%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET663+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 02:47:43 PM UTC 2026
% Result : Theorem 3.75s 1.26s
% Output : CNFRefutation 3.75s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f173ERROR: Could not build tree for root c_4707ERROR: MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ( subset(X0,empty_set)
=> X0 = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p1) ).
fof(f2,axiom,
! [X0] :
( ilf_type(X0,binary_relation_type)
=> ( ( range_of(X0) = empty_set
| domain_of(X0) = empty_set )
=> X0 = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2) ).
fof(f3,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,relation_type(X0,X1))
=> ( subset(range_of(X2),X1)
& subset(domain_of(X2),X0) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p3) ).
fof(f4,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ~ member(X0,empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p4) ).
fof(f5,axiom,
empty(empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p5a) ).
fof(f7,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(f16,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( ilf_type(X1,subset_type(X0))
<=> ilf_type(X1,member_type(power_set(X0))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p15) ).
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',p21) ).
fof(f23,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',p22) ).
fof(f25,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',p24) ).
fof(f28,axiom,
! [X0] :
( ( ilf_type(X0,set_type)
& empty(X0) )
=> relation_like(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p27) ).
fof(f29,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,subset_type(cross_product(X0,X1)))
=> relation_like(X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p28) ).
fof(f34,axiom,
! [X0] : ilf_type(X0,set_type),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p33) ).
fof(f35,conjecture,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,relation_type(X0,X1))
=> ( ilf_type(X2,relation_type(empty_set,X1))
=> X2 = empty_set ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_relset_1_26) ).
fof(f36,negated_conjecture,
~ ! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,relation_type(X0,X1))
=> ( ilf_type(X2,relation_type(empty_set,X1))
=> X2 = empty_set ) ) ) ),
inference(negated_conjecture,[status(cth)],[f35]) ).
fof(f38,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ~ subset(X0,empty_set)
| X0 = empty_set ),
inference(ennf_transformation,[],[f1]) ).
fof(f39,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ~ subset(X0,empty_set)
| X0 = empty_set ),
inference(flattening,[],[f38]) ).
fof(f40,plain,
! [X0] :
( ~ ilf_type(X0,binary_relation_type)
| ( empty_set != range_of(X0)
& empty_set != domain_of(X0) )
| X0 = empty_set ),
inference(ennf_transformation,[],[f2]) ).
fof(f41,plain,
! [X0] :
( ~ ilf_type(X0,binary_relation_type)
| ( empty_set != range_of(X0)
& empty_set != domain_of(X0) )
| X0 = empty_set ),
inference(flattening,[],[f40]) ).
fof(f42,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ! [X2] :
( ~ ilf_type(X2,relation_type(X0,X1))
| ( subset(range_of(X2),X1)
& subset(domain_of(X2),X0) ) ) ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f43,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ~ member(X0,empty_set) ),
inference(ennf_transformation,[],[f4]) ).
fof(f44,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,[],[f7]) ).
fof(f52,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ( ilf_type(X1,subset_type(X0))
<=> ilf_type(X1,member_type(power_set(X0))) ) ) ),
inference(ennf_transformation,[],[f16]) ).
fof(f60,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ( empty(X0)
<=> ! [X1] :
( ~ ilf_type(X1,set_type)
| ~ member(X1,X0) ) ) ),
inference(ennf_transformation,[],[f22]) ).
fof(f61,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,[],[f23]) ).
fof(f62,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,[],[f61]) ).
fof(f64,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,[],[f25]) ).
fof(f65,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,[],[f64]) ).
fof(f70,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ~ empty(X0)
| relation_like(X0) ),
inference(ennf_transformation,[],[f28]) ).
fof(f71,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ~ empty(X0)
| relation_like(X0) ),
inference(flattening,[],[f70]) ).
fof(f72,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ! [X2] :
( ~ ilf_type(X2,subset_type(cross_product(X0,X1)))
| relation_like(X2) ) ) ),
inference(ennf_transformation,[],[f29]) ).
fof(f77,plain,
? [X0] :
( ilf_type(X0,set_type)
& ? [X1] :
( ilf_type(X1,set_type)
& ? [X2] :
( ilf_type(X2,relation_type(X0,X1))
& ilf_type(X2,relation_type(empty_set,X1))
& empty_set != X2 ) ) ),
inference(ennf_transformation,[],[f36]) ).
fof(f78,plain,
? [X0] :
( ilf_type(X0,set_type)
& ? [X1] :
( ilf_type(X1,set_type)
& ? [X2] :
( ilf_type(X2,relation_type(X0,X1))
& ilf_type(X2,relation_type(empty_set,X1))
& empty_set != X2 ) ) ),
inference(flattening,[],[f77]) ).
fof(f87,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,[],[f52]) ).
fof(f92,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,[],[f60]) ).
fof(f93,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,[],[f92]) ).
fof(f94,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ( ( ~ empty(X0)
| ! [X2] :
( ~ ilf_type(X2,set_type)
| ~ member(X2,X0) ) )
& ( ( ilf_type(sK6(X0),set_type)
& member(sK6(X0),X0) )
| empty(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(X1,sK6(X0))],[f93]) ).
fof(f95,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,[],[f62]) ).
fof(f96,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,[],[f95]) ).
fof(f97,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(sK7(X0,X1),set_type)
& member(sK7(X0,X1),X0)
& ~ member(sK7(X0,X1),X1) )
| member(X0,power_set(X1)) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(X2,sK7(X0,X1))],[f96]) ).
fof(f98,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,[],[f65]) ).
fof(f103,plain,
( ilf_type(sK12,set_type)
& ilf_type(sK13,set_type)
& ilf_type(sK14,relation_type(sK12,sK13))
& ilf_type(sK14,relation_type(empty_set,sK13))
& empty_set != sK14 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12,sK13,sK14]),skolemize(X0,sK12),skolemize(X1,sK13),skolemize(X2,sK14)],[f78]) ).
fof(f104,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ~ subset(X0,empty_set)
| empty_set = X0 ),
inference(cnf_transformation,[],[f39]) ).
fof(f106,plain,
! [X0] :
( ~ ilf_type(X0,binary_relation_type)
| empty_set != domain_of(X0)
| empty_set = X0 ),
inference(cnf_transformation,[],[f41]) ).
fof(f108,plain,
! [X2,X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,relation_type(X0,X1))
| subset(domain_of(X2),X0) ),
inference(cnf_transformation,[],[f42]) ).
fof(f109,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ~ member(X0,empty_set) ),
inference(cnf_transformation,[],[f43]) ).
fof(f110,plain,
empty(empty_set),
inference(cnf_transformation,[],[f5]) ).
fof(f111,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,[],[f44]) ).
fof(f112,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,[],[f44]) ).
fof(f129,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,[],[f87]) ).
fof(f138,plain,
! [X2,X0] :
( ~ ilf_type(X0,set_type)
| ~ empty(X0)
| ~ ilf_type(X2,set_type)
| ~ member(X2,X0) ),
inference(cnf_transformation,[],[f94]) ).
fof(f143,plain,
! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| member(sK7(X0,X1),X0)
| member(X0,power_set(X1)) ),
inference(cnf_transformation,[],[f97]) ).
fof(f148,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,[],[f98]) ).
fof(f156,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ~ empty(X0)
| relation_like(X0) ),
inference(cnf_transformation,[],[f71]) ).
fof(f157,plain,
! [X2,X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,subset_type(cross_product(X0,X1)))
| relation_like(X2) ),
inference(cnf_transformation,[],[f72]) ).
fof(f162,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[],[f34]) ).
fof(f166,plain,
ilf_type(sK14,relation_type(empty_set,sK13)),
inference(cnf_transformation,[],[f103]) ).
fof(f167,plain,
empty_set != sK14,
inference(cnf_transformation,[],[f103]) ).
tcf(c_49,plain,
! [X0: $i] :
( ( X0 = empty_set )
| ~ ilf_type(X0,set_type)
| ~ subset(X0,empty_set) ),
inference(cnf_transformation,[],[f104]) ).
tcf(c_50,plain,
! [X0: $i] :
( ( X0 = empty_set )
| ~ ilf_type(X0,binary_relation_type)
| ( domain_of(X0) != empty_set ) ),
inference(cnf_transformation,[],[f106]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(domain_of(X0),X1)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(cnf_transformation,[],[f108]) ).
tcf(c_54,plain,
! [X0: $i] :
( ~ member(X0,empty_set)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f109]) ).
tcf(c_55,plain,
empty(empty_set),
inference(cnf_transformation,[],[f110]) ).
tcf(c_56,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,[],[f112]) ).
tcf(c_57,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,[],[f111]) ).
tcf(c_69,plain,
! [X0: $i] :
( ilf_type(X0,binary_relation_type)
| ~ relation_like(X0)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f173]) ).
tcf(c_72,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,[],[f129]) ).
tcf(c_83,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f138]) ).
tcf(c_85,plain,
! [X0: $i,X1: $i] :
( member(X0,power_set(X1))
| member(sK7(X0,X1),X0)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f143]) ).
tcf(c_90,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,[],[f148]) ).
tcf(c_99,plain,
! [X0: $i] :
( relation_like(X0)
| ~ empty(X0)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f156]) ).
tcf(c_100,plain,
! [X0: $i,X1: $i,X2: $i] :
( relation_like(X0)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,subset_type(cross_product(X1,X2))) ),
inference(cnf_transformation,[],[f157]) ).
tcf(c_105,plain,
! [X0: $i] : ilf_type(X0,set_type),
inference(cnf_transformation,[],[f162]) ).
tcf(c_106,negated_conjecture,
empty_set != sK14,
inference(cnf_transformation,[],[f167]) ).
tcf(c_107,negated_conjecture,
ilf_type(sK14,relation_type(empty_set,sK13)),
inference(cnf_transformation,[],[f166]) ).
tcf(c_164,plain,
! [X0: $i] : ~ member(X0,empty_set),
inference(global_subsumption_just,[status(thm)],[c_54,c_105,c_54]) ).
tcf(c_167,plain,
! [X0: $i] :
( relation_like(X0)
| ~ empty(X0) ),
inference(global_subsumption_just,[status(thm)],[c_99,c_105,c_99]) ).
tcf(c_188,plain,
! [X0: $i] :
( ilf_type(X0,binary_relation_type)
| ~ relation_like(X0) ),
inference(global_subsumption_just,[status(thm)],[c_69,c_105,c_69]) ).
tcf(c_227,plain,
! [X0: $i,X1: $i] :
( member(X0,power_set(X1))
| member(sK7(X0,X1),X0)
| ~ ilf_type(X1,set_type) ),
inference(global_subsumption_just,[status(thm)],[c_85,c_105,c_85]) ).
tcf(c_228,plain,
! [X0: $i,X1: $i] :
( member(X1,power_set(X0))
| member(sK7(X1,X0),X1)
| ~ ilf_type(X0,set_type) ),
inference(renaming,[status(thm)],[c_227]) ).
tcf(c_229,plain,
! [X0: $i,X1: $i] :
( member(X1,power_set(X0))
| member(sK7(X1,X0),X1) ),
inference(global_subsumption_just,[status(thm)],[c_228,c_105,c_228]) ).
tcf(c_230,plain,
! [X0: $i,X1: $i] :
( member(X0,power_set(X1))
| member(sK7(X0,X1),X0) ),
inference(renaming,[status(thm)],[c_229]) ).
tcf(c_236,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_90,c_105,c_83,c_90]) ).
tcf(c_237,plain,
! [X0: $i,X1: $i] :
( ilf_type(X0,member_type(X1))
| ~ ilf_type(X1,set_type)
| ~ member(X0,X1) ),
inference(renaming,[status(thm)],[c_236]) ).
tcf(c_243,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_72,c_105,c_72]) ).
tcf(c_259,plain,
! [X0: $i] :
( ilf_type(X0,binary_relation_type)
| ~ relation_like(X0) ),
inference(prop_impl_just,[status(thm)],[c_188]) ).
tcf(c_267,plain,
! [X0: $i] :
( ~ empty(X0)
| relation_like(X0) ),
inference(prop_impl_just,[status(thm)],[c_167]) ).
tcf(c_268,plain,
! [X0: $i] :
( relation_like(X0)
| ~ empty(X0) ),
inference(renaming,[status(thm)],[c_267]) ).
tcf(c_396,plain,
! [X0: $i] :
( ( X0 = empty_set )
| ~ relation_like(X0)
| ( domain_of(X0) != empty_set ) ),
inference(bin_hyper_res,[status(thm)],[c_50,c_259]) ).
tcf(c_416,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(domain_of(X0),X1)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_52,c_105]) ).
tcf(c_419,plain,
! [X0: $i,X1: $i] :
( ilf_type(X0,member_type(X1))
| ~ member(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[c_237,c_105]) ).
tcf(c_421,plain,
! [X0: $i,X1: $i,X2: $i] :
( relation_like(X0)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X0,subset_type(cross_product(X1,X2))) ),
inference(backward_subsumption_resolution,[status(thm)],[c_100,c_105]) ).
tcf(c_427,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_57,c_105]) ).
tcf(c_428,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_56,c_105]) ).
tcf(c_429,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_243,c_105]) ).
tcf(c_536,plain,
! [X0: $i,X1: $i,X2: $i] :
( relation_like(X0)
| ~ ilf_type(X0,subset_type(cross_product(X1,X2))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_421,c_105]) ).
tcf(c_547,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(domain_of(X0),X1)
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_416,c_105]) ).
tcf(c_586,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_427,c_105]) ).
tcf(c_597,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_428,c_105]) ).
tcf(c_891,plain,
! [X0: $i] :
( relation_like(X0)
| ( X0 != empty_set ) ),
inference(resolution_lifted,[status(thm)],[c_55,c_268]) ).
tcf(c_892,plain,
relation_like(empty_set),
inference(unflattening,[status(thm)],[c_891]) ).
tcf(c_1531,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_597]) ).
tcf(c_1532,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_1531]) ).
tcf(c_1535,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_429]) ).
tcf(c_1536,plain,
! [X0: $i,X1: $i] :
( ilf_type(X0,subset_type(X1))
| ~ ilf_type(X0,member_type(power_set(X1))) ),
inference(renaming,[status(thm)],[c_1535]) ).
tcf(c_1539,plain,
! [X0: $i] :
( ( X0 = empty_set )
| ~ subset(X0,empty_set) ),
inference(prop_impl_just,[status(thm)],[c_105,c_49]) ).
tcf(c_1541,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(domain_of(X0),X1)
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(prop_impl_just,[status(thm)],[c_547]) ).
tcf(c_1545,plain,
! [X0: $i,X1: $i,X2: $i] :
( relation_like(X0)
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(prop_impl_just,[status(thm)],[c_536,c_586]) ).
tcf(c_1575,plain,
! [X0: $i,X1: $i] :
( ilf_type(X0,member_type(X1))
| ~ member(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_419]) ).
tcf(c_1583,plain,
! [X0: $i,X1: $i] :
( member(sK7(X0,X1),X0)
| member(X0,power_set(X1)) ),
inference(prop_impl_just,[status(thm)],[c_230]) ).
tcf(c_1584,plain,
! [X0: $i,X1: $i] :
( member(X0,power_set(X1))
| member(sK7(X0,X1),X0) ),
inference(renaming,[status(thm)],[c_1583]) ).
tcf(c_2228,definition,
iPr_def_11 = relation_type(empty_set,sK13),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_2230,negated_conjecture,
ilf_type(sK14,iPr_def_11),
inference(demodulation,[status(thm)],[c_107,c_2228]) ).
tcf(c_2234,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_3151,plain,
! [X0: $i] :
( relation_like(X0)
| ~ ilf_type(X0,iPr_def_11) ),
inference(superposition,[status(thm)],[c_2228,c_1545]) ).
tcf(c_3183,plain,
relation_like(sK14),
inference(superposition,[status(thm)],[c_2230,c_3151]) ).
tcf(c_3246,plain,
! [X0: $i] :
( subset(domain_of(X0),empty_set)
| ~ ilf_type(X0,iPr_def_11) ),
inference(superposition,[status(thm)],[c_2228,c_1541]) ).
tcf(c_3292,plain,
! [X0: $i] :
( ( domain_of(X0) = empty_set )
| ~ ilf_type(X0,iPr_def_11) ),
inference(superposition,[status(thm)],[c_3246,c_1539]) ).
tcf(c_3357,plain,
! [X0: $i] : member(empty_set,power_set(X0)),
inference(superposition,[status(thm)],[c_1584,c_164]) ).
tcf(c_3402,plain,
domain_of(sK14) = empty_set,
inference(superposition,[status(thm)],[c_2230,c_3292]) ).
tcf(c_3412,plain,
! [X0: $i,X1: $i] :
( ilf_type(X0,subset_type(X1))
| ~ member(X0,power_set(X1)) ),
inference(superposition,[status(thm)],[c_1575,c_1536]) ).
tcf(c_3437,plain,
! [X0: $i] : ilf_type(empty_set,subset_type(X0)),
inference(superposition,[status(thm)],[c_3357,c_3412]) ).
tcf(c_3530,plain,
! [X0: $i] :
( ( empty_set = sK14 )
| ( sK14 != X0 )
| ( empty_set != X0 ) ),
inference(instantiation,[status(thm)],[c_2234]) ).
tcf(c_3600,plain,
! [X0: $i,X1: $i] : ilf_type(empty_set,relation_type(X0,X1)),
inference(superposition,[status(thm)],[c_3437,c_1532]) ).
tcf(c_3606,plain,
ilf_type(empty_set,iPr_def_11),
inference(superposition,[status(thm)],[c_2228,c_3600]) ).
tcf(c_3625,plain,
domain_of(empty_set) = empty_set,
inference(superposition,[status(thm)],[c_3606,c_3292]) ).
tcf(c_3658,plain,
( ( empty_set = sK14 )
| ( sK14 != empty_set )
| ( empty_set != empty_set ) ),
inference(instantiation,[status(thm)],[c_3530]) ).
tcf(c_3660,plain,
( ( empty_set = empty_set )
| ~ relation_like(empty_set)
| ( domain_of(empty_set) != empty_set ) ),
inference(instantiation,[status(thm)],[c_396]) ).
tcf(c_4705,plain,
( ( sK14 = empty_set )
| ~ relation_like(sK14)
| ( domain_of(sK14) != empty_set ) ),
inference(instantiation,[status(thm)],[c_396]) ).
tcf(c_4707,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_4705,c_3660,c_3658,c_3625,c_3402,c_3183,c_892,c_106]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET663+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.35 % Computer : n002.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Thu Sep 24 11:38:37 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.39 Running first-order theorem proving
% 0.10/0.39 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
% 0.10/0.40
% 0.10/0.40 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.40
% 0.10/0.41 % Detected problem language: tptp
% 0.10/0.42 % Proving...
% 3.75/1.26 % SZS status Started for theBenchmark.p
% 3.75/1.26 % SZS status Theorem for theBenchmark.p
% 3.75/1.26
% 3.75/1.26 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.75/1.26
% 3.75/1.26 % ------ iProver source info
% 3.75/1.26
% 3.75/1.26 % git: date: 2026-07-19 20:42:38 +0200
% 3.75/1.26 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.75/1.26 % git: non_committed_changes: false
% 3.75/1.26
% 3.75/1.26 % ------ Parsing...
% 3.75/1.26 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.75/1.26
% 3.75/1.26 % ------ 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 %
% 3.75/1.26
% 3.75/1.26 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.75/1.26
% 3.75/1.26 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.75/1.26 % ------ Proving...
% 3.75/1.26 % ------ Problem Properties
% 3.75/1.26
% 3.75/1.26 %
% 3.75/1.26 % clauses 46
% 3.75/1.26 % conjectures 3
% 3.75/1.26 % EPR 14
% 3.75/1.26 % Horn 39
% 3.75/1.26 % unary 13
% 3.75/1.26 % binary 25
% 3.75/1.26 % lits 91
% 3.75/1.26 % lits eq 14
% 3.75/1.26 % fd_pure 0
% 3.75/1.26 % fd_pseudo 0
% 3.75/1.26 % fd_cond 3
% 3.75/1.26 % fd_pseudo_cond 2
% 3.75/1.26 % AC symbols 0
% 3.75/1.26
% 3.75/1.26 % ------ Schedule dynamic 5 is on
% 3.75/1.26
% 3.75/1.26 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.75/1.26
% 3.75/1.26
% 3.75/1.26 % ------
% 3.75/1.26 % Current options:
% 3.75/1.26 % ------
% 3.75/1.26
% 3.75/1.26
% 3.75/1.26 %
% 3.75/1.26
% 3.75/1.26 % ------ Proving...
% 3.75/1.26 %
% 3.75/1.26
% 3.75/1.26 % SZS status Theorem for theBenchmark.p
% 3.75/1.26
% 3.75/1.26 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.75/1.27
% 3.75/1.27
%------------------------------------------------------------------------------