%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET659+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 : n017.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 22.93s 6.83s
% Output : CNFRefutation 22.93s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f197ERROR: Could not build tree for root c_7811ERROR: MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] :
( ilf_type(X0,binary_relation_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( member(X1,domain_of(X0))
<=> ? [X2] :
( member(ordered_pair(X1,X2),X0)
& ilf_type(X2,set_type) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p1) ).
fof(f3,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',p3) ).
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/sandbox2/benchmark/theBenchmark.p',p7) ).
fof(f9,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( X0 = X1
<=> ( subset(X1,X0)
& subset(X0,X1) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p9) ).
fof(f17,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/sandbox2/benchmark/theBenchmark.p',p17) ).
fof(f20,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',p20) ).
fof(f22,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/sandbox2/benchmark/theBenchmark.p',p22) ).
fof(f23,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ( ilf_type(power_set(X0),set_type)
& ~ empty(power_set(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p23) ).
fof(f24,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',p24) ).
fof(f27,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',p27) ).
fof(f28,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',p28) ).
fof(f30,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',p30) ).
fof(f31,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,relation_type(X0,X1))
=> ilf_type(domain(X0,X1,X2),subset_type(X0)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p31) ).
fof(f34,axiom,
! [X0] : ilf_type(X0,set_type),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p34) ).
fof(f35,conjecture,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,relation_type(X1,X0))
=> ( ! [X3] :
( ilf_type(X3,set_type)
=> ( member(X3,X1)
=> ? [X4] :
( member(ordered_pair(X3,X4),X2)
& ilf_type(X4,set_type) ) ) )
<=> domain(X1,X0,X2) = X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_relset_1_22) ).
fof(f36,negated_conjecture,
~ ! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,relation_type(X1,X0))
=> ( ! [X3] :
( ilf_type(X3,set_type)
=> ( member(X3,X1)
=> ? [X4] :
( member(ordered_pair(X3,X4),X2)
& ilf_type(X4,set_type) ) ) )
<=> domain(X1,X0,X2) = X1 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f35]) ).
fof(f37,plain,
! [X0] :
( ~ ilf_type(X0,binary_relation_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ( member(X1,domain_of(X0))
<=> ? [X2] :
( member(ordered_pair(X1,X2),X0)
& ilf_type(X2,set_type) ) ) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f39,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,[],[f3]) ).
fof(f40,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,[],[f39]) ).
fof(f45,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(f47,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ( X0 = X1
<=> ( subset(X1,X0)
& subset(X0,X1) ) ) ) ),
inference(ennf_transformation,[],[f9]) ).
fof(f54,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,[],[f17]) ).
fof(f57,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,[],[f20]) ).
fof(f58,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,[],[f57]) ).
fof(f60,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,[],[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(flattening,[],[f60]) ).
fof(f62,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ( ilf_type(power_set(X0),set_type)
& ~ empty(power_set(X0)) ) ),
inference(ennf_transformation,[],[f23]) ).
fof(f63,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,[],[f24]) ).
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(flattening,[],[f63]) ).
fof(f69,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,[],[f27]) ).
fof(f70,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ( empty(X0)
<=> ! [X1] :
( ~ ilf_type(X1,set_type)
| ~ member(X1,X0) ) ) ),
inference(ennf_transformation,[],[f28]) ).
fof(f73,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,[],[f30]) ).
fof(f74,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ! [X2] :
( ~ ilf_type(X2,relation_type(X0,X1))
| ilf_type(domain(X0,X1,X2),subset_type(X0)) ) ) ),
inference(ennf_transformation,[],[f31]) ).
fof(f77,plain,
? [X0] :
( ilf_type(X0,set_type)
& ? [X1] :
( ilf_type(X1,set_type)
& ? [X2] :
( ilf_type(X2,relation_type(X1,X0))
& ( ! [X3] :
( ~ ilf_type(X3,set_type)
| ~ member(X3,X1)
| ? [X4] :
( member(ordered_pair(X3,X4),X2)
& ilf_type(X4,set_type) ) )
<~> domain(X1,X0,X2) = X1 ) ) ) ),
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(X1,X0))
& ( ! [X3] :
( ~ ilf_type(X3,set_type)
| ~ member(X3,X1)
| ? [X4] :
( member(ordered_pair(X3,X4),X2)
& ilf_type(X4,set_type) ) )
<~> domain(X1,X0,X2) = X1 ) ) ) ),
inference(flattening,[],[f77]) ).
fof(f79,plain,
! [X0] :
( ~ ilf_type(X0,binary_relation_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ( ( ~ member(X1,domain_of(X0))
| ? [X2] :
( member(ordered_pair(X1,X2),X0)
& ilf_type(X2,set_type) ) )
& ( ! [X2] :
( ~ member(ordered_pair(X1,X2),X0)
| ~ ilf_type(X2,set_type) )
| member(X1,domain_of(X0)) ) ) ) ),
inference(nnf_transformation,[],[f37]) ).
fof(f80,plain,
! [X0] :
( ~ ilf_type(X0,binary_relation_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ( ( ~ member(X1,domain_of(X0))
| ? [X3] :
( member(ordered_pair(X1,X3),X0)
& ilf_type(X3,set_type) ) )
& ( ! [X2] :
( ~ member(ordered_pair(X1,X2),X0)
| ~ ilf_type(X2,set_type) )
| member(X1,domain_of(X0)) ) ) ) ),
inference(rectify,[],[f79]) ).
fof(f81,plain,
! [X0] :
( ~ ilf_type(X0,binary_relation_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ( ( ~ member(X1,domain_of(X0))
| ( member(ordered_pair(X1,sK0(X0,X1)),X0)
& ilf_type(sK0(X0,X1),set_type) ) )
& ( ! [X2] :
( ~ member(ordered_pair(X1,X2),X0)
| ~ ilf_type(X2,set_type) )
| member(X1,domain_of(X0)) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X3,sK0(X0,X1))],[f80]) ).
fof(f87,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ( ( X0 != X1
| ( subset(X1,X0)
& subset(X0,X1) ) )
& ( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ) ) ) ),
inference(nnf_transformation,[],[f47]) ).
fof(f88,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ( ( X0 != X1
| ( subset(X1,X0)
& subset(X0,X1) ) )
& ( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ) ) ) ),
inference(flattening,[],[f87]) ).
fof(f92,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,[],[f54]) ).
fof(f98,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,[],[f58]) ).
fof(f99,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,[],[f98]) ).
fof(f100,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))],[f99]) ).
fof(f101,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,[],[f61]) ).
fof(f102,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,[],[f101]) ).
fof(f103,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))],[f102]) ).
fof(f104,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,[],[f64]) ).
fof(f109,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,[],[f70]) ).
fof(f110,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,[],[f109]) ).
fof(f111,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ( ( ~ empty(X0)
| ! [X2] :
( ~ ilf_type(X2,set_type)
| ~ member(X2,X0) ) )
& ( ( ilf_type(sK12(X0),set_type)
& member(sK12(X0),X0) )
| empty(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(X1,sK12(X0))],[f110]) ).
fof(f112,plain,
? [X0] :
( ilf_type(X0,set_type)
& ? [X1] :
( ilf_type(X1,set_type)
& ? [X2] :
( ilf_type(X2,relation_type(X1,X0))
& ( ! [X3] :
( ~ ilf_type(X3,set_type)
| ~ member(X3,X1)
| ? [X4] :
( member(ordered_pair(X3,X4),X2)
& ilf_type(X4,set_type) ) )
| domain(X1,X0,X2) = X1 )
& ( ? [X3] :
( ilf_type(X3,set_type)
& member(X3,X1)
& ! [X4] :
( ~ member(ordered_pair(X3,X4),X2)
| ~ ilf_type(X4,set_type) ) )
| domain(X1,X0,X2) != X1 ) ) ) ),
inference(nnf_transformation,[],[f78]) ).
fof(f113,plain,
? [X0] :
( ilf_type(X0,set_type)
& ? [X1] :
( ilf_type(X1,set_type)
& ? [X2] :
( ilf_type(X2,relation_type(X1,X0))
& ( ! [X3] :
( ~ ilf_type(X3,set_type)
| ~ member(X3,X1)
| ? [X4] :
( member(ordered_pair(X3,X4),X2)
& ilf_type(X4,set_type) ) )
| domain(X1,X0,X2) = X1 )
& ( ? [X3] :
( ilf_type(X3,set_type)
& member(X3,X1)
& ! [X4] :
( ~ member(ordered_pair(X3,X4),X2)
| ~ ilf_type(X4,set_type) ) )
| domain(X1,X0,X2) != X1 ) ) ) ),
inference(flattening,[],[f112]) ).
fof(f114,plain,
? [X0] :
( ilf_type(X0,set_type)
& ? [X1] :
( ilf_type(X1,set_type)
& ? [X2] :
( ilf_type(X2,relation_type(X1,X0))
& ( ! [X5] :
( ~ ilf_type(X5,set_type)
| ~ member(X5,X1)
| ? [X6] :
( member(ordered_pair(X5,X6),X2)
& ilf_type(X6,set_type) ) )
| domain(X1,X0,X2) = X1 )
& ( ? [X3] :
( ilf_type(X3,set_type)
& member(X3,X1)
& ! [X4] :
( ~ member(ordered_pair(X3,X4),X2)
| ~ ilf_type(X4,set_type) ) )
| domain(X1,X0,X2) != X1 ) ) ) ),
inference(rectify,[],[f113]) ).
fof(f115,plain,
( ilf_type(sK13,set_type)
& ilf_type(sK14,set_type)
& ilf_type(sK15,relation_type(sK14,sK13))
& ( ! [X5] :
( ~ ilf_type(X5,set_type)
| ~ member(X5,sK14)
| ( member(ordered_pair(X5,sK17(X5)),sK15)
& ilf_type(sK17(X5),set_type) ) )
| sK14 = domain(sK14,sK13,sK15) )
& ( ( ilf_type(sK16,set_type)
& member(sK16,sK14)
& ! [X4] :
( ~ member(ordered_pair(sK16,X4),sK15)
| ~ ilf_type(X4,set_type) ) )
| sK14 != domain(sK14,sK13,sK15) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13,sK14,sK15,sK16,sK17]),skolemize(X0,sK13),skolemize(X1,sK14),skolemize(X2,sK15),skolemize(X3,sK16),skolemize(X6,sK17(X5))],[f114]) ).
fof(f116,plain,
! [X0,X1] :
( ~ ilf_type(X0,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ member(X1,domain_of(X0))
| member(ordered_pair(X1,sK0(X0,X1)),X0) ),
inference(cnf_transformation,[],[f81]) ).
fof(f118,plain,
! [X2,X0,X1] :
( ~ ilf_type(X0,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ member(ordered_pair(X1,X2),X0)
| ~ ilf_type(X2,set_type)
| member(X1,domain_of(X0)) ),
inference(cnf_transformation,[],[f81]) ).
fof(f121,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,[],[f40]) ).
fof(f128,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,[],[f45]) ).
fof(f133,plain,
! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f88]) ).
fof(f143,plain,
! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X1,subset_type(X0))
| ilf_type(X1,member_type(power_set(X0))) ),
inference(cnf_transformation,[],[f92]) ).
fof(f153,plain,
! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| member(sK6(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f100]) ).
fof(f154,plain,
! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ member(sK6(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f100]) ).
fof(f156,plain,
! [X3,X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ member(X0,power_set(X1))
| ~ ilf_type(X3,set_type)
| ~ member(X3,X0)
| member(X3,X1) ),
inference(cnf_transformation,[],[f103]) ).
fof(f161,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ~ empty(power_set(X0)) ),
inference(cnf_transformation,[],[f62]) ).
fof(f162,plain,
! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| empty(X1)
| ~ ilf_type(X0,member_type(X1))
| member(X0,X1) ),
inference(cnf_transformation,[],[f104]) ).
fof(f171,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,[],[f69]) ).
fof(f172,plain,
! [X2,X0] :
( ~ ilf_type(X0,set_type)
| ~ empty(X0)
| ~ ilf_type(X2,set_type)
| ~ member(X2,X0) ),
inference(cnf_transformation,[],[f111]) ).
fof(f176,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,[],[f73]) ).
fof(f177,plain,
! [X2,X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,relation_type(X0,X1))
| ilf_type(domain(X0,X1,X2),subset_type(X0)) ),
inference(cnf_transformation,[],[f74]) ).
fof(f180,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[],[f34]) ).
fof(f183,plain,
ilf_type(sK15,relation_type(sK14,sK13)),
inference(cnf_transformation,[],[f115]) ).
fof(f184,plain,
! [X5] :
( ~ ilf_type(X5,set_type)
| ~ member(X5,sK14)
| member(ordered_pair(X5,sK17(X5)),sK15)
| sK14 = domain(sK14,sK13,sK15) ),
inference(cnf_transformation,[],[f115]) ).
fof(f187,plain,
( member(sK16,sK14)
| sK14 != domain(sK14,sK13,sK15) ),
inference(cnf_transformation,[],[f115]) ).
fof(f188,plain,
! [X4] :
( ~ member(ordered_pair(sK16,X4),sK15)
| ~ ilf_type(X4,set_type)
| sK14 != domain(sK14,sK13,sK15) ),
inference(cnf_transformation,[],[f115]) ).
tcf(c_49,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,[],[f118]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i] :
( member(ordered_pair(X0,sK0(X1,X0)),X1)
| ~ ilf_type(X1,binary_relation_type)
| ~ ilf_type(X0,set_type)
| ~ member(X0,domain_of(X1)) ),
inference(cnf_transformation,[],[f116]) ).
tcf(c_53,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,[],[f121]) ).
tcf(c_62,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,[],[f128]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f133]) ).
tcf(c_72,plain,
! [X0: $i] :
( ilf_type(X0,binary_relation_type)
| ~ relation_like(X0)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f197]) ).
tcf(c_76,plain,
! [X0: $i,X1: $i] :
( ilf_type(X0,member_type(power_set(X1)))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X0,subset_type(X1)) ),
inference(cnf_transformation,[],[f143]) ).
tcf(c_83,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,[],[f154]) ).
tcf(c_84,plain,
! [X0: $i,X1: $i] :
( subset(X1,X0)
| member(sK6(X1,X0),X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f153]) ).
tcf(c_91,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X2,X1)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| ~ member(X2,X0)
| ~ member(X0,power_set(X1)) ),
inference(cnf_transformation,[],[f156]) ).
tcf(c_92,plain,
! [X0: $i] :
( ~ empty(power_set(X0))
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f161]) ).
tcf(c_95,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| member(X0,X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X0,member_type(X1)) ),
inference(cnf_transformation,[],[f162]) ).
tcf(c_103,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,[],[f171]) ).
tcf(c_106,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f172]) ).
tcf(c_108,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,[],[f176]) ).
tcf(c_109,plain,
! [X0: $i,X1: $i,X2: $i] :
( ilf_type(domain(X1,X2,X0),subset_type(X1))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(cnf_transformation,[],[f177]) ).
tcf(c_112,plain,
! [X0: $i] : ilf_type(X0,set_type),
inference(cnf_transformation,[],[f180]) ).
tcf(c_113,negated_conjecture,
! [X0: $i] :
( ~ ilf_type(X0,set_type)
| ~ member(ordered_pair(sK16,X0),sK15)
| ( domain(sK14,sK13,sK15) != sK14 ) ),
inference(cnf_transformation,[],[f188]) ).
tcf(c_114,negated_conjecture,
( member(sK16,sK14)
| ( domain(sK14,sK13,sK15) != sK14 ) ),
inference(cnf_transformation,[],[f187]) ).
tcf(c_117,negated_conjecture,
! [X0: $i] :
( member(ordered_pair(X0,sK17(X0)),sK15)
| ( domain(sK14,sK13,sK15) = sK14 )
| ~ ilf_type(X0,set_type)
| ~ member(X0,sK14) ),
inference(cnf_transformation,[],[f184]) ).
tcf(c_118,negated_conjecture,
ilf_type(sK15,relation_type(sK14,sK13)),
inference(cnf_transformation,[],[f183]) ).
tcf(c_187,plain,
! [X0: $i] : ~ empty(power_set(X0)),
inference(global_subsumption_just,[status(thm)],[c_92,c_112,c_92]) ).
tcf(c_214,plain,
! [X0: $i] :
( ilf_type(X0,binary_relation_type)
| ~ relation_like(X0) ),
inference(global_subsumption_just,[status(thm)],[c_72,c_112,c_72]) ).
tcf(c_235,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ ilf_type(X1,set_type)
| ~ member(X0,X1) ),
inference(global_subsumption_just,[status(thm)],[c_106,c_112,c_106]) ).
tcf(c_246,plain,
! [X0: $i,X1: $i] :
( subset(X1,X0)
| member(sK6(X1,X0),X1)
| ~ ilf_type(X1,set_type) ),
inference(global_subsumption_just,[status(thm)],[c_84,c_112,c_84]) ).
tcf(c_247,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| member(sK6(X0,X1),X0)
| ~ ilf_type(X0,set_type) ),
inference(renaming,[status(thm)],[c_246]) ).
tcf(c_265,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_83,c_112,c_83]) ).
tcf(c_280,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| member(X0,X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,member_type(X1)) ),
inference(global_subsumption_just,[status(thm)],[c_95,c_112,c_95]) ).
tcf(c_287,plain,
! [X0: $i,X1: $i] :
( ilf_type(X0,member_type(power_set(X1)))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,subset_type(X1)) ),
inference(global_subsumption_just,[status(thm)],[c_76,c_112,c_76]) ).
tcf(c_301,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ ilf_type(X1,set_type)
| ~ subset(X0,X1)
| ~ subset(X1,X0) ),
inference(global_subsumption_just,[status(thm)],[c_64,c_112,c_64]) ).
tcf(c_302,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ ilf_type(X1,set_type)
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(renaming,[status(thm)],[c_301]) ).
tcf(c_303,plain,
! [X0: $i,X1: $i] :
( member(ordered_pair(X0,sK0(X1,X0)),X1)
| ~ ilf_type(X1,binary_relation_type)
| ~ member(X0,domain_of(X1)) ),
inference(global_subsumption_just,[status(thm)],[c_51,c_112,c_51]) ).
tcf(c_306,negated_conjecture,
! [X0: $i] :
( member(ordered_pair(X0,sK17(X0)),sK15)
| ( domain(sK14,sK13,sK15) = sK14 )
| ~ member(X0,sK14) ),
inference(global_subsumption_just,[status(thm)],[c_117,c_112,c_117]) ).
tcf(c_325,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_49,c_112,c_53]) ).
tcf(c_331,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X2,X1)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ member(X0,power_set(X1))
| ~ member(X2,X0) ),
inference(global_subsumption_just,[status(thm)],[c_91,c_112,c_91]) ).
tcf(c_332,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X2,X1)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ member(X2,X0)
| ~ member(X0,power_set(X1)) ),
inference(renaming,[status(thm)],[c_331]) ).
tcf(c_528,plain,
! [X0: $i,X1: $i,X2: $i] :
( ilf_type(domain(X1,X2,X0),subset_type(X1))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_109,c_112]) ).
tcf(c_531,plain,
! [X0: $i,X1: $i] :
( ilf_type(X0,member_type(power_set(X1)))
| ~ ilf_type(X0,subset_type(X1)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_287,c_112]) ).
tcf(c_532,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X2,X1)
| ~ ilf_type(X2,set_type)
| ~ member(X2,X0)
| ~ member(X0,power_set(X1)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_332,c_112]) ).
tcf(c_533,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ member(sK6(X0,X1),X1) ),
inference(backward_subsumption_resolution,[status(thm)],[c_265,c_112]) ).
tcf(c_535,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[c_302,c_112]) ).
tcf(c_538,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_108,c_112]) ).
tcf(c_539,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ member(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[c_235,c_112]) ).
tcf(c_540,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| member(X0,X1)
| ~ ilf_type(X0,member_type(X1)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_280,c_112]) ).
tcf(c_541,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_325,c_112]) ).
tcf(c_544,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_103,c_112]) ).
tcf(c_546,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_62,c_112]) ).
tcf(c_654,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_544,c_112]) ).
tcf(c_718,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_546,c_112]) ).
tcf(c_763,plain,
! [X0: $i,X1: $i,X2: $i] :
( ilf_type(domain(X1,X2,X0),subset_type(X1))
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_528,c_112]) ).
tcf(c_785,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_538,c_112]) ).
tcf(c_811,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ member(X0,power_set(X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_532,c_112]) ).
tcf(c_1215,plain,
! [X0: $i] :
( ilf_type(X0,binary_relation_type)
| ~ relation_like(X0) ),
inference(prop_impl_just,[status(thm)],[c_214]) ).
tcf(c_1223,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_531]) ).
tcf(c_1225,plain,
! [X0: $i,X1: $i,X2: $i] :
( relation_like(X0)
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(prop_impl_just,[status(thm)],[c_654,c_718]) ).
tcf(c_1227,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_785]) ).
tcf(c_1229,plain,
! [X0: $i,X1: $i,X2: $i] :
( ilf_type(domain(X1,X2,X0),subset_type(X1))
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(prop_impl_just,[status(thm)],[c_763]) ).
tcf(c_1235,plain,
! [X0: $i,X1: $i] :
( ~ member(sK6(X0,X1),X1)
| subset(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_533]) ).
tcf(c_1236,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ member(sK6(X0,X1),X1) ),
inference(renaming,[status(thm)],[c_1235]) ).
tcf(c_1237,plain,
! [X0: $i,X1: $i] :
( member(sK6(X0,X1),X0)
| subset(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_112,c_247]) ).
tcf(c_1238,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| member(sK6(X0,X1),X0) ),
inference(renaming,[status(thm)],[c_1237]) ).
tcf(c_1247,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ member(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_539]) ).
tcf(c_1269,plain,
! [X0: $i] :
( ~ member(ordered_pair(sK16,X0),sK15)
| ( domain(sK14,sK13,sK15) != sK14 ) ),
inference(prop_impl_just,[status(thm)],[c_112,c_113]) ).
tcf(c_2904,plain,
relation_like(sK15),
inference(superposition,[status(thm)],[c_118,c_1225]) ).
tcf(c_4440,plain,
domain(sK14,sK13,sK15) = domain_of(sK15),
inference(superposition,[status(thm)],[c_118,c_1227]) ).
tcf(c_4445,plain,
! [X0: $i] :
( member(ordered_pair(X0,sK17(X0)),sK15)
| ( domain_of(sK15) = sK14 )
| ~ member(X0,sK14) ),
inference(demodulation,[status(thm)],[c_306,c_4440]) ).
tcf(c_4484,plain,
! [X0: $i] :
( member(X0,domain_of(sK15))
| ( domain_of(sK15) = sK14 )
| ~ ilf_type(sK15,binary_relation_type)
| ~ member(X0,sK14) ),
inference(superposition,[status(thm)],[c_4445,c_541]) ).
tcf(c_4661,plain,
! [X0: $i] :
( subset(X0,domain_of(sK15))
| ( domain_of(sK15) = sK14 )
| ~ ilf_type(sK15,binary_relation_type)
| ~ member(sK6(X0,domain_of(sK15)),sK14) ),
inference(superposition,[status(thm)],[c_4484,c_1236]) ).
tcf(c_4724,plain,
( subset(sK14,domain_of(sK15))
| ( domain_of(sK15) = sK14 )
| ~ ilf_type(sK15,binary_relation_type) ),
inference(superposition,[status(thm)],[c_1238,c_4661]) ).
tcf(c_4982,plain,
( ( domain_of(sK15) = sK14 )
| ~ ilf_type(sK15,binary_relation_type)
| ~ subset(domain_of(sK15),sK14) ),
inference(superposition,[status(thm)],[c_4724,c_535]) ).
tcf(c_6086,plain,
( ilf_type(sK15,binary_relation_type)
| ~ relation_like(sK15) ),
inference(instantiation,[status(thm)],[c_1215]) ).
tcf(c_6762,plain,
! [X0: $i] :
( ( domain(sK14,sK13,sK15) = sK14 )
| ~ empty(sK15)
| ~ member(X0,sK14) ),
inference(superposition,[status(thm)],[c_306,c_1247]) ).
tcf(c_6797,plain,
! [X0: $i,X1: $i] :
( empty(power_set(X1))
| member(X0,power_set(X1))
| ~ ilf_type(X0,subset_type(X1)) ),
inference(superposition,[status(thm)],[c_1223,c_540]) ).
tcf(c_6798,plain,
! [X0: $i,X1: $i] :
( member(X0,power_set(X1))
| ~ ilf_type(X0,subset_type(X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6797,c_187]) ).
tcf(c_6867,plain,
domain(sK14,sK13,sK15) = domain_of(sK15),
inference(superposition,[status(thm)],[c_118,c_1227]) ).
tcf(c_6873,plain,
! [X0: $i] :
( ( domain_of(sK15) = sK14 )
| ~ empty(sK15)
| ~ member(X0,sK14) ),
inference(demodulation,[status(thm)],[c_6762,c_6867]) ).
tcf(c_6875,plain,
( member(sK16,sK14)
| ( domain_of(sK15) != sK14 ) ),
inference(demodulation,[status(thm)],[c_114,c_6867]) ).
tcf(c_6876,plain,
( ilf_type(domain_of(sK15),subset_type(sK14))
| ~ ilf_type(sK15,relation_type(sK14,sK13)) ),
inference(superposition,[status(thm)],[c_6867,c_1229]) ).
tcf(c_6877,plain,
ilf_type(domain_of(sK15),subset_type(sK14)),
inference(forward_subsumption_resolution,[status(thm)],[c_6876,c_118]) ).
tcf(c_6929,plain,
! [X0: $i] :
( ~ member(ordered_pair(sK16,X0),sK15)
| ( domain_of(sK15) != sK14 ) ),
inference(light_normalisation,[status(thm)],[c_1269,c_6867]) ).
tcf(c_7034,plain,
member(domain_of(sK15),power_set(sK14)),
inference(superposition,[status(thm)],[c_6877,c_6798]) ).
tcf(c_7148,plain,
! [X0: $i] :
( member(X0,sK14)
| ~ member(X0,domain_of(sK15)) ),
inference(superposition,[status(thm)],[c_7034,c_811]) ).
tcf(c_7210,plain,
! [X0: $i] :
( subset(domain_of(sK15),X0)
| member(sK6(domain_of(sK15),X0),sK14) ),
inference(superposition,[status(thm)],[c_1238,c_7148]) ).
tcf(c_7509,plain,
subset(domain_of(sK15),sK14),
inference(superposition,[status(thm)],[c_7210,c_1236]) ).
tcf(c_7514,plain,
! [X0: $i] :
( subset(domain_of(sK15),X0)
| ( domain_of(sK15) = sK14 )
| ~ empty(sK15) ),
inference(superposition,[status(thm)],[c_7210,c_6873]) ).
tcf(c_7539,plain,
domain_of(sK15) = sK14,
inference(global_subsumption_just,[status(thm)],[c_7514,c_2904,c_4982,c_6086,c_7509]) ).
tcf(c_7575,plain,
! [X0: $i] :
( ~ member(ordered_pair(sK16,X0),sK15)
| ( sK14 != sK14 ) ),
inference(demodulation,[status(thm)],[c_6929,c_7539]) ).
tcf(c_7582,plain,
( member(sK16,sK14)
| ( sK14 != sK14 ) ),
inference(demodulation,[status(thm)],[c_6875,c_7539]) ).
tcf(c_7585,plain,
member(sK16,sK14),
inference(equality_resolution_simp,[status(thm)],[c_7582]) ).
tcf(c_7586,plain,
! [X0: $i] : ~ member(ordered_pair(sK16,X0),sK15),
inference(equality_resolution_simp,[status(thm)],[c_7575]) ).
tcf(c_7795,plain,
( ~ ilf_type(sK15,binary_relation_type)
| ~ member(sK16,domain_of(sK15)) ),
inference(superposition,[status(thm)],[c_303,c_7586]) ).
tcf(c_7808,plain,
~ member(sK16,domain_of(sK15)),
inference(global_subsumption_just,[status(thm)],[c_7795,c_2904,c_6086,c_7795]) ).
tcf(c_7810,plain,
~ member(sK16,sK14),
inference(light_normalisation,[status(thm)],[c_7808,c_7539]) ).
tcf(c_7811,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_7810,c_7585]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET659+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.37 % Computer : n017.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Thu Sep 24 11:30:47 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 0.10/0.43
% 0.10/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.43
% 0.10/0.43 % Detected problem language: tptp
% 0.10/0.44 % Proving...
% 22.93/6.83 % SZS status Started for theBenchmark.p
% 22.93/6.83 % SZS status Theorem for theBenchmark.p
% 22.93/6.83
% 22.93/6.83 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 22.93/6.83
% 22.93/6.83 % ------ iProver source info
% 22.93/6.83
% 22.93/6.83 % git: date: 2026-07-19 20:42:38 +0200
% 22.93/6.83 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 22.93/6.83 % git: non_committed_changes: false
% 22.93/6.83
% 22.93/6.83 % ------ Parsing...
% 22.93/6.83 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 22.93/6.83
% 22.93/6.83 % ------ Preprocessing... sup_sim: 1 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 %
% 22.93/6.83
% 22.93/6.83 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 22.93/6.83
% 22.93/6.83 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 22.93/6.83 % ------ Proving...
% 22.93/6.83 % ------ Problem Properties
% 22.93/6.83
% 22.93/6.83 %
% 22.93/6.83 % clauses 46
% 22.93/6.83 % conjectures 3
% 22.93/6.83 % EPR 9
% 22.93/6.83 % Horn 37
% 22.93/6.83 % unary 9
% 22.93/6.83 % binary 24
% 22.93/6.83 % lits 96
% 22.93/6.83 % lits eq 14
% 22.93/6.83 % fd_pure 0
% 22.93/6.83 % fd_pseudo 0
% 22.93/6.83 % fd_cond 0
% 22.93/6.83 % fd_pseudo_cond 5
% 22.93/6.83 % AC symbols 0
% 22.93/6.83
% 22.93/6.83 % ------ Input Options Time Limit: Unbounded
% 22.93/6.83
% 22.93/6.83
% 22.93/6.83 % ------
% 22.93/6.83 % Current options:
% 22.93/6.83 % ------
% 22.93/6.83
% 22.93/6.83
% 22.93/6.83 %
% 22.93/6.83
% 22.93/6.83 % ------ Proving...
% 22.93/6.83 %
% 22.93/6.83
% 22.93/6.83 % SZS status Theorem for theBenchmark.p
% 22.93/6.83
% 22.93/6.83 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 22.93/6.83
% 22.93/6.83
%------------------------------------------------------------------------------