%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU039+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 : n007.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 02:55:06 PM UTC 2026
% Result : Theorem 2.82s 1.28s
% Output : CNFRefutation 2.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 11
% Syntax : Number of formulae : 86 ( 26 unt; 4 def)
% Number of atoms : 407 ( 92 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 473 ( 187 ~; 185 |; 78 &)
% ( 11 <=>; 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 : 9 ( 7 usr; 5 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 3 con; 0-3 aty)
% Number of variables : 169 ( 0 sgn 148 !; 21 ?; 23 :)
% 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) )
=> ! [X1] :
( X1 = relation_rng(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( X2 = apply(X0,X3)
& in(X3,relation_dom(X0)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_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(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(f39,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(f41,axiom,
! [X0,X1,X2] :
( ( function(X2)
& relation(X2) )
=> ( in(X1,X0)
=> apply(relation_dom_restriction(X2,X0),X1) = apply(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t72_funct_1) ).
fof(f42,conjecture,
! [X0,X1,X2] :
( ( function(X2)
& relation(X2) )
=> ( ( in(X1,X0)
& in(X1,relation_dom(X2)) )
=> in(apply(X2,X1),relation_rng(relation_dom_restriction(X2,X0))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t73_funct_1) ).
fof(f43,negated_conjecture,
~ ! [X0,X1,X2] :
( ( function(X2)
& relation(X2) )
=> ( ( in(X1,X0)
& in(X1,relation_dom(X2)) )
=> in(apply(X2,X1),relation_rng(relation_dom_restriction(X2,X0))) ) ),
inference(negated_conjecture,[status(cth)],[f42]) ).
fof(f56,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1] :
( X1 = relation_rng(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( X2 = apply(X0,X3)
& in(X3,relation_dom(X0)) ) ) ) ),
inference(ennf_transformation,[],[f7]) ).
fof(f57,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1] :
( X1 = relation_rng(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( X2 = apply(X0,X3)
& in(X3,relation_dom(X0)) ) ) ) ),
inference(flattening,[],[f56]) ).
fof(f58,plain,
! [X0,X1] :
( ~ relation(X0)
| relation(relation_dom_restriction(X0,X1)) ),
inference(ennf_transformation,[],[f8]) ).
fof(f63,plain,
! [X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ( function(relation_dom_restriction(X0,X1))
& relation(relation_dom_restriction(X0,X1)) ) ),
inference(ennf_transformation,[],[f15]) ).
fof(f64,plain,
! [X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ( function(relation_dom_restriction(X0,X1))
& relation(relation_dom_restriction(X0,X1)) ) ),
inference(flattening,[],[f63]) ).
fof(f79,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,[],[f39]) ).
fof(f80,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,[],[f79]) ).
fof(f82,plain,
! [X0,X1,X2] :
( ~ function(X2)
| ~ relation(X2)
| ~ in(X1,X0)
| apply(relation_dom_restriction(X2,X0),X1) = apply(X2,X1) ),
inference(ennf_transformation,[],[f41]) ).
fof(f83,plain,
! [X0,X1,X2] :
( ~ function(X2)
| ~ relation(X2)
| ~ in(X1,X0)
| apply(relation_dom_restriction(X2,X0),X1) = apply(X2,X1) ),
inference(flattening,[],[f82]) ).
fof(f84,plain,
? [X0,X1,X2] :
( function(X2)
& relation(X2)
& in(X1,X0)
& in(X1,relation_dom(X2))
& ~ in(apply(X2,X1),relation_rng(relation_dom_restriction(X2,X0))) ),
inference(ennf_transformation,[],[f43]) ).
fof(f85,plain,
? [X0,X1,X2] :
( function(X2)
& relation(X2)
& in(X1,X0)
& in(X1,relation_dom(X2))
& ~ in(apply(X2,X1),relation_rng(relation_dom_restriction(X2,X0))) ),
inference(flattening,[],[f84]) ).
fof(f88,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(f89,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,[],[f88]) ).
fof(f90,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,[],[f89]) ).
fof(f91,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))],[f90]) ).
fof(f92,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1] :
( ( relation_rng(X0) != X1
| ! [X2] :
( ( ~ in(X2,X1)
| ? [X3] :
( X2 = apply(X0,X3)
& in(X3,relation_dom(X0)) ) )
& ( ! [X3] :
( apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0)) )
| in(X2,X1) ) ) )
& ( ? [X2] :
( ( in(X2,X1)
| ? [X3] :
( X2 = apply(X0,X3)
& in(X3,relation_dom(X0)) ) )
& ( ~ in(X2,X1)
| ! [X3] :
( apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0)) ) ) )
| X1 = relation_rng(X0) ) ) ),
inference(nnf_transformation,[],[f57]) ).
fof(f93,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1] :
( ( relation_rng(X0) != X1
| ! [X5] :
( ( ~ in(X5,X1)
| ? [X7] :
( apply(X0,X7) = X5
& in(X7,relation_dom(X0)) ) )
& ( ! [X6] :
( apply(X0,X6) != X5
| ~ in(X6,relation_dom(X0)) )
| in(X5,X1) ) ) )
& ( ? [X2] :
( ( in(X2,X1)
| ? [X4] :
( apply(X0,X4) = X2
& in(X4,relation_dom(X0)) ) )
& ( ~ in(X2,X1)
| ! [X3] :
( apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0)) ) ) )
| X1 = relation_rng(X0) ) ) ),
inference(rectify,[],[f92]) ).
fof(f94,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1] :
( ( relation_rng(X0) != X1
| ! [X5] :
( ( ~ in(X5,X1)
| ( apply(X0,sK3(X0,X5)) = X5
& in(sK3(X0,X5),relation_dom(X0)) ) )
& ( ! [X6] :
( apply(X0,X6) != X5
| ~ in(X6,relation_dom(X0)) )
| in(X5,X1) ) ) )
& ( ( ( in(sK1(X0,X1),X1)
| ( sK1(X0,X1) = apply(X0,sK2(X0,X1))
& in(sK2(X0,X1),relation_dom(X0)) ) )
& ( ~ in(sK1(X0,X1),X1)
| ! [X3] :
( apply(X0,X3) != sK1(X0,X1)
| ~ in(X3,relation_dom(X0)) ) ) )
| X1 = relation_rng(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3]),skolemize(X2,sK1(X0,X1)),skolemize(X4,sK2(X0,X1)),skolemize(X7,sK3(X0,X5))],[f93]) ).
fof(f106,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,[],[f80]) ).
fof(f107,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,[],[f106]) ).
fof(f108,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,[],[f107]) ).
fof(f109,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(sK15(X1,X2),relation_dom(X1))
& apply(X1,sK15(X1,X2)) != apply(X2,sK15(X1,X2)) )
| relation_dom(X1) != set_intersection2(relation_dom(X2),X0)
| X1 = relation_dom_restriction(X2,X0) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(X3,sK15(X1,X2))],[f108]) ).
fof(f110,plain,
( function(sK18)
& relation(sK18)
& in(sK17,sK16)
& in(sK17,relation_dom(sK18))
& ~ in(apply(sK18,sK17),relation_rng(relation_dom_restriction(sK18,sK16))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16,sK17,sK18]),skolemize(X0,sK16),skolemize(X1,sK17),skolemize(X2,sK18)],[f85]) ).
fof(f119,plain,
! [X2,X0,X1,X4] :
( set_intersection2(X0,X1) != X2
| ~ in(X4,X1)
| ~ in(X4,X0)
| in(X4,X2) ),
inference(cnf_transformation,[],[f91]) ).
fof(f125,plain,
! [X0,X1,X6,X5] :
( ~ function(X0)
| ~ relation(X0)
| relation_rng(X0) != X1
| apply(X0,X6) != X5
| ~ in(X6,relation_dom(X0))
| in(X5,X1) ),
inference(cnf_transformation,[],[f94]) ).
fof(f129,plain,
! [X0,X1] :
( ~ relation(X0)
| relation(relation_dom_restriction(X0,X1)) ),
inference(cnf_transformation,[],[f58]) ).
fof(f139,plain,
! [X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| function(relation_dom_restriction(X0,X1)) ),
inference(cnf_transformation,[],[f64]) ).
fof(f177,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,[],[f109]) ).
fof(f181,plain,
! [X2,X0,X1] :
( ~ function(X2)
| ~ relation(X2)
| ~ in(X1,X0)
| apply(relation_dom_restriction(X2,X0),X1) = apply(X2,X1) ),
inference(cnf_transformation,[],[f83]) ).
fof(f182,plain,
function(sK18),
inference(cnf_transformation,[],[f110]) ).
fof(f183,plain,
relation(sK18),
inference(cnf_transformation,[],[f110]) ).
fof(f184,plain,
in(sK17,sK16),
inference(cnf_transformation,[],[f110]) ).
fof(f185,plain,
in(sK17,relation_dom(sK18)),
inference(cnf_transformation,[],[f110]) ).
fof(f186,plain,
~ in(apply(sK18,sK17),relation_rng(relation_dom_restriction(sK18,sK16))),
inference(cnf_transformation,[],[f110]) ).
fof(f189,plain,
! [X0,X1,X4] :
( ~ in(X4,X1)
| ~ in(X4,X0)
| in(X4,set_intersection2(X0,X1)) ),
inference(equality_resolution,[],[f119]) ).
fof(f192,plain,
! [X0,X1,X6] :
( ~ function(X0)
| ~ relation(X0)
| relation_rng(X0) != X1
| ~ in(X6,relation_dom(X0))
| in(apply(X0,X6),X1) ),
inference(equality_resolution,[],[f125]) ).
fof(f193,plain,
! [X0,X6] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(X6,relation_dom(X0))
| in(apply(X0,X6),relation_rng(X0)) ),
inference(equality_resolution,[],[f192]) ).
fof(f196,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,[],[f177]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,set_intersection2(X2,X1))
| ~ in(X0,X2)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f189]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i] :
( in(apply(X1,X0),relation_rng(X1))
| ~ relation(X1)
| ~ function(X1)
| ~ in(X0,relation_dom(X1)) ),
inference(cnf_transformation,[],[f193]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i] :
( relation(relation_dom_restriction(X0,X1))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f129]) ).
tcf(c_76,plain,
! [X0: $i,X1: $i] :
( function(relation_dom_restriction(X0,X1))
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f139]) ).
tcf(c_114,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,[],[f196]) ).
tcf(c_117,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(relation_dom_restriction(X2,X1),X0) = apply(X2,X0) )
| ~ relation(X2)
| ~ function(X2)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f181]) ).
tcf(c_118,negated_conjecture,
~ in(apply(sK18,sK17),relation_rng(relation_dom_restriction(sK18,sK16))),
inference(cnf_transformation,[],[f186]) ).
tcf(c_119,negated_conjecture,
in(sK17,relation_dom(sK18)),
inference(cnf_transformation,[],[f185]) ).
tcf(c_120,negated_conjecture,
in(sK17,sK16),
inference(cnf_transformation,[],[f184]) ).
tcf(c_121,negated_conjecture,
relation(sK18),
inference(cnf_transformation,[],[f183]) ).
tcf(c_122,negated_conjecture,
function(sK18),
inference(cnf_transformation,[],[f182]) ).
tcf(c_163,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_114,c_65,c_76,c_114]) ).
tcf(c_1300,definition,
iPr_def_10 = relation_dom(sK18),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_1301,definition,
iPr_def_11 = apply(sK18,sK17),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_1302,definition,
iPr_def_12 = relation_dom_restriction(sK18,sK16),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_1303,definition,
iPr_def_13 = relation_rng(iPr_def_12),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_1304,negated_conjecture,
function(sK18),
inference(demodulation,[status(thm)],[c_122]) ).
tcf(c_1305,negated_conjecture,
relation(sK18),
inference(demodulation,[status(thm)],[c_121]) ).
tcf(c_1306,negated_conjecture,
in(sK17,sK16),
inference(demodulation,[status(thm)],[c_120]) ).
tcf(c_1307,negated_conjecture,
in(sK17,iPr_def_10),
inference(demodulation,[status(thm)],[c_119,c_1300]) ).
tcf(c_1308,negated_conjecture,
~ in(iPr_def_11,iPr_def_13),
inference(demodulation,[status(thm)],[c_118,c_1302,c_1303,c_1301]) ).
tcf(c_2180,plain,
( relation(iPr_def_12)
| ~ relation(sK18) ),
inference(superposition,[status(thm)],[c_1302,c_65]) ).
tcf(c_2181,plain,
relation(iPr_def_12),
inference(forward_subsumption_resolution,[status(thm)],[c_2180,c_1305]) ).
tcf(c_2469,plain,
( function(iPr_def_12)
| ~ relation(sK18)
| ~ function(sK18) ),
inference(superposition,[status(thm)],[c_1302,c_76]) ).
tcf(c_2470,plain,
function(iPr_def_12),
inference(forward_subsumption_resolution,[status(thm)],[c_2469,c_1305,c_1304]) ).
tcf(c_2927,plain,
! [X0: $i] :
( ( set_intersection2(relation_dom(sK18),X0) = relation_dom(relation_dom_restriction(sK18,X0)) )
| ~ relation(sK18) ),
inference(superposition,[status(thm)],[c_1304,c_163]) ).
tcf(c_2935,plain,
! [X0: $i] :
( ( relation_dom(relation_dom_restriction(sK18,X0)) = set_intersection2(iPr_def_10,X0) )
| ~ relation(sK18) ),
inference(light_normalisation,[status(thm)],[c_2927,c_1300]) ).
tcf(c_2936,plain,
! [X0: $i] : relation_dom(relation_dom_restriction(sK18,X0)) = set_intersection2(iPr_def_10,X0),
inference(forward_subsumption_resolution,[status(thm)],[c_2935,c_1305]) ).
tcf(c_2980,plain,
! [X0: $i] :
( in(apply(iPr_def_12,X0),iPr_def_13)
| ~ relation(iPr_def_12)
| ~ function(iPr_def_12)
| ~ in(X0,relation_dom(iPr_def_12)) ),
inference(superposition,[status(thm)],[c_1303,c_62]) ).
tcf(c_2990,plain,
! [X0: $i] :
( in(apply(iPr_def_12,X0),iPr_def_13)
| ~ in(X0,relation_dom(iPr_def_12)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2980,c_2181,c_2470]) ).
tcf(c_3023,plain,
set_intersection2(iPr_def_10,sK16) = relation_dom(iPr_def_12),
inference(superposition,[status(thm)],[c_1302,c_2936]) ).
tcf(c_3055,plain,
! [X0: $i] :
( in(X0,relation_dom(iPr_def_12))
| ~ in(X0,iPr_def_10)
| ~ in(X0,sK16) ),
inference(superposition,[status(thm)],[c_3023,c_56]) ).
tcf(c_3401,plain,
! [X0: $i] :
( ( apply(relation_dom_restriction(X0,sK16),sK17) = apply(X0,sK17) )
| ~ relation(X0)
| ~ function(X0) ),
inference(superposition,[status(thm)],[c_1306,c_117]) ).
tcf(c_3772,plain,
( ( apply(relation_dom_restriction(sK18,sK16),sK17) = apply(sK18,sK17) )
| ~ relation(sK18) ),
inference(superposition,[status(thm)],[c_1304,c_3401]) ).
tcf(c_3779,plain,
( ( apply(iPr_def_12,sK17) = iPr_def_11 )
| ~ relation(sK18) ),
inference(light_normalisation,[status(thm)],[c_3772,c_1301,c_1302]) ).
tcf(c_3780,plain,
apply(iPr_def_12,sK17) = iPr_def_11,
inference(forward_subsumption_resolution,[status(thm)],[c_3779,c_1305]) ).
tcf(c_3814,plain,
( in(iPr_def_11,iPr_def_13)
| ~ in(sK17,relation_dom(iPr_def_12)) ),
inference(superposition,[status(thm)],[c_3780,c_2990]) ).
tcf(c_3815,plain,
~ in(sK17,relation_dom(iPr_def_12)),
inference(forward_subsumption_resolution,[status(thm)],[c_3814,c_1308]) ).
tcf(c_5559,plain,
( ~ in(sK17,iPr_def_10)
| ~ in(sK17,sK16) ),
inference(superposition,[status(thm)],[c_3055,c_3815]) ).
tcf(c_5560,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_5559,c_1307,c_1306]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU039+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.35 % Computer : n007.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 12:35:07 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 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...
% 2.82/1.28 % SZS status Started for theBenchmark.p
% 2.82/1.28 % SZS status Theorem for theBenchmark.p
% 2.82/1.28
% 2.82/1.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.82/1.28
% 2.82/1.28 % ------ iProver source info
% 2.82/1.28
% 2.82/1.28 % git: date: 2026-07-19 20:42:38 +0200
% 2.82/1.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.82/1.28 % git: non_committed_changes: false
% 2.82/1.28
% 2.82/1.28 % ------ Parsing...
% 2.82/1.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.82/1.28
% 2.82/1.28 % ------ 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 %
% 2.82/1.28
% 2.82/1.28 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.82/1.28
% 2.82/1.28 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.82/1.28 % ------ Proving...
% 2.82/1.28 % ------ Problem Properties
% 2.82/1.28
% 2.82/1.28 %
% 2.82/1.28 % clauses 71
% 2.82/1.28 % conjectures 5
% 2.82/1.28 % EPR 29
% 2.82/1.28 % Horn 64
% 2.82/1.28 % unary 33
% 2.82/1.28 % binary 15
% 2.82/1.28 % lits 153
% 2.82/1.28 % lits eq 26
% 2.82/1.28 % fd_pure 0
% 2.82/1.28 % fd_pseudo 0
% 2.82/1.28 % fd_cond 1
% 2.82/1.28 % fd_pseudo_cond 9
% 2.82/1.28 % AC symbols 0
% 2.82/1.28
% 2.82/1.28 % ------ Schedule dynamic 5 is on
% 2.82/1.28
% 2.82/1.28 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.82/1.28
% 2.82/1.28
% 2.82/1.28 % ------
% 2.82/1.28 % Current options:
% 2.82/1.28 % ------
% 2.82/1.28
% 2.82/1.28
% 2.82/1.28 %
% 2.82/1.28
% 2.82/1.28 % ------ Proving...
% 2.82/1.28 %
% 2.82/1.28
% 2.82/1.28 % SZS status Theorem for theBenchmark.p
% 2.82/1.28
% 2.82/1.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.82/1.28
% 2.82/1.28
%------------------------------------------------------------------------------