TSTP Solution File: SET646+3 by iProver---3.8
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SET646+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 15:08:53 EDT 2023
% Result : Theorem 9.69s 2.14s
% Output : CNFRefutation 9.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 18
% Syntax : Number of formulae : 121 ( 14 unt; 0 def)
% Number of atoms : 564 ( 57 equ)
% Maximal formula atoms : 15 ( 4 avg)
% Number of connectives : 720 ( 277 ~; 275 |; 109 &)
% ( 16 <=>; 43 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 5 con; 0-2 aty)
% Number of variables : 281 ( 5 sgn; 133 !; 34 ?)
% Comments :
%------------------------------------------------------------------------------
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)
=> ( member(ordered_pair(X0,X1),cross_product(X2,X3))
<=> ( member(X1,X3)
& member(X0,X2) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2) ).
fof(f3,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',p3) ).
fof(f5,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ( singleton(X1) = X2
<=> ! [X3] :
( ilf_type(X3,set_type)
=> ( member(X3,X2)
<=> X1 = X3 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p5) ).
fof(f12,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',p12) ).
fof(f17,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',p17) ).
fof(f19,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',p19) ).
fof(f21,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',p21) ).
fof(f25,axiom,
! [X0] : ilf_type(X0,set_type),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p25) ).
fof(f26,conjecture,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,set_type)
=> ( ( member(X3,X1)
& member(X2,X0) )
=> ilf_type(singleton(ordered_pair(X2,X3)),relation_type(X0,X1)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_relset_1_8) ).
fof(f27,negated_conjecture,
~ ! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,set_type)
=> ( ( member(X3,X1)
& member(X2,X0) )
=> ilf_type(singleton(ordered_pair(X2,X3)),relation_type(X0,X1)) ) ) ) ) ),
inference(negated_conjecture,[],[f26]) ).
fof(f28,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,[],[f3]) ).
fof(f30,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ( member(ordered_pair(X0,X1),cross_product(X2,X3))
<=> ( member(X1,X3)
& member(X0,X2) ) )
| ~ 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(f31,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,[],[f28]) ).
fof(f33,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( singleton(X1) = X2
<=> ! [X3] :
( ( member(X3,X2)
<=> X1 = X3 )
| ~ ilf_type(X3,set_type) ) )
| ~ ilf_type(X2,set_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f5]) ).
fof(f40,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,[],[f12]) ).
fof(f46,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,[],[f17]) ).
fof(f47,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,[],[f46]) ).
fof(f49,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,[],[f19]) ).
fof(f50,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,[],[f49]) ).
fof(f53,plain,
! [X0] :
( ( empty(X0)
<=> ! [X1] :
( ~ member(X1,X0)
| ~ ilf_type(X1,set_type) ) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f21]) ).
fof(f59,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ~ ilf_type(singleton(ordered_pair(X2,X3)),relation_type(X0,X1))
& member(X3,X1)
& member(X2,X0)
& ilf_type(X3,set_type) )
& ilf_type(X2,set_type) )
& ilf_type(X1,set_type) )
& ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f27]) ).
fof(f60,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ~ ilf_type(singleton(ordered_pair(X2,X3)),relation_type(X0,X1))
& member(X3,X1)
& member(X2,X0)
& ilf_type(X3,set_type) )
& ilf_type(X2,set_type) )
& ilf_type(X1,set_type) )
& ilf_type(X0,set_type) ),
inference(flattening,[],[f59]) ).
fof(f62,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ( ( member(ordered_pair(X0,X1),cross_product(X2,X3))
| ~ member(X1,X3)
| ~ member(X0,X2) )
& ( ( member(X1,X3)
& member(X0,X2) )
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3)) ) )
| ~ ilf_type(X3,set_type) )
| ~ ilf_type(X2,set_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f30]) ).
fof(f63,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ( ( member(ordered_pair(X0,X1),cross_product(X2,X3))
| ~ member(X1,X3)
| ~ member(X0,X2) )
& ( ( member(X1,X3)
& member(X0,X2) )
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3)) ) )
| ~ ilf_type(X3,set_type) )
| ~ ilf_type(X2,set_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(flattening,[],[f62]) ).
fof(f66,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( singleton(X1) = X2
| ? [X3] :
( ( X1 != X3
| ~ member(X3,X2) )
& ( X1 = X3
| member(X3,X2) )
& ilf_type(X3,set_type) ) )
& ( ! [X3] :
( ( ( member(X3,X2)
| X1 != X3 )
& ( X1 = X3
| ~ member(X3,X2) ) )
| ~ ilf_type(X3,set_type) )
| singleton(X1) != X2 ) )
| ~ ilf_type(X2,set_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f33]) ).
fof(f67,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( singleton(X1) = X2
| ? [X3] :
( ( X1 != X3
| ~ member(X3,X2) )
& ( X1 = X3
| member(X3,X2) )
& ilf_type(X3,set_type) ) )
& ( ! [X3] :
( ( ( member(X3,X2)
| X1 != X3 )
& ( X1 = X3
| ~ member(X3,X2) ) )
| ~ ilf_type(X3,set_type) )
| singleton(X1) != X2 ) )
| ~ ilf_type(X2,set_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(flattening,[],[f66]) ).
fof(f68,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( singleton(X1) = X2
| ? [X3] :
( ( X1 != X3
| ~ member(X3,X2) )
& ( X1 = X3
| member(X3,X2) )
& ilf_type(X3,set_type) ) )
& ( ! [X4] :
( ( ( member(X4,X2)
| X1 != X4 )
& ( X1 = X4
| ~ member(X4,X2) ) )
| ~ ilf_type(X4,set_type) )
| singleton(X1) != X2 ) )
| ~ ilf_type(X2,set_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(rectify,[],[f67]) ).
fof(f69,plain,
! [X1,X2] :
( ? [X3] :
( ( X1 != X3
| ~ member(X3,X2) )
& ( X1 = X3
| member(X3,X2) )
& ilf_type(X3,set_type) )
=> ( ( sK1(X1,X2) != X1
| ~ member(sK1(X1,X2),X2) )
& ( sK1(X1,X2) = X1
| member(sK1(X1,X2),X2) )
& ilf_type(sK1(X1,X2),set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f70,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( singleton(X1) = X2
| ( ( sK1(X1,X2) != X1
| ~ member(sK1(X1,X2),X2) )
& ( sK1(X1,X2) = X1
| member(sK1(X1,X2),X2) )
& ilf_type(sK1(X1,X2),set_type) ) )
& ( ! [X4] :
( ( ( member(X4,X2)
| X1 != X4 )
& ( X1 = X4
| ~ member(X4,X2) ) )
| ~ ilf_type(X4,set_type) )
| singleton(X1) != X2 ) )
| ~ ilf_type(X2,set_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f68,f69]) ).
fof(f72,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,[],[f40]) ).
fof(f84,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,[],[f47]) ).
fof(f85,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,[],[f84]) ).
fof(f86,plain,
! [X0,X1] :
( ? [X2] :
( ~ member(X2,X1)
& member(X2,X0)
& ilf_type(X2,set_type) )
=> ( ~ member(sK5(X0,X1),X1)
& member(sK5(X0,X1),X0)
& ilf_type(sK5(X0,X1),set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f87,plain,
! [X0] :
( ! [X1] :
( ( ( member(X0,power_set(X1))
| ( ~ member(sK5(X0,X1),X1)
& member(sK5(X0,X1),X0)
& ilf_type(sK5(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,[sK5])],[f85,f86]) ).
fof(f88,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,[],[f50]) ).
fof(f91,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,[],[f53]) ).
fof(f92,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,[],[f91]) ).
fof(f93,plain,
! [X0] :
( ? [X1] :
( member(X1,X0)
& ilf_type(X1,set_type) )
=> ( member(sK7(X0),X0)
& ilf_type(sK7(X0),set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f94,plain,
! [X0] :
( ( ( empty(X0)
| ( member(sK7(X0),X0)
& ilf_type(sK7(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,[sK7])],[f92,f93]) ).
fof(f101,plain,
( ? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ~ ilf_type(singleton(ordered_pair(X2,X3)),relation_type(X0,X1))
& member(X3,X1)
& member(X2,X0)
& ilf_type(X3,set_type) )
& ilf_type(X2,set_type) )
& ilf_type(X1,set_type) )
& ilf_type(X0,set_type) )
=> ( ? [X1] :
( ? [X2] :
( ? [X3] :
( ~ ilf_type(singleton(ordered_pair(X2,X3)),relation_type(sK11,X1))
& member(X3,X1)
& member(X2,sK11)
& ilf_type(X3,set_type) )
& ilf_type(X2,set_type) )
& ilf_type(X1,set_type) )
& ilf_type(sK11,set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f102,plain,
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ~ ilf_type(singleton(ordered_pair(X2,X3)),relation_type(sK11,X1))
& member(X3,X1)
& member(X2,sK11)
& ilf_type(X3,set_type) )
& ilf_type(X2,set_type) )
& ilf_type(X1,set_type) )
=> ( ? [X2] :
( ? [X3] :
( ~ ilf_type(singleton(ordered_pair(X2,X3)),relation_type(sK11,sK12))
& member(X3,sK12)
& member(X2,sK11)
& ilf_type(X3,set_type) )
& ilf_type(X2,set_type) )
& ilf_type(sK12,set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f103,plain,
( ? [X2] :
( ? [X3] :
( ~ ilf_type(singleton(ordered_pair(X2,X3)),relation_type(sK11,sK12))
& member(X3,sK12)
& member(X2,sK11)
& ilf_type(X3,set_type) )
& ilf_type(X2,set_type) )
=> ( ? [X3] :
( ~ ilf_type(singleton(ordered_pair(sK13,X3)),relation_type(sK11,sK12))
& member(X3,sK12)
& member(sK13,sK11)
& ilf_type(X3,set_type) )
& ilf_type(sK13,set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f104,plain,
( ? [X3] :
( ~ ilf_type(singleton(ordered_pair(sK13,X3)),relation_type(sK11,sK12))
& member(X3,sK12)
& member(sK13,sK11)
& ilf_type(X3,set_type) )
=> ( ~ ilf_type(singleton(ordered_pair(sK13,sK14)),relation_type(sK11,sK12))
& member(sK14,sK12)
& member(sK13,sK11)
& ilf_type(sK14,set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f105,plain,
( ~ ilf_type(singleton(ordered_pair(sK13,sK14)),relation_type(sK11,sK12))
& member(sK14,sK12)
& member(sK13,sK11)
& ilf_type(sK14,set_type)
& ilf_type(sK13,set_type)
& ilf_type(sK12,set_type)
& ilf_type(sK11,set_type) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK11,sK12,sK13,sK14])],[f60,f104,f103,f102,f101]) ).
fof(f110,plain,
! [X2,X3,X0,X1] :
( member(ordered_pair(X0,X1),cross_product(X2,X3))
| ~ member(X1,X3)
| ~ member(X0,X2)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f63]) ).
fof(f111,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,[],[f31]) ).
fof(f114,plain,
! [X2,X0,X1,X4] :
( X1 = X4
| ~ member(X4,X2)
| ~ ilf_type(X4,set_type)
| singleton(X1) != X2
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f70]) ).
fof(f127,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,[],[f72]) ).
fof(f141,plain,
! [X0,X1] :
( member(X0,power_set(X1))
| member(sK5(X0,X1),X0)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f87]) ).
fof(f142,plain,
! [X0,X1] :
( member(X0,power_set(X1))
| ~ member(sK5(X0,X1),X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f87]) ).
fof(f146,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,[],[f88]) ).
fof(f148,plain,
! [X2,X0] :
( ~ member(X2,X0)
| ~ ilf_type(X2,set_type)
| ~ empty(X0)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f94]) ).
fof(f159,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[],[f25]) ).
fof(f164,plain,
member(sK13,sK11),
inference(cnf_transformation,[],[f105]) ).
fof(f165,plain,
member(sK14,sK12),
inference(cnf_transformation,[],[f105]) ).
fof(f166,plain,
~ ilf_type(singleton(ordered_pair(sK13,sK14)),relation_type(sK11,sK12)),
inference(cnf_transformation,[],[f105]) ).
fof(f169,plain,
! [X0,X1,X4] :
( X1 = X4
| ~ member(X4,singleton(X1))
| ~ ilf_type(X4,set_type)
| ~ ilf_type(singleton(X1),set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(equality_resolution,[],[f114]) ).
cnf(c_51,plain,
( ~ member(X0,X1)
| ~ member(X2,X3)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,set_type)
| member(ordered_pair(X0,X2),cross_product(X1,X3)) ),
inference(cnf_transformation,[],[f110]) ).
cnf(c_55,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,[],[f111]) ).
cnf(c_61,plain,
( ~ member(X0,singleton(X1))
| ~ ilf_type(singleton(X1),set_type)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| X0 = X1 ),
inference(cnf_transformation,[],[f169]) ).
cnf(c_69,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,[],[f127]) ).
cnf(c_82,plain,
( ~ member(sK5(X0,X1),X1)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| member(X0,power_set(X1)) ),
inference(cnf_transformation,[],[f142]) ).
cnf(c_83,plain,
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| member(sK5(X0,X1),X0)
| member(X0,power_set(X1)) ),
inference(cnf_transformation,[],[f141]) ).
cnf(c_88,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,[],[f146]) ).
cnf(c_93,plain,
( ~ member(X0,X1)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ empty(X1) ),
inference(cnf_transformation,[],[f148]) ).
cnf(c_102,plain,
ilf_type(X0,set_type),
inference(cnf_transformation,[],[f159]) ).
cnf(c_103,negated_conjecture,
~ ilf_type(singleton(ordered_pair(sK13,sK14)),relation_type(sK11,sK12)),
inference(cnf_transformation,[],[f166]) ).
cnf(c_104,negated_conjecture,
member(sK14,sK12),
inference(cnf_transformation,[],[f165]) ).
cnf(c_105,negated_conjecture,
member(sK13,sK11),
inference(cnf_transformation,[],[f164]) ).
cnf(c_233,plain,
( ~ ilf_type(X1,set_type)
| member(sK5(X0,X1),X0)
| member(X0,power_set(X1)) ),
inference(global_subsumption_just,[status(thm)],[c_83,c_102,c_83]) ).
cnf(c_234,plain,
( ~ ilf_type(X0,set_type)
| member(sK5(X1,X0),X1)
| member(X1,power_set(X0)) ),
inference(renaming,[status(thm)],[c_233]) ).
cnf(c_235,plain,
( member(sK5(X1,X0),X1)
| member(X1,power_set(X0)) ),
inference(global_subsumption_just,[status(thm)],[c_234,c_102,c_234]) ).
cnf(c_236,plain,
( member(sK5(X0,X1),X0)
| member(X0,power_set(X1)) ),
inference(renaming,[status(thm)],[c_235]) ).
cnf(c_253,plain,
( ilf_type(X0,member_type(X1))
| ~ ilf_type(X1,set_type)
| ~ member(X0,X1) ),
inference(global_subsumption_just,[status(thm)],[c_88,c_102,c_93,c_88]) ).
cnf(c_254,plain,
( ~ member(X0,X1)
| ~ ilf_type(X1,set_type)
| ilf_type(X0,member_type(X1)) ),
inference(renaming,[status(thm)],[c_253]) ).
cnf(c_256,plain,
( ~ member(sK5(X0,X1),X1)
| ~ ilf_type(X1,set_type)
| member(X0,power_set(X1)) ),
inference(global_subsumption_just,[status(thm)],[c_82,c_102,c_82]) ).
cnf(c_260,plain,
( ~ ilf_type(X0,member_type(power_set(X1)))
| ~ ilf_type(X1,set_type)
| ilf_type(X0,subset_type(X1)) ),
inference(global_subsumption_just,[status(thm)],[c_69,c_102,c_69]) ).
cnf(c_288,plain,
( ~ ilf_type(singleton(X1),set_type)
| ~ member(X0,singleton(X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| X0 = X1 ),
inference(global_subsumption_just,[status(thm)],[c_61,c_102,c_61]) ).
cnf(c_289,plain,
( ~ member(X0,singleton(X1))
| ~ ilf_type(singleton(X1),set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| X0 = X1 ),
inference(renaming,[status(thm)],[c_288]) ).
cnf(c_303,plain,
( ~ member(X2,X3)
| ~ member(X0,X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,set_type)
| member(ordered_pair(X0,X2),cross_product(X1,X3)) ),
inference(global_subsumption_just,[status(thm)],[c_51,c_102,c_51]) ).
cnf(c_304,plain,
( ~ member(X0,X1)
| ~ member(X2,X3)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,set_type)
| member(ordered_pair(X0,X2),cross_product(X1,X3)) ),
inference(renaming,[status(thm)],[c_303]) ).
cnf(c_322,plain,
( ~ ilf_type(X0,subset_type(cross_product(X1,X2)))
| ~ ilf_type(X2,set_type)
| ilf_type(X0,relation_type(X1,X2)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_55,c_102]) ).
cnf(c_324,plain,
( ~ member(X0,singleton(X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| X0 = X1 ),
inference(backward_subsumption_resolution,[status(thm)],[c_289,c_102]) ).
cnf(c_327,plain,
( ~ ilf_type(X0,member_type(power_set(X1)))
| ilf_type(X0,subset_type(X1)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_260,c_102]) ).
cnf(c_331,plain,
( ~ member(X0,X1)
| ~ member(X2,X3)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,set_type)
| member(ordered_pair(X0,X2),cross_product(X1,X3)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_304,c_102]) ).
cnf(c_337,plain,
( ~ member(X0,X1)
| ilf_type(X0,member_type(X1)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_254,c_102]) ).
cnf(c_340,plain,
( ~ member(sK5(X0,X1),X1)
| member(X0,power_set(X1)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_256,c_102]) ).
cnf(c_488,plain,
( ~ ilf_type(X0,subset_type(cross_product(X1,X2)))
| ilf_type(X0,relation_type(X1,X2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_322,c_102]) ).
cnf(c_534,plain,
( ~ member(X0,singleton(X1))
| X0 = X1 ),
inference(forward_subsumption_resolution,[status(thm)],[c_324,c_102,c_102]) ).
cnf(c_585,plain,
( ~ member(X0,X1)
| ~ member(X2,X3)
| member(ordered_pair(X0,X2),cross_product(X1,X3)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_331,c_102,c_102]) ).
cnf(c_842,plain,
( ilf_type(X0,relation_type(X1,X2))
| ~ ilf_type(X0,subset_type(cross_product(X1,X2))) ),
inference(prop_impl_just,[status(thm)],[c_488]) ).
cnf(c_843,plain,
( ~ ilf_type(X0,subset_type(cross_product(X1,X2)))
| ilf_type(X0,relation_type(X1,X2)) ),
inference(renaming,[status(thm)],[c_842]) ).
cnf(c_846,plain,
( ilf_type(X0,subset_type(X1))
| ~ ilf_type(X0,member_type(power_set(X1))) ),
inference(prop_impl_just,[status(thm)],[c_327]) ).
cnf(c_847,plain,
( ~ ilf_type(X0,member_type(power_set(X1)))
| ilf_type(X0,subset_type(X1)) ),
inference(renaming,[status(thm)],[c_846]) ).
cnf(c_850,plain,
( ~ member(X0,X1)
| ilf_type(X0,member_type(X1)) ),
inference(prop_impl_just,[status(thm)],[c_337]) ).
cnf(c_864,plain,
( ~ member(X0,singleton(X1))
| X0 = X1 ),
inference(prop_impl_just,[status(thm)],[c_534]) ).
cnf(c_872,plain,
( ~ member(sK5(X0,X1),X1)
| member(X0,power_set(X1)) ),
inference(prop_impl_just,[status(thm)],[c_340]) ).
cnf(c_876,plain,
( member(X0,power_set(X1))
| member(sK5(X0,X1),X0) ),
inference(prop_impl_just,[status(thm)],[c_236]) ).
cnf(c_877,plain,
( member(sK5(X0,X1),X0)
| member(X0,power_set(X1)) ),
inference(renaming,[status(thm)],[c_876]) ).
cnf(c_1368,plain,
X0 = X0,
theory(equality) ).
cnf(c_1373,plain,
( X0 != X1
| X2 != X3
| ~ member(X1,X3)
| member(X0,X2) ),
theory(equality) ).
cnf(c_2181,plain,
( ~ ilf_type(singleton(ordered_pair(sK13,sK14)),subset_type(cross_product(sK11,sK12)))
| ilf_type(singleton(ordered_pair(sK13,sK14)),relation_type(sK11,sK12)) ),
inference(instantiation,[status(thm)],[c_843]) ).
cnf(c_2189,plain,
( ~ ilf_type(singleton(ordered_pair(sK13,sK14)),member_type(power_set(cross_product(sK11,sK12))))
| ilf_type(singleton(ordered_pair(sK13,sK14)),subset_type(cross_product(sK11,sK12))) ),
inference(instantiation,[status(thm)],[c_847]) ).
cnf(c_2206,plain,
( ~ member(singleton(ordered_pair(sK13,sK14)),power_set(cross_product(sK11,sK12)))
| ilf_type(singleton(ordered_pair(sK13,sK14)),member_type(power_set(cross_product(sK11,sK12)))) ),
inference(instantiation,[status(thm)],[c_850]) ).
cnf(c_2288,plain,
( ~ member(sK5(singleton(ordered_pair(sK13,sK14)),cross_product(sK11,sK12)),cross_product(sK11,sK12))
| member(singleton(ordered_pair(sK13,sK14)),power_set(cross_product(sK11,sK12))) ),
inference(instantiation,[status(thm)],[c_872]) ).
cnf(c_2289,plain,
( member(sK5(singleton(ordered_pair(sK13,sK14)),cross_product(sK11,sK12)),singleton(ordered_pair(sK13,sK14)))
| member(singleton(ordered_pair(sK13,sK14)),power_set(cross_product(sK11,sK12))) ),
inference(instantiation,[status(thm)],[c_877]) ).
cnf(c_2684,plain,
( sK5(singleton(ordered_pair(sK13,sK14)),cross_product(sK11,sK12)) != X0
| cross_product(sK11,sK12) != X1
| ~ member(X0,X1)
| member(sK5(singleton(ordered_pair(sK13,sK14)),cross_product(sK11,sK12)),cross_product(sK11,sK12)) ),
inference(instantiation,[status(thm)],[c_1373]) ).
cnf(c_7396,plain,
( sK5(singleton(ordered_pair(sK13,sK14)),cross_product(sK11,sK12)) != X0
| cross_product(sK11,sK12) != cross_product(sK11,sK12)
| ~ member(X0,cross_product(sK11,sK12))
| member(sK5(singleton(ordered_pair(sK13,sK14)),cross_product(sK11,sK12)),cross_product(sK11,sK12)) ),
inference(instantiation,[status(thm)],[c_2684]) ).
cnf(c_10636,plain,
( ~ member(X0,singleton(ordered_pair(sK13,sK14)))
| X0 = ordered_pair(sK13,sK14) ),
inference(instantiation,[status(thm)],[c_864]) ).
cnf(c_13136,plain,
cross_product(sK11,sK12) = cross_product(sK11,sK12),
inference(instantiation,[status(thm)],[c_1368]) ).
cnf(c_14776,plain,
( sK5(singleton(X0),X1) = X0
| member(singleton(X0),power_set(X1)) ),
inference(superposition,[status(thm)],[c_877,c_864]) ).
cnf(c_14801,plain,
( ~ member(X0,power_set(X1))
| ilf_type(X0,subset_type(X1)) ),
inference(superposition,[status(thm)],[c_850,c_847]) ).
cnf(c_14878,plain,
( sK5(singleton(X0),X1) = X0
| ilf_type(singleton(X0),subset_type(X1)) ),
inference(superposition,[status(thm)],[c_14776,c_14801]) ).
cnf(c_20021,plain,
( ~ member(sK5(singleton(ordered_pair(sK13,sK14)),cross_product(sK11,sK12)),singleton(ordered_pair(sK13,sK14)))
| sK5(singleton(ordered_pair(sK13,sK14)),cross_product(sK11,sK12)) = ordered_pair(sK13,sK14) ),
inference(instantiation,[status(thm)],[c_10636]) ).
cnf(c_24347,plain,
( sK5(singleton(ordered_pair(sK13,sK14)),cross_product(sK11,sK12)) != ordered_pair(sK13,sK14)
| cross_product(sK11,sK12) != cross_product(sK11,sK12)
| ~ member(ordered_pair(sK13,sK14),cross_product(sK11,sK12))
| member(sK5(singleton(ordered_pair(sK13,sK14)),cross_product(sK11,sK12)),cross_product(sK11,sK12)) ),
inference(instantiation,[status(thm)],[c_7396]) ).
cnf(c_28293,plain,
( sK5(singleton(X0),cross_product(X1,X2)) = X0
| ilf_type(singleton(X0),relation_type(X1,X2)) ),
inference(superposition,[status(thm)],[c_14878,c_843]) ).
cnf(c_28325,plain,
sK5(singleton(ordered_pair(sK13,sK14)),cross_product(sK11,sK12)) = ordered_pair(sK13,sK14),
inference(superposition,[status(thm)],[c_28293,c_103]) ).
cnf(c_28417,plain,
( ~ member(ordered_pair(sK13,sK14),cross_product(sK11,sK12))
| member(singleton(ordered_pair(sK13,sK14)),power_set(cross_product(sK11,sK12))) ),
inference(superposition,[status(thm)],[c_28325,c_872]) ).
cnf(c_28429,plain,
~ member(ordered_pair(sK13,sK14),cross_product(sK11,sK12)),
inference(global_subsumption_just,[status(thm)],[c_28417,c_103,c_2181,c_2189,c_2206,c_2289,c_2288,c_13136,c_20021,c_24347]) ).
cnf(c_28431,plain,
( ~ member(sK13,sK11)
| ~ member(sK14,sK12) ),
inference(superposition,[status(thm)],[c_585,c_28429]) ).
cnf(c_28432,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_28431,c_104,c_105]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET646+3 : TPTP v8.1.2. Released v2.2.0.
% 0.07/0.13 % Command : run_iprover %s %d THM
% 0.14/0.34 % Computer : n017.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Sat Aug 26 13:51:26 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.20/0.47 Running first-order theorem proving
% 0.20/0.47 Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 9.69/2.14 % SZS status Started for theBenchmark.p
% 9.69/2.14 % SZS status Theorem for theBenchmark.p
% 9.69/2.14
% 9.69/2.14 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 9.69/2.14
% 9.69/2.14 ------ iProver source info
% 9.69/2.14
% 9.69/2.14 git: date: 2023-05-31 18:12:56 +0000
% 9.69/2.14 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 9.69/2.14 git: non_committed_changes: false
% 9.69/2.14 git: last_make_outside_of_git: false
% 9.69/2.14
% 9.69/2.14 ------ Parsing...
% 9.69/2.14 ------ Clausification by vclausify_rel & Parsing by iProver...
% 9.69/2.14
% 9.69/2.14 ------ Preprocessing... sup_sim: 1 sf_s rm: 1 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e
% 9.69/2.14
% 9.69/2.14 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 9.69/2.14
% 9.69/2.14 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 9.69/2.14 ------ Proving...
% 9.69/2.14 ------ Problem Properties
% 9.69/2.14
% 9.69/2.14
% 9.69/2.14 clauses 41
% 9.69/2.14 conjectures 3
% 9.69/2.14 EPR 7
% 9.69/2.14 Horn 33
% 9.69/2.14 unary 11
% 9.69/2.14 binary 21
% 9.69/2.14 lits 80
% 9.69/2.14 lits eq 11
% 9.69/2.14 fd_pure 0
% 9.69/2.14 fd_pseudo 0
% 9.69/2.14 fd_cond 0
% 9.69/2.14 fd_pseudo_cond 4
% 9.69/2.14 AC symbols 0
% 9.69/2.14
% 9.69/2.14 ------ Input Options Time Limit: Unbounded
% 9.69/2.14
% 9.69/2.14
% 9.69/2.14 ------
% 9.69/2.14 Current options:
% 9.69/2.14 ------
% 9.69/2.14
% 9.69/2.14
% 9.69/2.14
% 9.69/2.14
% 9.69/2.14 ------ Proving...
% 9.69/2.14
% 9.69/2.14
% 9.69/2.14 % SZS status Theorem for theBenchmark.p
% 9.69/2.14
% 9.69/2.14 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 9.69/2.14
% 9.69/2.14
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