%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET646+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 : n002.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 02:47:40 PM UTC 2026
% Result : Theorem 10.66s 22.31s
% Output : CNFRefutation 10.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 10
% Syntax : Number of formulae : 107 ( 10 unt; 0 def)
% Number of atoms : 464 ( 0 equ)
% Maximal formula atoms : 10 ( 4 avg)
% Number of connectives : 604 ( 247 ~; 250 |; 56 &)
% ( 17 <=>; 34 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 7 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 5 con; 0-2 aty)
% Number of variables : 240 ( 0 sgn 226 !; 14 ?; 104 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( subset(singleton(X0),X1)
<=> member(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,set_type)
=> ( member(ordered_pair(X0,X1),cross_product(X2,X3))
<=> ( member(X1,X3)
& member(X0,X2) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2) ).
fof(f3,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',p3) ).
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(f15,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',p15) ).
fof(f17,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',p17) ).
fof(f19,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',p19) ).
fof(f21,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',p21) ).
fof(f25,axiom,
! [X0] : ilf_type(X0,set_type),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p25) ).
fof(f26,conjecture,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,set_type)
=> ( ( member(X3,X1)
& member(X2,X0) )
=> ilf_type(singleton(ordered_pair(X2,X3)),relation_type(X0,X1)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_relset_1_8) ).
fof(f27,negated_conjecture,
~ ! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,set_type)
=> ( ( member(X3,X1)
& member(X2,X0) )
=> ilf_type(singleton(ordered_pair(X2,X3)),relation_type(X0,X1)) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f26]) ).
fof(f28,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ( subset(singleton(X0),X1)
<=> member(X0,X1) ) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f29,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ! [X2] :
( ~ ilf_type(X2,set_type)
| ! [X3] :
( ~ ilf_type(X3,set_type)
| ( member(ordered_pair(X0,X1),cross_product(X2,X3))
<=> ( member(X1,X3)
& member(X0,X2) ) ) ) ) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f30,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,[],[f3]) ).
fof(f39,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(f42,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,[],[f15]) ).
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(flattening,[],[f42]) ).
fof(f45,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,[],[f17]) ).
fof(f46,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,[],[f45]) ).
fof(f48,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,[],[f19]) ).
fof(f49,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,[],[f48]) ).
fof(f52,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ( empty(X0)
<=> ! [X1] :
( ~ ilf_type(X1,set_type)
| ~ member(X1,X0) ) ) ),
inference(ennf_transformation,[],[f21]) ).
fof(f58,plain,
? [X0] :
( ilf_type(X0,set_type)
& ? [X1] :
( ilf_type(X1,set_type)
& ? [X2] :
( ilf_type(X2,set_type)
& ? [X3] :
( ilf_type(X3,set_type)
& member(X3,X1)
& member(X2,X0)
& ~ ilf_type(singleton(ordered_pair(X2,X3)),relation_type(X0,X1)) ) ) ) ),
inference(ennf_transformation,[],[f27]) ).
fof(f59,plain,
? [X0] :
( ilf_type(X0,set_type)
& ? [X1] :
( ilf_type(X1,set_type)
& ? [X2] :
( ilf_type(X2,set_type)
& ? [X3] :
( ilf_type(X3,set_type)
& member(X3,X1)
& member(X2,X0)
& ~ ilf_type(singleton(ordered_pair(X2,X3)),relation_type(X0,X1)) ) ) ) ),
inference(flattening,[],[f58]) ).
fof(f60,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ( ( ~ subset(singleton(X0),X1)
| member(X0,X1) )
& ( ~ member(X0,X1)
| subset(singleton(X0),X1) ) ) ) ),
inference(nnf_transformation,[],[f28]) ).
fof(f61,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ! [X2] :
( ~ ilf_type(X2,set_type)
| ! [X3] :
( ~ ilf_type(X3,set_type)
| ( ( ~ member(ordered_pair(X0,X1),cross_product(X2,X3))
| ( member(X1,X3)
& member(X0,X2) ) )
& ( ~ member(X1,X3)
| ~ member(X0,X2)
| member(ordered_pair(X0,X1),cross_product(X2,X3)) ) ) ) ) ) ),
inference(nnf_transformation,[],[f29]) ).
fof(f62,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ! [X2] :
( ~ ilf_type(X2,set_type)
| ! [X3] :
( ~ ilf_type(X3,set_type)
| ( ( ~ member(ordered_pair(X0,X1),cross_product(X2,X3))
| ( member(X1,X3)
& member(X0,X2) ) )
& ( ~ member(X1,X3)
| ~ member(X0,X2)
| member(ordered_pair(X0,X1),cross_product(X2,X3)) ) ) ) ) ) ),
inference(flattening,[],[f61]) ).
fof(f69,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,[],[f39]) ).
fof(f75,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,[],[f43]) ).
fof(f76,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,[],[f75]) ).
fof(f77,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))],[f76]) ).
fof(f78,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,[],[f46]) ).
fof(f79,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,[],[f78]) ).
fof(f80,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))],[f79]) ).
fof(f81,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,[],[f49]) ).
fof(f83,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(f84,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,[],[f83]) ).
fof(f85,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ( ( ~ empty(X0)
| ! [X2] :
( ~ ilf_type(X2,set_type)
| ~ member(X2,X0) ) )
& ( ( ilf_type(sK7(X0),set_type)
& member(sK7(X0),X0) )
| empty(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(X1,sK7(X0))],[f84]) ).
fof(f89,plain,
( ilf_type(sK11,set_type)
& ilf_type(sK12,set_type)
& ilf_type(sK13,set_type)
& ilf_type(sK14,set_type)
& member(sK14,sK12)
& member(sK13,sK11)
& ~ ilf_type(singleton(ordered_pair(sK13,sK14)),relation_type(sK11,sK12)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11,sK12,sK13,sK14]),skolemize(X0,sK11),skolemize(X1,sK12),skolemize(X2,sK13),skolemize(X3,sK14)],[f59]) ).
fof(f91,plain,
! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ member(X0,X1)
| subset(singleton(X0),X1) ),
inference(cnf_transformation,[],[f60]) ).
fof(f94,plain,
! [X2,X3,X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,set_type)
| ~ member(X1,X3)
| ~ member(X0,X2)
| member(ordered_pair(X0,X1),cross_product(X2,X3)) ),
inference(cnf_transformation,[],[f62]) ).
fof(f96,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,[],[f30]) ).
fof(f111,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,[],[f69]) ).
fof(f118,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,[],[f77]) ).
fof(f125,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,[],[f80]) ).
fof(f126,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,[],[f80]) ).
fof(f130,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,[],[f81]) ).
fof(f132,plain,
! [X2,X0] :
( ~ ilf_type(X0,set_type)
| ~ empty(X0)
| ~ ilf_type(X2,set_type)
| ~ member(X2,X0) ),
inference(cnf_transformation,[],[f85]) ).
fof(f143,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[],[f25]) ).
fof(f148,plain,
member(sK14,sK12),
inference(cnf_transformation,[],[f89]) ).
fof(f149,plain,
member(sK13,sK11),
inference(cnf_transformation,[],[f89]) ).
fof(f150,plain,
~ ilf_type(singleton(ordered_pair(sK13,sK14)),relation_type(sK11,sK12)),
inference(cnf_transformation,[],[f89]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] :
( subset(singleton(X0),X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f91]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(ordered_pair(X0,X2),cross_product(X1,X3))
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| ~ member(X2,X3)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f94]) ).
tcf(c_54,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,[],[f96]) ).
tcf(c_69,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,[],[f111]) ).
tcf(c_80,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,[],[f118]) ).
tcf(c_82,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,[],[f126]) ).
tcf(c_83,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,[],[f125]) ).
tcf(c_88,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,[],[f130]) ).
tcf(c_93,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f132]) ).
tcf(c_102,plain,
! [X0: $i] : ilf_type(X0,set_type),
inference(cnf_transformation,[],[f143]) ).
tcf(c_103,negated_conjecture,
~ ilf_type(singleton(ordered_pair(sK13,sK14)),relation_type(sK11,sK12)),
inference(cnf_transformation,[],[f150]) ).
tcf(c_104,negated_conjecture,
member(sK13,sK11),
inference(cnf_transformation,[],[f149]) ).
tcf(c_105,negated_conjecture,
member(sK14,sK12),
inference(cnf_transformation,[],[f148]) ).
tcf(c_226,plain,
! [X0: $i,X1: $i] :
( subset(singleton(X0),X1)
| ~ ilf_type(X1,set_type)
| ~ member(X0,X1) ),
inference(global_subsumption_just,[status(thm)],[c_49,c_102,c_49]) ).
tcf(c_233,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_83,c_102,c_83]) ).
tcf(c_234,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_233]) ).
tcf(c_235,plain,
! [X0: $i,X1: $i] :
( member(X1,power_set(X0))
| member(sK5(X1,X0),X1) ),
inference(global_subsumption_just,[status(thm)],[c_234,c_102,c_234]) ).
tcf(c_236,plain,
! [X0: $i,X1: $i] :
( member(X0,power_set(X1))
| member(sK5(X0,X1),X0) ),
inference(renaming,[status(thm)],[c_235]) ).
tcf(c_253,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_88,c_102,c_93,c_88]) ).
tcf(c_254,plain,
! [X0: $i,X1: $i] :
( ilf_type(X0,member_type(X1))
| ~ ilf_type(X1,set_type)
| ~ member(X0,X1) ),
inference(renaming,[status(thm)],[c_253]) ).
tcf(c_256,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_82,c_102,c_82]) ).
tcf(c_260,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_69,c_102,c_69]) ).
tcf(c_282,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_80,c_102,c_80]) ).
tcf(c_283,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_282]) ).
tcf(c_303,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(ordered_pair(X0,X2),cross_product(X1,X3))
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ member(X0,X1)
| ~ member(X2,X3) ),
inference(global_subsumption_just,[status(thm)],[c_51,c_102,c_51]) ).
tcf(c_304,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(ordered_pair(X0,X2),cross_product(X1,X3))
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ member(X2,X3)
| ~ member(X0,X1) ),
inference(renaming,[status(thm)],[c_303]) ).
tcf(c_324,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_54,c_102]) ).
tcf(c_327,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_260,c_102]) ).
tcf(c_334,plain,
! [X0: $i,X1: $i] :
( ilf_type(X0,member_type(X1))
| ~ member(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[c_254,c_102]) ).
tcf(c_335,plain,
! [X0: $i,X1: $i] :
( subset(singleton(X0),X1)
| ~ member(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[c_226,c_102]) ).
tcf(c_336,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_283,c_102]) ).
tcf(c_339,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(ordered_pair(X0,X2),cross_product(X1,X3))
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type)
| ~ member(X2,X3)
| ~ member(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[c_304,c_102]) ).
tcf(c_340,plain,
! [X0: $i,X1: $i] :
( member(X0,power_set(X1))
| ~ member(sK5(X0,X1),X1) ),
inference(backward_subsumption_resolution,[status(thm)],[c_256,c_102]) ).
tcf(c_483,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_324,c_102]) ).
tcf(c_506,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subset(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_336,c_102]) ).
tcf(c_585,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(ordered_pair(X0,X2),cross_product(X1,X3))
| ~ member(X2,X3)
| ~ member(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_339,c_102,c_102]) ).
tcf(c_840,plain,
! [X0: $i,X1: $i] :
( subset(singleton(X0),X1)
| ~ member(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_335]) ).
tcf(c_842,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_483]) ).
tcf(c_843,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_842]) ).
tcf(c_846,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_327]) ).
tcf(c_847,plain,
! [X0: $i,X1: $i] :
( ilf_type(X0,subset_type(X1))
| ~ ilf_type(X0,member_type(power_set(X1))) ),
inference(renaming,[status(thm)],[c_846]) ).
tcf(c_850,plain,
! [X0: $i,X1: $i] :
( ilf_type(X0,member_type(X1))
| ~ member(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_334]) ).
tcf(c_872,plain,
! [X0: $i,X1: $i] :
( member(X0,power_set(X1))
| ~ member(sK5(X0,X1),X1) ),
inference(prop_impl_just,[status(thm)],[c_340]) ).
tcf(c_876,plain,
! [X0: $i,X1: $i] :
( member(sK5(X0,X1),X0)
| member(X0,power_set(X1)) ),
inference(prop_impl_just,[status(thm)],[c_236]) ).
tcf(c_877,plain,
! [X0: $i,X1: $i] :
( member(X0,power_set(X1))
| member(sK5(X0,X1),X0) ),
inference(renaming,[status(thm)],[c_876]) ).
tcf(c_2181,plain,
( ilf_type(singleton(ordered_pair(sK13,sK14)),relation_type(sK11,sK12))
| ~ ilf_type(singleton(ordered_pair(sK13,sK14)),subset_type(cross_product(sK11,sK12))) ),
inference(instantiation,[status(thm)],[c_843]) ).
tcf(c_2189,plain,
( ilf_type(singleton(ordered_pair(sK13,sK14)),subset_type(cross_product(sK11,sK12)))
| ~ ilf_type(singleton(ordered_pair(sK13,sK14)),member_type(power_set(cross_product(sK11,sK12)))) ),
inference(instantiation,[status(thm)],[c_847]) ).
tcf(c_2206,plain,
( ilf_type(singleton(ordered_pair(sK13,sK14)),member_type(power_set(cross_product(sK11,sK12))))
| ~ member(singleton(ordered_pair(sK13,sK14)),power_set(cross_product(sK11,sK12))) ),
inference(instantiation,[status(thm)],[c_850]) ).
tcf(c_2288,plain,
( member(singleton(ordered_pair(sK13,sK14)),power_set(cross_product(sK11,sK12)))
| ~ member(sK5(singleton(ordered_pair(sK13,sK14)),cross_product(sK11,sK12)),cross_product(sK11,sK12)) ),
inference(instantiation,[status(thm)],[c_872]) ).
tcf(c_2289,plain,
( member(singleton(ordered_pair(sK13,sK14)),power_set(cross_product(sK11,sK12)))
| member(sK5(singleton(ordered_pair(sK13,sK14)),cross_product(sK11,sK12)),singleton(ordered_pair(sK13,sK14))) ),
inference(instantiation,[status(thm)],[c_877]) ).
tcf(c_2689,plain,
! [X0: $i] :
( member(sK5(singleton(ordered_pair(sK13,sK14)),cross_product(sK11,sK12)),cross_product(sK11,sK12))
| ~ subset(X0,cross_product(sK11,sK12))
| ~ member(sK5(singleton(ordered_pair(sK13,sK14)),cross_product(sK11,sK12)),X0) ),
inference(instantiation,[status(thm)],[c_506]) ).
tcf(c_6026,plain,
( member(sK5(singleton(ordered_pair(sK13,sK14)),cross_product(sK11,sK12)),cross_product(sK11,sK12))
| ~ subset(singleton(ordered_pair(sK13,sK14)),cross_product(sK11,sK12))
| ~ member(sK5(singleton(ordered_pair(sK13,sK14)),cross_product(sK11,sK12)),singleton(ordered_pair(sK13,sK14))) ),
inference(instantiation,[status(thm)],[c_2689]) ).
tcf(c_10882,plain,
( subset(singleton(ordered_pair(sK13,sK14)),cross_product(sK11,sK12))
| ~ member(ordered_pair(sK13,sK14),cross_product(sK11,sK12)) ),
inference(instantiation,[status(thm)],[c_840]) ).
tcf(c_17756,plain,
( member(ordered_pair(sK13,sK14),cross_product(sK11,sK12))
| ~ member(sK14,sK12)
| ~ member(sK13,sK11) ),
inference(instantiation,[status(thm)],[c_585]) ).
tcf(c_17757,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_17756,c_10882,c_6026,c_2288,c_2289,c_2206,c_2189,c_2181,c_103,c_104,c_105]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET646+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/20.40 % Computer : n002.cluster.edu
% 0.12/20.40 % Model : x86_64 x86_64
% 0.12/20.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/20.40 % Memory : 8046.5625MB
% 0.12/20.40 % OS : Linux 6.8.0-71-generic
% 0.12/20.40 % CPULimit : 300
% 0.12/20.40 % WCLimit : 300
% 0.12/20.40 % DateTime : Thu Sep 24 11:36:55 UTC 2026
% 0.12/20.40 % CPUTime :
% 0.12/20.40 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/20.44 Running first-order theorem proving
% 0.12/20.44 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
% 0.12/20.45
% 0.12/20.45 % ======== iProver multi-core TPTP/SMT =========
% 0.12/20.45
% 0.12/20.45 % Detected problem language: tptp
% 0.12/20.46 % Proving...
% 10.66/22.31 % SZS status Started for theBenchmark.p
% 10.66/22.31 % SZS status Theorem for theBenchmark.p
% 10.66/22.31
% 10.66/22.31 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 10.66/22.31
% 10.66/22.31 % ------ iProver source info
% 10.66/22.31
% 10.66/22.31 % git: date: 2026-07-19 20:42:38 +0200
% 10.66/22.31 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 10.66/22.31 % git: non_committed_changes: false
% 10.66/22.31
% 10.66/22.31 % ------ Parsing...
% 10.66/22.31 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 10.66/22.31
% 10.66/22.31 % ------ Preprocessing... sup_sim: 1 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 %
% 10.66/22.31
% 10.66/22.31 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 10.66/22.31
% 10.66/22.31 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 10.66/22.31 % ------ Proving...
% 10.66/22.31 % ------ Problem Properties
% 10.66/22.31
% 10.66/22.31 %
% 10.66/22.31 % clauses 41
% 10.66/22.31 % conjectures 3
% 10.66/22.31 % EPR 7
% 10.66/22.31 % Horn 33
% 10.66/22.31 % unary 11
% 10.66/22.31 % binary 21
% 10.66/22.31 % lits 80
% 10.66/22.31 % lits eq 11
% 10.66/22.31 % fd_pure 0
% 10.66/22.31 % fd_pseudo 0
% 10.66/22.31 % fd_cond 0
% 10.66/22.31 % fd_pseudo_cond 4
% 10.66/22.31 % AC symbols 0
% 10.66/22.31
% 10.66/22.31 % ------ Input Options Time Limit: Unbounded
% 10.66/22.31
% 10.66/22.31
% 10.66/22.31 % ------
% 10.66/22.31 % Current options:
% 10.66/22.31 % ------
% 10.66/22.31
% 10.66/22.31
% 10.66/22.31 %
% 10.66/22.31
% 10.66/22.31 % ------ Proving...
% 10.66/22.31 %
% 10.66/22.31
% 10.66/22.31 % SZS status Theorem for theBenchmark.p
% 10.66/22.31
% 10.66/22.31 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 10.66/22.32
% 10.66/22.32
%------------------------------------------------------------------------------