TSTP Solution File: SET684+3 by iProver---3.8
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%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SET684+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n022.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 15:09:07 EDT 2023
% Result : Theorem 25.36s 5.34s
% Output : CNFRefutation 25.36s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f190)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,binary_relation_type)
=> ! [X3] :
( ilf_type(X3,binary_relation_type)
=> ( member(ordered_pair(X0,X1),compose(X2,X3))
<=> ? [X4] :
( member(ordered_pair(X4,X1),X3)
& member(ordered_pair(X0,X4),X2)
& ilf_type(X4,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(f26,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',p26) ).
fof(f27,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,relation_type(X0,X1))
=> ! [X4] :
( ilf_type(X4,relation_type(X1,X2))
=> compose5(X0,X1,X2,X3,X4) = compose(X3,X4) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p27) ).
fof(f29,axiom,
! [X0] : ilf_type(X0,set_type),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p29) ).
fof(f30,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,X1))
=> ! [X4] :
( ilf_type(X4,relation_type(X1,X2))
=> ! [X5] :
( ilf_type(X5,member_type(X0))
=> ! [X6] :
( ilf_type(X6,member_type(X2))
=> ( member(ordered_pair(X5,X6),compose5(X0,X1,X2,X3,X4))
<=> ? [X7] :
( member(ordered_pair(X7,X6),X4)
& member(ordered_pair(X5,X7),X3)
& ilf_type(X7,member_type(X1)) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_relset_1_51) ).
fof(f31,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,X1))
=> ! [X4] :
( ilf_type(X4,relation_type(X1,X2))
=> ! [X5] :
( ilf_type(X5,member_type(X0))
=> ! [X6] :
( ilf_type(X6,member_type(X2))
=> ( member(ordered_pair(X5,X6),compose5(X0,X1,X2,X3,X4))
<=> ? [X7] :
( member(ordered_pair(X7,X6),X4)
& member(ordered_pair(X5,X7),X3)
& ilf_type(X7,member_type(X1)) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[],[f30]) ).
fof(f32,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(f33,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ( member(ordered_pair(X0,X1),compose(X2,X3))
<=> ? [X4] :
( member(ordered_pair(X4,X1),X3)
& member(ordered_pair(X0,X4),X2)
& ilf_type(X4,set_type) ) )
| ~ ilf_type(X3,binary_relation_type) )
| ~ ilf_type(X2,binary_relation_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f1]) ).
fof(f34,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(f35,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,[],[f34]) ).
fof(f38,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,[],[f32]) ).
fof(f40,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(f41,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,[],[f40]) ).
fof(f44,plain,
! [X0] :
( ( empty(X0)
<=> ! [X1] :
( ~ member(X1,X0)
| ~ ilf_type(X1,set_type) ) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f9]) ).
fof(f64,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,[],[f26]) ).
fof(f65,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( compose5(X0,X1,X2,X3,X4) = compose(X3,X4)
| ~ ilf_type(X4,relation_type(X1,X2)) )
| ~ ilf_type(X3,relation_type(X0,X1)) )
| ~ ilf_type(X2,set_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f27]) ).
fof(f67,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ? [X6] :
( ( member(ordered_pair(X5,X6),compose5(X0,X1,X2,X3,X4))
<~> ? [X7] :
( member(ordered_pair(X7,X6),X4)
& member(ordered_pair(X5,X7),X3)
& ilf_type(X7,member_type(X1)) ) )
& ilf_type(X6,member_type(X2)) )
& ilf_type(X5,member_type(X0)) )
& ilf_type(X4,relation_type(X1,X2)) )
& ilf_type(X3,relation_type(X0,X1)) )
& ilf_type(X2,set_type)
& ~ empty(X2) )
& ilf_type(X1,set_type)
& ~ empty(X1) )
& ilf_type(X0,set_type)
& ~ empty(X0) ),
inference(ennf_transformation,[],[f31]) ).
fof(f68,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ? [X6] :
( ( member(ordered_pair(X5,X6),compose5(X0,X1,X2,X3,X4))
<~> ? [X7] :
( member(ordered_pair(X7,X6),X4)
& member(ordered_pair(X5,X7),X3)
& ilf_type(X7,member_type(X1)) ) )
& ilf_type(X6,member_type(X2)) )
& ilf_type(X5,member_type(X0)) )
& ilf_type(X4,relation_type(X1,X2)) )
& ilf_type(X3,relation_type(X0,X1)) )
& ilf_type(X2,set_type)
& ~ empty(X2) )
& ilf_type(X1,set_type)
& ~ empty(X1) )
& ilf_type(X0,set_type)
& ~ empty(X0) ),
inference(flattening,[],[f67]) ).
fof(f69,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ( ( member(ordered_pair(X0,X1),compose(X2,X3))
| ! [X4] :
( ~ member(ordered_pair(X4,X1),X3)
| ~ member(ordered_pair(X0,X4),X2)
| ~ ilf_type(X4,set_type) ) )
& ( ? [X4] :
( member(ordered_pair(X4,X1),X3)
& member(ordered_pair(X0,X4),X2)
& ilf_type(X4,set_type) )
| ~ member(ordered_pair(X0,X1),compose(X2,X3)) ) )
| ~ ilf_type(X3,binary_relation_type) )
| ~ ilf_type(X2,binary_relation_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f33]) ).
fof(f70,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ( ( member(ordered_pair(X0,X1),compose(X2,X3))
| ! [X4] :
( ~ member(ordered_pair(X4,X1),X3)
| ~ member(ordered_pair(X0,X4),X2)
| ~ ilf_type(X4,set_type) ) )
& ( ? [X5] :
( member(ordered_pair(X5,X1),X3)
& member(ordered_pair(X0,X5),X2)
& ilf_type(X5,set_type) )
| ~ member(ordered_pair(X0,X1),compose(X2,X3)) ) )
| ~ ilf_type(X3,binary_relation_type) )
| ~ ilf_type(X2,binary_relation_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(rectify,[],[f69]) ).
fof(f71,plain,
! [X0,X1,X2,X3] :
( ? [X5] :
( member(ordered_pair(X5,X1),X3)
& member(ordered_pair(X0,X5),X2)
& ilf_type(X5,set_type) )
=> ( member(ordered_pair(sK0(X0,X1,X2,X3),X1),X3)
& member(ordered_pair(X0,sK0(X0,X1,X2,X3)),X2)
& ilf_type(sK0(X0,X1,X2,X3),set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f72,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ( ( member(ordered_pair(X0,X1),compose(X2,X3))
| ! [X4] :
( ~ member(ordered_pair(X4,X1),X3)
| ~ member(ordered_pair(X0,X4),X2)
| ~ ilf_type(X4,set_type) ) )
& ( ( member(ordered_pair(sK0(X0,X1,X2,X3),X1),X3)
& member(ordered_pair(X0,sK0(X0,X1,X2,X3)),X2)
& ilf_type(sK0(X0,X1,X2,X3),set_type) )
| ~ member(ordered_pair(X0,X1),compose(X2,X3)) ) )
| ~ ilf_type(X3,binary_relation_type) )
| ~ ilf_type(X2,binary_relation_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f70,f71]) ).
fof(f76,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,[],[f41]) ).
fof(f79,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,[],[f44]) ).
fof(f80,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,[],[f79]) ).
fof(f81,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(f82,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])],[f80,f81]) ).
fof(f105,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ? [X6] :
( ( ! [X7] :
( ~ member(ordered_pair(X7,X6),X4)
| ~ member(ordered_pair(X5,X7),X3)
| ~ ilf_type(X7,member_type(X1)) )
| ~ member(ordered_pair(X5,X6),compose5(X0,X1,X2,X3,X4)) )
& ( ? [X7] :
( member(ordered_pair(X7,X6),X4)
& member(ordered_pair(X5,X7),X3)
& ilf_type(X7,member_type(X1)) )
| member(ordered_pair(X5,X6),compose5(X0,X1,X2,X3,X4)) )
& ilf_type(X6,member_type(X2)) )
& ilf_type(X5,member_type(X0)) )
& ilf_type(X4,relation_type(X1,X2)) )
& ilf_type(X3,relation_type(X0,X1)) )
& ilf_type(X2,set_type)
& ~ empty(X2) )
& ilf_type(X1,set_type)
& ~ empty(X1) )
& ilf_type(X0,set_type)
& ~ empty(X0) ),
inference(nnf_transformation,[],[f68]) ).
fof(f106,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ? [X6] :
( ( ! [X7] :
( ~ member(ordered_pair(X7,X6),X4)
| ~ member(ordered_pair(X5,X7),X3)
| ~ ilf_type(X7,member_type(X1)) )
| ~ member(ordered_pair(X5,X6),compose5(X0,X1,X2,X3,X4)) )
& ( ? [X7] :
( member(ordered_pair(X7,X6),X4)
& member(ordered_pair(X5,X7),X3)
& ilf_type(X7,member_type(X1)) )
| member(ordered_pair(X5,X6),compose5(X0,X1,X2,X3,X4)) )
& ilf_type(X6,member_type(X2)) )
& ilf_type(X5,member_type(X0)) )
& ilf_type(X4,relation_type(X1,X2)) )
& ilf_type(X3,relation_type(X0,X1)) )
& ilf_type(X2,set_type)
& ~ empty(X2) )
& ilf_type(X1,set_type)
& ~ empty(X1) )
& ilf_type(X0,set_type)
& ~ empty(X0) ),
inference(flattening,[],[f105]) ).
fof(f107,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ? [X6] :
( ( ! [X7] :
( ~ member(ordered_pair(X7,X6),X4)
| ~ member(ordered_pair(X5,X7),X3)
| ~ ilf_type(X7,member_type(X1)) )
| ~ member(ordered_pair(X5,X6),compose5(X0,X1,X2,X3,X4)) )
& ( ? [X8] :
( member(ordered_pair(X8,X6),X4)
& member(ordered_pair(X5,X8),X3)
& ilf_type(X8,member_type(X1)) )
| member(ordered_pair(X5,X6),compose5(X0,X1,X2,X3,X4)) )
& ilf_type(X6,member_type(X2)) )
& ilf_type(X5,member_type(X0)) )
& ilf_type(X4,relation_type(X1,X2)) )
& ilf_type(X3,relation_type(X0,X1)) )
& ilf_type(X2,set_type)
& ~ empty(X2) )
& ilf_type(X1,set_type)
& ~ empty(X1) )
& ilf_type(X0,set_type)
& ~ empty(X0) ),
inference(rectify,[],[f106]) ).
fof(f108,plain,
( ? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ? [X6] :
( ( ! [X7] :
( ~ member(ordered_pair(X7,X6),X4)
| ~ member(ordered_pair(X5,X7),X3)
| ~ ilf_type(X7,member_type(X1)) )
| ~ member(ordered_pair(X5,X6),compose5(X0,X1,X2,X3,X4)) )
& ( ? [X8] :
( member(ordered_pair(X8,X6),X4)
& member(ordered_pair(X5,X8),X3)
& ilf_type(X8,member_type(X1)) )
| member(ordered_pair(X5,X6),compose5(X0,X1,X2,X3,X4)) )
& ilf_type(X6,member_type(X2)) )
& ilf_type(X5,member_type(X0)) )
& ilf_type(X4,relation_type(X1,X2)) )
& ilf_type(X3,relation_type(X0,X1)) )
& 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] :
( ? [X6] :
( ( ! [X7] :
( ~ member(ordered_pair(X7,X6),X4)
| ~ member(ordered_pair(X5,X7),X3)
| ~ ilf_type(X7,member_type(X1)) )
| ~ member(ordered_pair(X5,X6),compose5(sK11,X1,X2,X3,X4)) )
& ( ? [X8] :
( member(ordered_pair(X8,X6),X4)
& member(ordered_pair(X5,X8),X3)
& ilf_type(X8,member_type(X1)) )
| member(ordered_pair(X5,X6),compose5(sK11,X1,X2,X3,X4)) )
& ilf_type(X6,member_type(X2)) )
& ilf_type(X5,member_type(sK11)) )
& ilf_type(X4,relation_type(X1,X2)) )
& ilf_type(X3,relation_type(sK11,X1)) )
& 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(f109,plain,
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ? [X6] :
( ( ! [X7] :
( ~ member(ordered_pair(X7,X6),X4)
| ~ member(ordered_pair(X5,X7),X3)
| ~ ilf_type(X7,member_type(X1)) )
| ~ member(ordered_pair(X5,X6),compose5(sK11,X1,X2,X3,X4)) )
& ( ? [X8] :
( member(ordered_pair(X8,X6),X4)
& member(ordered_pair(X5,X8),X3)
& ilf_type(X8,member_type(X1)) )
| member(ordered_pair(X5,X6),compose5(sK11,X1,X2,X3,X4)) )
& ilf_type(X6,member_type(X2)) )
& ilf_type(X5,member_type(sK11)) )
& ilf_type(X4,relation_type(X1,X2)) )
& ilf_type(X3,relation_type(sK11,X1)) )
& ilf_type(X2,set_type)
& ~ empty(X2) )
& ilf_type(X1,set_type)
& ~ empty(X1) )
=> ( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ? [X6] :
( ( ! [X7] :
( ~ member(ordered_pair(X7,X6),X4)
| ~ member(ordered_pair(X5,X7),X3)
| ~ ilf_type(X7,member_type(sK12)) )
| ~ member(ordered_pair(X5,X6),compose5(sK11,sK12,X2,X3,X4)) )
& ( ? [X8] :
( member(ordered_pair(X8,X6),X4)
& member(ordered_pair(X5,X8),X3)
& ilf_type(X8,member_type(sK12)) )
| member(ordered_pair(X5,X6),compose5(sK11,sK12,X2,X3,X4)) )
& ilf_type(X6,member_type(X2)) )
& ilf_type(X5,member_type(sK11)) )
& ilf_type(X4,relation_type(sK12,X2)) )
& ilf_type(X3,relation_type(sK11,sK12)) )
& ilf_type(X2,set_type)
& ~ empty(X2) )
& ilf_type(sK12,set_type)
& ~ empty(sK12) ) ),
introduced(choice_axiom,[]) ).
fof(f110,plain,
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ? [X6] :
( ( ! [X7] :
( ~ member(ordered_pair(X7,X6),X4)
| ~ member(ordered_pair(X5,X7),X3)
| ~ ilf_type(X7,member_type(sK12)) )
| ~ member(ordered_pair(X5,X6),compose5(sK11,sK12,X2,X3,X4)) )
& ( ? [X8] :
( member(ordered_pair(X8,X6),X4)
& member(ordered_pair(X5,X8),X3)
& ilf_type(X8,member_type(sK12)) )
| member(ordered_pair(X5,X6),compose5(sK11,sK12,X2,X3,X4)) )
& ilf_type(X6,member_type(X2)) )
& ilf_type(X5,member_type(sK11)) )
& ilf_type(X4,relation_type(sK12,X2)) )
& ilf_type(X3,relation_type(sK11,sK12)) )
& ilf_type(X2,set_type)
& ~ empty(X2) )
=> ( ? [X3] :
( ? [X4] :
( ? [X5] :
( ? [X6] :
( ( ! [X7] :
( ~ member(ordered_pair(X7,X6),X4)
| ~ member(ordered_pair(X5,X7),X3)
| ~ ilf_type(X7,member_type(sK12)) )
| ~ member(ordered_pair(X5,X6),compose5(sK11,sK12,sK13,X3,X4)) )
& ( ? [X8] :
( member(ordered_pair(X8,X6),X4)
& member(ordered_pair(X5,X8),X3)
& ilf_type(X8,member_type(sK12)) )
| member(ordered_pair(X5,X6),compose5(sK11,sK12,sK13,X3,X4)) )
& ilf_type(X6,member_type(sK13)) )
& ilf_type(X5,member_type(sK11)) )
& ilf_type(X4,relation_type(sK12,sK13)) )
& ilf_type(X3,relation_type(sK11,sK12)) )
& ilf_type(sK13,set_type)
& ~ empty(sK13) ) ),
introduced(choice_axiom,[]) ).
fof(f111,plain,
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ? [X6] :
( ( ! [X7] :
( ~ member(ordered_pair(X7,X6),X4)
| ~ member(ordered_pair(X5,X7),X3)
| ~ ilf_type(X7,member_type(sK12)) )
| ~ member(ordered_pair(X5,X6),compose5(sK11,sK12,sK13,X3,X4)) )
& ( ? [X8] :
( member(ordered_pair(X8,X6),X4)
& member(ordered_pair(X5,X8),X3)
& ilf_type(X8,member_type(sK12)) )
| member(ordered_pair(X5,X6),compose5(sK11,sK12,sK13,X3,X4)) )
& ilf_type(X6,member_type(sK13)) )
& ilf_type(X5,member_type(sK11)) )
& ilf_type(X4,relation_type(sK12,sK13)) )
& ilf_type(X3,relation_type(sK11,sK12)) )
=> ( ? [X4] :
( ? [X5] :
( ? [X6] :
( ( ! [X7] :
( ~ member(ordered_pair(X7,X6),X4)
| ~ member(ordered_pair(X5,X7),sK14)
| ~ ilf_type(X7,member_type(sK12)) )
| ~ member(ordered_pair(X5,X6),compose5(sK11,sK12,sK13,sK14,X4)) )
& ( ? [X8] :
( member(ordered_pair(X8,X6),X4)
& member(ordered_pair(X5,X8),sK14)
& ilf_type(X8,member_type(sK12)) )
| member(ordered_pair(X5,X6),compose5(sK11,sK12,sK13,sK14,X4)) )
& ilf_type(X6,member_type(sK13)) )
& ilf_type(X5,member_type(sK11)) )
& ilf_type(X4,relation_type(sK12,sK13)) )
& ilf_type(sK14,relation_type(sK11,sK12)) ) ),
introduced(choice_axiom,[]) ).
fof(f112,plain,
( ? [X4] :
( ? [X5] :
( ? [X6] :
( ( ! [X7] :
( ~ member(ordered_pair(X7,X6),X4)
| ~ member(ordered_pair(X5,X7),sK14)
| ~ ilf_type(X7,member_type(sK12)) )
| ~ member(ordered_pair(X5,X6),compose5(sK11,sK12,sK13,sK14,X4)) )
& ( ? [X8] :
( member(ordered_pair(X8,X6),X4)
& member(ordered_pair(X5,X8),sK14)
& ilf_type(X8,member_type(sK12)) )
| member(ordered_pair(X5,X6),compose5(sK11,sK12,sK13,sK14,X4)) )
& ilf_type(X6,member_type(sK13)) )
& ilf_type(X5,member_type(sK11)) )
& ilf_type(X4,relation_type(sK12,sK13)) )
=> ( ? [X5] :
( ? [X6] :
( ( ! [X7] :
( ~ member(ordered_pair(X7,X6),sK15)
| ~ member(ordered_pair(X5,X7),sK14)
| ~ ilf_type(X7,member_type(sK12)) )
| ~ member(ordered_pair(X5,X6),compose5(sK11,sK12,sK13,sK14,sK15)) )
& ( ? [X8] :
( member(ordered_pair(X8,X6),sK15)
& member(ordered_pair(X5,X8),sK14)
& ilf_type(X8,member_type(sK12)) )
| member(ordered_pair(X5,X6),compose5(sK11,sK12,sK13,sK14,sK15)) )
& ilf_type(X6,member_type(sK13)) )
& ilf_type(X5,member_type(sK11)) )
& ilf_type(sK15,relation_type(sK12,sK13)) ) ),
introduced(choice_axiom,[]) ).
fof(f113,plain,
( ? [X5] :
( ? [X6] :
( ( ! [X7] :
( ~ member(ordered_pair(X7,X6),sK15)
| ~ member(ordered_pair(X5,X7),sK14)
| ~ ilf_type(X7,member_type(sK12)) )
| ~ member(ordered_pair(X5,X6),compose5(sK11,sK12,sK13,sK14,sK15)) )
& ( ? [X8] :
( member(ordered_pair(X8,X6),sK15)
& member(ordered_pair(X5,X8),sK14)
& ilf_type(X8,member_type(sK12)) )
| member(ordered_pair(X5,X6),compose5(sK11,sK12,sK13,sK14,sK15)) )
& ilf_type(X6,member_type(sK13)) )
& ilf_type(X5,member_type(sK11)) )
=> ( ? [X6] :
( ( ! [X7] :
( ~ member(ordered_pair(X7,X6),sK15)
| ~ member(ordered_pair(sK16,X7),sK14)
| ~ ilf_type(X7,member_type(sK12)) )
| ~ member(ordered_pair(sK16,X6),compose5(sK11,sK12,sK13,sK14,sK15)) )
& ( ? [X8] :
( member(ordered_pair(X8,X6),sK15)
& member(ordered_pair(sK16,X8),sK14)
& ilf_type(X8,member_type(sK12)) )
| member(ordered_pair(sK16,X6),compose5(sK11,sK12,sK13,sK14,sK15)) )
& ilf_type(X6,member_type(sK13)) )
& ilf_type(sK16,member_type(sK11)) ) ),
introduced(choice_axiom,[]) ).
fof(f114,plain,
( ? [X6] :
( ( ! [X7] :
( ~ member(ordered_pair(X7,X6),sK15)
| ~ member(ordered_pair(sK16,X7),sK14)
| ~ ilf_type(X7,member_type(sK12)) )
| ~ member(ordered_pair(sK16,X6),compose5(sK11,sK12,sK13,sK14,sK15)) )
& ( ? [X8] :
( member(ordered_pair(X8,X6),sK15)
& member(ordered_pair(sK16,X8),sK14)
& ilf_type(X8,member_type(sK12)) )
| member(ordered_pair(sK16,X6),compose5(sK11,sK12,sK13,sK14,sK15)) )
& ilf_type(X6,member_type(sK13)) )
=> ( ( ! [X7] :
( ~ member(ordered_pair(X7,sK17),sK15)
| ~ member(ordered_pair(sK16,X7),sK14)
| ~ ilf_type(X7,member_type(sK12)) )
| ~ member(ordered_pair(sK16,sK17),compose5(sK11,sK12,sK13,sK14,sK15)) )
& ( ? [X8] :
( member(ordered_pair(X8,sK17),sK15)
& member(ordered_pair(sK16,X8),sK14)
& ilf_type(X8,member_type(sK12)) )
| member(ordered_pair(sK16,sK17),compose5(sK11,sK12,sK13,sK14,sK15)) )
& ilf_type(sK17,member_type(sK13)) ) ),
introduced(choice_axiom,[]) ).
fof(f115,plain,
( ? [X8] :
( member(ordered_pair(X8,sK17),sK15)
& member(ordered_pair(sK16,X8),sK14)
& ilf_type(X8,member_type(sK12)) )
=> ( member(ordered_pair(sK18,sK17),sK15)
& member(ordered_pair(sK16,sK18),sK14)
& ilf_type(sK18,member_type(sK12)) ) ),
introduced(choice_axiom,[]) ).
fof(f116,plain,
( ( ! [X7] :
( ~ member(ordered_pair(X7,sK17),sK15)
| ~ member(ordered_pair(sK16,X7),sK14)
| ~ ilf_type(X7,member_type(sK12)) )
| ~ member(ordered_pair(sK16,sK17),compose5(sK11,sK12,sK13,sK14,sK15)) )
& ( ( member(ordered_pair(sK18,sK17),sK15)
& member(ordered_pair(sK16,sK18),sK14)
& ilf_type(sK18,member_type(sK12)) )
| member(ordered_pair(sK16,sK17),compose5(sK11,sK12,sK13,sK14,sK15)) )
& ilf_type(sK17,member_type(sK13))
& ilf_type(sK16,member_type(sK11))
& ilf_type(sK15,relation_type(sK12,sK13))
& ilf_type(sK14,relation_type(sK11,sK12))
& 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,sK17,sK18])],[f107,f115,f114,f113,f112,f111,f110,f109,f108]) ).
fof(f118,plain,
! [X2,X3,X0,X1] :
( member(ordered_pair(X0,sK0(X0,X1,X2,X3)),X2)
| ~ member(ordered_pair(X0,X1),compose(X2,X3))
| ~ ilf_type(X3,binary_relation_type)
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f72]) ).
fof(f119,plain,
! [X2,X3,X0,X1] :
( member(ordered_pair(sK0(X0,X1,X2,X3),X1),X3)
| ~ member(ordered_pair(X0,X1),compose(X2,X3))
| ~ ilf_type(X3,binary_relation_type)
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f72]) ).
fof(f120,plain,
! [X2,X3,X0,X1,X4] :
( member(ordered_pair(X0,X1),compose(X2,X3))
| ~ member(ordered_pair(X4,X1),X3)
| ~ member(ordered_pair(X0,X4),X2)
| ~ ilf_type(X4,set_type)
| ~ ilf_type(X3,binary_relation_type)
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f72]) ).
fof(f121,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,[],[f35]) ).
fof(f127,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,[],[f38]) ).
fof(f130,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,[],[f76]) ).
fof(f132,plain,
! [X2,X0] :
( ~ member(X2,X0)
| ~ ilf_type(X2,set_type)
| ~ empty(X0)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f82]) ).
fof(f167,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,[],[f64]) ).
fof(f168,plain,
! [X2,X3,X0,X1,X4] :
( compose5(X0,X1,X2,X3,X4) = compose(X3,X4)
| ~ ilf_type(X4,relation_type(X1,X2))
| ~ ilf_type(X3,relation_type(X0,X1))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f65]) ).
fof(f170,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[],[f29]) ).
fof(f177,plain,
ilf_type(sK14,relation_type(sK11,sK12)),
inference(cnf_transformation,[],[f116]) ).
fof(f178,plain,
ilf_type(sK15,relation_type(sK12,sK13)),
inference(cnf_transformation,[],[f116]) ).
fof(f181,plain,
( ilf_type(sK18,member_type(sK12))
| member(ordered_pair(sK16,sK17),compose5(sK11,sK12,sK13,sK14,sK15)) ),
inference(cnf_transformation,[],[f116]) ).
fof(f182,plain,
( member(ordered_pair(sK16,sK18),sK14)
| member(ordered_pair(sK16,sK17),compose5(sK11,sK12,sK13,sK14,sK15)) ),
inference(cnf_transformation,[],[f116]) ).
fof(f183,plain,
( member(ordered_pair(sK18,sK17),sK15)
| member(ordered_pair(sK16,sK17),compose5(sK11,sK12,sK13,sK14,sK15)) ),
inference(cnf_transformation,[],[f116]) ).
fof(f184,plain,
! [X7] :
( ~ member(ordered_pair(X7,sK17),sK15)
| ~ member(ordered_pair(sK16,X7),sK14)
| ~ ilf_type(X7,member_type(sK12))
| ~ member(ordered_pair(sK16,sK17),compose5(sK11,sK12,sK13,sK14,sK15)) ),
inference(cnf_transformation,[],[f116]) ).
cnf(c_49,plain,
( ~ member(ordered_pair(X0,X1),X2)
| ~ member(ordered_pair(X1,X3),X4)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X4,binary_relation_type)
| member(ordered_pair(X0,X3),compose(X2,X4)) ),
inference(cnf_transformation,[],[f120]) ).
cnf(c_50,plain,
( ~ member(ordered_pair(X0,X1),compose(X2,X3))
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X3,binary_relation_type)
| member(ordered_pair(sK0(X0,X1,X2,X3),X1),X3) ),
inference(cnf_transformation,[],[f119]) ).
cnf(c_51,plain,
( ~ member(ordered_pair(X0,X1),compose(X2,X3))
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X3,binary_relation_type)
| member(ordered_pair(X0,sK0(X0,X1,X2,X3)),X2) ),
inference(cnf_transformation,[],[f118]) ).
cnf(c_54,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,[],[f121]) ).
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,[],[f127]) ).
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,[],[f130]) ).
cnf(c_66,plain,
( ~ member(X0,X1)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ empty(X1) ),
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,[],[f190]) ).
cnf(c_97,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,[],[f167]) ).
cnf(c_98,plain,
( ~ ilf_type(X0,relation_type(X1,X2))
| ~ ilf_type(X3,relation_type(X2,X4))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X4,set_type)
| compose5(X1,X2,X4,X0,X3) = compose(X0,X3) ),
inference(cnf_transformation,[],[f168]) ).
cnf(c_100,plain,
ilf_type(X0,set_type),
inference(cnf_transformation,[],[f170]) ).
cnf(c_101,negated_conjecture,
( ~ member(ordered_pair(sK16,sK17),compose5(sK11,sK12,sK13,sK14,sK15))
| ~ member(ordered_pair(X0,sK17),sK15)
| ~ member(ordered_pair(sK16,X0),sK14)
| ~ ilf_type(X0,member_type(sK12)) ),
inference(cnf_transformation,[],[f184]) ).
cnf(c_102,negated_conjecture,
( member(ordered_pair(sK16,sK17),compose5(sK11,sK12,sK13,sK14,sK15))
| member(ordered_pair(sK18,sK17),sK15) ),
inference(cnf_transformation,[],[f183]) ).
cnf(c_103,negated_conjecture,
( member(ordered_pair(sK16,sK17),compose5(sK11,sK12,sK13,sK14,sK15))
| member(ordered_pair(sK16,sK18),sK14) ),
inference(cnf_transformation,[],[f182]) ).
cnf(c_104,negated_conjecture,
( member(ordered_pair(sK16,sK17),compose5(sK11,sK12,sK13,sK14,sK15))
| ilf_type(sK18,member_type(sK12)) ),
inference(cnf_transformation,[],[f181]) ).
cnf(c_107,negated_conjecture,
ilf_type(sK15,relation_type(sK12,sK13)),
inference(cnf_transformation,[],[f178]) ).
cnf(c_108,negated_conjecture,
ilf_type(sK14,relation_type(sK11,sK12)),
inference(cnf_transformation,[],[f177]) ).
cnf(c_187,plain,
( ~ relation_like(X0)
| ilf_type(X0,binary_relation_type) ),
inference(global_subsumption_just,[status(thm)],[c_72,c_100,c_72]) ).
cnf(c_249,plain,
( ilf_type(X0,member_type(X1))
| ~ ilf_type(X1,set_type)
| ~ member(X0,X1) ),
inference(global_subsumption_just,[status(thm)],[c_61,c_100,c_66,c_61]) ).
cnf(c_250,plain,
( ~ member(X0,X1)
| ~ ilf_type(X1,set_type)
| ilf_type(X0,member_type(X1)) ),
inference(renaming,[status(thm)],[c_249]) ).
cnf(c_269,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_54,c_100,c_54]) ).
cnf(c_270,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_269]) ).
cnf(c_285,plain,
( ~ member(ordered_pair(X0,X1),compose(X2,X3))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X3,binary_relation_type)
| member(ordered_pair(X0,sK0(X0,X1,X2,X3)),X2) ),
inference(global_subsumption_just,[status(thm)],[c_51,c_100,c_51]) ).
cnf(c_287,plain,
( ~ member(ordered_pair(X0,X1),compose(X2,X3))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X3,binary_relation_type)
| member(ordered_pair(sK0(X0,X1,X2,X3),X1),X3) ),
inference(global_subsumption_just,[status(thm)],[c_50,c_100,c_50]) ).
cnf(c_291,plain,
( ~ member(ordered_pair(X1,X3),X4)
| ~ member(ordered_pair(X0,X1),X2)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X4,binary_relation_type)
| member(ordered_pair(X0,X3),compose(X2,X4)) ),
inference(global_subsumption_just,[status(thm)],[c_49,c_100,c_49]) ).
cnf(c_292,plain,
( ~ member(ordered_pair(X0,X1),X2)
| ~ member(ordered_pair(X1,X3),X4)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X4,binary_relation_type)
| member(ordered_pair(X0,X3),compose(X2,X4)) ),
inference(renaming,[status(thm)],[c_291]) ).
cnf(c_452,plain,
( ~ member(X0,X1)
| ilf_type(X0,member_type(X1)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_250,c_100]) ).
cnf(c_454,plain,
( ~ member(ordered_pair(X0,X1),compose(X2,X3))
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X3,binary_relation_type)
| member(ordered_pair(sK0(X0,X1,X2,X3),X1),X3) ),
inference(backward_subsumption_resolution,[status(thm)],[c_287,c_100]) ).
cnf(c_455,plain,
( ~ member(ordered_pair(X0,X1),compose(X2,X3))
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X3,binary_relation_type)
| member(ordered_pair(X0,sK0(X0,X1,X2,X3)),X2) ),
inference(backward_subsumption_resolution,[status(thm)],[c_285,c_100]) ).
cnf(c_457,plain,
( ~ member(ordered_pair(X0,X1),X2)
| ~ member(ordered_pair(X1,X3),X4)
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X4,binary_relation_type)
| member(ordered_pair(X0,X3),compose(X2,X4)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_292,c_100]) ).
cnf(c_458,plain,
( ~ ilf_type(X0,relation_type(X1,X2))
| ~ ilf_type(X3,relation_type(X2,X4))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X4,set_type)
| compose5(X1,X2,X4,X0,X3) = compose(X0,X3) ),
inference(backward_subsumption_resolution,[status(thm)],[c_98,c_100]) ).
cnf(c_460,plain,
( ~ ilf_type(X0,subset_type(cross_product(X1,X2)))
| ~ ilf_type(X2,set_type)
| relation_like(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[c_97,c_100]) ).
cnf(c_462,plain,
( ~ ilf_type(X0,relation_type(X1,X2))
| ~ ilf_type(X2,set_type)
| ilf_type(X0,subset_type(cross_product(X1,X2))) ),
inference(backward_subsumption_resolution,[status(thm)],[c_58,c_100]) ).
cnf(c_468,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_270,c_100]) ).
cnf(c_578,plain,
( ~ ilf_type(X0,subset_type(cross_product(X1,X2)))
| relation_like(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_460,c_100]) ).
cnf(c_629,plain,
( ~ ilf_type(X0,relation_type(X1,X2))
| ilf_type(X0,subset_type(cross_product(X1,X2))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_462,c_100]) ).
cnf(c_696,plain,
( ~ member(ordered_pair(X0,X1),X2)
| ~ ilf_type(X2,relation_type(X3,X4))
| member(X0,X3) ),
inference(forward_subsumption_resolution,[status(thm)],[c_468,c_100,c_100]) ).
cnf(c_727,plain,
( ~ ilf_type(X0,relation_type(X1,X2))
| ~ ilf_type(X3,relation_type(X2,X4))
| compose5(X1,X2,X4,X0,X3) = compose(X0,X3) ),
inference(forward_subsumption_resolution,[status(thm)],[c_458,c_100,c_100]) ).
cnf(c_744,plain,
( ~ member(ordered_pair(X0,X1),X2)
| ~ member(ordered_pair(X1,X3),X4)
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X4,binary_relation_type)
| member(ordered_pair(X0,X3),compose(X2,X4)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_457,c_100]) ).
cnf(c_1126,plain,
( ~ relation_like(X0)
| ilf_type(X0,binary_relation_type) ),
inference(prop_impl_just,[status(thm)],[c_187]) ).
cnf(c_1132,plain,
( ~ ilf_type(X0,relation_type(X1,X2))
| relation_like(X0) ),
inference(prop_impl_just,[status(thm)],[c_578,c_629]) ).
cnf(c_1134,plain,
( ~ member(X0,X1)
| ilf_type(X0,member_type(X1)) ),
inference(prop_impl_just,[status(thm)],[c_452]) ).
cnf(c_2541,plain,
( ~ ilf_type(sK15,relation_type(sK12,sK13))
| relation_like(sK15) ),
inference(instantiation,[status(thm)],[c_1132]) ).
cnf(c_2542,plain,
( ~ ilf_type(sK14,relation_type(sK11,sK12))
| relation_like(sK14) ),
inference(instantiation,[status(thm)],[c_1132]) ).
cnf(c_2933,plain,
( ~ relation_like(sK15)
| ilf_type(sK15,binary_relation_type) ),
inference(instantiation,[status(thm)],[c_1126]) ).
cnf(c_2938,plain,
( ~ relation_like(sK14)
| ilf_type(sK14,binary_relation_type) ),
inference(instantiation,[status(thm)],[c_1126]) ).
cnf(c_3131,plain,
( ~ member(ordered_pair(X0,sK18),X1)
| ~ member(ordered_pair(sK18,sK17),sK15)
| ~ ilf_type(X1,binary_relation_type)
| ~ ilf_type(sK15,binary_relation_type)
| member(ordered_pair(X0,sK17),compose(X1,sK15)) ),
inference(instantiation,[status(thm)],[c_744]) ).
cnf(c_3806,plain,
( ~ ilf_type(X0,relation_type(sK12,X1))
| compose5(sK11,sK12,X1,sK14,X0) = compose(sK14,X0) ),
inference(superposition,[status(thm)],[c_108,c_727]) ).
cnf(c_3879,plain,
compose5(sK11,sK12,sK13,sK14,sK15) = compose(sK14,sK15),
inference(superposition,[status(thm)],[c_107,c_3806]) ).
cnf(c_3918,plain,
( ~ member(ordered_pair(sK16,sK17),compose(sK14,sK15))
| ~ member(ordered_pair(X0,sK17),sK15)
| ~ member(ordered_pair(sK16,X0),sK14)
| ~ ilf_type(X0,member_type(sK12)) ),
inference(superposition,[status(thm)],[c_3879,c_101]) ).
cnf(c_3919,plain,
( member(ordered_pair(sK16,sK17),compose(sK14,sK15))
| member(ordered_pair(sK16,sK18),sK14) ),
inference(superposition,[status(thm)],[c_3879,c_103]) ).
cnf(c_3920,plain,
( member(ordered_pair(sK16,sK17),compose(sK14,sK15))
| member(ordered_pair(sK18,sK17),sK15) ),
inference(superposition,[status(thm)],[c_3879,c_102]) ).
cnf(c_4359,plain,
( ~ member(ordered_pair(sK16,sK18),sK14)
| ~ member(ordered_pair(sK18,sK17),sK15)
| ~ ilf_type(sK15,binary_relation_type)
| ~ ilf_type(sK14,binary_relation_type)
| member(ordered_pair(sK16,sK17),compose(sK14,sK15)) ),
inference(instantiation,[status(thm)],[c_3131]) ).
cnf(c_5503,negated_conjecture,
( ~ member(ordered_pair(X0,sK17),sK15)
| ~ member(ordered_pair(sK16,X0),sK14)
| ~ ilf_type(X0,member_type(sK12)) ),
inference(global_subsumption_just,[status(thm)],[c_101,c_108,c_107,c_2541,c_2542,c_2933,c_2938,c_3920,c_3919,c_3918,c_4359]) ).
cnf(c_5589,plain,
( ~ ilf_type(X0,relation_type(sK12,X1))
| compose5(sK11,sK12,X1,sK14,X0) = compose(sK14,X0) ),
inference(superposition,[status(thm)],[c_108,c_727]) ).
cnf(c_5593,plain,
( ~ member(ordered_pair(sK16,sK0(X0,sK17,X1,sK15)),sK14)
| ~ ilf_type(sK0(X0,sK17,X1,sK15),member_type(sK12))
| ~ member(ordered_pair(X0,sK17),compose(X1,sK15))
| ~ ilf_type(X1,binary_relation_type)
| ~ ilf_type(sK15,binary_relation_type) ),
inference(superposition,[status(thm)],[c_454,c_5503]) ).
cnf(c_5603,plain,
compose5(sK11,sK12,sK13,sK14,sK15) = compose(sK14,sK15),
inference(superposition,[status(thm)],[c_107,c_5589]) ).
cnf(c_5610,plain,
( member(ordered_pair(sK16,sK17),compose(sK14,sK15))
| ilf_type(sK18,member_type(sK12)) ),
inference(superposition,[status(thm)],[c_5603,c_104]) ).
cnf(c_5611,plain,
member(ordered_pair(sK16,sK17),compose(sK14,sK15)),
inference(global_subsumption_just,[status(thm)],[c_5610,c_108,c_107,c_2541,c_2542,c_2933,c_2938,c_3920,c_3919,c_4359]) ).
cnf(c_5637,plain,
( ~ ilf_type(X1,binary_relation_type)
| ~ member(ordered_pair(X0,sK17),compose(X1,sK15))
| ~ ilf_type(sK0(X0,sK17,X1,sK15),member_type(sK12))
| ~ member(ordered_pair(sK16,sK0(X0,sK17,X1,sK15)),sK14) ),
inference(global_subsumption_just,[status(thm)],[c_5593,c_107,c_2541,c_2933,c_5593]) ).
cnf(c_5638,plain,
( ~ member(ordered_pair(sK16,sK0(X0,sK17,X1,sK15)),sK14)
| ~ ilf_type(sK0(X0,sK17,X1,sK15),member_type(sK12))
| ~ member(ordered_pair(X0,sK17),compose(X1,sK15))
| ~ ilf_type(X1,binary_relation_type) ),
inference(renaming,[status(thm)],[c_5637]) ).
cnf(c_7360,plain,
( ~ member(ordered_pair(X0,X1),sK15)
| ~ ilf_type(sK15,relation_type(sK12,sK13))
| member(X0,sK12) ),
inference(instantiation,[status(thm)],[c_696]) ).
cnf(c_7367,plain,
( ~ member(ordered_pair(X0,sK17),compose(X1,sK15))
| ~ ilf_type(X1,binary_relation_type)
| ~ ilf_type(sK15,binary_relation_type)
| member(ordered_pair(sK0(X0,sK17,X1,sK15),sK17),sK15) ),
inference(instantiation,[status(thm)],[c_454]) ).
cnf(c_7476,plain,
( ~ member(sK0(X0,sK17,X1,sK15),sK12)
| ilf_type(sK0(X0,sK17,X1,sK15),member_type(sK12)) ),
inference(instantiation,[status(thm)],[c_1134]) ).
cnf(c_8293,plain,
( ~ member(ordered_pair(sK0(X0,sK17,X1,sK15),X2),sK15)
| ~ ilf_type(sK15,relation_type(sK12,sK13))
| member(sK0(X0,sK17,X1,sK15),sK12) ),
inference(instantiation,[status(thm)],[c_7360]) ).
cnf(c_13439,plain,
( ~ member(ordered_pair(sK0(X0,sK17,X1,sK15),sK17),sK15)
| ~ ilf_type(sK15,relation_type(sK12,sK13))
| member(sK0(X0,sK17,X1,sK15),sK12) ),
inference(instantiation,[status(thm)],[c_8293]) ).
cnf(c_20112,negated_conjecture,
( ~ member(ordered_pair(X0,sK17),sK15)
| ~ member(ordered_pair(sK16,X0),sK14)
| ~ ilf_type(X0,member_type(sK12)) ),
inference(global_subsumption_just,[status(thm)],[c_101,c_3918,c_5611]) ).
cnf(c_20193,plain,
( ~ member(ordered_pair(sK16,sK0(X0,sK17,X1,sK15)),sK14)
| ~ ilf_type(sK0(X0,sK17,X1,sK15),member_type(sK12))
| ~ member(ordered_pair(X0,sK17),compose(X1,sK15))
| ~ ilf_type(X1,binary_relation_type)
| ~ ilf_type(sK15,binary_relation_type) ),
inference(superposition,[status(thm)],[c_454,c_20112]) ).
cnf(c_20235,plain,
( ~ ilf_type(X1,binary_relation_type)
| ~ member(ordered_pair(X0,sK17),compose(X1,sK15))
| ~ member(ordered_pair(sK16,sK0(X0,sK17,X1,sK15)),sK14) ),
inference(global_subsumption_just,[status(thm)],[c_20193,c_107,c_2541,c_2933,c_5638,c_7367,c_7476,c_13439]) ).
cnf(c_20236,plain,
( ~ member(ordered_pair(sK16,sK0(X0,sK17,X1,sK15)),sK14)
| ~ member(ordered_pair(X0,sK17),compose(X1,sK15))
| ~ ilf_type(X1,binary_relation_type) ),
inference(renaming,[status(thm)],[c_20235]) ).
cnf(c_20238,plain,
( ~ member(ordered_pair(sK16,sK17),compose(sK14,sK15))
| ~ ilf_type(sK15,binary_relation_type)
| ~ ilf_type(sK14,binary_relation_type) ),
inference(superposition,[status(thm)],[c_455,c_20236]) ).
cnf(c_20239,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_20238,c_5611,c_2938,c_2933,c_2542,c_2541,c_107,c_108]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.14 % Problem : SET684+3 : TPTP v8.1.2. Released v2.2.0.
% 0.09/0.14 % Command : run_iprover %s %d THM
% 0.14/0.36 % Computer : n022.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Sat Aug 26 16:28:11 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.21/0.51 Running first-order theorem proving
% 0.21/0.51 Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 25.36/5.34 % SZS status Started for theBenchmark.p
% 25.36/5.34 % SZS status Theorem for theBenchmark.p
% 25.36/5.34
% 25.36/5.34 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 25.36/5.34
% 25.36/5.34 ------ iProver source info
% 25.36/5.34
% 25.36/5.34 git: date: 2023-05-31 18:12:56 +0000
% 25.36/5.34 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 25.36/5.34 git: non_committed_changes: false
% 25.36/5.34 git: last_make_outside_of_git: false
% 25.36/5.34
% 25.36/5.34 ------ Parsing...
% 25.36/5.34 ------ Clausification by vclausify_rel & Parsing by iProver...
% 25.36/5.34
% 25.36/5.34 ------ 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
% 25.36/5.34
% 25.36/5.34 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 25.36/5.34
% 25.36/5.34 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 25.36/5.34 ------ Proving...
% 25.36/5.34 ------ Problem Properties
% 25.36/5.34
% 25.36/5.34
% 25.36/5.34 clauses 47
% 25.36/5.34 conjectures 11
% 25.36/5.34 EPR 9
% 25.36/5.34 Horn 38
% 25.36/5.34 unary 14
% 25.36/5.34 binary 19
% 25.36/5.34 lits 99
% 25.36/5.34 lits eq 7
% 25.36/5.34 fd_pure 0
% 25.36/5.34 fd_pseudo 0
% 25.36/5.34 fd_cond 0
% 25.36/5.34 fd_pseudo_cond 2
% 25.36/5.34 AC symbols 0
% 25.36/5.34
% 25.36/5.34 ------ Input Options Time Limit: Unbounded
% 25.36/5.34
% 25.36/5.34
% 25.36/5.34 ------
% 25.36/5.34 Current options:
% 25.36/5.34 ------
% 25.36/5.34
% 25.36/5.34
% 25.36/5.34
% 25.36/5.34
% 25.36/5.34 ------ Proving...
% 25.36/5.34
% 25.36/5.34
% 25.36/5.34 % SZS status Theorem for theBenchmark.p
% 25.36/5.34
% 25.36/5.34 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 25.36/5.34
% 25.36/5.34
%------------------------------------------------------------------------------