sK14))),relation_inverse_image(sK15,set_intersection2(sK13,sK14))) ),
inference(instantiation,[status(thm)],[c_57]) ).
tcf(c_2575,plain,
( in(apply(sK15,sK1(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14),relation_inverse_image(sK15,set_intersection2(sK13,sK14)))),sK14)
| ~ relation(sK15)
| ~ function(sK15)
| ~ in(sK1(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14),relation_inverse_image(sK15,set_intersection2(sK13,sK14))),relation_inverse_image(sK15,sK14)) ),
inference(instantiation,[status(thm)],[c_58]) ).
tcf(c_2576,plain,
( in(sK1(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14),relation_inverse_image(sK15,set_intersection2(sK13,sK14))),relation_dom(sK15))
| ~ relation(sK15)
| ~ function(sK15)
| ~ in(sK1(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14),relation_inverse_image(sK15,set_intersection2(sK13,sK14))),relation_inverse_image(sK15,sK14)) ),
inference(instantiation,[status(thm)],[c_57]) ).
tcf(c_2598,plain,
( in(apply(sK15,sK1(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14),relation_inverse_image(sK15,set_intersection2(sK13,sK14)))),sK13)
| ~ relation(sK15)
| ~ function(sK15)
| ~ in(sK1(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14),relation_inverse_image(sK15,set_intersection2(sK13,sK14))),relation_inverse_image(sK15,sK13)) ),
inference(instantiation,[status(thm)],[c_58]) ).
tcf(c_2981,plain,
( in(sK1(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14),relation_inverse_image(sK15,set_intersection2(sK13,sK14))),relation_inverse_image(sK15,set_intersection2(sK13,sK14)))
| ~ relation(sK15)
| ~ function(sK15)
| ~ in(sK1(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14),relation_inverse_image(sK15,set_intersection2(sK13,sK14))),relation_dom(sK15))
| ~ in(apply(sK15,sK1(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14),relation_inverse_image(sK15,set_intersection2(sK13,sK14)))),set_intersection2(sK13,sK14)) ),
inference(instantiation,[status(thm)],[c_56]) ).
tcf(c_5338,plain,
! [X0: $i] :
( in(apply(sK15,sK1(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14),relation_inverse_image(sK15,set_intersection2(sK13,sK14)))),set_intersection2(sK13,X0))
| ~ in(apply(sK15,sK1(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14),relation_inverse_image(sK15,set_intersection2(sK13,sK14)))),sK13)
| ~ in(apply(sK15,sK1(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14),relation_inverse_image(sK15,set_intersection2(sK13,sK14)))),X0) ),
inference(instantiation,[status(thm)],[c_62]) ).
tcf(c_5350,plain,
! [X0: $i] :
( in(sK1(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14),relation_inverse_image(sK15,set_intersection2(sK13,sK14))),relation_inverse_image(sK15,X0))
| ~ relation(sK15)
| ~ function(sK15)
| ~ in(sK1(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14),relation_inverse_image(sK15,set_intersection2(sK13,sK14))),relation_dom(sK15))
| ~ in(apply(sK15,sK1(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14),relation_inverse_image(sK15,set_intersection2(sK13,sK14)))),X0) ),
inference(instantiation,[status(thm)],[c_56]) ).
tcf(c_11821,plain,
( in(apply(sK15,sK1(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14),relation_inverse_image(sK15,set_intersection2(sK13,sK14)))),set_intersection2(sK13,sK14))
| ~ in(apply(sK15,sK1(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14),relation_inverse_image(sK15,set_intersection2(sK13,sK14)))),sK14)
| ~ in(apply(sK15,sK1(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14),relation_inverse_image(sK15,set_intersection2(sK13,sK14)))),sK13) ),
inference(instantiation,[status(thm)],[c_5338]) ).
tcf(c_11943,plain,
( in(sK1(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14),relation_inverse_image(sK15,set_intersection2(sK13,sK14))),relation_inverse_image(sK15,sK14))
| ~ relation(sK15)
| ~ function(sK15)
| ~ in(sK1(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14),relation_inverse_image(sK15,set_intersection2(sK13,sK14))),relation_dom(sK15))
| ~ in(apply(sK15,sK1(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14),relation_inverse_image(sK15,set_intersection2(sK13,sK14)))),sK14) ),
inference(instantiation,[status(thm)],[c_5350]) ).
tcf(c_11944,plain,
( in(sK1(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14),relation_inverse_image(sK15,set_intersection2(sK13,sK14))),relation_inverse_image(sK15,sK13))
| ~ relation(sK15)
| ~ function(sK15)
| ~ in(sK1(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14),relation_inverse_image(sK15,set_intersection2(sK13,sK14))),relation_dom(sK15))
| ~ in(apply(sK15,sK1(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14),relation_inverse_image(sK15,set_intersection2(sK13,sK14)))),sK13) ),
inference(instantiation,[status(thm)],[c_5350]) ).
tcf(c_12111,plain,
( in(sK1(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14),relation_inverse_image(sK15,set_intersection2(sK13,sK14))),relation_inverse_image(sK15,sK14))
| in(sK1(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14),relation_inverse_image(sK15,set_intersection2(sK13,sK14))),relation_inverse_image(sK15,set_intersection2(sK13,sK14))) ),
inference(resolution,[status(thm)],[c_61,c_96]) ).
tcf(c_13329,plain,
( in(apply(sK15,sK1(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14),relation_inverse_image(sK15,set_intersection2(sK13,sK14)))),sK14)
| ~ in(apply(sK15,sK1(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14),relation_inverse_image(sK15,set_intersection2(sK13,sK14)))),set_intersection2(sK13,sK14)) ),
inference(instantiation,[status(thm)],[c_64]) ).
tcf(c_13330,plain,
( in(apply(sK15,sK1(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14),relation_inverse_image(sK15,set_intersection2(sK13,sK14)))),sK13)
| ~ in(apply(sK15,sK1(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14),relation_inverse_image(sK15,set_intersection2(sK13,sK14)))),set_intersection2(sK13,sK14)) ),
inference(instantiation,[status(thm)],[c_63]) ).
tcf(c_13331,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_13329,c_13330,c_12111,c_11944,c_11943,c_11821,c_2981,c_2598,c_2575,c_2576,c_2415,c_2416,c_2283,c_2284,c_2285,c_96,c_97,c_98]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU058+1 : TPTP v9.3.1. Bugfixed v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/5.58 % Computer : n006.cluster.edu
% 0.11/5.58 % Model : x86_64 x86_64
% 0.11/5.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.58 % Memory : 8046.5625MB
% 0.11/5.58 % OS : Linux 6.8.0-71-generic
% 0.11/5.58 % CPULimit : 300
% 0.11/5.58 % WCLimit : 300
% 0.11/5.58 % DateTime : Thu Sep 24 12:40:06 UTC 2026
% 0.11/5.59 % CPUTime :
% 0.11/5.59 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.15/5.62 Running first-order theorem proving
% 0.15/5.62 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/5.64
% 0.15/5.64 % ======== iProver multi-core TPTP/SMT =========
% 0.15/5.64
% 0.15/5.64 % Detected problem language: tptp
% 0.15/5.65 % Proving...
% 7.28/6.95 % SZS status Started for theBenchmark.p
% 7.28/6.95 % SZS status Theorem for theBenchmark.p
% 7.28/6.95
% 7.28/6.95 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 7.28/6.95
% 7.28/6.95 % ------ iProver source info
% 7.28/6.95
% 7.28/6.95 % git: date: 2026-07-19 20:42:38 +0200
% 7.28/6.95 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 7.28/6.95 % git: non_committed_changes: false
% 7.28/6.95
% 7.28/6.95 % ------ Parsing...
% 7.28/6.95 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 7.28/6.95
% 7.28/6.95 % ------ 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 %
% 7.28/6.95
% 7.28/6.95 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 7.28/6.95
% 7.28/6.95 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 7.28/6.95 % ------ Proving...
% 7.28/6.95 % ------ Problem Properties
% 7.28/6.95
% 7.28/6.95 %
% 7.28/6.95 % clauses 57
% 7.28/6.95 % conjectures 3
% 7.28/6.95 % EPR 26
% 7.28/6.95 % Horn 50
% 7.28/6.95 % unary 27
% 7.28/6.95 % binary 12
% 7.28/6.95 % lits 117
% 7.28/6.95 % lits eq 14
% 7.28/6.95 % fd_pure 0
% 7.28/6.95 % fd_pseudo 0
% 7.28/6.95 % fd_cond 1
% 7.28/6.95 % fd_pseudo_cond 9
% 7.28/6.95 % AC symbols 0
% 7.28/6.95
% 7.28/6.95 % ------ Input Options Time Limit: Unbounded
% 7.28/6.95
% 7.28/6.95
% 7.28/6.95 % ------
% 7.28/6.95 % Current options:
% 7.28/6.95 % ------
% 7.28/6.95
% 7.28/6.95
% 7.28/6.95 %
% 7.28/6.95
% 7.28/6.95 % ------ Proving...
% 7.28/6.95 %
% 7.28/6.95
% 7.28/6.95 % SZS status Theorem for theBenchmark.p
% 7.28/6.95
% 7.28/6.95 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 7.28/6.95
% 7.28/6.95
%------------------------------------------------------------------------------