TSTP Solution File: SET645+3 by iProver---3.8
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SET645+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n021.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 15:08:53 EDT 2023
% Result : Theorem 3.96s 1.18s
% Output : CNFRefutation 3.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 14
% Syntax : Number of formulae : 93 ( 11 unt; 0 def)
% Number of atoms : 423 ( 1 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 539 ( 209 ~; 194 |; 87 &)
% ( 10 <=>; 39 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 6 con; 0-2 aty)
% Number of variables : 246 ( 16 sgn; 95 !; 38 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,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',p1) ).
fof(f4,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',p4) ).
fof(f10,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',p10) ).
fof(f13,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',p13) ).
fof(f14,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',p14) ).
fof(f15,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',p15) ).
fof(f21,axiom,
! [X0] : ilf_type(X0,set_type),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p21) ).
fof(f22,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)
=> ! [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',prove_relset_1_7) ).
fof(f23,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)
=> ! [X4] :
( ilf_type(X4,relation_type(X0,X1))
=> ( member(ordered_pair(X2,X3),X4)
=> ( member(X3,X1)
& member(X2,X0) ) ) ) ) ) ) ),
inference(negated_conjecture,[],[f22]) ).
fof(f24,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,[],[f4]) ).
fof(f25,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,[],[f1]) ).
fof(f28,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,[],[f24]) ).
fof(f34,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,[],[f10]) ).
fof(f37,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,[],[f13]) ).
fof(f38,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,[],[f37]) ).
fof(f39,plain,
! [X0] :
( ( ilf_type(power_set(X0),set_type)
& ~ empty(power_set(X0)) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f14]) ).
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,[],[f15]) ).
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(f50,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,[],[f23]) ).
fof(f51,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,[],[f50]) ).
fof(f52,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,[],[f25]) ).
fof(f53,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,[],[f52]) ).
fof(f57,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,[],[f34]) ).
fof(f65,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,[],[f38]) ).
fof(f66,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,[],[f65]) ).
fof(f67,plain,
! [X0,X1] :
( ? [X2] :
( ~ member(X2,X1)
& member(X2,X0)
& ilf_type(X2,set_type) )
=> ( ~ member(sK3(X0,X1),X1)
& member(sK3(X0,X1),X0)
& ilf_type(sK3(X0,X1),set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f68,plain,
! [X0] :
( ! [X1] :
( ( ( member(X0,power_set(X1))
| ( ~ member(sK3(X0,X1),X1)
& member(sK3(X0,X1),X0)
& ilf_type(sK3(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,[sK3])],[f66,f67]) ).
fof(f69,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(f82,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) )
=> ( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ( ~ member(X3,X1)
| ~ member(X2,sK9) )
& member(ordered_pair(X2,X3),X4)
& ilf_type(X4,relation_type(sK9,X1)) )
& ilf_type(X3,set_type) )
& ilf_type(X2,set_type) )
& ilf_type(X1,set_type) )
& ilf_type(sK9,set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f83,plain,
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ( ~ member(X3,X1)
| ~ member(X2,sK9) )
& member(ordered_pair(X2,X3),X4)
& ilf_type(X4,relation_type(sK9,X1)) )
& ilf_type(X3,set_type) )
& ilf_type(X2,set_type) )
& ilf_type(X1,set_type) )
=> ( ? [X2] :
( ? [X3] :
( ? [X4] :
( ( ~ member(X3,sK10)
| ~ member(X2,sK9) )
& member(ordered_pair(X2,X3),X4)
& ilf_type(X4,relation_type(sK9,sK10)) )
& ilf_type(X3,set_type) )
& ilf_type(X2,set_type) )
& ilf_type(sK10,set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f84,plain,
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ( ~ member(X3,sK10)
| ~ member(X2,sK9) )
& member(ordered_pair(X2,X3),X4)
& ilf_type(X4,relation_type(sK9,sK10)) )
& ilf_type(X3,set_type) )
& ilf_type(X2,set_type) )
=> ( ? [X3] :
( ? [X4] :
( ( ~ member(X3,sK10)
| ~ member(sK11,sK9) )
& member(ordered_pair(sK11,X3),X4)
& ilf_type(X4,relation_type(sK9,sK10)) )
& ilf_type(X3,set_type) )
& ilf_type(sK11,set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f85,plain,
( ? [X3] :
( ? [X4] :
( ( ~ member(X3,sK10)
| ~ member(sK11,sK9) )
& member(ordered_pair(sK11,X3),X4)
& ilf_type(X4,relation_type(sK9,sK10)) )
& ilf_type(X3,set_type) )
=> ( ? [X4] :
( ( ~ member(sK12,sK10)
| ~ member(sK11,sK9) )
& member(ordered_pair(sK11,sK12),X4)
& ilf_type(X4,relation_type(sK9,sK10)) )
& ilf_type(sK12,set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f86,plain,
( ? [X4] :
( ( ~ member(sK12,sK10)
| ~ member(sK11,sK9) )
& member(ordered_pair(sK11,sK12),X4)
& ilf_type(X4,relation_type(sK9,sK10)) )
=> ( ( ~ member(sK12,sK10)
| ~ member(sK11,sK9) )
& member(ordered_pair(sK11,sK12),sK13)
& ilf_type(sK13,relation_type(sK9,sK10)) ) ),
introduced(choice_axiom,[]) ).
fof(f87,plain,
( ( ~ member(sK12,sK10)
| ~ member(sK11,sK9) )
& member(ordered_pair(sK11,sK12),sK13)
& ilf_type(sK13,relation_type(sK9,sK10))
& ilf_type(sK12,set_type)
& ilf_type(sK11,set_type)
& ilf_type(sK10,set_type)
& ilf_type(sK9,set_type) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9,sK10,sK11,sK12,sK13])],[f51,f86,f85,f84,f83,f82]) ).
fof(f88,plain,
! [X2,X3,X0,X1] :
( 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(cnf_transformation,[],[f53]) ).
fof(f89,plain,
! [X2,X3,X0,X1] :
( member(X1,X3)
| ~ 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(cnf_transformation,[],[f53]) ).
fof(f95,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,[],[f28]) ).
fof(f101,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,[],[f57]) ).
fof(f109,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,[],[f68]) ).
fof(f113,plain,
! [X0] :
( ~ empty(power_set(X0))
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f39]) ).
fof(f115,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,[],[f69]) ).
fof(f129,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[],[f21]) ).
fof(f134,plain,
ilf_type(sK13,relation_type(sK9,sK10)),
inference(cnf_transformation,[],[f87]) ).
fof(f135,plain,
member(ordered_pair(sK11,sK12),sK13),
inference(cnf_transformation,[],[f87]) ).
fof(f136,plain,
( ~ member(sK12,sK10)
| ~ member(sK11,sK9) ),
inference(cnf_transformation,[],[f87]) ).
cnf(c_50,plain,
( ~ member(ordered_pair(X0,X1),cross_product(X2,X3))
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,set_type)
| member(X1,X3) ),
inference(cnf_transformation,[],[f89]) ).
cnf(c_51,plain,
( ~ member(ordered_pair(X0,X1),cross_product(X2,X3))
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,set_type)
| member(X0,X2) ),
inference(cnf_transformation,[],[f88]) ).
cnf(c_55,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,[],[f95]) ).
cnf(c_63,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,[],[f101]) ).
cnf(c_73,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,[],[f109]) ).
cnf(c_75,plain,
( ~ ilf_type(X0,set_type)
| ~ empty(power_set(X0)) ),
inference(cnf_transformation,[],[f113]) ).
cnf(c_77,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,[],[f115]) ).
cnf(c_90,plain,
ilf_type(X0,set_type),
inference(cnf_transformation,[],[f129]) ).
cnf(c_91,negated_conjecture,
( ~ member(sK12,sK10)
| ~ member(sK11,sK9) ),
inference(cnf_transformation,[],[f136]) ).
cnf(c_92,negated_conjecture,
member(ordered_pair(sK11,sK12),sK13),
inference(cnf_transformation,[],[f135]) ).
cnf(c_93,negated_conjecture,
ilf_type(sK13,relation_type(sK9,sK10)),
inference(cnf_transformation,[],[f134]) ).
cnf(c_136,plain,
~ empty(power_set(X0)),
inference(global_subsumption_just,[status(thm)],[c_75,c_90,c_75]) ).
cnf(c_208,plain,
( ~ ilf_type(X0,member_type(X1))
| ~ ilf_type(X1,set_type)
| member(X0,X1)
| empty(X1) ),
inference(global_subsumption_just,[status(thm)],[c_77,c_90,c_77]) ).
cnf(c_215,plain,
( ~ ilf_type(X0,subset_type(X1))
| ~ ilf_type(X1,set_type)
| ilf_type(X0,member_type(power_set(X1))) ),
inference(global_subsumption_just,[status(thm)],[c_63,c_90,c_63]) ).
cnf(c_232,plain,
( ~ member(X2,X0)
| ~ member(X0,power_set(X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| member(X2,X1) ),
inference(global_subsumption_just,[status(thm)],[c_73,c_90,c_73]) ).
cnf(c_233,plain,
( ~ member(X0,power_set(X1))
| ~ member(X2,X0)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| member(X2,X1) ),
inference(renaming,[status(thm)],[c_232]) ).
cnf(c_236,plain,
( ~ member(ordered_pair(X0,X1),cross_product(X2,X3))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,set_type)
| member(X0,X2) ),
inference(global_subsumption_just,[status(thm)],[c_51,c_90,c_51]) ).
cnf(c_238,plain,
( ~ member(ordered_pair(X0,X1),cross_product(X2,X3))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,set_type)
| member(X1,X3) ),
inference(global_subsumption_just,[status(thm)],[c_50,c_90,c_50]) ).
cnf(c_258,plain,
( ~ member(X0,power_set(X1))
| ~ member(X2,X0)
| ~ ilf_type(X2,set_type)
| member(X2,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[c_233,c_90]) ).
cnf(c_260,plain,
( ~ ilf_type(X0,member_type(X1))
| member(X0,X1)
| empty(X1) ),
inference(backward_subsumption_resolution,[status(thm)],[c_208,c_90]) ).
cnf(c_261,plain,
( ~ ilf_type(X0,subset_type(X1))
| ilf_type(X0,member_type(power_set(X1))) ),
inference(backward_subsumption_resolution,[status(thm)],[c_215,c_90]) ).
cnf(c_264,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_55,c_90]) ).
cnf(c_268,plain,
( ~ member(ordered_pair(X0,X1),cross_product(X2,X3))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,set_type)
| member(X1,X3) ),
inference(backward_subsumption_resolution,[status(thm)],[c_238,c_90]) ).
cnf(c_269,plain,
( ~ member(ordered_pair(X0,X1),cross_product(X2,X3))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,set_type)
| member(X0,X2) ),
inference(backward_subsumption_resolution,[status(thm)],[c_236,c_90]) ).
cnf(c_381,plain,
( ~ ilf_type(X0,relation_type(X1,X2))
| ilf_type(X0,subset_type(cross_product(X1,X2))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_264,c_90]) ).
cnf(c_410,plain,
( ~ member(X0,power_set(X1))
| ~ member(X2,X0)
| member(X2,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_258,c_90]) ).
cnf(c_424,plain,
( ~ member(ordered_pair(X0,X1),cross_product(X2,X3))
| member(X1,X3) ),
inference(forward_subsumption_resolution,[status(thm)],[c_268,c_90,c_90]) ).
cnf(c_436,plain,
( ~ member(ordered_pair(X0,X1),cross_product(X2,X3))
| member(X0,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_269,c_90,c_90]) ).
cnf(c_546,plain,
( power_set(X0) != X1
| ~ ilf_type(X2,member_type(X1))
| member(X2,X1) ),
inference(resolution_lifted,[status(thm)],[c_136,c_260]) ).
cnf(c_547,plain,
( ~ ilf_type(X0,member_type(power_set(X1)))
| member(X0,power_set(X1)) ),
inference(unflattening,[status(thm)],[c_546]) ).
cnf(c_617,plain,
( ~ ilf_type(X0,relation_type(X1,X2))
| ilf_type(X0,subset_type(cross_product(X1,X2))) ),
inference(prop_impl_just,[status(thm)],[c_381]) ).
cnf(c_621,plain,
( ~ ilf_type(X0,subset_type(X1))
| ilf_type(X0,member_type(power_set(X1))) ),
inference(prop_impl_just,[status(thm)],[c_261]) ).
cnf(c_623,plain,
( ~ member(ordered_pair(X0,X1),cross_product(X2,X3))
| member(X1,X3) ),
inference(prop_impl_just,[status(thm)],[c_424]) ).
cnf(c_625,plain,
( ~ member(ordered_pair(X0,X1),cross_product(X2,X3))
| member(X0,X2) ),
inference(prop_impl_just,[status(thm)],[c_436]) ).
cnf(c_2163,plain,
( ~ ilf_type(X0,subset_type(X1))
| member(X0,power_set(X1))
| empty(power_set(X1)) ),
inference(superposition,[status(thm)],[c_621,c_260]) ).
cnf(c_2174,plain,
( member(X0,power_set(X1))
| ~ ilf_type(X0,subset_type(X1)) ),
inference(global_subsumption_just,[status(thm)],[c_2163,c_261,c_547]) ).
cnf(c_2175,plain,
( ~ ilf_type(X0,subset_type(X1))
| member(X0,power_set(X1)) ),
inference(renaming,[status(thm)],[c_2174]) ).
cnf(c_2926,plain,
( ~ ilf_type(X0,subset_type(X1))
| member(X0,power_set(X1))
| empty(power_set(X1)) ),
inference(superposition,[status(thm)],[c_621,c_260]) ).
cnf(c_2939,plain,
( member(X0,power_set(X1))
| ~ ilf_type(X0,subset_type(X1)) ),
inference(global_subsumption_just,[status(thm)],[c_2926,c_2175]) ).
cnf(c_2940,plain,
( ~ ilf_type(X0,subset_type(X1))
| member(X0,power_set(X1)) ),
inference(renaming,[status(thm)],[c_2939]) ).
cnf(c_2943,plain,
( ~ ilf_type(X0,relation_type(X1,X2))
| member(X0,power_set(cross_product(X1,X2))) ),
inference(superposition,[status(thm)],[c_617,c_2940]) ).
cnf(c_3082,plain,
( ~ ilf_type(X0,relation_type(X1,X2))
| ~ member(X3,X0)
| member(X3,cross_product(X1,X2)) ),
inference(superposition,[status(thm)],[c_2943,c_410]) ).
cnf(c_3736,plain,
( ~ member(X0,sK13)
| member(X0,cross_product(sK9,sK10)) ),
inference(superposition,[status(thm)],[c_93,c_3082]) ).
cnf(c_4050,plain,
( ~ member(ordered_pair(X0,X1),sK13)
| member(X0,sK9) ),
inference(superposition,[status(thm)],[c_3736,c_625]) ).
cnf(c_4051,plain,
( ~ member(ordered_pair(X0,X1),sK13)
| member(X1,sK10) ),
inference(superposition,[status(thm)],[c_3736,c_623]) ).
cnf(c_4198,plain,
member(sK11,sK9),
inference(superposition,[status(thm)],[c_92,c_4050]) ).
cnf(c_4688,plain,
member(sK12,sK10),
inference(superposition,[status(thm)],[c_92,c_4051]) ).
cnf(c_4691,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_4688,c_4198,c_91]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET645+3 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.14 % Command : run_iprover %s %d THM
% 0.14/0.36 % Computer : n021.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 08:51:12 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.22/0.49 Running first-order theorem proving
% 0.22/0.49 Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 3.96/1.18 % SZS status Started for theBenchmark.p
% 3.96/1.18 % SZS status Theorem for theBenchmark.p
% 3.96/1.18
% 3.96/1.18 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 3.96/1.18
% 3.96/1.18 ------ iProver source info
% 3.96/1.18
% 3.96/1.18 git: date: 2023-05-31 18:12:56 +0000
% 3.96/1.18 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 3.96/1.18 git: non_committed_changes: false
% 3.96/1.18 git: last_make_outside_of_git: false
% 3.96/1.18
% 3.96/1.18 ------ Parsing...
% 3.96/1.18 ------ Clausification by vclausify_rel & Parsing by iProver...
% 3.96/1.18
% 3.96/1.18 ------ 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
% 3.96/1.18
% 3.96/1.18 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 3.96/1.18
% 3.96/1.18 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.96/1.18 ------ Proving...
% 3.96/1.18 ------ Problem Properties
% 3.96/1.18
% 3.96/1.18
% 3.96/1.18 clauses 31
% 3.96/1.18 conjectures 3
% 3.96/1.18 EPR 4
% 3.96/1.18 Horn 25
% 3.96/1.18 unary 8
% 3.96/1.18 binary 17
% 3.96/1.18 lits 60
% 3.96/1.18 lits eq 6
% 3.96/1.18 fd_pure 0
% 3.96/1.18 fd_pseudo 0
% 3.96/1.18 fd_cond 0
% 3.96/1.18 fd_pseudo_cond 2
% 3.96/1.18 AC symbols 0
% 3.96/1.18
% 3.96/1.18 ------ Input Options Time Limit: Unbounded
% 3.96/1.18
% 3.96/1.18
% 3.96/1.18 ------
% 3.96/1.18 Current options:
% 3.96/1.18 ------
% 3.96/1.18
% 3.96/1.18
% 3.96/1.18
% 3.96/1.18
% 3.96/1.18 ------ Proving...
% 3.96/1.18
% 3.96/1.18
% 3.96/1.18 % SZS status Theorem for theBenchmark.p
% 3.96/1.18
% 3.96/1.18 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.96/1.18
% 3.96/1.18
%------------------------------------------------------------------------------