%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET680+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 : 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 02:47:46 PM UTC 2026
% Result : Theorem 3.70s 1.19s
% Output : CNFRefutation 3.70s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f160ERROR: Could not build tree for root c_3536ERROR: 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,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/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(f6,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( ! [X3] :
( ilf_type(X3,relation_type(X0,X1))
=> ilf_type(X3,subset_type(cross_product(X0,X1))) )
& ! [X2] :
( ilf_type(X2,subset_type(cross_product(X0,X1)))
=> ilf_type(X2,relation_type(X0,X1)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p6) ).
fof(f8,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/sandbox2/benchmark/theBenchmark.p',p8) ).
fof(f10,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ( empty(X0)
<=> ! [X1] :
( ilf_type(X1,set_type)
=> ~ member(X1,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p10) ).
fof(f26,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',p26) ).
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/sandbox2/benchmark/theBenchmark.p',p27) ).
fof(f31,axiom,
! [X0] : ilf_type(X0,set_type),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p31) ).
fof(f32,conjecture,
! [X0] :
( ( ilf_type(X0,set_type)
& ~ empty(X0) )
=> ! [X1] :
( ( ilf_type(X1,set_type)
& ~ empty(X1) )
=> ! [X2] :
( ilf_type(X2,relation_type(X0,X1))
=> ! [X3] :
( ilf_type(X3,member_type(X0))
=> ( member(X3,domain(X0,X1,X2))
<=> ? [X4] :
( member(ordered_pair(X3,X4),X2)
& ilf_type(X4,member_type(X1)) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_relset_1_47) ).
fof(f33,negated_conjecture,
~ ! [X0] :
( ( ilf_type(X0,set_type)
& ~ empty(X0) )
=> ! [X1] :
( ( ilf_type(X1,set_type)
& ~ empty(X1) )
=> ! [X2] :
( ilf_type(X2,relation_type(X0,X1))
=> ! [X3] :
( ilf_type(X3,member_type(X0))
=> ( member(X3,domain(X0,X1,X2))
<=> ? [X4] :
( member(ordered_pair(X3,X4),X2)
& ilf_type(X4,member_type(X1)) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f32]) ).
fof(f34,plain,
? [X0] :
( ilf_type(X0,set_type)
& ~ empty(X0)
& ? [X1] :
( ilf_type(X1,set_type)
& ~ empty(X1)
& ? [X2] :
( ilf_type(X2,relation_type(X0,X1))
& ? [X3] :
( ilf_type(X3,member_type(X0))
& ( member(X3,domain(X0,X1,X2))
<~> ? [X4] :
( member(ordered_pair(X3,X4),X2)
& ilf_type(X4,member_type(X1)) ) ) ) ) ) ),
inference(ennf_transformation,[],[f33]) ).
fof(f35,plain,
? [X0] :
( ilf_type(X0,set_type)
& ~ empty(X0)
& ? [X1] :
( ilf_type(X1,set_type)
& ~ empty(X1)
& ? [X2] :
( ilf_type(X2,relation_type(X0,X1))
& ? [X3] :
( ilf_type(X3,member_type(X0))
& ( member(X3,domain(X0,X1,X2))
<~> ? [X4] :
( member(ordered_pair(X3,X4),X2)
& ilf_type(X4,member_type(X1)) ) ) ) ) ) ),
inference(flattening,[],[f34]) ).
fof(f37,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ( empty(X0)
<=> ! [X1] :
( ~ ilf_type(X1,set_type)
| ~ member(X1,X0) ) ) ),
inference(ennf_transformation,[],[f10]) ).
fof(f38,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(f39,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,[],[f38]) ).
fof(f44,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,[],[f8]) ).
fof(f45,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,[],[f44]) ).
fof(f50,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(f53,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,[],[f26]) ).
fof(f60,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,[],[f2]) ).
fof(f61,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,[],[f60]) ).
fof(f62,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(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,[],[f6]) ).
fof(f68,plain,
? [X0] :
( ilf_type(X0,set_type)
& ~ empty(X0)
& ? [X1] :
( ilf_type(X1,set_type)
& ~ empty(X1)
& ? [X2] :
( ilf_type(X2,relation_type(X0,X1))
& ? [X3] :
( ilf_type(X3,member_type(X0))
& ( member(X3,domain(X0,X1,X2))
| ? [X4] :
( member(ordered_pair(X3,X4),X2)
& ilf_type(X4,member_type(X1)) ) )
& ( ~ member(X3,domain(X0,X1,X2))
| ! [X4] :
( ~ member(ordered_pair(X3,X4),X2)
| ~ ilf_type(X4,member_type(X1)) ) ) ) ) ) ),
inference(nnf_transformation,[],[f35]) ).
fof(f69,plain,
? [X0] :
( ilf_type(X0,set_type)
& ~ empty(X0)
& ? [X1] :
( ilf_type(X1,set_type)
& ~ empty(X1)
& ? [X2] :
( ilf_type(X2,relation_type(X0,X1))
& ? [X3] :
( ilf_type(X3,member_type(X0))
& ( member(X3,domain(X0,X1,X2))
| ? [X4] :
( member(ordered_pair(X3,X4),X2)
& ilf_type(X4,member_type(X1)) ) )
& ( ~ member(X3,domain(X0,X1,X2))
| ! [X4] :
( ~ member(ordered_pair(X3,X4),X2)
| ~ ilf_type(X4,member_type(X1)) ) ) ) ) ) ),
inference(flattening,[],[f68]) ).
fof(f70,plain,
? [X0] :
( ilf_type(X0,set_type)
& ~ empty(X0)
& ? [X1] :
( ilf_type(X1,set_type)
& ~ empty(X1)
& ? [X2] :
( ilf_type(X2,relation_type(X0,X1))
& ? [X3] :
( ilf_type(X3,member_type(X0))
& ( member(X3,domain(X0,X1,X2))
| ? [X5] :
( member(ordered_pair(X3,X5),X2)
& ilf_type(X5,member_type(X1)) ) )
& ( ~ member(X3,domain(X0,X1,X2))
| ! [X4] :
( ~ member(ordered_pair(X3,X4),X2)
| ~ ilf_type(X4,member_type(X1)) ) ) ) ) ) ),
inference(rectify,[],[f69]) ).
fof(f71,plain,
( ilf_type(sK0,set_type)
& ~ empty(sK0)
& ilf_type(sK1,set_type)
& ~ empty(sK1)
& ilf_type(sK2,relation_type(sK0,sK1))
& ilf_type(sK3,member_type(sK0))
& ( member(sK3,domain(sK0,sK1,sK2))
| ( member(ordered_pair(sK3,sK4),sK2)
& ilf_type(sK4,member_type(sK1)) ) )
& ( ~ member(sK3,domain(sK0,sK1,sK2))
| ! [X4] :
( ~ member(ordered_pair(sK3,X4),sK2)
| ~ ilf_type(X4,member_type(sK1)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X5,sK4)],[f70]) ).
fof(f76,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,[],[f37]) ).
fof(f77,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,[],[f76]) ).
fof(f78,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))],[f77]) ).
fof(f80,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,[],[f45]) ).
fof(f92,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,[],[f62]) ).
fof(f93,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,[],[f92]) ).
fof(f94,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,binary_relation_type)
| ( ( ~ member(X0,domain_of(X1))
| ( member(ordered_pair(X0,sK14(X0,X1)),X1)
& ilf_type(sK14(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,[sK14]),skolemize(X3,sK14(X0,X1))],[f93]) ).
fof(f100,plain,
ilf_type(sK2,relation_type(sK0,sK1)),
inference(cnf_transformation,[],[f71]) ).
fof(f102,plain,
( member(sK3,domain(sK0,sK1,sK2))
| member(ordered_pair(sK3,sK4),sK2) ),
inference(cnf_transformation,[],[f71]) ).
fof(f103,plain,
( member(sK3,domain(sK0,sK1,sK2))
| ilf_type(sK4,member_type(sK1)) ),
inference(cnf_transformation,[],[f71]) ).
fof(f104,plain,
! [X4] :
( ~ member(sK3,domain(sK0,sK1,sK2))
| ~ member(ordered_pair(sK3,X4),sK2)
| ~ ilf_type(X4,member_type(sK1)) ),
inference(cnf_transformation,[],[f71]) ).
fof(f105,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[],[f31]) ).
fof(f111,plain,
! [X2,X0] :
( ~ ilf_type(X0,set_type)
| ~ empty(X0)
| ~ ilf_type(X2,set_type)
| ~ member(X2,X0) ),
inference(cnf_transformation,[],[f78]) ).
fof(f114,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,[],[f39]) ).
fof(f119,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,[],[f80]) ).
fof(f125,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,[],[f50]) ).
fof(f132,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,[],[f53]) ).
fof(f145,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,[],[f61]) ).
fof(f146,plain,
! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,binary_relation_type)
| ~ member(X0,domain_of(X1))
| member(ordered_pair(X0,sK14(X0,X1)),X1) ),
inference(cnf_transformation,[],[f94]) ).
fof(f148,plain,
! [X2,X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,binary_relation_type)
| ~ member(ordered_pair(X0,X2),X1)
| ~ ilf_type(X2,set_type)
| member(X0,domain_of(X1)) ),
inference(cnf_transformation,[],[f94]) ).
fof(f150,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,
! [X0: $i] :
( ~ ilf_type(X0,member_type(sK1))
| ~ member(ordered_pair(sK3,X0),sK2)
| ~ member(sK3,domain(sK0,sK1,sK2)) ),
inference(cnf_transformation,[],[f104]) ).
tcf(c_50,negated_conjecture,
( ilf_type(sK4,member_type(sK1))
| member(sK3,domain(sK0,sK1,sK2)) ),
inference(cnf_transformation,[],[f103]) ).
tcf(c_51,negated_conjecture,
( member(ordered_pair(sK3,sK4),sK2)
| member(sK3,domain(sK0,sK1,sK2)) ),
inference(cnf_transformation,[],[f102]) ).
tcf(c_53,negated_conjecture,
ilf_type(sK2,relation_type(sK0,sK1)),
inference(cnf_transformation,[],[f100]) ).
tcf(c_58,plain,
! [X0: $i] : ilf_type(X0,set_type),
inference(cnf_transformation,[],[f105]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f111]) ).
tcf(c_68,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,[],[f114]) ).
tcf(c_71,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,[],[f119]) ).
tcf(c_78,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,[],[f125]) ).
tcf(c_85,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,[],[f132]) ).
tcf(c_86,plain,
! [X0: $i] :
( ilf_type(X0,binary_relation_type)
| ~ relation_like(X0)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f160]) ).
tcf(c_96,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,[],[f145]) ).
tcf(c_98,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,[],[f148]) ).
tcf(c_100,plain,
! [X0: $i,X1: $i] :
( member(ordered_pair(X0,sK14(X0,X1)),X1)
| ~ ilf_type(X1,binary_relation_type)
| ~ ilf_type(X0,set_type)
| ~ member(X0,domain_of(X1)) ),
inference(cnf_transformation,[],[f146]) ).
tcf(c_103,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,[],[f150]) ).
tcf(c_168,plain,
! [X0: $i] :
( ilf_type(X0,binary_relation_type)
| ~ relation_like(X0) ),
inference(global_subsumption_just,[status(thm)],[c_86,c_58,c_86]) ).
tcf(c_229,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_71,c_58,c_66,c_71]) ).
tcf(c_230,plain,
! [X0: $i,X1: $i] :
( ilf_type(X0,member_type(X1))
| ~ ilf_type(X1,set_type)
| ~ member(X0,X1) ),
inference(renaming,[status(thm)],[c_229]) ).
tcf(c_236,plain,
! [X0: $i,X1: $i] :
( member(ordered_pair(X0,sK14(X0,X1)),X1)
| ~ ilf_type(X1,binary_relation_type)
| ~ member(X0,domain_of(X1)) ),
inference(global_subsumption_just,[status(thm)],[c_100,c_58,c_100]) ).
tcf(c_239,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_98,c_58,c_98]) ).
tcf(c_243,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_96,c_239]) ).
tcf(c_410,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_85,c_58]) ).
tcf(c_421,plain,
! [X0: $i,X1: $i] :
( ilf_type(X0,member_type(X1))
| ~ member(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[c_230,c_58]) ).
tcf(c_423,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_243,c_58]) ).
tcf(c_424,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_103,c_58]) ).
tcf(c_426,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_78,c_58]) ).
tcf(c_428,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_68,c_58]) ).
tcf(c_517,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_410,c_58]) ).
tcf(c_575,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_424,c_58]) ).
tcf(c_636,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_426,c_58]) ).
tcf(c_664,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_428,c_58,c_58,c_58]) ).
tcf(c_1116,plain,
! [X0: $i] :
( ilf_type(X0,binary_relation_type)
| ~ relation_like(X0) ),
inference(prop_impl_just,[status(thm)],[c_168]) ).
tcf(c_1124,plain,
! [X0: $i,X1: $i] :
( ilf_type(X0,member_type(X1))
| ~ member(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_421]) ).
tcf(c_1130,plain,
! [X0: $i,X1: $i,X2: $i] :
( relation_like(X0)
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(prop_impl_just,[status(thm)],[c_517,c_575]) ).
tcf(c_1134,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_636]) ).
tcf(c_2664,plain,
! [X0: $i] :
( member(ordered_pair(sK3,sK4),sK2)
| ~ ilf_type(X0,member_type(sK1))
| ~ member(ordered_pair(sK3,X0),sK2) ),
inference(superposition,[status(thm)],[c_51,c_49]) ).
tcf(c_2665,plain,
! [X0: $i] :
( ilf_type(sK4,member_type(sK1))
| ~ ilf_type(X0,member_type(sK1))
| ~ member(ordered_pair(sK3,X0),sK2) ),
inference(superposition,[status(thm)],[c_50,c_49]) ).
tcf(c_2742,plain,
( member(ordered_pair(sK3,sK4),sK2)
| ~ ilf_type(sK2,binary_relation_type)
| ~ member(sK3,domain_of(sK2))
| ~ ilf_type(sK14(sK3,sK2),member_type(sK1)) ),
inference(superposition,[status(thm)],[c_236,c_2664]) ).
tcf(c_2743,plain,
( ilf_type(sK4,member_type(sK1))
| ~ ilf_type(sK2,binary_relation_type)
| ~ member(sK3,domain_of(sK2))
| ~ ilf_type(sK14(sK3,sK2),member_type(sK1)) ),
inference(superposition,[status(thm)],[c_236,c_2665]) ).
tcf(c_2761,plain,
relation_like(sK2),
inference(superposition,[status(thm)],[c_53,c_1130]) ).
tcf(c_2804,plain,
( ilf_type(sK4,member_type(sK1))
| ~ ilf_type(sK2,binary_relation_type)
| ~ member(sK3,domain_of(sK2))
| ~ member(sK14(sK3,sK2),sK1) ),
inference(superposition,[status(thm)],[c_1124,c_2743]) ).
tcf(c_2817,plain,
( member(ordered_pair(sK3,sK4),sK2)
| ~ ilf_type(sK2,binary_relation_type)
| ~ member(sK3,domain_of(sK2))
| ~ member(sK14(sK3,sK2),sK1) ),
inference(superposition,[status(thm)],[c_1124,c_2742]) ).
tcf(c_2997,plain,
domain(sK0,sK1,sK2) = domain_of(sK2),
inference(superposition,[status(thm)],[c_53,c_1134]) ).
tcf(c_3001,plain,
! [X0: $i] :
( ~ member(sK3,domain_of(sK2))
| ~ ilf_type(X0,member_type(sK1))
| ~ member(ordered_pair(sK3,X0),sK2) ),
inference(demodulation,[status(thm)],[c_49,c_2997]) ).
tcf(c_3002,plain,
( member(sK3,domain_of(sK2))
| member(ordered_pair(sK3,sK4),sK2) ),
inference(demodulation,[status(thm)],[c_51,c_2997]) ).
tcf(c_3003,plain,
( member(sK3,domain_of(sK2))
| ilf_type(sK4,member_type(sK1)) ),
inference(demodulation,[status(thm)],[c_50,c_2997]) ).
tcf(c_3085,plain,
! [X0: $i,X1: $i] :
( member(X1,sK1)
| ~ member(ordered_pair(X0,X1),sK2) ),
inference(superposition,[status(thm)],[c_53,c_664]) ).
tcf(c_3120,plain,
( ilf_type(sK4,member_type(sK1))
| ~ ilf_type(sK2,binary_relation_type)
| ~ member(sK14(sK3,sK2),sK1) ),
inference(backward_subsumption_resolution,[status(thm)],[c_2804,c_3003]) ).
tcf(c_3121,plain,
( ilf_type(sK4,member_type(sK1))
| ~ ilf_type(sK2,binary_relation_type)
| ~ ilf_type(sK14(sK3,sK2),member_type(sK1)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_2743,c_3003]) ).
tcf(c_3141,plain,
( member(ordered_pair(sK3,sK4),sK2)
| ~ ilf_type(sK2,binary_relation_type)
| ~ member(sK14(sK3,sK2),sK1) ),
inference(backward_subsumption_resolution,[status(thm)],[c_2817,c_3002]) ).
tcf(c_3142,plain,
( member(ordered_pair(sK3,sK4),sK2)
| ~ ilf_type(sK2,binary_relation_type)
| ~ ilf_type(sK14(sK3,sK2),member_type(sK1)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_2742,c_3002]) ).
tcf(c_3153,plain,
( member(sK3,domain_of(sK2))
| ~ ilf_type(sK2,binary_relation_type) ),
inference(superposition,[status(thm)],[c_3002,c_423]) ).
tcf(c_3170,plain,
! [X0: $i] :
( member(sK14(X0,sK2),sK1)
| ~ ilf_type(sK2,binary_relation_type)
| ~ member(X0,domain_of(sK2)) ),
inference(superposition,[status(thm)],[c_236,c_3085]) ).
tcf(c_3328,plain,
( ilf_type(sK4,member_type(sK1))
| ~ ilf_type(sK2,binary_relation_type)
| ~ member(sK3,domain_of(sK2)) ),
inference(superposition,[status(thm)],[c_3170,c_3120]) ).
tcf(c_3337,plain,
( ilf_type(sK4,member_type(sK1))
| ~ ilf_type(sK2,binary_relation_type) ),
inference(global_subsumption_just,[status(thm)],[c_3121,c_3153,c_3328]) ).
tcf(c_3363,plain,
( member(ordered_pair(sK3,sK4),sK2)
| ~ ilf_type(sK2,binary_relation_type)
| ~ member(sK3,domain_of(sK2)) ),
inference(superposition,[status(thm)],[c_3170,c_3141]) ).
tcf(c_3504,plain,
( member(ordered_pair(sK3,sK4),sK2)
| ~ ilf_type(sK2,binary_relation_type) ),
inference(global_subsumption_just,[status(thm)],[c_3142,c_3153,c_3363]) ).
tcf(c_3510,plain,
( ~ ilf_type(sK2,binary_relation_type)
| ~ member(sK3,domain_of(sK2))
| ~ ilf_type(sK4,member_type(sK1)) ),
inference(superposition,[status(thm)],[c_3504,c_3001]) ).
tcf(c_3533,plain,
~ ilf_type(sK2,binary_relation_type),
inference(global_subsumption_just,[status(thm)],[c_3510,c_3153,c_3337,c_3510]) ).
tcf(c_3535,plain,
~ relation_like(sK2),
inference(superposition,[status(thm)],[c_1116,c_3533]) ).
tcf(c_3536,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_3535,c_2761]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET680+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 : n002.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 11:41:19 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.40 Running first-order theorem proving
% 0.09/0.40 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
% 0.14/0.42 % Proving...
% 3.70/1.19 % SZS status Started for theBenchmark.p
% 3.70/1.19 % SZS status Theorem for theBenchmark.p
% 3.70/1.19
% 3.70/1.19 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.70/1.19
% 3.70/1.19 % ------ iProver source info
% 3.70/1.19
% 3.70/1.19 % git: date: 2026-07-19 20:42:38 +0200
% 3.70/1.19 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.70/1.19 % git: non_committed_changes: false
% 3.70/1.19
% 3.70/1.19 % ------ Parsing...
% 3.70/1.19 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.70/1.19
% 3.70/1.19 % ------ 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 %
% 3.70/1.19
% 3.70/1.19 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.70/1.19
% 3.70/1.19 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.70/1.19 % ------ Proving...
% 3.70/1.19 % ------ Problem Properties
% 3.70/1.19
% 3.70/1.19 %
% 3.70/1.19 % clauses 42
% 3.70/1.19 % conjectures 7
% 3.70/1.19 % EPR 8
% 3.70/1.19 % Horn 34
% 3.70/1.19 % unary 9
% 3.70/1.19 % binary 22
% 3.70/1.19 % lits 86
% 3.70/1.19 % lits eq 6
% 3.70/1.19 % fd_pure 0
% 3.70/1.19 % fd_pseudo 0
% 3.70/1.19 % fd_cond 0
% 3.70/1.19 % fd_pseudo_cond 2
% 3.70/1.19 % AC symbols 0
% 3.70/1.19
% 3.70/1.19 % ------ Schedule dynamic 5 is on
% 3.70/1.19
% 3.70/1.19 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.70/1.19
% 3.70/1.19
% 3.70/1.19 % ------
% 3.70/1.19 % Current options:
% 3.70/1.19 % ------
% 3.70/1.19
% 3.70/1.19
% 3.70/1.19 %
% 3.70/1.19
% 3.70/1.19 % ------ Proving...
% 3.70/1.19 %
% 3.70/1.19
% 3.70/1.19 % SZS status Theorem for theBenchmark.p
% 3.70/1.19
% 3.70/1.19 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.70/1.20
% 3.70/1.20
%------------------------------------------------------------------------------