%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET667+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 : n026.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 02:47:44 PM UTC 2026
% Result : Theorem 3.85s 1.22s
% Output : CNFRefutation 3.85s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f141ERROR: Could not build tree for root c_2966ERROR: MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,binary_relation_type)
=> ( member(ordered_pair(X0,X1),X2)
=> ( member(X1,range_of(X2))
& member(X0,domain_of(X2)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p1) ).
fof(f2,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( member(X1,X0)
<=> member(ordered_pair(X1,X1),identity_relation_of(X0)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2) ).
fof(f5,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',p5) ).
fof(f7,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',p7) ).
fof(f24,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',p24) ).
fof(f27,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,relation_type(X0,X1))
=> domain(X0,X1,X2) = domain_of(X2) ) ) ),
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,relation_type(X0,X1))
=> range(X0,X1,X2) = range_of(X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p29) ).
fof(f31,axiom,
! [X0] : ilf_type(X0,set_type),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p31) ).
fof(f32,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(X0,X1))
=> ( subset(identity_relation_of(X2),X3)
=> ( subset(X2,range(X0,X1,X3))
& subset(X2,domain(X0,X1,X3)) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_relset_1_30) ).
fof(f33,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(X0,X1))
=> ( subset(identity_relation_of(X2),X3)
=> ( subset(X2,range(X0,X1,X3))
& subset(X2,domain(X0,X1,X3)) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f32]) ).
fof(f34,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(X0,X1))
& subset(identity_relation_of(X2),X3)
& ( ~ subset(X2,range(X0,X1,X3))
| ~ subset(X2,domain(X0,X1,X3)) ) ) ) ) ),
inference(ennf_transformation,[],[f33]) ).
fof(f35,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(X0,X1))
& subset(identity_relation_of(X2),X3)
& ( ~ subset(X2,range(X0,X1,X3))
| ~ subset(X2,domain(X0,X1,X3)) ) ) ) ) ),
inference(flattening,[],[f34]) ).
fof(f40,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,[],[f7]) ).
fof(f41,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,[],[f40]) ).
fof(f44,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ( member(X1,X0)
<=> member(ordered_pair(X1,X1),identity_relation_of(X0)) ) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f47,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ! [X2] :
( ~ ilf_type(X2,relation_type(X0,X1))
| domain(X0,X1,X2) = domain_of(X2) ) ) ),
inference(ennf_transformation,[],[f27]) ).
fof(f49,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ! [X2] :
( ~ ilf_type(X2,relation_type(X0,X1))
| range(X0,X1,X2) = range_of(X2) ) ) ),
inference(ennf_transformation,[],[f29]) ).
fof(f55,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ! [X2] :
( ~ ilf_type(X2,binary_relation_type)
| ~ member(ordered_pair(X0,X1),X2)
| ( member(X1,range_of(X2))
& member(X0,domain_of(X2)) ) ) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f56,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ! [X2] :
( ~ ilf_type(X2,binary_relation_type)
| ~ member(ordered_pair(X0,X1),X2)
| ( member(X1,range_of(X2))
& member(X0,domain_of(X2)) ) ) ) ),
inference(flattening,[],[f55]) ).
fof(f60,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,[],[f24]) ).
fof(f64,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,[],[f5]) ).
fof(f65,plain,
( ilf_type(sK0,set_type)
& ilf_type(sK1,set_type)
& ilf_type(sK2,set_type)
& ilf_type(sK3,relation_type(sK0,sK1))
& subset(identity_relation_of(sK2),sK3)
& ( ~ subset(sK2,range(sK0,sK1,sK3))
| ~ subset(sK2,domain(sK0,sK1,sK3)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f35]) ).
fof(f69,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,[],[f41]) ).
fof(f70,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,[],[f69]) ).
fof(f71,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(sK6(X0,X1),set_type)
& member(sK6(X0,X1),X0)
& ~ member(sK6(X0,X1),X1) )
| subset(X0,X1) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(X2,sK6(X0,X1))],[f70]) ).
fof(f74,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ( ( ~ member(X1,X0)
| member(ordered_pair(X1,X1),identity_relation_of(X0)) )
& ( ~ member(ordered_pair(X1,X1),identity_relation_of(X0))
| member(X1,X0) ) ) ) ),
inference(nnf_transformation,[],[f44]) ).
fof(f89,plain,
ilf_type(sK3,relation_type(sK0,sK1)),
inference(cnf_transformation,[],[f65]) ).
fof(f90,plain,
subset(identity_relation_of(sK2),sK3),
inference(cnf_transformation,[],[f65]) ).
fof(f91,plain,
( ~ subset(sK2,range(sK0,sK1,sK3))
| ~ subset(sK2,domain(sK0,sK1,sK3)) ),
inference(cnf_transformation,[],[f65]) ).
fof(f92,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[],[f31]) ).
fof(f100,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,[],[f71]) ).
fof(f102,plain,
! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| member(sK6(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f71]) ).
fof(f103,plain,
! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ member(sK6(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f71]) ).
fof(f108,plain,
! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ member(X1,X0)
| member(ordered_pair(X1,X1),identity_relation_of(X0)) ),
inference(cnf_transformation,[],[f74]) ).
fof(f112,plain,
! [X2,X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,relation_type(X0,X1))
| domain_of(X2) = domain(X0,X1,X2) ),
inference(cnf_transformation,[],[f47]) ).
fof(f114,plain,
! [X2,X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,relation_type(X0,X1))
| range_of(X2) = range(X0,X1,X2) ),
inference(cnf_transformation,[],[f49]) ).
fof(f125,plain,
! [X2,X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,binary_relation_type)
| ~ member(ordered_pair(X0,X1),X2)
| member(X1,range_of(X2)) ),
inference(cnf_transformation,[],[f56]) ).
fof(f126,plain,
! [X2,X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,binary_relation_type)
| ~ member(ordered_pair(X0,X1),X2)
| member(X0,domain_of(X2)) ),
inference(cnf_transformation,[],[f56]) ).
fof(f129,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,[],[f60]) ).
fof(f137,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,[],[f64]) ).
tcf(c_49,negated_conjecture,
( ~ subset(sK2,range(sK0,sK1,sK3))
| ~ subset(sK2,domain(sK0,sK1,sK3)) ),
inference(cnf_transformation,[],[f91]) ).
tcf(c_50,negated_conjecture,
subset(identity_relation_of(sK2),sK3),
inference(cnf_transformation,[],[f90]) ).
tcf(c_51,negated_conjecture,
ilf_type(sK3,relation_type(sK0,sK1)),
inference(cnf_transformation,[],[f89]) ).
tcf(c_55,plain,
! [X0: $i] : ilf_type(X0,set_type),
inference(cnf_transformation,[],[f92]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| ~ member(sK6(X0,X1),X1) ),
inference(cnf_transformation,[],[f103]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| member(sK6(X0,X1),X0)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f102]) ).
tcf(c_66,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,[],[f100]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i] :
( member(ordered_pair(X0,X0),identity_relation_of(X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f140]) ).
tcf(c_72,plain,
! [X0: $i,X1: $i] :
( member(ordered_pair(X0,X0),identity_relation_of(X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f108]) ).
tcf(c_75,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( domain(X1,X2,X0) = domain_of(X0) )
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(cnf_transformation,[],[f112]) ).
tcf(c_77,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( range(X1,X2,X0) = range_of(X0) )
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(cnf_transformation,[],[f114]) ).
tcf(c_88,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,domain_of(X2))
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| ~ member(ordered_pair(X0,X1),X2) ),
inference(cnf_transformation,[],[f126]) ).
tcf(c_89,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X1,range_of(X2))
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| ~ member(ordered_pair(X0,X1),X2) ),
inference(cnf_transformation,[],[f125]) ).
tcf(c_92,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,[],[f129]) ).
tcf(c_93,plain,
! [X0: $i] :
( ilf_type(X0,binary_relation_type)
| ~ relation_like(X0)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f141]) ).
tcf(c_100,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,[],[f137]) ).
tcf(c_158,plain,
! [X0: $i] :
( ilf_type(X0,binary_relation_type)
| ~ relation_like(X0) ),
inference(global_subsumption_just,[status(thm)],[c_93,c_55,c_93]) ).
tcf(c_188,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| member(sK6(X0,X1),X0)
| ~ ilf_type(X1,set_type) ),
inference(global_subsumption_just,[status(thm)],[c_64,c_55,c_64]) ).
tcf(c_189,plain,
! [X0: $i,X1: $i] :
( subset(X1,X0)
| member(sK6(X1,X0),X1)
| ~ ilf_type(X0,set_type) ),
inference(renaming,[status(thm)],[c_188]) ).
tcf(c_190,plain,
! [X0: $i,X1: $i] :
( subset(X1,X0)
| member(sK6(X1,X0),X1) ),
inference(global_subsumption_just,[status(thm)],[c_189,c_55,c_189]) ).
tcf(c_191,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| member(sK6(X0,X1),X0) ),
inference(renaming,[status(thm)],[c_190]) ).
tcf(c_192,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ ilf_type(X1,set_type)
| ~ member(sK6(X0,X1),X1) ),
inference(global_subsumption_just,[status(thm)],[c_63,c_55,c_63]) ).
tcf(c_194,plain,
! [X0: $i,X1: $i] :
( member(ordered_pair(X0,X0),identity_relation_of(X1))
| ~ ilf_type(X1,set_type)
| ~ member(X0,X1) ),
inference(global_subsumption_just,[status(thm)],[c_72,c_55,c_72]) ).
tcf(c_198,plain,
! [X0: $i,X1: $i] :
( member(ordered_pair(X0,X0),identity_relation_of(X1))
| ~ ilf_type(X1,set_type)
| ~ member(X0,X1) ),
inference(global_subsumption_just,[status(thm)],[c_68,c_194]) ).
tcf(c_204,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X1,range_of(X2))
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ member(ordered_pair(X0,X1),X2) ),
inference(global_subsumption_just,[status(thm)],[c_89,c_55,c_89]) ).
tcf(c_206,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,domain_of(X2))
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ member(ordered_pair(X0,X1),X2) ),
inference(global_subsumption_just,[status(thm)],[c_88,c_55,c_88]) ).
tcf(c_216,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_66,c_55,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)
| ~ member(X2,X0)
| ~ subset(X0,X1) ),
inference(renaming,[status(thm)],[c_216]) ).
tcf(c_344,plain,
! [X0: $i,X1: $i] :
( member(ordered_pair(X0,X0),identity_relation_of(X1))
| ~ member(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[c_198,c_55]) ).
tcf(c_347,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,domain_of(X2))
| ~ ilf_type(X2,binary_relation_type)
| ~ member(ordered_pair(X0,X1),X2) ),
inference(backward_subsumption_resolution,[status(thm)],[c_206,c_55]) ).
tcf(c_349,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_217,c_55]) ).
tcf(c_351,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_92,c_55]) ).
tcf(c_352,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( range(X1,X2,X0) = range_of(X0) )
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_77,c_55]) ).
tcf(c_353,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_100,c_55]) ).
tcf(c_356,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ member(sK6(X0,X1),X1) ),
inference(backward_subsumption_resolution,[status(thm)],[c_192,c_55]) ).
tcf(c_358,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X1,range_of(X2))
| ~ ilf_type(X2,binary_relation_type)
| ~ member(ordered_pair(X0,X1),X2) ),
inference(backward_subsumption_resolution,[status(thm)],[c_204,c_55]) ).
tcf(c_361,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( domain(X1,X2,X0) = domain_of(X0) )
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_75,c_55]) ).
tcf(c_430,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_351,c_55]) ).
tcf(c_491,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_353,c_55]) ).
tcf(c_535,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( range(X1,X2,X0) = range_of(X0) )
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_352,c_55]) ).
tcf(c_546,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( domain(X1,X2,X0) = domain_of(X0) )
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_361,c_55]) ).
tcf(c_558,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subset(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_349,c_55]) ).
tcf(c_1021,plain,
! [X0: $i] :
( ilf_type(X0,binary_relation_type)
| ~ relation_like(X0) ),
inference(prop_impl_just,[status(thm)],[c_158]) ).
tcf(c_1031,plain,
! [X0: $i,X1: $i] :
( ~ member(sK6(X0,X1),X1)
| subset(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_356]) ).
tcf(c_1032,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ member(sK6(X0,X1),X1) ),
inference(renaming,[status(thm)],[c_1031]) ).
tcf(c_1033,plain,
! [X0: $i,X1: $i] :
( member(sK6(X0,X1),X0)
| subset(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_191]) ).
tcf(c_1034,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| member(sK6(X0,X1),X0) ),
inference(renaming,[status(thm)],[c_1033]) ).
tcf(c_1037,plain,
! [X0: $i,X1: $i] :
( member(ordered_pair(X0,X0),identity_relation_of(X1))
| ~ member(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_344]) ).
tcf(c_1049,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( domain(X1,X2,X0) = domain_of(X0) )
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(prop_impl_just,[status(thm)],[c_546]) ).
tcf(c_1053,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( range(X1,X2,X0) = range_of(X0) )
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(prop_impl_just,[status(thm)],[c_535]) ).
tcf(c_1055,plain,
! [X0: $i,X1: $i,X2: $i] :
( relation_like(X0)
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(prop_impl_just,[status(thm)],[c_430,c_491]) ).
tcf(c_2180,plain,
relation_like(sK3),
inference(superposition,[status(thm)],[c_51,c_1055]) ).
tcf(c_2303,plain,
! [X0: $i] :
( member(X0,sK3)
| ~ member(X0,identity_relation_of(sK2)) ),
inference(superposition,[status(thm)],[c_50,c_558]) ).
tcf(c_2314,plain,
! [X0: $i] :
( member(ordered_pair(X0,X0),sK3)
| ~ member(X0,sK2) ),
inference(superposition,[status(thm)],[c_1037,c_2303]) ).
tcf(c_2383,plain,
! [X0: $i] :
( member(X0,domain_of(sK3))
| ~ ilf_type(sK3,binary_relation_type)
| ~ member(X0,sK2) ),
inference(superposition,[status(thm)],[c_2314,c_347]) ).
tcf(c_2399,plain,
! [X0: $i] :
( member(X0,range_of(sK3))
| ~ ilf_type(sK3,binary_relation_type)
| ~ member(X0,sK2) ),
inference(superposition,[status(thm)],[c_2314,c_358]) ).
tcf(c_2412,plain,
domain(sK0,sK1,sK3) = domain_of(sK3),
inference(superposition,[status(thm)],[c_51,c_1049]) ).
tcf(c_2415,plain,
( ~ subset(sK2,domain_of(sK3))
| ~ subset(sK2,range(sK0,sK1,sK3)) ),
inference(demodulation,[status(thm)],[c_49,c_2412]) ).
tcf(c_2460,plain,
! [X0: $i] :
( subset(X0,domain_of(sK3))
| ~ ilf_type(sK3,binary_relation_type)
| ~ member(sK6(X0,domain_of(sK3)),sK2) ),
inference(superposition,[status(thm)],[c_2383,c_1032]) ).
tcf(c_2501,plain,
range(sK0,sK1,sK3) = range_of(sK3),
inference(superposition,[status(thm)],[c_51,c_1053]) ).
tcf(c_2507,plain,
( ~ subset(sK2,range_of(sK3))
| ~ subset(sK2,domain_of(sK3)) ),
inference(demodulation,[status(thm)],[c_2415,c_2501]) ).
tcf(c_2676,plain,
! [X0: $i] :
( subset(X0,range_of(sK3))
| ~ ilf_type(sK3,binary_relation_type)
| ~ member(sK6(X0,range_of(sK3)),sK2) ),
inference(superposition,[status(thm)],[c_2399,c_1032]) ).
tcf(c_2871,plain,
( subset(sK2,domain_of(sK3))
| ~ ilf_type(sK3,binary_relation_type) ),
inference(superposition,[status(thm)],[c_1034,c_2460]) ).
tcf(c_2880,plain,
( subset(sK2,range_of(sK3))
| ~ ilf_type(sK3,binary_relation_type) ),
inference(superposition,[status(thm)],[c_1034,c_2676]) ).
tcf(c_2963,plain,
~ ilf_type(sK3,binary_relation_type),
inference(global_subsumption_just,[status(thm)],[c_2871,c_2507,c_2871,c_2880]) ).
tcf(c_2965,plain,
~ relation_like(sK3),
inference(superposition,[status(thm)],[c_1021,c_2963]) ).
tcf(c_2966,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_2965,c_2180]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET667+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.07 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/0.40 % Computer : n026.cluster.edu
% 0.13/0.40 % Model : x86_64 x86_64
% 0.13/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.40 % Memory : 8046.5625MB
% 0.13/0.40 % OS : Linux 6.8.0-71-generic
% 0.13/0.40 % CPULimit : 300
% 0.13/0.40 % WCLimit : 300
% 0.13/0.40 % DateTime : Thu Sep 24 11:39:09 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.13/0.40 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/0.44 Running first-order theorem proving
% 0.13/0.44 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.45
% 0.13/0.45 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.45
% 0.13/0.45 % Detected problem language: tptp
% 0.19/0.46 % Proving...
% 3.85/1.22 % SZS status Started for theBenchmark.p
% 3.85/1.22 % SZS status Theorem for theBenchmark.p
% 3.85/1.22
% 3.85/1.22 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.85/1.22
% 3.85/1.22 % ------ iProver source info
% 3.85/1.22
% 3.85/1.22 % git: date: 2026-07-19 20:42:38 +0200
% 3.85/1.22 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.85/1.22 % git: non_committed_changes: false
% 3.85/1.22
% 3.85/1.22 % ------ Parsing...
% 3.85/1.22 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.85/1.22
% 3.85/1.22 % ------ 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 %
% 3.85/1.22
% 3.85/1.22 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.85/1.22
% 3.85/1.22 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.85/1.22 % ------ Proving...
% 3.85/1.22 % ------ Problem Properties
% 3.85/1.22
% 3.85/1.22 %
% 3.85/1.22 % clauses 34
% 3.85/1.22 % conjectures 3
% 3.85/1.22 % EPR 8
% 3.85/1.22 % Horn 30
% 3.85/1.22 % unary 8
% 3.85/1.22 % binary 20
% 3.85/1.22 % lits 68
% 3.85/1.22 % lits eq 5
% 3.85/1.22 % fd_pure 0
% 3.85/1.22 % fd_pseudo 0
% 3.85/1.22 % fd_cond 0
% 3.85/1.22 % fd_pseudo_cond 1
% 3.85/1.22 % AC symbols 0
% 3.85/1.22
% 3.85/1.22 % ------ Schedule dynamic 5 is on
% 3.85/1.22
% 3.85/1.22 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.85/1.22
% 3.85/1.22
% 3.85/1.22 % ------
% 3.85/1.22 % Current options:
% 3.85/1.22 % ------
% 3.85/1.22
% 3.85/1.22
% 3.85/1.22 %
% 3.85/1.22
% 3.85/1.22 % ------ Proving...
% 3.85/1.22 %
% 3.85/1.22
% 3.85/1.22 % SZS status Theorem for theBenchmark.p
% 3.85/1.22
% 3.85/1.22 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.85/1.23
% 3.85/1.23
%------------------------------------------------------------------------------