%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET669+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n016.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 02:47:44 PM UTC 2026
% Result : Theorem 3.00s 1.20s
% Output : CNFRefutation 3.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 15
% Syntax : Number of formulae : 129 ( 22 unt; 4 def)
% Number of atoms : 526 ( 30 equ)
% Maximal formula atoms : 10 ( 4 avg)
% Number of connectives : 628 ( 266 ~; 268 |; 47 &)
% ( 13 <=>; 34 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 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 : 10 ( 8 usr; 5 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 4 con; 0-3 aty)
% Number of variables : 243 ( 0 sgn 233 !; 10 ?; 114 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( ( subset(X1,X0)
& subset(X0,X1) )
=> X0 = X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p1) ).
fof(f2,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,relation_type(X0,X1))
=> ( subset(identity_relation_of(X2),X3)
=> ( subset(X2,range(X0,X1,X3))
& subset(X2,domain(X0,X1,X3)) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2) ).
fof(f7,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( subset(X0,X1)
<=> ! [X2] :
( ilf_type(X2,set_type)
=> ( member(X2,X0)
=> member(X2,X1) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p7) ).
fof(f9,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( X0 = X1
<=> ( subset(X1,X0)
& subset(X0,X1) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p9) ).
fof(f16,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( ilf_type(X1,subset_type(X0))
<=> ilf_type(X1,member_type(power_set(X0))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p16) ).
fof(f20,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( member(X0,power_set(X1))
<=> ! [X2] :
( ilf_type(X2,set_type)
=> ( member(X2,X0)
=> member(X2,X1) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p20) ).
fof(f21,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ( ilf_type(power_set(X0),set_type)
& ~ empty(power_set(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p21) ).
fof(f22,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ( ilf_type(X1,set_type)
& ~ empty(X1) )
=> ( ilf_type(X0,member_type(X1))
<=> member(X0,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p22) ).
fof(f31,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,relation_type(X0,X1))
=> ilf_type(range(X0,X1,X2),subset_type(X1)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p31) ).
fof(f32,axiom,
! [X0] : ilf_type(X0,set_type),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p32) ).
fof(f33,conjecture,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,relation_type(X0,X1))
=> ( subset(identity_relation_of(X1),X2)
=> ( X1 = range(X0,X1,X2)
& subset(X1,domain(X0,X1,X2)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_relset_1_32) ).
fof(f34,negated_conjecture,
~ ! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,relation_type(X0,X1))
=> ( subset(identity_relation_of(X1),X2)
=> ( X1 = range(X0,X1,X2)
& subset(X1,domain(X0,X1,X2)) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f33]) ).
fof(f35,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f36,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ) ),
inference(flattening,[],[f35]) ).
fof(f37,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ! [X2] :
( ~ ilf_type(X2,set_type)
| ! [X3] :
( ~ ilf_type(X3,relation_type(X0,X1))
| ~ subset(identity_relation_of(X2),X3)
| ( subset(X2,range(X0,X1,X3))
& subset(X2,domain(X0,X1,X3)) ) ) ) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f38,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ! [X2] :
( ~ ilf_type(X2,set_type)
| ! [X3] :
( ~ ilf_type(X3,relation_type(X0,X1))
| ~ subset(identity_relation_of(X2),X3)
| ( subset(X2,range(X0,X1,X3))
& subset(X2,domain(X0,X1,X3)) ) ) ) ) ),
inference(flattening,[],[f37]) ).
fof(f43,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ( subset(X0,X1)
<=> ! [X2] :
( ~ ilf_type(X2,set_type)
| ~ member(X2,X0)
| member(X2,X1) ) ) ) ),
inference(ennf_transformation,[],[f7]) ).
fof(f44,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ( subset(X0,X1)
<=> ! [X2] :
( ~ ilf_type(X2,set_type)
| ~ member(X2,X0)
| member(X2,X1) ) ) ) ),
inference(flattening,[],[f43]) ).
fof(f47,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ( X0 = X1
<=> ( subset(X1,X0)
& subset(X0,X1) ) ) ) ),
inference(ennf_transformation,[],[f9]) ).
fof(f53,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ( ilf_type(X1,subset_type(X0))
<=> ilf_type(X1,member_type(power_set(X0))) ) ) ),
inference(ennf_transformation,[],[f16]) ).
fof(f57,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ( member(X0,power_set(X1))
<=> ! [X2] :
( ~ ilf_type(X2,set_type)
| ~ member(X2,X0)
| member(X2,X1) ) ) ) ),
inference(ennf_transformation,[],[f20]) ).
fof(f58,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ( member(X0,power_set(X1))
<=> ! [X2] :
( ~ ilf_type(X2,set_type)
| ~ member(X2,X0)
| member(X2,X1) ) ) ) ),
inference(flattening,[],[f57]) ).
fof(f59,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ( ilf_type(power_set(X0),set_type)
& ~ empty(power_set(X0)) ) ),
inference(ennf_transformation,[],[f21]) ).
fof(f60,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| empty(X1)
| ( ilf_type(X0,member_type(X1))
<=> member(X0,X1) ) ) ),
inference(ennf_transformation,[],[f22]) ).
fof(f61,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| empty(X1)
| ( ilf_type(X0,member_type(X1))
<=> member(X0,X1) ) ) ),
inference(flattening,[],[f60]) ).
fof(f73,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ! [X2] :
( ~ ilf_type(X2,relation_type(X0,X1))
| ilf_type(range(X0,X1,X2),subset_type(X1)) ) ) ),
inference(ennf_transformation,[],[f31]) ).
fof(f74,plain,
? [X0] :
( ilf_type(X0,set_type)
& ? [X1] :
( ilf_type(X1,set_type)
& ? [X2] :
( ilf_type(X2,relation_type(X0,X1))
& subset(identity_relation_of(X1),X2)
& ( range(X0,X1,X2) != X1
| ~ subset(X1,domain(X0,X1,X2)) ) ) ) ),
inference(ennf_transformation,[],[f34]) ).
fof(f75,plain,
? [X0] :
( ilf_type(X0,set_type)
& ? [X1] :
( ilf_type(X1,set_type)
& ? [X2] :
( ilf_type(X2,relation_type(X0,X1))
& subset(identity_relation_of(X1),X2)
& ( range(X0,X1,X2) != X1
| ~ subset(X1,domain(X0,X1,X2)) ) ) ) ),
inference(flattening,[],[f74]) ).
fof(f79,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ( ( ~ subset(X0,X1)
| ! [X2] :
( ~ ilf_type(X2,set_type)
| ~ member(X2,X0)
| member(X2,X1) ) )
& ( ? [X2] :
( ilf_type(X2,set_type)
& member(X2,X0)
& ~ member(X2,X1) )
| subset(X0,X1) ) ) ) ),
inference(nnf_transformation,[],[f44]) ).
fof(f80,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ( ( ~ subset(X0,X1)
| ! [X3] :
( ~ ilf_type(X3,set_type)
| ~ member(X3,X0)
| member(X3,X1) ) )
& ( ? [X2] :
( ilf_type(X2,set_type)
& member(X2,X0)
& ~ member(X2,X1) )
| subset(X0,X1) ) ) ) ),
inference(rectify,[],[f79]) ).
fof(f81,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ( ( ~ subset(X0,X1)
| ! [X3] :
( ~ ilf_type(X3,set_type)
| ~ member(X3,X0)
| member(X3,X1) ) )
& ( ( ilf_type(sK1(X0,X1),set_type)
& member(sK1(X0,X1),X0)
& ~ member(sK1(X0,X1),X1) )
| subset(X0,X1) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X2,sK1(X0,X1))],[f80]) ).
fof(f85,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ( ( X0 != X1
| ( subset(X1,X0)
& subset(X0,X1) ) )
& ( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ) ) ) ),
inference(nnf_transformation,[],[f47]) ).
fof(f86,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ( ( X0 != X1
| ( subset(X1,X0)
& subset(X0,X1) ) )
& ( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ) ) ) ),
inference(flattening,[],[f85]) ).
fof(f90,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ( ( ~ ilf_type(X1,subset_type(X0))
| ilf_type(X1,member_type(power_set(X0))) )
& ( ~ ilf_type(X1,member_type(power_set(X0)))
| ilf_type(X1,subset_type(X0)) ) ) ) ),
inference(nnf_transformation,[],[f53]) ).
fof(f92,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ( ( ~ member(X0,power_set(X1))
| ! [X2] :
( ~ ilf_type(X2,set_type)
| ~ member(X2,X0)
| member(X2,X1) ) )
& ( ? [X2] :
( ilf_type(X2,set_type)
& member(X2,X0)
& ~ member(X2,X1) )
| member(X0,power_set(X1)) ) ) ) ),
inference(nnf_transformation,[],[f58]) ).
fof(f93,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ( ( ~ member(X0,power_set(X1))
| ! [X3] :
( ~ ilf_type(X3,set_type)
| ~ member(X3,X0)
| member(X3,X1) ) )
& ( ? [X2] :
( ilf_type(X2,set_type)
& member(X2,X0)
& ~ member(X2,X1) )
| member(X0,power_set(X1)) ) ) ) ),
inference(rectify,[],[f92]) ).
fof(f94,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ( ( ~ member(X0,power_set(X1))
| ! [X3] :
( ~ ilf_type(X3,set_type)
| ~ member(X3,X0)
| member(X3,X1) ) )
& ( ( ilf_type(sK6(X0,X1),set_type)
& member(sK6(X0,X1),X0)
& ~ member(sK6(X0,X1),X1) )
| member(X0,power_set(X1)) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(X2,sK6(X0,X1))],[f93]) ).
fof(f95,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| empty(X1)
| ( ( ~ ilf_type(X0,member_type(X1))
| member(X0,X1) )
& ( ~ member(X0,X1)
| ilf_type(X0,member_type(X1)) ) ) ) ),
inference(nnf_transformation,[],[f61]) ).
fof(f103,plain,
( ilf_type(sK12,set_type)
& ilf_type(sK13,set_type)
& ilf_type(sK14,relation_type(sK12,sK13))
& subset(identity_relation_of(sK13),sK14)
& ( sK13 != range(sK12,sK13,sK14)
| ~ subset(sK13,domain(sK12,sK13,sK14)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12,sK13,sK14]),skolemize(X0,sK12),skolemize(X1,sK13),skolemize(X2,sK14)],[f75]) ).
fof(f104,plain,
! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f36]) ).
fof(f105,plain,
! [X2,X3,X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,relation_type(X0,X1))
| ~ subset(identity_relation_of(X2),X3)
| subset(X2,range(X0,X1,X3)) ),
inference(cnf_transformation,[],[f38]) ).
fof(f106,plain,
! [X2,X3,X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,relation_type(X0,X1))
| ~ subset(identity_relation_of(X2),X3)
| subset(X2,domain(X0,X1,X3)) ),
inference(cnf_transformation,[],[f38]) ).
fof(f116,plain,
! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| member(sK1(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f81]) ).
fof(f117,plain,
! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ member(sK1(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f81]) ).
fof(f125,plain,
! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f86]) ).
fof(f134,plain,
! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X1,subset_type(X0))
| ilf_type(X1,member_type(power_set(X0))) ),
inference(cnf_transformation,[],[f90]) ).
fof(f139,plain,
! [X3,X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ member(X0,power_set(X1))
| ~ ilf_type(X3,set_type)
| ~ member(X3,X0)
| member(X3,X1) ),
inference(cnf_transformation,[],[f94]) ).
fof(f144,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ~ empty(power_set(X0)) ),
inference(cnf_transformation,[],[f59]) ).
fof(f145,plain,
! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| empty(X1)
| ~ ilf_type(X0,member_type(X1))
| member(X0,X1) ),
inference(cnf_transformation,[],[f95]) ).
fof(f162,plain,
! [X2,X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,relation_type(X0,X1))
| ilf_type(range(X0,X1,X2),subset_type(X1)) ),
inference(cnf_transformation,[],[f73]) ).
fof(f163,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[],[f32]) ).
fof(f166,plain,
ilf_type(sK14,relation_type(sK12,sK13)),
inference(cnf_transformation,[],[f103]) ).
fof(f167,plain,
subset(identity_relation_of(sK13),sK14),
inference(cnf_transformation,[],[f103]) ).
fof(f168,plain,
( sK13 != range(sK12,sK13,sK14)
| ~ subset(sK13,domain(sK12,sK13,sK14)) ),
inference(cnf_transformation,[],[f103]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f104]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(X3,domain(X1,X2,X0))
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ subset(identity_relation_of(X3),X0)
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(cnf_transformation,[],[f106]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(X3,range(X1,X2,X0))
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ subset(identity_relation_of(X3),X0)
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(cnf_transformation,[],[f105]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| ~ member(sK1(X0,X1),X1) ),
inference(cnf_transformation,[],[f117]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| member(sK1(X0,X1),X0)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f116]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f125]) ).
tcf(c_79,plain,
! [X0: $i,X1: $i] :
( ilf_type(X0,member_type(power_set(X1)))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X0,subset_type(X1)) ),
inference(cnf_transformation,[],[f134]) ).
tcf(c_86,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X2,X1)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| ~ member(X2,X0)
| ~ member(X0,power_set(X1)) ),
inference(cnf_transformation,[],[f139]) ).
tcf(c_87,plain,
! [X0: $i] :
( ~ empty(power_set(X0))
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f144]) ).
tcf(c_90,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| member(X0,X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X0,member_type(X1)) ),
inference(cnf_transformation,[],[f145]) ).
tcf(c_106,plain,
! [X0: $i,X1: $i,X2: $i] :
( ilf_type(range(X1,X2,X0),subset_type(X2))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(cnf_transformation,[],[f162]) ).
tcf(c_107,plain,
! [X0: $i] : ilf_type(X0,set_type),
inference(cnf_transformation,[],[f163]) ).
tcf(c_108,negated_conjecture,
( ~ subset(sK13,domain(sK12,sK13,sK14))
| ( range(sK12,sK13,sK14) != sK13 ) ),
inference(cnf_transformation,[],[f168]) ).
tcf(c_109,negated_conjecture,
subset(identity_relation_of(sK13),sK14),
inference(cnf_transformation,[],[f167]) ).
tcf(c_110,negated_conjecture,
ilf_type(sK14,relation_type(sK12,sK13)),
inference(cnf_transformation,[],[f166]) ).
tcf(c_170,plain,
! [X0: $i] : ~ empty(power_set(X0)),
inference(global_subsumption_just,[status(thm)],[c_87,c_107,c_87]) ).
tcf(c_224,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| member(sK1(X0,X1),X0)
| ~ ilf_type(X1,set_type) ),
inference(global_subsumption_just,[status(thm)],[c_60,c_107,c_60]) ).
tcf(c_225,plain,
! [X0: $i,X1: $i] :
( subset(X1,X0)
| member(sK1(X1,X0),X1)
| ~ ilf_type(X0,set_type) ),
inference(renaming,[status(thm)],[c_224]) ).
tcf(c_226,plain,
! [X0: $i,X1: $i] :
( subset(X1,X0)
| member(sK1(X1,X0),X1) ),
inference(global_subsumption_just,[status(thm)],[c_225,c_107,c_225]) ).
tcf(c_227,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| member(sK1(X0,X1),X0) ),
inference(renaming,[status(thm)],[c_226]) ).
tcf(c_238,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ ilf_type(X1,set_type)
| ~ member(sK1(X0,X1),X1) ),
inference(global_subsumption_just,[status(thm)],[c_59,c_107,c_59]) ).
tcf(c_240,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| member(X0,X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,member_type(X1)) ),
inference(global_subsumption_just,[status(thm)],[c_90,c_107,c_90]) ).
tcf(c_247,plain,
! [X0: $i,X1: $i] :
( ilf_type(X0,member_type(power_set(X1)))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,subset_type(X1)) ),
inference(global_subsumption_just,[status(thm)],[c_79,c_107,c_79]) ).
tcf(c_259,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ ilf_type(X1,set_type)
| ~ subset(X0,X1)
| ~ subset(X1,X0) ),
inference(global_subsumption_just,[status(thm)],[c_49,c_107,c_68]) ).
tcf(c_260,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ ilf_type(X1,set_type)
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(renaming,[status(thm)],[c_259]) ).
tcf(c_271,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X2,X1)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ member(X0,power_set(X1))
| ~ member(X2,X0) ),
inference(global_subsumption_just,[status(thm)],[c_86,c_107,c_86]) ).
tcf(c_272,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X2,X1)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ member(X2,X0)
| ~ member(X0,power_set(X1)) ),
inference(renaming,[status(thm)],[c_271]) ).
tcf(c_433,plain,
! [X0: $i,X1: $i,X2: $i] :
( ilf_type(range(X1,X2,X0),subset_type(X2))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_106,c_107]) ).
tcf(c_434,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[c_260,c_107]) ).
tcf(c_436,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(X3,range(X1,X2,X0))
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type)
| ~ subset(identity_relation_of(X3),X0)
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_51,c_107]) ).
tcf(c_437,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ member(sK1(X0,X1),X1) ),
inference(backward_subsumption_resolution,[status(thm)],[c_238,c_107]) ).
tcf(c_439,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X2,X1)
| ~ ilf_type(X2,set_type)
| ~ member(X2,X0)
| ~ member(X0,power_set(X1)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_272,c_107]) ).
tcf(c_448,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(X3,domain(X1,X2,X0))
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type)
| ~ subset(identity_relation_of(X3),X0)
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_50,c_107]) ).
tcf(c_450,plain,
! [X0: $i,X1: $i] :
( ilf_type(X0,member_type(power_set(X1)))
| ~ ilf_type(X0,subset_type(X1)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_247,c_107]) ).
tcf(c_453,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| member(X0,X1)
| ~ ilf_type(X0,member_type(X1)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_240,c_107]) ).
tcf(c_639,plain,
! [X0: $i,X1: $i,X2: $i] :
( ilf_type(range(X1,X2,X0),subset_type(X2))
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_433,c_107]) ).
tcf(c_687,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ member(X0,power_set(X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_439,c_107]) ).
tcf(c_718,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(X3,range(X1,X2,X0))
| ~ subset(identity_relation_of(X3),X0)
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_436,c_107,c_107]) ).
tcf(c_734,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(X3,domain(X1,X2,X0))
| ~ subset(identity_relation_of(X3),X0)
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_448,c_107,c_107]) ).
tcf(c_1310,plain,
! [X0: $i,X1: $i] :
( ilf_type(X0,member_type(power_set(X1)))
| ~ ilf_type(X0,subset_type(X1)) ),
inference(prop_impl_just,[status(thm)],[c_450]) ).
tcf(c_1312,plain,
! [X0: $i,X1: $i] :
( ~ member(sK1(X0,X1),X1)
| subset(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_437]) ).
tcf(c_1313,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ member(sK1(X0,X1),X1) ),
inference(renaming,[status(thm)],[c_1312]) ).
tcf(c_1314,plain,
! [X0: $i,X1: $i] :
( member(sK1(X0,X1),X0)
| subset(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_227]) ).
tcf(c_1315,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| member(sK1(X0,X1),X0) ),
inference(renaming,[status(thm)],[c_1314]) ).
tcf(c_1324,plain,
! [X0: $i,X1: $i,X2: $i] :
( ilf_type(range(X1,X2,X0),subset_type(X2))
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(prop_impl_just,[status(thm)],[c_639]) ).
tcf(c_1908,definition,
iPr_def_10 = relation_type(sK12,sK13),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_1909,definition,
iPr_def_11 = identity_relation_of(sK13),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_1910,definition,
iPr_def_12 = range(sK12,sK13,sK14),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_1911,definition,
iPr_def_13 = domain(sK12,sK13,sK14),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_1912,negated_conjecture,
ilf_type(sK14,iPr_def_10),
inference(demodulation,[status(thm)],[c_110,c_1908]) ).
tcf(c_1913,negated_conjecture,
subset(iPr_def_11,sK14),
inference(demodulation,[status(thm)],[c_109,c_1909]) ).
tcf(c_1914,negated_conjecture,
( ~ subset(sK13,iPr_def_13)
| ( iPr_def_12 != sK13 ) ),
inference(demodulation,[status(thm)],[c_108,c_1911,c_1910]) ).
tcf(c_2934,plain,
! [X0: $i,X1: $i] :
( empty(power_set(X1))
| member(X0,power_set(X1))
| ~ ilf_type(X0,subset_type(X1)) ),
inference(superposition,[status(thm)],[c_1310,c_453]) ).
tcf(c_2935,plain,
! [X0: $i,X1: $i] :
( member(X0,power_set(X1))
| ~ ilf_type(X0,subset_type(X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2934,c_170]) ).
tcf(c_3130,plain,
! [X0: $i] :
( subset(X0,iPr_def_12)
| ~ subset(identity_relation_of(X0),sK14)
| ~ ilf_type(sK14,relation_type(sK12,sK13)) ),
inference(superposition,[status(thm)],[c_1910,c_718]) ).
tcf(c_3132,plain,
! [X0: $i] :
( subset(X0,iPr_def_12)
| ~ ilf_type(sK14,iPr_def_10)
| ~ subset(identity_relation_of(X0),sK14) ),
inference(light_normalisation,[status(thm)],[c_3130,c_1908]) ).
tcf(c_3133,plain,
! [X0: $i] :
( subset(X0,iPr_def_12)
| ~ subset(identity_relation_of(X0),sK14) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3132,c_1912]) ).
tcf(c_3173,plain,
( ilf_type(iPr_def_12,subset_type(sK13))
| ~ ilf_type(sK14,relation_type(sK12,sK13)) ),
inference(superposition,[status(thm)],[c_1910,c_1324]) ).
tcf(c_3175,plain,
( ilf_type(iPr_def_12,subset_type(sK13))
| ~ ilf_type(sK14,iPr_def_10) ),
inference(light_normalisation,[status(thm)],[c_3173,c_1908]) ).
tcf(c_3176,plain,
ilf_type(iPr_def_12,subset_type(sK13)),
inference(forward_subsumption_resolution,[status(thm)],[c_3175,c_1912]) ).
tcf(c_3181,plain,
member(iPr_def_12,power_set(sK13)),
inference(superposition,[status(thm)],[c_3176,c_2935]) ).
tcf(c_3191,plain,
( subset(sK13,iPr_def_12)
| ~ subset(iPr_def_11,sK14) ),
inference(superposition,[status(thm)],[c_1909,c_3133]) ).
tcf(c_3192,plain,
subset(sK13,iPr_def_12),
inference(forward_subsumption_resolution,[status(thm)],[c_3191,c_1913]) ).
tcf(c_3196,plain,
( ( sK13 = iPr_def_12 )
| ~ subset(iPr_def_12,sK13) ),
inference(superposition,[status(thm)],[c_3192,c_434]) ).
tcf(c_3272,plain,
! [X0: $i] :
( subset(X0,iPr_def_13)
| ~ subset(identity_relation_of(X0),sK14)
| ~ ilf_type(sK14,relation_type(sK12,sK13)) ),
inference(superposition,[status(thm)],[c_1911,c_734]) ).
tcf(c_3274,plain,
! [X0: $i] :
( subset(X0,iPr_def_13)
| ~ ilf_type(sK14,iPr_def_10)
| ~ subset(identity_relation_of(X0),sK14) ),
inference(light_normalisation,[status(thm)],[c_3272,c_1908]) ).
tcf(c_3275,plain,
! [X0: $i] :
( subset(X0,iPr_def_13)
| ~ subset(identity_relation_of(X0),sK14) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3274,c_1912]) ).
tcf(c_3385,plain,
( subset(sK13,iPr_def_13)
| ~ subset(iPr_def_11,sK14) ),
inference(superposition,[status(thm)],[c_1909,c_3275]) ).
tcf(c_3386,plain,
subset(sK13,iPr_def_13),
inference(forward_subsumption_resolution,[status(thm)],[c_3385,c_1913]) ).
tcf(c_3389,plain,
sK13 != iPr_def_12,
inference(backward_subsumption_resolution,[status(thm)],[c_1914,c_3386]) ).
tcf(c_3391,plain,
~ subset(iPr_def_12,sK13),
inference(backward_subsumption_resolution,[status(thm)],[c_3196,c_3389]) ).
tcf(c_4224,plain,
! [X0: $i] :
( member(X0,sK13)
| ~ member(X0,iPr_def_12) ),
inference(superposition,[status(thm)],[c_3181,c_687]) ).
tcf(c_4384,plain,
! [X0: $i] :
( subset(iPr_def_12,X0)
| member(sK1(iPr_def_12,X0),sK13) ),
inference(superposition,[status(thm)],[c_1315,c_4224]) ).
tcf(c_5201,plain,
subset(iPr_def_12,sK13),
inference(superposition,[status(thm)],[c_4384,c_1313]) ).
tcf(c_5204,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_5201,c_3391]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET669+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.36 % Computer : n016.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 11:41:57 UTC 2026
% 0.03/0.37 % CPUTime :
% 0.03/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.03/0.40 Running first-order theorem proving
% 0.03/0.41 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
% 0.03/0.42
% 0.03/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.03/0.42
% 0.03/0.42 % Detected problem language: tptp
% 0.03/0.43 % Proving...
% 3.00/1.20 % SZS status Started for theBenchmark.p
% 3.00/1.20 % SZS status Theorem for theBenchmark.p
% 3.00/1.20
% 3.00/1.20 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.00/1.20
% 3.00/1.20 % ------ iProver source info
% 3.00/1.20
% 3.00/1.20 % git: date: 2026-07-19 20:42:38 +0200
% 3.00/1.20 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.00/1.20 % git: non_committed_changes: false
% 3.00/1.20
% 3.00/1.20 % ------ Parsing...
% 3.00/1.20 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.00/1.20
% 3.00/1.20 % ------ 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 %
% 3.00/1.20
% 3.00/1.20 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.00/1.20
% 3.00/1.20 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.00/1.20 % ------ Proving...
% 3.00/1.20 % ------ Problem Properties
% 3.00/1.20
% 3.00/1.20 %
% 3.00/1.20 % clauses 48
% 3.00/1.20 % conjectures 3
% 3.00/1.20 % EPR 12
% 3.00/1.20 % Horn 41
% 3.00/1.20 % unary 13
% 3.00/1.20 % binary 26
% 3.00/1.20 % lits 94
% 3.00/1.20 % lits eq 11
% 3.00/1.20 % fd_pure 0
% 3.00/1.20 % fd_pseudo 0
% 3.00/1.20 % fd_cond 0
% 3.00/1.20 % fd_pseudo_cond 2
% 3.00/1.20 % AC symbols 0
% 3.00/1.20
% 3.00/1.20 % ------ Schedule dynamic 5 is on
% 3.00/1.20
% 3.00/1.20 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.00/1.20
% 3.00/1.20
% 3.00/1.20 % ------
% 3.00/1.20 % Current options:
% 3.00/1.20 % ------
% 3.00/1.20
% 3.00/1.20
% 3.00/1.20 %
% 3.00/1.20
% 3.00/1.20 % ------ Proving...
% 3.00/1.20 %
% 3.00/1.20
% 3.00/1.20 % SZS status Theorem for theBenchmark.p
% 3.00/1.20
% 3.00/1.20 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.00/1.20
% 3.00/1.20
%------------------------------------------------------------------------------