%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU070+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 : n017.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 02:55:17 PM UTC 2026
% Result : Theorem 10.80s 7.74s
% Output : CNFRefutation 10.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 8
% Syntax : Number of formulae : 87 ( 16 unt; 0 def)
% Number of atoms : 368 ( 47 equ)
% Maximal formula atoms : 15 ( 4 avg)
% Number of connectives : 476 ( 195 ~; 201 |; 63 &)
% ( 12 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 7 avg)
% Maximal term depth : 8 ( 2 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 : 17 ( 17 usr; 3 con; 0-3 aty)
% Number of variables : 257 ( 0 sgn 233 !; 24 ?; 57 :)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f6,axiom,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
fof(f7,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/sandbox/benchmark/theBenchmark.p',d13_relat_1) ).
fof(f8,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(f9,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(f10,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(f11,axiom,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_tarski) ).
fof(f33,conjecture,
! [X0,X1,X2] :
( relation(X2)
=> subset(set_intersection2(X0,relation_inverse_image(X2,X1)),relation_inverse_image(X2,set_intersection2(relation_image(X2,X0),X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t151_funct_1) ).
fof(f34,negated_conjecture,
~ ! [X0,X1,X2] :
( relation(X2)
=> subset(set_intersection2(X0,relation_inverse_image(X2,X1)),relation_inverse_image(X2,set_intersection2(relation_image(X2,X0),X1))) ),
inference(negated_conjecture,[status(cth)],[f33]) ).
fof(f55,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,[],[f7]) ).
fof(f56,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,[],[f8]) ).
fof(f57,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( ~ in(X2,X0)
| in(X2,X1) ) ),
inference(ennf_transformation,[],[f9]) ).
fof(f61,plain,
? [X0,X1,X2] :
( relation(X2)
& ~ subset(set_intersection2(X0,relation_inverse_image(X2,X1)),relation_inverse_image(X2,set_intersection2(relation_image(X2,X0),X1))) ),
inference(ennf_transformation,[],[f34]) ).
fof(f71,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,[],[f55]) ).
fof(f72,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,[],[f71]) ).
fof(f73,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))],[f72]) ).
fof(f74,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,[],[f56]) ).
fof(f75,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,[],[f74]) ).
fof(f76,plain,
! [X0] :
( ~ relation(X0)
| ! [X1,X2] :
( ( relation_inverse_image(X0,X1) != X2
| ! [X6] :
( ( ~ in(X6,X2)
| ( in(sK5(X0,X1,X6),X1)
& in(ordered_pair(X6,sK5(X0,X1,X6)),X0) ) )
& ( ! [X7] :
( ~ in(X7,X1)
| ~ in(ordered_pair(X6,X7),X0) )
| in(X6,X2) ) ) )
& ( ( ( in(sK3(X0,X1,X2),X2)
| ( in(sK4(X0,X1,X2),X1)
& in(ordered_pair(sK3(X0,X1,X2),sK4(X0,X1,X2)),X0) ) )
& ( ~ in(sK3(X0,X1,X2),X2)
| ! [X4] :
( ~ in(X4,X1)
| ~ in(ordered_pair(sK3(X0,X1,X2),X4),X0) ) ) )
| X2 = relation_inverse_image(X0,X1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5]),skolemize(X3,sK3(X0,X1,X2)),skolemize(X5,sK4(X0,X1,X2)),skolemize(X8,sK5(X0,X1,X6))],[f75]) ).
fof(f77,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X2] :
( ~ in(X2,X0)
| in(X2,X1) ) )
& ( ? [X2] :
( in(X2,X0)
& ~ in(X2,X1) )
| subset(X0,X1) ) ),
inference(nnf_transformation,[],[f57]) ).
fof(f78,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X3] :
( ~ in(X3,X0)
| in(X3,X1) ) )
& ( ? [X2] :
( in(X2,X0)
& ~ in(X2,X1) )
| subset(X0,X1) ) ),
inference(rectify,[],[f77]) ).
fof(f79,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X3] :
( ~ in(X3,X0)
| in(X3,X1) ) )
& ( ( in(sK6(X0,X1),X0)
& ~ in(sK6(X0,X1),X1) )
| subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(X2,sK6(X0,X1))],[f78]) ).
fof(f80,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,[],[f10]) ).
fof(f81,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,[],[f80]) ).
fof(f82,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,[],[f81]) ).
fof(f83,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(sK7(X0,X1,X2),X2)
| ( in(sK7(X0,X1,X2),X1)
& in(sK7(X0,X1,X2),X0) ) )
& ( ~ in(sK7(X0,X1,X2),X2)
| ~ in(sK7(X0,X1,X2),X1)
| ~ in(sK7(X0,X1,X2),X0) ) )
| X2 = set_intersection2(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(X3,sK7(X0,X1,X2))],[f82]) ).
fof(f95,plain,
( relation(sK21)
& ~ subset(set_intersection2(sK19,relation_inverse_image(sK21,sK20)),relation_inverse_image(sK21,set_intersection2(relation_image(sK21,sK19),sK20))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19,sK20,sK21]),skolemize(X0,sK19),skolemize(X1,sK20),skolemize(X2,sK21)],[f61]) ).
fof(f102,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f5]) ).
fof(f103,plain,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[],[f6]) ).
fof(f106,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,[],[f73]) ).
fof(f110,plain,
! [X2,X0,X1,X6] :
( ~ relation(X0)
| relation_inverse_image(X0,X1) != X2
| ~ in(X6,X2)
| in(sK5(X0,X1,X6),X1) ),
inference(cnf_transformation,[],[f76]) ).
fof(f111,plain,
! [X2,X0,X1,X6] :
( ~ relation(X0)
| relation_inverse_image(X0,X1) != X2
| ~ in(X6,X2)
| in(ordered_pair(X6,sK5(X0,X1,X6)),X0) ),
inference(cnf_transformation,[],[f76]) ).
fof(f112,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,[],[f76]) ).
fof(f117,plain,
! [X0,X1] :
( in(sK6(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f79]) ).
fof(f118,plain,
! [X0,X1] :
( ~ in(sK6(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f79]) ).
fof(f119,plain,
! [X2,X0,X1,X4] :
( set_intersection2(X0,X1) != X2
| ~ in(X4,X2)
| in(X4,X1) ),
inference(cnf_transformation,[],[f83]) ).
fof(f120,plain,
! [X2,X0,X1,X4] :
( set_intersection2(X0,X1) != X2
| ~ in(X4,X2)
| in(X4,X0) ),
inference(cnf_transformation,[],[f83]) ).
fof(f121,plain,
! [X2,X0,X1,X4] :
( set_intersection2(X0,X1) != X2
| ~ in(X4,X1)
| ~ in(X4,X0)
| in(X4,X2) ),
inference(cnf_transformation,[],[f83]) ).
fof(f125,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f11]) ).
fof(f157,plain,
relation(sK21),
inference(cnf_transformation,[],[f95]) ).
fof(f158,plain,
~ subset(set_intersection2(sK19,relation_inverse_image(sK21,sK20)),relation_inverse_image(sK21,set_intersection2(relation_image(sK21,sK19),sK20))),
inference(cnf_transformation,[],[f95]) ).
fof(f171,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,[],[f106,f125]) ).
fof(f175,plain,
! [X2,X0,X1,X6,X7] :
( ~ relation(X0)
| relation_inverse_image(X0,X1) != X2
| ~ in(X7,X1)
| ~ in(unordered_pair(unordered_pair(X6,X7),singleton(X6)),X0)
| in(X6,X2) ),
inference(definition_unfolding,[],[f112,f125]) ).
fof(f176,plain,
! [X2,X0,X1,X6] :
( ~ relation(X0)
| relation_inverse_image(X0,X1) != X2
| ~ in(X6,X2)
| in(unordered_pair(unordered_pair(X6,sK5(X0,X1,X6)),singleton(X6)),X0) ),
inference(definition_unfolding,[],[f111,f125]) ).
fof(f178,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,[],[f171]) ).
fof(f181,plain,
! [X0,X1,X6,X7] :
( ~ relation(X0)
| ~ in(X7,X1)
| ~ in(unordered_pair(unordered_pair(X6,X7),singleton(X6)),X0)
| in(X6,relation_inverse_image(X0,X1)) ),
inference(equality_resolution,[],[f175]) ).
fof(f182,plain,
! [X0,X1,X6] :
( ~ relation(X0)
| ~ in(X6,relation_inverse_image(X0,X1))
| in(unordered_pair(unordered_pair(X6,sK5(X0,X1,X6)),singleton(X6)),X0) ),
inference(equality_resolution,[],[f176]) ).
fof(f183,plain,
! [X0,X1,X6] :
( ~ relation(X0)
| ~ in(X6,relation_inverse_image(X0,X1))
| in(sK5(X0,X1,X6),X1) ),
inference(equality_resolution,[],[f110]) ).
fof(f184,plain,
! [X0,X1,X4] :
( ~ in(X4,X1)
| ~ in(X4,X0)
| in(X4,set_intersection2(X0,X1)) ),
inference(equality_resolution,[],[f121]) ).
fof(f185,plain,
! [X0,X1,X4] :
( ~ in(X4,set_intersection2(X0,X1))
| in(X4,X0) ),
inference(equality_resolution,[],[f120]) ).
fof(f186,plain,
! [X0,X1,X4] :
( ~ in(X4,set_intersection2(X0,X1))
| in(X4,X1) ),
inference(equality_resolution,[],[f119]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f102]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[],[f103]) ).
tcf(c_57,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,[],[f178]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X0,relation_inverse_image(X2,X3))
| ~ relation(X2)
| ~ in(X1,X3)
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),X2) ),
inference(cnf_transformation,[],[f181]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(unordered_pair(unordered_pair(X0,sK5(X1,X2,X0)),singleton(X0)),X1)
| ~ relation(X1)
| ~ in(X0,relation_inverse_image(X1,X2)) ),
inference(cnf_transformation,[],[f182]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(X1,X2,X0),X2)
| ~ relation(X1)
| ~ in(X0,relation_inverse_image(X1,X2)) ),
inference(cnf_transformation,[],[f183]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ in(sK6(X0,X1),X1) ),
inference(cnf_transformation,[],[f118]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| in(sK6(X0,X1),X0) ),
inference(cnf_transformation,[],[f117]) ).
tcf(c_72,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,set_intersection2(X2,X1))
| ~ in(X0,X2)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f184]) ).
tcf(c_73,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X1)
| ~ in(X0,set_intersection2(X1,X2)) ),
inference(cnf_transformation,[],[f185]) ).
tcf(c_74,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| ~ in(X0,set_intersection2(X1,X2)) ),
inference(cnf_transformation,[],[f186]) ).
tcf(c_106,negated_conjecture,
~ subset(set_intersection2(sK19,relation_inverse_image(sK21,sK20)),relation_inverse_image(sK21,set_intersection2(relation_image(sK21,sK19),sK20))),
inference(cnf_transformation,[],[f158]) ).
tcf(c_107,negated_conjecture,
relation(sK21),
inference(cnf_transformation,[],[f157]) ).
tcf(c_175,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ in(sK6(X0,X1),X1) ),
inference(prop_impl_just,[status(thm)],[c_66]) ).
tcf(c_187,plain,
! [X0: $i,X1: $i] :
( in(sK6(X0,X1),X0)
| subset(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_67]) ).
tcf(c_188,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| in(sK6(X0,X1),X0) ),
inference(renaming,[status(thm)],[c_187]) ).
tcf(c_563,plain,
~ subset(set_intersection2(sK19,relation_inverse_image(sK21,sK20)),relation_inverse_image(sK21,set_intersection2(sK20,relation_image(sK21,sK19)))),
inference(demodulation,[status(thm)],[c_106,c_53]) ).
tcf(c_564,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,sK5(X1,X2,X0))),X1)
| ~ relation(X1)
| ~ in(X0,relation_inverse_image(X1,X2)) ),
inference(demodulation,[status(thm)],[c_64,c_52]) ).
tcf(c_565,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X0,relation_inverse_image(X2,X3))
| ~ relation(X2)
| ~ in(X1,X3)
| ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),X2) ),
inference(demodulation,[status(thm)],[c_63,c_52]) ).
tcf(c_566,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X1,relation_image(X2,X3))
| ~ relation(X2)
| ~ in(X0,X3)
| ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),X2) ),
inference(demodulation,[status(thm)],[c_57,c_52]) ).
tcf(c_832,plain,
! [X0: $i,X1: $i] :
( in(sK6(X0,X1),X0)
| ( set_intersection2(sK19,relation_inverse_image(sK21,sK20)) != X0 )
| ( relation_inverse_image(sK21,set_intersection2(sK20,relation_image(sK21,sK19))) != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_188,c_563]) ).
tcf(c_833,plain,
in(sK6(set_intersection2(sK19,relation_inverse_image(sK21,sK20)),relation_inverse_image(sK21,set_intersection2(sK20,relation_image(sK21,sK19)))),set_intersection2(sK19,relation_inverse_image(sK21,sK20))),
inference(unflattening,[status(thm)],[c_832]) ).
tcf(c_837,plain,
! [X0: $i,X1: $i] :
( ~ in(sK6(X0,X1),X1)
| ( set_intersection2(sK19,relation_inverse_image(sK21,sK20)) != X0 )
| ( relation_inverse_image(sK21,set_intersection2(sK20,relation_image(sK21,sK19))) != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_175,c_563]) ).
tcf(c_838,plain,
~ in(sK6(set_intersection2(sK19,relation_inverse_image(sK21,sK20)),relation_inverse_image(sK21,set_intersection2(sK20,relation_image(sK21,sK19)))),relation_inverse_image(sK21,set_intersection2(sK20,relation_image(sK21,sK19)))),
inference(unflattening,[status(thm)],[c_837]) ).
tcf(c_2587,plain,
! [X0: $i] :
( in(sK6(set_intersection2(sK19,relation_inverse_image(sK21,sK20)),relation_inverse_image(sK21,set_intersection2(sK20,relation_image(sK21,sK19)))),relation_inverse_image(sK21,set_intersection2(sK20,relation_image(sK21,sK19))))
| ~ relation(sK21)
| ~ in(X0,set_intersection2(sK20,relation_image(sK21,sK19)))
| ~ in(unordered_pair(singleton(sK6(set_intersection2(sK19,relation_inverse_image(sK21,sK20)),relation_inverse_image(sK21,set_intersection2(sK20,relation_image(sK21,sK19))))),unordered_pair(sK6(set_intersection2(sK19,relation_inverse_image(sK21,sK20)),relation_inverse_image(sK21,set_intersection2(sK20,relation_image(sK21,sK19)))),X0)),sK21) ),
inference(instantiation,[status(thm)],[c_565]) ).
tcf(c_2697,plain,
! [X0: $i] :
( in(X0,set_intersection2(sK20,relation_image(sK21,sK19)))
| ~ in(X0,sK20)
| ~ in(X0,relation_image(sK21,sK19)) ),
inference(instantiation,[status(thm)],[c_72]) ).
tcf(c_3050,plain,
! [X0: $i,X1: $i] :
( in(sK5(X0,sK20,X1),set_intersection2(sK20,relation_image(sK21,sK19)))
| ~ in(sK5(X0,sK20,X1),sK20)
| ~ in(sK5(X0,sK20,X1),relation_image(sK21,sK19)) ),
inference(instantiation,[status(thm)],[c_2697]) ).
tcf(c_3621,plain,
( in(sK6(set_intersection2(sK19,relation_inverse_image(sK21,sK20)),relation_inverse_image(sK21,set_intersection2(sK20,relation_image(sK21,sK19)))),sK19)
| ~ in(sK6(set_intersection2(sK19,relation_inverse_image(sK21,sK20)),relation_inverse_image(sK21,set_intersection2(sK20,relation_image(sK21,sK19)))),set_intersection2(sK19,relation_inverse_image(sK21,sK20))) ),
inference(instantiation,[status(thm)],[c_73]) ).
tcf(c_3787,plain,
( in(sK6(set_intersection2(sK19,relation_inverse_image(sK21,sK20)),relation_inverse_image(sK21,set_intersection2(sK20,relation_image(sK21,sK19)))),relation_inverse_image(sK21,sK20))
| ~ in(sK6(set_intersection2(sK19,relation_inverse_image(sK21,sK20)),relation_inverse_image(sK21,set_intersection2(sK20,relation_image(sK21,sK19)))),set_intersection2(sK19,relation_inverse_image(sK21,sK20))) ),
inference(instantiation,[status(thm)],[c_74]) ).
tcf(c_6722,plain,
( in(sK5(sK21,sK20,sK6(set_intersection2(sK19,relation_inverse_image(sK21,sK20)),relation_inverse_image(sK21,set_intersection2(sK20,relation_image(sK21,sK19))))),sK20)
| ~ relation(sK21)
| ~ in(sK6(set_intersection2(sK19,relation_inverse_image(sK21,sK20)),relation_inverse_image(sK21,set_intersection2(sK20,relation_image(sK21,sK19)))),relation_inverse_image(sK21,sK20)) ),
inference(instantiation,[status(thm)],[c_65]) ).
tcf(c_6792,plain,
( in(unordered_pair(singleton(sK6(set_intersection2(sK19,relation_inverse_image(sK21,sK20)),relation_inverse_image(sK21,set_intersection2(sK20,relation_image(sK21,sK19))))),unordered_pair(sK6(set_intersection2(sK19,relation_inverse_image(sK21,sK20)),relation_inverse_image(sK21,set_intersection2(sK20,relation_image(sK21,sK19)))),sK5(sK21,sK20,sK6(set_intersection2(sK19,relation_inverse_image(sK21,sK20)),relation_inverse_image(sK21,set_intersection2(sK20,relation_image(sK21,sK19))))))),sK21)
| ~ relation(sK21)
| ~ in(sK6(set_intersection2(sK19,relation_inverse_image(sK21,sK20)),relation_inverse_image(sK21,set_intersection2(sK20,relation_image(sK21,sK19)))),relation_inverse_image(sK21,sK20)) ),
inference(instantiation,[status(thm)],[c_564]) ).
tcf(c_12868,plain,
( in(sK5(sK21,sK20,sK6(set_intersection2(sK19,relation_inverse_image(sK21,sK20)),relation_inverse_image(sK21,set_intersection2(sK20,relation_image(sK21,sK19))))),set_intersection2(sK20,relation_image(sK21,sK19)))
| ~ in(sK5(sK21,sK20,sK6(set_intersection2(sK19,relation_inverse_image(sK21,sK20)),relation_inverse_image(sK21,set_intersection2(sK20,relation_image(sK21,sK19))))),sK20)
| ~ in(sK5(sK21,sK20,sK6(set_intersection2(sK19,relation_inverse_image(sK21,sK20)),relation_inverse_image(sK21,set_intersection2(sK20,relation_image(sK21,sK19))))),relation_image(sK21,sK19)) ),
inference(instantiation,[status(thm)],[c_3050]) ).
tcf(c_12913,plain,
! [X0: $i] :
( in(sK5(sK21,sK20,sK6(set_intersection2(sK19,relation_inverse_image(sK21,sK20)),relation_inverse_image(sK21,set_intersection2(sK20,relation_image(sK21,sK19))))),relation_image(sK21,X0))
| ~ relation(sK21)
| ~ in(sK6(set_intersection2(sK19,relation_inverse_image(sK21,sK20)),relation_inverse_image(sK21,set_intersection2(sK20,relation_image(sK21,sK19)))),X0)
| ~ in(unordered_pair(singleton(sK6(set_intersection2(sK19,relation_inverse_image(sK21,sK20)),relation_inverse_image(sK21,set_intersection2(sK20,relation_image(sK21,sK19))))),unordered_pair(sK6(set_intersection2(sK19,relation_inverse_image(sK21,sK20)),relation_inverse_image(sK21,set_intersection2(sK20,relation_image(sK21,sK19)))),sK5(sK21,sK20,sK6(set_intersection2(sK19,relation_inverse_image(sK21,sK20)),relation_inverse_image(sK21,set_intersection2(sK20,relation_image(sK21,sK19))))))),sK21) ),
inference(instantiation,[status(thm)],[c_566]) ).
tcf(c_25531,plain,
( in(sK5(sK21,sK20,sK6(set_intersection2(sK19,relation_inverse_image(sK21,sK20)),relation_inverse_image(sK21,set_intersection2(sK20,relation_image(sK21,sK19))))),relation_image(sK21,sK19))
| ~ relation(sK21)
| ~ in(sK6(set_intersection2(sK19,relation_inverse_image(sK21,sK20)),relation_inverse_image(sK21,set_intersection2(sK20,relation_image(sK21,sK19)))),sK19)
| ~ in(unordered_pair(singleton(sK6(set_intersection2(sK19,relation_inverse_image(sK21,sK20)),relation_inverse_image(sK21,set_intersection2(sK20,relation_image(sK21,sK19))))),unordered_pair(sK6(set_intersection2(sK19,relation_inverse_image(sK21,sK20)),relation_inverse_image(sK21,set_intersection2(sK20,relation_image(sK21,sK19)))),sK5(sK21,sK20,sK6(set_intersection2(sK19,relation_inverse_image(sK21,sK20)),relation_inverse_image(sK21,set_intersection2(sK20,relation_image(sK21,sK19))))))),sK21) ),
inference(instantiation,[status(thm)],[c_12913]) ).
tcf(c_39702,plain,
( in(sK6(set_intersection2(sK19,relation_inverse_image(sK21,sK20)),relation_inverse_image(sK21,set_intersection2(sK20,relation_image(sK21,sK19)))),relation_inverse_image(sK21,set_intersection2(sK20,relation_image(sK21,sK19))))
| ~ relation(sK21)
| ~ in(sK5(sK21,sK20,sK6(set_intersection2(sK19,relation_inverse_image(sK21,sK20)),relation_inverse_image(sK21,set_intersection2(sK20,relation_image(sK21,sK19))))),set_intersection2(sK20,relation_image(sK21,sK19)))
| ~ in(unordered_pair(singleton(sK6(set_intersection2(sK19,relation_inverse_image(sK21,sK20)),relation_inverse_image(sK21,set_intersection2(sK20,relation_image(sK21,sK19))))),unordered_pair(sK6(set_intersection2(sK19,relation_inverse_image(sK21,sK20)),relation_inverse_image(sK21,set_intersection2(sK20,relation_image(sK21,sK19)))),sK5(sK21,sK20,sK6(set_intersection2(sK19,relation_inverse_image(sK21,sK20)),relation_inverse_image(sK21,set_intersection2(sK20,relation_image(sK21,sK19))))))),sK21) ),
inference(instantiation,[status(thm)],[c_2587]) ).
tcf(c_39703,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_39702,c_25531,c_12868,c_6792,c_6722,c_3787,c_3621,c_838,c_833,c_107]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU070+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/5.37 % Computer : n017.cluster.edu
% 0.09/5.37 % Model : x86_64 x86_64
% 0.09/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.37 % Memory : 8046.5625MB
% 0.09/5.37 % OS : Linux 6.8.0-71-generic
% 0.09/5.37 % CPULimit : 300
% 0.09/5.37 % WCLimit : 300
% 0.09/5.37 % DateTime : Thu Sep 24 12:36:37 UTC 2026
% 0.09/5.37 % CPUTime :
% 0.09/5.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.14/5.41 Running first-order theorem proving
% 0.14/5.41 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
% 0.14/5.42
% 0.14/5.42 % ======== iProver multi-core TPTP/SMT =========
% 0.14/5.42
% 0.14/5.42 % Detected problem language: tptp
% 0.14/5.43 % Proving...
% 10.80/7.74 % SZS status Started for theBenchmark.p
% 10.80/7.74 % SZS status Theorem for theBenchmark.p
% 10.80/7.74
% 10.80/7.74 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 10.80/7.74
% 10.80/7.74 % ------ iProver source info
% 10.80/7.74
% 10.80/7.74 % git: date: 2026-07-19 20:42:38 +0200
% 10.80/7.74 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 10.80/7.74 % git: non_committed_changes: false
% 10.80/7.74
% 10.80/7.74 % ------ Parsing...
% 10.80/7.74 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 10.80/7.74
% 10.80/7.74 % ------ Preprocessing... sup_sim: 9 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 %
% 10.80/7.74
% 10.80/7.74 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 10.80/7.74
% 10.80/7.74 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 10.80/7.74 % ------ Proving...
% 10.80/7.74 % ------ Problem Properties
% 10.80/7.74
% 10.80/7.74 %
% 10.80/7.74 % clauses 61
% 10.80/7.74 % conjectures 1
% 10.80/7.74 % EPR 25
% 10.80/7.74 % Horn 52
% 10.80/7.74 % unary 26
% 10.80/7.74 % binary 13
% 10.80/7.74 % lits 129
% 10.80/7.74 % lits eq 15
% 10.80/7.74 % fd_pure 0
% 10.80/7.74 % fd_pseudo 0
% 10.80/7.74 % fd_cond 1
% 10.80/7.74 % fd_pseudo_cond 10
% 10.80/7.74 % AC symbols 0
% 10.80/7.74
% 10.80/7.74 % ------ Input Options Time Limit: Unbounded
% 10.80/7.74
% 10.80/7.74
% 10.80/7.74 % ------
% 10.80/7.74 % Current options:
% 10.80/7.74 % ------
% 10.80/7.74
% 10.80/7.74
% 10.80/7.74 %
% 10.80/7.74
% 10.80/7.74 % ------ Proving...
% 10.80/7.74 %
% 10.80/7.74
% 10.80/7.74 % SZS status Theorem for theBenchmark.p
% 10.80/7.74
% 10.80/7.74 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 10.80/7.74
% 10.80/7.74
%------------------------------------------------------------------------------