%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET660+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 : n016.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 27.48s 6.87s
% Output : CNFRefutation 27.48s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f197ERROR: Could not build tree for root c_9654ERROR: MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] :
( ilf_type(X0,binary_relation_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( member(X1,range_of(X0))
<=> ? [X2] :
( member(ordered_pair(X2,X1),X0)
& ilf_type(X2,set_type) ) ) ) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',p24) ).
fof(f26,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ( relation_like(X0)
<=> ! [X1] :
( ilf_type(X1,set_type)
=> ( member(X1,X0)
=> ? [X2] :
( ? [X3] :
( X1 = ordered_pair(X2,X3)
& ilf_type(X3,set_type) )
& ilf_type(X2,set_type) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p26) ).
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/sandbox/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/sandbox/benchmark/theBenchmark.p',p28) ).
fof(f32,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',p32) ).
fof(f33,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,relation_type(X0,X1))
=> ilf_type(range(X0,X1,X2),subset_type(X1)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p33) ).
fof(f34,axiom,
! [X0] : ilf_type(X0,set_type),
file('/export/starexec/sandbox/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(X0,X1))
=> ( ! [X3] :
( ilf_type(X3,set_type)
=> ( member(X3,X1)
=> ? [X4] :
( member(ordered_pair(X4,X3),X2)
& ilf_type(X4,set_type) ) ) )
<=> range(X0,X1,X2) = X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_relset_1_23) ).
fof(f36,negated_conjecture,
~ ! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,relation_type(X0,X1))
=> ( ! [X3] :
( ilf_type(X3,set_type)
=> ( member(X3,X1)
=> ? [X4] :
( member(ordered_pair(X4,X3),X2)
& ilf_type(X4,set_type) ) ) )
<=> range(X0,X1,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,range_of(X0))
<=> ? [X2] :
( member(ordered_pair(X2,X1),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(f67,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ( relation_like(X0)
<=> ! [X1] :
( ~ ilf_type(X1,set_type)
| ~ member(X1,X0)
| ? [X2] :
( ? [X3] :
( X1 = ordered_pair(X2,X3)
& ilf_type(X3,set_type) )
& ilf_type(X2,set_type) ) ) ) ),
inference(ennf_transformation,[],[f26]) ).
fof(f68,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ( relation_like(X0)
<=> ! [X1] :
( ~ ilf_type(X1,set_type)
| ~ member(X1,X0)
| ? [X2] :
( ? [X3] :
( X1 = ordered_pair(X2,X3)
& ilf_type(X3,set_type) )
& ilf_type(X2,set_type) ) ) ) ),
inference(flattening,[],[f67]) ).
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(f75,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,[],[f32]) ).
fof(f76,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ! [X2] :
( ~ ilf_type(X2,relation_type(X0,X1))
| ilf_type(range(X0,X1,X2),subset_type(X1)) ) ) ),
inference(ennf_transformation,[],[f33]) ).
fof(f77,plain,
? [X0] :
( ilf_type(X0,set_type)
& ? [X1] :
( ilf_type(X1,set_type)
& ? [X2] :
( ilf_type(X2,relation_type(X0,X1))
& ( ! [X3] :
( ~ ilf_type(X3,set_type)
| ~ member(X3,X1)
| ? [X4] :
( member(ordered_pair(X4,X3),X2)
& ilf_type(X4,set_type) ) )
<~> range(X0,X1,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(X0,X1))
& ( ! [X3] :
( ~ ilf_type(X3,set_type)
| ~ member(X3,X1)
| ? [X4] :
( member(ordered_pair(X4,X3),X2)
& ilf_type(X4,set_type) ) )
<~> range(X0,X1,X2) = X1 ) ) ) ),
inference(flattening,[],[f77]) ).
fof(f79,plain,
! [X0] :
( ~ ilf_type(X0,binary_relation_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ( ( ~ member(X1,range_of(X0))
| ? [X2] :
( member(ordered_pair(X2,X1),X0)
& ilf_type(X2,set_type) ) )
& ( ! [X2] :
( ~ member(ordered_pair(X2,X1),X0)
| ~ ilf_type(X2,set_type) )
| member(X1,range_of(X0)) ) ) ) ),
inference(nnf_transformation,[],[f37]) ).
fof(f80,plain,
! [X0] :
( ~ ilf_type(X0,binary_relation_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ( ( ~ member(X1,range_of(X0))
| ? [X3] :
( member(ordered_pair(X3,X1),X0)
& ilf_type(X3,set_type) ) )
& ( ! [X2] :
( ~ member(ordered_pair(X2,X1),X0)
| ~ ilf_type(X2,set_type) )
| member(X1,range_of(X0)) ) ) ) ),
inference(rectify,[],[f79]) ).
fof(f81,plain,
! [X0] :
( ~ ilf_type(X0,binary_relation_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ( ( ~ member(X1,range_of(X0))
| ( member(ordered_pair(sK0(X0,X1),X1),X0)
& ilf_type(sK0(X0,X1),set_type) ) )
& ( ! [X2] :
( ~ member(ordered_pair(X2,X1),X0)
| ~ ilf_type(X2,set_type) )
| member(X1,range_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(f106,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ( ( ~ relation_like(X0)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ~ member(X1,X0)
| ? [X2] :
( ? [X3] :
( X1 = ordered_pair(X2,X3)
& ilf_type(X3,set_type) )
& ilf_type(X2,set_type) ) ) )
& ( ? [X1] :
( ilf_type(X1,set_type)
& member(X1,X0)
& ! [X2] :
( ! [X3] :
( ordered_pair(X2,X3) != X1
| ~ ilf_type(X3,set_type) )
| ~ ilf_type(X2,set_type) ) )
| relation_like(X0) ) ) ),
inference(nnf_transformation,[],[f68]) ).
fof(f107,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ( ( ~ relation_like(X0)
| ! [X4] :
( ~ ilf_type(X4,set_type)
| ~ member(X4,X0)
| ? [X5] :
( ? [X6] :
( ordered_pair(X5,X6) = X4
& ilf_type(X6,set_type) )
& ilf_type(X5,set_type) ) ) )
& ( ? [X1] :
( ilf_type(X1,set_type)
& member(X1,X0)
& ! [X2] :
( ! [X3] :
( ordered_pair(X2,X3) != X1
| ~ ilf_type(X3,set_type) )
| ~ ilf_type(X2,set_type) ) )
| relation_like(X0) ) ) ),
inference(rectify,[],[f106]) ).
fof(f108,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ( ( ~ relation_like(X0)
| ! [X4] :
( ~ ilf_type(X4,set_type)
| ~ member(X4,X0)
| ( ordered_pair(sK10(X4),sK11(X4)) = X4
& ilf_type(sK11(X4),set_type)
& ilf_type(sK10(X4),set_type) ) ) )
& ( ( ilf_type(sK9(X0),set_type)
& member(sK9(X0),X0)
& ! [X2] :
( ! [X3] :
( ordered_pair(X2,X3) != sK9(X0)
| ~ ilf_type(X3,set_type) )
| ~ ilf_type(X2,set_type) ) )
| relation_like(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9,sK10,sK11]),skolemize(X1,sK9(X0)),skolemize(X5,sK10(X4)),skolemize(X6,sK11(X4))],[f107]) ).
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(X0,X1))
& ( ! [X3] :
( ~ ilf_type(X3,set_type)
| ~ member(X3,X1)
| ? [X4] :
( member(ordered_pair(X4,X3),X2)
& ilf_type(X4,set_type) ) )
| range(X0,X1,X2) = X1 )
& ( ? [X3] :
( ilf_type(X3,set_type)
& member(X3,X1)
& ! [X4] :
( ~ member(ordered_pair(X4,X3),X2)
| ~ ilf_type(X4,set_type) ) )
| range(X0,X1,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(X0,X1))
& ( ! [X3] :
( ~ ilf_type(X3,set_type)
| ~ member(X3,X1)
| ? [X4] :
( member(ordered_pair(X4,X3),X2)
& ilf_type(X4,set_type) ) )
| range(X0,X1,X2) = X1 )
& ( ? [X3] :
( ilf_type(X3,set_type)
& member(X3,X1)
& ! [X4] :
( ~ member(ordered_pair(X4,X3),X2)
| ~ ilf_type(X4,set_type) ) )
| range(X0,X1,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(X0,X1))
& ( ! [X5] :
( ~ ilf_type(X5,set_type)
| ~ member(X5,X1)
| ? [X6] :
( member(ordered_pair(X6,X5),X2)
& ilf_type(X6,set_type) ) )
| range(X0,X1,X2) = X1 )
& ( ? [X3] :
( ilf_type(X3,set_type)
& member(X3,X1)
& ! [X4] :
( ~ member(ordered_pair(X4,X3),X2)
| ~ ilf_type(X4,set_type) ) )
| range(X0,X1,X2) != X1 ) ) ) ),
inference(rectify,[],[f113]) ).
fof(f115,plain,
( ilf_type(sK13,set_type)
& ilf_type(sK14,set_type)
& ilf_type(sK15,relation_type(sK13,sK14))
& ( ! [X5] :
( ~ ilf_type(X5,set_type)
| ~ member(X5,sK14)
| ( member(ordered_pair(sK17(X5),X5),sK15)
& ilf_type(sK17(X5),set_type) ) )
| sK14 = range(sK13,sK14,sK15) )
& ( ( ilf_type(sK16,set_type)
& member(sK16,sK14)
& ! [X4] :
( ~ member(ordered_pair(X4,sK16),sK15)
| ~ ilf_type(X4,set_type) ) )
| sK14 != range(sK13,sK14,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,range_of(X0))
| member(ordered_pair(sK0(X0,X1),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(X2,X1),X0)
| ~ ilf_type(X2,set_type)
| member(X1,range_of(X0)) ),
inference(cnf_transformation,[],[f81]) ).
fof(f120,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,[],[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(f151,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,[],[f100]) ).
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(f169,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| member(sK9(X0),X0)
| relation_like(X0) ),
inference(cnf_transformation,[],[f108]) ).
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(f178,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,[],[f75]) ).
fof(f179,plain,
! [X2,X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,relation_type(X0,X1))
| ilf_type(range(X0,X1,X2),subset_type(X1)) ),
inference(cnf_transformation,[],[f76]) ).
fof(f180,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[],[f34]) ).
fof(f183,plain,
ilf_type(sK15,relation_type(sK13,sK14)),
inference(cnf_transformation,[],[f115]) ).
fof(f184,plain,
! [X5] :
( ~ ilf_type(X5,set_type)
| ~ member(X5,sK14)
| member(ordered_pair(sK17(X5),X5),sK15)
| sK14 = range(sK13,sK14,sK15) ),
inference(cnf_transformation,[],[f115]) ).
fof(f187,plain,
( member(sK16,sK14)
| sK14 != range(sK13,sK14,sK15) ),
inference(cnf_transformation,[],[f115]) ).
fof(f188,plain,
! [X4] :
( ~ member(ordered_pair(X4,sK16),sK15)
| ~ ilf_type(X4,set_type)
| sK14 != range(sK13,sK14,sK15) ),
inference(cnf_transformation,[],[f115]) ).
tcf(c_49,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,[],[f118]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i] :
( member(ordered_pair(sK0(X1,X0),X0),X1)
| ~ ilf_type(X1,binary_relation_type)
| ~ ilf_type(X0,set_type)
| ~ member(X0,range_of(X1)) ),
inference(cnf_transformation,[],[f116]) ).
tcf(c_54,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,[],[f120]) ).
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_86,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| ~ subset(X1,X2)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f151]) ).
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_98,plain,
! [X0: $i] :
( relation_like(X0)
| member(sK9(X0),X0)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f169]) ).
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_110,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,[],[f178]) ).
tcf(c_111,plain,
! [X0: $i,X1: $i,X2: $i] :
( ilf_type(range(X1,X2,X0),subset_type(X2))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(cnf_transformation,[],[f179]) ).
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(X0,sK16),sK15)
| ( range(sK13,sK14,sK15) != sK14 ) ),
inference(cnf_transformation,[],[f188]) ).
tcf(c_114,negated_conjecture,
( member(sK16,sK14)
| ( range(sK13,sK14,sK15) != sK14 ) ),
inference(cnf_transformation,[],[f187]) ).
tcf(c_117,negated_conjecture,
! [X0: $i] :
( member(ordered_pair(sK17(X0),X0),sK15)
| ( range(sK13,sK14,sK15) = sK14 )
| ~ ilf_type(X0,set_type)
| ~ member(X0,sK14) ),
inference(cnf_transformation,[],[f184]) ).
tcf(c_118,negated_conjecture,
ilf_type(sK15,relation_type(sK13,sK14)),
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(sK0(X1,X0),X0),X1)
| ~ ilf_type(X1,binary_relation_type)
| ~ member(X0,range_of(X1)) ),
inference(global_subsumption_just,[status(thm)],[c_51,c_112,c_51]) ).
tcf(c_306,negated_conjecture,
! [X0: $i] :
( member(ordered_pair(sK17(X0),X0),sK15)
| ( range(sK13,sK14,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(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_49,c_112,c_54]) ).
tcf(c_329,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ member(X0,X1)
| ~ subset(X1,X2) ),
inference(global_subsumption_just,[status(thm)],[c_86,c_112,c_86]) ).
tcf(c_330,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ subset(X1,X2)
| ~ member(X0,X1) ),
inference(renaming,[status(thm)],[c_329]) ).
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_527,plain,
! [X0: $i,X1: $i,X2: $i] :
( ilf_type(range(X1,X2,X0),subset_type(X2))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_111,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_534,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| ~ ilf_type(X2,set_type)
| ~ subset(X1,X2)
| ~ member(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[c_330,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_537,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_110,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_542,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_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_752,plain,
! [X0: $i,X1: $i,X2: $i] :
( ilf_type(range(X1,X2,X0),subset_type(X2))
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_527,c_112]) ).
tcf(c_774,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_537,c_112]) ).
tcf(c_797,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| ~ subset(X1,X2)
| ~ member(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_534,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_1231,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_774]) ).
tcf(c_1233,plain,
! [X0: $i,X1: $i,X2: $i] :
( ilf_type(range(X1,X2,X0),subset_type(X2))
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(prop_impl_just,[status(thm)],[c_752]) ).
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_1241,plain,
! [X0: $i] :
( member(sK9(X0),X0)
| relation_like(X0) ),
inference(prop_impl_just,[status(thm)],[c_112,c_98]) ).
tcf(c_1242,plain,
! [X0: $i] :
( relation_like(X0)
| member(sK9(X0),X0) ),
inference(renaming,[status(thm)],[c_1241]) ).
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(X0,sK16),sK15)
| ( range(sK13,sK14,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_4489,plain,
range(sK13,sK14,sK15) = range_of(sK15),
inference(superposition,[status(thm)],[c_118,c_1231]) ).
tcf(c_4496,plain,
! [X0: $i] :
( member(ordered_pair(sK17(X0),X0),sK15)
| ( range_of(sK15) = sK14 )
| ~ member(X0,sK14) ),
inference(demodulation,[status(thm)],[c_306,c_4489]) ).
tcf(c_4505,plain,
! [X0: $i] :
( member(X0,range_of(sK15))
| ( range_of(sK15) = sK14 )
| ~ ilf_type(sK15,binary_relation_type)
| ~ member(X0,sK14) ),
inference(superposition,[status(thm)],[c_4496,c_542]) ).
tcf(c_4609,plain,
! [X0: $i] :
( subset(X0,range_of(sK15))
| ( range_of(sK15) = sK14 )
| ~ ilf_type(sK15,binary_relation_type)
| ~ member(sK6(X0,range_of(sK15)),sK14) ),
inference(superposition,[status(thm)],[c_4505,c_1236]) ).
tcf(c_5585,plain,
( subset(sK14,range_of(sK15))
| ( range_of(sK15) = sK14 )
| ~ ilf_type(sK15,binary_relation_type) ),
inference(superposition,[status(thm)],[c_1238,c_4609]) ).
tcf(c_6533,plain,
( ( range_of(sK15) = sK14 )
| ~ ilf_type(sK15,binary_relation_type)
| ~ subset(range_of(sK15),sK14) ),
inference(superposition,[status(thm)],[c_5585,c_535]) ).
tcf(c_6800,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_6801,plain,
! [X0: $i,X1: $i] :
( member(X0,power_set(X1))
| ~ ilf_type(X0,subset_type(X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6800,c_187]) ).
tcf(c_6926,plain,
range(sK13,sK14,sK15) = range_of(sK15),
inference(superposition,[status(thm)],[c_118,c_1231]) ).
tcf(c_6928,plain,
! [X0: $i] :
( ~ member(ordered_pair(X0,sK16),sK15)
| ( range_of(sK15) != sK14 ) ),
inference(light_normalisation,[status(thm)],[c_1269,c_6926]) ).
tcf(c_6965,plain,
! [X0: $i] :
( member(ordered_pair(sK17(X0),X0),sK15)
| ( range_of(sK15) = sK14 )
| ~ member(X0,sK14) ),
inference(demodulation,[status(thm)],[c_306,c_6926]) ).
tcf(c_6966,plain,
( member(sK16,sK14)
| ( range_of(sK15) != sK14 ) ),
inference(demodulation,[status(thm)],[c_114,c_6926]) ).
tcf(c_6967,plain,
( ilf_type(range_of(sK15),subset_type(sK14))
| ~ ilf_type(sK15,relation_type(sK13,sK14)) ),
inference(superposition,[status(thm)],[c_6926,c_1233]) ).
tcf(c_6968,plain,
ilf_type(range_of(sK15),subset_type(sK14)),
inference(forward_subsumption_resolution,[status(thm)],[c_6967,c_118]) ).
tcf(c_7030,plain,
member(range_of(sK15),power_set(sK14)),
inference(superposition,[status(thm)],[c_6968,c_6801]) ).
tcf(c_7108,plain,
! [X0: $i,X1: $i] :
( member(ordered_pair(sK17(X0),X0),X1)
| ( range_of(sK15) = sK14 )
| ~ subset(sK15,X1)
| ~ member(X0,sK14) ),
inference(superposition,[status(thm)],[c_6965,c_797]) ).
tcf(c_7148,plain,
! [X0: $i] :
( member(X0,sK14)
| ~ member(X0,range_of(sK15)) ),
inference(superposition,[status(thm)],[c_7030,c_811]) ).
tcf(c_7195,plain,
! [X0: $i,X1: $i] :
( ( range_of(sK15) = sK14 )
| ~ empty(X1)
| ~ subset(sK15,X1)
| ~ member(X0,sK14) ),
inference(superposition,[status(thm)],[c_7108,c_1247]) ).
tcf(c_7308,plain,
! [X0: $i] :
( subset(range_of(sK15),X0)
| member(sK6(range_of(sK15),X0),sK14) ),
inference(superposition,[status(thm)],[c_1238,c_7148]) ).
tcf(c_7404,plain,
! [X0: $i] :
( relation_like(sK14)
| ( range_of(sK15) = sK14 )
| ~ empty(X0)
| ~ subset(sK15,X0) ),
inference(superposition,[status(thm)],[c_1242,c_7195]) ).
tcf(c_7470,plain,
subset(range_of(sK15),sK14),
inference(superposition,[status(thm)],[c_7308,c_1236]) ).
tcf(c_8217,plain,
( ilf_type(sK15,binary_relation_type)
| ~ relation_like(sK15) ),
inference(instantiation,[status(thm)],[c_1215]) ).
tcf(c_8241,plain,
range_of(sK15) = sK14,
inference(global_subsumption_just,[status(thm)],[c_7404,c_2904,c_6533,c_7470,c_8217]) ).
tcf(c_8281,plain,
( member(sK16,sK14)
| ( sK14 != sK14 ) ),
inference(demodulation,[status(thm)],[c_6966,c_8241]) ).
tcf(c_8283,plain,
! [X0: $i] :
( ~ member(ordered_pair(X0,sK16),sK15)
| ( sK14 != sK14 ) ),
inference(demodulation,[status(thm)],[c_6928,c_8241]) ).
tcf(c_8284,plain,
member(sK16,sK14),
inference(equality_resolution_simp,[status(thm)],[c_8281]) ).
tcf(c_8285,plain,
! [X0: $i] : ~ member(ordered_pair(X0,sK16),sK15),
inference(equality_resolution_simp,[status(thm)],[c_8283]) ).
tcf(c_9644,plain,
( ~ ilf_type(sK15,binary_relation_type)
| ~ member(sK16,range_of(sK15)) ),
inference(superposition,[status(thm)],[c_303,c_8285]) ).
tcf(c_9651,plain,
~ member(sK16,range_of(sK15)),
inference(global_subsumption_just,[status(thm)],[c_9644,c_2904,c_8217,c_9644]) ).
tcf(c_9653,plain,
~ member(sK16,sK14),
inference(light_normalisation,[status(thm)],[c_9651,c_8241]) ).
tcf(c_9654,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_9653,c_8284]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET660+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.36 % Computer : n016.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Thu Sep 24 11:39:57 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/0.40 Running first-order theorem proving
% 0.13/0.40 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
% 0.13/0.41
% 0.13/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.41
% 0.13/0.41 % Detected problem language: tptp
% 0.13/0.42 % Proving...
% 27.48/6.87 % SZS status Started for theBenchmark.p
% 27.48/6.87 % SZS status Theorem for theBenchmark.p
% 27.48/6.87
% 27.48/6.87 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 27.48/6.87
% 27.48/6.87 % ------ iProver source info
% 27.48/6.87
% 27.48/6.87 % git: date: 2026-07-19 20:42:38 +0200
% 27.48/6.87 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 27.48/6.87 % git: non_committed_changes: false
% 27.48/6.87
% 27.48/6.87 % ------ Parsing...
% 27.48/6.87 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 27.48/6.87
% 27.48/6.87 % ------ 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 %
% 27.48/6.87
% 27.48/6.87 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 27.48/6.87
% 27.48/6.87 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 27.48/6.87 % ------ Proving...
% 27.48/6.87 % ------ Problem Properties
% 27.48/6.87
% 27.48/6.87 %
% 27.48/6.87 % clauses 46
% 27.48/6.87 % conjectures 3
% 27.48/6.87 % EPR 9
% 27.48/6.87 % Horn 37
% 27.48/6.87 % unary 9
% 27.48/6.87 % binary 24
% 27.48/6.87 % lits 96
% 27.48/6.87 % lits eq 14
% 27.48/6.87 % fd_pure 0
% 27.48/6.87 % fd_pseudo 0
% 27.48/6.87 % fd_cond 0
% 27.48/6.87 % fd_pseudo_cond 5
% 27.48/6.87 % AC symbols 0
% 27.48/6.87
% 27.48/6.87 % ------ Input Options Time Limit: Unbounded
% 27.48/6.87
% 27.48/6.87
% 27.48/6.87 % ------
% 27.48/6.87 % Current options:
% 27.48/6.87 % ------
% 27.48/6.87
% 27.48/6.87
% 27.48/6.87 %
% 27.48/6.87
% 27.48/6.87 % ------ Proving...
% 27.48/6.87 %
% 27.48/6.87
% 27.48/6.87 % SZS status Theorem for theBenchmark.p
% 27.48/6.87
% 27.48/6.87 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 27.48/6.87
% 27.48/6.87
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