%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET656+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 : n006.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 02:47:42 PM UTC 2026
% Result : Theorem 5.32s 2.28s
% Output : CNFRefutation 5.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 13
% Syntax : Number of formulae : 162 ( 24 unt; 0 def)
% Number of atoms : 537 ( 43 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 663 ( 288 ~; 288 |; 37 &)
% ( 13 <=>; 37 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 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 : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 4 con; 0-4 aty)
% Number of variables : 295 ( 0 sgn 286 !; 9 ?; 156 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( subset(X0,X1)
=> intersection(X0,X1) = X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p1) ).
fof(f6,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',p6) ).
fof(f13,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',p13) ).
fof(f17,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',p17) ).
fof(f18,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> subset(X0,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p18) ).
fof(f19,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',p19) ).
fof(f20,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',p20) ).
fof(f21,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',p21) ).
fof(f26,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',p26) ).
fof(f28,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,relation_type(X0,X1))
=> ! [X3] :
( ilf_type(X3,relation_type(X0,X1))
=> intersection4(X0,X1,X2,X3) = intersection(X2,X3) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p28) ).
fof(f29,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,relation_type(X0,X1))
=> ! [X3] :
( ilf_type(X3,relation_type(X0,X1))
=> ilf_type(intersection4(X0,X1,X2,X3),relation_type(X0,X1)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p29) ).
fof(f30,axiom,
! [X0] : ilf_type(X0,set_type),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p30) ).
fof(f31,conjecture,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,relation_type(X0,X1))
=> intersection(X2,cross_product(X0,X1)) = X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_relset_1_18) ).
fof(f32,negated_conjecture,
~ ! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,relation_type(X0,X1))
=> intersection(X2,cross_product(X0,X1)) = X2 ) ) ),
inference(negated_conjecture,[status(cth)],[f31]) ).
fof(f33,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ~ subset(X0,X1)
| intersection(X0,X1) = X0 ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f34,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ~ subset(X0,X1)
| intersection(X0,X1) = X0 ) ),
inference(flattening,[],[f33]) ).
fof(f39,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,[],[f6]) ).
fof(f45,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,[],[f13]) ).
fof(f50,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,[],[f17]) ).
fof(f51,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,[],[f50]) ).
fof(f52,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| subset(X0,X0) ),
inference(ennf_transformation,[],[f18]) ).
fof(f53,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,[],[f19]) ).
fof(f54,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,[],[f53]) ).
fof(f55,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ( ilf_type(power_set(X0),set_type)
& ~ empty(power_set(X0)) ) ),
inference(ennf_transformation,[],[f20]) ).
fof(f56,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,[],[f21]) ).
fof(f57,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,[],[f56]) ).
fof(f64,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ( empty(X0)
<=> ! [X1] :
( ~ ilf_type(X1,set_type)
| ~ member(X1,X0) ) ) ),
inference(ennf_transformation,[],[f26]) ).
fof(f67,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ! [X2] :
( ~ ilf_type(X2,relation_type(X0,X1))
| ! [X3] :
( ~ ilf_type(X3,relation_type(X0,X1))
| intersection4(X0,X1,X2,X3) = intersection(X2,X3) ) ) ) ),
inference(ennf_transformation,[],[f28]) ).
fof(f68,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ! [X2] :
( ~ ilf_type(X2,relation_type(X0,X1))
| ! [X3] :
( ~ ilf_type(X3,relation_type(X0,X1))
| ilf_type(intersection4(X0,X1,X2,X3),relation_type(X0,X1)) ) ) ) ),
inference(ennf_transformation,[],[f29]) ).
fof(f69,plain,
? [X0] :
( ilf_type(X0,set_type)
& ? [X1] :
( ilf_type(X1,set_type)
& ? [X2] :
( ilf_type(X2,relation_type(X0,X1))
& intersection(X2,cross_product(X0,X1)) != X2 ) ) ),
inference(ennf_transformation,[],[f32]) ).
fof(f83,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,[],[f45]) ).
fof(f85,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,[],[f51]) ).
fof(f86,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,[],[f85]) ).
fof(f87,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(sK7(X0,X1),set_type)
& member(sK7(X0,X1),X0)
& ~ member(sK7(X0,X1),X1) )
| subset(X0,X1) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(X2,sK7(X0,X1))],[f86]) ).
fof(f88,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,[],[f54]) ).
fof(f89,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,[],[f88]) ).
fof(f90,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(sK8(X0,X1),set_type)
& member(sK8(X0,X1),X0)
& ~ member(sK8(X0,X1),X1) )
| member(X0,power_set(X1)) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(X2,sK8(X0,X1))],[f89]) ).
fof(f91,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,[],[f57]) ).
fof(f100,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,[],[f64]) ).
fof(f101,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,[],[f100]) ).
fof(f102,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ( ( ~ empty(X0)
| ! [X2] :
( ~ ilf_type(X2,set_type)
| ~ member(X2,X0) ) )
& ( ( ilf_type(sK14(X0),set_type)
& member(sK14(X0),X0) )
| empty(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(X1,sK14(X0))],[f101]) ).
fof(f103,plain,
( ilf_type(sK15,set_type)
& ilf_type(sK16,set_type)
& ilf_type(sK17,relation_type(sK15,sK16))
& sK17 != intersection(sK17,cross_product(sK15,sK16)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15,sK16,sK17]),skolemize(X0,sK15),skolemize(X1,sK16),skolemize(X2,sK17)],[f69]) ).
fof(f104,plain,
! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ subset(X0,X1)
| intersection(X0,X1) = X0 ),
inference(cnf_transformation,[],[f34]) ).
fof(f116,plain,
! [X3,X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X3,relation_type(X0,X1))
| ilf_type(X3,subset_type(cross_product(X0,X1))) ),
inference(cnf_transformation,[],[f39]) ).
fof(f131,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,[],[f83]) ).
fof(f138,plain,
! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| member(sK7(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f87]) ).
fof(f139,plain,
! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ member(sK7(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f87]) ).
fof(f140,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| subset(X0,X0) ),
inference(cnf_transformation,[],[f52]) ).
fof(f141,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,[],[f90]) ).
fof(f146,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ~ empty(power_set(X0)) ),
inference(cnf_transformation,[],[f55]) ).
fof(f147,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,[],[f91]) ).
fof(f162,plain,
! [X2,X0] :
( ~ ilf_type(X0,set_type)
| ~ empty(X0)
| ~ ilf_type(X2,set_type)
| ~ member(X2,X0) ),
inference(cnf_transformation,[],[f102]) ).
fof(f166,plain,
! [X2,X3,X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X3,relation_type(X0,X1))
| intersection4(X0,X1,X2,X3) = intersection(X2,X3) ),
inference(cnf_transformation,[],[f67]) ).
fof(f167,plain,
! [X2,X3,X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X3,relation_type(X0,X1))
| ilf_type(intersection4(X0,X1,X2,X3),relation_type(X0,X1)) ),
inference(cnf_transformation,[],[f68]) ).
fof(f168,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[],[f30]) ).
fof(f171,plain,
ilf_type(sK17,relation_type(sK15,sK16)),
inference(cnf_transformation,[],[f103]) ).
fof(f172,plain,
sK17 != intersection(sK17,cross_product(sK15,sK16)),
inference(cnf_transformation,[],[f103]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] :
( ( intersection(X0,X1) = X0 )
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f104]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i,X2: $i] :
( ilf_type(X0,subset_type(cross_product(X1,X2)))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(cnf_transformation,[],[f116]) ).
tcf(c_76,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,[],[f131]) ).
tcf(c_79,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| ~ member(sK7(X0,X1),X1) ),
inference(cnf_transformation,[],[f139]) ).
tcf(c_80,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| member(sK7(X0,X1),X0)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f138]) ).
tcf(c_83,plain,
! [X0: $i] :
( subset(X0,X0)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f140]) ).
tcf(c_87,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,[],[f141]) ).
tcf(c_88,plain,
! [X0: $i] :
( ~ empty(power_set(X0))
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f146]) ).
tcf(c_91,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,[],[f147]) ).
tcf(c_107,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f162]) ).
tcf(c_109,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( intersection4(X1,X2,X3,X0) = intersection(X3,X0) )
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X3,relation_type(X1,X2))
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(cnf_transformation,[],[f166]) ).
tcf(c_110,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ilf_type(intersection4(X1,X2,X3,X0),relation_type(X1,X2))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X3,relation_type(X1,X2))
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(cnf_transformation,[],[f167]) ).
tcf(c_111,plain,
! [X0: $i] : ilf_type(X0,set_type),
inference(cnf_transformation,[],[f168]) ).
tcf(c_112,negated_conjecture,
intersection(sK17,cross_product(sK15,sK16)) != sK17,
inference(cnf_transformation,[],[f172]) ).
tcf(c_113,negated_conjecture,
ilf_type(sK17,relation_type(sK15,sK16)),
inference(cnf_transformation,[],[f171]) ).
tcf(c_164,plain,
! [X0: $i] : subset(X0,X0),
inference(global_subsumption_just,[status(thm)],[c_83,c_111,c_83]) ).
tcf(c_170,plain,
! [X0: $i] : ~ empty(power_set(X0)),
inference(global_subsumption_just,[status(thm)],[c_88,c_111,c_88]) ).
tcf(c_215,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ ilf_type(X1,set_type)
| ~ member(X0,X1) ),
inference(global_subsumption_just,[status(thm)],[c_107,c_111,c_107]) ).
tcf(c_226,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| member(sK7(X0,X1),X0)
| ~ ilf_type(X1,set_type) ),
inference(global_subsumption_just,[status(thm)],[c_80,c_111,c_80]) ).
tcf(c_227,plain,
! [X0: $i,X1: $i] :
( subset(X1,X0)
| member(sK7(X1,X0),X1)
| ~ ilf_type(X0,set_type) ),
inference(renaming,[status(thm)],[c_226]) ).
tcf(c_228,plain,
! [X0: $i,X1: $i] :
( subset(X1,X0)
| member(sK7(X1,X0),X1) ),
inference(global_subsumption_just,[status(thm)],[c_227,c_111,c_227]) ).
tcf(c_229,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| member(sK7(X0,X1),X0) ),
inference(renaming,[status(thm)],[c_228]) ).
tcf(c_250,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ ilf_type(X1,set_type)
| ~ member(sK7(X0,X1),X1) ),
inference(global_subsumption_just,[status(thm)],[c_79,c_111,c_79]) ).
tcf(c_252,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_91,c_111,c_91]) ).
tcf(c_259,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_76,c_111,c_76]) ).
tcf(c_263,plain,
! [X0: $i,X1: $i] :
( ( intersection(X0,X1) = X0 )
| ~ ilf_type(X1,set_type)
| ~ subset(X0,X1) ),
inference(global_subsumption_just,[status(thm)],[c_49,c_111,c_49]) ).
tcf(c_286,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_87,c_111,c_87]) ).
tcf(c_287,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_286]) ).
tcf(c_452,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| member(X0,X1)
| ~ ilf_type(X0,member_type(X1)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_252,c_111]) ).
tcf(c_453,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ member(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[c_215,c_111]) ).
tcf(c_460,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( intersection4(X1,X2,X3,X0) = intersection(X3,X0) )
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,relation_type(X1,X2))
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_109,c_111]) ).
tcf(c_461,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ member(sK7(X0,X1),X1) ),
inference(backward_subsumption_resolution,[status(thm)],[c_250,c_111]) ).
tcf(c_462,plain,
! [X0: $i,X1: $i] :
( ( intersection(X0,X1) = X0 )
| ~ subset(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[c_263,c_111]) ).
tcf(c_467,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_259,c_111]) ).
tcf(c_468,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_287,c_111]) ).
tcf(c_471,plain,
! [X0: $i,X1: $i,X2: $i] :
( ilf_type(X0,subset_type(cross_product(X1,X2)))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_62,c_111]) ).
tcf(c_473,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ilf_type(intersection4(X1,X2,X3,X0),relation_type(X1,X2))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,relation_type(X1,X2))
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_110,c_111]) ).
tcf(c_651,plain,
! [X0: $i,X1: $i,X2: $i] :
( ilf_type(X0,subset_type(cross_product(X1,X2)))
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_471,c_111]) ).
tcf(c_699,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_468,c_111]) ).
tcf(c_728,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ilf_type(intersection4(X1,X2,X3,X0),relation_type(X1,X2))
| ~ ilf_type(X3,relation_type(X1,X2))
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_473,c_111]) ).
tcf(c_743,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( intersection4(X1,X2,X3,X0) = intersection(X3,X0) )
| ~ ilf_type(X3,relation_type(X1,X2))
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_460,c_111]) ).
tcf(c_890,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X2,X1)
| ~ ilf_type(X2,member_type(X1))
| ( power_set(X0) != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_170,c_452]) ).
tcf(c_891,plain,
! [X0: $i,X1: $i] :
( member(X0,power_set(X1))
| ~ ilf_type(X0,member_type(power_set(X1))) ),
inference(unflattening,[status(thm)],[c_890]) ).
tcf(c_1268,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_651]) ).
tcf(c_1276,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_467]) ).
tcf(c_1278,plain,
! [X0: $i,X1: $i] :
( ( intersection(X0,X1) = X0 )
| ~ subset(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_462]) ).
tcf(c_1280,plain,
! [X0: $i,X1: $i] :
( ~ member(sK7(X0,X1),X1)
| subset(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_461]) ).
tcf(c_1281,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ member(sK7(X0,X1),X1) ),
inference(renaming,[status(thm)],[c_1280]) ).
tcf(c_1282,plain,
! [X0: $i,X1: $i] :
( member(sK7(X0,X1),X0)
| subset(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_229]) ).
tcf(c_1283,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| member(sK7(X0,X1),X0) ),
inference(renaming,[status(thm)],[c_1282]) ).
tcf(c_1294,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ member(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_453]) ).
tcf(c_2682,plain,
( ( intersection(sK17,cross_product(sK15,sK16)) = sK17 )
| ~ subset(sK17,cross_product(sK15,sK16)) ),
inference(instantiation,[status(thm)],[c_1278]) ).
tcf(c_2699,plain,
( subset(sK17,cross_product(sK15,sK16))
| ~ member(sK7(sK17,cross_product(sK15,sK16)),cross_product(sK15,sK16)) ),
inference(instantiation,[status(thm)],[c_1281]) ).
tcf(c_2700,plain,
( subset(sK17,cross_product(sK15,sK16))
| member(sK7(sK17,cross_product(sK15,sK16)),sK17) ),
inference(instantiation,[status(thm)],[c_1283]) ).
tcf(c_2728,plain,
! [X0: $i] :
( member(sK7(sK17,cross_product(sK15,sK16)),cross_product(sK15,sK16))
| ~ member(X0,power_set(cross_product(sK15,sK16)))
| ~ member(sK7(sK17,cross_product(sK15,sK16)),X0) ),
inference(instantiation,[status(thm)],[c_699]) ).
tcf(c_3014,plain,
( member(sK7(sK17,cross_product(sK15,sK16)),cross_product(sK15,sK16))
| ~ member(sK17,power_set(cross_product(sK15,sK16)))
| ~ member(sK7(sK17,cross_product(sK15,sK16)),sK17) ),
inference(instantiation,[status(thm)],[c_2728]) ).
tcf(c_3115,plain,
! [X0: $i,X1: $i] :
( ilf_type(sK17,subset_type(cross_product(X0,X1)))
| ~ ilf_type(sK17,relation_type(X0,X1)) ),
inference(instantiation,[status(thm)],[c_1268]) ).
tcf(c_3633,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_1276,c_452]) ).
tcf(c_3635,plain,
! [X0: $i,X1: $i] :
( ~ ilf_type(X0,subset_type(X1))
| member(X0,power_set(X1)) ),
inference(global_subsumption_just,[status(thm)],[c_3633,c_467,c_891]) ).
tcf(c_3636,plain,
! [X0: $i,X1: $i] :
( member(X0,power_set(X1))
| ~ ilf_type(X0,subset_type(X1)) ),
inference(renaming,[status(thm)],[c_3635]) ).
tcf(c_4146,plain,
! [X0: $i] :
( ( intersection4(sK15,sK16,X0,sK17) = intersection(X0,sK17) )
| ~ ilf_type(X0,relation_type(sK15,sK16)) ),
inference(superposition,[status(thm)],[c_113,c_743]) ).
tcf(c_4321,plain,
( ilf_type(sK17,subset_type(cross_product(sK15,sK16)))
| ~ ilf_type(sK17,relation_type(sK15,sK16)) ),
inference(instantiation,[status(thm)],[c_3115]) ).
tcf(c_4324,plain,
! [X0: $i,X1: $i] :
( ilf_type(sK17,member_type(power_set(cross_product(X0,X1))))
| ~ ilf_type(sK17,subset_type(cross_product(X0,X1))) ),
inference(instantiation,[status(thm)],[c_1276]) ).
tcf(c_4443,plain,
intersection4(sK15,sK16,sK17,sK17) = intersection(sK17,sK17),
inference(superposition,[status(thm)],[c_113,c_4146]) ).
tcf(c_4464,plain,
! [X0: $i,X1: $i] :
( empty(power_set(X1))
| member(X0,power_set(X1))
| ~ ilf_type(X0,member_type(power_set(X1))) ),
inference(instantiation,[status(thm)],[c_452]) ).
tcf(c_4469,plain,
( ilf_type(intersection(sK17,sK17),relation_type(sK15,sK16))
| ~ ilf_type(sK17,relation_type(sK15,sK16)) ),
inference(superposition,[status(thm)],[c_4443,c_728]) ).
tcf(c_4916,plain,
! [X0: $i] : intersection(X0,X0) = X0,
inference(superposition,[status(thm)],[c_164,c_1278]) ).
tcf(c_5027,plain,
! [X0: $i] :
( ( intersection4(sK15,sK16,X0,sK17) = intersection(X0,sK17) )
| ~ ilf_type(X0,relation_type(sK15,sK16)) ),
inference(superposition,[status(thm)],[c_113,c_743]) ).
tcf(c_5049,plain,
! [X0: $i,X1: $i] :
( ( intersection4(sK15,sK16,intersection4(sK15,sK16,X1,X0),sK17) = intersection(intersection4(sK15,sK16,X1,X0),sK17) )
| ~ ilf_type(X1,relation_type(sK15,sK16))
| ~ ilf_type(X0,relation_type(sK15,sK16)) ),
inference(superposition,[status(thm)],[c_728,c_5027]) ).
tcf(c_5050,plain,
intersection4(sK15,sK16,sK17,sK17) = intersection(sK17,sK17),
inference(superposition,[status(thm)],[c_113,c_5027]) ).
tcf(c_5051,plain,
( ilf_type(intersection(sK17,sK17),relation_type(sK15,sK16))
| ~ ilf_type(sK17,relation_type(sK15,sK16)) ),
inference(superposition,[status(thm)],[c_5050,c_728]) ).
tcf(c_5052,plain,
ilf_type(intersection(sK17,sK17),relation_type(sK15,sK16)),
inference(global_subsumption_just,[status(thm)],[c_5051,c_113,c_4469]) ).
tcf(c_5057,plain,
intersection4(sK15,sK16,intersection(sK17,sK17),sK17) = intersection(intersection(sK17,sK17),sK17),
inference(superposition,[status(thm)],[c_5052,c_5027]) ).
tcf(c_5059,plain,
intersection4(sK15,sK16,sK17,sK17) = sK17,
inference(superposition,[status(thm)],[c_4916,c_5057]) ).
tcf(c_5063,plain,
! [X0: $i] :
( ( intersection4(sK15,sK16,intersection4(sK15,sK16,X0,sK17),sK17) = intersection(intersection4(sK15,sK16,X0,sK17),sK17) )
| ~ ilf_type(X0,relation_type(sK15,sK16)) ),
inference(superposition,[status(thm)],[c_113,c_5049]) ).
tcf(c_5066,plain,
! [X0: $i,X1: $i] :
( ( intersection4(sK15,sK16,intersection4(sK15,sK16,intersection4(sK15,sK16,X1,X0),sK17),sK17) = intersection(intersection4(sK15,sK16,intersection4(sK15,sK16,X1,X0),sK17),sK17) )
| ~ ilf_type(X1,relation_type(sK15,sK16))
| ~ ilf_type(X0,relation_type(sK15,sK16)) ),
inference(superposition,[status(thm)],[c_728,c_5063]) ).
tcf(c_5067,plain,
intersection4(sK15,sK16,intersection4(sK15,sK16,sK17,sK17),sK17) = intersection(intersection4(sK15,sK16,sK17,sK17),sK17),
inference(superposition,[status(thm)],[c_113,c_5063]) ).
tcf(c_5672,plain,
! [X0: $i] :
( ( intersection4(sK15,sK16,intersection4(sK15,sK16,intersection4(sK15,sK16,X0,sK17),sK17),sK17) = intersection(intersection4(sK15,sK16,intersection4(sK15,sK16,X0,sK17),sK17),sK17) )
| ~ ilf_type(X0,relation_type(sK15,sK16)) ),
inference(superposition,[status(thm)],[c_113,c_5066]) ).
tcf(c_5726,plain,
intersection4(sK15,sK16,intersection4(sK15,sK16,intersection4(sK15,sK16,sK17,sK17),sK17),sK17) = intersection(intersection4(sK15,sK16,intersection4(sK15,sK16,sK17,sK17),sK17),sK17),
inference(superposition,[status(thm)],[c_113,c_5672]) ).
tcf(c_5780,plain,
( ilf_type(intersection(intersection4(sK15,sK16,intersection4(sK15,sK16,sK17,sK17),sK17),sK17),relation_type(sK15,sK16))
| ~ ilf_type(sK17,relation_type(sK15,sK16))
| ~ ilf_type(intersection4(sK15,sK16,intersection4(sK15,sK16,sK17,sK17),sK17),relation_type(sK15,sK16)) ),
inference(superposition,[status(thm)],[c_5726,c_728]) ).
tcf(c_5899,plain,
( ilf_type(intersection(intersection4(sK15,sK16,intersection4(sK15,sK16,sK17,sK17),sK17),sK17),relation_type(sK15,sK16))
| ~ ilf_type(intersection4(sK15,sK16,intersection4(sK15,sK16,sK17,sK17),sK17),relation_type(sK15,sK16)) ),
inference(global_subsumption_just,[status(thm)],[c_5780,c_113,c_5780]) ).
tcf(c_5903,plain,
( ilf_type(intersection(intersection(intersection4(sK15,sK16,sK17,sK17),sK17),sK17),relation_type(sK15,sK16))
| ~ ilf_type(intersection4(sK15,sK16,intersection4(sK15,sK16,sK17,sK17),sK17),relation_type(sK15,sK16)) ),
inference(superposition,[status(thm)],[c_5067,c_5899]) ).
tcf(c_6054,plain,
( ilf_type(intersection(intersection(intersection4(sK15,sK16,sK17,sK17),sK17),sK17),relation_type(sK15,sK16))
| ~ ilf_type(sK17,relation_type(sK15,sK16)) ),
inference(superposition,[status(thm)],[c_5059,c_5903]) ).
tcf(c_7818,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_1276,c_452]) ).
tcf(c_7821,plain,
! [X0: $i,X1: $i] :
( ~ ilf_type(X0,subset_type(X1))
| member(X0,power_set(X1)) ),
inference(global_subsumption_just,[status(thm)],[c_7818,c_3636]) ).
tcf(c_7822,plain,
! [X0: $i,X1: $i] :
( member(X0,power_set(X1))
| ~ ilf_type(X0,subset_type(X1)) ),
inference(renaming,[status(thm)],[c_7821]) ).
tcf(c_7824,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,power_set(cross_product(X1,X2)))
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(superposition,[status(thm)],[c_1268,c_7822]) ).
tcf(c_7934,plain,
! [X0: $i] :
( ( intersection4(sK15,sK16,X0,sK17) = intersection(X0,sK17) )
| ~ ilf_type(X0,relation_type(sK15,sK16)) ),
inference(superposition,[status(thm)],[c_113,c_743]) ).
tcf(c_7961,plain,
! [X0: $i,X1: $i] :
( ( intersection4(sK15,sK16,intersection4(sK15,sK16,X1,X0),sK17) = intersection(intersection4(sK15,sK16,X1,X0),sK17) )
| ~ ilf_type(X1,relation_type(sK15,sK16))
| ~ ilf_type(X0,relation_type(sK15,sK16)) ),
inference(superposition,[status(thm)],[c_728,c_7934]) ).
tcf(c_7962,plain,
intersection4(sK15,sK16,sK17,sK17) = intersection(sK17,sK17),
inference(superposition,[status(thm)],[c_113,c_7934]) ).
tcf(c_7975,plain,
! [X0: $i] :
( ( intersection4(sK15,sK16,intersection4(sK15,sK16,X0,sK17),sK17) = intersection(intersection4(sK15,sK16,X0,sK17),sK17) )
| ~ ilf_type(X0,relation_type(sK15,sK16)) ),
inference(superposition,[status(thm)],[c_113,c_7961]) ).
tcf(c_7978,plain,
! [X0: $i,X1: $i] :
( ( intersection4(sK15,sK16,intersection4(sK15,sK16,intersection4(sK15,sK16,X1,X0),sK17),sK17) = intersection(intersection4(sK15,sK16,intersection4(sK15,sK16,X1,X0),sK17),sK17) )
| ~ ilf_type(X1,relation_type(sK15,sK16))
| ~ ilf_type(X0,relation_type(sK15,sK16)) ),
inference(superposition,[status(thm)],[c_728,c_7975]) ).
tcf(c_7979,plain,
intersection4(sK15,sK16,intersection4(sK15,sK16,sK17,sK17),sK17) = intersection(intersection4(sK15,sK16,sK17,sK17),sK17),
inference(superposition,[status(thm)],[c_113,c_7975]) ).
tcf(c_8052,plain,
! [X0: $i] :
( ( intersection4(sK15,sK16,intersection4(sK15,sK16,intersection4(sK15,sK16,X0,sK17),sK17),sK17) = intersection(intersection4(sK15,sK16,intersection4(sK15,sK16,X0,sK17),sK17),sK17) )
| ~ ilf_type(X0,relation_type(sK15,sK16)) ),
inference(superposition,[status(thm)],[c_113,c_7978]) ).
tcf(c_8107,plain,
intersection4(sK15,sK16,intersection4(sK15,sK16,intersection4(sK15,sK16,sK17,sK17),sK17),sK17) = intersection(intersection4(sK15,sK16,intersection4(sK15,sK16,sK17,sK17),sK17),sK17),
inference(superposition,[status(thm)],[c_113,c_8052]) ).
tcf(c_8114,plain,
( ilf_type(intersection(intersection4(sK15,sK16,intersection4(sK15,sK16,sK17,sK17),sK17),sK17),relation_type(sK15,sK16))
| ~ ilf_type(sK17,relation_type(sK15,sK16))
| ~ ilf_type(intersection4(sK15,sK16,intersection4(sK15,sK16,sK17,sK17),sK17),relation_type(sK15,sK16)) ),
inference(superposition,[status(thm)],[c_8107,c_728]) ).
tcf(c_8132,plain,
( ilf_type(intersection(intersection4(sK15,sK16,intersection4(sK15,sK16,sK17,sK17),sK17),sK17),relation_type(sK15,sK16))
| ~ ilf_type(intersection4(sK15,sK16,intersection4(sK15,sK16,sK17,sK17),sK17),relation_type(sK15,sK16)) ),
inference(global_subsumption_just,[status(thm)],[c_8114,c_113,c_5780]) ).
tcf(c_8136,plain,
( ilf_type(intersection(intersection(intersection4(sK15,sK16,sK17,sK17),sK17),sK17),relation_type(sK15,sK16))
| ~ ilf_type(intersection4(sK15,sK16,intersection4(sK15,sK16,sK17,sK17),sK17),relation_type(sK15,sK16)) ),
inference(superposition,[status(thm)],[c_7979,c_8132]) ).
tcf(c_8230,plain,
ilf_type(intersection(intersection(intersection4(sK15,sK16,sK17,sK17),sK17),sK17),relation_type(sK15,sK16)),
inference(global_subsumption_just,[status(thm)],[c_8136,c_113,c_6054]) ).
tcf(c_8236,plain,
ilf_type(intersection(intersection(intersection(sK17,sK17),sK17),sK17),relation_type(sK15,sK16)),
inference(superposition,[status(thm)],[c_7962,c_8230]) ).
tcf(c_8723,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ empty(power_set(cross_product(X1,X2)))
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(superposition,[status(thm)],[c_7824,c_1294]) ).
tcf(c_8830,plain,
~ empty(power_set(cross_product(sK15,sK16))),
inference(superposition,[status(thm)],[c_8236,c_8723]) ).
tcf(c_10406,plain,
( ilf_type(sK17,member_type(power_set(cross_product(sK15,sK16))))
| ~ ilf_type(sK17,subset_type(cross_product(sK15,sK16))) ),
inference(instantiation,[status(thm)],[c_4324]) ).
tcf(c_12548,plain,
( empty(power_set(cross_product(sK15,sK16)))
| member(sK17,power_set(cross_product(sK15,sK16)))
| ~ ilf_type(sK17,member_type(power_set(cross_product(sK15,sK16)))) ),
inference(instantiation,[status(thm)],[c_4464]) ).
tcf(c_12549,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_12548,c_10406,c_8830,c_4321,c_3014,c_2699,c_2700,c_2682,c_112,c_113]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET656+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.08/0.37 % Computer : n006.cluster.edu
% 0.08/0.37 % Model : x86_64 x86_64
% 0.08/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.37 % Memory : 8046.5625MB
% 0.08/0.37 % OS : Linux 6.8.0-71-generic
% 0.08/0.37 % CPULimit : 300
% 0.08/0.37 % WCLimit : 300
% 0.08/0.37 % DateTime : Thu Sep 24 11:34:27 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.08/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.08/0.41 Running first-order theorem proving
% 0.08/0.41 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
% 0.08/0.42
% 0.08/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.08/0.42
% 0.08/0.42 % Detected problem language: tptp
% 0.08/0.43 % Proving...
% 5.32/2.28 % SZS status Started for theBenchmark.p
% 5.32/2.28 % SZS status Theorem for theBenchmark.p
% 5.32/2.28
% 5.32/2.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 5.32/2.28
% 5.32/2.28 % ------ iProver source info
% 5.32/2.28
% 5.32/2.28 % git: date: 2026-07-19 20:42:38 +0200
% 5.32/2.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 5.32/2.28 % git: non_committed_changes: false
% 5.32/2.28
% 5.32/2.28 % ------ Parsing...
% 5.32/2.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 5.32/2.28
% 5.32/2.28 % ------ 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 %
% 5.32/2.28
% 5.32/2.28 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 5.32/2.28
% 5.32/2.28 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 5.32/2.28 % ------ Proving...
% 5.32/2.28 % ------ Problem Properties
% 5.32/2.28
% 5.32/2.28 %
% 5.32/2.28 % clauses 45
% 5.32/2.28 % conjectures 2
% 5.32/2.28 % EPR 8
% 5.32/2.28 % Horn 37
% 5.32/2.28 % unary 9
% 5.32/2.28 % binary 24
% 5.32/2.28 % lits 97
% 5.32/2.28 % lits eq 11
% 5.32/2.28 % fd_pure 0
% 5.32/2.28 % fd_pseudo 0
% 5.32/2.28 % fd_cond 0
% 5.32/2.28 % fd_pseudo_cond 4
% 5.32/2.28 % AC symbols 0
% 5.32/2.28
% 5.32/2.28 % ------ Input Options Time Limit: Unbounded
% 5.32/2.28
% 5.32/2.28
% 5.32/2.28 % ------
% 5.32/2.28 % Current options:
% 5.32/2.28 % ------
% 5.32/2.28
% 5.32/2.28
% 5.32/2.28 %
% 5.32/2.28
% 5.32/2.28 % ------ Proving...
% 5.32/2.28 %
% 5.32/2.28
% 5.32/2.28 % SZS status Theorem for theBenchmark.p
% 5.32/2.28
% 5.32/2.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 5.32/2.28
% 5.32/2.28
%------------------------------------------------------------------------------