%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU042+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/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 02:55:07 PM UTC 2026
% Result : Theorem 6.02s 1.69s
% Output : CNFRefutation 6.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 8
% Syntax : Number of formulae : 103 ( 23 unt; 1 def)
% Number of atoms : 522 ( 99 equ)
% Maximal formula atoms : 14 ( 5 avg)
% Number of connectives : 584 ( 243 ~; 249 |; 72 &)
% ( 8 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 2 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 2 con; 0-3 aty)
% Number of variables : 173 ( 0 sgn 159 !; 14 ?; 41 :)
% Comments :
%------------------------------------------------------------------------------
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] :
( ( 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/sandbox2/benchmark/theBenchmark.p',d8_funct_1) ).
fof(f8,axiom,
! [X0,X1] :
( relation(X0)
=> relation(relation_dom_restriction(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k7_relat_1) ).
fof(f11,axiom,
! [X0,X1] :
( ( relation_empty_yielding(X0)
& relation(X0) )
=> ( relation_empty_yielding(relation_dom_restriction(X0,X1))
& relation(relation_dom_restriction(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc13_relat_1) ).
fof(f15,axiom,
! [X0,X1] :
( ( function(X0)
& relation(X0) )
=> ( function(relation_dom_restriction(X0,X1))
& relation(relation_dom_restriction(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_funct_1) ).
fof(f37,axiom,
! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> ! [X2] :
( ( function(X2)
& relation(X2) )
=> ( X1 = relation_dom_restriction(X2,X0)
<=> ( ! [X3] :
( in(X3,relation_dom(X1))
=> apply(X1,X3) = apply(X2,X3) )
& relation_dom(X1) = set_intersection2(relation_dom(X2),X0) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t68_funct_1) ).
fof(f40,conjecture,
! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> ( one_to_one(X1)
=> one_to_one(relation_dom_restriction(X1,X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t84_funct_1) ).
fof(f41,negated_conjecture,
~ ! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> ( one_to_one(X1)
=> one_to_one(relation_dom_restriction(X1,X0)) ) ),
inference(negated_conjecture,[status(cth)],[f40]) ).
fof(f51,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(f52,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,[],[f51]) ).
fof(f53,plain,
! [X0,X1] :
( ~ relation(X0)
| relation(relation_dom_restriction(X0,X1)) ),
inference(ennf_transformation,[],[f8]) ).
fof(f54,plain,
! [X0,X1] :
( ~ relation_empty_yielding(X0)
| ~ relation(X0)
| ( relation_empty_yielding(relation_dom_restriction(X0,X1))
& relation(relation_dom_restriction(X0,X1)) ) ),
inference(ennf_transformation,[],[f11]) ).
fof(f55,plain,
! [X0,X1] :
( ~ relation_empty_yielding(X0)
| ~ relation(X0)
| ( relation_empty_yielding(relation_dom_restriction(X0,X1))
& relation(relation_dom_restriction(X0,X1)) ) ),
inference(flattening,[],[f54]) ).
fof(f58,plain,
! [X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ( function(relation_dom_restriction(X0,X1))
& relation(relation_dom_restriction(X0,X1)) ) ),
inference(ennf_transformation,[],[f15]) ).
fof(f59,plain,
! [X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ( function(relation_dom_restriction(X0,X1))
& relation(relation_dom_restriction(X0,X1)) ) ),
inference(flattening,[],[f58]) ).
fof(f71,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ! [X2] :
( ~ function(X2)
| ~ relation(X2)
| ( X1 = relation_dom_restriction(X2,X0)
<=> ( ! [X3] :
( ~ in(X3,relation_dom(X1))
| apply(X1,X3) = apply(X2,X3) )
& relation_dom(X1) = set_intersection2(relation_dom(X2),X0) ) ) ) ),
inference(ennf_transformation,[],[f37]) ).
fof(f72,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ! [X2] :
( ~ function(X2)
| ~ relation(X2)
| ( X1 = relation_dom_restriction(X2,X0)
<=> ( ! [X3] :
( ~ in(X3,relation_dom(X1))
| apply(X1,X3) = apply(X2,X3) )
& relation_dom(X1) = set_intersection2(relation_dom(X2),X0) ) ) ) ),
inference(flattening,[],[f71]) ).
fof(f75,plain,
? [X0,X1] :
( function(X1)
& relation(X1)
& one_to_one(X1)
& ~ one_to_one(relation_dom_restriction(X1,X0)) ),
inference(ennf_transformation,[],[f41]) ).
fof(f76,plain,
? [X0,X1] :
( function(X1)
& relation(X1)
& one_to_one(X1)
& ~ one_to_one(relation_dom_restriction(X1,X0)) ),
inference(flattening,[],[f75]) ).
fof(f78,plain,
! [X0,X1,X2] :
( ( set_intersection2(X0,X1) != X2
| ! [X3] :
( ( ~ in(X3,X2)
| ( in(X3,X1)
& in(X3,X0) ) )
& ( ~ in(X3,X1)
| ~ in(X3,X0)
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| ( in(X3,X1)
& in(X3,X0) ) )
& ( ~ in(X3,X2)
| ~ in(X3,X1)
| ~ in(X3,X0) ) )
| X2 = set_intersection2(X0,X1) ) ),
inference(nnf_transformation,[],[f6]) ).
fof(f79,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,[],[f78]) ).
fof(f80,plain,
! [X0,X1,X2] :
( ( set_intersection2(X0,X1) != X2
| ! [X4] :
( ( ~ in(X4,X2)
| ( in(X4,X1)
& in(X4,X0) ) )
& ( ~ in(X4,X1)
| ~ in(X4,X0)
| in(X4,X2) ) ) )
& ( ? [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,[],[f79]) ).
fof(f81,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(sK0(X0,X1,X2),X2)
| ( in(sK0(X0,X1,X2),X1)
& in(sK0(X0,X1,X2),X0) ) )
& ( ~ in(sK0(X0,X1,X2),X2)
| ~ in(sK0(X0,X1,X2),X1)
| ~ in(sK0(X0,X1,X2),X0) ) )
| X2 = set_intersection2(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X3,sK0(X0,X1,X2))],[f80]) ).
fof(f82,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,[],[f52]) ).
fof(f83,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ( ( ~ one_to_one(X0)
| ! [X3,X4] :
( apply(X0,X3) != apply(X0,X4)
| ~ 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,[],[f82]) ).
fof(f84,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ( ( ~ one_to_one(X0)
| ! [X3,X4] :
( apply(X0,X3) != apply(X0,X4)
| ~ in(X4,relation_dom(X0))
| ~ in(X3,relation_dom(X0))
| X3 = X4 ) )
& ( ( apply(X0,sK1(X0)) = apply(X0,sK2(X0))
& in(sK2(X0),relation_dom(X0))
& in(sK1(X0),relation_dom(X0))
& sK1(X0) != sK2(X0) )
| one_to_one(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(X1,sK1(X0)),skolemize(X2,sK2(X0))],[f83]) ).
fof(f96,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ! [X2] :
( ~ function(X2)
| ~ relation(X2)
| ( ( relation_dom_restriction(X2,X0) != X1
| ( ! [X3] :
( ~ in(X3,relation_dom(X1))
| apply(X1,X3) = apply(X2,X3) )
& relation_dom(X1) = set_intersection2(relation_dom(X2),X0) ) )
& ( ? [X3] :
( in(X3,relation_dom(X1))
& apply(X1,X3) != apply(X2,X3) )
| relation_dom(X1) != set_intersection2(relation_dom(X2),X0)
| X1 = relation_dom_restriction(X2,X0) ) ) ) ),
inference(nnf_transformation,[],[f72]) ).
fof(f97,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ! [X2] :
( ~ function(X2)
| ~ relation(X2)
| ( ( relation_dom_restriction(X2,X0) != X1
| ( ! [X3] :
( ~ in(X3,relation_dom(X1))
| apply(X1,X3) = apply(X2,X3) )
& relation_dom(X1) = set_intersection2(relation_dom(X2),X0) ) )
& ( ? [X3] :
( in(X3,relation_dom(X1))
& apply(X1,X3) != apply(X2,X3) )
| relation_dom(X1) != set_intersection2(relation_dom(X2),X0)
| X1 = relation_dom_restriction(X2,X0) ) ) ) ),
inference(flattening,[],[f96]) ).
fof(f98,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ! [X2] :
( ~ function(X2)
| ~ relation(X2)
| ( ( relation_dom_restriction(X2,X0) != X1
| ( ! [X4] :
( ~ in(X4,relation_dom(X1))
| apply(X1,X4) = apply(X2,X4) )
& relation_dom(X1) = set_intersection2(relation_dom(X2),X0) ) )
& ( ? [X3] :
( in(X3,relation_dom(X1))
& apply(X1,X3) != apply(X2,X3) )
| relation_dom(X1) != set_intersection2(relation_dom(X2),X0)
| X1 = relation_dom_restriction(X2,X0) ) ) ) ),
inference(rectify,[],[f97]) ).
fof(f99,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ! [X2] :
( ~ function(X2)
| ~ relation(X2)
| ( ( relation_dom_restriction(X2,X0) != X1
| ( ! [X4] :
( ~ in(X4,relation_dom(X1))
| apply(X1,X4) = apply(X2,X4) )
& relation_dom(X1) = set_intersection2(relation_dom(X2),X0) ) )
& ( ( in(sK14(X1,X2),relation_dom(X1))
& apply(X1,sK14(X1,X2)) != apply(X2,sK14(X1,X2)) )
| relation_dom(X1) != set_intersection2(relation_dom(X2),X0)
| X1 = relation_dom_restriction(X2,X0) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(X3,sK14(X1,X2))],[f98]) ).
fof(f100,plain,
( function(sK16)
& relation(sK16)
& one_to_one(sK16)
& ~ one_to_one(relation_dom_restriction(sK16,sK15)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15,sK16]),skolemize(X0,sK15),skolemize(X1,sK16)],[f76]) ).
fof(f109,plain,
! [X2,X0,X1,X4] :
( set_intersection2(X0,X1) != X2
| ~ in(X4,X2)
| in(X4,X0) ),
inference(cnf_transformation,[],[f81]) ).
fof(f114,plain,
! [X3,X0,X4] :
( ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| apply(X0,X3) != apply(X0,X4)
| ~ in(X4,relation_dom(X0))
| ~ in(X3,relation_dom(X0))
| X3 = X4 ),
inference(cnf_transformation,[],[f84]) ).
fof(f115,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| apply(X0,sK1(X0)) = apply(X0,sK2(X0))
| one_to_one(X0) ),
inference(cnf_transformation,[],[f84]) ).
fof(f116,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| in(sK2(X0),relation_dom(X0))
| one_to_one(X0) ),
inference(cnf_transformation,[],[f84]) ).
fof(f117,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| in(sK1(X0),relation_dom(X0))
| one_to_one(X0) ),
inference(cnf_transformation,[],[f84]) ).
fof(f118,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| sK1(X0) != sK2(X0)
| one_to_one(X0) ),
inference(cnf_transformation,[],[f84]) ).
fof(f119,plain,
! [X0,X1] :
( ~ relation(X0)
| relation(relation_dom_restriction(X0,X1)) ),
inference(cnf_transformation,[],[f53]) ).
fof(f125,plain,
! [X0,X1] :
( ~ relation_empty_yielding(X0)
| ~ relation(X0)
| relation(relation_dom_restriction(X0,X1)) ),
inference(cnf_transformation,[],[f55]) ).
fof(f129,plain,
! [X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| function(relation_dom_restriction(X0,X1)) ),
inference(cnf_transformation,[],[f59]) ).
fof(f164,plain,
! [X2,X0,X1,X4] :
( ~ function(X1)
| ~ relation(X1)
| ~ function(X2)
| ~ relation(X2)
| relation_dom_restriction(X2,X0) != X1
| ~ in(X4,relation_dom(X1))
| apply(X1,X4) = apply(X2,X4) ),
inference(cnf_transformation,[],[f99]) ).
fof(f165,plain,
! [X2,X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ~ function(X2)
| ~ relation(X2)
| relation_dom_restriction(X2,X0) != X1
| relation_dom(X1) = set_intersection2(relation_dom(X2),X0) ),
inference(cnf_transformation,[],[f99]) ).
fof(f170,plain,
function(sK16),
inference(cnf_transformation,[],[f100]) ).
fof(f171,plain,
relation(sK16),
inference(cnf_transformation,[],[f100]) ).
fof(f172,plain,
one_to_one(sK16),
inference(cnf_transformation,[],[f100]) ).
fof(f173,plain,
~ one_to_one(relation_dom_restriction(sK16,sK15)),
inference(cnf_transformation,[],[f100]) ).
fof(f176,plain,
! [X0,X1,X4] :
( ~ in(X4,set_intersection2(X0,X1))
| in(X4,X0) ),
inference(equality_resolution,[],[f109]) ).
fof(f178,plain,
! [X2,X0] :
( ~ function(relation_dom_restriction(X2,X0))
| ~ relation(relation_dom_restriction(X2,X0))
| ~ function(X2)
| ~ relation(X2)
| set_intersection2(relation_dom(X2),X0) = relation_dom(relation_dom_restriction(X2,X0)) ),
inference(equality_resolution,[],[f165]) ).
fof(f179,plain,
! [X2,X0,X4] :
( ~ function(relation_dom_restriction(X2,X0))
| ~ relation(relation_dom_restriction(X2,X0))
| ~ function(X2)
| ~ relation(X2)
| ~ in(X4,relation_dom(relation_dom_restriction(X2,X0)))
| apply(X2,X4) = apply(relation_dom_restriction(X2,X0),X4) ),
inference(equality_resolution,[],[f164]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X1)
| ~ in(X0,set_intersection2(X1,X2)) ),
inference(cnf_transformation,[],[f176]) ).
tcf(c_60,plain,
! [X0: $i] :
( one_to_one(X0)
| ~ relation(X0)
| ~ function(X0)
| ( sK1(X0) != sK2(X0) ) ),
inference(cnf_transformation,[],[f118]) ).
tcf(c_61,plain,
! [X0: $i] :
( one_to_one(X0)
| in(sK1(X0),relation_dom(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f117]) ).
tcf(c_62,plain,
! [X0: $i] :
( one_to_one(X0)
| in(sK2(X0),relation_dom(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f116]) ).
tcf(c_63,plain,
! [X0: $i] :
( one_to_one(X0)
| ( apply(X0,sK1(X0)) = apply(X0,sK2(X0)) )
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f115]) ).
tcf(c_64,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,[],[f114]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i] :
( relation(relation_dom_restriction(X0,X1))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f119]) ).
tcf(c_70,plain,
! [X0: $i,X1: $i] :
( relation(relation_dom_restriction(X0,X1))
| ~ relation_empty_yielding(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f125]) ).
tcf(c_76,plain,
! [X0: $i,X1: $i] :
( function(relation_dom_restriction(X0,X1))
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f129]) ).
tcf(c_112,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(relation_dom(X0),X1) = relation_dom(relation_dom_restriction(X0,X1)) )
| ~ relation(X0)
| ~ function(X0)
| ~ relation(relation_dom_restriction(X0,X1))
| ~ function(relation_dom_restriction(X0,X1)) ),
inference(cnf_transformation,[],[f178]) ).
tcf(c_113,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(relation_dom_restriction(X1,X2),X0) = apply(X1,X0) )
| ~ relation(X1)
| ~ function(X1)
| ~ relation(relation_dom_restriction(X1,X2))
| ~ function(relation_dom_restriction(X1,X2))
| ~ in(X0,relation_dom(relation_dom_restriction(X1,X2))) ),
inference(cnf_transformation,[],[f179]) ).
tcf(c_116,negated_conjecture,
~ one_to_one(relation_dom_restriction(sK16,sK15)),
inference(cnf_transformation,[],[f173]) ).
tcf(c_117,negated_conjecture,
one_to_one(sK16),
inference(cnf_transformation,[],[f172]) ).
tcf(c_118,negated_conjecture,
relation(sK16),
inference(cnf_transformation,[],[f171]) ).
tcf(c_119,negated_conjecture,
function(sK16),
inference(cnf_transformation,[],[f170]) ).
tcf(c_155,plain,
! [X0: $i,X1: $i] :
( relation(relation_dom_restriction(X0,X1))
| ~ relation(X0) ),
inference(global_subsumption_just,[status(thm)],[c_70,c_65]) ).
tcf(c_160,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(relation_dom(X0),X1) = relation_dom(relation_dom_restriction(X0,X1)) )
| ~ relation(X0)
| ~ function(X0) ),
inference(global_subsumption_just,[status(thm)],[c_112,c_65,c_76,c_112]) ).
tcf(c_269,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(relation_dom_restriction(X1,X2),X0) = apply(X1,X0) )
| ~ relation(X1)
| ~ function(X1)
| ~ function(relation_dom_restriction(X1,X2))
| ~ in(X0,relation_dom(relation_dom_restriction(X1,X2))) ),
inference(backward_subsumption_resolution,[status(thm)],[c_113,c_155]) ).
tcf(c_317,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(relation_dom_restriction(X1,X2),X0) = apply(X1,X0) )
| ~ relation(X1)
| ~ function(X1)
| ~ in(X0,relation_dom(relation_dom_restriction(X1,X2))) ),
inference(backward_subsumption_resolution,[status(thm)],[c_269,c_76]) ).
tcf(c_1706,definition,
iPr_def_10 = relation_dom_restriction(sK16,sK15),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_1707,negated_conjecture,
function(sK16),
inference(demodulation,[status(thm)],[c_119]) ).
tcf(c_1708,negated_conjecture,
relation(sK16),
inference(demodulation,[status(thm)],[c_118]) ).
tcf(c_1709,negated_conjecture,
one_to_one(sK16),
inference(demodulation,[status(thm)],[c_117]) ).
tcf(c_1710,negated_conjecture,
~ one_to_one(iPr_def_10),
inference(demodulation,[status(thm)],[c_116,c_1706]) ).
tcf(c_2484,plain,
( relation(iPr_def_10)
| ~ relation(sK16) ),
inference(superposition,[status(thm)],[c_1706,c_65]) ).
tcf(c_2485,plain,
relation(iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_2484,c_1708]) ).
tcf(c_2674,plain,
( function(iPr_def_10)
| ~ relation(sK16)
| ~ function(sK16) ),
inference(superposition,[status(thm)],[c_1706,c_76]) ).
tcf(c_2675,plain,
function(iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_2674,c_1708,c_1707]) ).
tcf(c_2959,plain,
! [X0: $i] :
( ( set_intersection2(relation_dom(sK16),X0) = relation_dom(relation_dom_restriction(sK16,X0)) )
| ~ relation(sK16) ),
inference(superposition,[status(thm)],[c_1707,c_160]) ).
tcf(c_2967,plain,
! [X0: $i] : set_intersection2(relation_dom(sK16),X0) = relation_dom(relation_dom_restriction(sK16,X0)),
inference(forward_subsumption_resolution,[status(thm)],[c_2959,c_1708]) ).
tcf(c_3042,plain,
( one_to_one(iPr_def_10)
| ~ relation(iPr_def_10)
| ~ function(iPr_def_10)
| ( sK1(iPr_def_10) != sK2(iPr_def_10) ) ),
inference(instantiation,[status(thm)],[c_60]) ).
tcf(c_3061,plain,
! [X0: $i,X1: $i] :
( in(X0,relation_dom(sK16))
| ~ in(X0,relation_dom(relation_dom_restriction(sK16,X1))) ),
inference(superposition,[status(thm)],[c_2967,c_58]) ).
tcf(c_3490,plain,
( one_to_one(iPr_def_10)
| ( apply(iPr_def_10,sK1(iPr_def_10)) = apply(iPr_def_10,sK2(iPr_def_10)) )
| ~ relation(iPr_def_10) ),
inference(superposition,[status(thm)],[c_2675,c_63]) ).
tcf(c_3495,plain,
apply(iPr_def_10,sK1(iPr_def_10)) = apply(iPr_def_10,sK2(iPr_def_10)),
inference(forward_subsumption_resolution,[status(thm)],[c_3490,c_1710,c_2485]) ).
tcf(c_3552,plain,
! [X0: $i] :
( ( apply(relation_dom_restriction(sK16,sK15),X0) = apply(sK16,X0) )
| ~ relation(sK16)
| ~ function(sK16)
| ~ in(X0,relation_dom(iPr_def_10)) ),
inference(superposition,[status(thm)],[c_1706,c_317]) ).
tcf(c_3559,plain,
! [X0: $i] :
( ( apply(sK16,X0) = apply(iPr_def_10,X0) )
| ~ relation(sK16)
| ~ function(sK16)
| ~ in(X0,relation_dom(iPr_def_10)) ),
inference(light_normalisation,[status(thm)],[c_3552,c_1706]) ).
tcf(c_3560,plain,
! [X0: $i] :
( ( apply(sK16,X0) = apply(iPr_def_10,X0) )
| ~ in(X0,relation_dom(iPr_def_10)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3559,c_1708,c_1707]) ).
tcf(c_3632,plain,
( one_to_one(iPr_def_10)
| ( apply(sK16,sK1(iPr_def_10)) = apply(iPr_def_10,sK1(iPr_def_10)) )
| ~ relation(iPr_def_10)
| ~ function(iPr_def_10) ),
inference(superposition,[status(thm)],[c_61,c_3560]) ).
tcf(c_3633,plain,
( one_to_one(iPr_def_10)
| ( apply(sK16,sK2(iPr_def_10)) = apply(iPr_def_10,sK2(iPr_def_10)) )
| ~ relation(iPr_def_10)
| ~ function(iPr_def_10) ),
inference(superposition,[status(thm)],[c_62,c_3560]) ).
tcf(c_3638,plain,
( one_to_one(iPr_def_10)
| ( apply(sK16,sK2(iPr_def_10)) = apply(iPr_def_10,sK1(iPr_def_10)) )
| ~ relation(iPr_def_10)
| ~ function(iPr_def_10) ),
inference(light_normalisation,[status(thm)],[c_3633,c_3495]) ).
tcf(c_3639,plain,
apply(sK16,sK2(iPr_def_10)) = apply(iPr_def_10,sK1(iPr_def_10)),
inference(forward_subsumption_resolution,[status(thm)],[c_3638,c_1710,c_2485,c_2675]) ).
tcf(c_3640,plain,
apply(sK16,sK1(iPr_def_10)) = apply(iPr_def_10,sK1(iPr_def_10)),
inference(forward_subsumption_resolution,[status(thm)],[c_3632,c_1710,c_2485,c_2675]) ).
tcf(c_3853,plain,
! [X0: $i] :
( ( sK2(iPr_def_10) = X0 )
| ~ one_to_one(sK16)
| ~ relation(sK16)
| ~ function(sK16)
| ~ in(X0,relation_dom(sK16))
| ~ in(sK2(iPr_def_10),relation_dom(sK16))
| ( apply(iPr_def_10,sK1(iPr_def_10)) != apply(sK16,X0) ) ),
inference(superposition,[status(thm)],[c_3639,c_64]) ).
tcf(c_3855,plain,
! [X0: $i] :
( ( sK2(iPr_def_10) = X0 )
| ~ in(X0,relation_dom(sK16))
| ~ in(sK2(iPr_def_10),relation_dom(sK16))
| ( apply(iPr_def_10,sK1(iPr_def_10)) != apply(sK16,X0) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3853,c_1709,c_1708,c_1707]) ).
tcf(c_4069,plain,
( ( sK1(iPr_def_10) = sK2(iPr_def_10) )
| ~ in(sK2(iPr_def_10),relation_dom(sK16))
| ~ in(sK1(iPr_def_10),relation_dom(sK16)) ),
inference(superposition,[status(thm)],[c_3640,c_3855]) ).
tcf(c_4357,plain,
! [X0: $i] :
( in(X0,relation_dom(sK16))
| ~ in(X0,relation_dom(iPr_def_10)) ),
inference(superposition,[status(thm)],[c_1706,c_3061]) ).
tcf(c_5304,plain,
( ~ in(sK1(iPr_def_10),relation_dom(sK16))
| ~ in(sK2(iPr_def_10),relation_dom(sK16)) ),
inference(global_subsumption_just,[status(thm)],[c_4069,c_1710,c_2485,c_2675,c_3042,c_4069]) ).
tcf(c_5305,plain,
( ~ in(sK2(iPr_def_10),relation_dom(sK16))
| ~ in(sK1(iPr_def_10),relation_dom(sK16)) ),
inference(renaming,[status(thm)],[c_5304]) ).
tcf(c_8577,plain,
( one_to_one(iPr_def_10)
| in(sK1(iPr_def_10),relation_dom(sK16))
| ~ relation(iPr_def_10)
| ~ function(iPr_def_10) ),
inference(superposition,[status(thm)],[c_61,c_4357]) ).
tcf(c_8578,plain,
( one_to_one(iPr_def_10)
| in(sK2(iPr_def_10),relation_dom(sK16))
| ~ relation(iPr_def_10)
| ~ function(iPr_def_10) ),
inference(superposition,[status(thm)],[c_62,c_4357]) ).
tcf(c_8594,plain,
in(sK2(iPr_def_10),relation_dom(sK16)),
inference(forward_subsumption_resolution,[status(thm)],[c_8578,c_1710,c_2485,c_2675]) ).
tcf(c_8595,plain,
in(sK1(iPr_def_10),relation_dom(sK16)),
inference(forward_subsumption_resolution,[status(thm)],[c_8577,c_1710,c_2485,c_2675]) ).
tcf(c_8629,plain,
~ in(sK1(iPr_def_10),relation_dom(sK16)),
inference(backward_subsumption_resolution,[status(thm)],[c_5305,c_8594]) ).
tcf(c_8632,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_8629,c_8595]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU042+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.08/0.35 % Computer : n008.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Thu Sep 24 12:38:25 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.13/0.39 Running first-order theorem proving
% 0.13/0.39 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
% 0.13/0.40
% 0.13/0.40 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.40
% 0.13/0.40 % Detected problem language: tptp
% 0.13/0.42 % Proving...
% 6.02/1.69 % SZS status Started for theBenchmark.p
% 6.02/1.69 % SZS status Theorem for theBenchmark.p
% 6.02/1.69
% 6.02/1.69 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 6.02/1.69
% 6.02/1.69 % ------ iProver source info
% 6.02/1.69
% 6.02/1.69 % git: date: 2026-07-19 20:42:38 +0200
% 6.02/1.69 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 6.02/1.69 % git: non_committed_changes: false
% 6.02/1.69
% 6.02/1.69 % ------ Parsing...
% 6.02/1.69 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 6.02/1.69
% 6.02/1.69 % ------ Preprocessing... sup_sim: 0 sf_s rm: 5 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e %
% 6.02/1.69
% 6.02/1.69 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 6.02/1.69
% 6.02/1.69 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 6.02/1.69 % ------ Proving...
% 6.02/1.69 % ------ Problem Properties
% 6.02/1.69
% 6.02/1.69 %
% 6.02/1.69 % clauses 64
% 6.02/1.69 % conjectures 4
% 6.02/1.69 % EPR 30
% 6.02/1.69 % Horn 56
% 6.02/1.69 % unary 30
% 6.02/1.69 % binary 14
% 6.02/1.69 % lits 136
% 6.02/1.69 % lits eq 20
% 6.02/1.69 % fd_pure 0
% 6.02/1.69 % fd_pseudo 0
% 6.02/1.69 % fd_cond 1
% 6.02/1.69 % fd_pseudo_cond 7
% 6.02/1.69 % AC symbols 0
% 6.02/1.69
% 6.02/1.69 % ------ Schedule dynamic 5 is on
% 6.02/1.69
% 6.02/1.69 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 6.02/1.69
% 6.02/1.69
% 6.02/1.69 % ------
% 6.02/1.69 % Current options:
% 6.02/1.69 % ------
% 6.02/1.69
% 6.02/1.69
% 6.02/1.69 %
% 6.02/1.69
% 6.02/1.69 % ------ Proving...
% 6.02/1.69 %
% 6.02/1.69
% 6.02/1.69 % SZS status Theorem for theBenchmark.p
% 6.02/1.69
% 6.02/1.69 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 6.02/1.69
% 6.02/1.69
%------------------------------------------------------------------------------