%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM860+1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n008.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 12:17:18 PM UTC 2026
% Result : Theorem 13.41s 2.84s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 32
% Syntax : Number of formulae : 345 ( 16 unt; 19 def)
% Number of atoms : 1049 ( 45 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 1280 ( 576 ~; 624 |; 46 &)
% ( 29 <=>; 4 =>; 0 <=; 1 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 27 ( 25 usr; 20 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 387 ( 0 sgn 372 !; 15 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : lesseq(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lesseq_ref) ).
fof(f2,axiom,
! [X0,X1,X2] :
( ( lesseq(X0,X1)
& lesseq(X1,X2) )
=> lesseq(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lesseq_trans) ).
fof(f3,axiom,
! [X0,X1] :
( ( lesseq(X0,X1)
& lesseq(X1,X0) )
=> X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lesseq_antisymmetric) ).
fof(f4,axiom,
! [X0,X1] :
( lesseq(X0,X1)
| lesseq(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lesseq_total) ).
fof(f6,axiom,
! [X0,X1] :
( lesseq(X0,X1)
<=> lesseq(summation(X0),summation(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',summation_monotone) ).
fof(f7,axiom,
! [X0,X1] :
( max(X0,X1) = X0
| ~ lesseq(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',max_1) ).
fof(f8,axiom,
! [X0,X1] :
( max(X0,X1) = X1
| ~ lesseq(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',max_2) ).
fof(f9,axiom,
! [X0,X1,X2] :
( ub(X0,X1,X2)
<=> ( lesseq(X0,X2)
& lesseq(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ub) ).
fof(f10,axiom,
! [X0,X1,X2] :
( model_max(X0,X1,X2)
<=> lesseq(summation(max(X0,X1)),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',model_max_3) ).
fof(f11,axiom,
! [X0,X1,X2] :
( model_ub(X0,X1,X2)
<=> ? [X3] :
( ub(X0,X1,X3)
& lesseq(summation(X3),X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',model_ub_3) ).
fof(f12,axiom,
! [X0,X1,X2] :
( minsol_model_max(X0,X1,X2)
<=> ( model_max(X0,X1,X2)
& ! [X3] :
( model_max(X0,X1,X3)
=> lesseq(X2,X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',minsol_model_max) ).
fof(f13,axiom,
! [X0,X1,X2] :
( minsol_model_ub(X0,X1,X2)
<=> ( model_ub(X0,X1,X2)
& ! [X3] :
( model_ub(X0,X1,X3)
=> lesseq(X2,X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',minsol_model_ub) ).
fof(f14,conjecture,
! [X0,X1,X2] :
( minsol_model_ub(X0,X1,X2)
<=> minsol_model_max(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',max_is_ub_1) ).
fof(f15,negated_conjecture,
~ ! [X0,X1,X2] :
( minsol_model_ub(X0,X1,X2)
<=> minsol_model_max(X0,X1,X2) ),
inference(negated_conjecture,[status(cth)],[f14]) ).
fof(f16,plain,
? [X0,X1,X2] :
( minsol_model_ub(X0,X1,X2)
<~> minsol_model_max(X0,X1,X2) ),
inference(ennf_transformation,[],[f15]) ).
fof(f17,plain,
! [X0,X1,X2] :
( minsol_model_max(X0,X1,X2)
<=> ( model_max(X0,X1,X2)
& ! [X3] :
( lesseq(X2,X3)
| ~ model_max(X0,X1,X3) ) ) ),
inference(ennf_transformation,[],[f12]) ).
fof(f18,plain,
! [X0,X1,X2] :
( minsol_model_ub(X0,X1,X2)
<=> ( model_ub(X0,X1,X2)
& ! [X3] :
( lesseq(X2,X3)
| ~ model_ub(X0,X1,X3) ) ) ),
inference(ennf_transformation,[],[f13]) ).
fof(f19,plain,
! [X0,X1] :
( X0 = X1
| ~ lesseq(X0,X1)
| ~ lesseq(X1,X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f20,plain,
! [X0,X1] :
( X0 = X1
| ~ lesseq(X0,X1)
| ~ lesseq(X1,X0) ),
inference(flattening,[],[f19]) ).
fof(f21,plain,
! [X0,X1,X2] :
( lesseq(X0,X2)
| ~ lesseq(X0,X1)
| ~ lesseq(X1,X2) ),
inference(ennf_transformation,[],[f2]) ).
fof(f22,plain,
! [X0,X1,X2] :
( lesseq(X0,X2)
| ~ lesseq(X0,X1)
| ~ lesseq(X1,X2) ),
inference(flattening,[],[f21]) ).
fof(f23,plain,
? [X0,X1,X2] :
( ( ~ minsol_model_max(X0,X1,X2)
| ~ minsol_model_ub(X0,X1,X2) )
& ( minsol_model_max(X0,X1,X2)
| minsol_model_ub(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f16]) ).
fof(f24,plain,
( ( ~ minsol_model_max(sK0,sK1,sK2)
| ~ minsol_model_ub(sK0,sK1,sK2) )
& ( minsol_model_max(sK0,sK1,sK2)
| minsol_model_ub(sK0,sK1,sK2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f23]) ).
fof(f25,plain,
! [X0,X1,X2] :
( ( minsol_model_max(X0,X1,X2)
| ~ model_max(X0,X1,X2)
| ? [X3] :
( ~ lesseq(X2,X3)
& model_max(X0,X1,X3) ) )
& ( ( model_max(X0,X1,X2)
& ! [X3] :
( lesseq(X2,X3)
| ~ model_max(X0,X1,X3) ) )
| ~ minsol_model_max(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f17]) ).
fof(f26,plain,
! [X0,X1,X2] :
( ( minsol_model_max(X0,X1,X2)
| ~ model_max(X0,X1,X2)
| ? [X3] :
( ~ lesseq(X2,X3)
& model_max(X0,X1,X3) ) )
& ( ( model_max(X0,X1,X2)
& ! [X3] :
( lesseq(X2,X3)
| ~ model_max(X0,X1,X3) ) )
| ~ minsol_model_max(X0,X1,X2) ) ),
inference(flattening,[],[f25]) ).
fof(f27,plain,
! [X0,X1,X2] :
( ( minsol_model_max(X0,X1,X2)
| ~ model_max(X0,X1,X2)
| ? [X3] :
( ~ lesseq(X2,X3)
& model_max(X0,X1,X3) ) )
& ( ( model_max(X0,X1,X2)
& ! [X4] :
( lesseq(X2,X4)
| ~ model_max(X0,X1,X4) ) )
| ~ minsol_model_max(X0,X1,X2) ) ),
inference(rectify,[],[f26]) ).
fof(f28,plain,
! [X0,X1,X2] :
( ( minsol_model_max(X0,X1,X2)
| ~ model_max(X0,X1,X2)
| ( ~ lesseq(X2,sK3(X0,X1,X2))
& model_max(X0,X1,sK3(X0,X1,X2)) ) )
& ( ( model_max(X0,X1,X2)
& ! [X4] :
( lesseq(X2,X4)
| ~ model_max(X0,X1,X4) ) )
| ~ minsol_model_max(X0,X1,X2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X3,sK3(X0,X1,X2))],[f27]) ).
fof(f29,plain,
! [X0,X1,X2] :
( ( minsol_model_ub(X0,X1,X2)
| ~ model_ub(X0,X1,X2)
| ? [X3] :
( ~ lesseq(X2,X3)
& model_ub(X0,X1,X3) ) )
& ( ( model_ub(X0,X1,X2)
& ! [X3] :
( lesseq(X2,X3)
| ~ model_ub(X0,X1,X3) ) )
| ~ minsol_model_ub(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f18]) ).
fof(f30,plain,
! [X0,X1,X2] :
( ( minsol_model_ub(X0,X1,X2)
| ~ model_ub(X0,X1,X2)
| ? [X3] :
( ~ lesseq(X2,X3)
& model_ub(X0,X1,X3) ) )
& ( ( model_ub(X0,X1,X2)
& ! [X3] :
( lesseq(X2,X3)
| ~ model_ub(X0,X1,X3) ) )
| ~ minsol_model_ub(X0,X1,X2) ) ),
inference(flattening,[],[f29]) ).
fof(f31,plain,
! [X0,X1,X2] :
( ( minsol_model_ub(X0,X1,X2)
| ~ model_ub(X0,X1,X2)
| ? [X3] :
( ~ lesseq(X2,X3)
& model_ub(X0,X1,X3) ) )
& ( ( model_ub(X0,X1,X2)
& ! [X4] :
( lesseq(X2,X4)
| ~ model_ub(X0,X1,X4) ) )
| ~ minsol_model_ub(X0,X1,X2) ) ),
inference(rectify,[],[f30]) ).
fof(f32,plain,
! [X0,X1,X2] :
( ( minsol_model_ub(X0,X1,X2)
| ~ model_ub(X0,X1,X2)
| ( ~ lesseq(X2,sK4(X0,X1,X2))
& model_ub(X0,X1,sK4(X0,X1,X2)) ) )
& ( ( model_ub(X0,X1,X2)
& ! [X4] :
( lesseq(X2,X4)
| ~ model_ub(X0,X1,X4) ) )
| ~ minsol_model_ub(X0,X1,X2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X3,sK4(X0,X1,X2))],[f31]) ).
fof(f33,plain,
! [X0,X1,X2] :
( ( model_ub(X0,X1,X2)
| ! [X3] :
( ~ ub(X0,X1,X3)
| ~ lesseq(summation(X3),X2) ) )
& ( ? [X3] :
( ub(X0,X1,X3)
& lesseq(summation(X3),X2) )
| ~ model_ub(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f11]) ).
fof(f34,plain,
! [X0,X1,X2] :
( ( model_ub(X0,X1,X2)
| ! [X3] :
( ~ ub(X0,X1,X3)
| ~ lesseq(summation(X3),X2) ) )
& ( ? [X4] :
( ub(X0,X1,X4)
& lesseq(summation(X4),X2) )
| ~ model_ub(X0,X1,X2) ) ),
inference(rectify,[],[f33]) ).
fof(f35,plain,
! [X0,X1,X2] :
( ( model_ub(X0,X1,X2)
| ! [X3] :
( ~ ub(X0,X1,X3)
| ~ lesseq(summation(X3),X2) ) )
& ( ( ub(X0,X1,sK5(X0,X1,X2))
& lesseq(summation(sK5(X0,X1,X2)),X2) )
| ~ model_ub(X0,X1,X2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(X4,sK5(X0,X1,X2))],[f34]) ).
fof(f36,plain,
! [X0,X1,X2] :
( ( model_max(X0,X1,X2)
| ~ lesseq(summation(max(X0,X1)),X2) )
& ( lesseq(summation(max(X0,X1)),X2)
| ~ model_max(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f10]) ).
fof(f37,plain,
! [X0,X1,X2] :
( ( ub(X0,X1,X2)
| ~ lesseq(X0,X2)
| ~ lesseq(X1,X2) )
& ( ( lesseq(X0,X2)
& lesseq(X1,X2) )
| ~ ub(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f9]) ).
fof(f38,plain,
! [X0,X1,X2] :
( ( ub(X0,X1,X2)
| ~ lesseq(X0,X2)
| ~ lesseq(X1,X2) )
& ( ( lesseq(X0,X2)
& lesseq(X1,X2) )
| ~ ub(X0,X1,X2) ) ),
inference(flattening,[],[f37]) ).
fof(f39,plain,
! [X0,X1] :
( ( lesseq(X0,X1)
| ~ lesseq(summation(X0),summation(X1)) )
& ( lesseq(summation(X0),summation(X1))
| ~ lesseq(X0,X1) ) ),
inference(nnf_transformation,[],[f6]) ).
fof(f41,plain,
( minsol_model_max(sK0,sK1,sK2)
| minsol_model_ub(sK0,sK1,sK2) ),
inference(cnf_transformation,[],[f24]) ).
fof(f42,plain,
( ~ minsol_model_max(sK0,sK1,sK2)
| ~ minsol_model_ub(sK0,sK1,sK2) ),
inference(cnf_transformation,[],[f24]) ).
fof(f43,plain,
! [X2,X0,X1,X4] :
( ~ minsol_model_max(X0,X1,X2)
| ~ model_max(X0,X1,X4)
| lesseq(X2,X4) ),
inference(cnf_transformation,[],[f28]) ).
fof(f44,plain,
! [X2,X0,X1] :
( ~ minsol_model_max(X0,X1,X2)
| model_max(X0,X1,X2) ),
inference(cnf_transformation,[],[f28]) ).
fof(f45,plain,
! [X2,X0,X1] :
( model_max(X0,X1,sK3(X0,X1,X2))
| ~ model_max(X0,X1,X2)
| minsol_model_max(X0,X1,X2) ),
inference(cnf_transformation,[],[f28]) ).
fof(f46,plain,
! [X2,X0,X1] :
( ~ lesseq(X2,sK3(X0,X1,X2))
| ~ model_max(X0,X1,X2)
| minsol_model_max(X0,X1,X2) ),
inference(cnf_transformation,[],[f28]) ).
fof(f47,plain,
! [X2,X0,X1,X4] :
( ~ minsol_model_ub(X0,X1,X2)
| ~ model_ub(X0,X1,X4)
| lesseq(X2,X4) ),
inference(cnf_transformation,[],[f32]) ).
fof(f48,plain,
! [X2,X0,X1] :
( ~ minsol_model_ub(X0,X1,X2)
| model_ub(X0,X1,X2) ),
inference(cnf_transformation,[],[f32]) ).
fof(f49,plain,
! [X2,X0,X1] :
( model_ub(X0,X1,sK4(X0,X1,X2))
| ~ model_ub(X0,X1,X2)
| minsol_model_ub(X0,X1,X2) ),
inference(cnf_transformation,[],[f32]) ).
fof(f50,plain,
! [X2,X0,X1] :
( ~ lesseq(X2,sK4(X0,X1,X2))
| ~ model_ub(X0,X1,X2)
| minsol_model_ub(X0,X1,X2) ),
inference(cnf_transformation,[],[f32]) ).
fof(f51,plain,
! [X2,X0,X1] :
( lesseq(summation(sK5(X0,X1,X2)),X2)
| ~ model_ub(X0,X1,X2) ),
inference(cnf_transformation,[],[f35]) ).
fof(f52,plain,
! [X2,X0,X1] :
( ub(X0,X1,sK5(X0,X1,X2))
| ~ model_ub(X0,X1,X2) ),
inference(cnf_transformation,[],[f35]) ).
fof(f53,plain,
! [X2,X3,X0,X1] :
( model_ub(X0,X1,X2)
| ~ ub(X0,X1,X3)
| ~ lesseq(summation(X3),X2) ),
inference(cnf_transformation,[],[f35]) ).
fof(f54,plain,
! [X2,X0,X1] :
( lesseq(summation(max(X0,X1)),X2)
| ~ model_max(X0,X1,X2) ),
inference(cnf_transformation,[],[f36]) ).
fof(f55,plain,
! [X2,X0,X1] :
( ~ lesseq(summation(max(X0,X1)),X2)
| model_max(X0,X1,X2) ),
inference(cnf_transformation,[],[f36]) ).
fof(f56,plain,
! [X2,X0,X1] :
( ~ ub(X0,X1,X2)
| lesseq(X1,X2) ),
inference(cnf_transformation,[],[f38]) ).
fof(f57,plain,
! [X2,X0,X1] :
( ~ ub(X0,X1,X2)
| lesseq(X0,X2) ),
inference(cnf_transformation,[],[f38]) ).
fof(f58,plain,
! [X2,X0,X1] :
( ub(X0,X1,X2)
| ~ lesseq(X0,X2)
| ~ lesseq(X1,X2) ),
inference(cnf_transformation,[],[f38]) ).
fof(f59,plain,
! [X0,X1] :
( max(X0,X1) = X1
| ~ lesseq(X0,X1) ),
inference(cnf_transformation,[],[f8]) ).
fof(f60,plain,
! [X0,X1] :
( max(X0,X1) = X0
| ~ lesseq(X1,X0) ),
inference(cnf_transformation,[],[f7]) ).
fof(f61,plain,
! [X0,X1] :
( lesseq(summation(X0),summation(X1))
| ~ lesseq(X0,X1) ),
inference(cnf_transformation,[],[f39]) ).
fof(f62,plain,
! [X0,X1] :
( ~ lesseq(summation(X0),summation(X1))
| lesseq(X0,X1) ),
inference(cnf_transformation,[],[f39]) ).
fof(f65,plain,
! [X0,X1] :
( lesseq(X1,X0)
| lesseq(X0,X1) ),
inference(cnf_transformation,[],[f4]) ).
fof(f66,plain,
! [X0,X1] :
( ~ lesseq(X1,X0)
| ~ lesseq(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f20]) ).
fof(f67,plain,
! [X2,X0,X1] :
( lesseq(X0,X2)
| ~ lesseq(X0,X1)
| ~ lesseq(X1,X2) ),
inference(cnf_transformation,[],[f22]) ).
fof(f68,plain,
! [X0] : lesseq(X0,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f70,definition,
( spl6_1
<=> minsol_model_ub(sK0,sK1,sK2) ),
introduced(definition,[new_symbols(definition,[spl6_1])],[avatar_definition]) ).
fof(f71,plain,
( ~ minsol_model_ub(sK0,sK1,sK2)
| spl6_1 ),
inference(avatar_component_clause,[],[f70]) ).
fof(f72,plain,
( minsol_model_ub(sK0,sK1,sK2)
| ~ spl6_1 ),
inference(avatar_component_clause,[],[f70]) ).
fof(f74,definition,
( spl6_2
<=> minsol_model_max(sK0,sK1,sK2) ),
introduced(definition,[new_symbols(definition,[spl6_2])],[avatar_definition]) ).
fof(f75,plain,
( ~ minsol_model_max(sK0,sK1,sK2)
| spl6_2 ),
inference(avatar_component_clause,[],[f74]) ).
fof(f76,plain,
( minsol_model_max(sK0,sK1,sK2)
| ~ spl6_2 ),
inference(avatar_component_clause,[],[f74]) ).
fof(f77,plain,
( spl6_1
| spl6_2 ),
inference(avatar_split_clause,[],[f41,f74,f70]) ).
fof(f78,plain,
( ~ spl6_1
| ~ spl6_2 ),
inference(avatar_split_clause,[],[f42,f74,f70]) ).
fof(f79,plain,
( model_max(sK0,sK1,sK2)
| ~ spl6_2 ),
inference(resolution,[],[f44,f76]) ).
fof(f80,plain,
( ! [X0] :
( ~ model_max(sK0,sK1,X0)
| lesseq(sK2,X0) )
| ~ spl6_2 ),
inference(resolution,[],[f43,f76]) ).
fof(f83,plain,
! [X2,X0,X1] :
( ~ lesseq(X0,summation(sK5(X1,X2,X0)))
| summation(sK5(X1,X2,X0)) = X0
| ~ model_ub(X1,X2,X0) ),
inference(resolution,[],[f66,f51]) ).
fof(f85,plain,
! [X2,X3,X0,X1] :
( ~ lesseq(X1,sK4(X2,X3,X0))
| ~ lesseq(X0,X1)
| ~ model_ub(X2,X3,X0)
| minsol_model_ub(X2,X3,X0) ),
inference(resolution,[],[f67,f50]) ).
fof(f86,plain,
! [X2,X3,X0,X1] :
( ~ lesseq(X1,sK3(X2,X3,X0))
| ~ lesseq(X0,X1)
| ~ model_max(X2,X3,X0)
| minsol_model_max(X2,X3,X0) ),
inference(resolution,[],[f67,f46]) ).
fof(f88,plain,
! [X2,X3,X0,X1] :
( ~ lesseq(summation(max(X0,X1)),X2)
| ~ lesseq(X2,X3)
| model_max(X0,X1,X3) ),
inference(resolution,[],[f67,f55]) ).
fof(f96,plain,
! [X2,X0,X1] :
( ~ lesseq(X2,summation(max(X0,X1)))
| ~ model_max(X0,X1,X2)
| summation(max(X0,X1)) = X2 ),
inference(resolution,[],[f54,f66]) ).
fof(f97,plain,
! [X2,X0,X1] :
( model_max(X0,X1,summation(X2))
| ~ lesseq(max(X0,X1),X2) ),
inference(resolution,[],[f61,f55]) ).
fof(f100,plain,
! [X2,X0,X1] :
( model_max(X0,X1,X2)
| ~ lesseq(summation(X0),X2)
| ~ lesseq(X1,X0) ),
inference(superposition,[],[f55,f60]) ).
fof(f103,plain,
! [X2,X0,X1] :
( ~ model_max(X1,X0,X2)
| lesseq(summation(X0),X2)
| ~ lesseq(X1,X0) ),
inference(superposition,[],[f54,f59]) ).
fof(f104,plain,
! [X2,X0,X1] :
( model_max(X1,X0,X2)
| ~ lesseq(summation(X0),X2)
| ~ lesseq(X1,X0) ),
inference(superposition,[],[f55,f59]) ).
fof(f106,plain,
! [X2,X0,X1] :
( lesseq(X0,sK5(X1,X0,X2))
| ~ model_ub(X1,X0,X2) ),
inference(resolution,[],[f56,f52]) ).
fof(f108,plain,
! [X2,X0,X1] :
( lesseq(X0,sK5(X0,X1,X2))
| ~ model_ub(X0,X1,X2) ),
inference(resolution,[],[f57,f52]) ).
fof(f112,plain,
! [X0,X1] : model_max(X0,X1,summation(max(X0,X1))),
inference(resolution,[],[f68,f55]) ).
fof(f114,plain,
! [X2,X0,X1] :
( lesseq(sK5(X0,X1,summation(X2)),X2)
| ~ model_ub(X0,X1,summation(X2)) ),
inference(resolution,[],[f62,f51]) ).
fof(f115,plain,
! [X2,X0,X1] :
( ~ model_max(X0,X1,summation(X2))
| lesseq(max(X0,X1),X2) ),
inference(resolution,[],[f62,f54]) ).
fof(f116,plain,
! [X0,X1] :
( lesseq(summation(X1),summation(X0))
| lesseq(X0,X1) ),
inference(resolution,[],[f62,f65]) ).
fof(f117,plain,
! [X2,X0,X1] :
( ~ lesseq(summation(X0),X2)
| lesseq(X0,X1)
| ~ lesseq(X2,summation(X1)) ),
inference(resolution,[],[f62,f67]) ).
fof(f119,plain,
( ! [X0] :
( ~ lesseq(summation(sK0),X0)
| ~ lesseq(sK1,sK0)
| lesseq(sK2,X0) )
| ~ spl6_2 ),
inference(resolution,[],[f100,f80]) ).
fof(f121,definition,
( spl6_3
<=> lesseq(sK1,sK0) ),
introduced(definition,[new_symbols(definition,[spl6_3])],[avatar_definition]) ).
fof(f122,plain,
( lesseq(sK1,sK0)
| ~ spl6_3 ),
inference(avatar_component_clause,[],[f121]) ).
fof(f123,plain,
( ~ lesseq(sK1,sK0)
| spl6_3 ),
inference(avatar_component_clause,[],[f121]) ).
fof(f125,definition,
( spl6_4
<=> ! [X0] :
( ~ lesseq(summation(sK0),X0)
| lesseq(sK2,X0) ) ),
introduced(definition,[new_symbols(definition,[spl6_4])],[avatar_definition]) ).
fof(f126,plain,
( ! [X0] :
( ~ lesseq(summation(sK0),X0)
| lesseq(sK2,X0) )
| ~ spl6_4 ),
inference(avatar_component_clause,[],[f125]) ).
fof(f127,plain,
( ~ spl6_3
| spl6_4
| ~ spl6_2 ),
inference(avatar_split_clause,[],[f119,f74,f125,f121]) ).
fof(f128,plain,
( lesseq(sK0,sK1)
| spl6_3 ),
inference(resolution,[],[f123,f65]) ).
fof(f131,plain,
( ! [X0] :
( ~ lesseq(summation(sK1),X0)
| ~ lesseq(sK0,sK1)
| lesseq(sK2,X0) )
| ~ spl6_2 ),
inference(resolution,[],[f104,f80]) ).
fof(f132,plain,
( ! [X0] :
( ~ lesseq(summation(sK1),X0)
| lesseq(sK2,X0) )
| ~ spl6_2
| spl6_3 ),
inference(forward_subsumption_resolution,[],[f131,f128]) ).
fof(f136,plain,
( lesseq(sK2,summation(sK1))
| ~ spl6_2
| spl6_3 ),
inference(resolution,[],[f132,f68]) ).
fof(f137,plain,
( ~ lesseq(summation(sK1),sK2)
| sK2 = summation(sK1)
| ~ spl6_2
| spl6_3 ),
inference(resolution,[],[f136,f66]) ).
fof(f139,definition,
( spl6_5
<=> sK2 = summation(sK1) ),
introduced(definition,[new_symbols(definition,[spl6_5])],[avatar_definition]) ).
fof(f140,plain,
( sK2 != summation(sK1)
| spl6_5 ),
inference(avatar_component_clause,[],[f139]) ).
fof(f141,plain,
( sK2 = summation(sK1)
| ~ spl6_5 ),
inference(avatar_component_clause,[],[f139]) ).
fof(f143,definition,
( spl6_6
<=> lesseq(summation(sK1),sK2) ),
introduced(definition,[new_symbols(definition,[spl6_6])],[avatar_definition]) ).
fof(f144,plain,
( lesseq(summation(sK1),sK2)
| ~ spl6_6 ),
inference(avatar_component_clause,[],[f143]) ).
fof(f145,plain,
( ~ lesseq(summation(sK1),sK2)
| spl6_6 ),
inference(avatar_component_clause,[],[f143]) ).
fof(f146,plain,
( spl6_5
| ~ spl6_6
| ~ spl6_2
| spl6_3 ),
inference(avatar_split_clause,[],[f137,f121,f74,f143,f139]) ).
fof(f155,plain,
! [X2,X3,X0,X1,X4] :
( ~ model_max(X1,X2,sK3(X3,X4,X0))
| ~ model_max(X3,X4,X0)
| minsol_model_max(X3,X4,X0)
| ~ lesseq(X0,summation(max(X1,X2))) ),
inference(resolution,[],[f86,f54]) ).
fof(f178,plain,
! [X2,X3,X0,X1] :
( model_max(X2,X3,X1)
| ~ lesseq(X0,X1)
| ~ model_max(X2,X3,X0) ),
inference(resolution,[],[f88,f54]) ).
fof(f188,plain,
! [X2,X0,X1] :
( ~ lesseq(sK5(X0,X1,X2),X1)
| ~ model_ub(X0,X1,X2)
| sK5(X0,X1,X2) = X1 ),
inference(resolution,[],[f106,f66]) ).
fof(f192,plain,
! [X2,X0,X1] :
( ~ lesseq(sK5(X0,X1,X2),X0)
| ~ model_ub(X0,X1,X2)
| sK5(X0,X1,X2) = X0 ),
inference(resolution,[],[f108,f66]) ).
fof(f240,plain,
( lesseq(summation(sK1),sK2)
| ~ lesseq(sK0,sK1)
| ~ spl6_2 ),
inference(resolution,[],[f103,f79]) ).
fof(f243,plain,
( ~ lesseq(sK0,sK1)
| ~ spl6_2
| spl6_6 ),
inference(forward_subsumption_resolution,[],[f240,f145]) ).
fof(f244,plain,
( $false
| ~ spl6_2
| spl6_3
| spl6_6 ),
inference(forward_subsumption_resolution,[],[f243,f128]) ).
fof(f245,plain,
( ~ spl6_2
| spl6_3
| spl6_6 ),
inference(avatar_contradiction_clause,[],[f244]) ).
fof(f246,plain,
( ! [X0] :
( ~ model_ub(sK0,sK1,X0)
| lesseq(sK2,X0) )
| ~ spl6_1 ),
inference(resolution,[],[f72,f47]) ).
fof(f247,plain,
( model_ub(sK0,sK1,sK2)
| ~ spl6_1 ),
inference(resolution,[],[f72,f48]) ).
fof(f250,plain,
( ! [X0,X1] :
( ~ ub(sK0,sK1,X1)
| lesseq(sK2,X0)
| ~ lesseq(summation(X1),X0) )
| ~ spl6_1 ),
inference(resolution,[],[f246,f53]) ).
fof(f257,plain,
( ! [X0,X1] :
( ~ lesseq(summation(sK5(sK0,sK1,X1)),X0)
| lesseq(sK2,X0)
| ~ model_ub(sK0,sK1,X1) )
| ~ spl6_1 ),
inference(resolution,[],[f250,f52]) ).
fof(f271,plain,
( ! [X0] :
( lesseq(sK2,summation(sK5(sK0,sK1,X0)))
| ~ model_ub(sK0,sK1,X0) )
| ~ spl6_1 ),
inference(resolution,[],[f257,f68]) ).
fof(f278,plain,
( ~ model_ub(sK0,sK1,sK2)
| sK2 = summation(sK5(sK0,sK1,sK2))
| ~ model_ub(sK0,sK1,sK2)
| ~ spl6_1 ),
inference(resolution,[],[f271,f83]) ).
fof(f280,plain,
( ~ model_ub(sK0,sK1,sK2)
| sK2 = summation(sK5(sK0,sK1,sK2))
| ~ spl6_1 ),
inference(duplicate_literal_removal,[],[f278]) ).
fof(f281,plain,
( sK2 = summation(sK5(sK0,sK1,sK2))
| ~ spl6_1 ),
inference(forward_subsumption_resolution,[],[f280,f247]) ).
fof(f287,plain,
( ! [X0] :
( lesseq(sK5(sK0,sK1,sK2),X0)
| ~ lesseq(sK2,summation(X0)) )
| ~ spl6_1 ),
inference(superposition,[],[f62,f281]) ).
fof(f300,plain,
( ~ lesseq(sK2,summation(sK1))
| ~ model_ub(sK0,sK1,sK2)
| sK1 = sK5(sK0,sK1,sK2)
| ~ spl6_1 ),
inference(resolution,[],[f287,f188]) ).
fof(f309,plain,
( ~ lesseq(sK2,summation(sK1))
| sK1 = sK5(sK0,sK1,sK2)
| ~ spl6_1 ),
inference(forward_subsumption_resolution,[],[f300,f247]) ).
fof(f320,definition,
( spl6_9
<=> sK1 = sK5(sK0,sK1,sK2) ),
introduced(definition,[new_symbols(definition,[spl6_9])],[avatar_definition]) ).
fof(f322,plain,
( sK1 = sK5(sK0,sK1,sK2)
| ~ spl6_9 ),
inference(avatar_component_clause,[],[f320]) ).
fof(f324,definition,
( spl6_10
<=> lesseq(sK2,summation(sK1)) ),
introduced(definition,[new_symbols(definition,[spl6_10])],[avatar_definition]) ).
fof(f325,plain,
( lesseq(sK2,summation(sK1))
| ~ spl6_10 ),
inference(avatar_component_clause,[],[f324]) ).
fof(f326,plain,
( ~ lesseq(sK2,summation(sK1))
| spl6_10 ),
inference(avatar_component_clause,[],[f324]) ).
fof(f327,plain,
( spl6_9
| ~ spl6_10
| ~ spl6_1 ),
inference(avatar_split_clause,[],[f309,f70,f324,f320]) ).
fof(f373,plain,
( ! [X0] :
( ~ model_max(sK0,sK1,X0)
| lesseq(sK2,X0) )
| ~ spl6_2 ),
inference(resolution,[],[f76,f43]) ).
fof(f381,plain,
( ! [X0] :
( ~ lesseq(max(sK0,sK1),X0)
| lesseq(sK2,summation(X0)) )
| ~ spl6_2 ),
inference(resolution,[],[f373,f97]) ).
fof(f390,plain,
( lesseq(sK2,summation(max(sK0,sK1)))
| ~ spl6_2 ),
inference(resolution,[],[f381,f68]) ).
fof(f415,plain,
! [X2,X3,X0,X1] :
( lesseq(max(X0,X1),X2)
| ~ lesseq(X3,summation(X2))
| ~ model_max(X0,X1,X3) ),
inference(resolution,[],[f115,f178]) ).
fof(f434,plain,
( ~ lesseq(summation(max(sK0,sK1)),sK2)
| sK2 = summation(max(sK0,sK1))
| ~ spl6_2 ),
inference(resolution,[],[f390,f66]) ).
fof(f439,definition,
( spl6_14
<=> sK2 = summation(max(sK0,sK1)) ),
introduced(definition,[new_symbols(definition,[spl6_14])],[avatar_definition]) ).
fof(f441,plain,
( sK2 = summation(max(sK0,sK1))
| ~ spl6_14 ),
inference(avatar_component_clause,[],[f439]) ).
fof(f443,definition,
( spl6_15
<=> lesseq(summation(max(sK0,sK1)),sK2) ),
introduced(definition,[new_symbols(definition,[spl6_15])],[avatar_definition]) ).
fof(f444,plain,
( lesseq(summation(max(sK0,sK1)),sK2)
| ~ spl6_15 ),
inference(avatar_component_clause,[],[f443]) ).
fof(f445,plain,
( ~ lesseq(summation(max(sK0,sK1)),sK2)
| spl6_15 ),
inference(avatar_component_clause,[],[f443]) ).
fof(f446,plain,
( spl6_14
| ~ spl6_15
| ~ spl6_2 ),
inference(avatar_split_clause,[],[f434,f74,f443,f439]) ).
fof(f448,plain,
( ~ model_max(sK0,sK1,sK2)
| spl6_15 ),
inference(resolution,[],[f445,f54]) ).
fof(f451,plain,
( ~ lesseq(summation(sK1),sK2)
| ~ lesseq(sK0,sK1)
| spl6_15 ),
inference(superposition,[],[f445,f59]) ).
fof(f454,plain,
( $false
| ~ spl6_2
| spl6_15 ),
inference(forward_subsumption_resolution,[],[f448,f79]) ).
fof(f455,plain,
( ~ spl6_2
| spl6_15 ),
inference(avatar_contradiction_clause,[],[f454]) ).
fof(f460,plain,
( ~ lesseq(summation(sK1),sK2)
| spl6_3
| spl6_15 ),
inference(forward_subsumption_resolution,[],[f451,f128]) ).
fof(f463,plain,
( ~ lesseq(sK2,sK2)
| spl6_3
| ~ spl6_5
| spl6_15 ),
inference(forward_demodulation,[],[f460,f141]) ).
fof(f464,plain,
( $false
| spl6_3
| ~ spl6_5
| spl6_15 ),
inference(forward_subsumption_resolution,[],[f463,f68]) ).
fof(f465,plain,
( spl6_3
| ~ spl6_5
| spl6_15 ),
inference(avatar_contradiction_clause,[],[f464]) ).
fof(f472,plain,
( ! [X0] :
( ~ model_ub(sK0,sK1,X0)
| lesseq(sK2,X0) )
| ~ spl6_1 ),
inference(resolution,[],[f72,f47]) ).
fof(f487,plain,
( ! [X0,X1] :
( ~ ub(sK0,sK1,X1)
| lesseq(sK2,X0)
| ~ lesseq(summation(X1),X0) )
| ~ spl6_1 ),
inference(resolution,[],[f472,f53]) ).
fof(f508,plain,
( ! [X0,X1] :
( ~ lesseq(summation(sK5(sK0,sK1,X1)),X0)
| lesseq(sK2,X0)
| ~ model_ub(sK0,sK1,X1) )
| ~ spl6_1 ),
inference(resolution,[],[f487,f52]) ).
fof(f511,plain,
( model_max(sK0,sK1,sK2)
| ~ spl6_15 ),
inference(resolution,[],[f444,f55]) ).
fof(f512,plain,
( ~ lesseq(sK2,summation(max(sK0,sK1)))
| sK2 = summation(max(sK0,sK1))
| ~ spl6_15 ),
inference(resolution,[],[f444,f66]) ).
fof(f518,definition,
( spl6_18
<=> lesseq(sK2,summation(max(sK0,sK1))) ),
introduced(definition,[new_symbols(definition,[spl6_18])],[avatar_definition]) ).
fof(f520,plain,
( ~ lesseq(sK2,summation(max(sK0,sK1)))
| spl6_18 ),
inference(avatar_component_clause,[],[f518]) ).
fof(f521,plain,
( spl6_14
| ~ spl6_18
| ~ spl6_15 ),
inference(avatar_split_clause,[],[f512,f443,f518,f439]) ).
fof(f543,plain,
( ! [X0] :
( lesseq(sK2,summation(sK5(sK0,sK1,X0)))
| ~ model_ub(sK0,sK1,X0) )
| ~ spl6_1 ),
inference(resolution,[],[f508,f68]) ).
fof(f554,plain,
( ~ model_ub(sK0,sK1,sK2)
| sK2 = summation(sK5(sK0,sK1,sK2))
| ~ model_ub(sK0,sK1,sK2)
| ~ spl6_1 ),
inference(resolution,[],[f543,f83]) ).
fof(f557,plain,
( ~ model_ub(sK0,sK1,sK2)
| sK2 = summation(sK5(sK0,sK1,sK2))
| ~ spl6_1 ),
inference(duplicate_literal_removal,[],[f554]) ).
fof(f559,plain,
( sK2 = summation(sK5(sK0,sK1,sK2))
| ~ spl6_1 ),
inference(forward_subsumption_resolution,[],[f557,f247]) ).
fof(f561,plain,
( sK2 = summation(sK1)
| ~ spl6_1
| ~ spl6_9 ),
inference(forward_demodulation,[],[f559,f322]) ).
fof(f566,plain,
( ~ lesseq(sK2,summation(sK1))
| ~ lesseq(sK0,sK1)
| spl6_18 ),
inference(superposition,[],[f520,f59]) ).
fof(f575,definition,
( spl6_19
<=> model_ub(sK0,sK1,sK2) ),
introduced(definition,[new_symbols(definition,[spl6_19])],[avatar_definition]) ).
fof(f576,plain,
( model_ub(sK0,sK1,sK2)
| ~ spl6_19 ),
inference(avatar_component_clause,[],[f575]) ).
fof(f577,plain,
( ~ model_ub(sK0,sK1,sK2)
| spl6_19 ),
inference(avatar_component_clause,[],[f575]) ).
fof(f579,definition,
( spl6_20
<=> lesseq(sK0,sK1) ),
introduced(definition,[new_symbols(definition,[spl6_20])],[avatar_definition]) ).
fof(f580,plain,
( ~ lesseq(sK0,sK1)
| spl6_20 ),
inference(avatar_component_clause,[],[f579]) ).
fof(f581,plain,
( lesseq(sK0,sK1)
| ~ spl6_20 ),
inference(avatar_component_clause,[],[f579]) ).
fof(f587,definition,
( spl6_21
<=> ub(sK0,sK1,sK1) ),
introduced(definition,[new_symbols(definition,[spl6_21])],[avatar_definition]) ).
fof(f588,plain,
( ~ ub(sK0,sK1,sK1)
| spl6_21 ),
inference(avatar_component_clause,[],[f587]) ).
fof(f589,plain,
( ub(sK0,sK1,sK1)
| ~ spl6_21 ),
inference(avatar_component_clause,[],[f587]) ).
fof(f604,plain,
( ~ lesseq(sK0,sK1)
| ~ spl6_10
| spl6_18 ),
inference(forward_subsumption_resolution,[],[f566,f325]) ).
fof(f606,plain,
( ~ spl6_20
| ~ spl6_10
| spl6_18 ),
inference(avatar_split_clause,[],[f604,f518,f324,f579]) ).
fof(f610,plain,
( ! [X0] :
( lesseq(sK2,summation(X0))
| ~ lesseq(sK0,X0) )
| ~ spl6_4 ),
inference(resolution,[],[f126,f61]) ).
fof(f619,plain,
( $false
| ~ spl6_1
| spl6_19 ),
inference(forward_subsumption_resolution,[],[f247,f577]) ).
fof(f620,plain,
( ~ spl6_1
| spl6_19 ),
inference(avatar_contradiction_clause,[],[f619]) ).
fof(f621,plain,
( $false
| ~ spl6_1
| spl6_5
| ~ spl6_9 ),
inference(forward_subsumption_resolution,[],[f561,f140]) ).
fof(f622,plain,
( ~ spl6_1
| spl6_5
| ~ spl6_9 ),
inference(avatar_contradiction_clause,[],[f621]) ).
fof(f626,plain,
( ! [X0] :
( ~ model_ub(sK0,sK1,X0)
| lesseq(sK2,X0) )
| ~ spl6_1 ),
inference(resolution,[],[f72,f47]) ).
fof(f630,plain,
( ! [X0,X1] :
( ~ ub(sK0,sK1,X1)
| lesseq(sK2,X0)
| ~ lesseq(summation(X1),X0) )
| ~ spl6_1 ),
inference(resolution,[],[f626,f53]) ).
fof(f632,plain,
( sK2 = summation(sK0)
| ~ lesseq(sK1,sK0)
| ~ spl6_14 ),
inference(superposition,[],[f441,f60]) ).
fof(f649,plain,
( sK2 = summation(sK0)
| ~ spl6_3
| ~ spl6_14 ),
inference(forward_subsumption_resolution,[],[f632,f122]) ).
fof(f673,plain,
( ! [X0,X1] :
( ~ lesseq(summation(X1),X0)
| lesseq(sK2,X0)
| ~ lesseq(sK0,X1)
| ~ lesseq(sK1,X1) )
| ~ spl6_1 ),
inference(resolution,[],[f630,f58]) ).
fof(f681,plain,
( ! [X0] :
( lesseq(sK2,summation(X0))
| ~ lesseq(sK0,X0)
| ~ lesseq(sK1,X0) )
| ~ spl6_1 ),
inference(resolution,[],[f673,f68]) ).
fof(f692,plain,
( lesseq(sK1,sK0)
| spl6_20 ),
inference(resolution,[],[f580,f65]) ).
fof(f742,plain,
( ~ lesseq(sK0,max(sK0,sK1))
| ~ lesseq(sK1,max(sK0,sK1))
| ~ spl6_1
| spl6_18 ),
inference(resolution,[],[f681,f520]) ).
fof(f744,plain,
( ~ lesseq(sK0,sK1)
| ~ lesseq(sK1,sK1)
| ~ spl6_1
| spl6_10 ),
inference(resolution,[],[f681,f326]) ).
fof(f750,definition,
( spl6_25
<=> lesseq(sK1,max(sK0,sK1)) ),
introduced(definition,[new_symbols(definition,[spl6_25])],[avatar_definition]) ).
fof(f752,plain,
( ~ lesseq(sK1,max(sK0,sK1))
| spl6_25 ),
inference(avatar_component_clause,[],[f750]) ).
fof(f754,definition,
( spl6_26
<=> lesseq(sK0,max(sK0,sK1)) ),
introduced(definition,[new_symbols(definition,[spl6_26])],[avatar_definition]) ).
fof(f756,plain,
( ~ lesseq(sK0,max(sK0,sK1))
| spl6_26 ),
inference(avatar_component_clause,[],[f754]) ).
fof(f757,plain,
( ~ spl6_25
| ~ spl6_26
| ~ spl6_1
| spl6_18 ),
inference(avatar_split_clause,[],[f742,f518,f70,f754,f750]) ).
fof(f762,plain,
( $false
| spl6_3
| spl6_20 ),
inference(forward_subsumption_resolution,[],[f692,f123]) ).
fof(f763,plain,
( spl6_3
| spl6_20 ),
inference(avatar_contradiction_clause,[],[f762]) ).
fof(f764,plain,
( ~ lesseq(sK1,sK1)
| ~ spl6_1
| spl6_10
| ~ spl6_20 ),
inference(forward_subsumption_resolution,[],[f744,f581]) ).
fof(f765,plain,
( $false
| ~ spl6_1
| spl6_10
| ~ spl6_20 ),
inference(forward_subsumption_resolution,[],[f764,f68]) ).
fof(f766,plain,
( ~ spl6_1
| spl6_10
| ~ spl6_20 ),
inference(avatar_contradiction_clause,[],[f765]) ).
fof(f812,plain,
( ! [X0] :
( lesseq(X0,max(sK0,sK1))
| ~ lesseq(summation(X0),sK2) )
| ~ spl6_14 ),
inference(superposition,[],[f62,f441]) ).
fof(f815,plain,
( ! [X0] :
( lesseq(max(sK0,sK1),X0)
| lesseq(summation(X0),sK2) )
| ~ spl6_14 ),
inference(superposition,[],[f116,f441]) ).
fof(f845,definition,
( spl6_27
<=> sK0 = max(sK0,sK1) ),
introduced(definition,[new_symbols(definition,[spl6_27])],[avatar_definition]) ).
fof(f846,plain,
( sK0 != max(sK0,sK1)
| spl6_27 ),
inference(avatar_component_clause,[],[f845]) ).
fof(f847,plain,
( sK0 = max(sK0,sK1)
| ~ spl6_27 ),
inference(avatar_component_clause,[],[f845]) ).
fof(f849,definition,
( spl6_28
<=> lesseq(max(sK0,sK1),sK0) ),
introduced(definition,[new_symbols(definition,[spl6_28])],[avatar_definition]) ).
fof(f850,plain,
( lesseq(max(sK0,sK1),sK0)
| ~ spl6_28 ),
inference(avatar_component_clause,[],[f849]) ).
fof(f851,plain,
( ~ lesseq(max(sK0,sK1),sK0)
| spl6_28 ),
inference(avatar_component_clause,[],[f849]) ).
fof(f960,plain,
! [X2,X3,X0,X1] :
( lesseq(sK5(X0,X1,X2),X3)
| ~ lesseq(X2,summation(X3))
| ~ model_ub(X0,X1,X2) ),
inference(resolution,[],[f117,f51]) ).
fof(f995,plain,
! [X2,X0,X1] :
( ~ lesseq(X0,summation(X1))
| ~ model_ub(X2,X1,X0)
| ~ model_ub(X2,X1,X0)
| sK5(X2,X1,X0) = X1 ),
inference(resolution,[],[f960,f188]) ).
fof(f996,plain,
! [X2,X0,X1] :
( ~ lesseq(X0,summation(X1))
| ~ model_ub(X1,X2,X0)
| ~ model_ub(X1,X2,X0)
| sK5(X1,X2,X0) = X1 ),
inference(resolution,[],[f960,f192]) ).
fof(f1006,plain,
! [X2,X0,X1] :
( sK5(X1,X2,X0) = X1
| ~ model_ub(X1,X2,X0)
| ~ lesseq(X0,summation(X1)) ),
inference(duplicate_literal_removal,[],[f996]) ).
fof(f1007,plain,
! [X2,X0,X1] :
( sK5(X2,X1,X0) = X1
| ~ model_ub(X2,X1,X0)
| ~ lesseq(X0,summation(X1)) ),
inference(duplicate_literal_removal,[],[f995]) ).
fof(f1029,plain,
( ! [X0] :
( ~ model_max(sK0,sK1,X0)
| ~ lesseq(X0,summation(sK0)) )
| spl6_28 ),
inference(resolution,[],[f415,f851]) ).
fof(f1051,plain,
! [X0,X1] :
( ~ model_ub(X0,X1,summation(X0))
| ~ model_ub(X0,X1,summation(X0))
| sK5(X0,X1,summation(X0)) = X0 ),
inference(resolution,[],[f114,f192]) ).
fof(f1058,plain,
! [X0,X1] :
( sK5(X0,X1,summation(X0)) = X0
| ~ model_ub(X0,X1,summation(X0)) ),
inference(duplicate_literal_removal,[],[f1051]) ).
fof(f1084,plain,
! [X0,X1] :
( lesseq(summation(X0),summation(max(X1,X0)))
| ~ lesseq(X1,X0) ),
inference(resolution,[],[f112,f103]) ).
fof(f1087,plain,
! [X0,X1] :
( model_max(X1,X0,summation(X0))
| ~ lesseq(X1,X0) ),
inference(superposition,[],[f112,f59]) ).
fof(f1115,plain,
! [X2,X0,X1] :
( lesseq(summation(X0),X2)
| ~ model_ub(X0,X1,X2)
| ~ model_ub(X0,X1,X2)
| ~ lesseq(X2,summation(X0)) ),
inference(superposition,[],[f51,f1006]) ).
fof(f1133,plain,
! [X2,X0,X1] :
( lesseq(summation(X0),X2)
| ~ model_ub(X0,X1,X2)
| ~ lesseq(X2,summation(X0)) ),
inference(duplicate_literal_removal,[],[f1115]) ).
fof(f1136,plain,
! [X2,X0,X1] :
( ~ model_ub(X0,X1,X2)
| lesseq(summation(X0),X2) ),
inference(forward_subsumption_resolution,[],[f1133,f65]) ).
fof(f1137,plain,
! [X2,X0,X1] :
( lesseq(summation(X0),sK4(X0,X1,X2))
| ~ model_ub(X0,X1,X2)
| minsol_model_ub(X0,X1,X2) ),
inference(resolution,[],[f1136,f49]) ).
fof(f1139,plain,
( lesseq(summation(sK0),sK2)
| ~ spl6_19 ),
inference(resolution,[],[f1136,f576]) ).
fof(f1158,plain,
! [X2,X0,X1] :
( ~ model_ub(X0,X1,X2)
| minsol_model_ub(X0,X1,X2)
| ~ lesseq(X2,summation(X0))
| ~ model_ub(X0,X1,X2)
| minsol_model_ub(X0,X1,X2) ),
inference(resolution,[],[f1137,f85]) ).
fof(f1162,plain,
! [X2,X0,X1] :
( minsol_model_ub(X0,X1,X2)
| ~ model_ub(X0,X1,X2)
| ~ lesseq(X2,summation(X0)) ),
inference(duplicate_literal_removal,[],[f1158]) ).
fof(f1169,plain,
( ~ model_ub(sK0,sK1,sK2)
| ~ lesseq(sK2,summation(sK0))
| spl6_1 ),
inference(resolution,[],[f1162,f71]) ).
fof(f1178,plain,
! [X2,X0,X1] :
( lesseq(summation(X0),X2)
| ~ model_ub(X1,X0,X2)
| ~ model_ub(X1,X0,X2)
| ~ lesseq(X2,summation(X0)) ),
inference(superposition,[],[f51,f1007]) ).
fof(f1197,plain,
! [X2,X0,X1] :
( lesseq(summation(X0),X2)
| ~ model_ub(X1,X0,X2)
| ~ lesseq(X2,summation(X0)) ),
inference(duplicate_literal_removal,[],[f1178]) ).
fof(f1201,plain,
! [X2,X0,X1] :
( ~ model_ub(X1,X0,X2)
| lesseq(summation(X0),X2) ),
inference(forward_subsumption_resolution,[],[f1197,f65]) ).
fof(f1202,plain,
! [X2,X0,X1] :
( lesseq(summation(X0),sK4(X1,X0,X2))
| ~ model_ub(X1,X0,X2)
| minsol_model_ub(X1,X0,X2) ),
inference(resolution,[],[f1201,f49]) ).
fof(f1223,plain,
! [X2,X0,X1] :
( ~ model_ub(X0,X1,X2)
| minsol_model_ub(X0,X1,X2)
| ~ lesseq(X2,summation(X1))
| ~ model_ub(X0,X1,X2)
| minsol_model_ub(X0,X1,X2) ),
inference(resolution,[],[f1202,f85]) ).
fof(f1227,plain,
! [X2,X0,X1] :
( minsol_model_ub(X0,X1,X2)
| ~ model_ub(X0,X1,X2)
| ~ lesseq(X2,summation(X1)) ),
inference(duplicate_literal_removal,[],[f1223]) ).
fof(f1234,plain,
( ~ model_ub(sK0,sK1,sK2)
| ~ lesseq(sK2,summation(sK1))
| spl6_1 ),
inference(resolution,[],[f1227,f71]) ).
fof(f1235,plain,
( ~ lesseq(sK2,summation(sK1))
| spl6_1
| ~ spl6_19 ),
inference(forward_subsumption_resolution,[],[f1234,f576]) ).
fof(f1236,plain,
( ~ lesseq(sK2,sK2)
| spl6_1
| ~ spl6_5
| ~ spl6_19 ),
inference(forward_demodulation,[],[f1235,f141]) ).
fof(f1237,plain,
( $false
| spl6_1
| ~ spl6_5
| ~ spl6_19 ),
inference(forward_subsumption_resolution,[],[f1236,f68]) ).
fof(f1238,plain,
( spl6_1
| ~ spl6_5
| ~ spl6_19 ),
inference(avatar_contradiction_clause,[],[f1237]) ).
fof(f1239,plain,
( ! [X0] :
( ~ ub(sK0,sK1,X0)
| ~ lesseq(summation(X0),sK2) )
| spl6_19 ),
inference(resolution,[],[f577,f53]) ).
fof(f1306,plain,
! [X2,X0,X1] :
( ~ model_max(X0,X1,X2)
| minsol_model_max(X0,X1,X2)
| ~ lesseq(X2,summation(max(X0,X1)))
| ~ model_max(X0,X1,X2)
| minsol_model_max(X0,X1,X2) ),
inference(resolution,[],[f155,f45]) ).
fof(f1313,plain,
! [X2,X0,X1] :
( ~ lesseq(X2,summation(max(X0,X1)))
| minsol_model_max(X0,X1,X2)
| ~ model_max(X0,X1,X2) ),
inference(duplicate_literal_removal,[],[f1306]) ).
fof(f1316,plain,
! [X0,X1] :
( minsol_model_max(X0,X1,summation(max(X0,X1)))
| ~ model_max(X0,X1,summation(max(X0,X1))) ),
inference(resolution,[],[f1313,f68]) ).
fof(f1338,plain,
! [X0,X1] : minsol_model_max(X0,X1,summation(max(X0,X1))),
inference(forward_subsumption_resolution,[],[f1316,f112]) ).
fof(f1692,plain,
! [X0,X1] :
( ub(X0,X1,X0)
| ~ model_ub(X0,X1,summation(X0))
| ~ model_ub(X0,X1,summation(X0)) ),
inference(superposition,[],[f52,f1058]) ).
fof(f1703,plain,
! [X0,X1] :
( ~ model_ub(X0,X1,summation(X0))
| ub(X0,X1,X0) ),
inference(duplicate_literal_removal,[],[f1692]) ).
fof(f1709,plain,
! [X2,X0,X1] :
( ~ lesseq(summation(X2),summation(X0))
| ~ ub(X0,X1,X2)
| ub(X0,X1,X0) ),
inference(resolution,[],[f1703,f53]) ).
fof(f1788,plain,
( ~ lesseq(sK2,summation(sK0))
| ~ spl6_15
| spl6_28 ),
inference(resolution,[],[f1029,f511]) ).
fof(f3649,plain,
( ! [X0] :
( lesseq(sK0,X0)
| lesseq(summation(X0),sK2)
| ~ lesseq(sK1,sK0) )
| ~ spl6_14 ),
inference(superposition,[],[f815,f60]) ).
fof(f3868,plain,
! [X0,X1] :
( ~ lesseq(X0,X1)
| ~ model_max(X0,X1,summation(X1))
| summation(X1) = summation(max(X0,X1)) ),
inference(resolution,[],[f1084,f96]) ).
fof(f3884,plain,
! [X0,X1] :
( summation(X1) = summation(max(X0,X1))
| ~ lesseq(X0,X1) ),
inference(forward_subsumption_resolution,[],[f3868,f1087]) ).
fof(f3935,plain,
( lesseq(summation(sK1),sK2)
| ~ lesseq(sK0,sK1)
| ~ spl6_15 ),
inference(superposition,[],[f444,f3884]) ).
fof(f3997,plain,
( ~ lesseq(summation(sK1),sK2)
| spl6_19
| ~ spl6_21 ),
inference(resolution,[],[f1239,f589]) ).
fof(f4001,plain,
( $false
| ~ spl6_6
| spl6_19
| ~ spl6_21 ),
inference(forward_subsumption_resolution,[],[f3997,f144]) ).
fof(f4002,plain,
( ~ spl6_6
| spl6_19
| ~ spl6_21 ),
inference(avatar_contradiction_clause,[],[f4001]) ).
fof(f4003,plain,
( ~ lesseq(sK0,sK1)
| ~ lesseq(sK1,sK1)
| spl6_21 ),
inference(resolution,[],[f588,f58]) ).
fof(f4012,plain,
( ~ lesseq(sK1,sK1)
| ~ spl6_20
| spl6_21 ),
inference(forward_subsumption_resolution,[],[f4003,f581]) ).
fof(f4016,plain,
( $false
| ~ spl6_20
| spl6_21 ),
inference(forward_subsumption_resolution,[],[f4012,f68]) ).
fof(f4017,plain,
( ~ spl6_20
| spl6_21 ),
inference(avatar_contradiction_clause,[],[f4016]) ).
fof(f4086,plain,
( ! [X0] :
( lesseq(summation(X0),sK2)
| lesseq(sK0,X0) )
| ~ spl6_3
| ~ spl6_14 ),
inference(forward_subsumption_resolution,[],[f3649,f122]) ).
fof(f4125,plain,
( ~ lesseq(sK1,sK0)
| spl6_25
| ~ spl6_27 ),
inference(forward_demodulation,[],[f752,f847]) ).
fof(f4391,plain,
( lesseq(summation(sK1),sK2)
| ~ spl6_3
| ~ spl6_14
| ~ spl6_15 ),
inference(forward_subsumption_resolution,[],[f3935,f4086]) ).
fof(f4398,definition,
( spl6_77
<=> ! [X0] :
( lesseq(sK1,X0)
| ~ lesseq(sK2,summation(X0)) ) ),
introduced(definition,[new_symbols(definition,[spl6_77])],[avatar_definition]) ).
fof(f4399,plain,
( ! [X0] :
( ~ lesseq(sK2,summation(X0))
| lesseq(sK1,X0) )
| ~ spl6_77 ),
inference(avatar_component_clause,[],[f4398]) ).
fof(f4440,plain,
( $false
| ~ spl6_3
| spl6_25
| ~ spl6_27 ),
inference(forward_subsumption_resolution,[],[f4125,f122]) ).
fof(f4441,plain,
( ~ spl6_3
| spl6_25
| ~ spl6_27 ),
inference(avatar_contradiction_clause,[],[f4440]) ).
fof(f4532,plain,
( $false
| ~ spl6_3
| spl6_6
| ~ spl6_14
| ~ spl6_15 ),
inference(forward_subsumption_resolution,[],[f4391,f145]) ).
fof(f4533,plain,
( ~ spl6_3
| spl6_6
| ~ spl6_14
| ~ spl6_15 ),
inference(avatar_contradiction_clause,[],[f4532]) ).
fof(f4587,plain,
( ~ lesseq(sK2,sK2)
| ~ spl6_3
| ~ spl6_14
| ~ spl6_15
| spl6_28 ),
inference(forward_demodulation,[],[f1788,f649]) ).
fof(f4606,plain,
( $false
| ~ spl6_3
| ~ spl6_14
| ~ spl6_15
| spl6_28 ),
inference(forward_subsumption_resolution,[],[f4587,f68]) ).
fof(f4607,plain,
( ~ spl6_3
| ~ spl6_14
| ~ spl6_15
| spl6_28 ),
inference(avatar_contradiction_clause,[],[f4606]) ).
fof(f4807,plain,
( sK0 != sK0
| ~ lesseq(sK1,sK0)
| spl6_27 ),
inference(superposition,[],[f846,f60]) ).
fof(f4808,plain,
( ~ lesseq(sK1,sK0)
| spl6_27 ),
inference(trivial_inequality_removal,[],[f4807]) ).
fof(f4809,plain,
( $false
| ~ spl6_3
| spl6_27 ),
inference(forward_subsumption_resolution,[],[f4808,f122]) ).
fof(f4810,plain,
( ~ spl6_3
| spl6_27 ),
inference(avatar_contradiction_clause,[],[f4809]) ).
fof(f4963,plain,
( ! [X0] :
( lesseq(sK1,X0)
| ~ lesseq(sK2,summation(X0)) )
| ~ spl6_6 ),
inference(resolution,[],[f144,f117]) ).
fof(f4966,plain,
( spl6_77
| ~ spl6_6 ),
inference(avatar_split_clause,[],[f4963,f143,f4398]) ).
fof(f4975,plain,
( ~ lesseq(sK0,sK0)
| ~ lesseq(sK1,sK0)
| spl6_26 ),
inference(superposition,[],[f756,f60]) ).
fof(f4977,plain,
( ~ lesseq(sK1,sK0)
| spl6_26 ),
inference(forward_subsumption_resolution,[],[f4975,f68]) ).
fof(f4986,plain,
( $false
| ~ spl6_3
| spl6_26 ),
inference(forward_subsumption_resolution,[],[f4977,f122]) ).
fof(f4987,plain,
( ~ spl6_3
| spl6_26 ),
inference(avatar_contradiction_clause,[],[f4986]) ).
fof(f4992,plain,
( ! [X0] :
( lesseq(sK1,X0)
| ~ lesseq(sK0,X0) )
| ~ spl6_4
| ~ spl6_77 ),
inference(resolution,[],[f4399,f610]) ).
fof(f6711,plain,
( minsol_model_max(sK0,sK1,sK2)
| ~ spl6_14 ),
inference(superposition,[],[f1338,f441]) ).
fof(f7425,plain,
! [X2,X0,X1] :
( ub(X0,X1,X0)
| ~ ub(X0,X1,X2)
| ~ lesseq(X2,X0) ),
inference(resolution,[],[f1709,f61]) ).
fof(f7547,plain,
( ! [X0] :
( ~ ub(sK0,sK1,X0)
| ~ lesseq(X0,sK0)
| ~ lesseq(summation(sK0),sK2) )
| spl6_19 ),
inference(resolution,[],[f7425,f1239]) ).
fof(f7548,plain,
( ! [X0] :
( ~ lesseq(sK2,sK2)
| ~ ub(sK0,sK1,X0)
| ~ lesseq(X0,sK0) )
| ~ spl6_3
| ~ spl6_14
| spl6_19 ),
inference(forward_demodulation,[],[f7547,f649]) ).
fof(f7550,plain,
( ! [X0] :
( ~ ub(sK0,sK1,X0)
| ~ lesseq(X0,sK0) )
| ~ spl6_3
| ~ spl6_14
| spl6_19 ),
inference(forward_subsumption_resolution,[],[f7548,f68]) ).
fof(f7554,plain,
( ! [X0] :
( ~ lesseq(X0,sK0)
| ~ lesseq(sK0,X0)
| ~ lesseq(sK1,X0) )
| ~ spl6_3
| ~ spl6_14
| spl6_19 ),
inference(resolution,[],[f7550,f58]) ).
fof(f7556,plain,
( ! [X0] :
( ~ lesseq(sK0,X0)
| ~ lesseq(X0,sK0) )
| ~ spl6_3
| ~ spl6_4
| ~ spl6_14
| spl6_19
| ~ spl6_77 ),
inference(forward_subsumption_resolution,[],[f7554,f4992]) ).
fof(f7569,plain,
( ~ lesseq(max(sK0,sK1),sK0)
| ~ lesseq(summation(sK0),sK2)
| ~ spl6_3
| ~ spl6_4
| ~ spl6_14
| spl6_19
| ~ spl6_77 ),
inference(resolution,[],[f7556,f812]) ).
fof(f7585,plain,
( ~ lesseq(summation(sK0),sK2)
| ~ spl6_3
| ~ spl6_4
| ~ spl6_14
| spl6_19
| ~ spl6_28
| ~ spl6_77 ),
inference(forward_subsumption_resolution,[],[f7569,f850]) ).
fof(f7588,plain,
( ~ lesseq(sK2,sK2)
| ~ spl6_3
| ~ spl6_4
| ~ spl6_14
| spl6_19
| ~ spl6_28
| ~ spl6_77 ),
inference(forward_demodulation,[],[f7585,f649]) ).
fof(f7589,plain,
( $false
| ~ spl6_3
| ~ spl6_4
| ~ spl6_14
| spl6_19
| ~ spl6_28
| ~ spl6_77 ),
inference(forward_subsumption_resolution,[],[f7588,f68]) ).
fof(f7590,plain,
( ~ spl6_3
| ~ spl6_4
| ~ spl6_14
| spl6_19
| ~ spl6_28
| ~ spl6_77 ),
inference(avatar_contradiction_clause,[],[f7589]) ).
fof(f7592,plain,
( ~ lesseq(sK2,summation(sK0))
| spl6_1
| ~ spl6_19 ),
inference(forward_subsumption_resolution,[],[f1169,f576]) ).
fof(f7597,plain,
( ~ lesseq(sK2,sK2)
| spl6_1
| ~ spl6_3
| ~ spl6_14
| ~ spl6_19 ),
inference(forward_demodulation,[],[f7592,f649]) ).
fof(f7600,plain,
( $false
| spl6_1
| ~ spl6_3
| ~ spl6_14
| ~ spl6_19 ),
inference(forward_subsumption_resolution,[],[f7597,f68]) ).
fof(f7601,plain,
( spl6_1
| ~ spl6_3
| ~ spl6_14
| ~ spl6_19 ),
inference(avatar_contradiction_clause,[],[f7600]) ).
fof(f7628,plain,
( $false
| spl6_2
| ~ spl6_14 ),
inference(forward_subsumption_resolution,[],[f6711,f75]) ).
fof(f7629,plain,
( spl6_2
| ~ spl6_14 ),
inference(avatar_contradiction_clause,[],[f7628]) ).
fof(f7657,plain,
( ~ lesseq(summation(sK0),sK2)
| spl6_15
| ~ spl6_27 ),
inference(forward_demodulation,[],[f445,f847]) ).
fof(f7660,plain,
( $false
| spl6_15
| ~ spl6_19
| ~ spl6_27 ),
inference(forward_subsumption_resolution,[],[f7657,f1139]) ).
fof(f7661,plain,
( spl6_15
| ~ spl6_19
| ~ spl6_27 ),
inference(avatar_contradiction_clause,[],[f7660]) ).
cnf(s1,plain,
( spl6_1
| spl6_2 ),
inference(sat_conversion,[],[f77]) ).
cnf(s2,plain,
( ~ spl6_1
| ~ spl6_2 ),
inference(sat_conversion,[],[f78]) ).
cnf(s3,plain,
( ~ spl6_2
| ~ spl6_3
| spl6_4 ),
inference(sat_conversion,[],[f127]) ).
cnf(s4,plain,
( ~ spl6_2
| spl6_3
| spl6_5
| ~ spl6_6 ),
inference(sat_conversion,[],[f146]) ).
cnf(s5,plain,
( ~ spl6_2
| spl6_3
| spl6_6 ),
inference(sat_conversion,[],[f245]) ).
cnf(s7,plain,
( ~ spl6_1
| spl6_9
| ~ spl6_10 ),
inference(sat_conversion,[],[f327]) ).
cnf(s12,plain,
( ~ spl6_2
| spl6_14
| ~ spl6_15 ),
inference(sat_conversion,[],[f446]) ).
cnf(s13,plain,
( ~ spl6_2
| spl6_15 ),
inference(sat_conversion,[],[f455]) ).
cnf(s16,plain,
( spl6_3
| ~ spl6_5
| spl6_15 ),
inference(sat_conversion,[],[f465]) ).
cnf(s20,plain,
( spl6_14
| ~ spl6_15
| ~ spl6_18 ),
inference(sat_conversion,[],[f521]) ).
cnf(s28,plain,
( ~ spl6_10
| spl6_18
| ~ spl6_20 ),
inference(sat_conversion,[],[f606]) ).
cnf(s30,plain,
( ~ spl6_1
| spl6_19 ),
inference(sat_conversion,[],[f620]) ).
cnf(s31,plain,
( ~ spl6_1
| spl6_5
| ~ spl6_9 ),
inference(sat_conversion,[],[f622]) ).
cnf(s36,plain,
( ~ spl6_1
| spl6_18
| ~ spl6_25
| ~ spl6_26 ),
inference(sat_conversion,[],[f757]) ).
cnf(s39,plain,
( spl6_3
| spl6_20 ),
inference(sat_conversion,[],[f763]) ).
cnf(s40,plain,
( ~ spl6_1
| spl6_10
| ~ spl6_20 ),
inference(sat_conversion,[],[f766]) ).
cnf(s48,plain,
( spl6_1
| ~ spl6_5
| ~ spl6_19 ),
inference(sat_conversion,[],[f1238]) ).
cnf(s84,plain,
( ~ spl6_6
| spl6_19
| ~ spl6_21 ),
inference(sat_conversion,[],[f4002]) ).
cnf(s87,plain,
( ~ spl6_20
| spl6_21 ),
inference(sat_conversion,[],[f4017]) ).
cnf(s153,plain,
( ~ spl6_3
| spl6_25
| ~ spl6_27 ),
inference(sat_conversion,[],[f4441]) ).
cnf(s164,plain,
( ~ spl6_3
| spl6_6
| ~ spl6_14
| ~ spl6_15 ),
inference(sat_conversion,[],[f4533]) ).
cnf(s176,plain,
( ~ spl6_3
| ~ spl6_14
| ~ spl6_15
| spl6_28 ),
inference(sat_conversion,[],[f4607]) ).
cnf(s203,plain,
( ~ spl6_3
| spl6_27 ),
inference(sat_conversion,[],[f4810]) ).
cnf(s209,plain,
( ~ spl6_6
| spl6_77 ),
inference(sat_conversion,[],[f4966]) ).
cnf(s212,plain,
( ~ spl6_3
| spl6_26 ),
inference(sat_conversion,[],[f4987]) ).
cnf(s279,plain,
( ~ spl6_3
| ~ spl6_4
| ~ spl6_14
| spl6_19
| ~ spl6_28
| ~ spl6_77 ),
inference(sat_conversion,[],[f7590]) ).
cnf(s282,plain,
( spl6_1
| ~ spl6_3
| ~ spl6_14
| ~ spl6_19 ),
inference(sat_conversion,[],[f7601]) ).
cnf(s290,plain,
( spl6_2
| ~ spl6_14 ),
inference(sat_conversion,[],[f7629]) ).
cnf(s298,plain,
( spl6_15
| ~ spl6_19
| ~ spl6_27 ),
inference(sat_conversion,[],[f7661]) ).
cnf(s299,plain,
( spl6_3
| spl6_1 ),
inference(rat,[],[s84,s48,s87,s4,s5,s39,s1]) ).
cnf(s300,plain,
spl6_1,
inference(rat,[],[s279,s209,s3,s164,s176,s282,s299,s12,s13,s1]) ).
cnf(s301,plain,
spl6_19,
inference(rat,[],[s30,s300]) ).
cnf(s302,plain,
~ spl6_2,
inference(rat,[],[s2,s300]) ).
cnf(s303,plain,
~ spl6_14,
inference(rat,[],[s290,s302]) ).
cnf(s304,plain,
spl6_3,
inference(rat,[],[s16,s31,s20,s7,s28,s40,s39,s300,s303]) ).
cnf(s305,plain,
spl6_26,
inference(rat,[],[s212,s304]) ).
cnf(s306,plain,
spl6_27,
inference(rat,[],[s203,s304]) ).
cnf(s308,plain,
spl6_25,
inference(rat,[],[s153,s306,s304]) ).
cnf(s311,plain,
spl6_15,
inference(rat,[],[s298,s301,s306]) ).
cnf(s312,plain,
spl6_18,
inference(rat,[],[s36,s305,s300,s308]) ).
cnf(s314,plain,
$false,
inference(rat,[],[s20,s303,s311,s312]) ).
fof(f7662,plain,
$false,
inference(avatar_sat_refutation,[],[s314]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM860+1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n008.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 27 21:36:45 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 12.41/2.60 % (1622113)Detected formulas, will run a generic FOF schedule.
% 12.41/2.60 % (1622121)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=4165514442:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 12.41/2.60 % (1622121)Refutation not found, incomplete strategy
% 12.41/2.60 % (1622121)------------------------------
% 12.41/2.60 % (1622121)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.41/2.60 % (1622121)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.41/2.60 % (1622121)CaDiCaL version: 2.1.3
% 12.41/2.60 % (1622121)Termination reason: Refutation not found, incomplete strategy
% 12.41/2.60 % (1622121)Time elapsed: 0.001 s
% 12.41/2.60 % (1622121)Peak memory usage: 88 MB
% 12.41/2.60 % (1622119)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=3012679334:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 12.41/2.60 % (1622122)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2760224113:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 12.41/2.60 % (1622118)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=1910240666:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 12.41/2.60 % (1622120)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=2505590444:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 12.41/2.60 % (1622124)dis-21_1_sil=8000:lcm=predicate:random_seed=2745503496: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)
% 12.41/2.60 % (1622123)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2313698090:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 12.41/2.60 % (1622122)Instruction limit reached!
% 12.41/2.60 % (1622122)------------------------------
% 12.41/2.60 % (1622122)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.41/2.60 % (1622122)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.41/2.60 % (1622122)CaDiCaL version: 2.1.3
% 12.41/2.60 % (1622122)Termination reason: Instruction limit
% 12.41/2.60 % (1622122)Termination phase: Saturation
% 12.41/2.60 % (1622122)Time elapsed: 0.073 s
% 12.41/2.60 % (1622122)Peak memory usage: 88 MB
% 12.41/2.60 % (1622122)Instructions burned: 121 (million)
% 12.41/2.60 % (1622124)Instruction limit reached!
% 12.41/2.60 % (1622124)------------------------------
% 12.41/2.60 % (1622124)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.41/2.60 % (1622124)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.41/2.60 % (1622124)CaDiCaL version: 2.1.3
% 12.41/2.60 % (1622124)Termination reason: Instruction limit
% 12.41/2.60 % (1622124)Termination phase: Saturation
% 12.41/2.60 % (1622124)Time elapsed: 0.082 s
% 12.41/2.60 % (1622124)Peak memory usage: 89 MB
% 12.41/2.60 % (1622124)Instructions burned: 130 (million)
% 12.41/2.60 % (1622123)Instruction limit reached!
% 12.41/2.60 % (1622123)------------------------------
% 12.41/2.60 % (1622123)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.41/2.60 % (1622123)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.41/2.60 % (1622123)CaDiCaL version: 2.1.3
% 12.41/2.60 % (1622123)Termination reason: Instruction limit
% 12.41/2.60 % (1622123)Termination phase: Saturation
% 12.41/2.60 % (1622123)Time elapsed: 0.098 s
% 12.41/2.60 % (1622123)Peak memory usage: 89 MB
% 12.41/2.60 % (1622123)Instructions burned: 140 (million)
% 12.41/2.60 % (1622121)------------------------------
% 12.41/2.60 % (1622121)------------------------------
% 12.41/2.60 % (1622132)lrs+10_1_sil=8000:sp=occurrence:random_seed=3700669179:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 12.41/2.60 % (1622135)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=3528732116:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 12.41/2.60 % (1622133)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3869277003:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 12.41/2.60 % (1622133)Refutation not found, incomplete strategy
% 12.41/2.60 % (1622133)------------------------------
% 12.41/2.60 % (1622133)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.41/2.84 % (1622133)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.41/2.84 % (1622133)CaDiCaL version: 2.1.3
% 13.41/2.84 % (1622133)Termination reason: Refutation not found, incomplete strategy
% 13.41/2.84 % (1622133)Time elapsed: 0.002 s
% 13.41/2.84 % (1622133)Peak memory usage: 89 MB
% 13.41/2.84 % (1622133)Instructions burned: 1 (million)
% 13.41/2.84 % (1622134)lrs+1011_1_sil=32000:sp=occurrence:random_seed=3079432366:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 13.41/2.84 % (1622134)Refutation not found, incomplete strategy
% 13.41/2.84 % (1622134)------------------------------
% 13.41/2.84 % (1622134)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.41/2.84 % (1622134)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.41/2.84 % (1622134)CaDiCaL version: 2.1.3
% 13.41/2.84 % (1622134)Termination reason: Refutation not found, incomplete strategy
% 13.41/2.84 % (1622134)Time elapsed: 0.002 s
% 13.41/2.84 % (1622134)Peak memory usage: 88 MB
% 13.41/2.84 % (1622135)Instruction limit reached!
% 13.41/2.84 % (1622135)------------------------------
% 13.41/2.84 % (1622135)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.41/2.84 % (1622135)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.41/2.84 % (1622135)CaDiCaL version: 2.1.3
% 13.41/2.84 % (1622135)Termination reason: Instruction limit
% 13.41/2.84 % (1622135)Termination phase: Saturation
% 13.41/2.84 % (1622135)Time elapsed: 0.085 s
% 13.41/2.84 % (1622135)Peak memory usage: 92 MB
% 13.41/2.84 % (1622135)Instructions burned: 251 (million)
% 13.41/2.84 % (1622132)Instruction limit reached!
% 13.41/2.84 % (1622132)------------------------------
% 13.41/2.84 % (1622132)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.41/2.84 % (1622132)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.41/2.84 % (1622132)CaDiCaL version: 2.1.3
% 13.41/2.84 % (1622132)Termination reason: Instruction limit
% 13.41/2.84 % (1622132)Termination phase: Saturation
% 13.41/2.84 % (1622132)Time elapsed: 0.183 s
% 13.41/2.84 % (1622132)Peak memory usage: 91 MB
% 13.41/2.84 % (1622132)Instructions burned: 286 (million)
% 13.41/2.84 % (1622140)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=1530990214:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 13.41/2.84 % (1622140)Refutation not found, incomplete strategy
% 13.41/2.84 % (1622140)------------------------------
% 13.41/2.84 % (1622140)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.41/2.84 % (1622140)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.41/2.84 % (1622140)CaDiCaL version: 2.1.3
% 13.41/2.84 % (1622140)Termination reason: Refutation not found, incomplete strategy
% 13.41/2.84 % (1622140)Time elapsed: 0.001 s
% 13.41/2.84 % (1622140)Peak memory usage: 88 MB
% 13.41/2.84 % (1622140)Instructions burned: 1 (million)
% 13.41/2.84 % (1622133)------------------------------
% 13.41/2.84 % (1622133)------------------------------
% 13.41/2.84 % (1622134)------------------------------
% 13.41/2.84 % (1622134)------------------------------
% 13.41/2.84 % (1622141)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=679365062:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 13.41/2.84 % (1622140)------------------------------
% 13.41/2.84 % (1622140)------------------------------
% 13.41/2.84 % (1622143)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=1849022221:cts=off:i=113:fsr=off:ss=included:sgt=4_2993 on theBenchmark for (2993ds/113Mi)
% 13.41/2.84 % (1622144)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=4239973074:i=127:av=off:fsr=off:sup=off_2993 on theBenchmark for (2993ds/127Mi)
% 13.41/2.84 % (1622146)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=3409581079:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2992 on theBenchmark for (2992ds/114Mi)
% 13.41/2.84 % (1622143)Instruction limit reached!
% 13.41/2.84 % (1622143)------------------------------
% 13.41/2.84 % (1622143)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.41/2.84 % (1622143)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.41/2.84 % (1622143)CaDiCaL version: 2.1.3
% 13.41/2.84 % (1622143)Termination reason: Instruction limit
% 13.41/2.84 % (1622143)Termination phase: Saturation
% 13.41/2.84 % (1622143)Time elapsed: 0.081 s
% 13.41/2.84 % (1622143)Peak memory usage: 89 MB
% 13.41/2.84 % (1622143)Instructions burned: 113 (million)
% 13.41/2.84 % (1622144)Instruction limit reached!
% 13.41/2.84 % (1622144)------------------------------
% 13.41/2.84 % (1622144)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.41/2.84 % (1622144)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.41/2.84 % (1622144)CaDiCaL version: 2.1.3
% 13.41/2.84 % (1622144)Termination reason: Instruction limit
% 13.41/2.84 % (1622144)Termination phase: Saturation
% 13.41/2.84 % (1622144)Time elapsed: 0.063 s
% 13.41/2.84 % (1622144)Peak memory usage: 89 MB
% 13.41/2.84 % (1622144)Instructions burned: 129 (million)
% 13.41/2.84 % (1622146)Instruction limit reached!
% 13.41/2.84 % (1622146)------------------------------
% 13.41/2.84 % (1622146)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.41/2.84 % (1622146)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.41/2.84 % (1622146)CaDiCaL version: 2.1.3
% 13.41/2.84 % (1622146)Termination reason: Instruction limit
% 13.41/2.84 % (1622146)Termination phase: Saturation
% 13.41/2.84 % (1622146)Time elapsed: 0.033 s
% 13.41/2.84 % (1622146)Peak memory usage: 88 MB
% 13.41/2.84 % (1622146)Instructions burned: 115 (million)
% 13.41/2.84 % (1622152)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=3422830911:i=5202:ss=axioms:sgt=16_2990 on theBenchmark for (2990ds/5202Mi)
% 13.41/2.84 % (1622150)lrs+10_1_sil=8000:sp=occurrence:random_seed=3608692990:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2991 on theBenchmark for (2991ds/907Mi)
% 13.41/2.84 % (1622151)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=1454452887:i=437:sd=1:aac=none:ss=included_2990 on theBenchmark for (2990ds/437Mi)
% 13.41/2.84 % (1622151)Instruction limit reached!
% 13.41/2.84 % (1622151)------------------------------
% 13.41/2.84 % (1622151)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.41/2.84 % (1622151)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.41/2.84 % (1622151)CaDiCaL version: 2.1.3
% 13.41/2.84 % (1622151)Termination reason: Instruction limit
% 13.41/2.84 % (1622151)Termination phase: Saturation
% 13.41/2.84 % (1622151)Time elapsed: 0.264 s
% 13.41/2.84 % (1622151)Peak memory usage: 91 MB
% 13.41/2.84 % (1622151)Instructions burned: 437 (million)
% 13.41/2.84 % (1622156)dis+10_3:1_sil=8000:acc=on:urr=on:br=off:sac=on:newcnf=on:random_seed=2369144669:i=134:sd=2:doe=on:nm=16:sup=off:ss=included_2986 on theBenchmark for (2986ds/134Mi)
% 13.41/2.84 % (1622156)Instruction limit reached!
% 13.41/2.84 % (1622156)------------------------------
% 13.41/2.84 % (1622156)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.41/2.84 % (1622156)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.41/2.84 % (1622156)CaDiCaL version: 2.1.3
% 13.41/2.84 % (1622156)Termination reason: Instruction limit
% 13.41/2.84 % (1622156)Termination phase: Saturation
% 13.41/2.84 % (1622156)Time elapsed: 0.087 s
% 13.41/2.84 % (1622156)Peak memory usage: 90 MB
% 13.41/2.84 % (1622156)Instructions burned: 134 (million)
% 13.41/2.84 % (1622150)Instruction limit reached!
% 13.41/2.84 % (1622150)------------------------------
% 13.41/2.84 % (1622150)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.41/2.84 % (1622150)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.41/2.84 % (1622150)CaDiCaL version: 2.1.3
% 13.41/2.84 % (1622150)Termination reason: Instruction limit
% 13.41/2.84 % (1622150)Termination phase: Saturation
% 13.41/2.84 % (1622150)Time elapsed: 0.563 s
% 13.41/2.84 % (1622150)Peak memory usage: 94 MB
% 13.41/2.84 % (1622150)Instructions burned: 907 (million)
% 13.41/2.84 % (1622158)lrs+1002_8_sil=8000:sp=occurrence:sos=on:sac=on:random_seed=2283957518:st=8:i=592:sd=3:ep=RST:ss=axioms_2984 on theBenchmark for (2984ds/592Mi)
% 13.41/2.84 % (1622158)Refutation not found, incomplete strategy
% 13.41/2.84 % (1622158)------------------------------
% 13.41/2.84 % (1622158)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.41/2.84 % (1622158)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.41/2.84 % (1622158)CaDiCaL version: 2.1.3
% 13.41/2.84 % (1622158)Termination reason: Refutation not found, incomplete strategy
% 13.41/2.84 % (1622158)Time elapsed: 0.002 s
% 13.41/2.84 % (1622158)Peak memory usage: 88 MB
% 13.41/2.84 % (1622158)Instructions burned: 1 (million)
% 13.41/2.84 % (1622159)lrs+10_1_ncem=casc2026/models/loop6.pt:sil=32000:npcc=on:random_seed=3556867079:st=3:i=13193:sd=3:ss=axioms_2984 on theBenchmark for (2984ds/13193Mi)
% 13.41/2.84 % (1622152)First to succeed.
% 13.41/2.84 % (1622152)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1622113"
% 13.41/2.84 % (1622158)------------------------------
% 13.41/2.84 % (1622158)------------------------------
% 13.41/2.84 % (1622152)Refutation found. Thanks to Tanya!
% 13.41/2.84 % SZS status Theorem for theBenchmark
% 13.41/2.84 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/3.04 % (1622152)------------------------------
% 0.16/3.04 % (1622152)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.16/3.04 % (1622152)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/3.04 % (1622152)CaDiCaL version: 2.1.3
% 0.16/3.04 % (1622152)Termination reason: Refutation
% 0.16/3.04 % (1622152)Time elapsed: 0.789 s
% 0.16/3.04 % (1622152)Peak memory usage: 139 MB
% 0.16/3.04 % (1622152)Instructions burned: 2171 (million)
% 0.16/3.04 % (1622152)------------------------------
% 0.16/3.04 % (1622152)------------------------------
% 0.16/3.04 % (1622113)Success in time 1.981 s
% 0.16/3.04 % Vampire exiting
%------------------------------------------------------------------------------