%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET666+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 : n001.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 3.09s 6.49s
% Output : CNFRefutation 3.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 12
% Syntax : Number of formulae : 101 ( 16 unt; 2 def)
% Number of atoms : 383 ( 2 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 466 ( 197 ~; 199 |; 32 &)
% ( 15 <=>; 23 =>; 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 : 8 ( 6 usr; 3 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 2 con; 0-2 aty)
% Number of variables : 197 ( 0 sgn 190 !; 7 ?; 91 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( ! [X3] :
( ilf_type(X3,relation_type(X0,X1))
=> ilf_type(X3,subset_type(cross_product(X0,X1))) )
& ! [X2] :
( ilf_type(X2,subset_type(cross_product(X0,X1)))
=> ilf_type(X2,relation_type(X0,X1)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p1) ).
fof(f3,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> subset(identity_relation_of(X0),cross_product(X0,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p3) ).
fof(f6,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( ilf_type(X1,identity_relation_of_type(X0))
<=> ilf_type(X1,relation_type(X0,X0)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p6) ).
fof(f12,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',p12) ).
fof(f14,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',p14) ).
fof(f16,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',p16) ).
fof(f18,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',p18) ).
fof(f22,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ( empty(X0)
<=> ! [X1] :
( ilf_type(X1,set_type)
=> ~ member(X1,X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p22) ).
fof(f24,axiom,
! [X0] : ilf_type(X0,set_type),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p24) ).
fof(f25,conjecture,
! [X0] :
( ilf_type(X0,set_type)
=> ilf_type(identity_relation_of(X0),identity_relation_of_type(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_relset_1_29) ).
fof(f26,negated_conjecture,
~ ! [X0] :
( ilf_type(X0,set_type)
=> ilf_type(identity_relation_of(X0),identity_relation_of_type(X0)) ),
inference(negated_conjecture,[status(cth)],[f25]) ).
fof(f27,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ( ! [X3] :
( ~ ilf_type(X3,relation_type(X0,X1))
| ilf_type(X3,subset_type(cross_product(X0,X1))) )
& ! [X2] :
( ~ ilf_type(X2,subset_type(cross_product(X0,X1)))
| ilf_type(X2,relation_type(X0,X1)) ) ) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f29,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| subset(identity_relation_of(X0),cross_product(X0,X0)) ),
inference(ennf_transformation,[],[f3]) ).
fof(f32,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ( ilf_type(X1,identity_relation_of_type(X0))
<=> ilf_type(X1,relation_type(X0,X0)) ) ) ),
inference(ennf_transformation,[],[f6]) ).
fof(f37,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,[],[f12]) ).
fof(f39,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,[],[f14]) ).
fof(f40,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,[],[f39]) ).
fof(f42,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,[],[f16]) ).
fof(f43,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,[],[f42]) ).
fof(f45,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,[],[f18]) ).
fof(f46,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,[],[f45]) ).
fof(f52,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ( empty(X0)
<=> ! [X1] :
( ~ ilf_type(X1,set_type)
| ~ member(X1,X0) ) ) ),
inference(ennf_transformation,[],[f22]) ).
fof(f55,plain,
? [X0] :
( ilf_type(X0,set_type)
& ~ ilf_type(identity_relation_of(X0),identity_relation_of_type(X0)) ),
inference(ennf_transformation,[],[f26]) ).
fof(f59,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ( ( ~ ilf_type(X1,identity_relation_of_type(X0))
| ilf_type(X1,relation_type(X0,X0)) )
& ( ~ ilf_type(X1,relation_type(X0,X0))
| ilf_type(X1,identity_relation_of_type(X0)) ) ) ) ),
inference(nnf_transformation,[],[f32]) ).
fof(f64,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,[],[f37]) ).
fof(f66,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,[],[f40]) ).
fof(f67,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,[],[f66]) ).
fof(f68,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(sK4(X0,X1),set_type)
& member(sK4(X0,X1),X0)
& ~ member(sK4(X0,X1),X1) )
| subset(X0,X1) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X2,sK4(X0,X1))],[f67]) ).
fof(f69,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,[],[f43]) ).
fof(f70,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,[],[f69]) ).
fof(f71,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(sK5(X0,X1),set_type)
& member(sK5(X0,X1),X0)
& ~ member(sK5(X0,X1),X1) )
| member(X0,power_set(X1)) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(X2,sK5(X0,X1))],[f70]) ).
fof(f72,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,[],[f46]) ).
fof(f77,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ( ( ~ empty(X0)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ~ member(X1,X0) ) )
& ( ? [X1] :
( ilf_type(X1,set_type)
& member(X1,X0) )
| empty(X0) ) ) ),
inference(nnf_transformation,[],[f52]) ).
fof(f78,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ( ( ~ empty(X0)
| ! [X2] :
( ~ ilf_type(X2,set_type)
| ~ member(X2,X0) ) )
& ( ? [X1] :
( ilf_type(X1,set_type)
& member(X1,X0) )
| empty(X0) ) ) ),
inference(rectify,[],[f77]) ).
fof(f79,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ( ( ~ empty(X0)
| ! [X2] :
( ~ ilf_type(X2,set_type)
| ~ member(X2,X0) ) )
& ( ( ilf_type(sK10(X0),set_type)
& member(sK10(X0),X0) )
| empty(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(X1,sK10(X0))],[f78]) ).
fof(f80,plain,
( ilf_type(sK11,set_type)
& ~ ilf_type(identity_relation_of(sK11),identity_relation_of_type(sK11)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(X0,sK11)],[f55]) ).
fof(f82,plain,
! [X2,X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,subset_type(cross_product(X0,X1)))
| ilf_type(X2,relation_type(X0,X1)) ),
inference(cnf_transformation,[],[f27]) ).
fof(f84,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| subset(identity_relation_of(X0),cross_product(X0,X0)) ),
inference(cnf_transformation,[],[f29]) ).
fof(f90,plain,
! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X1,relation_type(X0,X0))
| ilf_type(X1,identity_relation_of_type(X0)) ),
inference(cnf_transformation,[],[f59]) ).
fof(f99,plain,
! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X1,member_type(power_set(X0)))
| ilf_type(X1,subset_type(X0)) ),
inference(cnf_transformation,[],[f64]) ).
fof(f101,plain,
! [X3,X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ subset(X0,X1)
| ~ ilf_type(X3,set_type)
| ~ member(X3,X0)
| member(X3,X1) ),
inference(cnf_transformation,[],[f68]) ).
fof(f108,plain,
! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| member(sK5(X0,X1),X0)
| member(X0,power_set(X1)) ),
inference(cnf_transformation,[],[f71]) ).
fof(f109,plain,
! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ member(sK5(X0,X1),X1)
| member(X0,power_set(X1)) ),
inference(cnf_transformation,[],[f71]) ).
fof(f113,plain,
! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| empty(X1)
| ~ member(X0,X1)
| ilf_type(X0,member_type(X1)) ),
inference(cnf_transformation,[],[f72]) ).
fof(f122,plain,
! [X2,X0] :
( ~ ilf_type(X0,set_type)
| ~ empty(X0)
| ~ ilf_type(X2,set_type)
| ~ member(X2,X0) ),
inference(cnf_transformation,[],[f79]) ).
fof(f126,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[],[f24]) ).
fof(f128,plain,
~ ilf_type(identity_relation_of(sK11),identity_relation_of_type(sK11)),
inference(cnf_transformation,[],[f80]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i,X2: $i] :
( ilf_type(X0,relation_type(X1,X2))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,subset_type(cross_product(X1,X2))) ),
inference(cnf_transformation,[],[f82]) ).
tcf(c_52,plain,
! [X0: $i] :
( subset(identity_relation_of(X0),cross_product(X0,X0))
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f84]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i] :
( ilf_type(X0,identity_relation_of_type(X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X0,relation_type(X1,X1)) ),
inference(cnf_transformation,[],[f90]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i] :
( ilf_type(X0,subset_type(X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X0,member_type(power_set(X1))) ),
inference(cnf_transformation,[],[f99]) ).
tcf(c_71,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)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f101]) ).
tcf(c_73,plain,
! [X0: $i,X1: $i] :
( member(X0,power_set(X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| ~ member(sK5(X0,X1),X1) ),
inference(cnf_transformation,[],[f109]) ).
tcf(c_74,plain,
! [X0: $i,X1: $i] :
( member(X0,power_set(X1))
| member(sK5(X0,X1),X0)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f108]) ).
tcf(c_79,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| ilf_type(X0,member_type(X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f113]) ).
tcf(c_91,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f122]) ).
tcf(c_93,plain,
! [X0: $i] : ilf_type(X0,set_type),
inference(cnf_transformation,[],[f126]) ).
tcf(c_94,negated_conjecture,
~ ilf_type(identity_relation_of(sK11),identity_relation_of_type(sK11)),
inference(cnf_transformation,[],[f128]) ).
tcf(c_174,plain,
! [X0: $i] : subset(identity_relation_of(X0),cross_product(X0,X0)),
inference(global_subsumption_just,[status(thm)],[c_52,c_93,c_52]) ).
tcf(c_210,plain,
! [X0: $i,X1: $i] :
( member(X0,power_set(X1))
| member(sK5(X0,X1),X0)
| ~ ilf_type(X1,set_type) ),
inference(global_subsumption_just,[status(thm)],[c_74,c_93,c_74]) ).
tcf(c_211,plain,
! [X0: $i,X1: $i] :
( member(X1,power_set(X0))
| member(sK5(X1,X0),X1)
| ~ ilf_type(X0,set_type) ),
inference(renaming,[status(thm)],[c_210]) ).
tcf(c_212,plain,
! [X0: $i,X1: $i] :
( member(X1,power_set(X0))
| member(sK5(X1,X0),X1) ),
inference(global_subsumption_just,[status(thm)],[c_211,c_93,c_211]) ).
tcf(c_213,plain,
! [X0: $i,X1: $i] :
( member(X0,power_set(X1))
| member(sK5(X0,X1),X0) ),
inference(renaming,[status(thm)],[c_212]) ).
tcf(c_219,plain,
! [X0: $i,X1: $i] :
( ~ member(X0,X1)
| ~ ilf_type(X1,set_type)
| ilf_type(X0,member_type(X1)) ),
inference(global_subsumption_just,[status(thm)],[c_79,c_93,c_91,c_79]) ).
tcf(c_220,plain,
! [X0: $i,X1: $i] :
( ilf_type(X0,member_type(X1))
| ~ ilf_type(X1,set_type)
| ~ member(X0,X1) ),
inference(renaming,[status(thm)],[c_219]) ).
tcf(c_222,plain,
! [X0: $i,X1: $i] :
( member(X0,power_set(X1))
| ~ ilf_type(X1,set_type)
| ~ member(sK5(X0,X1),X1) ),
inference(global_subsumption_just,[status(thm)],[c_73,c_93,c_73]) ).
tcf(c_226,plain,
! [X0: $i,X1: $i] :
( ilf_type(X0,subset_type(X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,member_type(power_set(X1))) ),
inference(global_subsumption_just,[status(thm)],[c_65,c_93,c_65]) ).
tcf(c_230,plain,
! [X0: $i,X1: $i] :
( ilf_type(X0,identity_relation_of_type(X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,relation_type(X1,X1)) ),
inference(global_subsumption_just,[status(thm)],[c_57,c_93,c_57]) ).
tcf(c_244,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X2,X1)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ subset(X0,X1)
| ~ member(X2,X0) ),
inference(global_subsumption_just,[status(thm)],[c_71,c_93,c_71]) ).
tcf(c_245,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X2,X1)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ member(X2,X0)
| ~ subset(X0,X1) ),
inference(renaming,[status(thm)],[c_244]) ).
tcf(c_374,plain,
! [X0: $i,X1: $i,X2: $i] :
( ilf_type(X0,relation_type(X1,X2))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X0,subset_type(cross_product(X1,X2))) ),
inference(backward_subsumption_resolution,[status(thm)],[c_49,c_93]) ).
tcf(c_376,plain,
! [X0: $i,X1: $i] :
( ilf_type(X0,member_type(X1))
| ~ member(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[c_220,c_93]) ).
tcf(c_378,plain,
! [X0: $i,X1: $i] :
( member(X0,power_set(X1))
| ~ member(sK5(X0,X1),X1) ),
inference(backward_subsumption_resolution,[status(thm)],[c_222,c_93]) ).
tcf(c_379,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X2,X1)
| ~ ilf_type(X2,set_type)
| ~ member(X2,X0)
| ~ subset(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[c_245,c_93]) ).
tcf(c_381,plain,
! [X0: $i,X1: $i] :
( ilf_type(X0,subset_type(X1))
| ~ ilf_type(X0,member_type(power_set(X1))) ),
inference(backward_subsumption_resolution,[status(thm)],[c_226,c_93]) ).
tcf(c_384,plain,
! [X0: $i,X1: $i] :
( ilf_type(X0,identity_relation_of_type(X1))
| ~ ilf_type(X0,relation_type(X1,X1)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_230,c_93]) ).
tcf(c_550,plain,
! [X0: $i,X1: $i,X2: $i] :
( ilf_type(X0,relation_type(X1,X2))
| ~ ilf_type(X0,subset_type(cross_product(X1,X2))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_374,c_93]) ).
tcf(c_562,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subset(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_379,c_93]) ).
tcf(c_959,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ilf_type(X0,subset_type(cross_product(X1,X2)))
| ilf_type(X0,relation_type(X1,X2)) ),
inference(prop_impl_just,[status(thm)],[c_550]) ).
tcf(c_960,plain,
! [X0: $i,X1: $i,X2: $i] :
( ilf_type(X0,relation_type(X1,X2))
| ~ ilf_type(X0,subset_type(cross_product(X1,X2))) ),
inference(renaming,[status(thm)],[c_959]) ).
tcf(c_963,plain,
! [X0: $i,X1: $i] :
( ~ ilf_type(X0,relation_type(X1,X1))
| ilf_type(X0,identity_relation_of_type(X1)) ),
inference(prop_impl_just,[status(thm)],[c_384]) ).
tcf(c_964,plain,
! [X0: $i,X1: $i] :
( ilf_type(X0,identity_relation_of_type(X1))
| ~ ilf_type(X0,relation_type(X1,X1)) ),
inference(renaming,[status(thm)],[c_963]) ).
tcf(c_971,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_381]) ).
tcf(c_972,plain,
! [X0: $i,X1: $i] :
( ilf_type(X0,subset_type(X1))
| ~ ilf_type(X0,member_type(power_set(X1))) ),
inference(renaming,[status(thm)],[c_971]) ).
tcf(c_979,plain,
! [X0: $i,X1: $i] :
( ilf_type(X0,member_type(X1))
| ~ member(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_376]) ).
tcf(c_999,plain,
! [X0: $i,X1: $i] :
( member(X0,power_set(X1))
| ~ member(sK5(X0,X1),X1) ),
inference(prop_impl_just,[status(thm)],[c_378]) ).
tcf(c_1003,plain,
! [X0: $i,X1: $i] :
( member(sK5(X0,X1),X0)
| member(X0,power_set(X1)) ),
inference(prop_impl_just,[status(thm)],[c_213]) ).
tcf(c_1004,plain,
! [X0: $i,X1: $i] :
( member(X0,power_set(X1))
| member(sK5(X0,X1),X0) ),
inference(renaming,[status(thm)],[c_1003]) ).
tcf(c_1593,definition,
iPr_def_10 = identity_relation_of(sK11),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_1594,definition,
iPr_def_11 = identity_relation_of_type(sK11),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_1595,negated_conjecture,
~ ilf_type(iPr_def_10,iPr_def_11),
inference(demodulation,[status(thm)],[c_94,c_1594,c_1593]) ).
tcf(c_2364,plain,
subset(iPr_def_10,cross_product(sK11,sK11)),
inference(superposition,[status(thm)],[c_1593,c_174]) ).
tcf(c_2610,plain,
! [X0: $i,X1: $i] :
( ilf_type(X0,subset_type(X1))
| ~ member(X0,power_set(X1)) ),
inference(superposition,[status(thm)],[c_979,c_972]) ).
tcf(c_2970,plain,
! [X0: $i] :
( member(X0,cross_product(sK11,sK11))
| ~ member(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_2364,c_562]) ).
tcf(c_3168,plain,
! [X0: $i] :
( member(X0,power_set(cross_product(sK11,sK11)))
| ~ member(sK5(X0,cross_product(sK11,sK11)),iPr_def_10) ),
inference(superposition,[status(thm)],[c_2970,c_999]) ).
tcf(c_4301,plain,
member(iPr_def_10,power_set(cross_product(sK11,sK11))),
inference(superposition,[status(thm)],[c_1004,c_3168]) ).
tcf(c_4306,plain,
ilf_type(iPr_def_10,subset_type(cross_product(sK11,sK11))),
inference(superposition,[status(thm)],[c_4301,c_2610]) ).
tcf(c_4309,plain,
ilf_type(iPr_def_10,relation_type(sK11,sK11)),
inference(superposition,[status(thm)],[c_4306,c_960]) ).
tcf(c_4313,plain,
ilf_type(iPr_def_10,identity_relation_of_type(sK11)),
inference(superposition,[status(thm)],[c_4309,c_964]) ).
tcf(c_4314,plain,
ilf_type(iPr_def_10,iPr_def_11),
inference(light_normalisation,[status(thm)],[c_4313,c_1594]) ).
tcf(c_4315,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_4314,c_1595]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET666+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/5.67 % Computer : n001.cluster.edu
% 0.11/5.67 % Model : x86_64 x86_64
% 0.11/5.67 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.67 % Memory : 8046.5625MB
% 0.11/5.67 % OS : Linux 6.8.0-71-generic
% 0.11/5.67 % CPULimit : 300
% 0.11/5.67 % WCLimit : 300
% 0.11/5.67 % DateTime : Thu Sep 24 11:42:28 UTC 2026
% 0.11/5.67 % CPUTime :
% 0.11/5.67 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.16/5.71 Running first-order theorem proving
% 0.16/5.71 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
% 0.16/5.72
% 0.16/5.72 % ======== iProver multi-core TPTP/SMT =========
% 0.16/5.72
% 0.16/5.72 % Detected problem language: tptp
% 0.16/5.73 % Proving...
% 3.09/6.49 % SZS status Started for theBenchmark.p
% 3.09/6.49 % SZS status Theorem for theBenchmark.p
% 3.09/6.49
% 3.09/6.49 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.09/6.49
% 3.09/6.49 % ------ iProver source info
% 3.09/6.49
% 3.09/6.49 % git: date: 2026-07-19 20:42:38 +0200
% 3.09/6.49 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.09/6.49 % git: non_committed_changes: false
% 3.09/6.49
% 3.09/6.49 % ------ Parsing...
% 3.09/6.49 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.09/6.49
% 3.09/6.49 % ------ 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 %
% 3.09/6.49
% 3.09/6.49 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.09/6.49
% 3.09/6.49 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.09/6.49 % ------ Proving...
% 3.09/6.49 % ------ Problem Properties
% 3.09/6.49
% 3.09/6.49 %
% 3.09/6.49 % clauses 39
% 3.09/6.49 % conjectures 1
% 3.09/6.49 % EPR 9
% 3.09/6.49 % Horn 33
% 3.09/6.49 % unary 12
% 3.09/6.49 % binary 23
% 3.09/6.49 % lits 70
% 3.09/6.49 % lits eq 5
% 3.09/6.49 % fd_pure 0
% 3.09/6.49 % fd_pseudo 0
% 3.09/6.49 % fd_cond 0
% 3.09/6.49 % fd_pseudo_cond 1
% 3.09/6.49 % AC symbols 0
% 3.09/6.49
% 3.09/6.49 % ------ Schedule dynamic 5 is on
% 3.09/6.49
% 3.09/6.49 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.09/6.49
% 3.09/6.49
% 3.09/6.49 % ------
% 3.09/6.49 % Current options:
% 3.09/6.49 % ------
% 3.09/6.49
% 3.09/6.49
% 3.09/6.49 %
% 3.09/6.49
% 3.09/6.49 % ------ Proving...
% 3.09/6.49 %
% 3.09/6.49
% 3.09/6.49 % SZS status Theorem for theBenchmark.p
% 3.09/6.49
% 3.09/6.49 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.09/6.49
% 3.09/6.49
%------------------------------------------------------------------------------