%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET650+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n014.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 02:47:41 PM UTC 2026
% Result : Theorem 3.86s 1.20s
% Output : CNFRefutation 1.85s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f141ERROR: Could not build tree for root c_3518ERROR: MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,binary_relation_type)
=> ( member(X0,domain_of(X1))
<=> ? [X2] :
( member(ordered_pair(X0,X2),X1)
& ilf_type(X2,set_type) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p1) ).
fof(f2,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,binary_relation_type)
=> ( member(X0,range_of(X1))
<=> ? [X2] :
( member(ordered_pair(X2,X0),X1)
& ilf_type(X2,set_type) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2) ).
fof(f3,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)
=> ! [X4] :
( ilf_type(X4,relation_type(X0,X1))
=> ( member(ordered_pair(X2,X3),X4)
=> ( member(X3,X1)
& member(X2,X0) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p3) ).
fof(f8,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/sandbox2/benchmark/theBenchmark.p',p8) ).
fof(f10,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/sandbox2/benchmark/theBenchmark.p',p10) ).
fof(f23,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/sandbox2/benchmark/theBenchmark.p',p23) ).
fof(f26,axiom,
! [X0] : ilf_type(X0,set_type),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p26) ).
fof(f27,conjecture,
! [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/sandbox2/benchmark/theBenchmark.p',prove_relset_1_12) ).
fof(f28,negated_conjecture,
~ ! [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(negated_conjecture,[status(cth)],[f27]) ).
fof(f29,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,[],[f28]) ).
fof(f32,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,binary_relation_type)
| ( member(X0,domain_of(X1))
<=> ? [X2] :
( member(ordered_pair(X0,X2),X1)
& ilf_type(X2,set_type) ) ) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f34,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,[],[f10]) ).
fof(f35,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,[],[f34]) ).
fof(f38,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,binary_relation_type)
| ( member(X0,range_of(X1))
<=> ? [X2] :
( member(ordered_pair(X2,X0),X1)
& ilf_type(X2,set_type) ) ) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f40,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,[],[f8]) ).
fof(f41,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)
| ! [X4] :
( ~ ilf_type(X4,relation_type(X0,X1))
| ~ member(ordered_pair(X2,X3),X4)
| ( member(X3,X1)
& member(X2,X0) ) ) ) ) ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f42,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)
| ! [X4] :
( ~ ilf_type(X4,relation_type(X0,X1))
| ~ member(ordered_pair(X2,X3),X4)
| ( member(X3,X1)
& member(X2,X0) ) ) ) ) ) ),
inference(flattening,[],[f41]) ).
fof(f44,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,[],[f23]) ).
fof(f59,plain,
( ilf_type(sK0,set_type)
& ilf_type(sK1,set_type)
& ilf_type(sK2,relation_type(sK0,sK1))
& ( ~ subset(range_of(sK2),sK1)
| ~ subset(domain_of(sK2),sK0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f29]) ).
fof(f63,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,binary_relation_type)
| ( ( ~ member(X0,domain_of(X1))
| ? [X2] :
( member(ordered_pair(X0,X2),X1)
& ilf_type(X2,set_type) ) )
& ( ! [X2] :
( ~ member(ordered_pair(X0,X2),X1)
| ~ ilf_type(X2,set_type) )
| member(X0,domain_of(X1)) ) ) ) ),
inference(nnf_transformation,[],[f32]) ).
fof(f64,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,binary_relation_type)
| ( ( ~ member(X0,domain_of(X1))
| ? [X3] :
( member(ordered_pair(X0,X3),X1)
& ilf_type(X3,set_type) ) )
& ( ! [X2] :
( ~ member(ordered_pair(X0,X2),X1)
| ~ ilf_type(X2,set_type) )
| member(X0,domain_of(X1)) ) ) ) ),
inference(rectify,[],[f63]) ).
fof(f65,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,binary_relation_type)
| ( ( ~ member(X0,domain_of(X1))
| ( member(ordered_pair(X0,sK4(X0,X1)),X1)
& ilf_type(sK4(X0,X1),set_type) ) )
& ( ! [X2] :
( ~ member(ordered_pair(X0,X2),X1)
| ~ ilf_type(X2,set_type) )
| member(X0,domain_of(X1)) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X3,sK4(X0,X1))],[f64]) ).
fof(f66,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ( ( ~ subset(X0,X1)
| ! [X2] :
( ~ ilf_type(X2,set_type)
| ~ member(X2,X0)
| member(X2,X1) ) )
& ( ? [X2] :
( ilf_type(X2,set_type)
& member(X2,X0)
& ~ member(X2,X1) )
| subset(X0,X1) ) ) ) ),
inference(nnf_transformation,[],[f35]) ).
fof(f67,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ( ( ~ subset(X0,X1)
| ! [X3] :
( ~ ilf_type(X3,set_type)
| ~ member(X3,X0)
| member(X3,X1) ) )
& ( ? [X2] :
( ilf_type(X2,set_type)
& member(X2,X0)
& ~ member(X2,X1) )
| subset(X0,X1) ) ) ) ),
inference(rectify,[],[f66]) ).
fof(f68,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ( ( ~ subset(X0,X1)
| ! [X3] :
( ~ ilf_type(X3,set_type)
| ~ member(X3,X0)
| member(X3,X1) ) )
& ( ( ilf_type(sK5(X0,X1),set_type)
& member(sK5(X0,X1),X0)
& ~ member(sK5(X0,X1),X1) )
| subset(X0,X1) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(X2,sK5(X0,X1))],[f67]) ).
fof(f72,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,binary_relation_type)
| ( ( ~ member(X0,range_of(X1))
| ? [X2] :
( member(ordered_pair(X2,X0),X1)
& ilf_type(X2,set_type) ) )
& ( ! [X2] :
( ~ member(ordered_pair(X2,X0),X1)
| ~ ilf_type(X2,set_type) )
| member(X0,range_of(X1)) ) ) ) ),
inference(nnf_transformation,[],[f38]) ).
fof(f73,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,binary_relation_type)
| ( ( ~ member(X0,range_of(X1))
| ? [X3] :
( member(ordered_pair(X3,X0),X1)
& ilf_type(X3,set_type) ) )
& ( ! [X2] :
( ~ member(ordered_pair(X2,X0),X1)
| ~ ilf_type(X2,set_type) )
| member(X0,range_of(X1)) ) ) ) ),
inference(rectify,[],[f72]) ).
fof(f74,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,binary_relation_type)
| ( ( ~ member(X0,range_of(X1))
| ( member(ordered_pair(sK7(X0,X1),X0),X1)
& ilf_type(sK7(X0,X1),set_type) ) )
& ( ! [X2] :
( ~ member(ordered_pair(X2,X0),X1)
| ~ ilf_type(X2,set_type) )
| member(X0,range_of(X1)) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(X3,sK7(X0,X1))],[f73]) ).
fof(f91,plain,
ilf_type(sK2,relation_type(sK0,sK1)),
inference(cnf_transformation,[],[f59]) ).
fof(f92,plain,
( ~ subset(range_of(sK2),sK1)
| ~ subset(domain_of(sK2),sK0) ),
inference(cnf_transformation,[],[f59]) ).
fof(f93,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[],[f26]) ).
fof(f98,plain,
! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,binary_relation_type)
| ~ member(X0,domain_of(X1))
| member(ordered_pair(X0,sK4(X0,X1)),X1) ),
inference(cnf_transformation,[],[f65]) ).
fof(f104,plain,
! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| member(sK5(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f68]) ).
fof(f105,plain,
! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ member(sK5(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f68]) ).
fof(f110,plain,
! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,binary_relation_type)
| ~ member(X0,range_of(X1))
| member(ordered_pair(sK7(X0,X1),X0),X1) ),
inference(cnf_transformation,[],[f74]) ).
fof(f114,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,[],[f40]) ).
fof(f116,plain,
! [X2,X3,X0,X1,X4] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X4,relation_type(X0,X1))
| ~ member(ordered_pair(X2,X3),X4)
| member(X3,X1) ),
inference(cnf_transformation,[],[f42]) ).
fof(f117,plain,
! [X2,X3,X0,X1,X4] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X4,relation_type(X0,X1))
| ~ member(ordered_pair(X2,X3),X4)
| member(X2,X0) ),
inference(cnf_transformation,[],[f42]) ).
fof(f120,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,[],[f44]) ).
tcf(c_49,negated_conjecture,
( ~ subset(range_of(sK2),sK1)
| ~ subset(domain_of(sK2),sK0) ),
inference(cnf_transformation,[],[f92]) ).
tcf(c_50,negated_conjecture,
ilf_type(sK2,relation_type(sK0,sK1)),
inference(cnf_transformation,[],[f91]) ).
tcf(c_53,plain,
! [X0: $i] : ilf_type(X0,set_type),
inference(cnf_transformation,[],[f93]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i] :
( member(ordered_pair(X0,sK4(X0,X1)),X1)
| ~ ilf_type(X1,binary_relation_type)
| ~ ilf_type(X0,set_type)
| ~ member(X0,domain_of(X1)) ),
inference(cnf_transformation,[],[f98]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| ~ member(sK5(X0,X1),X1) ),
inference(cnf_transformation,[],[f105]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| member(sK5(X0,X1),X0)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f104]) ).
tcf(c_72,plain,
! [X0: $i,X1: $i] :
( member(ordered_pair(sK7(X0,X1),X0),X1)
| ~ ilf_type(X1,binary_relation_type)
| ~ ilf_type(X0,set_type)
| ~ member(X0,range_of(X1)) ),
inference(cnf_transformation,[],[f110]) ).
tcf(c_75,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,[],[f114]) ).
tcf(c_76,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( member(X3,X1)
| ~ ilf_type(X4,set_type)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ member(ordered_pair(X3,X4),X0)
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(cnf_transformation,[],[f117]) ).
tcf(c_77,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( member(X4,X2)
| ~ ilf_type(X4,set_type)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ member(ordered_pair(X3,X4),X0)
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(cnf_transformation,[],[f116]) ).
tcf(c_80,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,[],[f120]) ).
tcf(c_86,plain,
! [X0: $i] :
( ilf_type(X0,binary_relation_type)
| ~ relation_like(X0)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f141]) ).
tcf(c_162,plain,
! [X0: $i] :
( ilf_type(X0,binary_relation_type)
| ~ relation_like(X0) ),
inference(global_subsumption_just,[status(thm)],[c_86,c_53,c_86]) ).
tcf(c_189,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| member(sK5(X0,X1),X0)
| ~ ilf_type(X1,set_type) ),
inference(global_subsumption_just,[status(thm)],[c_63,c_53,c_63]) ).
tcf(c_190,plain,
! [X0: $i,X1: $i] :
( subset(X1,X0)
| member(sK5(X1,X0),X1)
| ~ ilf_type(X0,set_type) ),
inference(renaming,[status(thm)],[c_189]) ).
tcf(c_191,plain,
! [X0: $i,X1: $i] :
( subset(X1,X0)
| member(sK5(X1,X0),X1) ),
inference(global_subsumption_just,[status(thm)],[c_190,c_53,c_190]) ).
tcf(c_192,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| member(sK5(X0,X1),X0) ),
inference(renaming,[status(thm)],[c_191]) ).
tcf(c_203,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ ilf_type(X1,set_type)
| ~ member(sK5(X0,X1),X1) ),
inference(global_subsumption_just,[status(thm)],[c_62,c_53,c_62]) ).
tcf(c_228,plain,
! [X0: $i,X1: $i] :
( member(ordered_pair(sK7(X0,X1),X0),X1)
| ~ ilf_type(X1,binary_relation_type)
| ~ member(X0,range_of(X1)) ),
inference(global_subsumption_just,[status(thm)],[c_72,c_53,c_72]) ).
tcf(c_234,plain,
! [X0: $i,X1: $i] :
( member(ordered_pair(X0,sK4(X0,X1)),X1)
| ~ ilf_type(X1,binary_relation_type)
| ~ member(X0,domain_of(X1)) ),
inference(global_subsumption_just,[status(thm)],[c_60,c_53,c_60]) ).
tcf(c_254,plain,
! [X0: $i] :
( ilf_type(X0,binary_relation_type)
| ~ relation_like(X0) ),
inference(prop_impl_just,[status(thm)],[c_162]) ).
tcf(c_383,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_80,c_53]) ).
tcf(c_386,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ member(sK5(X0,X1),X1) ),
inference(backward_subsumption_resolution,[status(thm)],[c_203,c_53]) ).
tcf(c_387,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_75,c_53]) ).
tcf(c_388,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( member(X4,X2)
| ~ ilf_type(X4,set_type)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type)
| ~ member(ordered_pair(X3,X4),X0)
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_77,c_53]) ).
tcf(c_389,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( member(X3,X1)
| ~ ilf_type(X4,set_type)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type)
| ~ member(ordered_pair(X3,X4),X0)
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_76,c_53]) ).
tcf(c_480,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_383,c_53]) ).
tcf(c_527,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_387,c_53]) ).
tcf(c_580,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( member(X4,X2)
| ~ member(ordered_pair(X3,X4),X0)
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_388,c_53,c_53,c_53]) ).
tcf(c_597,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( member(X3,X1)
| ~ member(ordered_pair(X3,X4),X0)
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_389,c_53,c_53,c_53]) ).
tcf(c_607,plain,
! [X0: $i,X1: $i,X2: $i] :
( ilf_type(X0,binary_relation_type)
| ~ ilf_type(X0,subset_type(cross_product(X1,X2))) ),
inference(resolution,[status(thm)],[c_480,c_254]) ).
tcf(c_729,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ilf_type(X0,relation_type(X1,X2))
| ilf_type(X0,binary_relation_type) ),
inference(prop_impl_just,[status(thm)],[c_527,c_607]) ).
tcf(c_730,plain,
! [X0: $i,X1: $i,X2: $i] :
( ilf_type(X0,binary_relation_type)
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(renaming,[status(thm)],[c_729]) ).
tcf(c_733,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ member(sK5(X0,X1),X1) ),
inference(prop_impl_just,[status(thm)],[c_386]) ).
tcf(c_737,plain,
! [X0: $i,X1: $i] :
( member(sK5(X0,X1),X0)
| subset(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_192]) ).
tcf(c_738,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| member(sK5(X0,X1),X0) ),
inference(renaming,[status(thm)],[c_737]) ).
tcf(c_1046,plain,
( subset(domain_of(sK2),sK0)
| ~ member(sK5(domain_of(sK2),sK0),sK0) ),
inference(instantiation,[status(thm)],[c_733]) ).
tcf(c_1047,plain,
( subset(domain_of(sK2),sK0)
| member(sK5(domain_of(sK2),sK0),domain_of(sK2)) ),
inference(instantiation,[status(thm)],[c_738]) ).
tcf(c_1061,plain,
! [X0: $i,X1: $i] :
( member(X0,sK0)
| ~ ilf_type(sK2,relation_type(sK0,sK1))
| ~ member(ordered_pair(X0,X1),sK2) ),
inference(instantiation,[status(thm)],[c_597]) ).
tcf(c_1136,plain,
( member(ordered_pair(sK5(domain_of(sK2),sK0),sK4(sK5(domain_of(sK2),sK0),sK2)),sK2)
| ~ ilf_type(sK2,binary_relation_type)
| ~ member(sK5(domain_of(sK2),sK0),domain_of(sK2)) ),
inference(instantiation,[status(thm)],[c_234]) ).
tcf(c_1250,plain,
( member(sK5(domain_of(sK2),sK0),sK0)
| ~ ilf_type(sK2,relation_type(sK0,sK1))
| ~ member(ordered_pair(sK5(domain_of(sK2),sK0),sK4(sK5(domain_of(sK2),sK0),sK2)),sK2) ),
inference(instantiation,[status(thm)],[c_1061]) ).
tcf(c_1539,plain,
ilf_type(sK2,binary_relation_type),
inference(superposition,[status(thm)],[c_50,c_730]) ).
tcf(c_2670,plain,
! [X0: $i,X1: $i] :
( member(X1,sK1)
| ~ member(ordered_pair(X0,X1),sK2) ),
inference(superposition,[status(thm)],[c_50,c_580]) ).
tcf(c_3076,plain,
! [X0: $i] :
( member(X0,sK1)
| ~ ilf_type(sK2,binary_relation_type)
| ~ member(X0,range_of(sK2)) ),
inference(superposition,[status(thm)],[c_228,c_2670]) ).
tcf(c_3077,plain,
! [X0: $i] :
( member(X0,sK1)
| ~ member(X0,range_of(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3076,c_1539]) ).
tcf(c_3182,plain,
! [X0: $i] :
( subset(range_of(sK2),X0)
| member(sK5(range_of(sK2),X0),sK1) ),
inference(superposition,[status(thm)],[c_738,c_3077]) ).
tcf(c_3512,plain,
subset(range_of(sK2),sK1),
inference(superposition,[status(thm)],[c_3182,c_733]) ).
tcf(c_3518,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_3512,c_1539,c_1250,c_1136,c_1047,c_1046,c_49,c_50]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET650+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.36 % Computer : n014.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Thu Sep 24 11:34:03 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.14/0.40 Running first-order theorem proving
% 0.14/0.40 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.41
% 0.14/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.41
% 0.14/0.41 % Detected problem language: tptp
% 0.14/0.43 % Proving...
% 3.86/1.20 % SZS status Started for theBenchmark.p
% 3.86/1.20 % SZS status Theorem for theBenchmark.p
% 3.86/1.20
% 3.86/1.20 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.86/1.20
% 3.86/1.20 % ------ iProver source info
% 3.86/1.20
% 3.86/1.20 % git: date: 2026-07-19 20:42:38 +0200
% 3.86/1.20 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.86/1.20 % git: non_committed_changes: false
% 3.86/1.20
% 3.86/1.20 % ------ Parsing...
% 3.86/1.20 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.86/1.20
% 3.86/1.20 % ------ Preprocessing... sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e sf_s rm: 0 0s sf_e pe_s pe_e %
% 3.86/1.20
% 3.86/1.20 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 3.86/1.20 % ------ Proving...
% 3.86/1.20 % ------ Problem Properties
% 3.86/1.20
% 3.86/1.20 %
% 3.86/1.20 % clauses 32
% 3.86/1.20 % conjectures 2
% 3.86/1.20 % EPR 5
% 3.86/1.20 % Horn 27
% 3.86/1.20 % unary 6
% 3.86/1.20 % binary 15
% 3.86/1.20 % lits 69
% 3.86/1.20 % lits eq 0
% 3.86/1.20 % fd_pure 0
% 3.86/1.20 % fd_pseudo 0
% 3.86/1.20 % fd_cond 0
% 3.86/1.20 % fd_pseudo_cond 0
% 3.86/1.20 % AC symbols 0
% 3.86/1.20
% 3.86/1.20 % ------ Schedule dynamic 5 is on
% 3.86/1.20
% 3.86/1.20 % ------ no equalities: superposition off
% 3.86/1.20
% 3.86/1.20 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.86/1.20
% 3.86/1.20
% 3.86/1.20 % ------
% 3.86/1.20 % Current options:
% 3.86/1.20 % ------
% 3.86/1.20
% 3.86/1.20
% 3.86/1.20 %
% 3.86/1.20
% 3.86/1.20 % ------ Proving...
% 3.86/1.20 %
% 3.86/1.20
% 3.86/1.20 % SZS status Theorem for theBenchmark.p
% 3.86/1.20
% 3.86/1.20 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.85/1.20
% 1.85/1.20
%------------------------------------------------------------------------------