%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET640+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 : n013.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 02:47:39 PM UTC 2026
% Result : Theorem 8.29s 1.62s
% Output : CNFRefutation 8.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 8
% Syntax : Number of formulae : 96 ( 12 unt; 0 def)
% Number of atoms : 372 ( 1 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 468 ( 192 ~; 198 |; 40 &)
% ( 11 <=>; 27 =>; 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 : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 5 con; 0-2 aty)
% Number of variables : 211 ( 0 sgn 199 !; 12 ?; 111 :)
% Comments :
%------------------------------------------------------------------------------
fof(f4,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',p4) ).
fof(f6,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',p6) ).
fof(f8,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',p8) ).
fof(f11,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',p11) ).
fof(f12,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',p12) ).
fof(f13,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',p13) ).
fof(f19,axiom,
! [X0] : ilf_type(X0,set_type),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p19) ).
fof(f20,conjecture,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,relation_type(X1,X2))
=> ( subset(X0,X3)
=> subset(X0,cross_product(X1,X2)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_relset_1_2) ).
fof(f21,negated_conjecture,
~ ! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,relation_type(X1,X2))
=> ( subset(X0,X3)
=> subset(X0,cross_product(X1,X2)) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f20]) ).
fof(f26,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,[],[f4]) ).
fof(f28,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,[],[f6]) ).
fof(f29,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,[],[f28]) ).
fof(f31,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,[],[f8]) ).
fof(f34,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,[],[f11]) ).
fof(f35,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,[],[f34]) ).
fof(f36,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ( ilf_type(power_set(X0),set_type)
& ~ empty(power_set(X0)) ) ),
inference(ennf_transformation,[],[f12]) ).
fof(f37,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,[],[f13]) ).
fof(f38,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,[],[f37]) ).
fof(f47,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(X1,X2))
& subset(X0,X3)
& ~ subset(X0,cross_product(X1,X2)) ) ) ) ),
inference(ennf_transformation,[],[f21]) ).
fof(f48,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(X1,X2))
& subset(X0,X3)
& ~ subset(X0,cross_product(X1,X2)) ) ) ) ),
inference(flattening,[],[f47]) ).
fof(f53,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,[],[f29]) ).
fof(f54,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,[],[f53]) ).
fof(f55,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(sK3(X0,X1),set_type)
& member(sK3(X0,X1),X0)
& ~ member(sK3(X0,X1),X1) )
| subset(X0,X1) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X2,sK3(X0,X1))],[f54]) ).
fof(f56,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,[],[f31]) ).
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) ) )
& ( ? [X2] :
( ilf_type(X2,set_type)
& member(X2,X0)
& ~ member(X2,X1) )
| member(X0,power_set(X1)) ) ) ) ),
inference(nnf_transformation,[],[f35]) ).
fof(f59,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,[],[f58]) ).
fof(f60,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))],[f59]) ).
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) )
& ( ~ member(X0,X1)
| ilf_type(X0,member_type(X1)) ) ) ) ),
inference(nnf_transformation,[],[f38]) ).
fof(f69,plain,
( ilf_type(sK11,set_type)
& ilf_type(sK12,set_type)
& ilf_type(sK13,set_type)
& ilf_type(sK14,relation_type(sK12,sK13))
& subset(sK11,sK14)
& ~ subset(sK11,cross_product(sK12,sK13)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11,sK12,sK13,sK14]),skolemize(X0,sK11),skolemize(X1,sK12),skolemize(X2,sK13),skolemize(X3,sK14)],[f48]) ).
fof(f78,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,[],[f26]) ).
fof(f81,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,[],[f55]) ).
fof(f83,plain,
! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| member(sK3(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f55]) ).
fof(f84,plain,
! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ member(sK3(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f55]) ).
fof(f86,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,[],[f56]) ).
fof(f90,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,[],[f60]) ).
fof(f95,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ~ empty(power_set(X0)) ),
inference(cnf_transformation,[],[f36]) ).
fof(f96,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,[],[f61]) ).
fof(f110,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[],[f19]) ).
fof(f114,plain,
ilf_type(sK14,relation_type(sK12,sK13)),
inference(cnf_transformation,[],[f69]) ).
fof(f115,plain,
subset(sK11,sK14),
inference(cnf_transformation,[],[f69]) ).
fof(f116,plain,
~ subset(sK11,cross_product(sK12,sK13)),
inference(cnf_transformation,[],[f69]) ).
tcf(c_58,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,[],[f78]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| ~ member(sK3(X0,X1),X1) ),
inference(cnf_transformation,[],[f84]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| member(sK3(X0,X1),X0)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f83]) ).
tcf(c_63,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,[],[f81]) ).
tcf(c_66,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,[],[f86]) ).
tcf(c_72,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,[],[f90]) ).
tcf(c_73,plain,
! [X0: $i] :
( ~ empty(power_set(X0))
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f95]) ).
tcf(c_76,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,[],[f96]) ).
tcf(c_89,plain,
! [X0: $i] : ilf_type(X0,set_type),
inference(cnf_transformation,[],[f110]) ).
tcf(c_90,negated_conjecture,
~ subset(sK11,cross_product(sK12,sK13)),
inference(cnf_transformation,[],[f116]) ).
tcf(c_91,negated_conjecture,
subset(sK11,sK14),
inference(cnf_transformation,[],[f115]) ).
tcf(c_92,negated_conjecture,
ilf_type(sK14,relation_type(sK12,sK13)),
inference(cnf_transformation,[],[f114]) ).
tcf(c_137,plain,
! [X0: $i] : ~ empty(power_set(X0)),
inference(global_subsumption_just,[status(thm)],[c_73,c_89,c_73]) ).
tcf(c_182,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| member(sK3(X0,X1),X0)
| ~ ilf_type(X1,set_type) ),
inference(global_subsumption_just,[status(thm)],[c_61,c_89,c_61]) ).
tcf(c_183,plain,
! [X0: $i,X1: $i] :
( subset(X1,X0)
| member(sK3(X1,X0),X1)
| ~ ilf_type(X0,set_type) ),
inference(renaming,[status(thm)],[c_182]) ).
tcf(c_184,plain,
! [X0: $i,X1: $i] :
( subset(X1,X0)
| member(sK3(X1,X0),X1) ),
inference(global_subsumption_just,[status(thm)],[c_183,c_89,c_183]) ).
tcf(c_185,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| member(sK3(X0,X1),X0) ),
inference(renaming,[status(thm)],[c_184]) ).
tcf(c_196,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ ilf_type(X1,set_type)
| ~ member(sK3(X0,X1),X1) ),
inference(global_subsumption_just,[status(thm)],[c_60,c_89,c_60]) ).
tcf(c_198,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_76,c_89,c_76]) ).
tcf(c_205,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_66,c_89,c_66]) ).
tcf(c_217,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_63,c_89,c_63]) ).
tcf(c_218,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_217]) ).
tcf(c_221,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_72,c_89,c_72]) ).
tcf(c_222,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_221]) ).
tcf(c_240,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| member(X0,X1)
| ~ ilf_type(X0,member_type(X1)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_198,c_89]) ).
tcf(c_241,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_218,c_89]) ).
tcf(c_243,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_222,c_89]) ).
tcf(c_244,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_205,c_89]) ).
tcf(c_247,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_58,c_89]) ).
tcf(c_249,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ member(sK3(X0,X1),X1) ),
inference(backward_subsumption_resolution,[status(thm)],[c_196,c_89]) ).
tcf(c_385,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_247,c_89]) ).
tcf(c_419,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subset(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_241,c_89]) ).
tcf(c_447,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_243,c_89]) ).
tcf(c_561,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_137,c_240]) ).
tcf(c_562,plain,
! [X0: $i,X1: $i] :
( member(X0,power_set(X1))
| ~ ilf_type(X0,member_type(power_set(X1))) ),
inference(unflattening,[status(thm)],[c_561]) ).
tcf(c_632,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_385]) ).
tcf(c_636,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_244]) ).
tcf(c_638,plain,
! [X0: $i,X1: $i] :
( ~ member(sK3(X0,X1),X1)
| subset(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_249]) ).
tcf(c_639,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ member(sK3(X0,X1),X1) ),
inference(renaming,[status(thm)],[c_638]) ).
tcf(c_640,plain,
! [X0: $i,X1: $i] :
( member(sK3(X0,X1),X0)
| subset(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_185]) ).
tcf(c_641,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| member(sK3(X0,X1),X0) ),
inference(renaming,[status(thm)],[c_640]) ).
tcf(c_2591,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_636,c_240]) ).
tcf(c_2611,plain,
! [X0: $i,X1: $i] :
( ~ ilf_type(X0,subset_type(X1))
| member(X0,power_set(X1)) ),
inference(global_subsumption_just,[status(thm)],[c_2591,c_244,c_562]) ).
tcf(c_2612,plain,
! [X0: $i,X1: $i] :
( member(X0,power_set(X1))
| ~ ilf_type(X0,subset_type(X1)) ),
inference(renaming,[status(thm)],[c_2611]) ).
tcf(c_12160,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_636,c_240]) ).
tcf(c_12163,plain,
! [X0: $i,X1: $i] :
( ~ ilf_type(X0,subset_type(X1))
| member(X0,power_set(X1)) ),
inference(global_subsumption_just,[status(thm)],[c_12160,c_2612]) ).
tcf(c_12164,plain,
! [X0: $i,X1: $i] :
( member(X0,power_set(X1))
| ~ ilf_type(X0,subset_type(X1)) ),
inference(renaming,[status(thm)],[c_12163]) ).
tcf(c_12166,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_632,c_12164]) ).
tcf(c_12238,plain,
! [X0: $i] :
( member(X0,sK14)
| ~ member(X0,sK11) ),
inference(superposition,[status(thm)],[c_91,c_419]) ).
tcf(c_12242,plain,
! [X0: $i] :
( subset(sK11,X0)
| member(sK3(sK11,X0),sK14) ),
inference(superposition,[status(thm)],[c_641,c_12238]) ).
tcf(c_12413,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(X3,cross_product(X1,X2))
| ~ member(X3,X0)
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(superposition,[status(thm)],[c_12166,c_447]) ).
tcf(c_18999,plain,
! [X0: $i] :
( member(X0,cross_product(sK12,sK13))
| ~ member(X0,sK14) ),
inference(superposition,[status(thm)],[c_92,c_12413]) ).
tcf(c_19491,plain,
! [X0: $i] :
( subset(X0,cross_product(sK12,sK13))
| ~ member(sK3(X0,cross_product(sK12,sK13)),sK14) ),
inference(superposition,[status(thm)],[c_18999,c_639]) ).
tcf(c_20533,plain,
subset(sK11,cross_product(sK12,sK13)),
inference(superposition,[status(thm)],[c_12242,c_19491]) ).
tcf(c_20534,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_20533,c_90]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET640+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.08/0.35 % Computer : n013.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Thu Sep 24 11:32:06 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.39 Running first-order theorem proving
% 0.12/0.39 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
% 0.12/0.40
% 0.12/0.40 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.40
% 0.12/0.40 % Detected problem language: tptp
% 0.12/0.41 % Proving...
% 8.29/1.62 % SZS status Started for theBenchmark.p
% 8.29/1.62 % SZS status Theorem for theBenchmark.p
% 8.29/1.62
% 8.29/1.62 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 8.29/1.62
% 8.29/1.62 % ------ iProver source info
% 8.29/1.62
% 8.29/1.62 % git: date: 2026-07-19 20:42:38 +0200
% 8.29/1.62 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 8.29/1.62 % git: non_committed_changes: false
% 8.29/1.62
% 8.29/1.62 % ------ Parsing...
% 8.29/1.62 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 8.29/1.62
% 8.29/1.62 % ------ 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 %
% 8.29/1.62
% 8.29/1.62 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 8.29/1.62
% 8.29/1.62 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 8.29/1.62 % ------ Proving...
% 8.29/1.62 % ------ Problem Properties
% 8.29/1.62
% 8.29/1.62 %
% 8.29/1.62 % clauses 33
% 8.29/1.62 % conjectures 3
% 8.29/1.62 % EPR 7
% 8.29/1.62 % Horn 27
% 8.29/1.62 % unary 8
% 8.29/1.62 % binary 19
% 8.29/1.62 % lits 64
% 8.29/1.62 % lits eq 3
% 8.29/1.62 % fd_pure 0
% 8.29/1.62 % fd_pseudo 0
% 8.29/1.62 % fd_cond 0
% 8.29/1.62 % fd_pseudo_cond 0
% 8.29/1.62 % AC symbols 0
% 8.29/1.62
% 8.29/1.62 % ------ Input Options Time Limit: Unbounded
% 8.29/1.62
% 8.29/1.62
% 8.29/1.62 % ------
% 8.29/1.62 % Current options:
% 8.29/1.62 % ------
% 8.29/1.62
% 8.29/1.62
% 8.29/1.62 %
% 8.29/1.62
% 8.29/1.62 % ------ Proving...
% 8.29/1.62 %
% 8.29/1.62
% 8.29/1.62 % SZS status Theorem for theBenchmark.p
% 8.29/1.62
% 8.29/1.62 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 8.29/1.63
% 8.29/1.63
%------------------------------------------------------------------------------