TSTP Solution File: SET660+3 by iProver---3.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SET660+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n028.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 15:08:59 EDT 2023
% Result : Theorem 7.69s 1.66s
% Output : CNFRefutation 7.69s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f216)
% 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/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(f26,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ( relation_like(X0)
<=> ! [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) ) ) ) ) ),
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,subset_type(cross_product(X0,X1)))
=> relation_like(X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p27) ).
fof(f32,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,relation_type(X0,X1))
=> range_of(X2) = range(X0,X1,X2) ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',p33) ).
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(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/sandbox2/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,[],[f35]) ).
fof(f37,plain,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( ! [X2] :
( ilf_type(X2,relation_type(X0,X1))
=> ilf_type(X2,subset_type(cross_product(X0,X1))) )
& ! [X3] :
( ilf_type(X3,subset_type(cross_product(X0,X1)))
=> ilf_type(X3,relation_type(X0,X1)) ) ) ) ),
inference(rectify,[],[f7]) ).
fof(f38,plain,
! [X0] :
( ! [X1] :
( ( member(X1,range_of(X0))
<=> ? [X2] :
( member(ordered_pair(X2,X1),X0)
& ilf_type(X2,set_type) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,binary_relation_type) ),
inference(ennf_transformation,[],[f1]) ).
fof(f40,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( member(X1,range_of(X2))
& member(X0,domain_of(X2)) )
| ~ member(ordered_pair(X0,X1),X2)
| ~ ilf_type(X2,binary_relation_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f3]) ).
fof(f41,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( member(X1,range_of(X2))
& member(X0,domain_of(X2)) )
| ~ member(ordered_pair(X0,X1),X2)
| ~ ilf_type(X2,binary_relation_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(flattening,[],[f40]) ).
fof(f46,plain,
! [X0] :
( ! [X1] :
( ( ! [X2] :
( ilf_type(X2,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X2,relation_type(X0,X1)) )
& ! [X3] :
( ilf_type(X3,relation_type(X0,X1))
| ~ ilf_type(X3,subset_type(cross_product(X0,X1))) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f37]) ).
fof(f48,plain,
! [X0] :
( ! [X1] :
( ( X0 = X1
<=> ( subset(X1,X0)
& subset(X0,X1) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f9]) ).
fof(f55,plain,
! [X0] :
( ! [X1] :
( ( ilf_type(X1,subset_type(X0))
<=> ilf_type(X1,member_type(power_set(X0))) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f17]) ).
fof(f58,plain,
! [X0] :
( ! [X1] :
( ( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ ilf_type(X2,set_type) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f20]) ).
fof(f59,plain,
! [X0] :
( ! [X1] :
( ( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ ilf_type(X2,set_type) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(flattening,[],[f58]) ).
fof(f61,plain,
! [X0] :
( ! [X1] :
( ( member(X0,power_set(X1))
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ ilf_type(X2,set_type) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f22]) ).
fof(f62,plain,
! [X0] :
( ! [X1] :
( ( member(X0,power_set(X1))
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ ilf_type(X2,set_type) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(flattening,[],[f61]) ).
fof(f63,plain,
! [X0] :
( ( ilf_type(power_set(X0),set_type)
& ~ empty(power_set(X0)) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f23]) ).
fof(f64,plain,
! [X0] :
( ! [X1] :
( ( ilf_type(X0,member_type(X1))
<=> member(X0,X1) )
| ~ ilf_type(X1,set_type)
| empty(X1) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f24]) ).
fof(f65,plain,
! [X0] :
( ! [X1] :
( ( ilf_type(X0,member_type(X1))
<=> member(X0,X1) )
| ~ ilf_type(X1,set_type)
| empty(X1) )
| ~ ilf_type(X0,set_type) ),
inference(flattening,[],[f64]) ).
fof(f68,plain,
! [X0] :
( ( relation_like(X0)
<=> ! [X1] :
( ? [X2] :
( ? [X3] :
( ordered_pair(X2,X3) = X1
& ilf_type(X3,set_type) )
& ilf_type(X2,set_type) )
| ~ member(X1,X0)
| ~ ilf_type(X1,set_type) ) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f26]) ).
fof(f69,plain,
! [X0] :
( ( relation_like(X0)
<=> ! [X1] :
( ? [X2] :
( ? [X3] :
( ordered_pair(X2,X3) = X1
& ilf_type(X3,set_type) )
& ilf_type(X2,set_type) )
| ~ member(X1,X0)
| ~ ilf_type(X1,set_type) ) )
| ~ ilf_type(X0,set_type) ),
inference(flattening,[],[f68]) ).
fof(f70,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( relation_like(X2)
| ~ ilf_type(X2,subset_type(cross_product(X0,X1))) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f27]) ).
fof(f76,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( range_of(X2) = range(X0,X1,X2)
| ~ ilf_type(X2,relation_type(X0,X1)) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f32]) ).
fof(f77,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ilf_type(range(X0,X1,X2),subset_type(X1))
| ~ ilf_type(X2,relation_type(X0,X1)) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f33]) ).
fof(f78,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ( ! [X3] :
( ? [X4] :
( member(ordered_pair(X4,X3),X2)
& ilf_type(X4,set_type) )
| ~ member(X3,X1)
| ~ ilf_type(X3,set_type) )
<~> range(X0,X1,X2) = X1 )
& ilf_type(X2,relation_type(X0,X1)) )
& ilf_type(X1,set_type) )
& ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f36]) ).
fof(f79,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ( ! [X3] :
( ? [X4] :
( member(ordered_pair(X4,X3),X2)
& ilf_type(X4,set_type) )
| ~ member(X3,X1)
| ~ ilf_type(X3,set_type) )
<~> range(X0,X1,X2) = X1 )
& ilf_type(X2,relation_type(X0,X1)) )
& ilf_type(X1,set_type) )
& ilf_type(X0,set_type) ),
inference(flattening,[],[f78]) ).
fof(f80,plain,
! [X0] :
( ! [X1] :
( ( ( 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)) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,binary_relation_type) ),
inference(nnf_transformation,[],[f38]) ).
fof(f81,plain,
! [X0] :
( ! [X1] :
( ( ( member(X1,range_of(X0))
| ! [X2] :
( ~ member(ordered_pair(X2,X1),X0)
| ~ ilf_type(X2,set_type) ) )
& ( ? [X3] :
( member(ordered_pair(X3,X1),X0)
& ilf_type(X3,set_type) )
| ~ member(X1,range_of(X0)) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,binary_relation_type) ),
inference(rectify,[],[f80]) ).
fof(f82,plain,
! [X0,X1] :
( ? [X3] :
( member(ordered_pair(X3,X1),X0)
& ilf_type(X3,set_type) )
=> ( member(ordered_pair(sK0(X0,X1),X1),X0)
& ilf_type(sK0(X0,X1),set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f83,plain,
! [X0] :
( ! [X1] :
( ( ( member(X1,range_of(X0))
| ! [X2] :
( ~ member(ordered_pair(X2,X1),X0)
| ~ ilf_type(X2,set_type) ) )
& ( ( member(ordered_pair(sK0(X0,X1),X1),X0)
& ilf_type(sK0(X0,X1),set_type) )
| ~ member(X1,range_of(X0)) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,binary_relation_type) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f81,f82]) ).
fof(f91,plain,
! [X0] :
( ! [X1] :
( ( ( X0 = X1
| ~ subset(X1,X0)
| ~ subset(X0,X1) )
& ( ( subset(X1,X0)
& subset(X0,X1) )
| X0 != X1 ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f48]) ).
fof(f92,plain,
! [X0] :
( ! [X1] :
( ( ( X0 = X1
| ~ subset(X1,X0)
| ~ subset(X0,X1) )
& ( ( subset(X1,X0)
& subset(X0,X1) )
| X0 != X1 ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(flattening,[],[f91]) ).
fof(f97,plain,
! [X0] :
( ! [X1] :
( ( ( 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)) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f55]) ).
fof(f105,plain,
! [X0] :
( ! [X1] :
( ( ( subset(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0)
& ilf_type(X2,set_type) ) )
& ( ! [X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ ilf_type(X2,set_type) )
| ~ subset(X0,X1) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f59]) ).
fof(f106,plain,
! [X0] :
( ! [X1] :
( ( ( subset(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0)
& ilf_type(X2,set_type) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ ilf_type(X3,set_type) )
| ~ subset(X0,X1) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(rectify,[],[f105]) ).
fof(f107,plain,
! [X0,X1] :
( ? [X2] :
( ~ member(X2,X1)
& member(X2,X0)
& ilf_type(X2,set_type) )
=> ( ~ member(sK6(X0,X1),X1)
& member(sK6(X0,X1),X0)
& ilf_type(sK6(X0,X1),set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f108,plain,
! [X0] :
( ! [X1] :
( ( ( subset(X0,X1)
| ( ~ member(sK6(X0,X1),X1)
& member(sK6(X0,X1),X0)
& ilf_type(sK6(X0,X1),set_type) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ ilf_type(X3,set_type) )
| ~ subset(X0,X1) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f106,f107]) ).
fof(f109,plain,
! [X0] :
( ! [X1] :
( ( ( member(X0,power_set(X1))
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0)
& ilf_type(X2,set_type) ) )
& ( ! [X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ ilf_type(X2,set_type) )
| ~ member(X0,power_set(X1)) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f62]) ).
fof(f110,plain,
! [X0] :
( ! [X1] :
( ( ( member(X0,power_set(X1))
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0)
& ilf_type(X2,set_type) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ ilf_type(X3,set_type) )
| ~ member(X0,power_set(X1)) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(rectify,[],[f109]) ).
fof(f111,plain,
! [X0,X1] :
( ? [X2] :
( ~ member(X2,X1)
& member(X2,X0)
& ilf_type(X2,set_type) )
=> ( ~ member(sK7(X0,X1),X1)
& member(sK7(X0,X1),X0)
& ilf_type(sK7(X0,X1),set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f112,plain,
! [X0] :
( ! [X1] :
( ( ( member(X0,power_set(X1))
| ( ~ member(sK7(X0,X1),X1)
& member(sK7(X0,X1),X0)
& ilf_type(sK7(X0,X1),set_type) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ ilf_type(X3,set_type) )
| ~ member(X0,power_set(X1)) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f110,f111]) ).
fof(f113,plain,
! [X0] :
( ! [X1] :
( ( ( ilf_type(X0,member_type(X1))
| ~ member(X0,X1) )
& ( member(X0,X1)
| ~ ilf_type(X0,member_type(X1)) ) )
| ~ ilf_type(X1,set_type)
| empty(X1) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f65]) ).
fof(f116,plain,
! [X0] :
( ( ( relation_like(X0)
| ? [X1] :
( ! [X2] :
( ! [X3] :
( ordered_pair(X2,X3) != X1
| ~ ilf_type(X3,set_type) )
| ~ ilf_type(X2,set_type) )
& member(X1,X0)
& ilf_type(X1,set_type) ) )
& ( ! [X1] :
( ? [X2] :
( ? [X3] :
( ordered_pair(X2,X3) = X1
& ilf_type(X3,set_type) )
& ilf_type(X2,set_type) )
| ~ member(X1,X0)
| ~ ilf_type(X1,set_type) )
| ~ relation_like(X0) ) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f69]) ).
fof(f117,plain,
! [X0] :
( ( ( relation_like(X0)
| ? [X1] :
( ! [X2] :
( ! [X3] :
( ordered_pair(X2,X3) != X1
| ~ ilf_type(X3,set_type) )
| ~ ilf_type(X2,set_type) )
& member(X1,X0)
& ilf_type(X1,set_type) ) )
& ( ! [X4] :
( ? [X5] :
( ? [X6] :
( ordered_pair(X5,X6) = X4
& ilf_type(X6,set_type) )
& ilf_type(X5,set_type) )
| ~ member(X4,X0)
| ~ ilf_type(X4,set_type) )
| ~ relation_like(X0) ) )
| ~ ilf_type(X0,set_type) ),
inference(rectify,[],[f116]) ).
fof(f118,plain,
! [X0] :
( ? [X1] :
( ! [X2] :
( ! [X3] :
( ordered_pair(X2,X3) != X1
| ~ ilf_type(X3,set_type) )
| ~ ilf_type(X2,set_type) )
& member(X1,X0)
& ilf_type(X1,set_type) )
=> ( ! [X2] :
( ! [X3] :
( ordered_pair(X2,X3) != sK9(X0)
| ~ ilf_type(X3,set_type) )
| ~ ilf_type(X2,set_type) )
& member(sK9(X0),X0)
& ilf_type(sK9(X0),set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f119,plain,
! [X4] :
( ? [X5] :
( ? [X6] :
( ordered_pair(X5,X6) = X4
& ilf_type(X6,set_type) )
& ilf_type(X5,set_type) )
=> ( ? [X6] :
( ordered_pair(sK10(X4),X6) = X4
& ilf_type(X6,set_type) )
& ilf_type(sK10(X4),set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f120,plain,
! [X4] :
( ? [X6] :
( ordered_pair(sK10(X4),X6) = X4
& ilf_type(X6,set_type) )
=> ( ordered_pair(sK10(X4),sK11(X4)) = X4
& ilf_type(sK11(X4),set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f121,plain,
! [X0] :
( ( ( relation_like(X0)
| ( ! [X2] :
( ! [X3] :
( ordered_pair(X2,X3) != sK9(X0)
| ~ ilf_type(X3,set_type) )
| ~ ilf_type(X2,set_type) )
& member(sK9(X0),X0)
& ilf_type(sK9(X0),set_type) ) )
& ( ! [X4] :
( ( ordered_pair(sK10(X4),sK11(X4)) = X4
& ilf_type(sK11(X4),set_type)
& ilf_type(sK10(X4),set_type) )
| ~ member(X4,X0)
| ~ ilf_type(X4,set_type) )
| ~ relation_like(X0) ) )
| ~ ilf_type(X0,set_type) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9,sK10,sK11])],[f117,f120,f119,f118]) ).
fof(f126,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ( range(X0,X1,X2) != X1
| ? [X3] :
( ! [X4] :
( ~ member(ordered_pair(X4,X3),X2)
| ~ ilf_type(X4,set_type) )
& member(X3,X1)
& ilf_type(X3,set_type) ) )
& ( range(X0,X1,X2) = X1
| ! [X3] :
( ? [X4] :
( member(ordered_pair(X4,X3),X2)
& ilf_type(X4,set_type) )
| ~ member(X3,X1)
| ~ ilf_type(X3,set_type) ) )
& ilf_type(X2,relation_type(X0,X1)) )
& ilf_type(X1,set_type) )
& ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f79]) ).
fof(f127,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ( range(X0,X1,X2) != X1
| ? [X3] :
( ! [X4] :
( ~ member(ordered_pair(X4,X3),X2)
| ~ ilf_type(X4,set_type) )
& member(X3,X1)
& ilf_type(X3,set_type) ) )
& ( range(X0,X1,X2) = X1
| ! [X3] :
( ? [X4] :
( member(ordered_pair(X4,X3),X2)
& ilf_type(X4,set_type) )
| ~ member(X3,X1)
| ~ ilf_type(X3,set_type) ) )
& ilf_type(X2,relation_type(X0,X1)) )
& ilf_type(X1,set_type) )
& ilf_type(X0,set_type) ),
inference(flattening,[],[f126]) ).
fof(f128,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ( range(X0,X1,X2) != X1
| ? [X3] :
( ! [X4] :
( ~ member(ordered_pair(X4,X3),X2)
| ~ ilf_type(X4,set_type) )
& member(X3,X1)
& ilf_type(X3,set_type) ) )
& ( range(X0,X1,X2) = X1
| ! [X5] :
( ? [X6] :
( member(ordered_pair(X6,X5),X2)
& ilf_type(X6,set_type) )
| ~ member(X5,X1)
| ~ ilf_type(X5,set_type) ) )
& ilf_type(X2,relation_type(X0,X1)) )
& ilf_type(X1,set_type) )
& ilf_type(X0,set_type) ),
inference(rectify,[],[f127]) ).
fof(f129,plain,
( ? [X0] :
( ? [X1] :
( ? [X2] :
( ( range(X0,X1,X2) != X1
| ? [X3] :
( ! [X4] :
( ~ member(ordered_pair(X4,X3),X2)
| ~ ilf_type(X4,set_type) )
& member(X3,X1)
& ilf_type(X3,set_type) ) )
& ( range(X0,X1,X2) = X1
| ! [X5] :
( ? [X6] :
( member(ordered_pair(X6,X5),X2)
& ilf_type(X6,set_type) )
| ~ member(X5,X1)
| ~ ilf_type(X5,set_type) ) )
& ilf_type(X2,relation_type(X0,X1)) )
& ilf_type(X1,set_type) )
& ilf_type(X0,set_type) )
=> ( ? [X1] :
( ? [X2] :
( ( range(sK13,X1,X2) != X1
| ? [X3] :
( ! [X4] :
( ~ member(ordered_pair(X4,X3),X2)
| ~ ilf_type(X4,set_type) )
& member(X3,X1)
& ilf_type(X3,set_type) ) )
& ( range(sK13,X1,X2) = X1
| ! [X5] :
( ? [X6] :
( member(ordered_pair(X6,X5),X2)
& ilf_type(X6,set_type) )
| ~ member(X5,X1)
| ~ ilf_type(X5,set_type) ) )
& ilf_type(X2,relation_type(sK13,X1)) )
& ilf_type(X1,set_type) )
& ilf_type(sK13,set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f130,plain,
( ? [X1] :
( ? [X2] :
( ( range(sK13,X1,X2) != X1
| ? [X3] :
( ! [X4] :
( ~ member(ordered_pair(X4,X3),X2)
| ~ ilf_type(X4,set_type) )
& member(X3,X1)
& ilf_type(X3,set_type) ) )
& ( range(sK13,X1,X2) = X1
| ! [X5] :
( ? [X6] :
( member(ordered_pair(X6,X5),X2)
& ilf_type(X6,set_type) )
| ~ member(X5,X1)
| ~ ilf_type(X5,set_type) ) )
& ilf_type(X2,relation_type(sK13,X1)) )
& ilf_type(X1,set_type) )
=> ( ? [X2] :
( ( sK14 != range(sK13,sK14,X2)
| ? [X3] :
( ! [X4] :
( ~ member(ordered_pair(X4,X3),X2)
| ~ ilf_type(X4,set_type) )
& member(X3,sK14)
& ilf_type(X3,set_type) ) )
& ( sK14 = range(sK13,sK14,X2)
| ! [X5] :
( ? [X6] :
( member(ordered_pair(X6,X5),X2)
& ilf_type(X6,set_type) )
| ~ member(X5,sK14)
| ~ ilf_type(X5,set_type) ) )
& ilf_type(X2,relation_type(sK13,sK14)) )
& ilf_type(sK14,set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f131,plain,
( ? [X2] :
( ( sK14 != range(sK13,sK14,X2)
| ? [X3] :
( ! [X4] :
( ~ member(ordered_pair(X4,X3),X2)
| ~ ilf_type(X4,set_type) )
& member(X3,sK14)
& ilf_type(X3,set_type) ) )
& ( sK14 = range(sK13,sK14,X2)
| ! [X5] :
( ? [X6] :
( member(ordered_pair(X6,X5),X2)
& ilf_type(X6,set_type) )
| ~ member(X5,sK14)
| ~ ilf_type(X5,set_type) ) )
& ilf_type(X2,relation_type(sK13,sK14)) )
=> ( ( sK14 != range(sK13,sK14,sK15)
| ? [X3] :
( ! [X4] :
( ~ member(ordered_pair(X4,X3),sK15)
| ~ ilf_type(X4,set_type) )
& member(X3,sK14)
& ilf_type(X3,set_type) ) )
& ( sK14 = range(sK13,sK14,sK15)
| ! [X5] :
( ? [X6] :
( member(ordered_pair(X6,X5),sK15)
& ilf_type(X6,set_type) )
| ~ member(X5,sK14)
| ~ ilf_type(X5,set_type) ) )
& ilf_type(sK15,relation_type(sK13,sK14)) ) ),
introduced(choice_axiom,[]) ).
fof(f132,plain,
( ? [X3] :
( ! [X4] :
( ~ member(ordered_pair(X4,X3),sK15)
| ~ ilf_type(X4,set_type) )
& member(X3,sK14)
& ilf_type(X3,set_type) )
=> ( ! [X4] :
( ~ member(ordered_pair(X4,sK16),sK15)
| ~ ilf_type(X4,set_type) )
& member(sK16,sK14)
& ilf_type(sK16,set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f133,plain,
! [X5] :
( ? [X6] :
( member(ordered_pair(X6,X5),sK15)
& ilf_type(X6,set_type) )
=> ( member(ordered_pair(sK17(X5),X5),sK15)
& ilf_type(sK17(X5),set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f134,plain,
( ( sK14 != range(sK13,sK14,sK15)
| ( ! [X4] :
( ~ member(ordered_pair(X4,sK16),sK15)
| ~ ilf_type(X4,set_type) )
& member(sK16,sK14)
& ilf_type(sK16,set_type) ) )
& ( sK14 = range(sK13,sK14,sK15)
| ! [X5] :
( ( member(ordered_pair(sK17(X5),X5),sK15)
& ilf_type(sK17(X5),set_type) )
| ~ member(X5,sK14)
| ~ ilf_type(X5,set_type) ) )
& ilf_type(sK15,relation_type(sK13,sK14))
& ilf_type(sK14,set_type)
& ilf_type(sK13,set_type) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK13,sK14,sK15,sK16,sK17])],[f128,f133,f132,f131,f130,f129]) ).
fof(f136,plain,
! [X0,X1] :
( member(ordered_pair(sK0(X0,X1),X1),X0)
| ~ member(X1,range_of(X0))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,binary_relation_type) ),
inference(cnf_transformation,[],[f83]) ).
fof(f137,plain,
! [X2,X0,X1] :
( member(X1,range_of(X0))
| ~ member(ordered_pair(X2,X1),X0)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,binary_relation_type) ),
inference(cnf_transformation,[],[f83]) ).
fof(f140,plain,
! [X2,X0,X1] :
( member(X1,range_of(X2))
| ~ member(ordered_pair(X0,X1),X2)
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f41]) ).
fof(f148,plain,
! [X2,X0,X1] :
( ilf_type(X2,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f46]) ).
fof(f152,plain,
! [X0,X1] :
( X0 = X1
| ~ subset(X1,X0)
| ~ subset(X0,X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f92]) ).
fof(f162,plain,
! [X0,X1] :
( ilf_type(X1,member_type(power_set(X0)))
| ~ ilf_type(X1,subset_type(X0))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f97]) ).
fof(f172,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sK6(X0,X1),X0)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f108]) ).
fof(f173,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ member(sK6(X0,X1),X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f108]) ).
fof(f175,plain,
! [X3,X0,X1] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ ilf_type(X3,set_type)
| ~ member(X0,power_set(X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f112]) ).
fof(f179,plain,
! [X0] :
( ~ empty(power_set(X0))
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f63]) ).
fof(f181,plain,
! [X0,X1] :
( member(X0,X1)
| ~ ilf_type(X0,member_type(X1))
| ~ ilf_type(X1,set_type)
| empty(X1)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f113]) ).
fof(f186,plain,
! [X0,X4] :
( ordered_pair(sK10(X4),sK11(X4)) = X4
| ~ member(X4,X0)
| ~ ilf_type(X4,set_type)
| ~ relation_like(X0)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f121]) ).
fof(f190,plain,
! [X2,X0,X1] :
( relation_like(X2)
| ~ ilf_type(X2,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f70]) ).
fof(f197,plain,
! [X2,X0,X1] :
( range_of(X2) = range(X0,X1,X2)
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f76]) ).
fof(f198,plain,
! [X2,X0,X1] :
( ilf_type(range(X0,X1,X2),subset_type(X1))
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f77]) ).
fof(f199,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[],[f34]) ).
fof(f202,plain,
ilf_type(sK15,relation_type(sK13,sK14)),
inference(cnf_transformation,[],[f134]) ).
fof(f204,plain,
! [X5] :
( sK14 = range(sK13,sK14,sK15)
| member(ordered_pair(sK17(X5),X5),sK15)
| ~ member(X5,sK14)
| ~ ilf_type(X5,set_type) ),
inference(cnf_transformation,[],[f134]) ).
fof(f206,plain,
( sK14 != range(sK13,sK14,sK15)
| member(sK16,sK14) ),
inference(cnf_transformation,[],[f134]) ).
fof(f207,plain,
! [X4] :
( sK14 != range(sK13,sK14,sK15)
| ~ member(ordered_pair(X4,sK16),sK15)
| ~ ilf_type(X4,set_type) ),
inference(cnf_transformation,[],[f134]) ).
cnf(c_49,plain,
( ~ member(ordered_pair(X0,X1),X2)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,binary_relation_type)
| member(X1,range_of(X2)) ),
inference(cnf_transformation,[],[f137]) ).
cnf(c_50,plain,
( ~ member(X0,range_of(X1))
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,binary_relation_type)
| member(ordered_pair(sK0(X1,X0),X0),X1) ),
inference(cnf_transformation,[],[f136]) ).
cnf(c_53,plain,
( ~ member(ordered_pair(X0,X1),X2)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,binary_relation_type)
| member(X1,range_of(X2)) ),
inference(cnf_transformation,[],[f140]) ).
cnf(c_61,plain,
( ~ ilf_type(X0,relation_type(X1,X2))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ilf_type(X0,subset_type(cross_product(X1,X2))) ),
inference(cnf_transformation,[],[f148]) ).
cnf(c_64,plain,
( ~ subset(X0,X1)
| ~ subset(X1,X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| X0 = X1 ),
inference(cnf_transformation,[],[f152]) ).
cnf(c_72,plain,
( ~ ilf_type(X0,set_type)
| ~ relation_like(X0)
| ilf_type(X0,binary_relation_type) ),
inference(cnf_transformation,[],[f216]) ).
cnf(c_76,plain,
( ~ ilf_type(X0,subset_type(X1))
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ilf_type(X0,member_type(power_set(X1))) ),
inference(cnf_transformation,[],[f162]) ).
cnf(c_83,plain,
( ~ member(sK6(X0,X1),X1)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f173]) ).
cnf(c_84,plain,
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| member(sK6(X1,X0),X1)
| subset(X1,X0) ),
inference(cnf_transformation,[],[f172]) ).
cnf(c_91,plain,
( ~ member(X0,power_set(X1))
| ~ member(X2,X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| member(X2,X1) ),
inference(cnf_transformation,[],[f175]) ).
cnf(c_93,plain,
( ~ ilf_type(X0,set_type)
| ~ empty(power_set(X0)) ),
inference(cnf_transformation,[],[f179]) ).
cnf(c_95,plain,
( ~ ilf_type(X0,member_type(X1))
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| member(X0,X1)
| empty(X1) ),
inference(cnf_transformation,[],[f181]) ).
cnf(c_100,plain,
( ~ member(X0,X1)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ relation_like(X1)
| ordered_pair(sK10(X0),sK11(X0)) = X0 ),
inference(cnf_transformation,[],[f186]) ).
cnf(c_103,plain,
( ~ ilf_type(X0,subset_type(cross_product(X1,X2)))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| relation_like(X0) ),
inference(cnf_transformation,[],[f190]) ).
cnf(c_110,plain,
( ~ ilf_type(X0,relation_type(X1,X2))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| range(X1,X2,X0) = range_of(X0) ),
inference(cnf_transformation,[],[f197]) ).
cnf(c_111,plain,
( ~ ilf_type(X0,relation_type(X1,X2))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ilf_type(range(X1,X2,X0),subset_type(X2)) ),
inference(cnf_transformation,[],[f198]) ).
cnf(c_112,plain,
ilf_type(X0,set_type),
inference(cnf_transformation,[],[f199]) ).
cnf(c_113,negated_conjecture,
( range(sK13,sK14,sK15) != sK14
| ~ member(ordered_pair(X0,sK16),sK15)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f207]) ).
cnf(c_114,negated_conjecture,
( range(sK13,sK14,sK15) != sK14
| member(sK16,sK14) ),
inference(cnf_transformation,[],[f206]) ).
cnf(c_116,negated_conjecture,
( ~ member(X0,sK14)
| ~ ilf_type(X0,set_type)
| range(sK13,sK14,sK15) = sK14
| member(ordered_pair(sK17(X0),X0),sK15) ),
inference(cnf_transformation,[],[f204]) ).
cnf(c_118,negated_conjecture,
ilf_type(sK15,relation_type(sK13,sK14)),
inference(cnf_transformation,[],[f202]) ).
cnf(c_184,plain,
~ empty(power_set(X0)),
inference(global_subsumption_just,[status(thm)],[c_93,c_112,c_93]) ).
cnf(c_214,plain,
( ~ relation_like(X0)
| ilf_type(X0,binary_relation_type) ),
inference(global_subsumption_just,[status(thm)],[c_72,c_112,c_72]) ).
cnf(c_246,plain,
( ~ ilf_type(X1,set_type)
| member(sK6(X1,X0),X1)
| subset(X1,X0) ),
inference(global_subsumption_just,[status(thm)],[c_84,c_112,c_84]) ).
cnf(c_247,plain,
( ~ ilf_type(X0,set_type)
| member(sK6(X0,X1),X0)
| subset(X0,X1) ),
inference(renaming,[status(thm)],[c_246]) ).
cnf(c_265,plain,
( ~ member(sK6(X0,X1),X1)
| ~ ilf_type(X1,set_type)
| subset(X0,X1) ),
inference(global_subsumption_just,[status(thm)],[c_83,c_112,c_83]) ).
cnf(c_280,plain,
( ~ ilf_type(X0,member_type(X1))
| ~ ilf_type(X1,set_type)
| member(X0,X1)
| empty(X1) ),
inference(global_subsumption_just,[status(thm)],[c_95,c_112,c_95]) ).
cnf(c_287,plain,
( ~ ilf_type(X0,subset_type(X1))
| ~ ilf_type(X1,set_type)
| ilf_type(X0,member_type(power_set(X1))) ),
inference(global_subsumption_just,[status(thm)],[c_76,c_112,c_76]) ).
cnf(c_301,plain,
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| ~ ilf_type(X1,set_type)
| X0 = X1 ),
inference(global_subsumption_just,[status(thm)],[c_64,c_112,c_64]) ).
cnf(c_302,plain,
( ~ subset(X0,X1)
| ~ subset(X1,X0)
| ~ ilf_type(X1,set_type)
| X0 = X1 ),
inference(renaming,[status(thm)],[c_301]) ).
cnf(c_303,plain,
( ~ member(X0,range_of(X1))
| ~ ilf_type(X1,binary_relation_type)
| member(ordered_pair(sK0(X1,X0),X0),X1) ),
inference(global_subsumption_just,[status(thm)],[c_50,c_112,c_50]) ).
cnf(c_306,negated_conjecture,
( ~ member(X0,sK14)
| range(sK13,sK14,sK15) = sK14
| member(ordered_pair(sK17(X0),X0),sK15) ),
inference(global_subsumption_just,[status(thm)],[c_116,c_112,c_116]) ).
cnf(c_325,plain,
( ~ member(ordered_pair(X0,X1),X2)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,binary_relation_type)
| member(X1,range_of(X2)) ),
inference(global_subsumption_just,[status(thm)],[c_49,c_112,c_53]) ).
cnf(c_327,plain,
( ~ member(X0,X1)
| ~ ilf_type(X1,set_type)
| ~ relation_like(X1)
| ordered_pair(sK10(X0),sK11(X0)) = X0 ),
inference(global_subsumption_just,[status(thm)],[c_100,c_112,c_100]) ).
cnf(c_331,plain,
( ~ member(X2,X0)
| ~ member(X0,power_set(X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| member(X2,X1) ),
inference(global_subsumption_just,[status(thm)],[c_91,c_112,c_91]) ).
cnf(c_332,plain,
( ~ member(X0,power_set(X1))
| ~ member(X2,X0)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| member(X2,X1) ),
inference(renaming,[status(thm)],[c_331]) ).
cnf(c_528,plain,
( ~ ilf_type(X0,relation_type(X1,X2))
| ~ ilf_type(X2,set_type)
| ilf_type(X0,subset_type(cross_product(X1,X2))) ),
inference(backward_subsumption_resolution,[status(thm)],[c_61,c_112]) ).
cnf(c_531,plain,
( ~ ilf_type(X0,member_type(X1))
| member(X0,X1)
| empty(X1) ),
inference(backward_subsumption_resolution,[status(thm)],[c_280,c_112]) ).
cnf(c_533,plain,
( ~ ilf_type(X0,relation_type(X1,X2))
| ~ ilf_type(X2,set_type)
| ilf_type(range(X1,X2,X0),subset_type(X2)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_111,c_112]) ).
cnf(c_534,plain,
( ~ ilf_type(X0,relation_type(X1,X2))
| ~ ilf_type(X2,set_type)
| range(X1,X2,X0) = range_of(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[c_110,c_112]) ).
cnf(c_537,plain,
( ~ member(X0,power_set(X1))
| ~ member(X2,X0)
| ~ ilf_type(X2,set_type)
| member(X2,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[c_332,c_112]) ).
cnf(c_538,plain,
( ~ member(ordered_pair(X0,X1),X2)
| ~ ilf_type(X2,binary_relation_type)
| member(X1,range_of(X2)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_325,c_112]) ).
cnf(c_540,plain,
( ~ member(X0,X1)
| ~ relation_like(X1)
| ordered_pair(sK10(X0),sK11(X0)) = X0 ),
inference(backward_subsumption_resolution,[status(thm)],[c_327,c_112]) ).
cnf(c_543,plain,
( ~ member(sK6(X0,X1),X1)
| subset(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[c_265,c_112]) ).
cnf(c_544,plain,
( ~ ilf_type(X0,subset_type(cross_product(X1,X2)))
| ~ ilf_type(X2,set_type)
| relation_like(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[c_103,c_112]) ).
cnf(c_545,plain,
( ~ subset(X0,X1)
| ~ subset(X1,X0)
| X0 = X1 ),
inference(backward_subsumption_resolution,[status(thm)],[c_302,c_112]) ).
cnf(c_547,plain,
( ~ ilf_type(X0,subset_type(X1))
| ilf_type(X0,member_type(power_set(X1))) ),
inference(backward_subsumption_resolution,[status(thm)],[c_287,c_112]) ).
cnf(c_654,plain,
( ~ ilf_type(X0,subset_type(cross_product(X1,X2)))
| relation_like(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_544,c_112]) ).
cnf(c_723,plain,
( ~ ilf_type(X0,relation_type(X1,X2))
| ilf_type(X0,subset_type(cross_product(X1,X2))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_528,c_112]) ).
cnf(c_752,plain,
( ~ ilf_type(X0,relation_type(X1,X2))
| ilf_type(range(X1,X2,X0),subset_type(X2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_533,c_112]) ).
cnf(c_774,plain,
( ~ ilf_type(X0,relation_type(X1,X2))
| range(X1,X2,X0) = range_of(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_534,c_112]) ).
cnf(c_811,plain,
( ~ member(X0,power_set(X1))
| ~ member(X2,X0)
| member(X2,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_537,c_112]) ).
cnf(c_1215,plain,
( ~ relation_like(X0)
| ilf_type(X0,binary_relation_type) ),
inference(prop_impl_just,[status(thm)],[c_214]) ).
cnf(c_1223,plain,
( ~ ilf_type(X0,subset_type(X1))
| ilf_type(X0,member_type(power_set(X1))) ),
inference(prop_impl_just,[status(thm)],[c_547]) ).
cnf(c_1225,plain,
( ~ ilf_type(X0,relation_type(X1,X2))
| relation_like(X0) ),
inference(prop_impl_just,[status(thm)],[c_654,c_723]) ).
cnf(c_1231,plain,
( ~ ilf_type(X0,relation_type(X1,X2))
| range(X1,X2,X0) = range_of(X0) ),
inference(prop_impl_just,[status(thm)],[c_774]) ).
cnf(c_1233,plain,
( ~ ilf_type(X0,relation_type(X1,X2))
| ilf_type(range(X1,X2,X0),subset_type(X2)) ),
inference(prop_impl_just,[status(thm)],[c_752]) ).
cnf(c_1235,plain,
( subset(X0,X1)
| ~ member(sK6(X0,X1),X1) ),
inference(prop_impl_just,[status(thm)],[c_543]) ).
cnf(c_1236,plain,
( ~ member(sK6(X0,X1),X1)
| subset(X0,X1) ),
inference(renaming,[status(thm)],[c_1235]) ).
cnf(c_1237,plain,
( subset(X0,X1)
| member(sK6(X0,X1),X0) ),
inference(prop_impl_just,[status(thm)],[c_112,c_247]) ).
cnf(c_1238,plain,
( member(sK6(X0,X1),X0)
| subset(X0,X1) ),
inference(renaming,[status(thm)],[c_1237]) ).
cnf(c_1269,plain,
( range(sK13,sK14,sK15) != sK14
| ~ member(ordered_pair(X0,sK16),sK15) ),
inference(prop_impl_just,[status(thm)],[c_112,c_113]) ).
cnf(c_2885,plain,
relation_like(sK15),
inference(superposition,[status(thm)],[c_118,c_1225]) ).
cnf(c_2959,plain,
( ~ ilf_type(X0,subset_type(X1))
| member(X0,power_set(X1))
| empty(power_set(X1)) ),
inference(superposition,[status(thm)],[c_1223,c_531]) ).
cnf(c_2960,plain,
( ~ ilf_type(X0,subset_type(X1))
| member(X0,power_set(X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2959,c_184]) ).
cnf(c_3085,plain,
( ~ member(X0,sK14)
| ~ ilf_type(sK15,binary_relation_type)
| range(sK13,sK14,sK15) = sK14
| member(X0,range_of(sK15)) ),
inference(superposition,[status(thm)],[c_306,c_538]) ).
cnf(c_3156,plain,
( ~ member(sK6(X0,range_of(sK15)),sK14)
| ~ ilf_type(sK15,binary_relation_type)
| range(sK13,sK14,sK15) = sK14
| subset(X0,range_of(sK15)) ),
inference(superposition,[status(thm)],[c_3085,c_1236]) ).
cnf(c_3321,plain,
range(sK13,sK14,sK15) = range_of(sK15),
inference(superposition,[status(thm)],[c_118,c_1231]) ).
cnf(c_3328,plain,
( ~ member(sK6(X0,range_of(sK15)),sK14)
| ~ ilf_type(sK15,binary_relation_type)
| range_of(sK15) = sK14
| subset(X0,range_of(sK15)) ),
inference(demodulation,[status(thm)],[c_3156,c_3321]) ).
cnf(c_3336,plain,
( ~ member(X0,sK14)
| range_of(sK15) = sK14
| member(ordered_pair(sK17(X0),X0),sK15) ),
inference(demodulation,[status(thm)],[c_306,c_3321]) ).
cnf(c_3337,plain,
( range_of(sK15) != sK14
| member(sK16,sK14) ),
inference(demodulation,[status(thm)],[c_114,c_3321]) ).
cnf(c_3402,plain,
( range_of(sK15) != sK14
| ~ member(ordered_pair(X0,sK16),sK15) ),
inference(light_normalisation,[status(thm)],[c_1269,c_3321]) ).
cnf(c_3427,plain,
( ~ ilf_type(sK15,relation_type(sK13,sK14))
| ilf_type(range_of(sK15),subset_type(sK14)) ),
inference(superposition,[status(thm)],[c_3321,c_1233]) ).
cnf(c_3428,plain,
ilf_type(range_of(sK15),subset_type(sK14)),
inference(forward_subsumption_resolution,[status(thm)],[c_3427,c_118]) ).
cnf(c_3429,plain,
member(range_of(sK15),power_set(sK14)),
inference(superposition,[status(thm)],[c_3428,c_2960]) ).
cnf(c_3475,plain,
( ~ member(X0,sK14)
| ~ relation_like(sK15)
| ordered_pair(sK10(ordered_pair(sK17(X0),X0)),sK11(ordered_pair(sK17(X0),X0))) = ordered_pair(sK17(X0),X0)
| range_of(sK15) = sK14 ),
inference(superposition,[status(thm)],[c_3336,c_540]) ).
cnf(c_3509,plain,
( ~ member(X0,sK14)
| ordered_pair(sK10(ordered_pair(sK17(X0),X0)),sK11(ordered_pair(sK17(X0),X0))) = ordered_pair(sK17(X0),X0)
| range_of(sK15) = sK14 ),
inference(forward_subsumption_resolution,[status(thm)],[c_3475,c_2885]) ).
cnf(c_3860,plain,
( ~ member(X0,range_of(sK15))
| member(X0,sK14) ),
inference(superposition,[status(thm)],[c_3429,c_811]) ).
cnf(c_4678,plain,
( member(sK6(range_of(sK15),X0),sK14)
| subset(range_of(sK15),X0) ),
inference(superposition,[status(thm)],[c_1238,c_3860]) ).
cnf(c_4879,plain,
( ~ member(X0,sK14)
| ~ ilf_type(sK15,binary_relation_type)
| range(sK13,sK14,sK15) = sK14
| member(X0,range_of(sK15)) ),
inference(superposition,[status(thm)],[c_306,c_538]) ).
cnf(c_5404,plain,
( ~ member(sK6(X0,range_of(sK15)),sK14)
| ~ ilf_type(sK15,binary_relation_type)
| range(sK13,sK14,sK15) = sK14
| subset(X0,range_of(sK15)) ),
inference(superposition,[status(thm)],[c_4879,c_1236]) ).
cnf(c_6069,plain,
range(sK13,sK14,sK15) = range_of(sK15),
inference(superposition,[status(thm)],[c_118,c_1231]) ).
cnf(c_6076,plain,
( ~ member(sK6(X0,range_of(sK15)),sK14)
| ~ ilf_type(sK15,binary_relation_type)
| range_of(sK15) = sK14
| subset(X0,range_of(sK15)) ),
inference(demodulation,[status(thm)],[c_5404,c_6069]) ).
cnf(c_9020,plain,
( ~ relation_like(sK15)
| ilf_type(sK15,binary_relation_type) ),
inference(instantiation,[status(thm)],[c_1215]) ).
cnf(c_10585,plain,
( ~ member(sK6(X0,range_of(sK15)),sK14)
| range_of(sK15) = sK14
| subset(X0,range_of(sK15)) ),
inference(global_subsumption_just,[status(thm)],[c_6076,c_2885,c_3328,c_9020]) ).
cnf(c_10594,plain,
( range_of(sK15) = sK14
| subset(sK14,range_of(sK15)) ),
inference(superposition,[status(thm)],[c_1238,c_10585]) ).
cnf(c_12292,plain,
( ~ subset(range_of(sK15),sK14)
| range_of(sK15) = sK14 ),
inference(superposition,[status(thm)],[c_10594,c_545]) ).
cnf(c_15104,plain,
subset(range_of(sK15),sK14),
inference(superposition,[status(thm)],[c_4678,c_1236]) ).
cnf(c_15110,plain,
( ordered_pair(sK10(ordered_pair(sK17(sK6(range_of(sK15),X0)),sK6(range_of(sK15),X0))),sK11(ordered_pair(sK17(sK6(range_of(sK15),X0)),sK6(range_of(sK15),X0)))) = ordered_pair(sK17(sK6(range_of(sK15),X0)),sK6(range_of(sK15),X0))
| range_of(sK15) = sK14
| subset(range_of(sK15),X0) ),
inference(superposition,[status(thm)],[c_4678,c_3509]) ).
cnf(c_15154,plain,
range_of(sK15) = sK14,
inference(global_subsumption_just,[status(thm)],[c_15110,c_12292,c_15104]) ).
cnf(c_15242,plain,
( sK14 != sK14
| member(sK16,sK14) ),
inference(demodulation,[status(thm)],[c_3337,c_15154]) ).
cnf(c_15245,plain,
( sK14 != sK14
| ~ member(ordered_pair(X0,sK16),sK15) ),
inference(demodulation,[status(thm)],[c_3402,c_15154]) ).
cnf(c_15250,plain,
member(sK16,sK14),
inference(equality_resolution_simp,[status(thm)],[c_15242]) ).
cnf(c_15255,plain,
~ member(ordered_pair(X0,sK16),sK15),
inference(equality_resolution_simp,[status(thm)],[c_15245]) ).
cnf(c_15485,plain,
( ~ member(sK16,range_of(sK15))
| ~ ilf_type(sK15,binary_relation_type) ),
inference(superposition,[status(thm)],[c_303,c_15255]) ).
cnf(c_15486,plain,
( ~ member(sK16,sK14)
| ~ ilf_type(sK15,binary_relation_type) ),
inference(light_normalisation,[status(thm)],[c_15485,c_15154]) ).
cnf(c_15487,plain,
~ ilf_type(sK15,binary_relation_type),
inference(forward_subsumption_resolution,[status(thm)],[c_15486,c_15250]) ).
cnf(c_15488,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_15487,c_9020,c_2885]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET660+3 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.13 % Command : run_iprover %s %d THM
% 0.13/0.34 % Computer : n028.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Aug 26 11:11:22 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.47 Running first-order theorem proving
% 0.19/0.47 Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 7.69/1.66 % SZS status Started for theBenchmark.p
% 7.69/1.66 % SZS status Theorem for theBenchmark.p
% 7.69/1.66
% 7.69/1.66 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 7.69/1.66
% 7.69/1.66 ------ iProver source info
% 7.69/1.66
% 7.69/1.66 git: date: 2023-05-31 18:12:56 +0000
% 7.69/1.66 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 7.69/1.66 git: non_committed_changes: false
% 7.69/1.66 git: last_make_outside_of_git: false
% 7.69/1.66
% 7.69/1.66 ------ Parsing...
% 7.69/1.66 ------ Clausification by vclausify_rel & Parsing by iProver...
% 7.69/1.66
% 7.69/1.66 ------ 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
% 7.69/1.66
% 7.69/1.66 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 7.69/1.66
% 7.69/1.66 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 7.69/1.66 ------ Proving...
% 7.69/1.66 ------ Problem Properties
% 7.69/1.66
% 7.69/1.66
% 7.69/1.66 clauses 46
% 7.69/1.66 conjectures 3
% 7.69/1.66 EPR 9
% 7.69/1.66 Horn 37
% 7.69/1.66 unary 9
% 7.69/1.66 binary 24
% 7.69/1.66 lits 96
% 7.69/1.66 lits eq 14
% 7.69/1.66 fd_pure 0
% 7.69/1.66 fd_pseudo 0
% 7.69/1.66 fd_cond 0
% 7.69/1.66 fd_pseudo_cond 5
% 7.69/1.66 AC symbols 0
% 7.69/1.66
% 7.69/1.66 ------ Schedule dynamic 5 is on
% 7.69/1.66
% 7.69/1.66 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 7.69/1.66
% 7.69/1.66
% 7.69/1.66 ------
% 7.69/1.66 Current options:
% 7.69/1.66 ------
% 7.69/1.66
% 7.69/1.66
% 7.69/1.66
% 7.69/1.66
% 7.69/1.66 ------ Proving...
% 7.69/1.66
% 7.69/1.66
% 7.69/1.66 % SZS status Theorem for theBenchmark.p
% 7.69/1.66
% 7.69/1.66 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 7.69/1.66
% 7.69/1.66
%------------------------------------------------------------------------------