%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU205+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n011.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 02:55:53 PM UTC 2026
% Result : Theorem 5.36s 3.22s
% Output : CNFRefutation 5.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of formulae : 63 ( 7 unt; 0 def)
% Number of atoms : 301 ( 41 equ)
% Maximal formula atoms : 15 ( 4 avg)
% Number of connectives : 395 ( 157 ~; 173 |; 53 &)
% ( 8 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 7 avg)
% Maximal term depth : 7 ( 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; 2 con; 0-3 aty)
% Number of variables : 181 ( 0 sgn 164 !; 17 ?; 35 :)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0] :
( relation(X0)
=> ! [X1,X2] :
( X2 = relation_image(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(X4,X1)
& in(ordered_pair(X4,X3),X0) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d13_relat_1) ).
fof(f6,axiom,
! [X0,X1,X2] :
( X2 = set_intersection2(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X1)
& in(X3,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_xboole_0) ).
fof(f7,axiom,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tarski) ).
fof(f30,axiom,
! [X0,X1,X2] :
( relation(X2)
=> ( in(X0,relation_image(X2,X1))
<=> ? [X3] :
( in(X3,X1)
& in(ordered_pair(X3,X0),X2)
& in(X3,relation_dom(X2)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t143_relat_1) ).
fof(f31,conjecture,
! [X0,X1] :
( relation(X1)
=> relation_image(X1,X0) = relation_image(X1,set_intersection2(relation_dom(X1),X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t145_relat_1) ).
fof(f32,negated_conjecture,
~ ! [X0,X1] :
( relation(X1)
=> relation_image(X1,X0) = relation_image(X1,set_intersection2(relation_dom(X1),X0)) ),
inference(negated_conjecture,[status(cth)],[f31]) ).
fof(f43,plain,
! [X0] :
( ~ relation(X0)
| ! [X1,X2] :
( X2 = relation_image(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(X4,X1)
& in(ordered_pair(X4,X3),X0) ) ) ) ),
inference(ennf_transformation,[],[f5]) ).
fof(f49,plain,
! [X0,X1,X2] :
( ~ relation(X2)
| ( in(X0,relation_image(X2,X1))
<=> ? [X3] :
( in(X3,X1)
& in(ordered_pair(X3,X0),X2)
& in(X3,relation_dom(X2)) ) ) ),
inference(ennf_transformation,[],[f30]) ).
fof(f50,plain,
? [X0,X1] :
( relation(X1)
& relation_image(X1,X0) != relation_image(X1,set_intersection2(relation_dom(X1),X0)) ),
inference(ennf_transformation,[],[f32]) ).
fof(f58,plain,
! [X0] :
( ~ relation(X0)
| ! [X1,X2] :
( ( relation_image(X0,X1) != X2
| ! [X3] :
( ( ~ in(X3,X2)
| ? [X4] :
( in(X4,X1)
& in(ordered_pair(X4,X3),X0) ) )
& ( ! [X4] :
( ~ in(X4,X1)
| ~ in(ordered_pair(X4,X3),X0) )
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| ? [X4] :
( in(X4,X1)
& in(ordered_pair(X4,X3),X0) ) )
& ( ~ in(X3,X2)
| ! [X4] :
( ~ in(X4,X1)
| ~ in(ordered_pair(X4,X3),X0) ) ) )
| X2 = relation_image(X0,X1) ) ) ),
inference(nnf_transformation,[],[f43]) ).
fof(f59,plain,
! [X0] :
( ~ relation(X0)
| ! [X1,X2] :
( ( relation_image(X0,X1) != X2
| ! [X6] :
( ( ~ in(X6,X2)
| ? [X8] :
( in(X8,X1)
& in(ordered_pair(X8,X6),X0) ) )
& ( ! [X7] :
( ~ in(X7,X1)
| ~ in(ordered_pair(X7,X6),X0) )
| in(X6,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| ? [X5] :
( in(X5,X1)
& in(ordered_pair(X5,X3),X0) ) )
& ( ~ in(X3,X2)
| ! [X4] :
( ~ in(X4,X1)
| ~ in(ordered_pair(X4,X3),X0) ) ) )
| X2 = relation_image(X0,X1) ) ) ),
inference(rectify,[],[f58]) ).
fof(f60,plain,
! [X0] :
( ~ relation(X0)
| ! [X1,X2] :
( ( relation_image(X0,X1) != X2
| ! [X6] :
( ( ~ in(X6,X2)
| ( in(sK2(X0,X1,X6),X1)
& in(ordered_pair(sK2(X0,X1,X6),X6),X0) ) )
& ( ! [X7] :
( ~ in(X7,X1)
| ~ in(ordered_pair(X7,X6),X0) )
| in(X6,X2) ) ) )
& ( ( ( in(sK0(X0,X1,X2),X2)
| ( in(sK1(X0,X1,X2),X1)
& in(ordered_pair(sK1(X0,X1,X2),sK0(X0,X1,X2)),X0) ) )
& ( ~ in(sK0(X0,X1,X2),X2)
| ! [X4] :
( ~ in(X4,X1)
| ~ in(ordered_pair(X4,sK0(X0,X1,X2)),X0) ) ) )
| X2 = relation_image(X0,X1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X3,sK0(X0,X1,X2)),skolemize(X5,sK1(X0,X1,X2)),skolemize(X8,sK2(X0,X1,X6))],[f59]) ).
fof(f61,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,[],[f6]) ).
fof(f62,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,[],[f61]) ).
fof(f63,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,[],[f62]) ).
fof(f64,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))],[f63]) ).
fof(f70,plain,
! [X0,X1,X2] :
( ~ relation(X2)
| ( ( ~ in(X0,relation_image(X2,X1))
| ? [X3] :
( in(X3,X1)
& in(ordered_pair(X3,X0),X2)
& in(X3,relation_dom(X2)) ) )
& ( ! [X3] :
( ~ in(X3,X1)
| ~ in(ordered_pair(X3,X0),X2)
| ~ in(X3,relation_dom(X2)) )
| in(X0,relation_image(X2,X1)) ) ) ),
inference(nnf_transformation,[],[f49]) ).
fof(f71,plain,
! [X0,X1,X2] :
( ~ relation(X2)
| ( ( ~ in(X0,relation_image(X2,X1))
| ? [X4] :
( in(X4,X1)
& in(ordered_pair(X4,X0),X2)
& in(X4,relation_dom(X2)) ) )
& ( ! [X3] :
( ~ in(X3,X1)
| ~ in(ordered_pair(X3,X0),X2)
| ~ in(X3,relation_dom(X2)) )
| in(X0,relation_image(X2,X1)) ) ) ),
inference(rectify,[],[f70]) ).
fof(f72,plain,
! [X0,X1,X2] :
( ~ relation(X2)
| ( ( ~ in(X0,relation_image(X2,X1))
| ( in(sK9(X0,X1,X2),X1)
& in(ordered_pair(sK9(X0,X1,X2),X0),X2)
& in(sK9(X0,X1,X2),relation_dom(X2)) ) )
& ( ! [X3] :
( ~ in(X3,X1)
| ~ in(ordered_pair(X3,X0),X2)
| ~ in(X3,relation_dom(X2)) )
| in(X0,relation_image(X2,X1)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(X4,sK9(X0,X1,X2))],[f71]) ).
fof(f73,plain,
( relation(sK11)
& relation_image(sK11,sK10) != relation_image(sK11,set_intersection2(relation_dom(sK11),sK10)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10,sK11]),skolemize(X0,sK10),skolemize(X1,sK11)],[f50]) ).
fof(f82,plain,
! [X2,X0,X1,X6,X7] :
( ~ relation(X0)
| relation_image(X0,X1) != X2
| ~ in(X7,X1)
| ~ in(ordered_pair(X7,X6),X0)
| in(X6,X2) ),
inference(cnf_transformation,[],[f60]) ).
fof(f83,plain,
! [X2,X0,X1] :
( ~ relation(X0)
| in(sK0(X0,X1,X2),X2)
| in(sK1(X0,X1,X2),X1)
| relation_image(X0,X1) = X2 ),
inference(cnf_transformation,[],[f60]) ).
fof(f84,plain,
! [X2,X0,X1] :
( ~ relation(X0)
| in(sK0(X0,X1,X2),X2)
| in(ordered_pair(sK1(X0,X1,X2),sK0(X0,X1,X2)),X0)
| relation_image(X0,X1) = X2 ),
inference(cnf_transformation,[],[f60]) ).
fof(f85,plain,
! [X2,X0,X1,X4] :
( ~ relation(X0)
| ~ in(sK0(X0,X1,X2),X2)
| ~ in(X4,X1)
| ~ in(ordered_pair(X4,sK0(X0,X1,X2)),X0)
| relation_image(X0,X1) = X2 ),
inference(cnf_transformation,[],[f60]) ).
fof(f86,plain,
! [X2,X0,X1,X4] :
( set_intersection2(X0,X1) != X2
| ~ in(X4,X2)
| in(X4,X1) ),
inference(cnf_transformation,[],[f64]) ).
fof(f88,plain,
! [X2,X0,X1,X4] :
( set_intersection2(X0,X1) != X2
| ~ in(X4,X1)
| ~ in(X4,X0)
| in(X4,X2) ),
inference(cnf_transformation,[],[f64]) ).
fof(f92,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f7]) ).
fof(f111,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| ~ in(X0,relation_image(X2,X1))
| in(sK9(X0,X1,X2),X1) ),
inference(cnf_transformation,[],[f72]) ).
fof(f112,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| ~ in(X0,relation_image(X2,X1))
| in(ordered_pair(sK9(X0,X1,X2),X0),X2) ),
inference(cnf_transformation,[],[f72]) ).
fof(f113,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| ~ in(X0,relation_image(X2,X1))
| in(sK9(X0,X1,X2),relation_dom(X2)) ),
inference(cnf_transformation,[],[f72]) ).
fof(f115,plain,
relation(sK11),
inference(cnf_transformation,[],[f73]) ).
fof(f116,plain,
relation_image(sK11,sK10) != relation_image(sK11,set_intersection2(relation_dom(sK11),sK10)),
inference(cnf_transformation,[],[f73]) ).
fof(f125,plain,
! [X2,X0,X1,X4] :
( ~ relation(X0)
| ~ in(sK0(X0,X1,X2),X2)
| ~ in(X4,X1)
| ~ in(unordered_pair(unordered_pair(X4,sK0(X0,X1,X2)),singleton(X4)),X0)
| relation_image(X0,X1) = X2 ),
inference(definition_unfolding,[],[f85,f92]) ).
fof(f126,plain,
! [X2,X0,X1] :
( ~ relation(X0)
| in(sK0(X0,X1,X2),X2)
| in(unordered_pair(unordered_pair(sK1(X0,X1,X2),sK0(X0,X1,X2)),singleton(sK1(X0,X1,X2))),X0)
| relation_image(X0,X1) = X2 ),
inference(definition_unfolding,[],[f84,f92]) ).
fof(f127,plain,
! [X2,X0,X1,X6,X7] :
( ~ relation(X0)
| relation_image(X0,X1) != X2
| ~ in(X7,X1)
| ~ in(unordered_pair(unordered_pair(X7,X6),singleton(X7)),X0)
| in(X6,X2) ),
inference(definition_unfolding,[],[f82,f92]) ).
fof(f131,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| ~ in(X0,relation_image(X2,X1))
| in(unordered_pair(unordered_pair(sK9(X0,X1,X2),X0),singleton(sK9(X0,X1,X2))),X2) ),
inference(definition_unfolding,[],[f112,f92]) ).
fof(f132,plain,
! [X0,X1,X6,X7] :
( ~ relation(X0)
| ~ in(X7,X1)
| ~ in(unordered_pair(unordered_pair(X7,X6),singleton(X7)),X0)
| in(X6,relation_image(X0,X1)) ),
inference(equality_resolution,[],[f127]) ).
fof(f135,plain,
! [X0,X1,X4] :
( ~ in(X4,X1)
| ~ in(X4,X0)
| in(X4,set_intersection2(X0,X1)) ),
inference(equality_resolution,[],[f88]) ).
fof(f137,plain,
! [X0,X1,X4] :
( ~ in(X4,set_intersection2(X0,X1))
| in(X4,X1) ),
inference(equality_resolution,[],[f86]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(X1,X2) = X3 )
| ~ relation(X1)
| ~ in(X0,X2)
| ~ in(sK0(X1,X2,X3),X3)
| ~ in(unordered_pair(unordered_pair(X0,sK0(X1,X2,X3)),singleton(X0)),X1) ),
inference(cnf_transformation,[],[f125]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK0(X0,X1,X2),X2)
| in(unordered_pair(unordered_pair(sK1(X0,X1,X2),sK0(X0,X1,X2)),singleton(sK1(X0,X1,X2))),X0)
| ( relation_image(X0,X1) = X2 )
| ~ relation(X0) ),
inference(cnf_transformation,[],[f126]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK1(X0,X1,X2),X1)
| in(sK0(X0,X1,X2),X2)
| ( relation_image(X0,X1) = X2 )
| ~ relation(X0) ),
inference(cnf_transformation,[],[f83]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X1,relation_image(X2,X3))
| ~ relation(X2)
| ~ in(X0,X3)
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),X2) ),
inference(cnf_transformation,[],[f132]) ).
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,[],[f135]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| ~ in(X0,set_intersection2(X1,X2)) ),
inference(cnf_transformation,[],[f137]) ).
tcf(c_84,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK9(X0,X2,X1),relation_dom(X1))
| ~ relation(X1)
| ~ in(X0,relation_image(X1,X2)) ),
inference(cnf_transformation,[],[f113]) ).
tcf(c_85,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(unordered_pair(unordered_pair(sK9(X0,X2,X1),X0),singleton(sK9(X0,X2,X1))),X1)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,X2)) ),
inference(cnf_transformation,[],[f131]) ).
tcf(c_86,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK9(X0,X2,X1),X2)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,X2)) ),
inference(cnf_transformation,[],[f111]) ).
tcf(c_87,negated_conjecture,
relation_image(sK11,set_intersection2(relation_dom(sK11),sK10)) != relation_image(sK11,sK10),
inference(cnf_transformation,[],[f116]) ).
tcf(c_88,negated_conjecture,
relation(sK11),
inference(cnf_transformation,[],[f115]) ).
tcf(c_1046,plain,
( in(sK0(sK11,set_intersection2(relation_dom(sK11),sK10),relation_image(sK11,sK10)),relation_image(sK11,sK10))
| in(sK1(sK11,set_intersection2(relation_dom(sK11),sK10),relation_image(sK11,sK10)),set_intersection2(relation_dom(sK11),sK10))
| ( relation_image(sK11,set_intersection2(relation_dom(sK11),sK10)) = relation_image(sK11,sK10) )
| ~ relation(sK11) ),
inference(instantiation,[status(thm)],[c_55]) ).
tcf(c_1047,plain,
( in(sK0(sK11,set_intersection2(relation_dom(sK11),sK10),relation_image(sK11,sK10)),relation_image(sK11,sK10))
| in(unordered_pair(unordered_pair(sK1(sK11,set_intersection2(relation_dom(sK11),sK10),relation_image(sK11,sK10)),sK0(sK11,set_intersection2(relation_dom(sK11),sK10),relation_image(sK11,sK10))),singleton(sK1(sK11,set_intersection2(relation_dom(sK11),sK10),relation_image(sK11,sK10)))),sK11)
| ( relation_image(sK11,set_intersection2(relation_dom(sK11),sK10)) = relation_image(sK11,sK10) )
| ~ relation(sK11) ),
inference(instantiation,[status(thm)],[c_54]) ).
tcf(c_1080,plain,
( in(sK9(sK0(sK11,set_intersection2(relation_dom(sK11),sK10),relation_image(sK11,sK10)),sK10,sK11),sK10)
| ~ relation(sK11)
| ~ in(sK0(sK11,set_intersection2(relation_dom(sK11),sK10),relation_image(sK11,sK10)),relation_image(sK11,sK10)) ),
inference(instantiation,[status(thm)],[c_86]) ).
tcf(c_1081,plain,
( in(unordered_pair(unordered_pair(sK9(sK0(sK11,set_intersection2(relation_dom(sK11),sK10),relation_image(sK11,sK10)),sK10,sK11),sK0(sK11,set_intersection2(relation_dom(sK11),sK10),relation_image(sK11,sK10))),singleton(sK9(sK0(sK11,set_intersection2(relation_dom(sK11),sK10),relation_image(sK11,sK10)),sK10,sK11))),sK11)
| ~ relation(sK11)
| ~ in(sK0(sK11,set_intersection2(relation_dom(sK11),sK10),relation_image(sK11,sK10)),relation_image(sK11,sK10)) ),
inference(instantiation,[status(thm)],[c_85]) ).
tcf(c_1082,plain,
( in(sK9(sK0(sK11,set_intersection2(relation_dom(sK11),sK10),relation_image(sK11,sK10)),sK10,sK11),relation_dom(sK11))
| ~ relation(sK11)
| ~ in(sK0(sK11,set_intersection2(relation_dom(sK11),sK10),relation_image(sK11,sK10)),relation_image(sK11,sK10)) ),
inference(instantiation,[status(thm)],[c_84]) ).
tcf(c_1224,plain,
( in(sK1(sK11,set_intersection2(relation_dom(sK11),sK10),relation_image(sK11,sK10)),sK10)
| ~ in(sK1(sK11,set_intersection2(relation_dom(sK11),sK10),relation_image(sK11,sK10)),set_intersection2(relation_dom(sK11),sK10)) ),
inference(instantiation,[status(thm)],[c_64]) ).
tcf(c_1705,plain,
! [X0: $i,X1: $i] :
( in(X0,relation_image(X1,sK10))
| ~ relation(X1)
| ~ in(sK1(sK11,set_intersection2(relation_dom(sK11),sK10),relation_image(sK11,sK10)),sK10)
| ~ in(unordered_pair(unordered_pair(sK1(sK11,set_intersection2(relation_dom(sK11),sK10),relation_image(sK11,sK10)),X0),singleton(sK1(sK11,set_intersection2(relation_dom(sK11),sK10),relation_image(sK11,sK10)))),X1) ),
inference(instantiation,[status(thm)],[c_56]) ).
tcf(c_1859,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(sK11,set_intersection2(relation_dom(sK11),sK10)) = relation_image(X1,X2) )
| ~ relation(sK11)
| ~ in(X0,set_intersection2(relation_dom(sK11),sK10))
| ~ in(sK0(sK11,set_intersection2(relation_dom(sK11),sK10),relation_image(X1,X2)),relation_image(X1,X2))
| ~ in(unordered_pair(unordered_pair(X0,sK0(sK11,set_intersection2(relation_dom(sK11),sK10),relation_image(X1,X2))),singleton(X0)),sK11) ),
inference(instantiation,[status(thm)],[c_53]) ).
tcf(c_2244,plain,
! [X0: $i] :
( in(sK9(sK0(sK11,set_intersection2(relation_dom(sK11),sK10),relation_image(sK11,sK10)),sK10,sK11),set_intersection2(relation_dom(sK11),X0))
| ~ in(sK9(sK0(sK11,set_intersection2(relation_dom(sK11),sK10),relation_image(sK11,sK10)),sK10,sK11),X0)
| ~ in(sK9(sK0(sK11,set_intersection2(relation_dom(sK11),sK10),relation_image(sK11,sK10)),sK10,sK11),relation_dom(sK11)) ),
inference(instantiation,[status(thm)],[c_62]) ).
tcf(c_2714,plain,
( ( relation_image(sK11,set_intersection2(relation_dom(sK11),sK10)) = relation_image(sK11,sK10) )
| ~ relation(sK11)
| ~ in(sK0(sK11,set_intersection2(relation_dom(sK11),sK10),relation_image(sK11,sK10)),relation_image(sK11,sK10))
| ~ in(sK9(sK0(sK11,set_intersection2(relation_dom(sK11),sK10),relation_image(sK11,sK10)),sK10,sK11),set_intersection2(relation_dom(sK11),sK10))
| ~ in(unordered_pair(unordered_pair(sK9(sK0(sK11,set_intersection2(relation_dom(sK11),sK10),relation_image(sK11,sK10)),sK10,sK11),sK0(sK11,set_intersection2(relation_dom(sK11),sK10),relation_image(sK11,sK10))),singleton(sK9(sK0(sK11,set_intersection2(relation_dom(sK11),sK10),relation_image(sK11,sK10)),sK10,sK11))),sK11) ),
inference(instantiation,[status(thm)],[c_1859]) ).
tcf(c_4859,plain,
( in(sK9(sK0(sK11,set_intersection2(relation_dom(sK11),sK10),relation_image(sK11,sK10)),sK10,sK11),set_intersection2(relation_dom(sK11),sK10))
| ~ in(sK9(sK0(sK11,set_intersection2(relation_dom(sK11),sK10),relation_image(sK11,sK10)),sK10,sK11),sK10)
| ~ in(sK9(sK0(sK11,set_intersection2(relation_dom(sK11),sK10),relation_image(sK11,sK10)),sK10,sK11),relation_dom(sK11)) ),
inference(instantiation,[status(thm)],[c_2244]) ).
tcf(c_4940,plain,
( in(sK0(sK11,set_intersection2(relation_dom(sK11),sK10),relation_image(sK11,sK10)),relation_image(sK11,sK10))
| ~ relation(sK11)
| ~ in(sK1(sK11,set_intersection2(relation_dom(sK11),sK10),relation_image(sK11,sK10)),sK10)
| ~ in(unordered_pair(unordered_pair(sK1(sK11,set_intersection2(relation_dom(sK11),sK10),relation_image(sK11,sK10)),sK0(sK11,set_intersection2(relation_dom(sK11),sK10),relation_image(sK11,sK10))),singleton(sK1(sK11,set_intersection2(relation_dom(sK11),sK10),relation_image(sK11,sK10)))),sK11) ),
inference(instantiation,[status(thm)],[c_1705]) ).
tcf(c_4984,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_4940,c_4859,c_2714,c_1224,c_1080,c_1081,c_1082,c_1046,c_1047,c_87,c_88]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU205+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.35 % Computer : n011.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Thu Sep 24 13:10:27 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.10/0.35 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.14/0.39 Running first-order theorem proving
% 0.14/0.39 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.40
% 0.14/0.40 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.40
% 0.14/0.40 % Detected problem language: tptp
% 0.14/0.41 % Proving...
% 5.36/3.22 % SZS status Started for theBenchmark.p
% 5.36/3.22 % SZS status Theorem for theBenchmark.p
% 5.36/3.22
% 5.36/3.22 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 5.36/3.22
% 5.36/3.22 % ------ iProver source info
% 5.36/3.22
% 5.36/3.22 % git: date: 2026-07-19 20:42:38 +0200
% 5.36/3.22 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 5.36/3.22 % git: non_committed_changes: false
% 5.36/3.22
% 5.36/3.22 % ------ Parsing...
% 5.36/3.22 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 5.36/3.22
% 5.36/3.22 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e %
% 5.36/3.22
% 5.36/3.22 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 5.36/3.22
% 5.36/3.22 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 5.36/3.22 % ------ Proving...
% 5.36/3.22 % ------ Problem Properties
% 5.36/3.22
% 5.36/3.22 %
% 5.36/3.22 % clauses 43
% 5.36/3.22 % conjectures 2
% 5.36/3.22 % EPR 14
% 5.36/3.22 % Horn 37
% 5.36/3.22 % unary 16
% 5.36/3.22 % binary 9
% 5.36/3.22 % lits 94
% 5.36/3.22 % lits eq 15
% 5.36/3.22 % fd_pure 0
% 5.36/3.22 % fd_pseudo 0
% 5.36/3.22 % fd_cond 1
% 5.36/3.22 % fd_pseudo_cond 9
% 5.36/3.22 % AC symbols 0
% 5.36/3.22
% 5.36/3.22 % ------ Input Options Time Limit: Unbounded
% 5.36/3.22
% 5.36/3.22
% 5.36/3.22 % ------
% 5.36/3.22 % Current options:
% 5.36/3.22 % ------
% 5.36/3.22
% 5.36/3.22
% 5.36/3.22 %
% 5.36/3.22
% 5.36/3.22 % ------ Proving...
% 5.36/3.22 %
% 5.36/3.22
% 5.36/3.22 % SZS status Theorem for theBenchmark.p
% 5.36/3.22
% 5.36/3.22 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 5.36/3.22
% 5.36/3.22
%------------------------------------------------------------------------------