%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL450+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 11:52:28 AM UTC 2026
% Result : Theorem 24.27s 6.30s
% Output : Refutation 39.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 64
% Syntax : Number of formulae : 418 ( 111 unt; 29 def)
% Number of atoms : 916 ( 33 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 864 ( 366 ~; 397 |; 41 &)
% ( 32 <=>; 28 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 39 ( 37 usr; 37 prp; 0-2 aty)
% Number of functors : 24 ( 24 usr; 19 con; 0-2 aty)
% Number of variables : 463 ( 0 sgn 432 !; 31 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
( modus_ponens
<=> ! [X0,X1] :
( ( is_a_theorem(X0)
& is_a_theorem(implies(X0,X1)) )
=> is_a_theorem(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',modus_ponens) ).
fof(f3,axiom,
( modus_tollens
<=> ! [X0,X1] : is_a_theorem(implies(implies(not(X1),not(X0)),implies(X0,X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',modus_tollens) ).
fof(f4,axiom,
( implies_1
<=> ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',implies_1) ).
fof(f5,axiom,
( implies_2
<=> ! [X0,X1] : is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',implies_2) ).
fof(f6,axiom,
( implies_3
<=> ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',implies_3) ).
fof(f7,axiom,
( and_1
<=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_1) ).
fof(f8,axiom,
( and_2
<=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_2) ).
fof(f9,axiom,
( and_3
<=> ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,and(X0,X1)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_3) ).
fof(f10,axiom,
( or_1
<=> ! [X0,X1] : is_a_theorem(implies(X0,or(X0,X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',or_1) ).
fof(f11,axiom,
( or_2
<=> ! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',or_2) ).
fof(f12,axiom,
( or_3
<=> ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X2),implies(implies(X1,X2),implies(or(X0,X1),X2)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',or_3) ).
fof(f13,axiom,
( equivalence_1
<=> ! [X0,X1] : is_a_theorem(implies(equiv(X0,X1),implies(X0,X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equivalence_1) ).
fof(f14,axiom,
( equivalence_2
<=> ! [X0,X1] : is_a_theorem(implies(equiv(X0,X1),implies(X1,X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equivalence_2) ).
fof(f15,axiom,
( equivalence_3
<=> ! [X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equivalence_3) ).
fof(f27,axiom,
( op_or
=> ! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',op_or) ).
fof(f29,axiom,
( op_implies_and
=> ! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',op_implies_and) ).
fof(f31,axiom,
( op_equiv
=> ! [X0,X1] : equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',op_equiv) ).
fof(f32,axiom,
op_or,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_op_or) ).
fof(f33,axiom,
op_implies_and,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_op_implies_and) ).
fof(f34,axiom,
op_equiv,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_op_equiv) ).
fof(f35,axiom,
modus_ponens,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_modus_ponens) ).
fof(f36,axiom,
modus_tollens,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_modus_tollens) ).
fof(f37,axiom,
implies_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_implies_1) ).
fof(f38,axiom,
implies_2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_implies_2) ).
fof(f39,axiom,
implies_3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_implies_3) ).
fof(f40,axiom,
and_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_and_1) ).
fof(f41,axiom,
and_2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_and_2) ).
fof(f42,axiom,
and_3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_and_3) ).
fof(f43,axiom,
or_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_or_1) ).
fof(f44,axiom,
or_2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_or_2) ).
fof(f45,axiom,
or_3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_or_3) ).
fof(f46,axiom,
equivalence_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_equivalence_1) ).
fof(f47,axiom,
equivalence_2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_equivalence_2) ).
fof(f48,axiom,
equivalence_3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_equivalence_3) ).
fof(f49,conjecture,
( ! [X0] : is_a_theorem(equiv(X0,X0))
& ! [X0,X1] :
( is_a_theorem(equiv(X0,X1))
=> is_a_theorem(equiv(not(X0),not(X1))) )
& ! [X2,X3,X4,X5] :
( ( is_a_theorem(equiv(X2,X3))
& is_a_theorem(equiv(X4,X5)) )
=> is_a_theorem(equiv(and(X2,X4),and(X3,X5))) )
& ! [X0,X1] :
( ( is_a_theorem(X0)
& is_a_theorem(equiv(X0,X1)) )
=> is_a_theorem(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equiv_congruence) ).
fof(f50,negated_conjecture,
~ ( ! [X0] : is_a_theorem(equiv(X0,X0))
& ! [X0,X1] :
( is_a_theorem(equiv(X0,X1))
=> is_a_theorem(equiv(not(X0),not(X1))) )
& ! [X2,X3,X4,X5] :
( ( is_a_theorem(equiv(X2,X3))
& is_a_theorem(equiv(X4,X5)) )
=> is_a_theorem(equiv(and(X2,X4),and(X3,X5))) )
& ! [X0,X1] :
( ( is_a_theorem(X0)
& is_a_theorem(equiv(X0,X1)) )
=> is_a_theorem(X1) ) ),
inference(negated_conjecture,[status(cth)],[f49]) ).
fof(f51,plain,
~ ( ! [X0] : is_a_theorem(equiv(X0,X0))
& ! [X1,X2] :
( is_a_theorem(equiv(X1,X2))
=> is_a_theorem(equiv(not(X1),not(X2))) )
& ! [X3,X4,X5,X6] :
( ( is_a_theorem(equiv(X3,X4))
& is_a_theorem(equiv(X5,X6)) )
=> is_a_theorem(equiv(and(X3,X5),and(X4,X6))) )
& ! [X7,X8] :
( ( is_a_theorem(X7)
& is_a_theorem(equiv(X7,X8)) )
=> is_a_theorem(X8) ) ),
inference(rectify,[],[f50]) ).
fof(f52,plain,
( equivalence_3
=> ! [X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1)))) ),
inference(unused_predicate_definition_removal,[],[f15]) ).
fof(f53,plain,
( equivalence_2
=> ! [X0,X1] : is_a_theorem(implies(equiv(X0,X1),implies(X1,X0))) ),
inference(unused_predicate_definition_removal,[],[f14]) ).
fof(f54,plain,
( equivalence_1
=> ! [X0,X1] : is_a_theorem(implies(equiv(X0,X1),implies(X0,X1))) ),
inference(unused_predicate_definition_removal,[],[f13]) ).
fof(f55,plain,
( or_3
=> ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X2),implies(implies(X1,X2),implies(or(X0,X1),X2)))) ),
inference(unused_predicate_definition_removal,[],[f12]) ).
fof(f56,plain,
( or_2
=> ! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1))) ),
inference(unused_predicate_definition_removal,[],[f11]) ).
fof(f57,plain,
( or_1
=> ! [X0,X1] : is_a_theorem(implies(X0,or(X0,X1))) ),
inference(unused_predicate_definition_removal,[],[f10]) ).
fof(f58,plain,
( and_3
=> ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,and(X0,X1)))) ),
inference(unused_predicate_definition_removal,[],[f9]) ).
fof(f59,plain,
( and_2
=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X1)) ),
inference(unused_predicate_definition_removal,[],[f8]) ).
fof(f60,plain,
( and_1
=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0)) ),
inference(unused_predicate_definition_removal,[],[f7]) ).
fof(f61,plain,
( implies_3
=> ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))) ),
inference(unused_predicate_definition_removal,[],[f6]) ).
fof(f62,plain,
( implies_2
=> ! [X0,X1] : is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))) ),
inference(unused_predicate_definition_removal,[],[f5]) ).
fof(f63,plain,
( implies_1
=> ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X0))) ),
inference(unused_predicate_definition_removal,[],[f4]) ).
fof(f64,plain,
( modus_tollens
=> ! [X0,X1] : is_a_theorem(implies(implies(not(X1),not(X0)),implies(X0,X1))) ),
inference(unused_predicate_definition_removal,[],[f3]) ).
fof(f65,plain,
( modus_ponens
=> ! [X0,X1] :
( ( is_a_theorem(X0)
& is_a_theorem(implies(X0,X1)) )
=> is_a_theorem(X1) ) ),
inference(unused_predicate_definition_removal,[],[f1]) ).
fof(f68,plain,
( ! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1)) )
| ~ modus_ponens ),
inference(ennf_transformation,[],[f65]) ).
fof(f69,plain,
( ! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1)) )
| ~ modus_ponens ),
inference(flattening,[],[f68]) ).
fof(f70,plain,
( ! [X0,X1] : is_a_theorem(implies(implies(not(X1),not(X0)),implies(X0,X1)))
| ~ modus_tollens ),
inference(ennf_transformation,[],[f64]) ).
fof(f71,plain,
( ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X0)))
| ~ implies_1 ),
inference(ennf_transformation,[],[f63]) ).
fof(f72,plain,
( ! [X0,X1] : is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1)))
| ~ implies_2 ),
inference(ennf_transformation,[],[f62]) ).
fof(f73,plain,
( ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))))
| ~ implies_3 ),
inference(ennf_transformation,[],[f61]) ).
fof(f74,plain,
( ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0))
| ~ and_1 ),
inference(ennf_transformation,[],[f60]) ).
fof(f75,plain,
( ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X1))
| ~ and_2 ),
inference(ennf_transformation,[],[f59]) ).
fof(f76,plain,
( ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,and(X0,X1))))
| ~ and_3 ),
inference(ennf_transformation,[],[f58]) ).
fof(f77,plain,
( ! [X0,X1] : is_a_theorem(implies(X0,or(X0,X1)))
| ~ or_1 ),
inference(ennf_transformation,[],[f57]) ).
fof(f78,plain,
( ! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1)))
| ~ or_2 ),
inference(ennf_transformation,[],[f56]) ).
fof(f79,plain,
( ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X2),implies(implies(X1,X2),implies(or(X0,X1),X2))))
| ~ or_3 ),
inference(ennf_transformation,[],[f55]) ).
fof(f80,plain,
( ! [X0,X1] : is_a_theorem(implies(equiv(X0,X1),implies(X0,X1)))
| ~ equivalence_1 ),
inference(ennf_transformation,[],[f54]) ).
fof(f81,plain,
( ! [X0,X1] : is_a_theorem(implies(equiv(X0,X1),implies(X1,X0)))
| ~ equivalence_2 ),
inference(ennf_transformation,[],[f53]) ).
fof(f82,plain,
( ! [X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1))))
| ~ equivalence_3 ),
inference(ennf_transformation,[],[f52]) ).
fof(f83,plain,
( ! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1)))
| ~ op_or ),
inference(ennf_transformation,[],[f27]) ).
fof(f84,plain,
( ! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1)))
| ~ op_implies_and ),
inference(ennf_transformation,[],[f29]) ).
fof(f85,plain,
( ! [X0,X1] : equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0))
| ~ op_equiv ),
inference(ennf_transformation,[],[f31]) ).
fof(f86,plain,
( ? [X0] : ~ is_a_theorem(equiv(X0,X0))
| ? [X1,X2] :
( ~ is_a_theorem(equiv(not(X1),not(X2)))
& is_a_theorem(equiv(X1,X2)) )
| ? [X3,X4,X5,X6] :
( ~ is_a_theorem(equiv(and(X3,X5),and(X4,X6)))
& is_a_theorem(equiv(X3,X4))
& is_a_theorem(equiv(X5,X6)) )
| ? [X7,X8] :
( ~ is_a_theorem(X8)
& is_a_theorem(X7)
& is_a_theorem(equiv(X7,X8)) ) ),
inference(ennf_transformation,[],[f51]) ).
fof(f87,plain,
( ? [X0] : ~ is_a_theorem(equiv(X0,X0))
| ? [X1,X2] :
( ~ is_a_theorem(equiv(not(X1),not(X2)))
& is_a_theorem(equiv(X1,X2)) )
| ? [X3,X4,X5,X6] :
( ~ is_a_theorem(equiv(and(X3,X5),and(X4,X6)))
& is_a_theorem(equiv(X3,X4))
& is_a_theorem(equiv(X5,X6)) )
| ? [X7,X8] :
( ~ is_a_theorem(X8)
& is_a_theorem(X7)
& is_a_theorem(equiv(X7,X8)) ) ),
inference(flattening,[],[f86]) ).
fof(f88,definition,
( ? [X7,X8] :
( ~ is_a_theorem(X8)
& is_a_theorem(X7)
& is_a_theorem(equiv(X7,X8)) )
| ~ sP0 ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f89,plain,
( ? [X0] : ~ is_a_theorem(equiv(X0,X0))
| ? [X1,X2] :
( ~ is_a_theorem(equiv(not(X1),not(X2)))
& is_a_theorem(equiv(X1,X2)) )
| ? [X3,X4,X5,X6] :
( ~ is_a_theorem(equiv(and(X3,X5),and(X4,X6)))
& is_a_theorem(equiv(X3,X4))
& is_a_theorem(equiv(X5,X6)) )
| sP0 ),
inference(definition_folding,[],[f87,f88]) ).
fof(f90,plain,
( ? [X7,X8] :
( ~ is_a_theorem(X8)
& is_a_theorem(X7)
& is_a_theorem(equiv(X7,X8)) )
| ~ sP0 ),
inference(nnf_transformation,[],[f88]) ).
fof(f91,plain,
( ? [X0,X1] :
( ~ is_a_theorem(X1)
& is_a_theorem(X0)
& is_a_theorem(equiv(X0,X1)) )
| ~ sP0 ),
inference(rectify,[],[f90]) ).
fof(f92,plain,
( ( ~ is_a_theorem(sK2)
& is_a_theorem(sK1)
& is_a_theorem(equiv(sK1,sK2)) )
| ~ sP0 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(X0,sK1),skolemize(X1,sK2)],[f91]) ).
fof(f93,plain,
( ~ is_a_theorem(equiv(sK3,sK3))
| ( ~ is_a_theorem(equiv(not(sK4),not(sK5)))
& is_a_theorem(equiv(sK4,sK5)) )
| ( ~ is_a_theorem(equiv(and(sK6,sK8),and(sK7,sK9)))
& is_a_theorem(equiv(sK6,sK7))
& is_a_theorem(equiv(sK8,sK9)) )
| sP0 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5,sK6,sK7,sK8,sK9]),skolemize(X0,sK3),skolemize(X1,sK4),skolemize(X2,sK5),skolemize(X3,sK6),skolemize(X4,sK7),skolemize(X5,sK8),skolemize(X6,sK9)],[f89]) ).
fof(f94,plain,
! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1))
| ~ modus_ponens ),
inference(cnf_transformation,[],[f69]) ).
fof(f95,plain,
! [X0,X1] :
( is_a_theorem(implies(implies(not(X1),not(X0)),implies(X0,X1)))
| ~ modus_tollens ),
inference(cnf_transformation,[],[f70]) ).
fof(f96,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,implies(X1,X0)))
| ~ implies_1 ),
inference(cnf_transformation,[],[f71]) ).
fof(f97,plain,
! [X0,X1] :
( is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1)))
| ~ implies_2 ),
inference(cnf_transformation,[],[f72]) ).
fof(f98,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))))
| ~ implies_3 ),
inference(cnf_transformation,[],[f73]) ).
fof(f99,plain,
! [X0,X1] :
( is_a_theorem(implies(and(X0,X1),X0))
| ~ and_1 ),
inference(cnf_transformation,[],[f74]) ).
fof(f100,plain,
! [X0,X1] :
( is_a_theorem(implies(and(X0,X1),X1))
| ~ and_2 ),
inference(cnf_transformation,[],[f75]) ).
fof(f101,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,implies(X1,and(X0,X1))))
| ~ and_3 ),
inference(cnf_transformation,[],[f76]) ).
fof(f102,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,or(X0,X1)))
| ~ or_1 ),
inference(cnf_transformation,[],[f77]) ).
fof(f103,plain,
! [X0,X1] :
( is_a_theorem(implies(X1,or(X0,X1)))
| ~ or_2 ),
inference(cnf_transformation,[],[f78]) ).
fof(f104,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(implies(X0,X2),implies(implies(X1,X2),implies(or(X0,X1),X2))))
| ~ or_3 ),
inference(cnf_transformation,[],[f79]) ).
fof(f105,plain,
! [X0,X1] :
( is_a_theorem(implies(equiv(X0,X1),implies(X0,X1)))
| ~ equivalence_1 ),
inference(cnf_transformation,[],[f80]) ).
fof(f106,plain,
! [X0,X1] :
( is_a_theorem(implies(equiv(X0,X1),implies(X1,X0)))
| ~ equivalence_2 ),
inference(cnf_transformation,[],[f81]) ).
fof(f107,plain,
! [X0,X1] :
( is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1))))
| ~ equivalence_3 ),
inference(cnf_transformation,[],[f82]) ).
fof(f108,plain,
! [X0,X1] :
( or(X0,X1) = not(and(not(X0),not(X1)))
| ~ op_or ),
inference(cnf_transformation,[],[f83]) ).
fof(f109,plain,
! [X0,X1] :
( implies(X0,X1) = not(and(X0,not(X1)))
| ~ op_implies_and ),
inference(cnf_transformation,[],[f84]) ).
fof(f110,plain,
! [X0,X1] :
( equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0))
| ~ op_equiv ),
inference(cnf_transformation,[],[f85]) ).
fof(f111,plain,
op_or,
inference(cnf_transformation,[],[f32]) ).
fof(f112,plain,
op_implies_and,
inference(cnf_transformation,[],[f33]) ).
fof(f113,plain,
op_equiv,
inference(cnf_transformation,[],[f34]) ).
fof(f114,plain,
modus_ponens,
inference(cnf_transformation,[],[f35]) ).
fof(f115,plain,
modus_tollens,
inference(cnf_transformation,[],[f36]) ).
fof(f116,plain,
implies_1,
inference(cnf_transformation,[],[f37]) ).
fof(f117,plain,
implies_2,
inference(cnf_transformation,[],[f38]) ).
fof(f118,plain,
implies_3,
inference(cnf_transformation,[],[f39]) ).
fof(f119,plain,
and_1,
inference(cnf_transformation,[],[f40]) ).
fof(f120,plain,
and_2,
inference(cnf_transformation,[],[f41]) ).
fof(f121,plain,
and_3,
inference(cnf_transformation,[],[f42]) ).
fof(f122,plain,
or_1,
inference(cnf_transformation,[],[f43]) ).
fof(f123,plain,
or_2,
inference(cnf_transformation,[],[f44]) ).
fof(f124,plain,
or_3,
inference(cnf_transformation,[],[f45]) ).
fof(f125,plain,
equivalence_1,
inference(cnf_transformation,[],[f46]) ).
fof(f126,plain,
equivalence_2,
inference(cnf_transformation,[],[f47]) ).
fof(f127,plain,
equivalence_3,
inference(cnf_transformation,[],[f48]) ).
fof(f128,plain,
( is_a_theorem(equiv(sK1,sK2))
| ~ sP0 ),
inference(cnf_transformation,[],[f92]) ).
fof(f129,plain,
( is_a_theorem(sK1)
| ~ sP0 ),
inference(cnf_transformation,[],[f92]) ).
fof(f130,plain,
( ~ is_a_theorem(sK2)
| ~ sP0 ),
inference(cnf_transformation,[],[f92]) ).
fof(f131,plain,
( ~ is_a_theorem(equiv(sK3,sK3))
| is_a_theorem(equiv(sK4,sK5))
| is_a_theorem(equiv(sK8,sK9))
| sP0 ),
inference(cnf_transformation,[],[f93]) ).
fof(f132,plain,
( ~ is_a_theorem(equiv(sK3,sK3))
| is_a_theorem(equiv(sK4,sK5))
| is_a_theorem(equiv(sK6,sK7))
| sP0 ),
inference(cnf_transformation,[],[f93]) ).
fof(f133,plain,
( ~ is_a_theorem(equiv(sK3,sK3))
| is_a_theorem(equiv(sK4,sK5))
| ~ is_a_theorem(equiv(and(sK6,sK8),and(sK7,sK9)))
| sP0 ),
inference(cnf_transformation,[],[f93]) ).
fof(f134,plain,
( ~ is_a_theorem(equiv(sK3,sK3))
| ~ is_a_theorem(equiv(not(sK4),not(sK5)))
| is_a_theorem(equiv(sK8,sK9))
| sP0 ),
inference(cnf_transformation,[],[f93]) ).
fof(f135,plain,
( ~ is_a_theorem(equiv(sK3,sK3))
| ~ is_a_theorem(equiv(not(sK4),not(sK5)))
| is_a_theorem(equiv(sK6,sK7))
| sP0 ),
inference(cnf_transformation,[],[f93]) ).
fof(f136,plain,
( ~ is_a_theorem(equiv(sK3,sK3))
| ~ is_a_theorem(equiv(not(sK4),not(sK5)))
| ~ is_a_theorem(equiv(and(sK6,sK8),and(sK7,sK9)))
| sP0 ),
inference(cnf_transformation,[],[f93]) ).
fof(f137,definition,
sF10 = equiv(sK3,sK3),
introduced(definition,[new_symbols(definition,[sF10])],[function_definition]) ).
fof(f138,plain,
equiv(sK3,sK3) = sF10,
inference(reorient_equations,[],[f137]) ).
fof(f139,definition,
sF11 = not(sK4),
introduced(definition,[new_symbols(definition,[sF11])],[function_definition]) ).
fof(f140,plain,
not(sK4) = sF11,
inference(reorient_equations,[],[f139]) ).
fof(f141,definition,
sF12 = not(sK5),
introduced(definition,[new_symbols(definition,[sF12])],[function_definition]) ).
fof(f142,plain,
not(sK5) = sF12,
inference(reorient_equations,[],[f141]) ).
fof(f143,definition,
sF13 = equiv(sF11,sF12),
introduced(definition,[new_symbols(definition,[sF13])],[function_definition]) ).
fof(f144,plain,
equiv(sF11,sF12) = sF13,
inference(reorient_equations,[],[f143]) ).
fof(f145,definition,
sF14 = and(sK6,sK8),
introduced(definition,[new_symbols(definition,[sF14])],[function_definition]) ).
fof(f146,plain,
and(sK6,sK8) = sF14,
inference(reorient_equations,[],[f145]) ).
fof(f147,definition,
sF15 = and(sK7,sK9),
introduced(definition,[new_symbols(definition,[sF15])],[function_definition]) ).
fof(f148,plain,
and(sK7,sK9) = sF15,
inference(reorient_equations,[],[f147]) ).
fof(f149,definition,
sF16 = equiv(sF14,sF15),
introduced(definition,[new_symbols(definition,[sF16])],[function_definition]) ).
fof(f150,plain,
equiv(sF14,sF15) = sF16,
inference(reorient_equations,[],[f149]) ).
fof(f151,plain,
( ~ is_a_theorem(sF10)
| ~ is_a_theorem(sF13)
| ~ is_a_theorem(sF16)
| sP0 ),
inference(definition_folding,[],[f136,f150,f148,f146,f144,f142,f140,f138]) ).
fof(f152,definition,
sF17 = equiv(sK6,sK7),
introduced(definition,[new_symbols(definition,[sF17])],[function_definition]) ).
fof(f153,plain,
equiv(sK6,sK7) = sF17,
inference(reorient_equations,[],[f152]) ).
fof(f154,plain,
( ~ is_a_theorem(sF10)
| ~ is_a_theorem(sF13)
| is_a_theorem(sF17)
| sP0 ),
inference(definition_folding,[],[f135,f153,f144,f142,f140,f138]) ).
fof(f155,definition,
sF18 = equiv(sK8,sK9),
introduced(definition,[new_symbols(definition,[sF18])],[function_definition]) ).
fof(f156,plain,
equiv(sK8,sK9) = sF18,
inference(reorient_equations,[],[f155]) ).
fof(f157,plain,
( ~ is_a_theorem(sF10)
| ~ is_a_theorem(sF13)
| is_a_theorem(sF18)
| sP0 ),
inference(definition_folding,[],[f134,f156,f144,f142,f140,f138]) ).
fof(f158,definition,
sF19 = equiv(sK4,sK5),
introduced(definition,[new_symbols(definition,[sF19])],[function_definition]) ).
fof(f159,plain,
equiv(sK4,sK5) = sF19,
inference(reorient_equations,[],[f158]) ).
fof(f160,plain,
( ~ is_a_theorem(sF10)
| is_a_theorem(sF19)
| ~ is_a_theorem(sF16)
| sP0 ),
inference(definition_folding,[],[f133,f150,f148,f146,f159,f138]) ).
fof(f161,plain,
( ~ is_a_theorem(sF10)
| is_a_theorem(sF19)
| is_a_theorem(sF17)
| sP0 ),
inference(definition_folding,[],[f132,f153,f159,f138]) ).
fof(f162,plain,
( ~ is_a_theorem(sF10)
| is_a_theorem(sF19)
| is_a_theorem(sF18)
| sP0 ),
inference(definition_folding,[],[f131,f156,f159,f138]) ).
fof(f164,definition,
( spl20_1
<=> sP0 ),
introduced(definition,[new_symbols(definition,[spl20_1])],[avatar_definition]) ).
fof(f168,definition,
( spl20_2
<=> is_a_theorem(sF18) ),
introduced(definition,[new_symbols(definition,[spl20_2])],[avatar_definition]) ).
fof(f170,plain,
( is_a_theorem(sF18)
| ~ spl20_2 ),
inference(avatar_component_clause,[],[f168]) ).
fof(f172,definition,
( spl20_3
<=> is_a_theorem(sF19) ),
introduced(definition,[new_symbols(definition,[spl20_3])],[avatar_definition]) ).
fof(f174,plain,
( is_a_theorem(sF19)
| ~ spl20_3 ),
inference(avatar_component_clause,[],[f172]) ).
fof(f176,definition,
( spl20_4
<=> is_a_theorem(sF10) ),
introduced(definition,[new_symbols(definition,[spl20_4])],[avatar_definition]) ).
fof(f177,plain,
( is_a_theorem(sF10)
| ~ spl20_4 ),
inference(avatar_component_clause,[],[f176]) ).
fof(f178,plain,
( ~ is_a_theorem(sF10)
| spl20_4 ),
inference(avatar_component_clause,[],[f176]) ).
fof(f179,plain,
( spl20_1
| spl20_2
| spl20_3
| ~ spl20_4 ),
inference(avatar_split_clause,[],[f162,f176,f172,f168,f164]) ).
fof(f181,definition,
( spl20_5
<=> is_a_theorem(sF17) ),
introduced(definition,[new_symbols(definition,[spl20_5])],[avatar_definition]) ).
fof(f183,plain,
( is_a_theorem(sF17)
| ~ spl20_5 ),
inference(avatar_component_clause,[],[f181]) ).
fof(f184,plain,
( spl20_1
| spl20_5
| spl20_3
| ~ spl20_4 ),
inference(avatar_split_clause,[],[f161,f176,f172,f181,f164]) ).
fof(f186,definition,
( spl20_6
<=> is_a_theorem(sF16) ),
introduced(definition,[new_symbols(definition,[spl20_6])],[avatar_definition]) ).
fof(f188,plain,
( ~ is_a_theorem(sF16)
| spl20_6 ),
inference(avatar_component_clause,[],[f186]) ).
fof(f189,plain,
( spl20_1
| ~ spl20_6
| spl20_3
| ~ spl20_4 ),
inference(avatar_split_clause,[],[f160,f176,f172,f186,f164]) ).
fof(f191,definition,
( spl20_7
<=> is_a_theorem(sF13) ),
introduced(definition,[new_symbols(definition,[spl20_7])],[avatar_definition]) ).
fof(f193,plain,
( ~ is_a_theorem(sF13)
| spl20_7 ),
inference(avatar_component_clause,[],[f191]) ).
fof(f194,plain,
( spl20_1
| spl20_2
| ~ spl20_7
| ~ spl20_4 ),
inference(avatar_split_clause,[],[f157,f176,f191,f168,f164]) ).
fof(f195,plain,
( spl20_1
| spl20_5
| ~ spl20_7
| ~ spl20_4 ),
inference(avatar_split_clause,[],[f154,f176,f191,f181,f164]) ).
fof(f196,plain,
( spl20_1
| ~ spl20_6
| ~ spl20_7
| ~ spl20_4 ),
inference(avatar_split_clause,[],[f151,f176,f191,f186,f164]) ).
fof(f198,definition,
( spl20_8
<=> is_a_theorem(equiv(sK1,sK2)) ),
introduced(definition,[new_symbols(definition,[spl20_8])],[avatar_definition]) ).
fof(f200,plain,
( is_a_theorem(equiv(sK1,sK2))
| ~ spl20_8 ),
inference(avatar_component_clause,[],[f198]) ).
fof(f201,plain,
( ~ spl20_1
| spl20_8 ),
inference(avatar_split_clause,[],[f128,f198,f164]) ).
fof(f203,definition,
( spl20_9
<=> is_a_theorem(sK1) ),
introduced(definition,[new_symbols(definition,[spl20_9])],[avatar_definition]) ).
fof(f205,plain,
( is_a_theorem(sK1)
| ~ spl20_9 ),
inference(avatar_component_clause,[],[f203]) ).
fof(f206,plain,
( ~ spl20_1
| spl20_9 ),
inference(avatar_split_clause,[],[f129,f203,f164]) ).
fof(f208,definition,
( spl20_10
<=> is_a_theorem(sK2) ),
introduced(definition,[new_symbols(definition,[spl20_10])],[avatar_definition]) ).
fof(f210,plain,
( ~ is_a_theorem(sK2)
| spl20_10 ),
inference(avatar_component_clause,[],[f208]) ).
fof(f211,plain,
( ~ spl20_1
| ~ spl20_10 ),
inference(avatar_split_clause,[],[f130,f208,f164]) ).
fof(f212,plain,
! [X0,X1] : equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0)),
inference(forward_subsumption_resolution,[],[f110,f113]) ).
fof(f213,plain,
! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1))),
inference(forward_subsumption_resolution,[],[f109,f112]) ).
fof(f214,plain,
! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1))),
inference(forward_subsumption_resolution,[],[f108,f111]) ).
fof(f215,plain,
! [X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1)))),
inference(forward_subsumption_resolution,[],[f107,f127]) ).
fof(f216,plain,
! [X0,X1] : is_a_theorem(implies(equiv(X0,X1),implies(X1,X0))),
inference(forward_subsumption_resolution,[],[f106,f126]) ).
fof(f217,plain,
! [X0,X1] : is_a_theorem(implies(equiv(X0,X1),implies(X0,X1))),
inference(forward_subsumption_resolution,[],[f105,f125]) ).
fof(f218,plain,
! [X2,X0,X1] : is_a_theorem(implies(implies(X0,X2),implies(implies(X1,X2),implies(or(X0,X1),X2)))),
inference(forward_subsumption_resolution,[],[f104,f124]) ).
fof(f219,plain,
! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1))),
inference(forward_subsumption_resolution,[],[f103,f123]) ).
fof(f220,plain,
! [X0,X1] : is_a_theorem(implies(X0,or(X0,X1))),
inference(forward_subsumption_resolution,[],[f102,f122]) ).
fof(f221,plain,
! [X0,X1] : is_a_theorem(implies(X0,implies(X1,and(X0,X1)))),
inference(forward_subsumption_resolution,[],[f101,f121]) ).
fof(f222,plain,
! [X0,X1] : is_a_theorem(implies(and(X0,X1),X1)),
inference(forward_subsumption_resolution,[],[f100,f120]) ).
fof(f223,plain,
! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0)),
inference(forward_subsumption_resolution,[],[f99,f119]) ).
fof(f224,plain,
! [X2,X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))),
inference(forward_subsumption_resolution,[],[f98,f118]) ).
fof(f225,plain,
! [X0,X1] : is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))),
inference(forward_subsumption_resolution,[],[f97,f117]) ).
fof(f226,plain,
! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X0))),
inference(forward_subsumption_resolution,[],[f96,f116]) ).
fof(f227,plain,
! [X0,X1] : is_a_theorem(implies(implies(not(X1),not(X0)),implies(X0,X1))),
inference(forward_subsumption_resolution,[],[f95,f115]) ).
fof(f228,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| is_a_theorem(X1) ),
inference(forward_subsumption_resolution,[],[f94,f114]) ).
fof(f229,plain,
! [X0,X1] : or(X0,X1) = implies(not(X0),X1),
inference(forward_demodulation,[],[f214,f213]) ).
fof(f241,plain,
! [X0,X1] :
( is_a_theorem(implies(X1,X0))
| ~ is_a_theorem(X0) ),
inference(resolution,[],[f226,f228]) ).
fof(f245,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(implies(X1,X2),implies(X0,X2)))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f224,f228]) ).
fof(f246,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(implies(X0,X2)) ),
inference(resolution,[],[f245,f228]) ).
fof(f247,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(implies(X0,and(X1,X2)))
| is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f246,f223]) ).
fof(f249,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(X0,implies(X2,X1)))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f246,f226]) ).
fof(f251,plain,
! [X2,X3,X0,X1] :
( ~ is_a_theorem(implies(X0,implies(X1,X2)))
| is_a_theorem(implies(X0,implies(X3,X2)))
| ~ is_a_theorem(implies(X3,X1)) ),
inference(resolution,[],[f246,f245]) ).
fof(f262,plain,
! [X2,X3,X0,X1] :
( ~ is_a_theorem(implies(X2,X0))
| ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(implies(X2,implies(X3,X1))) ),
inference(resolution,[],[f249,f246]) ).
fof(f263,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| is_a_theorem(implies(X2,X1)) ),
inference(resolution,[],[f249,f228]) ).
fof(f264,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(implies(X0,implies(X1,implies(X1,X2))))
| is_a_theorem(implies(X0,implies(X1,X2))) ),
inference(resolution,[],[f225,f246]) ).
fof(f265,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X0,implies(X0,X1)))
| is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f225,f228]) ).
fof(f266,plain,
! [X0] : is_a_theorem(implies(X0,X0)),
inference(resolution,[],[f265,f226]) ).
fof(f269,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(implies(X0,X1),X0))
| is_a_theorem(implies(implies(X0,X1),X1)) ),
inference(resolution,[],[f265,f245]) ).
fof(f277,plain,
! [X0,X1] :
( ~ is_a_theorem(equiv(X0,X1))
| is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f217,f228]) ).
fof(f278,plain,
is_a_theorem(implies(sF10,implies(sK3,sK3))),
inference(superposition,[],[f217,f138]) ).
fof(f279,plain,
is_a_theorem(implies(sF19,implies(sK4,sK5))),
inference(superposition,[],[f217,f159]) ).
fof(f280,plain,
is_a_theorem(implies(sF17,implies(sK6,sK7))),
inference(superposition,[],[f217,f153]) ).
fof(f281,plain,
is_a_theorem(implies(sF18,implies(sK8,sK9))),
inference(superposition,[],[f217,f156]) ).
fof(f291,definition,
( spl20_11
<=> is_a_theorem(implies(sF14,sF15)) ),
introduced(definition,[new_symbols(definition,[spl20_11])],[avatar_definition]) ).
fof(f292,plain,
( ~ is_a_theorem(implies(sF14,sF15))
| spl20_11 ),
inference(avatar_component_clause,[],[f291]) ).
fof(f293,plain,
( is_a_theorem(implies(sF14,sF15))
| ~ spl20_11 ),
inference(avatar_component_clause,[],[f291]) ).
fof(f296,definition,
( spl20_12
<=> is_a_theorem(implies(sF11,sF12)) ),
introduced(definition,[new_symbols(definition,[spl20_12])],[avatar_definition]) ).
fof(f297,plain,
( ~ is_a_theorem(implies(sF11,sF12))
| spl20_12 ),
inference(avatar_component_clause,[],[f296]) ).
fof(f298,plain,
( is_a_theorem(implies(sF11,sF12))
| ~ spl20_12 ),
inference(avatar_component_clause,[],[f296]) ).
fof(f318,plain,
is_a_theorem(implies(sF19,implies(sK5,sK4))),
inference(superposition,[],[f216,f159]) ).
fof(f319,plain,
is_a_theorem(implies(sF17,implies(sK7,sK6))),
inference(superposition,[],[f216,f153]) ).
fof(f320,plain,
is_a_theorem(implies(sF18,implies(sK9,sK8))),
inference(superposition,[],[f216,f156]) ).
fof(f336,plain,
! [X2,X3,X0,X1] :
( is_a_theorem(implies(implies(X0,X1),implies(X2,implies(X0,X3))))
| ~ is_a_theorem(implies(X2,implies(X1,X3))) ),
inference(resolution,[],[f251,f224]) ).
fof(f337,plain,
! [X2,X3,X0,X1] :
( ~ is_a_theorem(implies(X3,X0))
| ~ is_a_theorem(implies(X2,X3))
| is_a_theorem(implies(implies(X0,X1),implies(X2,X1))) ),
inference(resolution,[],[f251,f245]) ).
fof(f338,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X2,X1)))
| ~ is_a_theorem(implies(X2,X0)) ),
inference(resolution,[],[f251,f225]) ).
fof(f382,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(or(X0,and(X1,X2)))
| is_a_theorem(implies(not(X0),X1)) ),
inference(superposition,[],[f247,f229]) ).
fof(f383,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(or(X0,and(X1,X2)))
| is_a_theorem(or(X0,X1)) ),
inference(forward_demodulation,[],[f382,f229]) ).
fof(f395,plain,
! [X0] : is_a_theorem(implies(X0,and(X0,X0))),
inference(resolution,[],[f221,f265]) ).
fof(f398,plain,
! [X0,X1] :
( is_a_theorem(implies(X1,and(X0,X1)))
| ~ is_a_theorem(X0) ),
inference(resolution,[],[f221,f228]) ).
fof(f400,plain,
is_a_theorem(implies(sK6,implies(sK8,sF14))),
inference(superposition,[],[f221,f146]) ).
fof(f401,plain,
is_a_theorem(implies(sK7,implies(sK9,sF15))),
inference(superposition,[],[f221,f148]) ).
fof(f413,plain,
! [X0,X1] :
( is_a_theorem(and(X0,X1))
| ~ is_a_theorem(X1)
| ~ is_a_theorem(X0) ),
inference(resolution,[],[f398,f228]) ).
fof(f436,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X1,X0))
| is_a_theorem(equiv(X0,X1))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(superposition,[],[f413,f212]) ).
fof(f439,plain,
! [X0] :
( is_a_theorem(equiv(X0,X0))
| ~ is_a_theorem(implies(X0,X0)) ),
inference(resolution,[],[f436,f266]) ).
fof(f459,plain,
! [X0] : is_a_theorem(equiv(X0,X0)),
inference(forward_subsumption_resolution,[],[f439,f266]) ).
fof(f462,plain,
is_a_theorem(sF10),
inference(superposition,[],[f459,f138]) ).
fof(f463,plain,
( $false
| spl20_4 ),
inference(forward_subsumption_resolution,[],[f462,f178]) ).
fof(f464,plain,
spl20_4,
inference(avatar_contradiction_clause,[],[f463]) ).
fof(f522,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(not(X0),not(X1)))
| is_a_theorem(implies(X1,X0)) ),
inference(resolution,[],[f227,f228]) ).
fof(f535,plain,
! [X0,X1] : is_a_theorem(implies(or(X0,not(X1)),implies(X1,X0))),
inference(superposition,[],[f227,f229]) ).
fof(f536,plain,
! [X0,X1] : is_a_theorem(implies(implies(not(X1),not(not(X0))),or(X0,X1))),
inference(superposition,[],[f227,f229]) ).
fof(f537,plain,
! [X0,X1] : is_a_theorem(implies(or(X1,not(not(X0))),or(X0,X1))),
inference(forward_demodulation,[],[f536,f229]) ).
fof(f545,plain,
! [X0,X1] :
( ~ is_a_theorem(or(X0,not(X1)))
| is_a_theorem(implies(X1,X0)) ),
inference(forward_demodulation,[],[f522,f229]) ).
fof(f615,definition,
( spl20_28
<=> is_a_theorem(implies(sF12,sF11)) ),
introduced(definition,[new_symbols(definition,[spl20_28])],[avatar_definition]) ).
fof(f616,plain,
( is_a_theorem(implies(sF12,sF11))
| ~ spl20_28 ),
inference(avatar_component_clause,[],[f615]) ).
fof(f617,plain,
( ~ is_a_theorem(implies(sF12,sF11))
| spl20_28 ),
inference(avatar_component_clause,[],[f615]) ).
fof(f622,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(X0,implies(implies(X2,X1),equiv(X1,X2))))
| ~ is_a_theorem(implies(X0,implies(X1,X2))) ),
inference(resolution,[],[f215,f246]) ).
fof(f916,plain,
! [X0,X1] :
( is_a_theorem(implies(implies(X0,X1),X1))
| ~ is_a_theorem(X0) ),
inference(resolution,[],[f269,f241]) ).
fof(f947,plain,
! [X0,X1] :
( is_a_theorem(implies(X1,and(X0,X0)))
| ~ is_a_theorem(X0) ),
inference(resolution,[],[f263,f395]) ).
fof(f984,plain,
! [X0] :
( ~ is_a_theorem(sF19)
| is_a_theorem(implies(X0,implies(sK4,sK5))) ),
inference(resolution,[],[f263,f279]) ).
fof(f985,plain,
! [X0] :
( ~ is_a_theorem(sF19)
| is_a_theorem(implies(X0,implies(sK5,sK4))) ),
inference(resolution,[],[f263,f318]) ).
fof(f1140,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(implies(X1,implies(X1,X2)))
| ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(implies(X0,X2)) ),
inference(resolution,[],[f338,f228]) ).
fof(f1181,plain,
! [X2,X3,X0,X1] :
( ~ is_a_theorem(implies(or(X0,X1),X2))
| is_a_theorem(implies(X0,implies(X3,X2))) ),
inference(resolution,[],[f262,f220]) ).
fof(f1223,plain,
! [X2,X0,X1] : is_a_theorem(implies(X0,implies(X1,implies(X2,X0)))),
inference(resolution,[],[f1181,f535]) ).
fof(f1395,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(implies(X0,X1),implies(X0,X2)))
| ~ is_a_theorem(implies(X0,implies(X1,X2))) ),
inference(resolution,[],[f336,f264]) ).
fof(f1505,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(X0,implies(or(X1,X1),X2)))
| ~ is_a_theorem(implies(X0,implies(X1,X2))) ),
inference(resolution,[],[f218,f1140]) ).
fof(f1589,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(implies(X0,implies(X1,X2)))
| ~ is_a_theorem(X0)
| is_a_theorem(implies(or(X1,X1),X2)) ),
inference(resolution,[],[f1505,f228]) ).
fof(f1620,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X0,implies(X0,X1)))
| is_a_theorem(implies(or(X0,X0),X1)) ),
inference(resolution,[],[f1589,f225]) ).
fof(f1635,plain,
( ~ is_a_theorem(sF10)
| is_a_theorem(implies(or(sK3,sK3),sK3)) ),
inference(resolution,[],[f1589,f278]) ).
fof(f1652,plain,
( is_a_theorem(implies(or(sK3,sK3),sK3))
| ~ spl20_4 ),
inference(forward_subsumption_resolution,[],[f1635,f177]) ).
fof(f1659,definition,
( spl20_55
<=> ! [X0] : ~ is_a_theorem(X0) ),
introduced(definition,[new_symbols(definition,[spl20_55])],[avatar_definition]) ).
fof(f1660,plain,
( ! [X0] : ~ is_a_theorem(X0)
| ~ spl20_55 ),
inference(avatar_component_clause,[],[f1659]) ).
fof(f1678,definition,
( spl20_59
<=> is_a_theorem(implies(or(sK3,sK3),sK3)) ),
introduced(definition,[new_symbols(definition,[spl20_59])],[avatar_definition]) ).
fof(f1680,plain,
( is_a_theorem(implies(or(sK3,sK3),sK3))
| ~ spl20_59 ),
inference(avatar_component_clause,[],[f1678]) ).
fof(f1690,plain,
( spl20_59
| ~ spl20_4 ),
inference(avatar_split_clause,[],[f1652,f176,f1678]) ).
fof(f1691,plain,
( $false
| ~ spl20_55
| ~ spl20_59 ),
inference(forward_subsumption_resolution,[],[f1680,f1660]) ).
fof(f1692,plain,
( ~ spl20_55
| ~ spl20_59 ),
inference(avatar_contradiction_clause,[],[f1691]) ).
fof(f1726,plain,
! [X0] : is_a_theorem(implies(or(X0,X0),and(X0,X0))),
inference(resolution,[],[f1620,f221]) ).
fof(f1751,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X0,or(X1,X1)))
| is_a_theorem(implies(X0,and(X1,X1))) ),
inference(resolution,[],[f1726,f246]) ).
fof(f2331,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(implies(X1,implies(X0,X2)))
| ~ is_a_theorem(X0)
| is_a_theorem(implies(X1,X2)) ),
inference(resolution,[],[f916,f246]) ).
fof(f2361,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(implies(X2,X0),implies(X2,X1)))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f2331,f224]) ).
fof(f2374,plain,
! [X0,X1] :
( is_a_theorem(implies(equiv(X0,X1),X1))
| ~ is_a_theorem(X0) ),
inference(resolution,[],[f2331,f217]) ).
fof(f2453,plain,
! [X2,X3,X0,X1] :
( ~ is_a_theorem(implies(X2,implies(X3,X0)))
| ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(implies(X2,implies(X3,X1))) ),
inference(resolution,[],[f2361,f246]) ).
fof(f2464,plain,
! [X0,X1] :
( ~ is_a_theorem(equiv(X0,X1))
| ~ is_a_theorem(X0)
| is_a_theorem(X1) ),
inference(resolution,[],[f2374,f228]) ).
fof(f2717,plain,
! [X2,X3,X0,X1] :
( ~ is_a_theorem(implies(X0,and(X1,X2)))
| is_a_theorem(implies(implies(X1,X3),implies(X0,X3))) ),
inference(resolution,[],[f337,f223]) ).
fof(f2718,plain,
! [X2,X3,X0,X1] :
( ~ is_a_theorem(implies(X0,and(X1,X2)))
| is_a_theorem(implies(implies(X2,X3),implies(X0,X3))) ),
inference(resolution,[],[f337,f222]) ).
fof(f2759,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(implies(X0,X1),implies(X2,X1)))
| ~ is_a_theorem(X0) ),
inference(resolution,[],[f2717,f947]) ).
fof(f2763,plain,
! [X2,X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(and(X0,X2),X1))),
inference(resolution,[],[f2717,f266]) ).
fof(f2789,plain,
! [X2,X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(and(X2,X0),X1))),
inference(resolution,[],[f2718,f266]) ).
fof(f2816,plain,
! [X2,X3,X0,X1] :
( is_a_theorem(implies(X0,implies(and(X1,X3),X2)))
| ~ is_a_theorem(implies(X0,implies(X1,X2))) ),
inference(resolution,[],[f2763,f246]) ).
fof(f2862,plain,
! [X2,X3,X0,X1] :
( is_a_theorem(implies(X0,implies(and(X3,X1),X2)))
| ~ is_a_theorem(implies(X0,implies(X1,X2))) ),
inference(resolution,[],[f2789,f246]) ).
fof(f4447,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(implies(X0,implies(X1,X2)))
| ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(implies(X0,X2)) ),
inference(resolution,[],[f1395,f228]) ).
fof(f4448,plain,
! [X2,X3,X0,X1] :
( ~ is_a_theorem(implies(X3,implies(X0,X1)))
| ~ is_a_theorem(implies(X0,implies(X1,X2)))
| is_a_theorem(implies(X3,implies(X0,X2))) ),
inference(resolution,[],[f1395,f246]) ).
fof(f5245,plain,
! [X2,X3,X0,X1] :
( ~ is_a_theorem(implies(X1,implies(X0,X2)))
| ~ is_a_theorem(X0)
| is_a_theorem(implies(X1,implies(X3,X2))) ),
inference(resolution,[],[f2759,f246]) ).
fof(f5648,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X2,X1)))
| ~ is_a_theorem(X0) ),
inference(resolution,[],[f5245,f225]) ).
fof(f6614,plain,
( ! [X0] : is_a_theorem(implies(X0,implies(sK5,sK4)))
| ~ spl20_3 ),
inference(forward_subsumption_resolution,[],[f985,f174]) ).
fof(f6615,plain,
( ! [X0] : is_a_theorem(implies(X0,implies(sK4,sK5)))
| ~ spl20_3 ),
inference(forward_subsumption_resolution,[],[f984,f174]) ).
fof(f6843,definition,
( spl20_104
<=> is_a_theorem(implies(sF15,sF14)) ),
introduced(definition,[new_symbols(definition,[spl20_104])],[avatar_definition]) ).
fof(f6844,plain,
( is_a_theorem(implies(sF15,sF14))
| ~ spl20_104 ),
inference(avatar_component_clause,[],[f6843]) ).
fof(f6845,plain,
( ~ is_a_theorem(implies(sF15,sF14))
| spl20_104 ),
inference(avatar_component_clause,[],[f6843]) ).
fof(f8637,plain,
( is_a_theorem(implies(sK1,sK2))
| ~ spl20_8 ),
inference(resolution,[],[f200,f277]) ).
fof(f8762,plain,
( ~ is_a_theorem(sK1)
| is_a_theorem(sK2)
| ~ spl20_8 ),
inference(resolution,[],[f8637,f228]) ).
fof(f8778,plain,
( is_a_theorem(sK2)
| ~ spl20_8
| ~ spl20_9 ),
inference(forward_subsumption_resolution,[],[f8762,f205]) ).
fof(f8779,plain,
( $false
| ~ spl20_8
| ~ spl20_9
| spl20_10 ),
inference(forward_subsumption_resolution,[],[f8778,f210]) ).
fof(f8780,plain,
( ~ spl20_8
| ~ spl20_9
| spl20_10 ),
inference(avatar_contradiction_clause,[],[f8779]) ).
fof(f9041,plain,
( is_a_theorem(equiv(sF14,sF15))
| ~ is_a_theorem(implies(sF14,sF15))
| ~ spl20_104 ),
inference(resolution,[],[f6844,f436]) ).
fof(f9047,plain,
( is_a_theorem(equiv(sF14,sF15))
| ~ spl20_11
| ~ spl20_104 ),
inference(forward_subsumption_resolution,[],[f9041,f293]) ).
fof(f9048,plain,
( is_a_theorem(sF16)
| ~ spl20_11
| ~ spl20_104 ),
inference(forward_demodulation,[],[f9047,f150]) ).
fof(f9054,plain,
( is_a_theorem(equiv(sF11,sF12))
| ~ is_a_theorem(implies(sF11,sF12))
| ~ spl20_28 ),
inference(resolution,[],[f616,f436]) ).
fof(f9060,plain,
( is_a_theorem(equiv(sF11,sF12))
| ~ spl20_12
| ~ spl20_28 ),
inference(forward_subsumption_resolution,[],[f9054,f298]) ).
fof(f9061,plain,
( is_a_theorem(sF13)
| ~ spl20_12
| ~ spl20_28 ),
inference(forward_demodulation,[],[f9060,f144]) ).
fof(f9062,plain,
( $false
| spl20_7
| ~ spl20_12
| ~ spl20_28 ),
inference(forward_subsumption_resolution,[],[f9061,f193]) ).
fof(f9063,plain,
( spl20_7
| ~ spl20_12
| ~ spl20_28 ),
inference(avatar_contradiction_clause,[],[f9062]) ).
fof(f16600,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(equiv(X0,X1),implies(X0,X2)))
| ~ is_a_theorem(implies(X0,implies(X1,X2))) ),
inference(resolution,[],[f4448,f217]) ).
fof(f17940,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X0,implies(sK8,X1)))
| is_a_theorem(implies(X0,implies(sF14,X1))) ),
inference(superposition,[],[f2862,f146]) ).
fof(f17941,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X0,implies(sK9,X1)))
| is_a_theorem(implies(X0,implies(sF15,X1))) ),
inference(superposition,[],[f2862,f148]) ).
fof(f18042,plain,
is_a_theorem(implies(sF18,implies(sF14,sK9))),
inference(resolution,[],[f17940,f281]) ).
fof(f18145,plain,
is_a_theorem(implies(sF18,implies(sF15,sK8))),
inference(resolution,[],[f17941,f320]) ).
fof(f18162,plain,
! [X0] :
( ~ is_a_theorem(sF18)
| is_a_theorem(implies(X0,implies(sF14,sK9))) ),
inference(resolution,[],[f18042,f263]) ).
fof(f18184,definition,
( spl20_186
<=> is_a_theorem(implies(sF14,sK9)) ),
introduced(definition,[new_symbols(definition,[spl20_186])],[avatar_definition]) ).
fof(f18185,plain,
( ~ is_a_theorem(implies(sF14,sK9))
| spl20_186 ),
inference(avatar_component_clause,[],[f18184]) ).
fof(f18186,plain,
( is_a_theorem(implies(sF14,sK9))
| ~ spl20_186 ),
inference(avatar_component_clause,[],[f18184]) ).
fof(f18215,plain,
! [X0] :
( ~ is_a_theorem(sF18)
| is_a_theorem(implies(X0,implies(sF15,sK8))) ),
inference(resolution,[],[f18145,f263]) ).
fof(f18336,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X0,implies(sK6,X1)))
| is_a_theorem(implies(X0,implies(sF14,X1))) ),
inference(superposition,[],[f2816,f146]) ).
fof(f18337,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X0,implies(sK7,X1)))
| is_a_theorem(implies(X0,implies(sF15,X1))) ),
inference(superposition,[],[f2816,f148]) ).
fof(f18439,plain,
is_a_theorem(implies(sF17,implies(sF14,sK7))),
inference(resolution,[],[f18336,f280]) ).
fof(f18542,plain,
is_a_theorem(implies(sF17,implies(sF15,sK6))),
inference(resolution,[],[f18337,f319]) ).
fof(f18552,plain,
! [X0] :
( is_a_theorem(implies(sF17,implies(sF14,X0)))
| ~ is_a_theorem(implies(sK7,X0)) ),
inference(resolution,[],[f18439,f2453]) ).
fof(f18588,plain,
! [X0] :
( is_a_theorem(implies(sF17,implies(sF15,X0)))
| ~ is_a_theorem(implies(sK6,X0)) ),
inference(resolution,[],[f18542,f2453]) ).
fof(f20336,definition,
( spl20_232
<=> is_a_theorem(implies(sF15,sK8)) ),
introduced(definition,[new_symbols(definition,[spl20_232])],[avatar_definition]) ).
fof(f20337,plain,
( ~ is_a_theorem(implies(sF15,sK8))
| spl20_232 ),
inference(avatar_component_clause,[],[f20336]) ).
fof(f20338,plain,
( is_a_theorem(implies(sF15,sK8))
| ~ spl20_232 ),
inference(avatar_component_clause,[],[f20336]) ).
fof(f21927,plain,
! [X0] :
( ~ is_a_theorem(implies(sK7,X0))
| ~ is_a_theorem(sF17)
| is_a_theorem(implies(sF14,X0)) ),
inference(resolution,[],[f18552,f228]) ).
fof(f28072,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(implies(X0,implies(X1,X2)))
| ~ is_a_theorem(X0)
| is_a_theorem(implies(implies(X2,X1),equiv(X1,X2))) ),
inference(resolution,[],[f622,f228]) ).
fof(f28251,plain,
! [X0,X1] :
( is_a_theorem(implies(implies(X1,X0),equiv(X0,X1)))
| ~ is_a_theorem(implies(X0,implies(X0,X1))) ),
inference(resolution,[],[f28072,f225]) ).
fof(f28493,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X0,implies(X0,X1)))
| ~ is_a_theorem(implies(X1,X0))
| is_a_theorem(equiv(X0,X1)) ),
inference(resolution,[],[f28251,f228]) ).
fof(f28646,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X0,implies(X1,implies(X1,X0))))
| is_a_theorem(equiv(implies(X1,implies(X1,X0)),X0))
| ~ is_a_theorem(X1) ),
inference(resolution,[],[f28493,f5648]) ).
fof(f28704,plain,
! [X0,X1] :
( is_a_theorem(equiv(implies(X1,implies(X1,X0)),X0))
| ~ is_a_theorem(X1) ),
inference(forward_subsumption_resolution,[],[f28646,f1223]) ).
fof(f28797,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X0,implies(X0,X1)))
| ~ is_a_theorem(X0)
| is_a_theorem(X1) ),
inference(resolution,[],[f28704,f2464]) ).
fof(f28868,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(implies(X0,X1),X0))
| is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f28797,f245]) ).
fof(f28967,plain,
( ! [X0] :
( ~ is_a_theorem(implies(implies(sK4,sK5),X0))
| is_a_theorem(X0) )
| ~ spl20_3 ),
inference(resolution,[],[f28868,f6615]) ).
fof(f28968,plain,
( ! [X0] :
( ~ is_a_theorem(implies(implies(sK5,sK4),X0))
| is_a_theorem(X0) )
| ~ spl20_3 ),
inference(resolution,[],[f28868,f6614]) ).
fof(f29078,plain,
( ! [X0] :
( ~ is_a_theorem(implies(sK5,X0))
| is_a_theorem(implies(sK4,X0)) )
| ~ spl20_3 ),
inference(resolution,[],[f28967,f2361]) ).
fof(f29443,plain,
( ! [X0] :
( ~ is_a_theorem(implies(sK4,X0))
| is_a_theorem(implies(sK5,X0)) )
| ~ spl20_3 ),
inference(resolution,[],[f28968,f2361]) ).
fof(f41218,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(implies(X0,implies(X1,X2)))
| ~ is_a_theorem(equiv(X0,X1))
| is_a_theorem(implies(X0,X2)) ),
inference(resolution,[],[f16600,f228]) ).
fof(f41305,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(equiv(X0,X1))
| is_a_theorem(implies(X0,X2))
| ~ is_a_theorem(implies(X1,X2)) ),
inference(resolution,[],[f41218,f241]) ).
fof(f48117,plain,
! [X0] : is_a_theorem(implies(or(X0,not(not(X0))),and(X0,X0))),
inference(resolution,[],[f537,f1751]) ).
fof(f48205,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X0,or(X1,not(not(X1)))))
| is_a_theorem(implies(X0,and(X1,X1))) ),
inference(resolution,[],[f48117,f246]) ).
fof(f48699,plain,
! [X0] : is_a_theorem(implies(not(not(X0)),and(X0,X0))),
inference(resolution,[],[f48205,f219]) ).
fof(f48780,plain,
! [X0] : is_a_theorem(or(not(X0),and(X0,X0))),
inference(forward_demodulation,[],[f48699,f229]) ).
fof(f48784,plain,
! [X0] : is_a_theorem(or(not(X0),X0)),
inference(resolution,[],[f48780,f383]) ).
fof(f48807,plain,
! [X0] : is_a_theorem(implies(X0,not(not(X0)))),
inference(resolution,[],[f48784,f545]) ).
fof(f48835,plain,
! [X0] :
( is_a_theorem(equiv(not(not(X0)),X0))
| ~ is_a_theorem(implies(not(not(X0)),X0)) ),
inference(resolution,[],[f48807,f436]) ).
fof(f48922,plain,
( is_a_theorem(implies(sK5,not(not(sK4))))
| ~ spl20_3 ),
inference(resolution,[],[f48807,f29443]) ).
fof(f48923,plain,
( is_a_theorem(implies(sK4,not(not(sK5))))
| ~ spl20_3 ),
inference(resolution,[],[f48807,f29078]) ).
fof(f48953,plain,
( is_a_theorem(implies(sK4,not(sF12)))
| ~ spl20_3 ),
inference(forward_demodulation,[],[f48923,f142]) ).
fof(f48954,plain,
( is_a_theorem(implies(sK5,not(sF11)))
| ~ spl20_3 ),
inference(forward_demodulation,[],[f48922,f140]) ).
fof(f48970,plain,
! [X0] :
( ~ is_a_theorem(or(not(X0),X0))
| is_a_theorem(equiv(not(not(X0)),X0)) ),
inference(forward_demodulation,[],[f48835,f229]) ).
fof(f48974,plain,
! [X0] : is_a_theorem(equiv(not(not(X0)),X0)),
inference(forward_subsumption_resolution,[],[f48970,f48784]) ).
fof(f48983,plain,
! [X0,X1] :
( is_a_theorem(implies(not(not(X0)),X1))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f48974,f41305]) ).
fof(f48997,plain,
! [X0,X1] :
( is_a_theorem(or(not(X0),X1))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(forward_demodulation,[],[f48983,f229]) ).
fof(f49012,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X0,not(X1)))
| is_a_theorem(implies(X1,not(X0))) ),
inference(resolution,[],[f48997,f545]) ).
fof(f53933,plain,
! [X0] :
( ~ is_a_theorem(implies(sK6,X0))
| ~ is_a_theorem(sF17)
| is_a_theorem(implies(sF15,X0)) ),
inference(resolution,[],[f18588,f228]) ).
fof(f63900,plain,
( is_a_theorem(implies(sF11,not(sK5)))
| ~ spl20_3 ),
inference(resolution,[],[f48954,f49012]) ).
fof(f63938,plain,
( is_a_theorem(implies(sF11,sF12))
| ~ spl20_3 ),
inference(forward_demodulation,[],[f63900,f142]) ).
fof(f63949,plain,
( $false
| ~ spl20_3
| spl20_12 ),
inference(forward_subsumption_resolution,[],[f63938,f297]) ).
fof(f63950,plain,
( ~ spl20_3
| spl20_12 ),
inference(avatar_contradiction_clause,[],[f63949]) ).
fof(f71527,plain,
( is_a_theorem(implies(sF12,not(sK4)))
| ~ spl20_3 ),
inference(resolution,[],[f48953,f49012]) ).
fof(f71572,plain,
( is_a_theorem(implies(sF12,sF11))
| ~ spl20_3 ),
inference(forward_demodulation,[],[f71527,f140]) ).
fof(f71583,plain,
( $false
| ~ spl20_3
| spl20_28 ),
inference(forward_subsumption_resolution,[],[f71572,f617]) ).
fof(f71584,plain,
( ~ spl20_3
| spl20_28 ),
inference(avatar_contradiction_clause,[],[f71583]) ).
fof(f71660,plain,
( $false
| spl20_6
| ~ spl20_11
| ~ spl20_104 ),
inference(forward_subsumption_resolution,[],[f9048,f188]) ).
fof(f71661,plain,
( spl20_6
| ~ spl20_11
| ~ spl20_104 ),
inference(avatar_contradiction_clause,[],[f71660]) ).
fof(f71787,plain,
( ! [X0] :
( ~ is_a_theorem(implies(sK7,X0))
| is_a_theorem(implies(sF14,X0)) )
| ~ spl20_5 ),
inference(forward_subsumption_resolution,[],[f21927,f183]) ).
fof(f71810,plain,
( ! [X0] :
( ~ is_a_theorem(implies(sK6,X0))
| is_a_theorem(implies(sF15,X0)) )
| ~ spl20_5 ),
inference(forward_subsumption_resolution,[],[f53933,f183]) ).
fof(f71911,plain,
( ! [X0] : is_a_theorem(implies(X0,implies(sF14,sK9)))
| ~ spl20_2 ),
inference(forward_subsumption_resolution,[],[f18162,f170]) ).
fof(f71919,plain,
( ! [X0] : is_a_theorem(implies(X0,implies(sF15,sK8)))
| ~ spl20_2 ),
inference(forward_subsumption_resolution,[],[f18215,f170]) ).
fof(f72243,plain,
( is_a_theorem(implies(sF14,implies(sK9,sF15)))
| ~ spl20_5 ),
inference(resolution,[],[f71787,f401]) ).
fof(f72493,plain,
( is_a_theorem(implies(sF15,implies(sK8,sF14)))
| ~ spl20_5 ),
inference(resolution,[],[f71810,f400]) ).
fof(f74600,plain,
( ! [X0] :
( ~ is_a_theorem(X0)
| is_a_theorem(implies(sF14,sK9)) )
| ~ spl20_2 ),
inference(resolution,[],[f71911,f228]) ).
fof(f75397,plain,
( ! [X0] :
( ~ is_a_theorem(X0)
| is_a_theorem(implies(sF15,sK8)) )
| ~ spl20_2 ),
inference(resolution,[],[f71919,f228]) ).
fof(f77162,plain,
( ~ is_a_theorem(implies(sF14,sK9))
| is_a_theorem(implies(sF14,sF15))
| ~ spl20_5 ),
inference(resolution,[],[f72243,f4447]) ).
fof(f77210,plain,
( is_a_theorem(implies(sF14,sF15))
| ~ spl20_5
| ~ spl20_186 ),
inference(forward_subsumption_resolution,[],[f77162,f18186]) ).
fof(f77212,plain,
( $false
| ~ spl20_5
| spl20_11
| ~ spl20_186 ),
inference(forward_subsumption_resolution,[],[f77210,f292]) ).
fof(f77213,plain,
( ~ spl20_5
| spl20_11
| ~ spl20_186 ),
inference(avatar_contradiction_clause,[],[f77212]) ).
fof(f77287,plain,
( ! [X0] : ~ is_a_theorem(X0)
| ~ spl20_2
| spl20_186 ),
inference(forward_subsumption_resolution,[],[f74600,f18185]) ).
fof(f77305,plain,
( spl20_55
| ~ spl20_2
| spl20_186 ),
inference(avatar_split_clause,[],[f77287,f18184,f168,f1659]) ).
fof(f77559,plain,
( ~ is_a_theorem(implies(sF15,sK8))
| is_a_theorem(implies(sF15,sF14))
| ~ spl20_5 ),
inference(resolution,[],[f72493,f4447]) ).
fof(f77607,plain,
( is_a_theorem(implies(sF15,sF14))
| ~ spl20_5
| ~ spl20_232 ),
inference(forward_subsumption_resolution,[],[f77559,f20338]) ).
fof(f77609,plain,
( $false
| ~ spl20_5
| spl20_104
| ~ spl20_232 ),
inference(forward_subsumption_resolution,[],[f77607,f6845]) ).
fof(f77610,plain,
( ~ spl20_5
| spl20_104
| ~ spl20_232 ),
inference(avatar_contradiction_clause,[],[f77609]) ).
fof(f77665,plain,
( ! [X0] : ~ is_a_theorem(X0)
| ~ spl20_2
| spl20_232 ),
inference(forward_subsumption_resolution,[],[f75397,f20337]) ).
fof(f77679,plain,
( spl20_55
| ~ spl20_2
| spl20_232 ),
inference(avatar_split_clause,[],[f77665,f20336,f168,f1659]) ).
cnf(s1,plain,
( spl20_1
| spl20_2
| spl20_3
| ~ spl20_4 ),
inference(sat_conversion,[],[f179]) ).
cnf(s2,plain,
( spl20_1
| spl20_3
| ~ spl20_4
| spl20_5 ),
inference(sat_conversion,[],[f184]) ).
cnf(s3,plain,
( spl20_1
| spl20_3
| ~ spl20_4
| ~ spl20_6 ),
inference(sat_conversion,[],[f189]) ).
cnf(s4,plain,
( spl20_1
| spl20_2
| ~ spl20_4
| ~ spl20_7 ),
inference(sat_conversion,[],[f194]) ).
cnf(s5,plain,
( spl20_1
| ~ spl20_4
| spl20_5
| ~ spl20_7 ),
inference(sat_conversion,[],[f195]) ).
cnf(s6,plain,
( spl20_1
| ~ spl20_4
| ~ spl20_6
| ~ spl20_7 ),
inference(sat_conversion,[],[f196]) ).
cnf(s7,plain,
( ~ spl20_1
| spl20_8 ),
inference(sat_conversion,[],[f201]) ).
cnf(s8,plain,
( ~ spl20_1
| spl20_9 ),
inference(sat_conversion,[],[f206]) ).
cnf(s9,plain,
( ~ spl20_1
| ~ spl20_10 ),
inference(sat_conversion,[],[f211]) ).
cnf(s17,plain,
spl20_4,
inference(sat_conversion,[],[f464]) ).
cnf(s52,plain,
( ~ spl20_4
| spl20_59 ),
inference(sat_conversion,[],[f1690]) ).
cnf(s53,plain,
( ~ spl20_55
| ~ spl20_59 ),
inference(sat_conversion,[],[f1692]) ).
cnf(s129,plain,
( ~ spl20_8
| ~ spl20_9
| spl20_10 ),
inference(sat_conversion,[],[f8780]) ).
cnf(s130,plain,
( spl20_7
| ~ spl20_12
| ~ spl20_28 ),
inference(sat_conversion,[],[f9063]) ).
cnf(s657,plain,
( ~ spl20_3
| spl20_12 ),
inference(sat_conversion,[],[f63950]) ).
cnf(s1058,plain,
( ~ spl20_3
| spl20_28 ),
inference(sat_conversion,[],[f71584]) ).
cnf(s1088,plain,
( spl20_6
| ~ spl20_11
| ~ spl20_104 ),
inference(sat_conversion,[],[f71661]) ).
cnf(s1190,plain,
( ~ spl20_5
| spl20_11
| ~ spl20_186 ),
inference(sat_conversion,[],[f77213]) ).
cnf(s1228,plain,
( ~ spl20_2
| spl20_55
| spl20_186 ),
inference(sat_conversion,[],[f77305]) ).
cnf(s1231,plain,
( ~ spl20_5
| spl20_104
| ~ spl20_232 ),
inference(sat_conversion,[],[f77610]) ).
cnf(s1263,plain,
( ~ spl20_2
| spl20_55
| spl20_232 ),
inference(sat_conversion,[],[f77679]) ).
cnf(s1264,plain,
spl20_59,
inference(rat,[],[s52,s17]) ).
cnf(s1265,plain,
~ spl20_55,
inference(rat,[],[s53,s1264]) ).
cnf(s1354,plain,
( spl20_1
| ~ spl20_6
| ~ spl20_7 ),
inference(rat,[],[s6,s17]) ).
cnf(s1355,plain,
( spl20_1
| spl20_5
| ~ spl20_7 ),
inference(rat,[],[s5,s17]) ).
cnf(s1356,plain,
( spl20_1
| spl20_2
| ~ spl20_7 ),
inference(rat,[],[s4,s17]) ).
cnf(s1357,plain,
( spl20_1
| spl20_3
| ~ spl20_6 ),
inference(rat,[],[s3,s17]) ).
cnf(s1358,plain,
( spl20_1
| spl20_3
| spl20_5 ),
inference(rat,[],[s2,s17]) ).
cnf(s1359,plain,
( spl20_1
| spl20_2
| spl20_3 ),
inference(rat,[],[s1,s17]) ).
cnf(s1360,plain,
( spl20_2
| spl20_1 ),
inference(rat,[],[s130,s657,s1058,s1356,s1359]) ).
cnf(s1361,plain,
( ~ spl20_7
| spl20_1 ),
inference(rat,[],[s1088,s1190,s1231,s1355,s1354,s1263,s1228,s1360,s1265]) ).
cnf(s1362,plain,
( ~ spl20_3
| spl20_7 ),
inference(rat,[],[s130,s657,s1058]) ).
cnf(s1363,plain,
spl20_1,
inference(rat,[],[s1088,s1190,s1231,s1358,s1357,s1362,s1361,s1228,s1263,s1360,s1265]) ).
cnf(s1364,plain,
~ spl20_10,
inference(rat,[],[s9,s1363]) ).
cnf(s1365,plain,
spl20_9,
inference(rat,[],[s8,s1363]) ).
cnf(s1366,plain,
spl20_8,
inference(rat,[],[s7,s1363]) ).
cnf(s1368,plain,
$false,
inference(rat,[],[s129,s1364,s1365,s1366]) ).
fof(f77680,plain,
$false,
inference(avatar_sat_refutation,[],[s1368]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL450+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.35 % Computer : n003.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sun Sep 27 15:45:42 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.38 Running first-order theorem proving
% 0.14/0.38 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 11.55/2.50 % (732616)Detected formulas, will run a generic FOF schedule.
% 11.55/2.50 % (732621)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=1626343136:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 11.55/2.50 % (732624)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=979295702:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 11.55/2.50 % (732626)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=249344871:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 11.55/2.50 % (732624)Refutation not found, incomplete strategy
% 11.55/2.50 % (732624)------------------------------
% 11.55/2.50 % (732624)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.55/2.50 % (732624)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.55/2.50 % (732624)CaDiCaL version: 2.1.3
% 11.55/2.50 % (732624)Termination reason: Refutation not found, incomplete strategy
% 11.55/2.50 % (732624)Time elapsed: 0.001 s
% 11.55/2.50 % (732624)Peak memory usage: 87 MB
% 11.55/2.50 % (732623)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=4027904900:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 11.55/2.50 % (732622)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=1993377720:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 11.55/2.50 % (732625)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=927365204:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 11.55/2.50 % (732625)Refutation not found, incomplete strategy
% 11.55/2.50 % (732625)------------------------------
% 11.55/2.50 % (732625)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.55/2.50 % (732625)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.55/2.50 % (732625)CaDiCaL version: 2.1.3
% 11.55/2.50 % (732625)Termination reason: Refutation not found, incomplete strategy
% 11.55/2.50 % (732625)Time elapsed: 0.001 s
% 11.55/2.50 % (732625)Peak memory usage: 88 MB
% 11.55/2.50 % (732627)dis-21_1_sil=8000:lcm=predicate:random_seed=3298910884:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 11.55/2.50 % (732626)Instruction limit reached!
% 11.55/2.50 % (732626)------------------------------
% 11.55/2.50 % (732626)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.55/2.50 % (732626)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.55/2.50 % (732626)CaDiCaL version: 2.1.3
% 11.55/2.50 % (732626)Termination reason: Instruction limit
% 11.55/2.50 % (732626)Termination phase: Saturation
% 11.55/2.50 % (732626)Time elapsed: 0.097 s
% 11.55/2.50 % (732626)Peak memory usage: 90 MB
% 11.55/2.50 % (732626)Instructions burned: 139 (million)
% 11.55/2.50 % (732627)Instruction limit reached!
% 11.55/2.50 % (732627)------------------------------
% 11.55/2.50 % (732627)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.55/2.50 % (732627)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.55/2.50 % (732627)CaDiCaL version: 2.1.3
% 11.55/2.50 % (732627)Termination reason: Instruction limit
% 11.55/2.50 % (732627)Termination phase: Saturation
% 11.55/2.50 % (732627)Time elapsed: 0.078 s
% 11.55/2.50 % (732627)Peak memory usage: 90 MB
% 11.55/2.50 % (732627)Instructions burned: 130 (million)
% 11.55/2.50 % (732624)------------------------------
% 11.55/2.50 % (732624)------------------------------
% 11.55/2.50 % (732635)lrs+10_1_sil=8000:sp=occurrence:random_seed=494297795:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 11.55/2.50 % (732636)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2914875250:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 11.55/2.50 % (732636)Refutation not found, incomplete strategy
% 11.55/2.50 % (732636)------------------------------
% 11.55/2.50 % (732636)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.55/2.50 % (732636)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.55/2.50 % (732636)CaDiCaL version: 2.1.3
% 11.55/2.50 % (732636)Termination reason: Refutation not found, incomplete strategy
% 11.55/2.50 % (732636)Time elapsed: 0.001 s
% 11.55/2.50 % (732636)Peak memory usage: 88 MB
% 19.80/3.64 % (732636)Instructions burned: 1 (million)
% 19.80/3.64 % (732625)------------------------------
% 19.80/3.64 % (732625)------------------------------
% 19.80/3.64 % (732639)lrs+1011_1_sil=32000:sp=occurrence:random_seed=733654343:i=325:sd=1:ss=axioms:sgt=32_2996 on theBenchmark for (2996ds/325Mi)
% 19.80/3.64 % (732639)Refutation not found, incomplete strategy
% 19.80/3.64 % (732639)------------------------------
% 19.80/3.64 % (732639)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 19.80/3.64 % (732639)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 19.80/3.64 % (732639)CaDiCaL version: 2.1.3
% 19.80/3.64 % (732639)Termination reason: Refutation not found, incomplete strategy
% 19.80/3.64 % (732639)Time elapsed: 0.001 s
% 19.80/3.64 % (732639)Peak memory usage: 88 MB
% 19.80/3.64 % (732639)Instructions burned: 1 (million)
% 19.80/3.64 % (732640)dis+10_5:1_slsqr=1,4:sil=8000:fde=unused:erd=off:urr=full:fd=off:s2agt=8:br=off:slsq=on:random_seed=3323414283:s2a=on:i=248:s2at=1.23:gtg=position_2996 on theBenchmark for (2996ds/248Mi)
% 19.80/3.64 % (732635)Instruction limit reached!
% 19.80/3.64 % (732635)------------------------------
% 19.80/3.64 % (732635)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 19.80/3.64 % (732635)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 19.80/3.64 % (732635)CaDiCaL version: 2.1.3
% 19.80/3.64 % (732635)Termination reason: Instruction limit
% 19.80/3.64 % (732635)Termination phase: Saturation
% 19.80/3.64 % (732635)Time elapsed: 0.164 s
% 19.80/3.64 % (732635)Peak memory usage: 92 MB
% 19.80/3.64 % (732635)Instructions burned: 285 (million)
% 19.80/3.64 % (732636)------------------------------
% 19.80/3.64 % (732636)------------------------------
% 19.80/3.64 % (732643)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=988306380:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2994 on theBenchmark for (2994ds/294Mi)
% 19.80/3.64 % (732643)Refutation not found, incomplete strategy
% 19.80/3.64 % (732643)------------------------------
% 19.80/3.64 % (732643)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 19.80/3.64 % (732643)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 19.80/3.64 % (732643)CaDiCaL version: 2.1.3
% 19.80/3.64 % (732643)Termination reason: Refutation not found, incomplete strategy
% 19.80/3.64 % (732643)Time elapsed: 0.002 s
% 19.80/3.64 % (732643)Peak memory usage: 88 MB
% 19.80/3.64 % (732643)Instructions burned: 1 (million)
% 19.80/3.64 % (732640)Instruction limit reached!
% 19.80/3.64 % (732640)------------------------------
% 19.80/3.64 % (732640)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 19.80/3.64 % (732640)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 19.80/3.64 % (732640)CaDiCaL version: 2.1.3
% 19.80/3.64 % (732640)Termination reason: Instruction limit
% 19.80/3.64 % (732640)Termination phase: Saturation
% 19.80/3.64 % (732640)Time elapsed: 0.149 s
% 19.80/3.64 % (732640)Peak memory usage: 92 MB
% 19.80/3.64 % (732640)Instructions burned: 248 (million)
% 19.80/3.64 % (732639)------------------------------
% 19.80/3.64 % (732639)------------------------------
% 19.80/3.64 % (732644)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=1852795687:i=2350_2993 on theBenchmark for (2993ds/2350Mi)
% 19.80/3.64 % (732646)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=4258331839:cts=off:i=113:fsr=off:ss=included:sgt=4_2993 on theBenchmark for (2993ds/113Mi)
% 19.80/3.64 % (732648)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=2719304035:i=127:av=off:fsr=off:sup=off_2992 on theBenchmark for (2992ds/127Mi)
% 19.80/3.64 % (732646)Instruction limit reached!
% 19.80/3.64 % (732646)------------------------------
% 19.80/3.64 % (732646)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 19.80/3.64 % (732646)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 19.80/3.64 % (732646)CaDiCaL version: 2.1.3
% 19.80/3.64 % (732646)Termination reason: Instruction limit
% 19.80/3.64 % (732646)Termination phase: Saturation
% 19.80/3.64 % (732646)Time elapsed: 0.071 s
% 19.80/3.64 % (732646)Peak memory usage: 90 MB
% 19.80/3.64 % (732646)Instructions burned: 114 (million)
% 19.80/3.64 % (732643)------------------------------
% 19.80/3.64 % (732643)------------------------------
% 19.80/3.64 % (732648)Instruction limit reached!
% 19.80/3.64 % (732648)------------------------------
% 19.80/3.64 % (732648)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 19.80/3.64 % (732648)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 24.27/6.30 % (732648)CaDiCaL version: 2.1.3
% 24.27/6.30 % (732648)Termination reason: Instruction limit
% 24.27/6.30 % (732648)Termination phase: Saturation
% 24.27/6.30 % (732648)Time elapsed: 0.065 s
% 24.27/6.30 % (732648)Peak memory usage: 88 MB
% 24.27/6.30 % (732648)Instructions burned: 129 (million)
% 24.27/6.30 % (732651)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=2881187948:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2991 on theBenchmark for (2991ds/114Mi)
% 24.27/6.30 % (732651)Refutation not found, incomplete strategy
% 24.27/6.30 % (732651)------------------------------
% 24.27/6.30 % (732651)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 24.27/6.30 % (732651)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 24.27/6.30 % (732651)CaDiCaL version: 2.1.3
% 24.27/6.30 % (732651)Termination reason: Refutation not found, incomplete strategy
% 24.27/6.30 % (732651)Time elapsed: 0.001 s
% 24.27/6.30 % (732651)Peak memory usage: 88 MB
% 24.27/6.30 % (732651)Instructions burned: 1 (million)
% 24.27/6.30 % (732652)lrs+10_1_sil=8000:sp=occurrence:random_seed=2883814340:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2990 on theBenchmark for (2990ds/907Mi)
% 24.27/6.30 % (732653)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=3052709792:i=437:sd=1:aac=none:ss=included_2990 on theBenchmark for (2990ds/437Mi)
% 24.27/6.30 % (732653)Refutation not found, incomplete strategy
% 24.27/6.30 % (732653)------------------------------
% 24.27/6.30 % (732653)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 24.27/6.30 % (732653)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 24.27/6.30 % (732653)CaDiCaL version: 2.1.3
% 24.27/6.30 % (732653)Termination reason: Refutation not found, incomplete strategy
% 24.27/6.30 % (732653)Time elapsed: 0.002 s
% 24.27/6.30 % (732653)Peak memory usage: 88 MB
% 24.27/6.30 % (732653)Instructions burned: 2 (million)
% 24.27/6.30 % (732651)------------------------------
% 24.27/6.30 % (732651)------------------------------
% 24.27/6.30 % (732653)------------------------------
% 24.27/6.30 % (732653)------------------------------
% 24.27/6.30 % (732657)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=3656730433:i=5202:ss=axioms:sgt=16_2987 on theBenchmark for (2987ds/5202Mi)
% 24.27/6.30 % (732658)dis+10_3:1_sil=8000:acc=on:urr=on:br=off:sac=on:newcnf=on:random_seed=4163020731:i=134:sd=2:doe=on:nm=16:sup=off:ss=included_2986 on theBenchmark for (2986ds/134Mi)
% 24.27/6.30 % (732658)Instruction limit reached!
% 24.27/6.30 % (732658)------------------------------
% 24.27/6.30 % (732658)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 24.27/6.30 % (732658)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 24.27/6.30 % (732658)CaDiCaL version: 2.1.3
% 24.27/6.30 % (732658)Termination reason: Instruction limit
% 24.27/6.30 % (732658)Termination phase: Saturation
% 24.27/6.30 % (732658)Time elapsed: 0.075 s
% 24.27/6.30 % (732658)Peak memory usage: 91 MB
% 24.27/6.30 % (732658)Instructions burned: 134 (million)
% 24.27/6.30 % (732652)Instruction limit reached!
% 24.27/6.30 % (732652)------------------------------
% 24.27/6.30 % (732652)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 24.27/6.30 % (732652)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 24.27/6.30 % (732652)CaDiCaL version: 2.1.3
% 24.27/6.30 % (732652)Termination reason: Instruction limit
% 24.27/6.30 % (732652)Termination phase: Saturation
% 24.27/6.30 % (732652)Time elapsed: 0.522 s
% 24.27/6.30 % (732652)Peak memory usage: 101 MB
% 24.27/6.30 % (732652)Instructions burned: 907 (million)
% 24.27/6.30 % (732661)lrs+1002_8_sil=8000:sp=occurrence:sos=on:sac=on:random_seed=767671421:st=8:i=592:sd=3:ep=RST:ss=axioms_2984 on theBenchmark for (2984ds/592Mi)
% 24.27/6.30 % (732661)Refutation not found, incomplete strategy
% 24.27/6.30 % (732661)------------------------------
% 24.27/6.30 % (732661)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 24.27/6.30 % (732661)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 24.27/6.30 % (732661)CaDiCaL version: 2.1.3
% 24.27/6.30 % (732661)Termination reason: Refutation not found, incomplete strategy
% 24.27/6.30 % (732661)Time elapsed: 0.002 s
% 24.27/6.30 % (732661)Peak memory usage: 88 MB
% 24.27/6.30 % (732661)Instructions burned: 1 (million)
% 24.27/6.30 % (732662)lrs+10_1_ncem=casc2026/models/loop6.pt:sil=32000:npcc=on:random_seed=564696322:st=3:i=13193:sd=3:ss=axioms_2984 on theBenchmark for (2984ds/13193Mi)
% 24.27/6.30 % (732661)------------------------------
% 24.27/6.30 % (732661)------------------------------
% 24.27/6.30 % (732665)lrs+1666_7_slsqr=4,1:sil=8000:plsq=on:plsqc=1:sos=on:urr=on:plsql=on:rp=on:alpa=false:sac=on:slsq=on:random_seed=2806015918:i=125:slsql=off:bs=unit_only:gtg=position:fdi=2:gsp=on:ss=axioms:sgt=8_2981 on theBenchmark for (2981ds/125Mi)
% 24.27/6.30 % (732665)Instruction limit reached!
% 24.27/6.30 % (732665)------------------------------
% 24.27/6.30 % (732665)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 24.27/6.30 % (732665)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 24.27/6.30 % (732665)CaDiCaL version: 2.1.3
% 24.27/6.30 % (732665)Termination reason: Instruction limit
% 24.27/6.30 % (732665)Termination phase: Saturation
% 24.27/6.30 % (732665)Time elapsed: 0.087 s
% 24.27/6.30 % (732665)Peak memory usage: 90 MB
% 24.27/6.30 % (732665)Instructions burned: 125 (million)
% 24.27/6.30 % (732667)lrs+10_1024_to=lpo:sil=8000:tgt=full:sp=arity:slsq=on:random_seed=2184525785:i=134:gtgl=5:slsql=off:gtg=exists_sym_2979 on theBenchmark for (2979ds/134Mi)
% 24.27/6.30 % (732644)Instruction limit reached!
% 24.27/6.30 % (732644)------------------------------
% 24.27/6.30 % (732644)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 24.27/6.30 % (732644)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 24.27/6.30 % (732644)CaDiCaL version: 2.1.3
% 24.27/6.30 % (732644)Termination reason: Instruction limit
% 24.27/6.30 % (732644)Termination phase: Saturation
% 24.27/6.30 % (732644)Time elapsed: 1.479 s
% 24.27/6.30 % (732644)Peak memory usage: 142 MB
% 24.27/6.30 % (732644)Instructions burned: 2351 (million)
% 24.27/6.30 % (732667)Instruction limit reached!
% 24.27/6.30 % (732667)------------------------------
% 24.27/6.30 % (732667)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 24.27/6.30 % (732667)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 24.27/6.30 % (732667)CaDiCaL version: 2.1.3
% 24.27/6.30 % (732667)Termination reason: Instruction limit
% 24.27/6.30 % (732667)Termination phase: Saturation
% 24.27/6.30 % (732667)Time elapsed: 0.088 s
% 24.27/6.30 % (732667)Peak memory usage: 90 MB
% 24.27/6.30 % (732667)Instructions burned: 134 (million)
% 24.27/6.30 % (732669)lrs+10_1_sil=16000:plsq=on:plsqc=1:plsqr=32,1:sos=on:lcm=reverse:fd=off:newcnf=on:random_seed=2051653086:i=141:sd=1:gsp=on:sup=off:ss=axioms:sgt=8_2977 on theBenchmark for (2977ds/141Mi)
% 24.27/6.30 % (732669)Refutation not found, incomplete strategy
% 24.27/6.30 % (732669)------------------------------
% 24.27/6.30 % (732669)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 24.27/6.30 % (732669)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 24.27/6.30 % (732669)CaDiCaL version: 2.1.3
% 24.27/6.30 % (732669)Termination reason: Refutation not found, incomplete strategy
% 24.27/6.30 % (732669)Time elapsed: 0.001 s
% 24.27/6.30 % (732669)Peak memory usage: 88 MB
% 24.27/6.30 % (732669)Instructions burned: 1 (million)
% 24.27/6.30 % (732670)lrs+1011_1_sil=8000:plsq=on:sp=occurrence:fs=off:random_seed=2422286398:i=431:sd=1:fsr=off:sup=off:ss=axioms:sgt=64_2976 on theBenchmark for (2976ds/431Mi)
% 24.27/6.30 % (732670)Refutation not found, incomplete strategy
% 24.27/6.30 % (732670)------------------------------
% 24.27/6.30 % (732670)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 24.27/6.30 % (732670)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 24.27/6.30 % (732670)CaDiCaL version: 2.1.3
% 24.27/6.30 % (732670)Termination reason: Refutation not found, incomplete strategy
% 24.27/6.30 % (732670)Time elapsed: 0.001 s
% 24.27/6.30 % (732670)Peak memory usage: 88 MB
% 24.27/6.30 % (732670)Instructions burned: 1 (million)
% 24.27/6.30 % (732669)------------------------------
% 24.27/6.30 % (732669)------------------------------
% 24.27/6.30 % (732670)------------------------------
% 24.27/6.30 % (732670)------------------------------
% 24.27/6.30 % (732673)lrs+1010_1_ncem=casc2026/models/loop6.pt:sil=64000:tgt=full:npcc=on:prc=on:urr=ec_only:bsr=on:fd=preordered:gs=on:sac=on:newcnf=on:random_seed=2403194855:i=6060:aac=none:ins=25_2973 on theBenchmark for (2973ds/6060Mi)
% 24.27/6.30 % (732674)lrs+10_16_anc=all:slsqr=32,1:sil=8000:avsql=on:sp=unary_frequency:lcm=predicate:urr=full:rp=on:br=off:slsqc=4:flr=on:sac=on:slsq=on:avsqc=1:random_seed=1205346622:avsq=on:s2a=on:i=150:kws=precedence:nicw=on:gsp=on:rawr=on_2973 on theBenchmark for (2973ds/150Mi)
% 24.27/6.30 % (732674)Instruction limit reached!
% 24.27/6.30 % (732674)------------------------------
% 24.27/6.30 % (732674)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 24.27/6.30 % (732674)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 24.27/6.30 % (732674)CaDiCaL version: 2.1.3
% 24.27/6.30 % (732674)Termination reason: Instruction limit
% 24.27/6.30 % (732674)Termination phase: Saturation
% 24.27/6.30 % (732674)Time elapsed: 0.087 s
% 24.27/6.30 % (732674)Peak memory usage: 90 MB
% 24.27/6.30 % (732674)Instructions burned: 151 (million)
% 24.27/6.30 % (732677)lrs+1010_1_ncem=casc2026/models/loop8.pt:sil=64000:tgt=ground:npcc=on:sp=arity:urr=on:random_seed=1168571538:i=14155:bd=all_2970 on theBenchmark for (2970ds/14155Mi)
% 24.27/6.30 % (732657)Instruction limit reached!
% 24.27/6.30 % (732657)------------------------------
% 24.27/6.30 % (732657)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 24.27/6.30 % (732657)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 24.27/6.30 % (732657)CaDiCaL version: 2.1.3
% 24.27/6.30 % (732657)Termination reason: Instruction limit
% 24.27/6.30 % (732657)Termination phase: Saturation
% 24.27/6.30 % (732657)Time elapsed: 3.037 s
% 24.27/6.30 % (732657)Peak memory usage: 174 MB
% 24.27/6.30 % (732657)Instructions burned: 5202 (million)
% 24.27/6.30 % (732679)lrs+10_1024_sil=16000:plsq=on:plsqr=32,1:sos=all:fs=off:gs=on:newcnf=on:random_seed=569986471:i=667:av=off:fsr=off_2955 on theBenchmark for (2955ds/667Mi)
% 24.27/6.30 % (732679)Refutation not found, incomplete strategy
% 24.27/6.30 % (732679)------------------------------
% 24.27/6.30 % (732679)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 24.27/6.30 % (732679)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 24.27/6.30 % (732679)CaDiCaL version: 2.1.3
% 24.27/6.30 % (732679)Termination reason: Refutation not found, incomplete strategy
% 24.27/6.30 % (732679)Time elapsed: 0.003 s
% 24.27/6.30 % (732679)Peak memory usage: 88 MB
% 24.27/6.30 % (732679)Instructions burned: 3 (million)
% 24.27/6.30 % (732679)------------------------------
% 24.27/6.30 % (732679)------------------------------
% 24.27/6.30 % (732681)ott-1011_3:1_anc=all_dependent:to=lpo:sil=8000:drc=ordering:sas=cadical:fdtod=off:sp=reverse_frequency:spb=goal_then_units:urr=full:lftc=20:newcnf=on:random_seed=1632758902:s2a=on:i=185:s2at=1.8:fdi=4_2951 on theBenchmark for (2951ds/185Mi)
% 24.27/6.30 % (732681)Instruction limit reached!
% 24.27/6.30 % (732681)------------------------------
% 24.27/6.30 % (732681)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 24.27/6.30 % (732681)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 24.27/6.30 % (732681)CaDiCaL version: 2.1.3
% 24.27/6.30 % (732681)Termination reason: Instruction limit
% 24.27/6.30 % (732681)Termination phase: Saturation
% 24.27/6.30 % (732681)Time elapsed: 0.102 s
% 24.27/6.30 % (732681)Peak memory usage: 93 MB
% 24.27/6.30 % (732681)Instructions burned: 185 (million)
% 24.27/6.30 % (732683)dis+1010_14_anc=all:to=lpo:sil=8000:sp=arity:slsq=on:random_seed=1033549872:i=193:ins=10:fsr=off:ss=axioms:fsd=on_2949 on theBenchmark for (2949ds/193Mi)
% 24.27/6.30 % (732683)Refutation not found, incomplete strategy
% 24.27/6.30 % (732683)------------------------------
% 24.27/6.30 % (732683)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 24.27/6.30 % (732683)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 24.27/6.30 % (732683)CaDiCaL version: 2.1.3
% 24.27/6.30 % (732683)Termination reason: Refutation not found, incomplete strategy
% 24.27/6.30 % (732683)Time elapsed: 0.001 s
% 24.27/6.30 % (732683)Peak memory usage: 88 MB
% 24.27/6.30 % (732683)Instructions burned: 1 (million)
% 24.27/6.30 % (732621)First to succeed.
% 24.27/6.30 % (732621)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-732616"
% 24.27/6.30 % (732683)------------------------------
% 24.27/6.30 % (732683)------------------------------
% 24.27/6.30 % (732621)Refutation found. Thanks to Tanya!
% 24.27/6.30 % SZS status Theorem for theBenchmark
% 24.27/6.30 % SZS output start Proof for theBenchmark
% See solution above
% 39.33/6.49 % (732621)------------------------------
% 39.33/6.49 % (732621)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 39.33/6.49 % (732621)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 39.33/6.49 % (732621)CaDiCaL version: 2.1.3
% 39.33/6.49 % (732621)Termination reason: Refutation
% 39.33/6.49 % (732621)Time elapsed: 5.198 s
% 39.33/6.49 % (732621)Peak memory usage: 258 MB
% 39.33/6.49 % (732621)Instructions burned: 15438 (million)
% 39.33/6.49 % (732621)------------------------------
% 39.33/6.49 % (732621)------------------------------
% 39.33/6.49 % (732616)Success in time 5.48 s
% 39.33/6.49 % Vampire exiting
%------------------------------------------------------------------------------