TSTP Solution File: SET686+3 by iProver---3.8
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%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SET686+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n002.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 15:09:08 EDT 2023
% Result : Theorem 7.31s 1.66s
% Output : CNFRefutation 7.31s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f178)
% Comments :
%------------------------------------------------------------------------------
fof(f1,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/sandbox2/benchmark/theBenchmark.p',p1) ).
fof(f2,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,set_type)
=> ! [X4] :
( ilf_type(X4,relation_type(X0,X1))
=> ( member(ordered_pair(X2,X3),X4)
=> ( member(X3,X1)
& member(X2,X0) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2) ).
fof(f5,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',p5) ).
fof(f7,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',p7) ).
fof(f9,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ( empty(X0)
<=> ! [X1] :
( ilf_type(X1,set_type)
=> ~ member(X1,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p9) ).
fof(f14,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] : ilf_type(X1,set_type) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p14) ).
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)
=> ( member(X0,power_set(X1))
<=> ! [X2] :
( ilf_type(X2,set_type)
=> ( member(X2,X0)
=> member(X2,X1) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p20) ).
fof(f21,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',p21) ).
fof(f24,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',p24) ).
fof(f25,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/sandbox2/benchmark/theBenchmark.p',p25) ).
fof(f27,axiom,
! [X0] : ilf_type(X0,set_type),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p27) ).
fof(f28,conjecture,
! [X0] :
( ( ilf_type(X0,set_type)
& ~ empty(X0) )
=> ! [X1] :
( ( ilf_type(X1,set_type)
& ~ empty(X1) )
=> ! [X2] :
( ( ilf_type(X2,set_type)
& ~ empty(X2) )
=> ! [X3] :
( ilf_type(X3,relation_type(X0,X2))
=> ! [X4] :
( ilf_type(X4,member_type(X0))
=> ( member(X4,inverse4(X0,X2,X3,X1))
<=> ? [X5] :
( member(X5,X1)
& member(ordered_pair(X4,X5),X3)
& ilf_type(X5,member_type(X2)) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_relset_1_53) ).
fof(f29,negated_conjecture,
~ ! [X0] :
( ( ilf_type(X0,set_type)
& ~ empty(X0) )
=> ! [X1] :
( ( ilf_type(X1,set_type)
& ~ empty(X1) )
=> ! [X2] :
( ( ilf_type(X2,set_type)
& ~ empty(X2) )
=> ! [X3] :
( ilf_type(X3,relation_type(X0,X2))
=> ! [X4] :
( ilf_type(X4,member_type(X0))
=> ( member(X4,inverse4(X0,X2,X3,X1))
<=> ? [X5] :
( member(X5,X1)
& member(ordered_pair(X4,X5),X3)
& ilf_type(X5,member_type(X2)) ) ) ) ) ) ) ),
inference(negated_conjecture,[],[f28]) ).
fof(f30,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,[],[f5]) ).
fof(f31,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,[],[f1]) ).
fof(f32,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,[],[f2]) ).
fof(f33,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,[],[f32]) ).
fof(f36,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,[],[f30]) ).
fof(f38,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,[],[f7]) ).
fof(f39,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,[],[f38]) ).
fof(f42,plain,
! [X0] :
( ( empty(X0)
<=> ! [X1] :
( ~ member(X1,X0)
| ~ ilf_type(X1,set_type) ) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f9]) ).
fof(f47,plain,
! [X0] :
( ! [X1] : ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f14]) ).
fof(f49,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(f52,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,[],[f20]) ).
fof(f53,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,[],[f52]) ).
fof(f54,plain,
! [X0] :
( ( ilf_type(power_set(X0),set_type)
& ~ empty(power_set(X0)) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f21]) ).
fof(f59,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,[],[f24]) ).
fof(f60,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,[],[f25]) ).
fof(f62,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ( member(X4,inverse4(X0,X2,X3,X1))
<~> ? [X5] :
( member(X5,X1)
& member(ordered_pair(X4,X5),X3)
& ilf_type(X5,member_type(X2)) ) )
& ilf_type(X4,member_type(X0)) )
& ilf_type(X3,relation_type(X0,X2)) )
& ilf_type(X2,set_type)
& ~ empty(X2) )
& ilf_type(X1,set_type)
& ~ empty(X1) )
& ilf_type(X0,set_type)
& ~ empty(X0) ),
inference(ennf_transformation,[],[f29]) ).
fof(f63,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ( member(X4,inverse4(X0,X2,X3,X1))
<~> ? [X5] :
( member(X5,X1)
& member(ordered_pair(X4,X5),X3)
& ilf_type(X5,member_type(X2)) ) )
& ilf_type(X4,member_type(X0)) )
& ilf_type(X3,relation_type(X0,X2)) )
& ilf_type(X2,set_type)
& ~ empty(X2) )
& ilf_type(X1,set_type)
& ~ empty(X1) )
& ilf_type(X0,set_type)
& ~ empty(X0) ),
inference(flattening,[],[f62]) ).
fof(f64,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,[],[f31]) ).
fof(f65,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,[],[f64]) ).
fof(f66,plain,
! [X0,X1,X2] :
( ? [X4] :
( member(X4,X0)
& member(ordered_pair(X1,X4),X2)
& ilf_type(X4,set_type) )
=> ( member(sK0(X0,X1,X2),X0)
& member(ordered_pair(X1,sK0(X0,X1,X2)),X2)
& ilf_type(sK0(X0,X1,X2),set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f67,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(sK0(X0,X1,X2),X0)
& member(ordered_pair(X1,sK0(X0,X1,X2)),X2)
& ilf_type(sK0(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,[sK0])],[f65,f66]) ).
fof(f71,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,[],[f39]) ).
fof(f74,plain,
! [X0] :
( ( ( empty(X0)
| ? [X1] :
( member(X1,X0)
& ilf_type(X1,set_type) ) )
& ( ! [X1] :
( ~ member(X1,X0)
| ~ ilf_type(X1,set_type) )
| ~ empty(X0) ) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f42]) ).
fof(f75,plain,
! [X0] :
( ( ( empty(X0)
| ? [X1] :
( member(X1,X0)
& ilf_type(X1,set_type) ) )
& ( ! [X2] :
( ~ member(X2,X0)
| ~ ilf_type(X2,set_type) )
| ~ empty(X0) ) )
| ~ ilf_type(X0,set_type) ),
inference(rectify,[],[f74]) ).
fof(f76,plain,
! [X0] :
( ? [X1] :
( member(X1,X0)
& ilf_type(X1,set_type) )
=> ( member(sK3(X0),X0)
& ilf_type(sK3(X0),set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f77,plain,
! [X0] :
( ( ( empty(X0)
| ( member(sK3(X0),X0)
& ilf_type(sK3(X0),set_type) ) )
& ( ! [X2] :
( ~ member(X2,X0)
| ~ ilf_type(X2,set_type) )
| ~ empty(X0) ) )
| ~ ilf_type(X0,set_type) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f75,f76]) ).
fof(f82,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,[],[f49]) ).
fof(f90,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,[],[f53]) ).
fof(f91,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,[],[f90]) ).
fof(f92,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(f93,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])],[f91,f92]) ).
fof(f100,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ( ! [X5] :
( ~ member(X5,X1)
| ~ member(ordered_pair(X4,X5),X3)
| ~ ilf_type(X5,member_type(X2)) )
| ~ member(X4,inverse4(X0,X2,X3,X1)) )
& ( ? [X5] :
( member(X5,X1)
& member(ordered_pair(X4,X5),X3)
& ilf_type(X5,member_type(X2)) )
| member(X4,inverse4(X0,X2,X3,X1)) )
& ilf_type(X4,member_type(X0)) )
& ilf_type(X3,relation_type(X0,X2)) )
& ilf_type(X2,set_type)
& ~ empty(X2) )
& ilf_type(X1,set_type)
& ~ empty(X1) )
& ilf_type(X0,set_type)
& ~ empty(X0) ),
inference(nnf_transformation,[],[f63]) ).
fof(f101,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ( ! [X5] :
( ~ member(X5,X1)
| ~ member(ordered_pair(X4,X5),X3)
| ~ ilf_type(X5,member_type(X2)) )
| ~ member(X4,inverse4(X0,X2,X3,X1)) )
& ( ? [X5] :
( member(X5,X1)
& member(ordered_pair(X4,X5),X3)
& ilf_type(X5,member_type(X2)) )
| member(X4,inverse4(X0,X2,X3,X1)) )
& ilf_type(X4,member_type(X0)) )
& ilf_type(X3,relation_type(X0,X2)) )
& ilf_type(X2,set_type)
& ~ empty(X2) )
& ilf_type(X1,set_type)
& ~ empty(X1) )
& ilf_type(X0,set_type)
& ~ empty(X0) ),
inference(flattening,[],[f100]) ).
fof(f102,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ( ! [X5] :
( ~ member(X5,X1)
| ~ member(ordered_pair(X4,X5),X3)
| ~ ilf_type(X5,member_type(X2)) )
| ~ member(X4,inverse4(X0,X2,X3,X1)) )
& ( ? [X6] :
( member(X6,X1)
& member(ordered_pair(X4,X6),X3)
& ilf_type(X6,member_type(X2)) )
| member(X4,inverse4(X0,X2,X3,X1)) )
& ilf_type(X4,member_type(X0)) )
& ilf_type(X3,relation_type(X0,X2)) )
& ilf_type(X2,set_type)
& ~ empty(X2) )
& ilf_type(X1,set_type)
& ~ empty(X1) )
& ilf_type(X0,set_type)
& ~ empty(X0) ),
inference(rectify,[],[f101]) ).
fof(f103,plain,
( ? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ( ! [X5] :
( ~ member(X5,X1)
| ~ member(ordered_pair(X4,X5),X3)
| ~ ilf_type(X5,member_type(X2)) )
| ~ member(X4,inverse4(X0,X2,X3,X1)) )
& ( ? [X6] :
( member(X6,X1)
& member(ordered_pair(X4,X6),X3)
& ilf_type(X6,member_type(X2)) )
| member(X4,inverse4(X0,X2,X3,X1)) )
& ilf_type(X4,member_type(X0)) )
& ilf_type(X3,relation_type(X0,X2)) )
& ilf_type(X2,set_type)
& ~ empty(X2) )
& ilf_type(X1,set_type)
& ~ empty(X1) )
& ilf_type(X0,set_type)
& ~ empty(X0) )
=> ( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ( ! [X5] :
( ~ member(X5,X1)
| ~ member(ordered_pair(X4,X5),X3)
| ~ ilf_type(X5,member_type(X2)) )
| ~ member(X4,inverse4(sK11,X2,X3,X1)) )
& ( ? [X6] :
( member(X6,X1)
& member(ordered_pair(X4,X6),X3)
& ilf_type(X6,member_type(X2)) )
| member(X4,inverse4(sK11,X2,X3,X1)) )
& ilf_type(X4,member_type(sK11)) )
& ilf_type(X3,relation_type(sK11,X2)) )
& ilf_type(X2,set_type)
& ~ empty(X2) )
& ilf_type(X1,set_type)
& ~ empty(X1) )
& ilf_type(sK11,set_type)
& ~ empty(sK11) ) ),
introduced(choice_axiom,[]) ).
fof(f104,plain,
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ( ! [X5] :
( ~ member(X5,X1)
| ~ member(ordered_pair(X4,X5),X3)
| ~ ilf_type(X5,member_type(X2)) )
| ~ member(X4,inverse4(sK11,X2,X3,X1)) )
& ( ? [X6] :
( member(X6,X1)
& member(ordered_pair(X4,X6),X3)
& ilf_type(X6,member_type(X2)) )
| member(X4,inverse4(sK11,X2,X3,X1)) )
& ilf_type(X4,member_type(sK11)) )
& ilf_type(X3,relation_type(sK11,X2)) )
& ilf_type(X2,set_type)
& ~ empty(X2) )
& ilf_type(X1,set_type)
& ~ empty(X1) )
=> ( ? [X2] :
( ? [X3] :
( ? [X4] :
( ( ! [X5] :
( ~ member(X5,sK12)
| ~ member(ordered_pair(X4,X5),X3)
| ~ ilf_type(X5,member_type(X2)) )
| ~ member(X4,inverse4(sK11,X2,X3,sK12)) )
& ( ? [X6] :
( member(X6,sK12)
& member(ordered_pair(X4,X6),X3)
& ilf_type(X6,member_type(X2)) )
| member(X4,inverse4(sK11,X2,X3,sK12)) )
& ilf_type(X4,member_type(sK11)) )
& ilf_type(X3,relation_type(sK11,X2)) )
& ilf_type(X2,set_type)
& ~ empty(X2) )
& ilf_type(sK12,set_type)
& ~ empty(sK12) ) ),
introduced(choice_axiom,[]) ).
fof(f105,plain,
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ( ! [X5] :
( ~ member(X5,sK12)
| ~ member(ordered_pair(X4,X5),X3)
| ~ ilf_type(X5,member_type(X2)) )
| ~ member(X4,inverse4(sK11,X2,X3,sK12)) )
& ( ? [X6] :
( member(X6,sK12)
& member(ordered_pair(X4,X6),X3)
& ilf_type(X6,member_type(X2)) )
| member(X4,inverse4(sK11,X2,X3,sK12)) )
& ilf_type(X4,member_type(sK11)) )
& ilf_type(X3,relation_type(sK11,X2)) )
& ilf_type(X2,set_type)
& ~ empty(X2) )
=> ( ? [X3] :
( ? [X4] :
( ( ! [X5] :
( ~ member(X5,sK12)
| ~ member(ordered_pair(X4,X5),X3)
| ~ ilf_type(X5,member_type(sK13)) )
| ~ member(X4,inverse4(sK11,sK13,X3,sK12)) )
& ( ? [X6] :
( member(X6,sK12)
& member(ordered_pair(X4,X6),X3)
& ilf_type(X6,member_type(sK13)) )
| member(X4,inverse4(sK11,sK13,X3,sK12)) )
& ilf_type(X4,member_type(sK11)) )
& ilf_type(X3,relation_type(sK11,sK13)) )
& ilf_type(sK13,set_type)
& ~ empty(sK13) ) ),
introduced(choice_axiom,[]) ).
fof(f106,plain,
( ? [X3] :
( ? [X4] :
( ( ! [X5] :
( ~ member(X5,sK12)
| ~ member(ordered_pair(X4,X5),X3)
| ~ ilf_type(X5,member_type(sK13)) )
| ~ member(X4,inverse4(sK11,sK13,X3,sK12)) )
& ( ? [X6] :
( member(X6,sK12)
& member(ordered_pair(X4,X6),X3)
& ilf_type(X6,member_type(sK13)) )
| member(X4,inverse4(sK11,sK13,X3,sK12)) )
& ilf_type(X4,member_type(sK11)) )
& ilf_type(X3,relation_type(sK11,sK13)) )
=> ( ? [X4] :
( ( ! [X5] :
( ~ member(X5,sK12)
| ~ member(ordered_pair(X4,X5),sK14)
| ~ ilf_type(X5,member_type(sK13)) )
| ~ member(X4,inverse4(sK11,sK13,sK14,sK12)) )
& ( ? [X6] :
( member(X6,sK12)
& member(ordered_pair(X4,X6),sK14)
& ilf_type(X6,member_type(sK13)) )
| member(X4,inverse4(sK11,sK13,sK14,sK12)) )
& ilf_type(X4,member_type(sK11)) )
& ilf_type(sK14,relation_type(sK11,sK13)) ) ),
introduced(choice_axiom,[]) ).
fof(f107,plain,
( ? [X4] :
( ( ! [X5] :
( ~ member(X5,sK12)
| ~ member(ordered_pair(X4,X5),sK14)
| ~ ilf_type(X5,member_type(sK13)) )
| ~ member(X4,inverse4(sK11,sK13,sK14,sK12)) )
& ( ? [X6] :
( member(X6,sK12)
& member(ordered_pair(X4,X6),sK14)
& ilf_type(X6,member_type(sK13)) )
| member(X4,inverse4(sK11,sK13,sK14,sK12)) )
& ilf_type(X4,member_type(sK11)) )
=> ( ( ! [X5] :
( ~ member(X5,sK12)
| ~ member(ordered_pair(sK15,X5),sK14)
| ~ ilf_type(X5,member_type(sK13)) )
| ~ member(sK15,inverse4(sK11,sK13,sK14,sK12)) )
& ( ? [X6] :
( member(X6,sK12)
& member(ordered_pair(sK15,X6),sK14)
& ilf_type(X6,member_type(sK13)) )
| member(sK15,inverse4(sK11,sK13,sK14,sK12)) )
& ilf_type(sK15,member_type(sK11)) ) ),
introduced(choice_axiom,[]) ).
fof(f108,plain,
( ? [X6] :
( member(X6,sK12)
& member(ordered_pair(sK15,X6),sK14)
& ilf_type(X6,member_type(sK13)) )
=> ( member(sK16,sK12)
& member(ordered_pair(sK15,sK16),sK14)
& ilf_type(sK16,member_type(sK13)) ) ),
introduced(choice_axiom,[]) ).
fof(f109,plain,
( ( ! [X5] :
( ~ member(X5,sK12)
| ~ member(ordered_pair(sK15,X5),sK14)
| ~ ilf_type(X5,member_type(sK13)) )
| ~ member(sK15,inverse4(sK11,sK13,sK14,sK12)) )
& ( ( member(sK16,sK12)
& member(ordered_pair(sK15,sK16),sK14)
& ilf_type(sK16,member_type(sK13)) )
| member(sK15,inverse4(sK11,sK13,sK14,sK12)) )
& ilf_type(sK15,member_type(sK11))
& ilf_type(sK14,relation_type(sK11,sK13))
& ilf_type(sK13,set_type)
& ~ empty(sK13)
& ilf_type(sK12,set_type)
& ~ empty(sK12)
& ilf_type(sK11,set_type)
& ~ empty(sK11) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK11,sK12,sK13,sK14,sK15,sK16])],[f102,f108,f107,f106,f105,f104,f103]) ).
fof(f111,plain,
! [X2,X0,X1] :
( member(ordered_pair(X1,sK0(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,[],[f67]) ).
fof(f112,plain,
! [X2,X0,X1] :
( member(sK0(X0,X1,X2),X0)
| ~ member(X1,inverse2(X2,X0))
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f67]) ).
fof(f113,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,[],[f67]) ).
fof(f115,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,[],[f33]) ).
fof(f119,plain,
! [X3,X0,X1] :
( 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(cnf_transformation,[],[f36]) ).
fof(f120,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,[],[f36]) ).
fof(f122,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,[],[f71]) ).
fof(f123,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(cnf_transformation,[],[f71]) ).
fof(f125,plain,
! [X2,X0] :
( ~ member(X2,X0)
| ~ ilf_type(X2,set_type)
| ~ empty(X0)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f77]) ).
fof(f132,plain,
! [X0,X1] :
( ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f47]) ).
fof(f137,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,[],[f82]) ).
fof(f138,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(cnf_transformation,[],[f82]) ).
fof(f145,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,[],[f93]) ).
fof(f147,plain,
! [X0,X1] :
( member(X0,power_set(X1))
| member(sK7(X0,X1),X0)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f93]) ).
fof(f148,plain,
! [X0,X1] :
( member(X0,power_set(X1))
| ~ member(sK7(X0,X1),X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f93]) ).
fof(f149,plain,
! [X0] :
( ~ empty(power_set(X0))
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f54]) ).
fof(f158,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,[],[f59]) ).
fof(f159,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,[],[f60]) ).
fof(f161,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[],[f27]) ).
fof(f168,plain,
ilf_type(sK14,relation_type(sK11,sK13)),
inference(cnf_transformation,[],[f109]) ).
fof(f171,plain,
( member(ordered_pair(sK15,sK16),sK14)
| member(sK15,inverse4(sK11,sK13,sK14,sK12)) ),
inference(cnf_transformation,[],[f109]) ).
fof(f172,plain,
( member(sK16,sK12)
| member(sK15,inverse4(sK11,sK13,sK14,sK12)) ),
inference(cnf_transformation,[],[f109]) ).
fof(f173,plain,
! [X5] :
( ~ member(X5,sK12)
| ~ member(ordered_pair(sK15,X5),sK14)
| ~ ilf_type(X5,member_type(sK13))
| ~ member(sK15,inverse4(sK11,sK13,sK14,sK12)) ),
inference(cnf_transformation,[],[f109]) ).
cnf(c_49,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,[],[f113]) ).
cnf(c_50,plain,
( ~ member(X0,inverse2(X1,X2))
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,binary_relation_type)
| ~ ilf_type(X2,set_type)
| member(sK0(X2,X0,X1),X2) ),
inference(cnf_transformation,[],[f112]) ).
cnf(c_51,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,sK0(X2,X0,X1)),X1) ),
inference(cnf_transformation,[],[f111]) ).
cnf(c_53,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,[],[f115]) ).
cnf(c_58,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,[],[f120]) ).
cnf(c_59,plain,
( ~ ilf_type(X0,subset_type(cross_product(X1,X2)))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ilf_type(X0,relation_type(X1,X2)) ),
inference(cnf_transformation,[],[f119]) ).
cnf(c_61,plain,
( ~ member(X0,X1)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ilf_type(X0,member_type(X1))
| empty(X1) ),
inference(cnf_transformation,[],[f123]) ).
cnf(c_62,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,[],[f122]) ).
cnf(c_66,plain,
( ~ member(X0,X1)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ empty(X1) ),
inference(cnf_transformation,[],[f125]) ).
cnf(c_71,plain,
( ~ ilf_type(X0,set_type)
| ilf_type(X1,set_type) ),
inference(cnf_transformation,[],[f132]) ).
cnf(c_72,plain,
( ~ ilf_type(X0,set_type)
| ~ relation_like(X0)
| ilf_type(X0,binary_relation_type) ),
inference(cnf_transformation,[],[f178]) ).
cnf(c_75,plain,
( ~ ilf_type(X0,member_type(power_set(X1)))
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ilf_type(X0,subset_type(X1)) ),
inference(cnf_transformation,[],[f138]) ).
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,[],[f137]) ).
cnf(c_83,plain,
( ~ member(sK7(X0,X1),X1)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| member(X0,power_set(X1)) ),
inference(cnf_transformation,[],[f148]) ).
cnf(c_84,plain,
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| member(sK7(X1,X0),X1)
| member(X1,power_set(X0)) ),
inference(cnf_transformation,[],[f147]) ).
cnf(c_86,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,[],[f145]) ).
cnf(c_88,plain,
( ~ ilf_type(X0,set_type)
| ~ empty(power_set(X0)) ),
inference(cnf_transformation,[],[f149]) ).
cnf(c_96,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,[],[f158]) ).
cnf(c_97,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,[],[f159]) ).
cnf(c_99,plain,
ilf_type(X0,set_type),
inference(cnf_transformation,[],[f161]) ).
cnf(c_100,negated_conjecture,
( ~ member(sK15,inverse4(sK11,sK13,sK14,sK12))
| ~ member(ordered_pair(sK15,X0),sK14)
| ~ ilf_type(X0,member_type(sK13))
| ~ member(X0,sK12) ),
inference(cnf_transformation,[],[f173]) ).
cnf(c_101,negated_conjecture,
( member(sK15,inverse4(sK11,sK13,sK14,sK12))
| member(sK16,sK12) ),
inference(cnf_transformation,[],[f172]) ).
cnf(c_102,negated_conjecture,
( member(sK15,inverse4(sK11,sK13,sK14,sK12))
| member(ordered_pair(sK15,sK16),sK14) ),
inference(cnf_transformation,[],[f171]) ).
cnf(c_105,negated_conjecture,
ilf_type(sK14,relation_type(sK11,sK13)),
inference(cnf_transformation,[],[f168]) ).
cnf(c_158,plain,
ilf_type(X1,set_type),
inference(global_subsumption_just,[status(thm)],[c_71,c_99,c_71]) ).
cnf(c_159,plain,
ilf_type(X0,set_type),
inference(renaming,[status(thm)],[c_158]) ).
cnf(c_160,plain,
~ empty(power_set(X0)),
inference(global_subsumption_just,[status(thm)],[c_88,c_99,c_88]) ).
cnf(c_208,plain,
( ~ member(X0,X1)
| ~ empty(X1) ),
inference(global_subsumption_just,[status(thm)],[c_66,c_99,c_71,c_66]) ).
cnf(c_214,plain,
( ~ ilf_type(X0,subset_type(cross_product(X1,X2)))
| ~ ilf_type(X2,set_type)
| relation_like(X0) ),
inference(global_subsumption_just,[status(thm)],[c_96,c_99,c_71,c_96]) ).
cnf(c_219,plain,
( member(sK7(X1,X0),X1)
| member(X1,power_set(X0)) ),
inference(global_subsumption_just,[status(thm)],[c_84,c_99,c_71,c_84]) ).
cnf(c_220,plain,
( member(sK7(X0,X1),X0)
| member(X0,power_set(X1)) ),
inference(renaming,[status(thm)],[c_219]) ).
cnf(c_225,plain,
( ~ member(sK7(X0,X1),X1)
| member(X0,power_set(X1)) ),
inference(global_subsumption_just,[status(thm)],[c_83,c_99,c_71,c_83]) ).
cnf(c_228,plain,
( ~ ilf_type(X0,subset_type(X1))
| ilf_type(X0,member_type(power_set(X1))) ),
inference(global_subsumption_just,[status(thm)],[c_76,c_99,c_71,c_76]) ).
cnf(c_231,plain,
( ~ ilf_type(X0,member_type(power_set(X1)))
| ilf_type(X0,subset_type(X1)) ),
inference(global_subsumption_just,[status(thm)],[c_75,c_99,c_71,c_75]) ).
cnf(c_234,plain,
( ~ ilf_type(X0,member_type(X1))
| member(X0,X1)
| empty(X1) ),
inference(global_subsumption_just,[status(thm)],[c_62,c_99,c_71,c_62]) ).
cnf(c_237,plain,
( ilf_type(X0,member_type(X1))
| ~ member(X0,X1) ),
inference(global_subsumption_just,[status(thm)],[c_61,c_99,c_71,c_61,c_208]) ).
cnf(c_238,plain,
( ~ member(X0,X1)
| ilf_type(X0,member_type(X1)) ),
inference(renaming,[status(thm)],[c_237]) ).
cnf(c_246,plain,
( ~ ilf_type(X0,subset_type(cross_product(X1,X2)))
| ~ ilf_type(X2,set_type)
| ilf_type(X0,relation_type(X1,X2)) ),
inference(global_subsumption_just,[status(thm)],[c_59,c_99,c_71,c_59]) ).
cnf(c_248,plain,
( ~ ilf_type(X0,relation_type(X1,X2))
| ~ ilf_type(X2,set_type)
| ilf_type(X0,subset_type(cross_product(X1,X2))) ),
inference(global_subsumption_just,[status(thm)],[c_58,c_99,c_71,c_58]) ).
cnf(c_258,plain,
( ~ member(X0,power_set(X1))
| ~ member(X2,X0)
| ~ ilf_type(X2,set_type)
| member(X2,X1) ),
inference(global_subsumption_just,[status(thm)],[c_86,c_99,c_71,c_86]) ).
cnf(c_265,plain,
( ~ member(X0,inverse2(X1,X2))
| ~ ilf_type(X1,binary_relation_type)
| ~ ilf_type(X2,set_type)
| member(sK0(X2,X0,X1),X2) ),
inference(global_subsumption_just,[status(thm)],[c_50,c_99,c_50]) ).
cnf(c_269,plain,
( ~ member(X0,inverse2(X1,X2))
| ~ ilf_type(X1,binary_relation_type)
| ~ ilf_type(X2,set_type)
| member(ordered_pair(X0,sK0(X2,X0,X1)),X1) ),
inference(global_subsumption_just,[status(thm)],[c_51,c_99,c_51]) ).
cnf(c_271,plain,
( ~ ilf_type(X0,relation_type(X1,X2))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,set_type)
| inverse4(X1,X2,X0,X3) = inverse2(X0,X3) ),
inference(global_subsumption_just,[status(thm)],[c_97,c_99,c_71,c_97]) ).
cnf(c_275,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(X1,X4) ),
inference(global_subsumption_just,[status(thm)],[c_53,c_99,c_71,c_53]) ).
cnf(c_277,plain,
( ~ member(ordered_pair(X0,X1),X2)
| ~ member(X1,X3)
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X3,set_type)
| member(X0,inverse2(X2,X3)) ),
inference(global_subsumption_just,[status(thm)],[c_49,c_99,c_71,c_49]) ).
cnf(c_463,plain,
( ~ ilf_type(X0,relation_type(X1,X2))
| ilf_type(X0,subset_type(cross_product(X1,X2))) ),
inference(backward_subsumption_resolution,[status(thm)],[c_248,c_159]) ).
cnf(c_464,plain,
( ~ ilf_type(X0,subset_type(cross_product(X1,X2)))
| ilf_type(X0,relation_type(X1,X2)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_246,c_159]) ).
cnf(c_466,plain,
( ~ ilf_type(X0,relation_type(X1,X2))
| ~ ilf_type(X3,set_type)
| inverse4(X1,X2,X0,X3) = inverse2(X0,X3) ),
inference(backward_subsumption_resolution,[status(thm)],[c_271,c_159]) ).
cnf(c_467,plain,
( ~ member(X0,inverse2(X1,X2))
| ~ ilf_type(X1,binary_relation_type)
| member(sK0(X2,X0,X1),X2) ),
inference(backward_subsumption_resolution,[status(thm)],[c_265,c_159]) ).
cnf(c_468,plain,
( ~ member(X0,inverse2(X1,X2))
| ~ ilf_type(X1,binary_relation_type)
| member(ordered_pair(X0,sK0(X2,X0,X1)),X1) ),
inference(backward_subsumption_resolution,[status(thm)],[c_269,c_159]) ).
cnf(c_469,plain,
( ~ member(ordered_pair(X0,X1),X2)
| ~ member(X1,X3)
| ~ ilf_type(X2,binary_relation_type)
| member(X0,inverse2(X2,X3)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_277,c_159]) ).
cnf(c_470,plain,
( ~ member(ordered_pair(X0,X1),X2)
| ~ ilf_type(X2,relation_type(X3,X4))
| ~ ilf_type(X4,set_type)
| member(X1,X4) ),
inference(backward_subsumption_resolution,[status(thm)],[c_275,c_159]) ).
cnf(c_472,plain,
( ~ ilf_type(X0,subset_type(cross_product(X1,X2)))
| relation_like(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[c_214,c_159]) ).
cnf(c_474,plain,
( ~ member(X0,power_set(X1))
| ~ member(X2,X0)
| member(X2,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[c_258,c_159]) ).
cnf(c_626,plain,
( ~ ilf_type(X0,relation_type(X1,X2))
| inverse4(X1,X2,X0,X3) = inverse2(X0,X3) ),
inference(forward_subsumption_resolution,[status(thm)],[c_466,c_159]) ).
cnf(c_646,plain,
( ~ member(ordered_pair(X0,X1),X2)
| ~ ilf_type(X2,relation_type(X3,X4))
| member(X1,X4) ),
inference(forward_subsumption_resolution,[status(thm)],[c_470,c_159]) ).
cnf(c_1118,plain,
( ilf_type(X0,relation_type(X1,X2))
| ~ ilf_type(X0,subset_type(cross_product(X1,X2))) ),
inference(prop_impl_just,[status(thm)],[c_464]) ).
cnf(c_1119,plain,
( ~ ilf_type(X0,subset_type(cross_product(X1,X2)))
| ilf_type(X0,relation_type(X1,X2)) ),
inference(renaming,[status(thm)],[c_1118]) ).
cnf(c_1120,plain,
( ~ ilf_type(X0,relation_type(X1,X2))
| ilf_type(X0,subset_type(cross_product(X1,X2))) ),
inference(prop_impl_just,[status(thm)],[c_463]) ).
cnf(c_1124,plain,
( ~ relation_like(X0)
| ilf_type(X0,binary_relation_type) ),
inference(prop_impl_just,[status(thm)],[c_99,c_72]) ).
cnf(c_1126,plain,
( ilf_type(X0,subset_type(X1))
| ~ ilf_type(X0,member_type(power_set(X1))) ),
inference(prop_impl_just,[status(thm)],[c_231]) ).
cnf(c_1127,plain,
( ~ ilf_type(X0,member_type(power_set(X1)))
| ilf_type(X0,subset_type(X1)) ),
inference(renaming,[status(thm)],[c_1126]) ).
cnf(c_1128,plain,
( ~ ilf_type(X0,subset_type(X1))
| ilf_type(X0,member_type(power_set(X1))) ),
inference(prop_impl_just,[status(thm)],[c_228]) ).
cnf(c_1130,plain,
( ~ ilf_type(X0,relation_type(X1,X2))
| relation_like(X0) ),
inference(prop_impl_just,[status(thm)],[c_472,c_463]) ).
cnf(c_1132,plain,
( ~ ilf_type(X0,relation_type(X1,X2))
| inverse4(X1,X2,X0,X3) = inverse2(X0,X3) ),
inference(prop_impl_just,[status(thm)],[c_626]) ).
cnf(c_1138,plain,
( ~ member(X0,X1)
| ilf_type(X0,member_type(X1)) ),
inference(prop_impl_just,[status(thm)],[c_238]) ).
cnf(c_1154,plain,
( ~ member(sK7(X0,X1),X1)
| member(X0,power_set(X1)) ),
inference(prop_impl_just,[status(thm)],[c_225]) ).
cnf(c_1158,plain,
( member(X0,power_set(X1))
| member(sK7(X0,X1),X0) ),
inference(prop_impl_just,[status(thm)],[c_220]) ).
cnf(c_1159,plain,
( member(sK7(X0,X1),X0)
| member(X0,power_set(X1)) ),
inference(renaming,[status(thm)],[c_1158]) ).
cnf(c_2756,plain,
( ~ member(ordered_pair(sK15,X0),sK14)
| ~ ilf_type(X0,member_type(sK13))
| ~ member(X0,sK12)
| member(sK16,sK12) ),
inference(superposition,[status(thm)],[c_101,c_100]) ).
cnf(c_2837,plain,
relation_like(sK14),
inference(superposition,[status(thm)],[c_105,c_1130]) ).
cnf(c_3343,plain,
inverse4(sK11,sK13,sK14,X0) = inverse2(sK14,X0),
inference(superposition,[status(thm)],[c_105,c_1132]) ).
cnf(c_3351,plain,
( ~ member(ordered_pair(sK15,X0),sK14)
| ~ member(sK15,inverse2(sK14,sK12))
| ~ ilf_type(X0,member_type(sK13))
| ~ member(X0,sK12) ),
inference(demodulation,[status(thm)],[c_100,c_3343]) ).
cnf(c_3352,plain,
( member(ordered_pair(sK15,sK16),sK14)
| member(sK15,inverse2(sK14,sK12)) ),
inference(demodulation,[status(thm)],[c_102,c_3343]) ).
cnf(c_3354,plain,
( member(sK15,inverse2(sK14,sK12))
| member(sK16,sK12) ),
inference(demodulation,[status(thm)],[c_101,c_3343]) ).
cnf(c_5008,plain,
( ~ relation_like(sK14)
| ilf_type(sK14,binary_relation_type) ),
inference(instantiation,[status(thm)],[c_1124]) ).
cnf(c_7834,plain,
( ~ member(ordered_pair(sK15,sK16),sK14)
| ~ member(sK16,X0)
| ~ ilf_type(sK14,binary_relation_type)
| member(sK15,inverse2(sK14,X0)) ),
inference(instantiation,[status(thm)],[c_469]) ).
cnf(c_8822,plain,
( ~ member(ordered_pair(sK15,sK16),sK14)
| ~ member(sK16,sK12)
| ~ ilf_type(sK14,binary_relation_type)
| member(sK15,inverse2(sK14,sK12)) ),
inference(instantiation,[status(thm)],[c_7834]) ).
cnf(c_10164,plain,
( ~ ilf_type(sK0(X0,sK15,sK14),member_type(sK13))
| ~ member(sK0(X0,sK15,sK14),sK12)
| ~ member(sK15,inverse2(sK14,X0))
| ~ member(sK15,inverse2(sK14,sK12))
| ~ ilf_type(sK14,binary_relation_type) ),
inference(superposition,[status(thm)],[c_468,c_3351]) ).
cnf(c_10167,plain,
( ~ ilf_type(sK0(X0,sK15,sK14),member_type(sK13))
| ~ member(sK0(X0,sK15,sK14),sK12)
| ~ member(sK15,inverse2(sK14,X0))
| ~ ilf_type(sK14,binary_relation_type)
| member(sK16,sK12) ),
inference(superposition,[status(thm)],[c_468,c_2756]) ).
cnf(c_10952,plain,
( ~ ilf_type(sK0(X0,sK15,sK14),member_type(sK13))
| ~ member(sK0(X0,sK15,sK14),sK12)
| ~ member(sK15,inverse2(sK14,X0)) ),
inference(global_subsumption_just,[status(thm)],[c_10167,c_2837,c_3354,c_3352,c_5008,c_8822,c_10164]) ).
cnf(c_10961,plain,
( ~ member(sK0(X0,sK15,sK14),sK12)
| ~ member(sK0(X0,sK15,sK14),sK13)
| ~ member(sK15,inverse2(sK14,X0)) ),
inference(superposition,[status(thm)],[c_1138,c_10952]) ).
cnf(c_11004,plain,
( ~ member(sK0(sK12,sK15,sK14),sK13)
| ~ member(sK15,inverse2(sK14,sK12))
| ~ ilf_type(sK14,binary_relation_type) ),
inference(superposition,[status(thm)],[c_467,c_10961]) ).
cnf(c_12407,plain,
~ member(sK0(sK12,sK15,sK14),sK13),
inference(global_subsumption_just,[status(thm)],[c_11004,c_2837,c_3354,c_3352,c_5008,c_8822,c_11004]) ).
cnf(c_13367,plain,
( ~ member(sK16,X0)
| ~ ilf_type(sK14,binary_relation_type)
| member(sK15,inverse2(sK14,X0))
| member(sK15,inverse2(sK14,sK12)) ),
inference(superposition,[status(thm)],[c_3352,c_469]) ).
cnf(c_13593,plain,
member(sK15,inverse2(sK14,sK12)),
inference(global_subsumption_just,[status(thm)],[c_13367,c_2837,c_3354,c_3352,c_5008,c_8822]) ).
cnf(c_21815,negated_conjecture,
( ~ member(ordered_pair(sK15,X0),sK14)
| ~ ilf_type(X0,member_type(sK13))
| ~ member(X0,sK12) ),
inference(global_subsumption_just,[status(thm)],[c_100,c_3351,c_13593]) ).
cnf(c_21885,plain,
( ~ ilf_type(X0,subset_type(X1))
| member(X0,power_set(X1))
| empty(power_set(X1)) ),
inference(superposition,[status(thm)],[c_1128,c_234]) ).
cnf(c_21886,plain,
( ~ ilf_type(X0,subset_type(X1))
| member(X0,power_set(X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_21885,c_160]) ).
cnf(c_21918,plain,
( ~ ilf_type(X0,relation_type(X1,X2))
| member(X0,power_set(cross_product(X1,X2))) ),
inference(superposition,[status(thm)],[c_1120,c_21886]) ).
cnf(c_21927,plain,
( ~ member(X0,power_set(X1))
| ilf_type(X0,subset_type(X1)) ),
inference(superposition,[status(thm)],[c_1138,c_1127]) ).
cnf(c_21950,plain,
member(X0,power_set(X0)),
inference(superposition,[status(thm)],[c_1159,c_1154]) ).
cnf(c_22086,plain,
ilf_type(X0,subset_type(X0)),
inference(superposition,[status(thm)],[c_21950,c_21927]) ).
cnf(c_22129,plain,
inverse4(sK11,sK13,sK14,X0) = inverse2(sK14,X0),
inference(superposition,[status(thm)],[c_105,c_1132]) ).
cnf(c_22139,plain,
( member(sK15,inverse2(sK14,sK12))
| member(sK16,sK12) ),
inference(demodulation,[status(thm)],[c_101,c_22129]) ).
cnf(c_22163,plain,
member(sK15,inverse2(sK14,sK12)),
inference(global_subsumption_just,[status(thm)],[c_22139,c_2837,c_3354,c_3352,c_5008,c_8822]) ).
cnf(c_22275,plain,
ilf_type(cross_product(X0,X1),relation_type(X0,X1)),
inference(superposition,[status(thm)],[c_22086,c_1119]) ).
cnf(c_22460,plain,
( ~ ilf_type(X0,relation_type(X1,X2))
| ~ member(X3,X0)
| member(X3,cross_product(X1,X2)) ),
inference(superposition,[status(thm)],[c_21918,c_474]) ).
cnf(c_22521,plain,
( ~ member(X0,sK14)
| member(X0,cross_product(sK11,sK13)) ),
inference(superposition,[status(thm)],[c_105,c_22460]) ).
cnf(c_22563,plain,
( ~ ilf_type(cross_product(sK11,sK13),relation_type(X0,X1))
| ~ member(ordered_pair(X2,X3),sK14)
| member(X3,X1) ),
inference(superposition,[status(thm)],[c_22521,c_646]) ).
cnf(c_22601,plain,
( ~ member(ordered_pair(X0,X1),sK14)
| member(X1,sK13) ),
inference(superposition,[status(thm)],[c_22275,c_22563]) ).
cnf(c_23442,plain,
( ~ ilf_type(sK0(X0,sK15,sK14),member_type(sK13))
| ~ member(sK0(X0,sK15,sK14),sK12)
| ~ member(sK15,inverse2(sK14,X0))
| ~ ilf_type(sK14,binary_relation_type) ),
inference(superposition,[status(thm)],[c_468,c_21815]) ).
cnf(c_23450,plain,
( ~ member(X0,inverse2(sK14,X1))
| ~ ilf_type(sK14,binary_relation_type)
| member(sK0(X1,X0,sK14),sK13) ),
inference(superposition,[status(thm)],[c_468,c_22601]) ).
cnf(c_23671,plain,
( ~ member(sK15,inverse2(sK14,X0))
| ~ member(sK0(X0,sK15,sK14),sK12)
| ~ ilf_type(sK0(X0,sK15,sK14),member_type(sK13)) ),
inference(global_subsumption_just,[status(thm)],[c_23442,c_10952]) ).
cnf(c_23672,plain,
( ~ ilf_type(sK0(X0,sK15,sK14),member_type(sK13))
| ~ member(sK0(X0,sK15,sK14),sK12)
| ~ member(sK15,inverse2(sK14,X0)) ),
inference(renaming,[status(thm)],[c_23671]) ).
cnf(c_23679,plain,
( ~ member(sK0(X0,sK15,sK14),sK12)
| ~ member(sK0(X0,sK15,sK14),sK13)
| ~ member(sK15,inverse2(sK14,X0)) ),
inference(superposition,[status(thm)],[c_1138,c_23672]) ).
cnf(c_23691,plain,
( ~ member(sK0(sK12,sK15,sK14),sK13)
| ~ member(sK15,inverse2(sK14,sK12))
| ~ ilf_type(sK14,binary_relation_type) ),
inference(superposition,[status(thm)],[c_467,c_23679]) ).
cnf(c_23692,plain,
( ~ member(sK0(sK12,sK15,sK14),sK13)
| ~ ilf_type(sK14,binary_relation_type) ),
inference(forward_subsumption_resolution,[status(thm)],[c_23691,c_22163]) ).
cnf(c_23695,plain,
~ member(sK0(sK12,sK15,sK14),sK13),
inference(global_subsumption_just,[status(thm)],[c_23692,c_12407]) ).
cnf(c_24081,plain,
( ~ member(X0,inverse2(sK14,X1))
| member(sK0(X1,X0,sK14),sK13) ),
inference(global_subsumption_just,[status(thm)],[c_23450,c_2837,c_5008,c_23450]) ).
cnf(c_24094,plain,
~ member(sK15,inverse2(sK14,sK12)),
inference(superposition,[status(thm)],[c_24081,c_23695]) ).
cnf(c_24095,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_24094,c_22163]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET686+3 : TPTP v8.1.2. Released v2.2.0.
% 0.07/0.13 % Command : run_iprover %s %d THM
% 0.14/0.35 % Computer : n002.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 10:46:33 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.20/0.48 Running first-order theorem proving
% 0.20/0.48 Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 7.31/1.66 % SZS status Started for theBenchmark.p
% 7.31/1.66 % SZS status Theorem for theBenchmark.p
% 7.31/1.66
% 7.31/1.66 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 7.31/1.66
% 7.31/1.66 ------ iProver source info
% 7.31/1.66
% 7.31/1.66 git: date: 2023-05-31 18:12:56 +0000
% 7.31/1.66 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 7.31/1.66 git: non_committed_changes: false
% 7.31/1.66 git: last_make_outside_of_git: false
% 7.31/1.66
% 7.31/1.66 ------ Parsing...
% 7.31/1.66 ------ Clausification by vclausify_rel & Parsing by iProver...
% 7.31/1.66
% 7.31/1.66 ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e
% 7.31/1.66
% 7.31/1.66 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 7.31/1.66
% 7.31/1.66 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 7.31/1.66 ------ Proving...
% 7.31/1.66 ------ Problem Properties
% 7.31/1.66
% 7.31/1.66
% 7.31/1.66 clauses 43
% 7.31/1.66 conjectures 9
% 7.31/1.66 EPR 9
% 7.31/1.66 Horn 34
% 7.31/1.66 unary 11
% 7.31/1.66 binary 21
% 7.31/1.66 lits 88
% 7.31/1.66 lits eq 6
% 7.31/1.66 fd_pure 0
% 7.31/1.66 fd_pseudo 0
% 7.31/1.66 fd_cond 0
% 7.31/1.66 fd_pseudo_cond 2
% 7.31/1.66 AC symbols 0
% 7.31/1.66
% 7.31/1.66 ------ Schedule dynamic 5 is on
% 7.31/1.66
% 7.31/1.66 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 7.31/1.66
% 7.31/1.66
% 7.31/1.66 ------
% 7.31/1.66 Current options:
% 7.31/1.66 ------
% 7.31/1.66
% 7.31/1.66
% 7.31/1.66
% 7.31/1.66
% 7.31/1.66 ------ Proving...
% 7.31/1.66
% 7.31/1.66
% 7.31/1.66 % SZS status Theorem for theBenchmark.p
% 7.31/1.66
% 7.31/1.66 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 7.31/1.67
% 7.31/1.67
%------------------------------------------------------------------------------