TSTP Solution File: SEU363+1 by iProver---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : SEU363+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n019.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 : Fri May 3 03:05:57 EDT 2024
% Result : Theorem 4.19s 1.18s
% Output : CNFRefutation 4.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 17
% Syntax : Number of formulae : 116 ( 34 unt; 0 def)
% Number of atoms : 463 ( 68 equ)
% Maximal formula atoms : 26 ( 3 avg)
% Number of connectives : 510 ( 163 ~; 141 |; 166 &)
% ( 8 <=>; 32 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 6 con; 0-2 aty)
% Number of variables : 238 ( 2 sgn 111 !; 48 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0,X1,X2] :
( element(X2,powerset(cartesian_product2(X0,X1)))
=> relation(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relset_1) ).
fof(f5,axiom,
! [X0] :
( rel_str(X0)
=> ! [X1] :
( subrelstr(X1,X0)
=> ( full_subrelstr(X1,X0)
<=> the_InternalRel(X1) = relation_restriction_as_relation_of(the_InternalRel(X0),the_carrier(X1)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d14_yellow_0) ).
fof(f6,axiom,
! [X0] :
( rel_str(X0)
=> ! [X1] :
( element(X1,the_carrier(X0))
=> ! [X2] :
( element(X2,the_carrier(X0))
=> ( related(X0,X1,X2)
<=> in(ordered_pair(X1,X2),the_InternalRel(X0)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d9_orders_2) ).
fof(f17,axiom,
! [X0] :
( rel_str(X0)
=> ! [X1] :
( subrelstr(X1,X0)
=> rel_str(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_yellow_0) ).
fof(f18,axiom,
! [X0,X1,X2] :
( relation_of2_as_subset(X2,X0,X1)
=> element(X2,powerset(cartesian_product2(X0,X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m2_relset_1) ).
fof(f19,axiom,
! [X0] :
( rel_str(X0)
=> relation_of2_as_subset(the_InternalRel(X0),the_carrier(X0),the_carrier(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_u1_orders_2) ).
fof(f34,axiom,
! [X0,X1] :
( relation(X0)
=> relation_restriction_as_relation_of(X0,X1) = relation_restriction(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k1_toler_1) ).
fof(f35,axiom,
! [X0,X1,X2] :
( relation_of2_as_subset(X2,X0,X1)
<=> relation_of2(X2,X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
fof(f37,axiom,
! [X0,X1,X2,X3] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
<=> ( in(X1,X3)
& in(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t106_zfmisc_1) ).
fof(f38,axiom,
! [X0,X1,X2] :
( relation(X2)
=> ( in(X0,relation_restriction(X2,X1))
<=> ( in(X0,cartesian_product2(X1,X1))
& in(X0,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_wellord1) ).
fof(f44,conjecture,
! [X0] :
( rel_str(X0)
=> ! [X1] :
( ( subrelstr(X1,X0)
& full_subrelstr(X1,X0) )
=> ! [X2] :
( element(X2,the_carrier(X0))
=> ! [X3] :
( element(X3,the_carrier(X0))
=> ! [X4] :
( element(X4,the_carrier(X1))
=> ! [X5] :
( element(X5,the_carrier(X1))
=> ( ( in(X5,the_carrier(X1))
& in(X4,the_carrier(X1))
& related(X0,X2,X3)
& X3 = X5
& X2 = X4 )
=> related(X1,X4,X5) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t61_yellow_0) ).
fof(f45,negated_conjecture,
~ ! [X0] :
( rel_str(X0)
=> ! [X1] :
( ( subrelstr(X1,X0)
& full_subrelstr(X1,X0) )
=> ! [X2] :
( element(X2,the_carrier(X0))
=> ! [X3] :
( element(X3,the_carrier(X0))
=> ! [X4] :
( element(X4,the_carrier(X1))
=> ! [X5] :
( element(X5,the_carrier(X1))
=> ( ( in(X5,the_carrier(X1))
& in(X4,the_carrier(X1))
& related(X0,X2,X3)
& X3 = X5
& X2 = X4 )
=> related(X1,X4,X5) ) ) ) ) ) ) ),
inference(negated_conjecture,[],[f44]) ).
fof(f55,plain,
! [X0,X1,X2] :
( relation(X2)
| ~ element(X2,powerset(cartesian_product2(X0,X1))) ),
inference(ennf_transformation,[],[f3]) ).
fof(f57,plain,
! [X0] :
( ! [X1] :
( ( full_subrelstr(X1,X0)
<=> the_InternalRel(X1) = relation_restriction_as_relation_of(the_InternalRel(X0),the_carrier(X1)) )
| ~ subrelstr(X1,X0) )
| ~ rel_str(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f58,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( related(X0,X1,X2)
<=> in(ordered_pair(X1,X2),the_InternalRel(X0)) )
| ~ element(X2,the_carrier(X0)) )
| ~ element(X1,the_carrier(X0)) )
| ~ rel_str(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f61,plain,
! [X0] :
( ! [X1] :
( rel_str(X1)
| ~ subrelstr(X1,X0) )
| ~ rel_str(X0) ),
inference(ennf_transformation,[],[f17]) ).
fof(f62,plain,
! [X0,X1,X2] :
( element(X2,powerset(cartesian_product2(X0,X1)))
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(ennf_transformation,[],[f18]) ).
fof(f63,plain,
! [X0] :
( relation_of2_as_subset(the_InternalRel(X0),the_carrier(X0),the_carrier(X0))
| ~ rel_str(X0) ),
inference(ennf_transformation,[],[f19]) ).
fof(f69,plain,
! [X0,X1] :
( relation_restriction_as_relation_of(X0,X1) = relation_restriction(X0,X1)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f34]) ).
fof(f70,plain,
! [X0,X1,X2] :
( ( in(X0,relation_restriction(X2,X1))
<=> ( in(X0,cartesian_product2(X1,X1))
& in(X0,X2) ) )
| ~ relation(X2) ),
inference(ennf_transformation,[],[f38]) ).
fof(f78,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ related(X1,X4,X5)
& in(X5,the_carrier(X1))
& in(X4,the_carrier(X1))
& related(X0,X2,X3)
& X3 = X5
& X2 = X4
& element(X5,the_carrier(X1)) )
& element(X4,the_carrier(X1)) )
& element(X3,the_carrier(X0)) )
& element(X2,the_carrier(X0)) )
& subrelstr(X1,X0)
& full_subrelstr(X1,X0) )
& rel_str(X0) ),
inference(ennf_transformation,[],[f45]) ).
fof(f79,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ related(X1,X4,X5)
& in(X5,the_carrier(X1))
& in(X4,the_carrier(X1))
& related(X0,X2,X3)
& X3 = X5
& X2 = X4
& element(X5,the_carrier(X1)) )
& element(X4,the_carrier(X1)) )
& element(X3,the_carrier(X0)) )
& element(X2,the_carrier(X0)) )
& subrelstr(X1,X0)
& full_subrelstr(X1,X0) )
& rel_str(X0) ),
inference(flattening,[],[f78]) ).
fof(f83,plain,
! [X0] :
( ! [X1] :
( ( ( full_subrelstr(X1,X0)
| the_InternalRel(X1) != relation_restriction_as_relation_of(the_InternalRel(X0),the_carrier(X1)) )
& ( the_InternalRel(X1) = relation_restriction_as_relation_of(the_InternalRel(X0),the_carrier(X1))
| ~ full_subrelstr(X1,X0) ) )
| ~ subrelstr(X1,X0) )
| ~ rel_str(X0) ),
inference(nnf_transformation,[],[f57]) ).
fof(f84,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( related(X0,X1,X2)
| ~ in(ordered_pair(X1,X2),the_InternalRel(X0)) )
& ( in(ordered_pair(X1,X2),the_InternalRel(X0))
| ~ related(X0,X1,X2) ) )
| ~ element(X2,the_carrier(X0)) )
| ~ element(X1,the_carrier(X0)) )
| ~ rel_str(X0) ),
inference(nnf_transformation,[],[f58]) ).
fof(f105,plain,
! [X0,X1,X2] :
( ( relation_of2_as_subset(X2,X0,X1)
| ~ relation_of2(X2,X0,X1) )
& ( relation_of2(X2,X0,X1)
| ~ relation_of2_as_subset(X2,X0,X1) ) ),
inference(nnf_transformation,[],[f35]) ).
fof(f106,plain,
! [X0,X1,X2,X3] :
( ( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ~ in(X1,X3)
| ~ in(X0,X2) )
& ( ( in(X1,X3)
& in(X0,X2) )
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ) ),
inference(nnf_transformation,[],[f37]) ).
fof(f107,plain,
! [X0,X1,X2,X3] :
( ( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ~ in(X1,X3)
| ~ in(X0,X2) )
& ( ( in(X1,X3)
& in(X0,X2) )
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ) ),
inference(flattening,[],[f106]) ).
fof(f108,plain,
! [X0,X1,X2] :
( ( ( in(X0,relation_restriction(X2,X1))
| ~ in(X0,cartesian_product2(X1,X1))
| ~ in(X0,X2) )
& ( ( in(X0,cartesian_product2(X1,X1))
& in(X0,X2) )
| ~ in(X0,relation_restriction(X2,X1)) ) )
| ~ relation(X2) ),
inference(nnf_transformation,[],[f70]) ).
fof(f109,plain,
! [X0,X1,X2] :
( ( ( in(X0,relation_restriction(X2,X1))
| ~ in(X0,cartesian_product2(X1,X1))
| ~ in(X0,X2) )
& ( ( in(X0,cartesian_product2(X1,X1))
& in(X0,X2) )
| ~ in(X0,relation_restriction(X2,X1)) ) )
| ~ relation(X2) ),
inference(flattening,[],[f108]) ).
fof(f110,plain,
( ? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ related(X1,X4,X5)
& in(X5,the_carrier(X1))
& in(X4,the_carrier(X1))
& related(X0,X2,X3)
& X3 = X5
& X2 = X4
& element(X5,the_carrier(X1)) )
& element(X4,the_carrier(X1)) )
& element(X3,the_carrier(X0)) )
& element(X2,the_carrier(X0)) )
& subrelstr(X1,X0)
& full_subrelstr(X1,X0) )
& rel_str(X0) )
=> ( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ related(X1,X4,X5)
& in(X5,the_carrier(X1))
& in(X4,the_carrier(X1))
& related(sK10,X2,X3)
& X3 = X5
& X2 = X4
& element(X5,the_carrier(X1)) )
& element(X4,the_carrier(X1)) )
& element(X3,the_carrier(sK10)) )
& element(X2,the_carrier(sK10)) )
& subrelstr(X1,sK10)
& full_subrelstr(X1,sK10) )
& rel_str(sK10) ) ),
introduced(choice_axiom,[]) ).
fof(f111,plain,
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ related(X1,X4,X5)
& in(X5,the_carrier(X1))
& in(X4,the_carrier(X1))
& related(sK10,X2,X3)
& X3 = X5
& X2 = X4
& element(X5,the_carrier(X1)) )
& element(X4,the_carrier(X1)) )
& element(X3,the_carrier(sK10)) )
& element(X2,the_carrier(sK10)) )
& subrelstr(X1,sK10)
& full_subrelstr(X1,sK10) )
=> ( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ related(sK11,X4,X5)
& in(X5,the_carrier(sK11))
& in(X4,the_carrier(sK11))
& related(sK10,X2,X3)
& X3 = X5
& X2 = X4
& element(X5,the_carrier(sK11)) )
& element(X4,the_carrier(sK11)) )
& element(X3,the_carrier(sK10)) )
& element(X2,the_carrier(sK10)) )
& subrelstr(sK11,sK10)
& full_subrelstr(sK11,sK10) ) ),
introduced(choice_axiom,[]) ).
fof(f112,plain,
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ related(sK11,X4,X5)
& in(X5,the_carrier(sK11))
& in(X4,the_carrier(sK11))
& related(sK10,X2,X3)
& X3 = X5
& X2 = X4
& element(X5,the_carrier(sK11)) )
& element(X4,the_carrier(sK11)) )
& element(X3,the_carrier(sK10)) )
& element(X2,the_carrier(sK10)) )
=> ( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ related(sK11,X4,X5)
& in(X5,the_carrier(sK11))
& in(X4,the_carrier(sK11))
& related(sK10,sK12,X3)
& X3 = X5
& sK12 = X4
& element(X5,the_carrier(sK11)) )
& element(X4,the_carrier(sK11)) )
& element(X3,the_carrier(sK10)) )
& element(sK12,the_carrier(sK10)) ) ),
introduced(choice_axiom,[]) ).
fof(f113,plain,
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ related(sK11,X4,X5)
& in(X5,the_carrier(sK11))
& in(X4,the_carrier(sK11))
& related(sK10,sK12,X3)
& X3 = X5
& sK12 = X4
& element(X5,the_carrier(sK11)) )
& element(X4,the_carrier(sK11)) )
& element(X3,the_carrier(sK10)) )
=> ( ? [X4] :
( ? [X5] :
( ~ related(sK11,X4,X5)
& in(X5,the_carrier(sK11))
& in(X4,the_carrier(sK11))
& related(sK10,sK12,sK13)
& sK13 = X5
& sK12 = X4
& element(X5,the_carrier(sK11)) )
& element(X4,the_carrier(sK11)) )
& element(sK13,the_carrier(sK10)) ) ),
introduced(choice_axiom,[]) ).
fof(f114,plain,
( ? [X4] :
( ? [X5] :
( ~ related(sK11,X4,X5)
& in(X5,the_carrier(sK11))
& in(X4,the_carrier(sK11))
& related(sK10,sK12,sK13)
& sK13 = X5
& sK12 = X4
& element(X5,the_carrier(sK11)) )
& element(X4,the_carrier(sK11)) )
=> ( ? [X5] :
( ~ related(sK11,sK14,X5)
& in(X5,the_carrier(sK11))
& in(sK14,the_carrier(sK11))
& related(sK10,sK12,sK13)
& sK13 = X5
& sK12 = sK14
& element(X5,the_carrier(sK11)) )
& element(sK14,the_carrier(sK11)) ) ),
introduced(choice_axiom,[]) ).
fof(f115,plain,
( ? [X5] :
( ~ related(sK11,sK14,X5)
& in(X5,the_carrier(sK11))
& in(sK14,the_carrier(sK11))
& related(sK10,sK12,sK13)
& sK13 = X5
& sK12 = sK14
& element(X5,the_carrier(sK11)) )
=> ( ~ related(sK11,sK14,sK15)
& in(sK15,the_carrier(sK11))
& in(sK14,the_carrier(sK11))
& related(sK10,sK12,sK13)
& sK13 = sK15
& sK12 = sK14
& element(sK15,the_carrier(sK11)) ) ),
introduced(choice_axiom,[]) ).
fof(f116,plain,
( ~ related(sK11,sK14,sK15)
& in(sK15,the_carrier(sK11))
& in(sK14,the_carrier(sK11))
& related(sK10,sK12,sK13)
& sK13 = sK15
& sK12 = sK14
& element(sK15,the_carrier(sK11))
& element(sK14,the_carrier(sK11))
& element(sK13,the_carrier(sK10))
& element(sK12,the_carrier(sK10))
& subrelstr(sK11,sK10)
& full_subrelstr(sK11,sK10)
& rel_str(sK10) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10,sK11,sK12,sK13,sK14,sK15])],[f79,f115,f114,f113,f112,f111,f110]) ).
fof(f119,plain,
! [X2,X0,X1] :
( relation(X2)
| ~ element(X2,powerset(cartesian_product2(X0,X1))) ),
inference(cnf_transformation,[],[f55]) ).
fof(f121,plain,
! [X0,X1] :
( the_InternalRel(X1) = relation_restriction_as_relation_of(the_InternalRel(X0),the_carrier(X1))
| ~ full_subrelstr(X1,X0)
| ~ subrelstr(X1,X0)
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f83]) ).
fof(f123,plain,
! [X2,X0,X1] :
( in(ordered_pair(X1,X2),the_InternalRel(X0))
| ~ related(X0,X1,X2)
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f84]) ).
fof(f124,plain,
! [X2,X0,X1] :
( related(X0,X1,X2)
| ~ in(ordered_pair(X1,X2),the_InternalRel(X0))
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f84]) ).
fof(f127,plain,
! [X0,X1] :
( rel_str(X1)
| ~ subrelstr(X1,X0)
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f61]) ).
fof(f128,plain,
! [X2,X0,X1] :
( element(X2,powerset(cartesian_product2(X0,X1)))
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(cnf_transformation,[],[f62]) ).
fof(f129,plain,
! [X0] :
( relation_of2_as_subset(the_InternalRel(X0),the_carrier(X0),the_carrier(X0))
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f63]) ).
fof(f147,plain,
! [X0,X1] :
( relation_restriction_as_relation_of(X0,X1) = relation_restriction(X0,X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f69]) ).
fof(f148,plain,
! [X2,X0,X1] :
( relation_of2(X2,X0,X1)
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(cnf_transformation,[],[f105]) ).
fof(f149,plain,
! [X2,X0,X1] :
( relation_of2_as_subset(X2,X0,X1)
| ~ relation_of2(X2,X0,X1) ),
inference(cnf_transformation,[],[f105]) ).
fof(f153,plain,
! [X2,X3,X0,X1] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ~ in(X1,X3)
| ~ in(X0,X2) ),
inference(cnf_transformation,[],[f107]) ).
fof(f156,plain,
! [X2,X0,X1] :
( in(X0,relation_restriction(X2,X1))
| ~ in(X0,cartesian_product2(X1,X1))
| ~ in(X0,X2)
| ~ relation(X2) ),
inference(cnf_transformation,[],[f109]) ).
fof(f162,plain,
rel_str(sK10),
inference(cnf_transformation,[],[f116]) ).
fof(f163,plain,
full_subrelstr(sK11,sK10),
inference(cnf_transformation,[],[f116]) ).
fof(f164,plain,
subrelstr(sK11,sK10),
inference(cnf_transformation,[],[f116]) ).
fof(f165,plain,
element(sK12,the_carrier(sK10)),
inference(cnf_transformation,[],[f116]) ).
fof(f166,plain,
element(sK13,the_carrier(sK10)),
inference(cnf_transformation,[],[f116]) ).
fof(f167,plain,
element(sK14,the_carrier(sK11)),
inference(cnf_transformation,[],[f116]) ).
fof(f168,plain,
element(sK15,the_carrier(sK11)),
inference(cnf_transformation,[],[f116]) ).
fof(f169,plain,
sK12 = sK14,
inference(cnf_transformation,[],[f116]) ).
fof(f170,plain,
sK13 = sK15,
inference(cnf_transformation,[],[f116]) ).
fof(f171,plain,
related(sK10,sK12,sK13),
inference(cnf_transformation,[],[f116]) ).
fof(f172,plain,
in(sK14,the_carrier(sK11)),
inference(cnf_transformation,[],[f116]) ).
fof(f173,plain,
in(sK15,the_carrier(sK11)),
inference(cnf_transformation,[],[f116]) ).
fof(f174,plain,
~ related(sK11,sK14,sK15),
inference(cnf_transformation,[],[f116]) ).
fof(f178,plain,
related(sK10,sK14,sK15),
inference(definition_unfolding,[],[f171,f169,f170]) ).
fof(f179,plain,
element(sK15,the_carrier(sK10)),
inference(definition_unfolding,[],[f166,f170]) ).
fof(f180,plain,
element(sK14,the_carrier(sK10)),
inference(definition_unfolding,[],[f165,f169]) ).
cnf(c_51,plain,
( ~ element(X0,powerset(cartesian_product2(X1,X2)))
| relation(X0) ),
inference(cnf_transformation,[],[f119]) ).
cnf(c_54,plain,
( ~ full_subrelstr(X0,X1)
| ~ subrelstr(X0,X1)
| ~ rel_str(X1)
| relation_restriction_as_relation_of(the_InternalRel(X1),the_carrier(X0)) = the_InternalRel(X0) ),
inference(cnf_transformation,[],[f121]) ).
cnf(c_55,plain,
( ~ in(ordered_pair(X0,X1),the_InternalRel(X2))
| ~ element(X0,the_carrier(X2))
| ~ element(X1,the_carrier(X2))
| ~ rel_str(X2)
| related(X2,X0,X1) ),
inference(cnf_transformation,[],[f124]) ).
cnf(c_56,plain,
( ~ related(X0,X1,X2)
| ~ element(X1,the_carrier(X0))
| ~ element(X2,the_carrier(X0))
| ~ rel_str(X0)
| in(ordered_pair(X1,X2),the_InternalRel(X0)) ),
inference(cnf_transformation,[],[f123]) ).
cnf(c_59,plain,
( ~ subrelstr(X0,X1)
| ~ rel_str(X1)
| rel_str(X0) ),
inference(cnf_transformation,[],[f127]) ).
cnf(c_60,plain,
( ~ relation_of2_as_subset(X0,X1,X2)
| element(X0,powerset(cartesian_product2(X1,X2))) ),
inference(cnf_transformation,[],[f128]) ).
cnf(c_61,plain,
( ~ rel_str(X0)
| relation_of2_as_subset(the_InternalRel(X0),the_carrier(X0),the_carrier(X0)) ),
inference(cnf_transformation,[],[f129]) ).
cnf(c_79,plain,
( ~ relation(X0)
| relation_restriction_as_relation_of(X0,X1) = relation_restriction(X0,X1) ),
inference(cnf_transformation,[],[f147]) ).
cnf(c_80,plain,
( ~ relation_of2(X0,X1,X2)
| relation_of2_as_subset(X0,X1,X2) ),
inference(cnf_transformation,[],[f149]) ).
cnf(c_81,plain,
( ~ relation_of2_as_subset(X0,X1,X2)
| relation_of2(X0,X1,X2) ),
inference(cnf_transformation,[],[f148]) ).
cnf(c_83,plain,
( ~ in(X0,X1)
| ~ in(X2,X3)
| in(ordered_pair(X2,X0),cartesian_product2(X3,X1)) ),
inference(cnf_transformation,[],[f153]) ).
cnf(c_86,plain,
( ~ in(X0,cartesian_product2(X1,X1))
| ~ in(X0,X2)
| ~ relation(X2)
| in(X0,relation_restriction(X2,X1)) ),
inference(cnf_transformation,[],[f156]) ).
cnf(c_94,negated_conjecture,
~ related(sK11,sK14,sK15),
inference(cnf_transformation,[],[f174]) ).
cnf(c_95,negated_conjecture,
in(sK15,the_carrier(sK11)),
inference(cnf_transformation,[],[f173]) ).
cnf(c_96,negated_conjecture,
in(sK14,the_carrier(sK11)),
inference(cnf_transformation,[],[f172]) ).
cnf(c_97,negated_conjecture,
related(sK10,sK14,sK15),
inference(cnf_transformation,[],[f178]) ).
cnf(c_98,negated_conjecture,
element(sK15,the_carrier(sK11)),
inference(cnf_transformation,[],[f168]) ).
cnf(c_99,negated_conjecture,
element(sK14,the_carrier(sK11)),
inference(cnf_transformation,[],[f167]) ).
cnf(c_100,negated_conjecture,
element(sK15,the_carrier(sK10)),
inference(cnf_transformation,[],[f179]) ).
cnf(c_101,negated_conjecture,
element(sK14,the_carrier(sK10)),
inference(cnf_transformation,[],[f180]) ).
cnf(c_102,negated_conjecture,
subrelstr(sK11,sK10),
inference(cnf_transformation,[],[f164]) ).
cnf(c_103,negated_conjecture,
full_subrelstr(sK11,sK10),
inference(cnf_transformation,[],[f163]) ).
cnf(c_104,negated_conjecture,
rel_str(sK10),
inference(cnf_transformation,[],[f162]) ).
cnf(c_143,plain,
( relation_of2(X0,X1,X2)
| ~ relation_of2_as_subset(X0,X1,X2) ),
inference(prop_impl_just,[status(thm)],[c_81]) ).
cnf(c_144,plain,
( ~ relation_of2_as_subset(X0,X1,X2)
| relation_of2(X0,X1,X2) ),
inference(renaming,[status(thm)],[c_143]) ).
cnf(c_175,plain,
( element(X0,powerset(cartesian_product2(X1,X2)))
| ~ relation_of2(X0,X1,X2) ),
inference(prop_impl_just,[status(thm)],[c_80,c_60]) ).
cnf(c_176,plain,
( ~ relation_of2(X0,X1,X2)
| element(X0,powerset(cartesian_product2(X1,X2))) ),
inference(renaming,[status(thm)],[c_175]) ).
cnf(c_185,plain,
( ~ rel_str(X0)
| relation_of2_as_subset(the_InternalRel(X0),the_carrier(X0),the_carrier(X0)) ),
inference(prop_impl_just,[status(thm)],[c_61]) ).
cnf(c_586,plain,
( X0 != X1
| X2 != X3
| X4 != X5
| ~ relation_of2_as_subset(X0,X2,X4)
| element(X1,powerset(cartesian_product2(X3,X5))) ),
inference(resolution_lifted,[status(thm)],[c_144,c_176]) ).
cnf(c_587,plain,
( ~ relation_of2_as_subset(X0,X1,X2)
| element(X0,powerset(cartesian_product2(X1,X2))) ),
inference(unflattening,[status(thm)],[c_586]) ).
cnf(c_621,plain,
( the_InternalRel(X0) != X1
| the_carrier(X0) != X2
| the_carrier(X0) != X3
| ~ rel_str(X0)
| element(X1,powerset(cartesian_product2(X2,X3))) ),
inference(resolution_lifted,[status(thm)],[c_587,c_185]) ).
cnf(c_622,plain,
( ~ rel_str(X0)
| element(the_InternalRel(X0),powerset(cartesian_product2(the_carrier(X0),the_carrier(X0)))) ),
inference(unflattening,[status(thm)],[c_621]) ).
cnf(c_645,plain,
( X0 != sK11
| X1 != sK10
| ~ subrelstr(X0,X1)
| ~ rel_str(X1)
| relation_restriction_as_relation_of(the_InternalRel(X1),the_carrier(X0)) = the_InternalRel(X0) ),
inference(resolution_lifted,[status(thm)],[c_54,c_103]) ).
cnf(c_646,plain,
( ~ subrelstr(sK11,sK10)
| ~ rel_str(sK10)
| relation_restriction_as_relation_of(the_InternalRel(sK10),the_carrier(sK11)) = the_InternalRel(sK11) ),
inference(unflattening,[status(thm)],[c_645]) ).
cnf(c_647,plain,
relation_restriction_as_relation_of(the_InternalRel(sK10),the_carrier(sK11)) = the_InternalRel(sK11),
inference(global_subsumption_just,[status(thm)],[c_646,c_104,c_102,c_646]) ).
cnf(c_662,plain,
( X0 != sK11
| X1 != sK10
| ~ rel_str(X1)
| rel_str(X0) ),
inference(resolution_lifted,[status(thm)],[c_59,c_102]) ).
cnf(c_663,plain,
( ~ rel_str(sK10)
| rel_str(sK11) ),
inference(unflattening,[status(thm)],[c_662]) ).
cnf(c_674,plain,
( X0 != sK14
| X1 != sK15
| X2 != sK11
| ~ in(ordered_pair(X0,X1),the_InternalRel(X2))
| ~ element(X0,the_carrier(X2))
| ~ element(X1,the_carrier(X2))
| ~ rel_str(X2) ),
inference(resolution_lifted,[status(thm)],[c_55,c_94]) ).
cnf(c_675,plain,
( ~ in(ordered_pair(sK14,sK15),the_InternalRel(sK11))
| ~ element(sK14,the_carrier(sK11))
| ~ element(sK15,the_carrier(sK11))
| ~ rel_str(sK11) ),
inference(unflattening,[status(thm)],[c_674]) ).
cnf(c_681,plain,
( X0 != sK10
| X1 != sK14
| X2 != sK15
| ~ element(X1,the_carrier(X0))
| ~ element(X2,the_carrier(X0))
| ~ rel_str(X0)
| in(ordered_pair(X1,X2),the_InternalRel(X0)) ),
inference(resolution_lifted,[status(thm)],[c_56,c_97]) ).
cnf(c_682,plain,
( ~ element(sK14,the_carrier(sK10))
| ~ element(sK15,the_carrier(sK10))
| ~ rel_str(sK10)
| in(ordered_pair(sK14,sK15),the_InternalRel(sK10)) ),
inference(unflattening,[status(thm)],[c_681]) ).
cnf(c_683,plain,
in(ordered_pair(sK14,sK15),the_InternalRel(sK10)),
inference(global_subsumption_just,[status(thm)],[c_682,c_104,c_101,c_100,c_682]) ).
cnf(c_1410,plain,
( ~ rel_str(X0)
| relation(the_InternalRel(X0)) ),
inference(superposition,[status(thm)],[c_622,c_51]) ).
cnf(c_1515,plain,
( ~ rel_str(X0)
| relation_restriction_as_relation_of(the_InternalRel(X0),X1) = relation_restriction(the_InternalRel(X0),X1) ),
inference(superposition,[status(thm)],[c_1410,c_79]) ).
cnf(c_1530,plain,
relation_restriction_as_relation_of(the_InternalRel(sK10),X0) = relation_restriction(the_InternalRel(sK10),X0),
inference(superposition,[status(thm)],[c_104,c_1515]) ).
cnf(c_1536,plain,
relation_restriction(the_InternalRel(sK10),the_carrier(sK11)) = the_InternalRel(sK11),
inference(superposition,[status(thm)],[c_647,c_1530]) ).
cnf(c_1635,plain,
( ~ in(ordered_pair(X0,X1),X2)
| ~ in(X0,X3)
| ~ in(X1,X3)
| ~ relation(X2)
| in(ordered_pair(X0,X1),relation_restriction(X2,X3)) ),
inference(superposition,[status(thm)],[c_83,c_86]) ).
cnf(c_1657,plain,
( ~ in(ordered_pair(X0,X1),the_InternalRel(sK10))
| ~ in(X0,the_carrier(sK11))
| ~ in(X1,the_carrier(sK11))
| ~ relation(the_InternalRel(sK10))
| in(ordered_pair(X0,X1),the_InternalRel(sK11)) ),
inference(superposition,[status(thm)],[c_1536,c_1635]) ).
cnf(c_1710,plain,
( ~ in(sK14,the_carrier(sK11))
| ~ in(sK15,the_carrier(sK11))
| ~ relation(the_InternalRel(sK10))
| in(ordered_pair(sK14,sK15),the_InternalRel(sK11)) ),
inference(superposition,[status(thm)],[c_683,c_1657]) ).
cnf(c_1711,plain,
~ relation(the_InternalRel(sK10)),
inference(global_subsumption_just,[status(thm)],[c_1710,c_104,c_99,c_98,c_96,c_95,c_663,c_675,c_1710]) ).
cnf(c_1713,plain,
~ rel_str(sK10),
inference(superposition,[status(thm)],[c_1410,c_1711]) ).
cnf(c_1714,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_1713,c_104]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU363+1 : TPTP v8.1.2. Released v3.3.0.
% 0.07/0.13 % Command : run_iprover %s %d THM
% 0.13/0.34 % Computer : n019.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.35 % DateTime : Thu May 2 17:46:29 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.20/0.48 Running first-order theorem proving
% 0.20/0.48 Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 4.19/1.18 % SZS status Started for theBenchmark.p
% 4.19/1.18 % SZS status Theorem for theBenchmark.p
% 4.19/1.18
% 4.19/1.18 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 4.19/1.18
% 4.19/1.18 ------ iProver source info
% 4.19/1.18
% 4.19/1.18 git: date: 2024-05-02 19:28:25 +0000
% 4.19/1.18 git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 4.19/1.18 git: non_committed_changes: false
% 4.19/1.18
% 4.19/1.18 ------ Parsing...
% 4.19/1.18 ------ Clausification by vclausify_rel & Parsing by iProver...
% 4.19/1.18
% 4.19/1.18 ------ Preprocessing... sup_sim: 0 sf_s rm: 8 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe_e sup_sim: 0 sf_s rm: 7 0s sf_e pe_s pe_e
% 4.19/1.18
% 4.19/1.18 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 4.19/1.18
% 4.19/1.18 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 4.19/1.18 ------ Proving...
% 4.19/1.18 ------ Problem Properties
% 4.19/1.18
% 4.19/1.18
% 4.19/1.18 clauses 45
% 4.19/1.18 conjectures 7
% 4.19/1.18 EPR 14
% 4.19/1.18 Horn 42
% 4.19/1.18 unary 21
% 4.19/1.18 binary 16
% 4.19/1.18 lits 78
% 4.19/1.18 lits eq 5
% 4.19/1.18 fd_pure 0
% 4.19/1.18 fd_pseudo 0
% 4.19/1.18 fd_cond 1
% 4.19/1.18 fd_pseudo_cond 1
% 4.19/1.18 AC symbols 0
% 4.19/1.18
% 4.19/1.18 ------ Input Options Time Limit: Unbounded
% 4.19/1.18
% 4.19/1.18
% 4.19/1.18 ------
% 4.19/1.18 Current options:
% 4.19/1.18 ------
% 4.19/1.18
% 4.19/1.18
% 4.19/1.18
% 4.19/1.18
% 4.19/1.18 ------ Proving...
% 4.19/1.18
% 4.19/1.18
% 4.19/1.18 % SZS status Theorem for theBenchmark.p
% 4.19/1.18
% 4.19/1.18 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.19/1.18
% 4.19/1.18
%------------------------------------------------------------------------------