%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU076+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 : n008.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 02:55:19 PM UTC 2026
% Result : Theorem 71.99s 12.46s
% Output : CNFRefutation 71.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 7
% Syntax : Number of formulae : 88 ( 18 unt; 0 def)
% Number of atoms : 403 ( 93 equ)
% Maximal formula atoms : 20 ( 4 avg)
% Number of connectives : 542 ( 227 ~; 226 |; 70 &)
% ( 11 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 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 : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 3 con; 0-3 aty)
% Number of variables : 190 ( 0 sgn 169 !; 21 ?; 57 :)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ! [X1,X2] :
( X2 = relation_image(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( X3 = apply(X0,X4)
& in(X4,X1)
& in(X4,relation_dom(X0)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d12_funct_1) ).
fof(f6,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(f7,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ( one_to_one(X0)
<=> ! [X1,X2] :
( ( apply(X0,X1) = apply(X0,X2)
& in(X2,relation_dom(X0))
& in(X1,relation_dom(X0)) )
=> X1 = X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_funct_1) ).
fof(f26,conjecture,
! [X0,X1,X2] :
( ( function(X2)
& relation(X2) )
=> ( ( one_to_one(X2)
& subset(X0,relation_dom(X2))
& subset(relation_image(X2,X0),relation_image(X2,X1)) )
=> subset(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t157_funct_1) ).
fof(f27,negated_conjecture,
~ ! [X0,X1,X2] :
( ( function(X2)
& relation(X2) )
=> ( ( one_to_one(X2)
& subset(X0,relation_dom(X2))
& subset(relation_image(X2,X0),relation_image(X2,X1)) )
=> subset(X0,X1) ) ),
inference(negated_conjecture,[status(cth)],[f26]) ).
fof(f44,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1,X2] :
( X2 = relation_image(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( X3 = apply(X0,X4)
& in(X4,X1)
& in(X4,relation_dom(X0)) ) ) ) ),
inference(ennf_transformation,[],[f5]) ).
fof(f45,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1,X2] :
( X2 = relation_image(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( X3 = apply(X0,X4)
& in(X4,X1)
& in(X4,relation_dom(X0)) ) ) ) ),
inference(flattening,[],[f44]) ).
fof(f46,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( ~ in(X2,X0)
| in(X2,X1) ) ),
inference(ennf_transformation,[],[f6]) ).
fof(f47,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ( one_to_one(X0)
<=> ! [X1,X2] :
( apply(X0,X1) != apply(X0,X2)
| ~ in(X2,relation_dom(X0))
| ~ in(X1,relation_dom(X0))
| X1 = X2 ) ) ),
inference(ennf_transformation,[],[f7]) ).
fof(f48,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ( one_to_one(X0)
<=> ! [X1,X2] :
( apply(X0,X1) != apply(X0,X2)
| ~ in(X2,relation_dom(X0))
| ~ in(X1,relation_dom(X0))
| X1 = X2 ) ) ),
inference(flattening,[],[f47]) ).
fof(f53,plain,
? [X0,X1,X2] :
( function(X2)
& relation(X2)
& one_to_one(X2)
& subset(X0,relation_dom(X2))
& subset(relation_image(X2,X0),relation_image(X2,X1))
& ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f27]) ).
fof(f54,plain,
? [X0,X1,X2] :
( function(X2)
& relation(X2)
& one_to_one(X2)
& subset(X0,relation_dom(X2))
& subset(relation_image(X2,X0),relation_image(X2,X1))
& ~ subset(X0,X1) ),
inference(flattening,[],[f53]) ).
fof(f64,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1,X2] :
( ( relation_image(X0,X1) != X2
| ! [X3] :
( ( ~ in(X3,X2)
| ? [X4] :
( X3 = apply(X0,X4)
& in(X4,X1)
& in(X4,relation_dom(X0)) ) )
& ( ! [X4] :
( apply(X0,X4) != X3
| ~ in(X4,X1)
| ~ in(X4,relation_dom(X0)) )
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| ? [X4] :
( X3 = apply(X0,X4)
& in(X4,X1)
& in(X4,relation_dom(X0)) ) )
& ( ~ in(X3,X2)
| ! [X4] :
( apply(X0,X4) != X3
| ~ in(X4,X1)
| ~ in(X4,relation_dom(X0)) ) ) )
| X2 = relation_image(X0,X1) ) ) ),
inference(nnf_transformation,[],[f45]) ).
fof(f65,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1,X2] :
( ( relation_image(X0,X1) != X2
| ! [X6] :
( ( ~ in(X6,X2)
| ? [X8] :
( apply(X0,X8) = X6
& in(X8,X1)
& in(X8,relation_dom(X0)) ) )
& ( ! [X7] :
( apply(X0,X7) != X6
| ~ in(X7,X1)
| ~ in(X7,relation_dom(X0)) )
| in(X6,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| ? [X5] :
( apply(X0,X5) = X3
& in(X5,X1)
& in(X5,relation_dom(X0)) ) )
& ( ~ in(X3,X2)
| ! [X4] :
( apply(X0,X4) != X3
| ~ in(X4,X1)
| ~ in(X4,relation_dom(X0)) ) ) )
| X2 = relation_image(X0,X1) ) ) ),
inference(rectify,[],[f64]) ).
fof(f66,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1,X2] :
( ( relation_image(X0,X1) != X2
| ! [X6] :
( ( ~ in(X6,X2)
| ( apply(X0,sK2(X0,X1,X6)) = X6
& in(sK2(X0,X1,X6),X1)
& in(sK2(X0,X1,X6),relation_dom(X0)) ) )
& ( ! [X7] :
( apply(X0,X7) != X6
| ~ in(X7,X1)
| ~ in(X7,relation_dom(X0)) )
| in(X6,X2) ) ) )
& ( ( ( in(sK0(X0,X1,X2),X2)
| ( sK0(X0,X1,X2) = apply(X0,sK1(X0,X1,X2))
& in(sK1(X0,X1,X2),X1)
& in(sK1(X0,X1,X2),relation_dom(X0)) ) )
& ( ~ in(sK0(X0,X1,X2),X2)
| ! [X4] :
( apply(X0,X4) != sK0(X0,X1,X2)
| ~ in(X4,X1)
| ~ in(X4,relation_dom(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))],[f65]) ).
fof(f67,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,[],[f46]) ).
fof(f68,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,[],[f67]) ).
fof(f69,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X3] :
( ~ in(X3,X0)
| in(X3,X1) ) )
& ( ( in(sK3(X0,X1),X0)
& ~ in(sK3(X0,X1),X1) )
| subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X2,sK3(X0,X1))],[f68]) ).
fof(f70,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ( ( ~ one_to_one(X0)
| ! [X1,X2] :
( apply(X0,X1) != apply(X0,X2)
| ~ in(X2,relation_dom(X0))
| ~ in(X1,relation_dom(X0))
| X1 = X2 ) )
& ( ? [X1,X2] :
( apply(X0,X1) = apply(X0,X2)
& in(X2,relation_dom(X0))
& in(X1,relation_dom(X0))
& X1 != X2 )
| one_to_one(X0) ) ) ),
inference(nnf_transformation,[],[f48]) ).
fof(f71,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ( ( ~ one_to_one(X0)
| ! [X3,X4] :
( apply(X0,X4) != apply(X0,X3)
| ~ in(X4,relation_dom(X0))
| ~ in(X3,relation_dom(X0))
| X3 = X4 ) )
& ( ? [X1,X2] :
( apply(X0,X1) = apply(X0,X2)
& in(X2,relation_dom(X0))
& in(X1,relation_dom(X0))
& X1 != X2 )
| one_to_one(X0) ) ) ),
inference(rectify,[],[f70]) ).
fof(f72,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ( ( ~ one_to_one(X0)
| ! [X3,X4] :
( apply(X0,X4) != apply(X0,X3)
| ~ in(X4,relation_dom(X0))
| ~ in(X3,relation_dom(X0))
| X3 = X4 ) )
& ( ( apply(X0,sK4(X0)) = apply(X0,sK5(X0))
& in(sK5(X0),relation_dom(X0))
& in(sK4(X0),relation_dom(X0))
& sK4(X0) != sK5(X0) )
| one_to_one(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5]),skolemize(X1,sK4(X0)),skolemize(X2,sK5(X0))],[f71]) ).
fof(f84,plain,
( function(sK19)
& relation(sK19)
& one_to_one(sK19)
& subset(sK17,relation_dom(sK19))
& subset(relation_image(sK19,sK17),relation_image(sK19,sK18))
& ~ subset(sK17,sK18) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17,sK18,sK19]),skolemize(X0,sK17),skolemize(X1,sK18),skolemize(X2,sK19)],[f54]) ).
fof(f92,plain,
! [X2,X0,X1,X6] :
( ~ function(X0)
| ~ relation(X0)
| relation_image(X0,X1) != X2
| ~ in(X6,X2)
| apply(X0,sK2(X0,X1,X6)) = X6 ),
inference(cnf_transformation,[],[f66]) ).
fof(f93,plain,
! [X2,X0,X1,X6] :
( ~ function(X0)
| ~ relation(X0)
| relation_image(X0,X1) != X2
| ~ in(X6,X2)
| in(sK2(X0,X1,X6),X1) ),
inference(cnf_transformation,[],[f66]) ).
fof(f94,plain,
! [X2,X0,X1,X6] :
( ~ function(X0)
| ~ relation(X0)
| relation_image(X0,X1) != X2
| ~ in(X6,X2)
| in(sK2(X0,X1,X6),relation_dom(X0)) ),
inference(cnf_transformation,[],[f66]) ).
fof(f95,plain,
! [X2,X0,X1,X6,X7] :
( ~ function(X0)
| ~ relation(X0)
| relation_image(X0,X1) != X2
| apply(X0,X7) != X6
| ~ in(X7,X1)
| ~ in(X7,relation_dom(X0))
| in(X6,X2) ),
inference(cnf_transformation,[],[f66]) ).
fof(f100,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ in(X3,X0)
| in(X3,X1) ),
inference(cnf_transformation,[],[f69]) ).
fof(f101,plain,
! [X0,X1] :
( in(sK3(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f69]) ).
fof(f102,plain,
! [X0,X1] :
( ~ in(sK3(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f69]) ).
fof(f103,plain,
! [X3,X0,X4] :
( ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| apply(X0,X4) != apply(X0,X3)
| ~ in(X4,relation_dom(X0))
| ~ in(X3,relation_dom(X0))
| X3 = X4 ),
inference(cnf_transformation,[],[f72]) ).
fof(f138,plain,
function(sK19),
inference(cnf_transformation,[],[f84]) ).
fof(f139,plain,
relation(sK19),
inference(cnf_transformation,[],[f84]) ).
fof(f140,plain,
one_to_one(sK19),
inference(cnf_transformation,[],[f84]) ).
fof(f141,plain,
subset(sK17,relation_dom(sK19)),
inference(cnf_transformation,[],[f84]) ).
fof(f142,plain,
subset(relation_image(sK19,sK17),relation_image(sK19,sK18)),
inference(cnf_transformation,[],[f84]) ).
fof(f143,plain,
~ subset(sK17,sK18),
inference(cnf_transformation,[],[f84]) ).
fof(f153,plain,
! [X2,X0,X1,X7] :
( ~ function(X0)
| ~ relation(X0)
| relation_image(X0,X1) != X2
| ~ in(X7,X1)
| ~ in(X7,relation_dom(X0))
| in(apply(X0,X7),X2) ),
inference(equality_resolution,[],[f95]) ).
fof(f154,plain,
! [X0,X1,X7] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(X7,X1)
| ~ in(X7,relation_dom(X0))
| in(apply(X0,X7),relation_image(X0,X1)) ),
inference(equality_resolution,[],[f153]) ).
fof(f155,plain,
! [X0,X1,X6] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(X6,relation_image(X0,X1))
| in(sK2(X0,X1,X6),relation_dom(X0)) ),
inference(equality_resolution,[],[f94]) ).
fof(f156,plain,
! [X0,X1,X6] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(X6,relation_image(X0,X1))
| in(sK2(X0,X1,X6),X1) ),
inference(equality_resolution,[],[f93]) ).
fof(f157,plain,
! [X0,X1,X6] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(X6,relation_image(X0,X1))
| apply(X0,sK2(X0,X1,X6)) = X6 ),
inference(equality_resolution,[],[f92]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(X1,X0),relation_image(X1,X2))
| ~ relation(X1)
| ~ function(X1)
| ~ in(X0,X2)
| ~ in(X0,relation_dom(X1)) ),
inference(cnf_transformation,[],[f154]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X1,X2,X0),relation_dom(X1))
| ~ relation(X1)
| ~ function(X1)
| ~ in(X0,relation_image(X1,X2)) ),
inference(cnf_transformation,[],[f155]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X1,X2,X0),X2)
| ~ relation(X1)
| ~ function(X1)
| ~ in(X0,relation_image(X1,X2)) ),
inference(cnf_transformation,[],[f156]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(X1,sK2(X1,X2,X0)) = X0 )
| ~ relation(X1)
| ~ function(X1)
| ~ in(X0,relation_image(X1,X2)) ),
inference(cnf_transformation,[],[f157]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ in(sK3(X0,X1),X1) ),
inference(cnf_transformation,[],[f102]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| in(sK3(X0,X1),X0) ),
inference(cnf_transformation,[],[f101]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| ~ subset(X1,X2)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f100]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ~ one_to_one(X0)
| ~ relation(X0)
| ~ function(X0)
| ~ in(X2,relation_dom(X0))
| ~ in(X1,relation_dom(X0))
| ( apply(X0,X1) != apply(X0,X2) ) ),
inference(cnf_transformation,[],[f103]) ).
tcf(c_99,negated_conjecture,
~ subset(sK17,sK18),
inference(cnf_transformation,[],[f143]) ).
tcf(c_100,negated_conjecture,
subset(relation_image(sK19,sK17),relation_image(sK19,sK18)),
inference(cnf_transformation,[],[f142]) ).
tcf(c_101,negated_conjecture,
subset(sK17,relation_dom(sK19)),
inference(cnf_transformation,[],[f141]) ).
tcf(c_102,negated_conjecture,
one_to_one(sK19),
inference(cnf_transformation,[],[f140]) ).
tcf(c_103,negated_conjecture,
relation(sK19),
inference(cnf_transformation,[],[f139]) ).
tcf(c_104,negated_conjecture,
function(sK19),
inference(cnf_transformation,[],[f138]) ).
tcf(c_176,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ in(sK3(X0,X1),X1) ),
inference(prop_impl_just,[status(thm)],[c_61]) ).
tcf(c_188,plain,
! [X0: $i,X1: $i] :
( in(sK3(X0,X1),X0)
| subset(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_62]) ).
tcf(c_189,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| in(sK3(X0,X1),X0) ),
inference(renaming,[status(thm)],[c_188]) ).
tcf(c_1230,plain,
! [X0: $i,X1: $i] :
( in(sK3(X0,X1),X0)
| ( X1 != sK18 )
| ( X0 != sK17 ) ),
inference(resolution_lifted,[status(thm)],[c_189,c_99]) ).
tcf(c_1231,plain,
in(sK3(sK17,sK18),sK17),
inference(unflattening,[status(thm)],[c_1230]) ).
tcf(c_1235,plain,
! [X0: $i,X1: $i] :
( ~ in(sK3(X0,X1),X1)
| ( X1 != sK18 )
| ( X0 != sK17 ) ),
inference(resolution_lifted,[status(thm)],[c_176,c_99]) ).
tcf(c_1236,plain,
~ in(sK3(sK17,sK18),sK18),
inference(unflattening,[status(thm)],[c_1235]) ).
tcf(c_8595,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_8597,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_8598,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X0,X2)
| ~ in(X1,X3)
| ( X2 != X3 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_9680,plain,
! [X0: $i] :
( in(sK3(sK17,sK18),X0)
| ~ subset(sK17,X0)
| ~ in(sK3(sK17,sK18),sK17) ),
inference(instantiation,[status(thm)],[c_63]) ).
tcf(c_9686,plain,
! [X0: $i] :
( in(apply(X0,sK3(sK17,sK18)),relation_image(X0,sK17))
| ~ relation(X0)
| ~ function(X0)
| ~ in(sK3(sK17,sK18),sK17)
| ~ in(sK3(sK17,sK18),relation_dom(X0)) ),
inference(instantiation,[status(thm)],[c_57]) ).
tcf(c_9702,plain,
sK18 = sK18,
inference(instantiation,[status(thm)],[c_8595]) ).
tcf(c_10096,plain,
( in(sK3(sK17,sK18),relation_dom(sK19))
| ~ subset(sK17,relation_dom(sK19))
| ~ in(sK3(sK17,sK18),sK17) ),
inference(instantiation,[status(thm)],[c_9680]) ).
tcf(c_11159,plain,
( in(apply(sK19,sK3(sK17,sK18)),relation_image(sK19,sK17))
| ~ relation(sK19)
| ~ function(sK19)
| ~ in(sK3(sK17,sK18),sK17)
| ~ in(sK3(sK17,sK18),relation_dom(sK19)) ),
inference(instantiation,[status(thm)],[c_9686]) ).
tcf(c_11645,plain,
! [X0: $i,X1: $i] :
( ( X1 = sK3(sK17,sK18) )
| ~ one_to_one(X0)
| ~ relation(X0)
| ~ function(X0)
| ~ in(X1,relation_dom(X0))
| ~ in(sK3(sK17,sK18),relation_dom(X0))
| ( apply(X0,X1) != apply(X0,sK3(sK17,sK18)) ) ),
inference(instantiation,[status(thm)],[c_68]) ).
tcf(c_12351,plain,
sK3(sK17,sK18) = sK3(sK17,sK18),
inference(instantiation,[status(thm)],[c_8595]) ).
tcf(c_14581,plain,
! [X0: $i] :
( in(apply(sK19,sK3(sK17,sK18)),X0)
| ~ subset(relation_image(sK19,sK17),X0)
| ~ in(apply(sK19,sK3(sK17,sK18)),relation_image(sK19,sK17)) ),
inference(instantiation,[status(thm)],[c_63]) ).
tcf(c_18047,plain,
! [X0: $i] :
( ( X0 = sK3(sK17,sK18) )
| ~ one_to_one(sK19)
| ~ relation(sK19)
| ~ function(sK19)
| ~ in(X0,relation_dom(sK19))
| ~ in(sK3(sK17,sK18),relation_dom(sK19))
| ( apply(sK19,X0) != apply(sK19,sK3(sK17,sK18)) ) ),
inference(instantiation,[status(thm)],[c_11645]) ).
tcf(c_24341,plain,
( in(apply(sK19,sK3(sK17,sK18)),relation_image(sK19,sK18))
| ~ subset(relation_image(sK19,sK17),relation_image(sK19,sK18))
| ~ in(apply(sK19,sK3(sK17,sK18)),relation_image(sK19,sK17)) ),
inference(instantiation,[status(thm)],[c_14581]) ).
tcf(c_30710,plain,
( ( apply(sK19,sK2(sK19,sK18,apply(sK19,sK3(sK17,sK18)))) = apply(sK19,sK3(sK17,sK18)) )
| ~ relation(sK19)
| ~ function(sK19)
| ~ in(apply(sK19,sK3(sK17,sK18)),relation_image(sK19,sK18)) ),
inference(instantiation,[status(thm)],[c_60]) ).
tcf(c_30711,plain,
( in(sK2(sK19,sK18,apply(sK19,sK3(sK17,sK18))),sK18)
| ~ relation(sK19)
| ~ function(sK19)
| ~ in(apply(sK19,sK3(sK17,sK18)),relation_image(sK19,sK18)) ),
inference(instantiation,[status(thm)],[c_59]) ).
tcf(c_30712,plain,
( in(sK2(sK19,sK18,apply(sK19,sK3(sK17,sK18))),relation_dom(sK19))
| ~ relation(sK19)
| ~ function(sK19)
| ~ in(apply(sK19,sK3(sK17,sK18)),relation_image(sK19,sK18)) ),
inference(instantiation,[status(thm)],[c_58]) ).
tcf(c_42344,plain,
( ( sK2(sK19,sK18,apply(sK19,sK3(sK17,sK18))) = sK3(sK17,sK18) )
| ~ one_to_one(sK19)
| ~ relation(sK19)
| ~ function(sK19)
| ~ in(sK3(sK17,sK18),relation_dom(sK19))
| ~ in(sK2(sK19,sK18,apply(sK19,sK3(sK17,sK18))),relation_dom(sK19))
| ( apply(sK19,sK2(sK19,sK18,apply(sK19,sK3(sK17,sK18)))) != apply(sK19,sK3(sK17,sK18)) ) ),
inference(instantiation,[status(thm)],[c_18047]) ).
tcf(c_54477,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| ~ in(X1,sK18)
| ( X2 != sK18 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_8598]) ).
tcf(c_55854,plain,
! [X0: $i,X1: $i] :
( in(X0,sK18)
| ~ in(X1,sK18)
| ( sK18 != sK18 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_54477]) ).
tcf(c_58684,plain,
! [X0: $i,X1: $i] :
( ( sK3(sK17,sK18) = X1 )
| ( X1 != X0 )
| ( sK3(sK17,sK18) != X0 ) ),
inference(instantiation,[status(thm)],[c_8597]) ).
tcf(c_58727,plain,
! [X0: $i,X1: $i] :
( in(sK3(X0,sK18),sK18)
| ~ in(X1,sK18)
| ( sK18 != sK18 )
| ( sK3(X0,sK18) != X1 ) ),
inference(instantiation,[status(thm)],[c_55854]) ).
tcf(c_64222,plain,
! [X0: $i] :
( ( sK3(sK17,sK18) = X0 )
| ( X0 != sK3(sK17,sK18) )
| ( sK3(sK17,sK18) != sK3(sK17,sK18) ) ),
inference(instantiation,[status(thm)],[c_58684]) ).
tcf(c_75339,plain,
( ( sK3(sK17,sK18) = sK2(sK19,sK18,apply(sK19,sK3(sK17,sK18))) )
| ( sK3(sK17,sK18) != sK3(sK17,sK18) )
| ( sK2(sK19,sK18,apply(sK19,sK3(sK17,sK18))) != sK3(sK17,sK18) ) ),
inference(instantiation,[status(thm)],[c_64222]) ).
tcf(c_89199,plain,
! [X0: $i] :
( in(sK3(sK17,sK18),sK18)
| ~ in(X0,sK18)
| ( sK18 != sK18 )
| ( sK3(sK17,sK18) != X0 ) ),
inference(instantiation,[status(thm)],[c_58727]) ).
tcf(c_93300,plain,
( in(sK3(sK17,sK18),sK18)
| ~ in(sK2(sK19,sK18,apply(sK19,sK3(sK17,sK18))),sK18)
| ( sK18 != sK18 )
| ( sK3(sK17,sK18) != sK2(sK19,sK18,apply(sK19,sK3(sK17,sK18))) ) ),
inference(instantiation,[status(thm)],[c_89199]) ).
tcf(c_93309,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_93300,c_75339,c_42344,c_30710,c_30711,c_30712,c_24341,c_12351,c_11159,c_10096,c_9702,c_1236,c_1231,c_100,c_101,c_102,c_103,c_104]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU076+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.36 % Computer : n008.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Thu Sep 24 12:43:25 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 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
% 0.10/0.41
% 0.10/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.41
% 0.10/0.41 % Detected problem language: tptp
% 0.10/0.42 % Proving...
% 71.99/12.46 % SZS status Started for theBenchmark.p
% 71.99/12.46 % SZS status Theorem for theBenchmark.p
% 71.99/12.46
% 71.99/12.46 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 71.99/12.46
% 71.99/12.46 % ------ iProver source info
% 71.99/12.46
% 71.99/12.46 % git: date: 2026-07-19 20:42:38 +0200
% 71.99/12.46 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 71.99/12.46 % git: non_committed_changes: false
% 71.99/12.46
% 71.99/12.46 % ------ Parsing...
% 71.99/12.46 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 71.99/12.46
% 71.99/12.46 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 71.99/12.46
% 71.99/12.46 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 71.99/12.46
% 71.99/12.46 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 71.99/12.46 % ------ Proving...
% 71.99/12.46 % ------ Problem Properties
% 71.99/12.46
% 71.99/12.46 %
% 71.99/12.46 % clauses 62
% 71.99/12.46 % conjectures 6
% 71.99/12.46 % EPR 34
% 71.99/12.46 % Horn 53
% 71.99/12.46 % unary 28
% 71.99/12.46 % binary 15
% 71.99/12.46 % lits 138
% 71.99/12.46 % lits eq 13
% 71.99/12.46 % fd_pure 0
% 71.99/12.46 % fd_pseudo 0
% 71.99/12.46 % fd_cond 1
% 71.99/12.46 % fd_pseudo_cond 6
% 71.99/12.46 % AC symbols 0
% 71.99/12.46
% 71.99/12.46 % ------ Input Options Time Limit: Unbounded
% 71.99/12.46
% 71.99/12.46
% 71.99/12.46 % ------
% 71.99/12.46 % Current options:
% 71.99/12.46 % ------
% 71.99/12.46
% 71.99/12.46
% 71.99/12.46 %
% 71.99/12.46
% 71.99/12.46 % ------ Proving...
% 71.99/12.46 %
% 71.99/12.46
% 71.99/12.46 % SZS status Theorem for theBenchmark.p
% 71.99/12.46
% 71.99/12.46 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 71.99/12.46
% 71.99/12.46
%------------------------------------------------------------------------------