TSTP Solution File: SET674+3 by iProver---3.8
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SET674+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n021.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 15:09:03 EDT 2023
% Result : Theorem 207.09s 27.94s
% Output : CNFRefutation 207.09s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f242)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,binary_relation_type)
=> ( member(X0,domain_of(X1))
<=> ? [X2] :
( member(ordered_pair(X0,X2),X1)
& ilf_type(X2,set_type) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p1) ).
fof(f2,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,binary_relation_type)
=> ( member(X0,range_of(X1))
<=> ? [X2] :
( member(ordered_pair(X2,X0),X1)
& ilf_type(X2,set_type) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2) ).
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(f4,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,binary_relation_type)
=> ( member(X1,image(X2,X0))
<=> ? [X3] :
( member(X3,X0)
& member(ordered_pair(X3,X1),X2)
& ilf_type(X3,set_type) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p4) ).
fof(f5,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,binary_relation_type)
=> ( member(X1,inverse2(X2,X0))
<=> ? [X3] :
( member(X3,X0)
& member(ordered_pair(X1,X3),X2)
& ilf_type(X3,set_type) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p5) ).
fof(f6,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( ! [X2] :
( ilf_type(X2,set_type)
=> ( member(X2,X0)
<=> member(X2,X1) ) )
=> X0 = X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p6) ).
fof(f7,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,set_type)
=> ! [X4] :
( ilf_type(X4,relation_type(X0,X1))
=> ( member(ordered_pair(X2,X3),X4)
=> ( member(X3,X1)
& member(X2,X0) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p7) ).
fof(f8,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',p8) ).
fof(f12,axiom,
! [X0] :
( ilf_type(X0,binary_relation_type)
=> ilf_type(domain_of(X0),set_type) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p12) ).
fof(f19,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',p19) ).
fof(f21,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( X0 = X1
<=> ! [X2] :
( ilf_type(X2,set_type)
=> ( member(X2,X0)
<=> member(X2,X1) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p21) ).
fof(f22,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',p22) ).
fof(f24,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',p24) ).
fof(f25,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',p25) ).
fof(f26,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',p26) ).
fof(f29,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',p29) ).
fof(f32,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,relation_type(X0,X1))
=> domain_of(X2) = domain(X0,X1,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(domain(X0,X1,X2),subset_type(X0)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p33) ).
fof(f34,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/sandbox/benchmark/theBenchmark.p',p34) ).
fof(f36,axiom,
! [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)
=> image4(X0,X1,X2,X3) = image(X2,X3) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p36) ).
fof(f38,axiom,
! [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)
=> inverse4(X0,X1,X2,X3) = inverse2(X2,X3) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p38) ).
fof(f40,axiom,
! [X0] : ilf_type(X0,set_type),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p40) ).
fof(f41,conjecture,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,relation_type(X0,X1))
=> ( domain(X0,X1,X2) = inverse4(X0,X1,X2,X1)
& range(X0,X1,X2) = image4(X0,X1,X2,X0) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_relset_1_38) ).
fof(f42,negated_conjecture,
~ ! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,relation_type(X0,X1))
=> ( domain(X0,X1,X2) = inverse4(X0,X1,X2,X1)
& range(X0,X1,X2) = image4(X0,X1,X2,X0) ) ) ) ),
inference(negated_conjecture,[],[f41]) ).
fof(f43,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,[],[f8]) ).
fof(f44,plain,
! [X0] :
( ! [X1] :
( ( member(X0,domain_of(X1))
<=> ? [X2] :
( member(ordered_pair(X0,X2),X1)
& ilf_type(X2,set_type) ) )
| ~ ilf_type(X1,binary_relation_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f1]) ).
fof(f45,plain,
! [X0] :
( ! [X1] :
( ( member(X0,range_of(X1))
<=> ? [X2] :
( member(ordered_pair(X2,X0),X1)
& ilf_type(X2,set_type) ) )
| ~ ilf_type(X1,binary_relation_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f2]) ).
fof(f46,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(f47,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,[],[f46]) ).
fof(f48,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( member(X1,image(X2,X0))
<=> ? [X3] :
( member(X3,X0)
& member(ordered_pair(X3,X1),X2)
& ilf_type(X3,set_type) ) )
| ~ ilf_type(X2,binary_relation_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f4]) ).
fof(f49,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( member(X1,inverse2(X2,X0))
<=> ? [X3] :
( member(X3,X0)
& member(ordered_pair(X1,X3),X2)
& ilf_type(X3,set_type) ) )
| ~ ilf_type(X2,binary_relation_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f5]) ).
fof(f50,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| ? [X2] :
( ( member(X2,X0)
<~> member(X2,X1) )
& ilf_type(X2,set_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f6]) ).
fof(f51,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| ? [X2] :
( ( member(X2,X0)
<~> member(X2,X1) )
& ilf_type(X2,set_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(flattening,[],[f50]) ).
fof(f52,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ( member(X3,X1)
& member(X2,X0) )
| ~ member(ordered_pair(X2,X3),X4)
| ~ ilf_type(X4,relation_type(X0,X1)) )
| ~ ilf_type(X3,set_type) )
| ~ ilf_type(X2,set_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f7]) ).
fof(f53,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ( member(X3,X1)
& member(X2,X0) )
| ~ member(ordered_pair(X2,X3),X4)
| ~ ilf_type(X4,relation_type(X0,X1)) )
| ~ ilf_type(X3,set_type) )
| ~ ilf_type(X2,set_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(flattening,[],[f52]) ).
fof(f54,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,[],[f43]) ).
fof(f58,plain,
! [X0] :
( ilf_type(domain_of(X0),set_type)
| ~ ilf_type(X0,binary_relation_type) ),
inference(ennf_transformation,[],[f12]) ).
fof(f64,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,[],[f19]) ).
fof(f66,plain,
! [X0] :
( ! [X1] :
( ( X0 = X1
<=> ! [X2] :
( ( member(X2,X0)
<=> member(X2,X1) )
| ~ ilf_type(X2,set_type) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f21]) ).
fof(f67,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,[],[f22]) ).
fof(f68,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,[],[f67]) ).
fof(f70,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,[],[f24]) ).
fof(f71,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,[],[f70]) ).
fof(f72,plain,
! [X0] :
( ( ilf_type(power_set(X0),set_type)
& ~ empty(power_set(X0)) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f25]) ).
fof(f73,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,[],[f26]) ).
fof(f74,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,[],[f73]) ).
fof(f79,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,[],[f29]) ).
fof(f83,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( domain_of(X2) = domain(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(f84,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ilf_type(domain(X0,X1,X2),subset_type(X0))
| ~ ilf_type(X2,relation_type(X0,X1)) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f33]) ).
fof(f85,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,[],[f34]) ).
fof(f87,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( image4(X0,X1,X2,X3) = image(X2,X3)
| ~ ilf_type(X3,set_type) )
| ~ ilf_type(X2,relation_type(X0,X1)) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f36]) ).
fof(f89,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( inverse4(X0,X1,X2,X3) = inverse2(X2,X3)
| ~ ilf_type(X3,set_type) )
| ~ ilf_type(X2,relation_type(X0,X1)) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f38]) ).
fof(f91,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ( domain(X0,X1,X2) != inverse4(X0,X1,X2,X1)
| range(X0,X1,X2) != image4(X0,X1,X2,X0) )
& ilf_type(X2,relation_type(X0,X1)) )
& ilf_type(X1,set_type) )
& ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f42]) ).
fof(f92,plain,
! [X0] :
( ! [X1] :
( ( ( member(X0,domain_of(X1))
| ! [X2] :
( ~ member(ordered_pair(X0,X2),X1)
| ~ ilf_type(X2,set_type) ) )
& ( ? [X2] :
( member(ordered_pair(X0,X2),X1)
& ilf_type(X2,set_type) )
| ~ member(X0,domain_of(X1)) ) )
| ~ ilf_type(X1,binary_relation_type) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f44]) ).
fof(f93,plain,
! [X0] :
( ! [X1] :
( ( ( member(X0,domain_of(X1))
| ! [X2] :
( ~ member(ordered_pair(X0,X2),X1)
| ~ ilf_type(X2,set_type) ) )
& ( ? [X3] :
( member(ordered_pair(X0,X3),X1)
& ilf_type(X3,set_type) )
| ~ member(X0,domain_of(X1)) ) )
| ~ ilf_type(X1,binary_relation_type) )
| ~ ilf_type(X0,set_type) ),
inference(rectify,[],[f92]) ).
fof(f94,plain,
! [X0,X1] :
( ? [X3] :
( member(ordered_pair(X0,X3),X1)
& ilf_type(X3,set_type) )
=> ( member(ordered_pair(X0,sK0(X0,X1)),X1)
& ilf_type(sK0(X0,X1),set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f95,plain,
! [X0] :
( ! [X1] :
( ( ( member(X0,domain_of(X1))
| ! [X2] :
( ~ member(ordered_pair(X0,X2),X1)
| ~ ilf_type(X2,set_type) ) )
& ( ( member(ordered_pair(X0,sK0(X0,X1)),X1)
& ilf_type(sK0(X0,X1),set_type) )
| ~ member(X0,domain_of(X1)) ) )
| ~ ilf_type(X1,binary_relation_type) )
| ~ ilf_type(X0,set_type) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f93,f94]) ).
fof(f96,plain,
! [X0] :
( ! [X1] :
( ( ( member(X0,range_of(X1))
| ! [X2] :
( ~ member(ordered_pair(X2,X0),X1)
| ~ ilf_type(X2,set_type) ) )
& ( ? [X2] :
( member(ordered_pair(X2,X0),X1)
& ilf_type(X2,set_type) )
| ~ member(X0,range_of(X1)) ) )
| ~ ilf_type(X1,binary_relation_type) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f45]) ).
fof(f97,plain,
! [X0] :
( ! [X1] :
( ( ( member(X0,range_of(X1))
| ! [X2] :
( ~ member(ordered_pair(X2,X0),X1)
| ~ ilf_type(X2,set_type) ) )
& ( ? [X3] :
( member(ordered_pair(X3,X0),X1)
& ilf_type(X3,set_type) )
| ~ member(X0,range_of(X1)) ) )
| ~ ilf_type(X1,binary_relation_type) )
| ~ ilf_type(X0,set_type) ),
inference(rectify,[],[f96]) ).
fof(f98,plain,
! [X0,X1] :
( ? [X3] :
( member(ordered_pair(X3,X0),X1)
& ilf_type(X3,set_type) )
=> ( member(ordered_pair(sK1(X0,X1),X0),X1)
& ilf_type(sK1(X0,X1),set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f99,plain,
! [X0] :
( ! [X1] :
( ( ( member(X0,range_of(X1))
| ! [X2] :
( ~ member(ordered_pair(X2,X0),X1)
| ~ ilf_type(X2,set_type) ) )
& ( ( member(ordered_pair(sK1(X0,X1),X0),X1)
& ilf_type(sK1(X0,X1),set_type) )
| ~ member(X0,range_of(X1)) ) )
| ~ ilf_type(X1,binary_relation_type) )
| ~ ilf_type(X0,set_type) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f97,f98]) ).
fof(f100,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( member(X1,image(X2,X0))
| ! [X3] :
( ~ member(X3,X0)
| ~ member(ordered_pair(X3,X1),X2)
| ~ ilf_type(X3,set_type) ) )
& ( ? [X3] :
( member(X3,X0)
& member(ordered_pair(X3,X1),X2)
& ilf_type(X3,set_type) )
| ~ member(X1,image(X2,X0)) ) )
| ~ ilf_type(X2,binary_relation_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f48]) ).
fof(f101,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( member(X1,image(X2,X0))
| ! [X3] :
( ~ member(X3,X0)
| ~ member(ordered_pair(X3,X1),X2)
| ~ ilf_type(X3,set_type) ) )
& ( ? [X4] :
( member(X4,X0)
& member(ordered_pair(X4,X1),X2)
& ilf_type(X4,set_type) )
| ~ member(X1,image(X2,X0)) ) )
| ~ ilf_type(X2,binary_relation_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(rectify,[],[f100]) ).
fof(f102,plain,
! [X0,X1,X2] :
( ? [X4] :
( member(X4,X0)
& member(ordered_pair(X4,X1),X2)
& ilf_type(X4,set_type) )
=> ( member(sK2(X0,X1,X2),X0)
& member(ordered_pair(sK2(X0,X1,X2),X1),X2)
& ilf_type(sK2(X0,X1,X2),set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f103,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( member(X1,image(X2,X0))
| ! [X3] :
( ~ member(X3,X0)
| ~ member(ordered_pair(X3,X1),X2)
| ~ ilf_type(X3,set_type) ) )
& ( ( member(sK2(X0,X1,X2),X0)
& member(ordered_pair(sK2(X0,X1,X2),X1),X2)
& ilf_type(sK2(X0,X1,X2),set_type) )
| ~ member(X1,image(X2,X0)) ) )
| ~ ilf_type(X2,binary_relation_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f101,f102]) ).
fof(f104,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( member(X1,inverse2(X2,X0))
| ! [X3] :
( ~ member(X3,X0)
| ~ member(ordered_pair(X1,X3),X2)
| ~ ilf_type(X3,set_type) ) )
& ( ? [X3] :
( member(X3,X0)
& member(ordered_pair(X1,X3),X2)
& ilf_type(X3,set_type) )
| ~ member(X1,inverse2(X2,X0)) ) )
| ~ ilf_type(X2,binary_relation_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f49]) ).
fof(f105,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( member(X1,inverse2(X2,X0))
| ! [X3] :
( ~ member(X3,X0)
| ~ member(ordered_pair(X1,X3),X2)
| ~ ilf_type(X3,set_type) ) )
& ( ? [X4] :
( member(X4,X0)
& member(ordered_pair(X1,X4),X2)
& ilf_type(X4,set_type) )
| ~ member(X1,inverse2(X2,X0)) ) )
| ~ ilf_type(X2,binary_relation_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(rectify,[],[f104]) ).
fof(f106,plain,
! [X0,X1,X2] :
( ? [X4] :
( member(X4,X0)
& member(ordered_pair(X1,X4),X2)
& ilf_type(X4,set_type) )
=> ( member(sK3(X0,X1,X2),X0)
& member(ordered_pair(X1,sK3(X0,X1,X2)),X2)
& ilf_type(sK3(X0,X1,X2),set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f107,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( member(X1,inverse2(X2,X0))
| ! [X3] :
( ~ member(X3,X0)
| ~ member(ordered_pair(X1,X3),X2)
| ~ ilf_type(X3,set_type) ) )
& ( ( member(sK3(X0,X1,X2),X0)
& member(ordered_pair(X1,sK3(X0,X1,X2)),X2)
& ilf_type(sK3(X0,X1,X2),set_type) )
| ~ member(X1,inverse2(X2,X0)) ) )
| ~ ilf_type(X2,binary_relation_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f105,f106]) ).
fof(f108,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| ? [X2] :
( ( ~ member(X2,X1)
| ~ member(X2,X0) )
& ( member(X2,X1)
| member(X2,X0) )
& ilf_type(X2,set_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f51]) ).
fof(f109,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| ? [X2] :
( ( ~ member(X2,X1)
| ~ member(X2,X0) )
& ( member(X2,X1)
| member(X2,X0) )
& ilf_type(X2,set_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(flattening,[],[f108]) ).
fof(f110,plain,
! [X0,X1] :
( ? [X2] :
( ( ~ member(X2,X1)
| ~ member(X2,X0) )
& ( member(X2,X1)
| member(X2,X0) )
& ilf_type(X2,set_type) )
=> ( ( ~ member(sK4(X0,X1),X1)
| ~ member(sK4(X0,X1),X0) )
& ( member(sK4(X0,X1),X1)
| member(sK4(X0,X1),X0) )
& ilf_type(sK4(X0,X1),set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f111,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| ( ( ~ member(sK4(X0,X1),X1)
| ~ member(sK4(X0,X1),X0) )
& ( member(sK4(X0,X1),X1)
| member(sK4(X0,X1),X0) )
& ilf_type(sK4(X0,X1),set_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f109,f110]) ).
fof(f120,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,[],[f64]) ).
fof(f123,plain,
! [X0] :
( ! [X1] :
( ( ( X0 = X1
| ? [X2] :
( ( ~ member(X2,X1)
| ~ member(X2,X0) )
& ( member(X2,X1)
| member(X2,X0) )
& ilf_type(X2,set_type) ) )
& ( ! [X2] :
( ( ( member(X2,X0)
| ~ member(X2,X1) )
& ( member(X2,X1)
| ~ member(X2,X0) ) )
| ~ ilf_type(X2,set_type) )
| X0 != X1 ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f66]) ).
fof(f124,plain,
! [X0] :
( ! [X1] :
( ( ( X0 = X1
| ? [X2] :
( ( ~ member(X2,X1)
| ~ member(X2,X0) )
& ( member(X2,X1)
| member(X2,X0) )
& ilf_type(X2,set_type) ) )
& ( ! [X2] :
( ( ( member(X2,X0)
| ~ member(X2,X1) )
& ( member(X2,X1)
| ~ member(X2,X0) ) )
| ~ ilf_type(X2,set_type) )
| X0 != X1 ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(flattening,[],[f123]) ).
fof(f125,plain,
! [X0] :
( ! [X1] :
( ( ( X0 = X1
| ? [X2] :
( ( ~ member(X2,X1)
| ~ member(X2,X0) )
& ( member(X2,X1)
| member(X2,X0) )
& ilf_type(X2,set_type) ) )
& ( ! [X3] :
( ( ( member(X3,X0)
| ~ member(X3,X1) )
& ( member(X3,X1)
| ~ member(X3,X0) ) )
| ~ ilf_type(X3,set_type) )
| X0 != X1 ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(rectify,[],[f124]) ).
fof(f126,plain,
! [X0,X1] :
( ? [X2] :
( ( ~ member(X2,X1)
| ~ member(X2,X0) )
& ( member(X2,X1)
| member(X2,X0) )
& ilf_type(X2,set_type) )
=> ( ( ~ member(sK8(X0,X1),X1)
| ~ member(sK8(X0,X1),X0) )
& ( member(sK8(X0,X1),X1)
| member(sK8(X0,X1),X0) )
& ilf_type(sK8(X0,X1),set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f127,plain,
! [X0] :
( ! [X1] :
( ( ( X0 = X1
| ( ( ~ member(sK8(X0,X1),X1)
| ~ member(sK8(X0,X1),X0) )
& ( member(sK8(X0,X1),X1)
| member(sK8(X0,X1),X0) )
& ilf_type(sK8(X0,X1),set_type) ) )
& ( ! [X3] :
( ( ( member(X3,X0)
| ~ member(X3,X1) )
& ( member(X3,X1)
| ~ member(X3,X0) ) )
| ~ ilf_type(X3,set_type) )
| X0 != X1 ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f125,f126]) ).
fof(f128,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,[],[f68]) ).
fof(f129,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,[],[f128]) ).
fof(f130,plain,
! [X0,X1] :
( ? [X2] :
( ~ member(X2,X1)
& member(X2,X0)
& ilf_type(X2,set_type) )
=> ( ~ member(sK9(X0,X1),X1)
& member(sK9(X0,X1),X0)
& ilf_type(sK9(X0,X1),set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f131,plain,
! [X0] :
( ! [X1] :
( ( ( subset(X0,X1)
| ( ~ member(sK9(X0,X1),X1)
& member(sK9(X0,X1),X0)
& ilf_type(sK9(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,[sK9])],[f129,f130]) ).
fof(f132,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,[],[f71]) ).
fof(f133,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,[],[f132]) ).
fof(f134,plain,
! [X0,X1] :
( ? [X2] :
( ~ member(X2,X1)
& member(X2,X0)
& ilf_type(X2,set_type) )
=> ( ~ member(sK10(X0,X1),X1)
& member(sK10(X0,X1),X0)
& ilf_type(sK10(X0,X1),set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f135,plain,
! [X0] :
( ! [X1] :
( ( ( member(X0,power_set(X1))
| ( ~ member(sK10(X0,X1),X1)
& member(sK10(X0,X1),X0)
& ilf_type(sK10(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,[sK10])],[f133,f134]) ).
fof(f136,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,[],[f74]) ).
fof(f149,plain,
( ? [X0] :
( ? [X1] :
( ? [X2] :
( ( domain(X0,X1,X2) != inverse4(X0,X1,X2,X1)
| range(X0,X1,X2) != image4(X0,X1,X2,X0) )
& ilf_type(X2,relation_type(X0,X1)) )
& ilf_type(X1,set_type) )
& ilf_type(X0,set_type) )
=> ( ? [X1] :
( ? [X2] :
( ( domain(sK16,X1,X2) != inverse4(sK16,X1,X2,X1)
| range(sK16,X1,X2) != image4(sK16,X1,X2,sK16) )
& ilf_type(X2,relation_type(sK16,X1)) )
& ilf_type(X1,set_type) )
& ilf_type(sK16,set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f150,plain,
( ? [X1] :
( ? [X2] :
( ( domain(sK16,X1,X2) != inverse4(sK16,X1,X2,X1)
| range(sK16,X1,X2) != image4(sK16,X1,X2,sK16) )
& ilf_type(X2,relation_type(sK16,X1)) )
& ilf_type(X1,set_type) )
=> ( ? [X2] :
( ( domain(sK16,sK17,X2) != inverse4(sK16,sK17,X2,sK17)
| range(sK16,sK17,X2) != image4(sK16,sK17,X2,sK16) )
& ilf_type(X2,relation_type(sK16,sK17)) )
& ilf_type(sK17,set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f151,plain,
( ? [X2] :
( ( domain(sK16,sK17,X2) != inverse4(sK16,sK17,X2,sK17)
| range(sK16,sK17,X2) != image4(sK16,sK17,X2,sK16) )
& ilf_type(X2,relation_type(sK16,sK17)) )
=> ( ( domain(sK16,sK17,sK18) != inverse4(sK16,sK17,sK18,sK17)
| range(sK16,sK17,sK18) != image4(sK16,sK17,sK18,sK16) )
& ilf_type(sK18,relation_type(sK16,sK17)) ) ),
introduced(choice_axiom,[]) ).
fof(f152,plain,
( ( domain(sK16,sK17,sK18) != inverse4(sK16,sK17,sK18,sK17)
| range(sK16,sK17,sK18) != image4(sK16,sK17,sK18,sK16) )
& ilf_type(sK18,relation_type(sK16,sK17))
& ilf_type(sK17,set_type)
& ilf_type(sK16,set_type) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK16,sK17,sK18])],[f91,f151,f150,f149]) ).
fof(f154,plain,
! [X0,X1] :
( member(ordered_pair(X0,sK0(X0,X1)),X1)
| ~ member(X0,domain_of(X1))
| ~ ilf_type(X1,binary_relation_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f95]) ).
fof(f155,plain,
! [X2,X0,X1] :
( member(X0,domain_of(X1))
| ~ member(ordered_pair(X0,X2),X1)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,binary_relation_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f95]) ).
fof(f157,plain,
! [X0,X1] :
( member(ordered_pair(sK1(X0,X1),X0),X1)
| ~ member(X0,range_of(X1))
| ~ ilf_type(X1,binary_relation_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f99]) ).
fof(f158,plain,
! [X2,X0,X1] :
( member(X0,range_of(X1))
| ~ member(ordered_pair(X2,X0),X1)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,binary_relation_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f99]) ).
fof(f159,plain,
! [X2,X0,X1] :
( 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(cnf_transformation,[],[f47]) ).
fof(f160,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,[],[f47]) ).
fof(f162,plain,
! [X2,X0,X1] :
( member(ordered_pair(sK2(X0,X1,X2),X1),X2)
| ~ member(X1,image(X2,X0))
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f103]) ).
fof(f164,plain,
! [X2,X3,X0,X1] :
( member(X1,image(X2,X0))
| ~ member(X3,X0)
| ~ member(ordered_pair(X3,X1),X2)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f103]) ).
fof(f166,plain,
! [X2,X0,X1] :
( member(ordered_pair(X1,sK3(X0,X1,X2)),X2)
| ~ member(X1,inverse2(X2,X0))
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f107]) ).
fof(f168,plain,
! [X2,X3,X0,X1] :
( member(X1,inverse2(X2,X0))
| ~ member(X3,X0)
| ~ member(ordered_pair(X1,X3),X2)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f107]) ).
fof(f170,plain,
! [X0,X1] :
( X0 = X1
| member(sK4(X0,X1),X1)
| member(sK4(X0,X1),X0)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f111]) ).
fof(f171,plain,
! [X0,X1] :
( X0 = X1
| ~ member(sK4(X0,X1),X1)
| ~ member(sK4(X0,X1),X0)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f111]) ).
fof(f172,plain,
! [X2,X3,X0,X1,X4] :
( member(X2,X0)
| ~ member(ordered_pair(X2,X3),X4)
| ~ ilf_type(X4,relation_type(X0,X1))
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f53]) ).
fof(f173,plain,
! [X2,X3,X0,X1,X4] :
( member(X3,X1)
| ~ member(ordered_pair(X2,X3),X4)
| ~ ilf_type(X4,relation_type(X0,X1))
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f53]) ).
fof(f175,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,[],[f54]) ).
fof(f181,plain,
! [X0] :
( ilf_type(domain_of(X0),set_type)
| ~ ilf_type(X0,binary_relation_type) ),
inference(cnf_transformation,[],[f58]) ).
fof(f190,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,[],[f120]) ).
fof(f196,plain,
! [X0,X1] :
( X0 = X1
| member(sK8(X0,X1),X1)
| member(sK8(X0,X1),X0)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f127]) ).
fof(f197,plain,
! [X0,X1] :
( X0 = X1
| ~ member(sK8(X0,X1),X1)
| ~ member(sK8(X0,X1),X0)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f127]) ).
fof(f198,plain,
! [X3,X0,X1] :
( 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(cnf_transformation,[],[f131]) ).
fof(f203,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,[],[f135]) ).
fof(f207,plain,
! [X0] :
( ~ empty(power_set(X0))
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f72]) ).
fof(f209,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,[],[f136]) ).
fof(f218,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,[],[f79]) ).
fof(f223,plain,
! [X2,X0,X1] :
( domain_of(X2) = domain(X0,X1,X2)
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f83]) ).
fof(f224,plain,
! [X2,X0,X1] :
( ilf_type(domain(X0,X1,X2),subset_type(X0))
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f84]) ).
fof(f225,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,[],[f85]) ).
fof(f227,plain,
! [X2,X3,X0,X1] :
( image4(X0,X1,X2,X3) = image(X2,X3)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f87]) ).
fof(f229,plain,
! [X2,X3,X0,X1] :
( inverse4(X0,X1,X2,X3) = inverse2(X2,X3)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f89]) ).
fof(f231,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[],[f40]) ).
fof(f232,plain,
ilf_type(sK16,set_type),
inference(cnf_transformation,[],[f152]) ).
fof(f233,plain,
ilf_type(sK17,set_type),
inference(cnf_transformation,[],[f152]) ).
fof(f234,plain,
ilf_type(sK18,relation_type(sK16,sK17)),
inference(cnf_transformation,[],[f152]) ).
fof(f235,plain,
( domain(sK16,sK17,sK18) != inverse4(sK16,sK17,sK18,sK17)
| range(sK16,sK17,sK18) != image4(sK16,sK17,sK18,sK16) ),
inference(cnf_transformation,[],[f152]) ).
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(X0,domain_of(X2)) ),
inference(cnf_transformation,[],[f155]) ).
cnf(c_50,plain,
( ~ member(X0,domain_of(X1))
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,binary_relation_type)
| member(ordered_pair(X0,sK0(X0,X1)),X1) ),
inference(cnf_transformation,[],[f154]) ).
cnf(c_52,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,[],[f158]) ).
cnf(c_53,plain,
( ~ member(X0,range_of(X1))
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,binary_relation_type)
| member(ordered_pair(sK1(X0,X1),X0),X1) ),
inference(cnf_transformation,[],[f157]) ).
cnf(c_55,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,[],[f160]) ).
cnf(c_56,plain,
( ~ member(ordered_pair(X0,X1),X2)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,binary_relation_type)
| member(X0,domain_of(X2)) ),
inference(cnf_transformation,[],[f159]) ).
cnf(c_57,plain,
( ~ member(ordered_pair(X0,X1),X2)
| ~ member(X0,X3)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X3,set_type)
| member(X1,image(X2,X3)) ),
inference(cnf_transformation,[],[f164]) ).
cnf(c_59,plain,
( ~ member(X0,image(X1,X2))
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,binary_relation_type)
| ~ ilf_type(X2,set_type)
| member(ordered_pair(sK2(X2,X0,X1),X0),X1) ),
inference(cnf_transformation,[],[f162]) ).
cnf(c_61,plain,
( ~ member(ordered_pair(X0,X1),X2)
| ~ member(X1,X3)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X3,set_type)
| member(X0,inverse2(X2,X3)) ),
inference(cnf_transformation,[],[f168]) ).
cnf(c_63,plain,
( ~ member(X0,inverse2(X1,X2))
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,binary_relation_type)
| ~ ilf_type(X2,set_type)
| member(ordered_pair(X0,sK3(X2,X0,X1)),X1) ),
inference(cnf_transformation,[],[f166]) ).
cnf(c_65,plain,
( ~ member(sK4(X0,X1),X0)
| ~ member(sK4(X0,X1),X1)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| X0 = X1 ),
inference(cnf_transformation,[],[f171]) ).
cnf(c_66,plain,
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| X0 = X1
| member(sK4(X0,X1),X0)
| member(sK4(X0,X1),X1) ),
inference(cnf_transformation,[],[f170]) ).
cnf(c_68,plain,
( ~ member(ordered_pair(X0,X1),X2)
| ~ ilf_type(X2,relation_type(X3,X4))
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X4,set_type)
| member(X1,X4) ),
inference(cnf_transformation,[],[f173]) ).
cnf(c_69,plain,
( ~ member(ordered_pair(X0,X1),X2)
| ~ ilf_type(X2,relation_type(X3,X4))
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X4,set_type)
| member(X0,X3) ),
inference(cnf_transformation,[],[f172]) ).
cnf(c_70,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,[],[f175]) ).
cnf(c_77,plain,
( ~ ilf_type(X0,binary_relation_type)
| ilf_type(domain_of(X0),set_type) ),
inference(cnf_transformation,[],[f181]) ).
cnf(c_82,plain,
( ~ ilf_type(X0,set_type)
| ~ relation_like(X0)
| ilf_type(X0,binary_relation_type) ),
inference(cnf_transformation,[],[f242]) ).
cnf(c_86,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,[],[f190]) ).
cnf(c_88,plain,
( ~ member(sK8(X0,X1),X0)
| ~ member(sK8(X0,X1),X1)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| X0 = X1 ),
inference(cnf_transformation,[],[f197]) ).
cnf(c_89,plain,
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| X0 = X1
| member(sK8(X0,X1),X0)
| member(sK8(X0,X1),X1) ),
inference(cnf_transformation,[],[f196]) ).
cnf(c_96,plain,
( ~ member(X0,X1)
| ~ subset(X1,X2)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| member(X0,X2) ),
inference(cnf_transformation,[],[f198]) ).
cnf(c_101,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,[],[f203]) ).
cnf(c_103,plain,
( ~ ilf_type(X0,set_type)
| ~ empty(power_set(X0)) ),
inference(cnf_transformation,[],[f207]) ).
cnf(c_105,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,[],[f209]) ).
cnf(c_113,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,[],[f218]) ).
cnf(c_118,plain,
( ~ ilf_type(X0,relation_type(X1,X2))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| domain(X1,X2,X0) = domain_of(X0) ),
inference(cnf_transformation,[],[f223]) ).
cnf(c_119,plain,
( ~ ilf_type(X0,relation_type(X1,X2))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ilf_type(domain(X1,X2,X0),subset_type(X1)) ),
inference(cnf_transformation,[],[f224]) ).
cnf(c_120,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,[],[f225]) ).
cnf(c_122,plain,
( ~ ilf_type(X0,relation_type(X1,X2))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,set_type)
| image4(X1,X2,X0,X3) = image(X0,X3) ),
inference(cnf_transformation,[],[f227]) ).
cnf(c_124,plain,
( ~ ilf_type(X0,relation_type(X1,X2))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,set_type)
| inverse4(X1,X2,X0,X3) = inverse2(X0,X3) ),
inference(cnf_transformation,[],[f229]) ).
cnf(c_126,plain,
ilf_type(X0,set_type),
inference(cnf_transformation,[],[f231]) ).
cnf(c_127,negated_conjecture,
( image4(sK16,sK17,sK18,sK16) != range(sK16,sK17,sK18)
| inverse4(sK16,sK17,sK18,sK17) != domain(sK16,sK17,sK18) ),
inference(cnf_transformation,[],[f235]) ).
cnf(c_128,negated_conjecture,
ilf_type(sK18,relation_type(sK16,sK17)),
inference(cnf_transformation,[],[f234]) ).
cnf(c_129,negated_conjecture,
ilf_type(sK17,set_type),
inference(cnf_transformation,[],[f233]) ).
cnf(c_130,negated_conjecture,
ilf_type(sK16,set_type),
inference(cnf_transformation,[],[f232]) ).
cnf(c_203,plain,
~ empty(power_set(X0)),
inference(global_subsumption_just,[status(thm)],[c_103,c_126,c_103]) ).
cnf(c_230,plain,
( ~ relation_like(X0)
| ilf_type(X0,binary_relation_type) ),
inference(global_subsumption_just,[status(thm)],[c_82,c_126,c_82]) ).
cnf(c_283,plain,
( ~ ilf_type(X0,member_type(X1))
| ~ ilf_type(X1,set_type)
| member(X0,X1)
| empty(X1) ),
inference(global_subsumption_just,[status(thm)],[c_105,c_126,c_105]) ).
cnf(c_290,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_86,c_126,c_86]) ).
cnf(c_306,plain,
( ~ member(X0,range_of(X1))
| ~ ilf_type(X1,binary_relation_type)
| member(ordered_pair(sK1(X0,X1),X0),X1) ),
inference(global_subsumption_just,[status(thm)],[c_53,c_126,c_53]) ).
cnf(c_309,plain,
( ~ member(X0,domain_of(X1))
| ~ ilf_type(X1,binary_relation_type)
| member(ordered_pair(X0,sK0(X0,X1)),X1) ),
inference(global_subsumption_just,[status(thm)],[c_50,c_126,c_50]) ).
cnf(c_314,plain,
( ~ ilf_type(X1,set_type)
| X0 = X1
| member(sK8(X0,X1),X0)
| member(sK8(X0,X1),X1) ),
inference(global_subsumption_just,[status(thm)],[c_89,c_126,c_89]) ).
cnf(c_315,plain,
( ~ ilf_type(X0,set_type)
| X1 = X0
| member(sK8(X1,X0),X0)
| member(sK8(X1,X0),X1) ),
inference(renaming,[status(thm)],[c_314]) ).
cnf(c_316,plain,
( X1 = X0
| member(sK8(X1,X0),X0)
| member(sK8(X1,X0),X1) ),
inference(global_subsumption_just,[status(thm)],[c_315,c_126,c_315]) ).
cnf(c_317,plain,
( X0 = X1
| member(sK8(X0,X1),X0)
| member(sK8(X0,X1),X1) ),
inference(renaming,[status(thm)],[c_316]) ).
cnf(c_319,plain,
( ~ ilf_type(X1,set_type)
| X0 = X1
| member(sK4(X0,X1),X0)
| member(sK4(X0,X1),X1) ),
inference(global_subsumption_just,[status(thm)],[c_66,c_126,c_66]) ).
cnf(c_320,plain,
( ~ ilf_type(X0,set_type)
| X1 = X0
| member(sK4(X1,X0),X0)
| member(sK4(X1,X0),X1) ),
inference(renaming,[status(thm)],[c_319]) ).
cnf(c_321,plain,
( X1 = X0
| member(sK4(X1,X0),X0)
| member(sK4(X1,X0),X1) ),
inference(global_subsumption_just,[status(thm)],[c_320,c_126,c_320]) ).
cnf(c_322,plain,
( X0 = X1
| member(sK4(X0,X1),X0)
| member(sK4(X0,X1),X1) ),
inference(renaming,[status(thm)],[c_321]) ).
cnf(c_328,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_52,c_126,c_55]) ).
cnf(c_330,plain,
( ~ member(ordered_pair(X0,X1),X2)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,binary_relation_type)
| member(X0,domain_of(X2)) ),
inference(global_subsumption_just,[status(thm)],[c_49,c_126,c_56]) ).
cnf(c_334,plain,
( ~ subset(X1,X2)
| ~ member(X0,X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| member(X0,X2) ),
inference(global_subsumption_just,[status(thm)],[c_96,c_126,c_96]) ).
cnf(c_335,plain,
( ~ member(X0,X1)
| ~ subset(X1,X2)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| member(X0,X2) ),
inference(renaming,[status(thm)],[c_334]) ).
cnf(c_336,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_101,c_126,c_101]) ).
cnf(c_337,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_336]) ).
cnf(c_338,plain,
( ~ member(sK8(X0,X1),X1)
| ~ member(sK8(X0,X1),X0)
| ~ ilf_type(X1,set_type)
| X0 = X1 ),
inference(global_subsumption_just,[status(thm)],[c_88,c_126,c_88]) ).
cnf(c_339,plain,
( ~ member(sK8(X0,X1),X0)
| ~ member(sK8(X0,X1),X1)
| ~ ilf_type(X1,set_type)
| X0 = X1 ),
inference(renaming,[status(thm)],[c_338]) ).
cnf(c_340,plain,
( ~ member(sK4(X0,X1),X1)
| ~ member(sK4(X0,X1),X0)
| ~ ilf_type(X1,set_type)
| X0 = X1 ),
inference(global_subsumption_just,[status(thm)],[c_65,c_126,c_65]) ).
cnf(c_341,plain,
( ~ member(sK4(X0,X1),X0)
| ~ member(sK4(X0,X1),X1)
| ~ ilf_type(X1,set_type)
| X0 = X1 ),
inference(renaming,[status(thm)],[c_340]) ).
cnf(c_350,plain,
( ~ member(X0,inverse2(X1,X2))
| ~ ilf_type(X1,binary_relation_type)
| ~ ilf_type(X2,set_type)
| member(ordered_pair(X0,sK3(X2,X0,X1)),X1) ),
inference(global_subsumption_just,[status(thm)],[c_63,c_126,c_63]) ).
cnf(c_352,plain,
( ~ member(X0,image(X1,X2))
| ~ ilf_type(X1,binary_relation_type)
| ~ ilf_type(X2,set_type)
| member(ordered_pair(sK2(X2,X0,X1),X0),X1) ),
inference(global_subsumption_just,[status(thm)],[c_59,c_126,c_59]) ).
cnf(c_354,plain,
( ~ ilf_type(X2,relation_type(X3,X4))
| ~ member(ordered_pair(X0,X1),X2)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X4,set_type)
| member(X0,X3) ),
inference(global_subsumption_just,[status(thm)],[c_69,c_126,c_69]) ).
cnf(c_355,plain,
( ~ member(ordered_pair(X0,X1),X2)
| ~ ilf_type(X2,relation_type(X3,X4))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X4,set_type)
| member(X0,X3) ),
inference(renaming,[status(thm)],[c_354]) ).
cnf(c_356,plain,
( ~ ilf_type(X2,relation_type(X3,X4))
| ~ member(ordered_pair(X0,X1),X2)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X4,set_type)
| member(X1,X4) ),
inference(global_subsumption_just,[status(thm)],[c_68,c_126,c_68]) ).
cnf(c_357,plain,
( ~ member(ordered_pair(X0,X1),X2)
| ~ ilf_type(X2,relation_type(X3,X4))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X4,set_type)
| member(X1,X4) ),
inference(renaming,[status(thm)],[c_356]) ).
cnf(c_358,plain,
( ~ member(X1,X3)
| ~ member(ordered_pair(X0,X1),X2)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X3,set_type)
| member(X0,inverse2(X2,X3)) ),
inference(global_subsumption_just,[status(thm)],[c_61,c_126,c_61]) ).
cnf(c_359,plain,
( ~ member(ordered_pair(X0,X1),X2)
| ~ member(X1,X3)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X3,set_type)
| member(X0,inverse2(X2,X3)) ),
inference(renaming,[status(thm)],[c_358]) ).
cnf(c_360,plain,
( ~ member(X0,X3)
| ~ member(ordered_pair(X0,X1),X2)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X3,set_type)
| member(X1,image(X2,X3)) ),
inference(global_subsumption_just,[status(thm)],[c_57,c_126,c_57]) ).
cnf(c_361,plain,
( ~ member(ordered_pair(X0,X1),X2)
| ~ member(X0,X3)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X3,set_type)
| member(X1,image(X2,X3)) ),
inference(renaming,[status(thm)],[c_360]) ).
cnf(c_390,plain,
X0 = X0,
theory(equality) ).
cnf(c_392,plain,
( X0 != X1
| X2 != X1
| X2 = X0 ),
theory(equality) ).
cnf(c_395,plain,
( X0 != X1
| X2 != X3
| ~ ilf_type(X1,X3)
| ilf_type(X0,X2) ),
theory(equality) ).
cnf(c_458,plain,
( ~ ilf_type(sK18,relation_type(sK16,sK17))
| ~ ilf_type(sK16,set_type)
| ~ ilf_type(sK17,set_type)
| ilf_type(sK18,subset_type(cross_product(sK16,sK17))) ),
inference(instantiation,[status(thm)],[c_70]) ).
cnf(c_511,plain,
( ~ ilf_type(sK18,relation_type(sK16,sK17))
| ~ ilf_type(sK16,set_type)
| ~ ilf_type(sK17,set_type)
| domain(sK16,sK17,sK18) = domain_of(sK18) ),
inference(instantiation,[status(thm)],[c_118]) ).
cnf(c_519,plain,
( ~ ilf_type(sK18,relation_type(sK16,sK17))
| ~ ilf_type(sK16,set_type)
| ~ ilf_type(sK17,set_type)
| range(sK16,sK17,sK18) = range_of(sK18) ),
inference(instantiation,[status(thm)],[c_120]) ).
cnf(c_597,plain,
( ~ ilf_type(sK18,relation_type(sK16,sK17))
| ~ ilf_type(X0,set_type)
| ~ ilf_type(sK16,set_type)
| ~ ilf_type(sK17,set_type)
| image4(sK16,sK17,sK18,X0) = image(sK18,X0) ),
inference(instantiation,[status(thm)],[c_122]) ).
cnf(c_602,plain,
( ~ ilf_type(sK18,relation_type(sK16,sK17))
| ~ ilf_type(X0,set_type)
| ~ ilf_type(sK16,set_type)
| ~ ilf_type(sK17,set_type)
| inverse4(sK16,sK17,sK18,X0) = inverse2(sK18,X0) ),
inference(instantiation,[status(thm)],[c_124]) ).
cnf(c_618,plain,
( ~ member(sK4(X0,X1),X0)
| ~ member(sK4(X0,X1),X1)
| X0 = X1 ),
inference(backward_subsumption_resolution,[status(thm)],[c_341,c_126]) ).
cnf(c_619,plain,
( ~ member(X0,power_set(X1))
| ~ member(X2,X0)
| ~ ilf_type(X2,set_type)
| member(X2,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[c_337,c_126]) ).
cnf(c_620,plain,
( ~ ilf_type(X0,member_type(X1))
| member(X0,X1)
| empty(X1) ),
inference(backward_subsumption_resolution,[status(thm)],[c_283,c_126]) ).
cnf(c_626,plain,
( ~ ilf_type(X0,subset_type(X1))
| ilf_type(X0,member_type(power_set(X1))) ),
inference(backward_subsumption_resolution,[status(thm)],[c_290,c_126]) ).
cnf(c_627,plain,
( ~ member(X0,image(X1,X2))
| ~ ilf_type(X1,binary_relation_type)
| member(ordered_pair(sK2(X2,X0,X1),X0),X1) ),
inference(backward_subsumption_resolution,[status(thm)],[c_352,c_126]) ).
cnf(c_628,plain,
( ~ member(ordered_pair(X0,X1),X2)
| ~ member(X0,X3)
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X3,set_type)
| member(X1,image(X2,X3)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_361,c_126]) ).
cnf(c_630,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_328,c_126]) ).
cnf(c_631,plain,
( ~ member(ordered_pair(X0,X1),X2)
| ~ ilf_type(X2,binary_relation_type)
| member(X0,domain_of(X2)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_330,c_126]) ).
cnf(c_633,plain,
( ~ member(ordered_pair(X0,X1),X2)
| ~ ilf_type(X2,relation_type(X3,X4))
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X4,set_type)
| member(X0,X3) ),
inference(backward_subsumption_resolution,[status(thm)],[c_355,c_126]) ).
cnf(c_635,plain,
( ~ member(X0,X1)
| ~ subset(X1,X2)
| ~ ilf_type(X2,set_type)
| member(X0,X2) ),
inference(backward_subsumption_resolution,[status(thm)],[c_335,c_126]) ).
cnf(c_638,plain,
( ~ ilf_type(X0,relation_type(X1,X2))
| ~ ilf_type(X2,set_type)
| ilf_type(domain(X1,X2,X0),subset_type(X1)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_119,c_126]) ).
cnf(c_639,plain,
( ~ ilf_type(X0,relation_type(X1,X2))
| ~ ilf_type(X2,set_type)
| domain(X1,X2,X0) = domain_of(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[c_118,c_126]) ).
cnf(c_719,plain,
( ~ ilf_type(sK18,subset_type(cross_product(sK16,sK17)))
| ~ ilf_type(sK16,set_type)
| ~ ilf_type(sK17,set_type)
| relation_like(sK18) ),
inference(instantiation,[status(thm)],[c_113]) ).
cnf(c_909,plain,
( ~ ilf_type(X0,subset_type(X1))
| member(X0,power_set(X1))
| empty(power_set(X1)) ),
inference(resolution,[status(thm)],[c_626,c_620]) ).
cnf(c_1022,plain,
( ~ ilf_type(X0,subset_type(X1))
| member(X0,power_set(X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_909,c_203]) ).
cnf(c_1126,plain,
( X0 != X1
| X1 = X0 ),
inference(resolution,[status(thm)],[c_392,c_390]) ).
cnf(c_1298,plain,
( ~ member(X0,X1)
| ~ subset(X1,X2)
| member(X0,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_635,c_126]) ).
cnf(c_1432,plain,
( ~ member(X0,power_set(X1))
| ~ member(X2,X0)
| member(X2,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_619,c_126]) ).
cnf(c_1752,plain,
( X0 != X1
| ~ ilf_type(X1,X2)
| ilf_type(X0,X2) ),
inference(resolution,[status(thm)],[c_395,c_390]) ).
cnf(c_1979,plain,
( ~ ilf_type(sK16,set_type)
| ~ ilf_type(sK17,set_type)
| domain(sK16,sK17,sK18) = domain_of(sK18) ),
inference(superposition,[status(thm)],[c_128,c_118]) ).
cnf(c_1980,plain,
domain(sK16,sK17,sK18) = domain_of(sK18),
inference(global_subsumption_just,[status(thm)],[c_1979,c_130,c_129,c_128,c_511]) ).
cnf(c_2040,plain,
( ~ ilf_type(sK16,set_type)
| ~ ilf_type(sK17,set_type)
| range(sK16,sK17,sK18) = range_of(sK18) ),
inference(superposition,[status(thm)],[c_128,c_120]) ).
cnf(c_2041,plain,
range(sK16,sK17,sK18) = range_of(sK18),
inference(global_subsumption_just,[status(thm)],[c_2040,c_130,c_129,c_128,c_519]) ).
cnf(c_2078,plain,
( ~ ilf_type(X0,set_type)
| ~ ilf_type(sK16,set_type)
| ~ ilf_type(sK17,set_type)
| image4(sK16,sK17,sK18,X0) = image(sK18,X0) ),
inference(superposition,[status(thm)],[c_128,c_122]) ).
cnf(c_2080,plain,
image4(sK16,sK17,sK18,X0) = image(sK18,X0),
inference(global_subsumption_just,[status(thm)],[c_2078,c_130,c_129,c_126,c_128,c_597]) ).
cnf(c_2122,plain,
( ~ ilf_type(X0,set_type)
| ~ ilf_type(sK16,set_type)
| ~ ilf_type(sK17,set_type)
| inverse4(sK16,sK17,sK18,X0) = inverse2(sK18,X0) ),
inference(superposition,[status(thm)],[c_128,c_124]) ).
cnf(c_2124,plain,
inverse4(sK16,sK17,sK18,X0) = inverse2(sK18,X0),
inference(global_subsumption_just,[status(thm)],[c_2122,c_130,c_129,c_126,c_128,c_602]) ).
cnf(c_2147,plain,
( image4(sK16,sK17,sK18,sK16) != range(sK16,sK17,sK18)
| domain(sK16,sK17,sK18) != inverse2(sK18,sK17) ),
inference(superposition,[status(thm)],[c_2124,c_127]) ).
cnf(c_2150,plain,
( image4(sK16,sK17,sK18,sK16) != range_of(sK18)
| inverse2(sK18,sK17) != domain_of(sK18) ),
inference(light_normalisation,[status(thm)],[c_2147,c_1980,c_2041]) ).
cnf(c_2151,plain,
( image(sK18,sK16) != range_of(sK18)
| inverse2(sK18,sK17) != domain_of(sK18) ),
inference(demodulation,[status(thm)],[c_2150,c_2080]) ).
cnf(c_2602,plain,
( ~ relation_like(sK18)
| ilf_type(sK18,binary_relation_type) ),
inference(instantiation,[status(thm)],[c_230]) ).
cnf(c_3056,plain,
( ~ ilf_type(X0,relation_type(X1,X2))
| ilf_type(domain(X1,X2,X0),subset_type(X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_638,c_126]) ).
cnf(c_4225,plain,
( ~ ilf_type(X0,relation_type(X1,X2))
| domain(X1,X2,X0) = domain_of(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_639,c_126]) ).
cnf(c_4717,plain,
( ~ ilf_type(X0,relation_type(X1,X2))
| domain_of(X0) = domain(X1,X2,X0) ),
inference(resolution,[status(thm)],[c_4225,c_1126]) ).
cnf(c_4747,plain,
( ~ ilf_type(domain(X0,X1,X2),X3)
| ~ ilf_type(X2,relation_type(X0,X1))
| ilf_type(domain_of(X2),X3) ),
inference(resolution,[status(thm)],[c_4717,c_1752]) ).
cnf(c_7450,plain,
( ~ ilf_type(X0,relation_type(X1,X2))
| ilf_type(domain_of(X0),subset_type(X1)) ),
inference(resolution,[status(thm)],[c_4747,c_3056]) ).
cnf(c_7626,plain,
ilf_type(domain_of(sK18),subset_type(sK16)),
inference(resolution,[status(thm)],[c_7450,c_128]) ).
cnf(c_7639,plain,
member(domain_of(sK18),power_set(sK16)),
inference(resolution,[status(thm)],[c_7626,c_1022]) ).
cnf(c_8240,plain,
( ~ member(X0,range_of(sK18))
| ~ ilf_type(sK18,binary_relation_type)
| member(ordered_pair(sK1(X0,sK18),X0),sK18) ),
inference(instantiation,[status(thm)],[c_306]) ).
cnf(c_9266,plain,
( ~ ilf_type(sK18,binary_relation_type)
| ilf_type(domain_of(sK18),set_type) ),
inference(instantiation,[status(thm)],[c_77]) ).
cnf(c_21350,plain,
( ~ member(ordered_pair(X0,X1),X2)
| ~ member(X0,X3)
| ~ ilf_type(X2,binary_relation_type)
| member(X1,image(X2,X3)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_628,c_126]) ).
cnf(c_24131,plain,
( ~ member(ordered_pair(X0,X1),X2)
| ~ ilf_type(X2,relation_type(X3,X4))
| member(X0,X3) ),
inference(forward_subsumption_resolution,[status(thm)],[c_633,c_126,c_126]) ).
cnf(c_150247,plain,
( inverse2(sK18,sK17) = domain_of(sK18)
| member(sK8(inverse2(sK18,sK17),domain_of(sK18)),inverse2(sK18,sK17))
| member(sK8(inverse2(sK18,sK17),domain_of(sK18)),domain_of(sK18)) ),
inference(instantiation,[status(thm)],[c_317]) ).
cnf(c_150386,plain,
( ~ member(sK8(inverse2(sK18,sK17),domain_of(sK18)),domain_of(sK18))
| ~ ilf_type(sK18,binary_relation_type)
| member(ordered_pair(sK8(inverse2(sK18,sK17),domain_of(sK18)),sK0(sK8(inverse2(sK18,sK17),domain_of(sK18)),sK18)),sK18) ),
inference(instantiation,[status(thm)],[c_309]) ).
cnf(c_150389,plain,
( ~ member(sK8(inverse2(sK18,sK17),domain_of(sK18)),inverse2(sK18,sK17))
| ~ member(sK8(inverse2(sK18,sK17),domain_of(sK18)),domain_of(sK18))
| ~ ilf_type(domain_of(sK18),set_type)
| inverse2(sK18,sK17) = domain_of(sK18) ),
inference(instantiation,[status(thm)],[c_339]) ).
cnf(c_151398,plain,
( ~ member(sK8(inverse2(sK18,sK17),domain_of(sK18)),inverse2(sK18,sK17))
| ~ ilf_type(sK17,set_type)
| ~ ilf_type(sK18,binary_relation_type)
| member(ordered_pair(sK8(inverse2(sK18,sK17),domain_of(sK18)),sK3(sK17,sK8(inverse2(sK18,sK17),domain_of(sK18)),sK18)),sK18) ),
inference(instantiation,[status(thm)],[c_350]) ).
cnf(c_156108,plain,
( ~ member(ordered_pair(sK8(inverse2(sK18,sK17),domain_of(sK18)),sK3(sK17,sK8(inverse2(sK18,sK17),domain_of(sK18)),sK18)),sK18)
| ~ ilf_type(sK3(sK17,sK8(inverse2(sK18,sK17),domain_of(sK18)),sK18),set_type)
| ~ ilf_type(sK18,binary_relation_type)
| member(sK8(inverse2(sK18,sK17),domain_of(sK18)),domain_of(sK18)) ),
inference(instantiation,[status(thm)],[c_330]) ).
cnf(c_169385,plain,
ilf_type(sK0(sK8(inverse2(sK18,sK17),domain_of(sK18)),sK18),set_type),
inference(instantiation,[status(thm)],[c_126]) ).
cnf(c_169442,plain,
ilf_type(sK3(sK17,sK8(inverse2(sK18,sK17),domain_of(sK18)),sK18),set_type),
inference(instantiation,[status(thm)],[c_126]) ).
cnf(c_172063,plain,
( ~ member(ordered_pair(X0,sK0(X0,X1)),X1)
| ~ member(sK0(X0,X1),X2)
| ~ ilf_type(sK0(X0,X1),set_type)
| ~ ilf_type(X1,binary_relation_type)
| ~ ilf_type(X2,set_type)
| member(X0,inverse2(X1,X2)) ),
inference(instantiation,[status(thm)],[c_359]) ).
cnf(c_172064,plain,
( ~ member(ordered_pair(X0,sK0(X0,X1)),X1)
| ~ ilf_type(X1,relation_type(X2,X3))
| ~ ilf_type(sK0(X0,X1),set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,set_type)
| member(sK0(X0,X1),X3) ),
inference(instantiation,[status(thm)],[c_357]) ).
cnf(c_204280,plain,
( ~ member(ordered_pair(X0,sK0(X0,sK18)),sK18)
| ~ ilf_type(sK0(X0,sK18),set_type)
| ~ ilf_type(sK18,relation_type(sK16,sK17))
| ~ ilf_type(sK16,set_type)
| ~ ilf_type(sK17,set_type)
| member(sK0(X0,sK18),sK17) ),
inference(instantiation,[status(thm)],[c_172064]) ).
cnf(c_241657,plain,
( ~ member(ordered_pair(X0,sK0(X0,sK18)),sK18)
| ~ member(sK0(X0,sK18),sK17)
| ~ ilf_type(sK0(X0,sK18),set_type)
| ~ ilf_type(sK17,set_type)
| ~ ilf_type(sK18,binary_relation_type)
| member(X0,inverse2(sK18,sK17)) ),
inference(instantiation,[status(thm)],[c_172063]) ).
cnf(c_244104,plain,
( ~ member(ordered_pair(sK8(inverse2(sK18,sK17),domain_of(sK18)),sK0(sK8(inverse2(sK18,sK17),domain_of(sK18)),sK18)),sK18)
| ~ member(sK0(sK8(inverse2(sK18,sK17),domain_of(sK18)),sK18),sK17)
| ~ ilf_type(sK0(sK8(inverse2(sK18,sK17),domain_of(sK18)),sK18),set_type)
| ~ ilf_type(sK17,set_type)
| ~ ilf_type(sK18,binary_relation_type)
| member(sK8(inverse2(sK18,sK17),domain_of(sK18)),inverse2(sK18,sK17)) ),
inference(instantiation,[status(thm)],[c_241657]) ).
cnf(c_250231,plain,
( ~ member(ordered_pair(sK8(inverse2(sK18,sK17),domain_of(sK18)),sK0(sK8(inverse2(sK18,sK17),domain_of(sK18)),sK18)),sK18)
| ~ ilf_type(sK0(sK8(inverse2(sK18,sK17),domain_of(sK18)),sK18),set_type)
| ~ ilf_type(sK18,relation_type(sK16,sK17))
| ~ ilf_type(sK16,set_type)
| ~ ilf_type(sK17,set_type)
| member(sK0(sK8(inverse2(sK18,sK17),domain_of(sK18)),sK18),sK17) ),
inference(instantiation,[status(thm)],[c_204280]) ).
cnf(c_403373,plain,
( ~ member(ordered_pair(X0,X1),X2)
| ~ ilf_type(X2,binary_relation_type)
| member(X1,range_of(X2)) ),
inference(global_subsumption_just,[status(thm)],[c_328,c_630]) ).
cnf(c_403377,plain,
( ~ member(ordered_pair(X0,X1),X2)
| ~ ilf_type(X2,binary_relation_type)
| member(X0,domain_of(X2)) ),
inference(global_subsumption_just,[status(thm)],[c_330,c_631]) ).
cnf(c_403383,plain,
( ~ member(ordered_pair(sK1(X0,X1),X0),X1)
| ~ ilf_type(X1,binary_relation_type)
| member(sK1(X0,X1),domain_of(X1)) ),
inference(instantiation,[status(thm)],[c_403377]) ).
cnf(c_403444,plain,
( ~ member(X0,X1)
| ~ subset(X1,X2)
| member(X0,X2) ),
inference(global_subsumption_just,[status(thm)],[c_335,c_1298]) ).
cnf(c_403454,plain,
( ~ member(X0,power_set(X1))
| ~ member(X2,X0)
| member(X2,X1) ),
inference(global_subsumption_just,[status(thm)],[c_337,c_1432]) ).
cnf(c_403552,plain,
( ~ member(sK4(X0,X1),X1)
| ~ member(sK4(X0,X1),X0)
| X0 = X1 ),
inference(global_subsumption_just,[status(thm)],[c_341,c_618]) ).
cnf(c_403553,plain,
( ~ member(sK4(X0,X1),X0)
| ~ member(sK4(X0,X1),X1)
| X0 = X1 ),
inference(renaming,[status(thm)],[c_403552]) ).
cnf(c_403555,plain,
( ~ member(sK4(image(sK18,sK16),range_of(sK18)),image(sK18,sK16))
| ~ member(sK4(image(sK18,sK16),range_of(sK18)),range_of(sK18))
| image(sK18,sK16) = range_of(sK18) ),
inference(instantiation,[status(thm)],[c_403553]) ).
cnf(c_403611,plain,
( ~ ilf_type(X1,binary_relation_type)
| ~ member(X0,image(X1,X2))
| member(ordered_pair(sK2(X2,X0,X1),X0),X1) ),
inference(global_subsumption_just,[status(thm)],[c_352,c_627]) ).
cnf(c_403612,plain,
( ~ member(X0,image(X1,X2))
| ~ ilf_type(X1,binary_relation_type)
| member(ordered_pair(sK2(X2,X0,X1),X0),X1) ),
inference(renaming,[status(thm)],[c_403611]) ).
cnf(c_403668,plain,
( ~ ilf_type(X2,relation_type(X3,X4))
| ~ member(ordered_pair(X0,X1),X2)
| member(X0,X3) ),
inference(global_subsumption_just,[status(thm)],[c_355,c_24131]) ).
cnf(c_403669,plain,
( ~ member(ordered_pair(X0,X1),X2)
| ~ ilf_type(X2,relation_type(X3,X4))
| member(X0,X3) ),
inference(renaming,[status(thm)],[c_403668]) ).
cnf(c_403672,plain,
( ~ member(ordered_pair(sK1(X0,X1),X0),X1)
| ~ ilf_type(X1,relation_type(X2,X3))
| member(sK1(X0,X1),X2) ),
inference(instantiation,[status(thm)],[c_403669]) ).
cnf(c_403698,plain,
( ~ ilf_type(X2,binary_relation_type)
| ~ member(ordered_pair(X0,X1),X2)
| ~ member(X0,X3)
| member(X1,image(X2,X3)) ),
inference(global_subsumption_just,[status(thm)],[c_361,c_21350]) ).
cnf(c_403699,plain,
( ~ member(ordered_pair(X0,X1),X2)
| ~ member(X0,X3)
| ~ ilf_type(X2,binary_relation_type)
| member(X1,image(X2,X3)) ),
inference(renaming,[status(thm)],[c_403698]) ).
cnf(c_403702,plain,
( ~ member(ordered_pair(sK1(X0,X1),X0),X1)
| ~ member(sK1(X0,X1),X2)
| ~ ilf_type(X1,binary_relation_type)
| member(X0,image(X1,X2)) ),
inference(instantiation,[status(thm)],[c_403699]) ).
cnf(c_404239,plain,
( ~ member(sK1(X0,X1),domain_of(X1))
| ~ subset(domain_of(X1),X2)
| member(sK1(X0,X1),X2) ),
inference(instantiation,[status(thm)],[c_403444]) ).
cnf(c_404243,plain,
( ~ member(sK1(X0,X1),domain_of(X1))
| ~ member(domain_of(X1),power_set(X2))
| member(sK1(X0,X1),X2) ),
inference(instantiation,[status(thm)],[c_403454]) ).
cnf(c_404983,plain,
( ~ member(ordered_pair(sK1(sK4(image(sK18,sK16),range_of(sK18)),sK18),sK4(image(sK18,sK16),range_of(sK18))),sK18)
| ~ member(sK1(sK4(image(sK18,sK16),range_of(sK18)),sK18),sK16)
| ~ ilf_type(sK18,binary_relation_type)
| member(sK4(image(sK18,sK16),range_of(sK18)),image(sK18,sK16)) ),
inference(instantiation,[status(thm)],[c_403702]) ).
cnf(c_404995,plain,
( image(sK18,sK16) = range_of(sK18)
| member(sK4(image(sK18,sK16),range_of(sK18)),image(sK18,sK16))
| member(sK4(image(sK18,sK16),range_of(sK18)),range_of(sK18)) ),
inference(instantiation,[status(thm)],[c_322]) ).
cnf(c_405844,plain,
( ~ member(X0,range_of(sK18))
| ~ ilf_type(sK18,binary_relation_type)
| member(ordered_pair(sK1(X0,sK18),X0),sK18) ),
inference(instantiation,[status(thm)],[c_306]) ).
cnf(c_405850,plain,
( ~ member(X0,image(sK18,X1))
| ~ ilf_type(sK18,binary_relation_type)
| member(ordered_pair(sK2(X1,X0,sK18),X0),sK18) ),
inference(instantiation,[status(thm)],[c_403612]) ).
cnf(c_406031,plain,
( ~ member(sK1(sK4(image(sK18,sK16),range_of(sK18)),sK18),sK16)
| ~ member(ordered_pair(sK1(sK4(image(sK18,sK16),range_of(sK18)),sK18),sK4(image(sK18,sK16),range_of(sK18))),sK18)
| member(sK4(image(sK18,sK16),range_of(sK18)),image(sK18,sK16)) ),
inference(global_subsumption_just,[status(thm)],[c_404983,c_130,c_129,c_128,c_458,c_719,c_2602,c_404983]) ).
cnf(c_406032,plain,
( ~ member(ordered_pair(sK1(sK4(image(sK18,sK16),range_of(sK18)),sK18),sK4(image(sK18,sK16),range_of(sK18))),sK18)
| ~ member(sK1(sK4(image(sK18,sK16),range_of(sK18)),sK18),sK16)
| member(sK4(image(sK18,sK16),range_of(sK18)),image(sK18,sK16)) ),
inference(renaming,[status(thm)],[c_406031]) ).
cnf(c_406033,plain,
( ~ member(ordered_pair(sK1(sK4(image(sK18,sK16),range_of(sK18)),sK18),sK4(image(sK18,sK16),range_of(sK18))),sK18)
| ~ ilf_type(sK18,relation_type(sK16,X0))
| member(sK1(sK4(image(sK18,sK16),range_of(sK18)),sK18),sK16) ),
inference(instantiation,[status(thm)],[c_403672]) ).
cnf(c_408175,plain,
( ~ member(sK1(sK4(image(sK18,sK16),range_of(sK18)),sK18),domain_of(sK18))
| ~ subset(domain_of(sK18),sK16)
| member(sK1(sK4(image(sK18,sK16),range_of(sK18)),sK18),sK16) ),
inference(instantiation,[status(thm)],[c_404239]) ).
cnf(c_408195,plain,
( ~ member(sK1(sK4(image(sK18,sK16),range_of(sK18)),sK18),domain_of(sK18))
| ~ member(domain_of(sK18),power_set(sK16))
| member(sK1(sK4(image(sK18,sK16),range_of(sK18)),sK18),sK16) ),
inference(instantiation,[status(thm)],[c_404243]) ).
cnf(c_409757,plain,
( ~ member(X0,range_of(sK18))
| member(ordered_pair(sK1(X0,sK18),X0),sK18) ),
inference(global_subsumption_just,[status(thm)],[c_405844,c_130,c_129,c_128,c_458,c_719,c_2602,c_8240]) ).
cnf(c_409762,plain,
( ~ member(ordered_pair(X0,X1),sK18)
| ~ ilf_type(sK18,binary_relation_type)
| member(X1,range_of(sK18)) ),
inference(instantiation,[status(thm)],[c_403373]) ).
cnf(c_409887,plain,
( ~ member(X0,image(sK18,X1))
| member(ordered_pair(sK2(X1,X0,sK18),X0),sK18) ),
inference(global_subsumption_just,[status(thm)],[c_405850,c_130,c_129,c_128,c_458,c_719,c_2602,c_405850]) ).
cnf(c_409999,plain,
( ~ member(sK4(image(sK18,sK16),range_of(sK18)),image(sK18,sK16))
| member(ordered_pair(sK2(sK16,sK4(image(sK18,sK16),range_of(sK18)),sK18),sK4(image(sK18,sK16),range_of(sK18))),sK18) ),
inference(instantiation,[status(thm)],[c_409887]) ).
cnf(c_411331,plain,
( ~ member(sK1(sK4(image(sK18,sK16),range_of(sK18)),sK18),domain_of(sK18))
| member(sK1(sK4(image(sK18,sK16),range_of(sK18)),sK18),sK16) ),
inference(global_subsumption_just,[status(thm)],[c_408175,c_7639,c_408195]) ).
cnf(c_411333,plain,
( ~ member(ordered_pair(sK1(sK4(image(sK18,sK16),range_of(sK18)),sK18),sK4(image(sK18,sK16),range_of(sK18))),sK18)
| ~ ilf_type(sK18,binary_relation_type)
| member(sK1(sK4(image(sK18,sK16),range_of(sK18)),sK18),domain_of(sK18)) ),
inference(instantiation,[status(thm)],[c_403383]) ).
cnf(c_411353,plain,
( ~ member(ordered_pair(sK1(sK4(image(sK18,sK16),range_of(sK18)),sK18),sK4(image(sK18,sK16),range_of(sK18))),sK18)
| member(sK1(sK4(image(sK18,sK16),range_of(sK18)),sK18),sK16) ),
inference(global_subsumption_just,[status(thm)],[c_406033,c_130,c_129,c_128,c_458,c_719,c_2602,c_411331,c_411333]) ).
cnf(c_414429,plain,
( ~ member(ordered_pair(X0,X1),sK18)
| member(X1,range_of(sK18)) ),
inference(global_subsumption_just,[status(thm)],[c_409762,c_130,c_129,c_128,c_458,c_719,c_2602,c_409762]) ).
cnf(c_414479,plain,
( ~ member(ordered_pair(sK2(sK16,sK4(image(sK18,sK16),range_of(sK18)),sK18),sK4(image(sK18,sK16),range_of(sK18))),sK18)
| member(sK4(image(sK18,sK16),range_of(sK18)),range_of(sK18)) ),
inference(instantiation,[status(thm)],[c_414429]) ).
cnf(c_424800,plain,
( ~ member(sK4(image(sK18,sK16),range_of(sK18)),range_of(sK18))
| member(ordered_pair(sK1(sK4(image(sK18,sK16),range_of(sK18)),sK18),sK4(image(sK18,sK16),range_of(sK18))),sK18) ),
inference(instantiation,[status(thm)],[c_409757]) ).
cnf(c_424806,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_424800,c_414479,c_411353,c_409999,c_406032,c_404995,c_403555,c_250231,c_244104,c_169442,c_169385,c_156108,c_151398,c_150389,c_150386,c_150247,c_9266,c_2602,c_2151,c_719,c_458,c_128,c_129,c_130]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET674+3 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.14 % Command : run_iprover %s %d THM
% 0.14/0.35 % Computer : n021.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sat Aug 26 14:06:27 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.20/0.48 Running first-order theorem proving
% 0.20/0.48 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 207.09/27.94 % SZS status Started for theBenchmark.p
% 207.09/27.94 % SZS status Theorem for theBenchmark.p
% 207.09/27.94
% 207.09/27.94 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 207.09/27.94
% 207.09/27.94 ------ iProver source info
% 207.09/27.94
% 207.09/27.94 git: date: 2023-05-31 18:12:56 +0000
% 207.09/27.94 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 207.09/27.94 git: non_committed_changes: false
% 207.09/27.94 git: last_make_outside_of_git: false
% 207.09/27.94
% 207.09/27.94 ------ Parsing...
% 207.09/27.94 ------ Clausification by vclausify_rel & Parsing by iProver...
% 207.09/27.94
% 207.09/27.94 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 1 0s sf_e
% 207.09/27.94
% 207.09/27.94 ------ Preprocessing...
% 207.09/27.94
% 207.09/27.94 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 207.09/27.94 ------ Proving...
% 207.09/27.94 ------ Problem Properties
% 207.09/27.94
% 207.09/27.94
% 207.09/27.94 clauses 76
% 207.09/27.94 conjectures 4
% 207.09/27.94 EPR 11
% 207.09/27.94 Horn 62
% 207.09/27.94 unary 12
% 207.09/27.94 binary 17
% 207.09/27.94 lits 234
% 207.09/27.94 lits eq 15
% 207.09/27.94 fd_pure 0
% 207.09/27.94 fd_pseudo 0
% 207.09/27.94 fd_cond 0
% 207.09/27.94 fd_pseudo_cond 7
% 207.09/27.94 AC symbols 0
% 207.09/27.94
% 207.09/27.94 ------ Input Options Time Limit: Unbounded
% 207.09/27.94
% 207.09/27.94
% 207.09/27.94 ------
% 207.09/27.94 Current options:
% 207.09/27.94 ------
% 207.09/27.94
% 207.09/27.94
% 207.09/27.94
% 207.09/27.94
% 207.09/27.94 ------ Proving...
% 207.09/27.94
% 207.09/27.94
% 207.09/27.94 % SZS status Theorem for theBenchmark.p
% 207.09/27.94
% 207.09/27.94 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 207.09/27.94
% 207.09/27.95
%------------------------------------------------------------------------------