%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU060+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n003.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 02:55:11 PM UTC 2026
% Result : Theorem 14.73s 2.82s
% Output : CNFRefutation 14.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of formulae : 83 ( 5 unt; 0 def)
% Number of atoms : 407 ( 52 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 552 ( 228 ~; 246 |; 62 &)
% ( 10 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 7 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 3 con; 0-3 aty)
% Number of variables : 252 ( 0 sgn 232 !; 20 ?; 63 :)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
! [X0] :
( relation(X0)
=> ! [X1,X2] :
( relation(X2)
=> ( X2 = relation_dom_restriction(X0,X1)
<=> ! [X3,X4] :
( in(ordered_pair(X3,X4),X2)
<=> ( in(ordered_pair(X3,X4),X0)
& in(X3,X1) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d11_relat_1) ).
fof(f9,axiom,
! [X0] :
( relation(X0)
=> ! [X1,X2] :
( X2 = relation_inverse_image(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(X4,X1)
& in(ordered_pair(X3,X4),X0) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d14_relat_1) ).
fof(f11,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(f13,axiom,
! [X0,X1] :
( relation(X0)
=> relation(relation_dom_restriction(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_relat_1) ).
fof(f37,conjecture,
! [X0,X1,X2] :
( relation(X2)
=> relation_inverse_image(relation_dom_restriction(X2,X0),X1) = set_intersection2(X0,relation_inverse_image(X2,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t139_funct_1) ).
fof(f38,negated_conjecture,
~ ! [X0,X1,X2] :
( relation(X2)
=> relation_inverse_image(relation_dom_restriction(X2,X0),X1) = set_intersection2(X0,relation_inverse_image(X2,X1)) ),
inference(negated_conjecture,[status(cth)],[f37]) ).
fof(f51,plain,
? [X0,X1,X2] :
( relation(X2)
& relation_inverse_image(relation_dom_restriction(X2,X0),X1) != set_intersection2(X0,relation_inverse_image(X2,X1)) ),
inference(ennf_transformation,[],[f38]) ).
fof(f58,plain,
! [X0,X1] :
( ~ relation(X0)
| relation(relation_dom_restriction(X0,X1)) ),
inference(ennf_transformation,[],[f13]) ).
fof(f59,plain,
! [X0] :
( ~ relation(X0)
| ! [X1,X2] :
( ~ relation(X2)
| ( X2 = relation_dom_restriction(X0,X1)
<=> ! [X3,X4] :
( in(ordered_pair(X3,X4),X2)
<=> ( in(ordered_pair(X3,X4),X0)
& in(X3,X1) ) ) ) ) ),
inference(ennf_transformation,[],[f8]) ).
fof(f61,plain,
! [X0] :
( ~ relation(X0)
| ! [X1,X2] :
( X2 = relation_inverse_image(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(X4,X1)
& in(ordered_pair(X3,X4),X0) ) ) ) ),
inference(ennf_transformation,[],[f9]) ).
fof(f74,plain,
( relation(sK2)
& relation_inverse_image(relation_dom_restriction(sK2,sK0),sK1) != set_intersection2(sK0,relation_inverse_image(sK2,sK1)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f51]) ).
fof(f75,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,[],[f11]) ).
fof(f76,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,[],[f75]) ).
fof(f77,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,[],[f76]) ).
fof(f78,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(sK3(X0,X1,X2),X2)
| ( in(sK3(X0,X1,X2),X1)
& in(sK3(X0,X1,X2),X0) ) )
& ( ~ in(sK3(X0,X1,X2),X2)
| ~ in(sK3(X0,X1,X2),X1)
| ~ in(sK3(X0,X1,X2),X0) ) )
| X2 = set_intersection2(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X3,sK3(X0,X1,X2))],[f77]) ).
fof(f79,plain,
! [X0] :
( ~ relation(X0)
| ! [X1,X2] :
( ~ relation(X2)
| ( ( relation_dom_restriction(X0,X1) != X2
| ! [X3,X4] :
( ( ~ in(ordered_pair(X3,X4),X2)
| ( in(ordered_pair(X3,X4),X0)
& in(X3,X1) ) )
& ( ~ in(ordered_pair(X3,X4),X0)
| ~ in(X3,X1)
| in(ordered_pair(X3,X4),X2) ) ) )
& ( ? [X3,X4] :
( ( in(ordered_pair(X3,X4),X2)
| ( in(ordered_pair(X3,X4),X0)
& in(X3,X1) ) )
& ( ~ in(ordered_pair(X3,X4),X2)
| ~ in(ordered_pair(X3,X4),X0)
| ~ in(X3,X1) ) )
| X2 = relation_dom_restriction(X0,X1) ) ) ) ),
inference(nnf_transformation,[],[f59]) ).
fof(f80,plain,
! [X0] :
( ~ relation(X0)
| ! [X1,X2] :
( ~ relation(X2)
| ( ( relation_dom_restriction(X0,X1) != X2
| ! [X3,X4] :
( ( ~ in(ordered_pair(X3,X4),X2)
| ( in(ordered_pair(X3,X4),X0)
& in(X3,X1) ) )
& ( ~ in(ordered_pair(X3,X4),X0)
| ~ in(X3,X1)
| in(ordered_pair(X3,X4),X2) ) ) )
& ( ? [X3,X4] :
( ( in(ordered_pair(X3,X4),X2)
| ( in(ordered_pair(X3,X4),X0)
& in(X3,X1) ) )
& ( ~ in(ordered_pair(X3,X4),X2)
| ~ in(ordered_pair(X3,X4),X0)
| ~ in(X3,X1) ) )
| X2 = relation_dom_restriction(X0,X1) ) ) ) ),
inference(flattening,[],[f79]) ).
fof(f81,plain,
! [X0] :
( ~ relation(X0)
| ! [X1,X2] :
( ~ relation(X2)
| ( ( relation_dom_restriction(X0,X1) != X2
| ! [X5,X6] :
( ( ~ in(ordered_pair(X5,X6),X2)
| ( in(ordered_pair(X5,X6),X0)
& in(X5,X1) ) )
& ( ~ in(ordered_pair(X5,X6),X0)
| ~ in(X5,X1)
| in(ordered_pair(X5,X6),X2) ) ) )
& ( ? [X3,X4] :
( ( in(ordered_pair(X3,X4),X2)
| ( in(ordered_pair(X3,X4),X0)
& in(X3,X1) ) )
& ( ~ in(ordered_pair(X3,X4),X2)
| ~ in(ordered_pair(X3,X4),X0)
| ~ in(X3,X1) ) )
| X2 = relation_dom_restriction(X0,X1) ) ) ) ),
inference(rectify,[],[f80]) ).
fof(f82,plain,
! [X0] :
( ~ relation(X0)
| ! [X1,X2] :
( ~ relation(X2)
| ( ( relation_dom_restriction(X0,X1) != X2
| ! [X5,X6] :
( ( ~ in(ordered_pair(X5,X6),X2)
| ( in(ordered_pair(X5,X6),X0)
& in(X5,X1) ) )
& ( ~ in(ordered_pair(X5,X6),X0)
| ~ in(X5,X1)
| in(ordered_pair(X5,X6),X2) ) ) )
& ( ( ( in(ordered_pair(sK4(X0,X1,X2),sK5(X0,X1,X2)),X2)
| ( in(ordered_pair(sK4(X0,X1,X2),sK5(X0,X1,X2)),X0)
& in(sK4(X0,X1,X2),X1) ) )
& ( ~ in(ordered_pair(sK4(X0,X1,X2),sK5(X0,X1,X2)),X2)
| ~ in(ordered_pair(sK4(X0,X1,X2),sK5(X0,X1,X2)),X0)
| ~ in(sK4(X0,X1,X2),X1) ) )
| X2 = relation_dom_restriction(X0,X1) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5]),skolemize(X3,sK4(X0,X1,X2)),skolemize(X4,sK5(X0,X1,X2))],[f81]) ).
fof(f85,plain,
! [X0] :
( ~ relation(X0)
| ! [X1,X2] :
( ( relation_inverse_image(X0,X1) != X2
| ! [X3] :
( ( ~ in(X3,X2)
| ? [X4] :
( in(X4,X1)
& in(ordered_pair(X3,X4),X0) ) )
& ( ! [X4] :
( ~ in(X4,X1)
| ~ in(ordered_pair(X3,X4),X0) )
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| ? [X4] :
( in(X4,X1)
& in(ordered_pair(X3,X4),X0) ) )
& ( ~ in(X3,X2)
| ! [X4] :
( ~ in(X4,X1)
| ~ in(ordered_pair(X3,X4),X0) ) ) )
| X2 = relation_inverse_image(X0,X1) ) ) ),
inference(nnf_transformation,[],[f61]) ).
fof(f86,plain,
! [X0] :
( ~ relation(X0)
| ! [X1,X2] :
( ( relation_inverse_image(X0,X1) != X2
| ! [X6] :
( ( ~ in(X6,X2)
| ? [X8] :
( in(X8,X1)
& in(ordered_pair(X6,X8),X0) ) )
& ( ! [X7] :
( ~ in(X7,X1)
| ~ in(ordered_pair(X6,X7),X0) )
| in(X6,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| ? [X5] :
( in(X5,X1)
& in(ordered_pair(X3,X5),X0) ) )
& ( ~ in(X3,X2)
| ! [X4] :
( ~ in(X4,X1)
| ~ in(ordered_pair(X3,X4),X0) ) ) )
| X2 = relation_inverse_image(X0,X1) ) ) ),
inference(rectify,[],[f85]) ).
fof(f87,plain,
! [X0] :
( ~ relation(X0)
| ! [X1,X2] :
( ( relation_inverse_image(X0,X1) != X2
| ! [X6] :
( ( ~ in(X6,X2)
| ( in(sK10(X0,X1,X6),X1)
& in(ordered_pair(X6,sK10(X0,X1,X6)),X0) ) )
& ( ! [X7] :
( ~ in(X7,X1)
| ~ in(ordered_pair(X6,X7),X0) )
| in(X6,X2) ) ) )
& ( ( ( in(sK8(X0,X1,X2),X2)
| ( in(sK9(X0,X1,X2),X1)
& in(ordered_pair(sK8(X0,X1,X2),sK9(X0,X1,X2)),X0) ) )
& ( ~ in(sK8(X0,X1,X2),X2)
| ! [X4] :
( ~ in(X4,X1)
| ~ in(ordered_pair(sK8(X0,X1,X2),X4),X0) ) ) )
| X2 = relation_inverse_image(X0,X1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8,sK9,sK10]),skolemize(X3,sK8(X0,X1,X2)),skolemize(X5,sK9(X0,X1,X2)),skolemize(X8,sK10(X0,X1,X6))],[f86]) ).
fof(f101,plain,
relation(sK2),
inference(cnf_transformation,[],[f74]) ).
fof(f102,plain,
relation_inverse_image(relation_dom_restriction(sK2,sK0),sK1) != set_intersection2(sK0,relation_inverse_image(sK2,sK1)),
inference(cnf_transformation,[],[f74]) ).
fof(f107,plain,
! [X2,X0,X1,X4] :
( set_intersection2(X0,X1) != X2
| ~ in(X4,X2)
| in(X4,X1) ),
inference(cnf_transformation,[],[f78]) ).
fof(f108,plain,
! [X2,X0,X1,X4] :
( set_intersection2(X0,X1) != X2
| ~ in(X4,X2)
| in(X4,X0) ),
inference(cnf_transformation,[],[f78]) ).
fof(f109,plain,
! [X2,X0,X1,X4] :
( set_intersection2(X0,X1) != X2
| ~ in(X4,X1)
| ~ in(X4,X0)
| in(X4,X2) ),
inference(cnf_transformation,[],[f78]) ).
fof(f117,plain,
! [X0,X1] :
( ~ relation(X0)
| relation(relation_dom_restriction(X0,X1)) ),
inference(cnf_transformation,[],[f58]) ).
fof(f118,plain,
! [X2,X0,X1,X6,X5] :
( ~ relation(X0)
| ~ relation(X2)
| relation_dom_restriction(X0,X1) != X2
| ~ in(ordered_pair(X5,X6),X2)
| in(ordered_pair(X5,X6),X0) ),
inference(cnf_transformation,[],[f82]) ).
fof(f119,plain,
! [X2,X0,X1,X6,X5] :
( ~ relation(X0)
| ~ relation(X2)
| relation_dom_restriction(X0,X1) != X2
| ~ in(ordered_pair(X5,X6),X2)
| in(X5,X1) ),
inference(cnf_transformation,[],[f82]) ).
fof(f120,plain,
! [X2,X0,X1,X6,X5] :
( ~ relation(X0)
| ~ relation(X2)
| relation_dom_restriction(X0,X1) != X2
| ~ in(ordered_pair(X5,X6),X0)
| ~ in(X5,X1)
| in(ordered_pair(X5,X6),X2) ),
inference(cnf_transformation,[],[f82]) ).
fof(f129,plain,
! [X2,X0,X1,X6] :
( ~ relation(X0)
| relation_inverse_image(X0,X1) != X2
| ~ in(X6,X2)
| in(sK10(X0,X1,X6),X1) ),
inference(cnf_transformation,[],[f87]) ).
fof(f130,plain,
! [X2,X0,X1,X6] :
( ~ relation(X0)
| relation_inverse_image(X0,X1) != X2
| ~ in(X6,X2)
| in(ordered_pair(X6,sK10(X0,X1,X6)),X0) ),
inference(cnf_transformation,[],[f87]) ).
fof(f131,plain,
! [X2,X0,X1,X6,X7] :
( ~ relation(X0)
| relation_inverse_image(X0,X1) != X2
| ~ in(X7,X1)
| ~ in(ordered_pair(X6,X7),X0)
| in(X6,X2) ),
inference(cnf_transformation,[],[f87]) ).
fof(f132,plain,
! [X2,X0,X1] :
( ~ relation(X0)
| in(sK8(X0,X1,X2),X2)
| in(sK9(X0,X1,X2),X1)
| relation_inverse_image(X0,X1) = X2 ),
inference(cnf_transformation,[],[f87]) ).
fof(f133,plain,
! [X2,X0,X1] :
( ~ relation(X0)
| in(sK8(X0,X1,X2),X2)
| in(ordered_pair(sK8(X0,X1,X2),sK9(X0,X1,X2)),X0)
| relation_inverse_image(X0,X1) = X2 ),
inference(cnf_transformation,[],[f87]) ).
fof(f134,plain,
! [X2,X0,X1,X4] :
( ~ relation(X0)
| ~ in(sK8(X0,X1,X2),X2)
| ~ in(X4,X1)
| ~ in(ordered_pair(sK8(X0,X1,X2),X4),X0)
| relation_inverse_image(X0,X1) = X2 ),
inference(cnf_transformation,[],[f87]) ).
fof(f169,plain,
! [X0,X1,X4] :
( ~ in(X4,X1)
| ~ in(X4,X0)
| in(X4,set_intersection2(X0,X1)) ),
inference(equality_resolution,[],[f109]) ).
fof(f170,plain,
! [X0,X1,X4] :
( ~ in(X4,set_intersection2(X0,X1))
| in(X4,X0) ),
inference(equality_resolution,[],[f108]) ).
fof(f171,plain,
! [X0,X1,X4] :
( ~ in(X4,set_intersection2(X0,X1))
| in(X4,X1) ),
inference(equality_resolution,[],[f107]) ).
fof(f172,plain,
! [X0,X1,X6,X5] :
( ~ relation(X0)
| ~ relation(relation_dom_restriction(X0,X1))
| ~ in(ordered_pair(X5,X6),X0)
| ~ in(X5,X1)
| in(ordered_pair(X5,X6),relation_dom_restriction(X0,X1)) ),
inference(equality_resolution,[],[f120]) ).
fof(f173,plain,
! [X0,X1,X6,X5] :
( ~ relation(X0)
| ~ relation(relation_dom_restriction(X0,X1))
| ~ in(ordered_pair(X5,X6),relation_dom_restriction(X0,X1))
| in(X5,X1) ),
inference(equality_resolution,[],[f119]) ).
fof(f174,plain,
! [X0,X1,X6,X5] :
( ~ relation(X0)
| ~ relation(relation_dom_restriction(X0,X1))
| ~ in(ordered_pair(X5,X6),relation_dom_restriction(X0,X1))
| in(ordered_pair(X5,X6),X0) ),
inference(equality_resolution,[],[f118]) ).
fof(f175,plain,
! [X0,X1,X6,X7] :
( ~ relation(X0)
| ~ in(X7,X1)
| ~ in(ordered_pair(X6,X7),X0)
| in(X6,relation_inverse_image(X0,X1)) ),
inference(equality_resolution,[],[f131]) ).
fof(f176,plain,
! [X0,X1,X6] :
( ~ relation(X0)
| ~ in(X6,relation_inverse_image(X0,X1))
| in(ordered_pair(X6,sK10(X0,X1,X6)),X0) ),
inference(equality_resolution,[],[f130]) ).
fof(f177,plain,
! [X0,X1,X6] :
( ~ relation(X0)
| ~ in(X6,relation_inverse_image(X0,X1))
| in(sK10(X0,X1,X6),X1) ),
inference(equality_resolution,[],[f129]) ).
tcf(c_49,negated_conjecture,
relation_inverse_image(relation_dom_restriction(sK2,sK0),sK1) != set_intersection2(sK0,relation_inverse_image(sK2,sK1)),
inference(cnf_transformation,[],[f102]) ).
tcf(c_50,negated_conjecture,
relation(sK2),
inference(cnf_transformation,[],[f101]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,set_intersection2(X1,X2))
| ~ in(X0,X2)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f169]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X1)
| ~ in(X0,set_intersection2(X1,X2)) ),
inference(cnf_transformation,[],[f170]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| ~ in(X0,set_intersection2(X1,X2)) ),
inference(cnf_transformation,[],[f171]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i] :
( relation(relation_dom_restriction(X0,X1))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f117]) ).
tcf(c_69,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(ordered_pair(X0,X1),relation_dom_restriction(X2,X3))
| ~ relation(X2)
| ~ in(X0,X3)
| ~ relation(relation_dom_restriction(X2,X3))
| ~ in(ordered_pair(X0,X1),X2) ),
inference(cnf_transformation,[],[f172]) ).
tcf(c_70,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X0,X3)
| ~ relation(X2)
| ~ relation(relation_dom_restriction(X2,X3))
| ~ in(ordered_pair(X0,X1),relation_dom_restriction(X2,X3)) ),
inference(cnf_transformation,[],[f173]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(ordered_pair(X0,X1),X2)
| ~ relation(X2)
| ~ relation(relation_dom_restriction(X2,X3))
| ~ in(ordered_pair(X0,X1),relation_dom_restriction(X2,X3)) ),
inference(cnf_transformation,[],[f174]) ).
tcf(c_77,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_inverse_image(X0,X1) = X2 )
| ~ relation(X0)
| ~ in(X3,X1)
| ~ in(sK8(X0,X1,X2),X2)
| ~ in(ordered_pair(sK8(X0,X1,X2),X3),X0) ),
inference(cnf_transformation,[],[f134]) ).
tcf(c_78,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK8(X0,X1,X2),X2)
| in(ordered_pair(sK8(X0,X1,X2),sK9(X0,X1,X2)),X0)
| ( relation_inverse_image(X0,X1) = X2 )
| ~ relation(X0) ),
inference(cnf_transformation,[],[f133]) ).
tcf(c_79,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK9(X0,X1,X2),X1)
| in(sK8(X0,X1,X2),X2)
| ( relation_inverse_image(X0,X1) = X2 )
| ~ relation(X0) ),
inference(cnf_transformation,[],[f132]) ).
tcf(c_80,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X0,relation_inverse_image(X2,X3))
| ~ relation(X2)
| ~ in(X1,X3)
| ~ in(ordered_pair(X0,X1),X2) ),
inference(cnf_transformation,[],[f175]) ).
tcf(c_81,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(ordered_pair(X0,sK10(X1,X2,X0)),X1)
| ~ relation(X1)
| ~ in(X0,relation_inverse_image(X1,X2)) ),
inference(cnf_transformation,[],[f176]) ).
tcf(c_82,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK10(X1,X2,X0),X2)
| ~ relation(X1)
| ~ in(X0,relation_inverse_image(X1,X2)) ),
inference(cnf_transformation,[],[f177]) ).
tcf(c_167,plain,
! [X0: $i,X1: $i] :
( relation(relation_dom_restriction(X0,X1))
| ~ relation(X0) ),
inference(prop_impl_just,[status(thm)],[c_65]) ).
tcf(c_384,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X0,X3)
| ~ relation(X2)
| ~ in(ordered_pair(X0,X1),relation_dom_restriction(X2,X3)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_70,c_167]) ).
tcf(c_385,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(ordered_pair(X0,X1),X2)
| ~ relation(X2)
| ~ in(ordered_pair(X0,X1),relation_dom_restriction(X2,X3)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_71,c_167]) ).
tcf(c_386,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(ordered_pair(X0,X1),relation_dom_restriction(X2,X3))
| ~ relation(X2)
| ~ in(X0,X3)
| ~ in(ordered_pair(X0,X1),X2) ),
inference(backward_subsumption_resolution,[status(thm)],[c_69,c_167]) ).
tcf(c_3304,plain,
( in(sK9(relation_dom_restriction(sK2,sK0),sK1,set_intersection2(sK0,relation_inverse_image(sK2,sK1))),sK1)
| in(sK8(relation_dom_restriction(sK2,sK0),sK1,set_intersection2(sK0,relation_inverse_image(sK2,sK1))),set_intersection2(sK0,relation_inverse_image(sK2,sK1)))
| ( relation_inverse_image(relation_dom_restriction(sK2,sK0),sK1) = set_intersection2(sK0,relation_inverse_image(sK2,sK1)) )
| ~ relation(relation_dom_restriction(sK2,sK0)) ),
inference(instantiation,[status(thm)],[c_79]) ).
tcf(c_3342,plain,
! [X0: $i] :
( ( relation_inverse_image(relation_dom_restriction(sK2,sK0),sK1) = set_intersection2(sK0,relation_inverse_image(sK2,sK1)) )
| ~ in(X0,sK1)
| ~ relation(relation_dom_restriction(sK2,sK0))
| ~ in(sK8(relation_dom_restriction(sK2,sK0),sK1,set_intersection2(sK0,relation_inverse_image(sK2,sK1))),set_intersection2(sK0,relation_inverse_image(sK2,sK1)))
| ~ in(ordered_pair(sK8(relation_dom_restriction(sK2,sK0),sK1,set_intersection2(sK0,relation_inverse_image(sK2,sK1))),X0),relation_dom_restriction(sK2,sK0)) ),
inference(instantiation,[status(thm)],[c_77]) ).
tcf(c_3344,plain,
( in(sK8(relation_dom_restriction(sK2,sK0),sK1,set_intersection2(sK0,relation_inverse_image(sK2,sK1))),set_intersection2(sK0,relation_inverse_image(sK2,sK1)))
| in(ordered_pair(sK8(relation_dom_restriction(sK2,sK0),sK1,set_intersection2(sK0,relation_inverse_image(sK2,sK1))),sK9(relation_dom_restriction(sK2,sK0),sK1,set_intersection2(sK0,relation_inverse_image(sK2,sK1)))),relation_dom_restriction(sK2,sK0))
| ( relation_inverse_image(relation_dom_restriction(sK2,sK0),sK1) = set_intersection2(sK0,relation_inverse_image(sK2,sK1)) )
| ~ relation(relation_dom_restriction(sK2,sK0)) ),
inference(instantiation,[status(thm)],[c_78]) ).
tcf(c_3672,plain,
( relation(relation_dom_restriction(sK2,sK0))
| ~ relation(sK2) ),
inference(instantiation,[status(thm)],[c_65]) ).
tcf(c_5362,plain,
( in(sK8(relation_dom_restriction(sK2,sK0),sK1,set_intersection2(sK0,relation_inverse_image(sK2,sK1))),relation_inverse_image(sK2,sK1))
| ~ in(sK8(relation_dom_restriction(sK2,sK0),sK1,set_intersection2(sK0,relation_inverse_image(sK2,sK1))),set_intersection2(sK0,relation_inverse_image(sK2,sK1))) ),
inference(instantiation,[status(thm)],[c_60]) ).
tcf(c_5363,plain,
( in(sK8(relation_dom_restriction(sK2,sK0),sK1,set_intersection2(sK0,relation_inverse_image(sK2,sK1))),sK0)
| ~ in(sK8(relation_dom_restriction(sK2,sK0),sK1,set_intersection2(sK0,relation_inverse_image(sK2,sK1))),set_intersection2(sK0,relation_inverse_image(sK2,sK1))) ),
inference(instantiation,[status(thm)],[c_59]) ).
tcf(c_7902,plain,
! [X0: $i,X1: $i] :
( in(X0,relation_inverse_image(X1,sK1))
| ~ relation(X1)
| ~ in(sK9(relation_dom_restriction(sK2,sK0),sK1,set_intersection2(sK0,relation_inverse_image(sK2,sK1))),sK1)
| ~ in(ordered_pair(X0,sK9(relation_dom_restriction(sK2,sK0),sK1,set_intersection2(sK0,relation_inverse_image(sK2,sK1)))),X1) ),
inference(instantiation,[status(thm)],[c_80]) ).
tcf(c_8036,plain,
( in(ordered_pair(sK8(relation_dom_restriction(sK2,sK0),sK1,set_intersection2(sK0,relation_inverse_image(sK2,sK1))),sK9(relation_dom_restriction(sK2,sK0),sK1,set_intersection2(sK0,relation_inverse_image(sK2,sK1)))),sK2)
| ~ relation(sK2)
| ~ in(ordered_pair(sK8(relation_dom_restriction(sK2,sK0),sK1,set_intersection2(sK0,relation_inverse_image(sK2,sK1))),sK9(relation_dom_restriction(sK2,sK0),sK1,set_intersection2(sK0,relation_inverse_image(sK2,sK1)))),relation_dom_restriction(sK2,sK0)) ),
inference(instantiation,[status(thm)],[c_385]) ).
tcf(c_8037,plain,
( in(sK8(relation_dom_restriction(sK2,sK0),sK1,set_intersection2(sK0,relation_inverse_image(sK2,sK1))),sK0)
| ~ relation(sK2)
| ~ in(ordered_pair(sK8(relation_dom_restriction(sK2,sK0),sK1,set_intersection2(sK0,relation_inverse_image(sK2,sK1))),sK9(relation_dom_restriction(sK2,sK0),sK1,set_intersection2(sK0,relation_inverse_image(sK2,sK1)))),relation_dom_restriction(sK2,sK0)) ),
inference(instantiation,[status(thm)],[c_384]) ).
tcf(c_11356,plain,
! [X0: $i] :
( in(sK8(relation_dom_restriction(sK2,sK0),sK1,set_intersection2(sK0,relation_inverse_image(sK2,sK1))),set_intersection2(sK0,X0))
| ~ in(sK8(relation_dom_restriction(sK2,sK0),sK1,set_intersection2(sK0,relation_inverse_image(sK2,sK1))),sK0)
| ~ in(sK8(relation_dom_restriction(sK2,sK0),sK1,set_intersection2(sK0,relation_inverse_image(sK2,sK1))),X0) ),
inference(instantiation,[status(thm)],[c_58]) ).
tcf(c_11363,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK8(relation_dom_restriction(sK2,sK0),sK1,set_intersection2(sK0,relation_inverse_image(sK2,sK1))),X0),relation_dom_restriction(X1,sK0))
| ~ relation(X1)
| ~ in(sK8(relation_dom_restriction(sK2,sK0),sK1,set_intersection2(sK0,relation_inverse_image(sK2,sK1))),sK0)
| ~ in(ordered_pair(sK8(relation_dom_restriction(sK2,sK0),sK1,set_intersection2(sK0,relation_inverse_image(sK2,sK1))),X0),X1) ),
inference(instantiation,[status(thm)],[c_386]) ).
tcf(c_11794,plain,
( in(ordered_pair(sK8(relation_dom_restriction(sK2,sK0),sK1,set_intersection2(sK0,relation_inverse_image(sK2,sK1))),sK10(sK2,sK1,sK8(relation_dom_restriction(sK2,sK0),sK1,set_intersection2(sK0,relation_inverse_image(sK2,sK1))))),sK2)
| ~ relation(sK2)
| ~ in(sK8(relation_dom_restriction(sK2,sK0),sK1,set_intersection2(sK0,relation_inverse_image(sK2,sK1))),relation_inverse_image(sK2,sK1)) ),
inference(instantiation,[status(thm)],[c_81]) ).
tcf(c_11795,plain,
( in(sK10(sK2,sK1,sK8(relation_dom_restriction(sK2,sK0),sK1,set_intersection2(sK0,relation_inverse_image(sK2,sK1)))),sK1)
| ~ relation(sK2)
| ~ in(sK8(relation_dom_restriction(sK2,sK0),sK1,set_intersection2(sK0,relation_inverse_image(sK2,sK1))),relation_inverse_image(sK2,sK1)) ),
inference(instantiation,[status(thm)],[c_82]) ).
tcf(c_26915,plain,
( ( relation_inverse_image(relation_dom_restriction(sK2,sK0),sK1) = set_intersection2(sK0,relation_inverse_image(sK2,sK1)) )
| ~ relation(relation_dom_restriction(sK2,sK0))
| ~ in(sK10(sK2,sK1,sK8(relation_dom_restriction(sK2,sK0),sK1,set_intersection2(sK0,relation_inverse_image(sK2,sK1)))),sK1)
| ~ in(sK8(relation_dom_restriction(sK2,sK0),sK1,set_intersection2(sK0,relation_inverse_image(sK2,sK1))),set_intersection2(sK0,relation_inverse_image(sK2,sK1)))
| ~ in(ordered_pair(sK8(relation_dom_restriction(sK2,sK0),sK1,set_intersection2(sK0,relation_inverse_image(sK2,sK1))),sK10(sK2,sK1,sK8(relation_dom_restriction(sK2,sK0),sK1,set_intersection2(sK0,relation_inverse_image(sK2,sK1))))),relation_dom_restriction(sK2,sK0)) ),
inference(instantiation,[status(thm)],[c_3342]) ).
tcf(c_32811,plain,
( in(sK8(relation_dom_restriction(sK2,sK0),sK1,set_intersection2(sK0,relation_inverse_image(sK2,sK1))),set_intersection2(sK0,relation_inverse_image(sK2,sK1)))
| ~ in(sK8(relation_dom_restriction(sK2,sK0),sK1,set_intersection2(sK0,relation_inverse_image(sK2,sK1))),sK0)
| ~ in(sK8(relation_dom_restriction(sK2,sK0),sK1,set_intersection2(sK0,relation_inverse_image(sK2,sK1))),relation_inverse_image(sK2,sK1)) ),
inference(instantiation,[status(thm)],[c_11356]) ).
tcf(c_39581,plain,
( in(ordered_pair(sK8(relation_dom_restriction(sK2,sK0),sK1,set_intersection2(sK0,relation_inverse_image(sK2,sK1))),sK10(sK2,sK1,sK8(relation_dom_restriction(sK2,sK0),sK1,set_intersection2(sK0,relation_inverse_image(sK2,sK1))))),relation_dom_restriction(sK2,sK0))
| ~ relation(sK2)
| ~ in(sK8(relation_dom_restriction(sK2,sK0),sK1,set_intersection2(sK0,relation_inverse_image(sK2,sK1))),sK0)
| ~ in(ordered_pair(sK8(relation_dom_restriction(sK2,sK0),sK1,set_intersection2(sK0,relation_inverse_image(sK2,sK1))),sK10(sK2,sK1,sK8(relation_dom_restriction(sK2,sK0),sK1,set_intersection2(sK0,relation_inverse_image(sK2,sK1))))),sK2) ),
inference(instantiation,[status(thm)],[c_11363]) ).
tcf(c_42281,plain,
( in(sK8(relation_dom_restriction(sK2,sK0),sK1,set_intersection2(sK0,relation_inverse_image(sK2,sK1))),relation_inverse_image(sK2,sK1))
| ~ relation(sK2)
| ~ in(sK9(relation_dom_restriction(sK2,sK0),sK1,set_intersection2(sK0,relation_inverse_image(sK2,sK1))),sK1)
| ~ in(ordered_pair(sK8(relation_dom_restriction(sK2,sK0),sK1,set_intersection2(sK0,relation_inverse_image(sK2,sK1))),sK9(relation_dom_restriction(sK2,sK0),sK1,set_intersection2(sK0,relation_inverse_image(sK2,sK1)))),sK2) ),
inference(instantiation,[status(thm)],[c_7902]) ).
tcf(c_42282,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_42281,c_39581,c_32811,c_26915,c_11794,c_11795,c_8036,c_8037,c_5362,c_5363,c_3672,c_3344,c_3304,c_49,c_50]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU060+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.08/0.37 % Computer : n003.cluster.edu
% 0.08/0.37 % Model : x86_64 x86_64
% 0.08/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.37 % Memory : 8046.5625MB
% 0.08/0.37 % OS : Linux 6.8.0-71-generic
% 0.08/0.37 % CPULimit : 300
% 0.08/0.37 % WCLimit : 300
% 0.08/0.37 % DateTime : Thu Sep 24 12:41:51 UTC 2026
% 0.13/0.37 % CPUTime :
% 0.13/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/0.41 Running first-order theorem proving
% 0.13/0.41 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
% 0.13/0.42
% 0.13/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.42
% 0.13/0.42 % Detected problem language: tptp
% 0.13/0.44 % Proving...
% 14.73/2.82 % SZS status Started for theBenchmark.p
% 14.73/2.82 % SZS status Theorem for theBenchmark.p
% 14.73/2.82
% 14.73/2.82 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 14.73/2.82
% 14.73/2.82 % ------ iProver source info
% 14.73/2.82
% 14.73/2.82 % git: date: 2026-07-19 20:42:38 +0200
% 14.73/2.82 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 14.73/2.82 % git: non_committed_changes: false
% 14.73/2.82
% 14.73/2.82 % ------ Parsing...
% 14.73/2.82 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 14.73/2.82
% 14.73/2.82 % ------ Preprocessing... sup_sim: 0 sf_s rm: 6 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e %
% 14.73/2.82
% 14.73/2.82 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 14.73/2.82
% 14.73/2.82 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 14.73/2.82 % ------ Proving...
% 14.73/2.82 % ------ Problem Properties
% 14.73/2.82
% 14.73/2.82 %
% 14.73/2.82 % clauses 60
% 14.73/2.82 % conjectures 2
% 14.73/2.82 % EPR 24
% 14.73/2.82 % Horn 51
% 14.73/2.82 % unary 22
% 14.73/2.82 % binary 15
% 14.73/2.82 % lits 135
% 14.73/2.82 % lits eq 16
% 14.73/2.82 % fd_pure 0
% 14.73/2.82 % fd_pseudo 0
% 14.73/2.82 % fd_cond 1
% 14.73/2.82 % fd_pseudo_cond 11
% 14.73/2.82 % AC symbols 0
% 14.73/2.82
% 14.73/2.82 % ------ Schedule dynamic 5 is on
% 14.73/2.82
% 14.73/2.82 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 14.73/2.82
% 14.73/2.82
% 14.73/2.82 % ------
% 14.73/2.82 % Current options:
% 14.73/2.82 % ------
% 14.73/2.82
% 14.73/2.82
% 14.73/2.82 %
% 14.73/2.82
% 14.73/2.82 % ------ Proving...
% 14.73/2.82 %
% 14.73/2.82
% 14.73/2.82 % SZS status Theorem for theBenchmark.p
% 14.73/2.82
% 14.73/2.82 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 14.73/2.82
% 14.73/2.82
%------------------------------------------------------------------------------