%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM858+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 : n012.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 12:17:17 PM UTC 2026
% Result : Theorem 1.06s 0.80s
% Output : Refutation 1.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 40
% Number of leaves : 12
% Syntax : Number of formulae : 140 ( 10 unt; 0 def)
% Number of atoms : 442 ( 55 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 528 ( 226 ~; 249 |; 39 &)
% ( 9 <=>; 4 =>; 0 <=; 1 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-3 aty)
% Number of variables : 258 ( 246 !; 12 ?)
% 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(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)
<=> X2 = max(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',model_max_1) ).
fof(f11,axiom,
! [X0,X1,X2] :
( model_ub(X0,X1,X2)
<=> ub(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',model_ub_1) ).
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,X2] :
( lesseq(X0,X2)
| ~ lesseq(X0,X1)
| ~ lesseq(X1,X2) ),
inference(ennf_transformation,[],[f2]) ).
fof(f20,plain,
! [X0,X1,X2] :
( lesseq(X0,X2)
| ~ lesseq(X0,X1)
| ~ lesseq(X1,X2) ),
inference(flattening,[],[f19]) ).
fof(f21,plain,
! [X0,X1] :
( X0 = X1
| ~ lesseq(X0,X1)
| ~ lesseq(X1,X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f22,plain,
! [X0,X1] :
( X0 = X1
| ~ lesseq(X0,X1)
| ~ lesseq(X1,X0) ),
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_max(X0,X1,X2)
| max(X0,X1) != X2 )
& ( X2 = max(X0,X1)
| ~ model_max(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f10]) ).
fof(f34,plain,
! [X0,X1,X2] :
( ( model_ub(X0,X1,X2)
| ~ ub(X0,X1,X2) )
& ( ub(X0,X1,X2)
| ~ model_ub(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f11]) ).
fof(f35,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(f36,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,[],[f35]) ).
fof(f37,plain,
( minsol_model_ub(sK0,sK1,sK2)
| minsol_model_max(sK0,sK1,sK2) ),
inference(cnf_transformation,[],[f24]) ).
fof(f38,plain,
( ~ minsol_model_ub(sK0,sK1,sK2)
| ~ minsol_model_max(sK0,sK1,sK2) ),
inference(cnf_transformation,[],[f24]) ).
fof(f39,plain,
! [X2,X0,X1,X4] :
( ~ minsol_model_max(X0,X1,X2)
| ~ model_max(X0,X1,X4)
| lesseq(X2,X4) ),
inference(cnf_transformation,[],[f28]) ).
fof(f40,plain,
! [X2,X0,X1] :
( model_max(X0,X1,X2)
| ~ minsol_model_max(X0,X1,X2) ),
inference(cnf_transformation,[],[f28]) ).
fof(f41,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(f42,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(f43,plain,
! [X2,X0,X1,X4] :
( ~ minsol_model_ub(X0,X1,X2)
| ~ model_ub(X0,X1,X4)
| lesseq(X2,X4) ),
inference(cnf_transformation,[],[f32]) ).
fof(f44,plain,
! [X2,X0,X1] :
( model_ub(X0,X1,X2)
| ~ minsol_model_ub(X0,X1,X2) ),
inference(cnf_transformation,[],[f32]) ).
fof(f45,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(f46,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(f47,plain,
! [X0,X1] :
( lesseq(X1,X0)
| lesseq(X0,X1) ),
inference(cnf_transformation,[],[f4]) ).
fof(f48,plain,
! [X2,X0,X1] :
( lesseq(X0,X2)
| ~ lesseq(X0,X1)
| ~ lesseq(X1,X2) ),
inference(cnf_transformation,[],[f20]) ).
fof(f49,plain,
! [X0] : lesseq(X0,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f50,plain,
! [X2,X0,X1] :
( max(X0,X1) = X2
| ~ model_max(X0,X1,X2) ),
inference(cnf_transformation,[],[f33]) ).
fof(f51,plain,
! [X2,X0,X1] :
( model_max(X0,X1,X2)
| max(X0,X1) != X2 ),
inference(cnf_transformation,[],[f33]) ).
fof(f52,plain,
! [X2,X0,X1] :
( ub(X0,X1,X2)
| ~ model_ub(X0,X1,X2) ),
inference(cnf_transformation,[],[f34]) ).
fof(f53,plain,
! [X2,X0,X1] :
( model_ub(X0,X1,X2)
| ~ ub(X0,X1,X2) ),
inference(cnf_transformation,[],[f34]) ).
fof(f54,plain,
! [X0,X1] :
( ~ lesseq(X1,X0)
| ~ lesseq(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f22]) ).
fof(f55,plain,
! [X0,X1] :
( max(X0,X1) = X1
| ~ lesseq(X0,X1) ),
inference(cnf_transformation,[],[f8]) ).
fof(f56,plain,
! [X0,X1] :
( max(X0,X1) = X0
| ~ lesseq(X1,X0) ),
inference(cnf_transformation,[],[f7]) ).
fof(f57,plain,
! [X2,X0,X1] :
( ~ ub(X0,X1,X2)
| lesseq(X1,X2) ),
inference(cnf_transformation,[],[f36]) ).
fof(f58,plain,
! [X2,X0,X1] :
( ~ ub(X0,X1,X2)
| lesseq(X0,X2) ),
inference(cnf_transformation,[],[f36]) ).
fof(f59,plain,
! [X2,X0,X1] :
( ub(X0,X1,X2)
| ~ lesseq(X0,X2)
| ~ lesseq(X1,X2) ),
inference(cnf_transformation,[],[f36]) ).
fof(f60,plain,
! [X0,X1] : model_max(X0,X1,max(X0,X1)),
inference(equality_resolution,[],[f51]) ).
fof(f62,plain,
! [X2,X0,X1] :
( ~ model_ub(X0,X1,X2)
| lesseq(X0,X2) ),
inference(resolution,[],[f52,f58]) ).
fof(f63,plain,
! [X2,X0,X1] :
( ~ model_ub(X0,X1,X2)
| lesseq(X1,X2) ),
inference(resolution,[],[f52,f57]) ).
fof(f64,plain,
! [X2,X0,X1] :
( ~ minsol_model_ub(X0,X2,X1)
| lesseq(X0,X1) ),
inference(resolution,[],[f62,f44]) ).
fof(f67,plain,
! [X2,X0,X1] :
( ~ minsol_model_ub(X2,X0,X1)
| lesseq(X0,X1) ),
inference(resolution,[],[f63,f44]) ).
fof(f68,plain,
! [X0,X1] :
( model_max(X1,X0,X0)
| ~ lesseq(X1,X0) ),
inference(superposition,[],[f60,f55]) ).
fof(f69,plain,
( minsol_model_max(sK0,sK1,sK2)
| lesseq(sK0,sK2) ),
inference(resolution,[],[f64,f37]) ).
fof(f72,plain,
! [X0,X1] :
( model_max(X0,X1,X0)
| ~ lesseq(X1,X0) ),
inference(superposition,[],[f60,f56]) ).
fof(f73,plain,
( minsol_model_max(sK0,sK1,sK2)
| lesseq(sK1,sK2) ),
inference(resolution,[],[f67,f37]) ).
fof(f74,plain,
! [X2,X3,X0,X1] :
( ~ model_max(X1,X2,X3)
| X0 = X3
| ~ model_max(X1,X2,X0) ),
inference(superposition,[],[f50,f50]) ).
fof(f75,plain,
! [X2,X0,X1] :
( ~ model_max(X0,X1,X2)
| X0 = X2
| ~ lesseq(X1,X0) ),
inference(superposition,[],[f50,f56]) ).
fof(f76,plain,
! [X2,X0,X1] :
( ~ model_max(X1,X0,X2)
| X0 = X2
| ~ lesseq(X1,X0) ),
inference(superposition,[],[f50,f55]) ).
fof(f88,plain,
! [X2,X0,X1] :
( ~ minsol_model_max(X0,X2,X1)
| ~ lesseq(X2,X0)
| X0 = X1 ),
inference(resolution,[],[f75,f40]) ).
fof(f101,plain,
! [X0] :
( minsol_model_max(sK0,sK1,sK2)
| lesseq(sK2,X0)
| ~ model_ub(sK0,sK1,X0) ),
inference(resolution,[],[f43,f37]) ).
fof(f109,plain,
! [X2,X3,X0,X1] :
( ~ lesseq(X3,sK4(X0,X1,X2))
| minsol_model_ub(X0,X1,X2)
| ~ lesseq(X2,X3)
| ~ model_ub(X0,X1,X2) ),
inference(resolution,[],[f46,f48]) ).
fof(f115,plain,
! [X2,X0,X1] :
( sK3(X0,X1,X2) = X0
| minsol_model_max(X0,X1,X2)
| ~ model_max(X0,X1,X2)
| ~ lesseq(X1,X0) ),
inference(resolution,[],[f41,f75]) ).
fof(f119,plain,
! [X2,X0,X1] :
( lesseq(X1,sK4(X0,X1,X2))
| minsol_model_ub(X0,X1,X2)
| ~ model_ub(X0,X1,X2) ),
inference(resolution,[],[f45,f63]) ).
fof(f120,plain,
! [X2,X0,X1] :
( lesseq(X0,sK4(X0,X1,X2))
| minsol_model_ub(X0,X1,X2)
| ~ model_ub(X0,X1,X2) ),
inference(resolution,[],[f45,f62]) ).
fof(f125,plain,
! [X0,X1] :
( ~ model_ub(sK0,sK1,X0)
| lesseq(sK2,X0)
| ~ model_max(sK0,sK1,X1)
| lesseq(sK2,X1) ),
inference(resolution,[],[f101,f39]) ).
fof(f137,plain,
! [X2,X0,X1] :
( ~ minsol_model_max(X2,X0,X1)
| ~ lesseq(X2,X0)
| X0 = X1 ),
inference(resolution,[],[f76,f40]) ).
fof(f139,plain,
! [X2,X0,X1] :
( sK3(X1,X0,X2) = X0
| ~ lesseq(X1,X0)
| ~ model_max(X1,X0,X2)
| minsol_model_max(X1,X0,X2) ),
inference(resolution,[],[f76,f41]) ).
fof(f162,plain,
! [X2,X3,X0,X1] :
( ~ minsol_model_max(X2,X3,X1)
| ~ model_max(X2,X3,X0)
| X0 = X1 ),
inference(resolution,[],[f74,f40]) ).
fof(f170,plain,
! [X0,X1] :
( ~ model_max(sK0,sK1,X1)
| lesseq(sK2,X0)
| lesseq(sK2,X1)
| ~ ub(sK0,sK1,X0) ),
inference(resolution,[],[f125,f53]) ).
fof(f184,plain,
! [X0] :
( ~ ub(sK0,sK1,X0)
| lesseq(sK2,sK0)
| lesseq(sK2,X0)
| ~ lesseq(sK1,sK0) ),
inference(resolution,[],[f170,f72]) ).
fof(f185,plain,
! [X0] :
( ~ ub(sK0,sK1,X0)
| lesseq(sK2,sK1)
| lesseq(sK2,X0)
| ~ lesseq(sK0,sK1) ),
inference(resolution,[],[f170,f68]) ).
fof(f196,plain,
! [X0] :
( lesseq(sK2,sK0)
| lesseq(sK2,X0)
| ~ lesseq(sK1,sK0)
| ~ lesseq(sK0,X0)
| ~ lesseq(sK1,X0) ),
inference(resolution,[],[f184,f59]) ).
fof(f198,plain,
! [X0] :
( lesseq(sK2,X0)
| ~ lesseq(sK1,sK0)
| ~ lesseq(sK0,X0)
| ~ lesseq(sK1,X0) ),
inference(forward_subsumption_resolution,[],[f196,f48]) ).
fof(f199,plain,
! [X0] :
( lesseq(sK2,X0)
| ~ lesseq(sK1,sK0)
| ~ lesseq(sK0,X0) ),
inference(forward_subsumption_resolution,[],[f198,f48]) ).
fof(f222,plain,
! [X0] :
( lesseq(sK2,sK1)
| lesseq(sK2,X0)
| ~ lesseq(sK0,sK1)
| ~ lesseq(sK0,X0)
| ~ lesseq(sK1,X0) ),
inference(resolution,[],[f185,f59]) ).
fof(f224,plain,
! [X0] :
( lesseq(sK2,X0)
| ~ lesseq(sK0,sK1)
| ~ lesseq(sK0,X0)
| ~ lesseq(sK1,X0) ),
inference(forward_subsumption_resolution,[],[f222,f48]) ).
fof(f225,plain,
! [X0] :
( lesseq(sK2,X0)
| ~ lesseq(sK0,sK1)
| ~ lesseq(sK1,X0) ),
inference(forward_subsumption_resolution,[],[f224,f48]) ).
fof(f228,plain,
( lesseq(sK0,sK2)
| sK0 = sK2
| ~ lesseq(sK1,sK0) ),
inference(resolution,[],[f88,f69]) ).
fof(f232,plain,
( sK0 = sK2
| ~ lesseq(sK1,sK0)
| ~ lesseq(sK2,sK0)
| sK0 = sK2 ),
inference(resolution,[],[f228,f54]) ).
fof(f233,plain,
( ~ lesseq(sK2,sK0)
| ~ lesseq(sK1,sK0)
| sK0 = sK2 ),
inference(duplicate_literal_removal,[],[f232]) ).
fof(f235,plain,
( lesseq(sK1,sK2)
| sK1 = sK2
| ~ lesseq(sK0,sK1) ),
inference(resolution,[],[f137,f73]) ).
fof(f238,plain,
( sK1 = sK2
| ~ lesseq(sK0,sK1)
| ~ lesseq(sK2,sK1)
| sK1 = sK2 ),
inference(resolution,[],[f235,f54]) ).
fof(f239,plain,
( ~ lesseq(sK2,sK1)
| ~ lesseq(sK0,sK1)
| sK1 = sK2 ),
inference(duplicate_literal_removal,[],[f238]) ).
fof(f242,plain,
! [X0] :
( ~ model_max(sK0,sK1,X0)
| sK2 = X0
| lesseq(sK0,sK2) ),
inference(resolution,[],[f162,f69]) ).
fof(f251,plain,
! [X0,X1] :
( minsol_model_ub(X0,X1,X1)
| ~ model_ub(X0,X1,X1)
| ~ model_ub(X0,X1,X1)
| minsol_model_ub(X0,X1,X1) ),
inference(resolution,[],[f119,f46]) ).
fof(f256,plain,
! [X0,X1] :
( minsol_model_ub(X0,X1,X1)
| ~ model_ub(X0,X1,X1) ),
inference(duplicate_literal_removal,[],[f251]) ).
fof(f259,plain,
( ~ lesseq(sK1,sK0)
| sK0 = sK2
| ~ lesseq(sK1,sK0)
| ~ lesseq(sK0,sK0) ),
inference(resolution,[],[f233,f199]) ).
fof(f262,plain,
( ~ lesseq(sK1,sK0)
| sK0 = sK2
| ~ lesseq(sK0,sK0) ),
inference(duplicate_literal_removal,[],[f259]) ).
fof(f265,plain,
( ~ lesseq(sK1,sK0)
| sK0 = sK2 ),
inference(forward_subsumption_resolution,[],[f262,f49]) ).
fof(f267,plain,
! [X2,X0,X1] :
( minsol_model_ub(X0,X1,X2)
| ~ model_ub(X0,X1,X2)
| minsol_model_ub(X0,X1,X2)
| ~ lesseq(X2,X0)
| ~ model_ub(X0,X1,X2) ),
inference(resolution,[],[f120,f109]) ).
fof(f270,plain,
! [X2,X0,X1] :
( minsol_model_ub(X0,X1,X2)
| ~ model_ub(X0,X1,X2)
| ~ lesseq(X2,X0) ),
inference(duplicate_literal_removal,[],[f267]) ).
fof(f273,plain,
( lesseq(sK0,sK1)
| sK0 = sK2 ),
inference(resolution,[],[f265,f47]) ).
fof(f301,plain,
( ~ lesseq(sK0,sK1)
| sK1 = sK2
| ~ lesseq(sK0,sK1)
| ~ lesseq(sK1,sK1) ),
inference(resolution,[],[f239,f225]) ).
fof(f306,plain,
( ~ lesseq(sK0,sK1)
| sK1 = sK2
| ~ lesseq(sK1,sK1) ),
inference(duplicate_literal_removal,[],[f301]) ).
fof(f308,plain,
( ~ lesseq(sK0,sK1)
| sK1 = sK2 ),
inference(forward_subsumption_resolution,[],[f306,f49]) ).
fof(f312,plain,
! [X2,X0,X1] :
( ~ lesseq(X1,X0)
| ~ model_max(X0,X2,X1)
| minsol_model_max(X0,X2,X1)
| minsol_model_max(X0,X2,X1)
| ~ model_max(X0,X2,X1)
| ~ lesseq(X2,X0) ),
inference(superposition,[],[f42,f115]) ).
fof(f313,plain,
! [X2,X0,X1] :
( minsol_model_max(X0,X2,X1)
| ~ model_max(X0,X2,X1)
| ~ lesseq(X1,X0)
| ~ lesseq(X2,X0) ),
inference(duplicate_literal_removal,[],[f312]) ).
fof(f317,plain,
( sK1 = sK2
| sK0 = sK2 ),
inference(resolution,[],[f308,f273]) ).
fof(f331,plain,
! [X2,X0,X1] :
( ~ lesseq(X1,X0)
| ~ model_max(X2,X0,X1)
| minsol_model_max(X2,X0,X1)
| ~ lesseq(X2,X0)
| ~ model_max(X2,X0,X1)
| minsol_model_max(X2,X0,X1) ),
inference(superposition,[],[f42,f139]) ).
fof(f332,plain,
! [X2,X0,X1] :
( minsol_model_max(X2,X0,X1)
| ~ model_max(X2,X0,X1)
| ~ lesseq(X1,X0)
| ~ lesseq(X2,X0) ),
inference(duplicate_literal_removal,[],[f331]) ).
fof(f339,plain,
( ~ minsol_model_ub(sK0,sK1,sK1)
| ~ minsol_model_max(sK0,sK1,sK1)
| sK0 = sK2 ),
inference(superposition,[],[f38,f317]) ).
fof(f517,plain,
( sK2 = max(sK0,sK1)
| lesseq(sK0,sK2) ),
inference(resolution,[],[f242,f60]) ).
fof(f544,plain,
( model_max(sK0,sK1,sK2)
| lesseq(sK0,sK2) ),
inference(superposition,[],[f60,f517]) ).
fof(f556,plain,
( model_max(sK0,sK1,sK1)
| lesseq(sK0,sK1)
| sK0 = sK2 ),
inference(superposition,[],[f544,f317]) ).
fof(f560,plain,
( model_max(sK0,sK1,sK1)
| sK0 = sK2 ),
inference(forward_subsumption_resolution,[],[f556,f68]) ).
fof(f659,plain,
( ~ minsol_model_max(sK0,sK1,sK1)
| ~ model_ub(sK0,sK1,sK1)
| sK0 = sK2 ),
inference(resolution,[],[f256,f339]) ).
fof(f689,plain,
( ~ minsol_model_max(sK0,sK1,sK2)
| ~ lesseq(sK2,sK0)
| ~ model_ub(sK0,sK1,sK2) ),
inference(resolution,[],[f270,f38]) ).
fof(f757,plain,
( ~ model_max(sK0,sK1,sK1)
| ~ lesseq(sK1,sK1)
| ~ lesseq(sK0,sK1)
| ~ model_ub(sK0,sK1,sK1)
| sK0 = sK2 ),
inference(resolution,[],[f332,f659]) ).
fof(f763,plain,
( ~ lesseq(sK1,sK1)
| ~ lesseq(sK0,sK1)
| ~ model_ub(sK0,sK1,sK1)
| sK0 = sK2 ),
inference(forward_subsumption_resolution,[],[f757,f560]) ).
fof(f766,plain,
( ~ lesseq(sK0,sK1)
| ~ model_ub(sK0,sK1,sK1)
| sK0 = sK2 ),
inference(forward_subsumption_resolution,[],[f763,f49]) ).
fof(f767,plain,
( ~ model_ub(sK0,sK1,sK1)
| sK0 = sK2 ),
inference(forward_subsumption_resolution,[],[f766,f62]) ).
fof(f768,plain,
( ~ ub(sK0,sK1,sK1)
| sK0 = sK2 ),
inference(resolution,[],[f767,f53]) ).
fof(f770,plain,
( sK0 = sK2
| ~ lesseq(sK0,sK1)
| ~ lesseq(sK1,sK1) ),
inference(resolution,[],[f768,f59]) ).
fof(f772,plain,
( sK0 = sK2
| ~ lesseq(sK1,sK1) ),
inference(forward_subsumption_resolution,[],[f770,f273]) ).
fof(f773,plain,
sK0 = sK2,
inference(forward_subsumption_resolution,[],[f772,f49]) ).
fof(f808,plain,
( lesseq(sK1,sK0)
| sK0 = sK1
| ~ lesseq(sK0,sK1) ),
inference(superposition,[],[f235,f773]) ).
fof(f814,plain,
( ~ minsol_model_max(sK0,sK1,sK0)
| ~ lesseq(sK0,sK0)
| ~ model_ub(sK0,sK1,sK0) ),
inference(superposition,[],[f689,f773]) ).
fof(f816,plain,
( ~ minsol_model_max(sK0,sK1,sK0)
| ~ model_ub(sK0,sK1,sK0) ),
inference(forward_subsumption_resolution,[],[f814,f49]) ).
fof(f818,plain,
( lesseq(sK1,sK0)
| sK0 = sK1 ),
inference(forward_subsumption_resolution,[],[f808,f47]) ).
fof(f1180,plain,
( ~ model_ub(sK0,sK1,sK0)
| ~ model_max(sK0,sK1,sK0)
| ~ lesseq(sK0,sK0)
| ~ lesseq(sK1,sK0) ),
inference(resolution,[],[f816,f313]) ).
fof(f1197,plain,
( ~ model_ub(sK0,sK1,sK0)
| ~ lesseq(sK0,sK0)
| ~ lesseq(sK1,sK0) ),
inference(forward_subsumption_resolution,[],[f1180,f72]) ).
fof(f1200,plain,
( ~ model_ub(sK0,sK1,sK0)
| ~ lesseq(sK1,sK0) ),
inference(forward_subsumption_resolution,[],[f1197,f49]) ).
fof(f1201,plain,
~ model_ub(sK0,sK1,sK0),
inference(forward_subsumption_resolution,[],[f1200,f63]) ).
fof(f1230,plain,
~ ub(sK0,sK1,sK0),
inference(resolution,[],[f1201,f53]) ).
fof(f1232,plain,
( ~ lesseq(sK0,sK0)
| ~ lesseq(sK1,sK0) ),
inference(resolution,[],[f1230,f59]) ).
fof(f1234,plain,
~ lesseq(sK1,sK0),
inference(forward_subsumption_resolution,[],[f1232,f49]) ).
fof(f1262,plain,
sK0 = sK1,
inference(resolution,[],[f1234,f818]) ).
fof(f1354,plain,
~ lesseq(sK0,sK0),
inference(superposition,[],[f1234,f1262]) ).
fof(f1356,plain,
$false,
inference(forward_subsumption_resolution,[],[f1354,f49]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : NUM858+1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.03/0.31 % Computer : n012.cluster.edu
% 0.03/0.31 % Model : x86_64 x86_64
% 0.03/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.31 % Memory : 8046.5625MB
% 0.03/0.31 % OS : Linux 6.8.0-71-generic
% 0.03/0.31 % CPULimit : 300
% 0.03/0.31 % WCLimit : 300
% 0.03/0.31 % DateTime : Sun Sep 27 21:35:40 UTC 2026
% 0.03/0.31 % CPUTime :
% 0.03/0.31 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.33 Running first-order theorem proving
% 0.08/0.33 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
% 1.06/0.80 % (2766327)Detected formulas, will run a generic FOF schedule.
% 1.06/0.80 % (2766334)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=2773076031:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 1.06/0.80 % (2766335)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=4071345982:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 1.06/0.80 % (2766333)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=2070280794:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 1.06/0.80 % (2766332)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=199872876:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 1.06/0.80 % (2766336)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=597528117:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 1.06/0.80 % (2766335)Refutation not found, incomplete strategy
% 1.06/0.80 % (2766335)------------------------------
% 1.06/0.80 % (2766335)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.06/0.80 % (2766335)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.06/0.80 % (2766335)CaDiCaL version: 2.1.3
% 1.06/0.80 % (2766335)Termination reason: Refutation not found, incomplete strategy
% 1.06/0.80 % (2766335)Time elapsed: 0.0000 s
% 1.06/0.80 % (2766335)Peak memory usage: 87 MB
% 1.06/0.80 % (2766337)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3440546582:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 1.06/0.80 % (2766338)dis-21_1_sil=8000:lcm=predicate:random_seed=2133921393: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)
% 1.06/0.80 % (2766336)First to succeed.
% 1.06/0.80 % (2766336)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2766327"
% 1.06/0.80 % (2766338)Instruction limit reached!
% 1.06/0.80 % (2766338)------------------------------
% 1.06/0.80 % (2766338)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.06/0.80 % (2766338)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.06/0.80 % (2766338)CaDiCaL version: 2.1.3
% 1.06/0.80 % (2766338)Termination reason: Instruction limit
% 1.06/0.80 % (2766338)Termination phase: Saturation
% 1.06/0.80 % (2766338)Time elapsed: 0.046 s
% 1.06/0.80 % (2766338)Peak memory usage: 89 MB
% 1.06/0.80 % (2766338)Instructions burned: 130 (million)
% 1.06/0.80 % (2766337)Instruction limit reached!
% 1.06/0.80 % (2766337)------------------------------
% 1.06/0.80 % (2766337)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.06/0.80 % (2766337)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.06/0.80 % (2766337)CaDiCaL version: 2.1.3
% 1.06/0.80 % (2766337)Termination reason: Instruction limit
% 1.06/0.80 % (2766337)Termination phase: Saturation
% 1.06/0.80 % (2766337)Time elapsed: 0.051 s
% 1.06/0.80 % (2766337)Peak memory usage: 89 MB
% 1.06/0.80 % (2766337)Instructions burned: 142 (million)
% 1.06/0.80 % (2766335)------------------------------
% 1.06/0.80 % (2766335)------------------------------
% 1.06/0.80 % (2766347)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1805062486:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/157Mi)
% 1.06/0.80 % (2766346)lrs+10_1_sil=8000:sp=occurrence:random_seed=2629357297:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 1.06/0.80 % (2766347)Refutation not found, incomplete strategy
% 1.06/0.80 % (2766347)------------------------------
% 1.06/0.80 % (2766347)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.06/0.80 % (2766347)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.06/0.80 % (2766347)CaDiCaL version: 2.1.3
% 1.06/0.80 % (2766347)Termination reason: Refutation not found, incomplete strategy
% 1.06/0.80 % (2766347)Time elapsed: 0.001 s
% 1.06/0.80 % (2766347)Peak memory usage: 88 MB
% 1.06/0.80 % (2766347)Instructions burned: 1 (million)
% 1.06/0.80 % (2766336)Refutation found. Thanks to Tanya!
% 1.06/0.80 % SZS status Theorem for theBenchmark
% 1.06/0.80 % SZS output start Proof for theBenchmark
% See solution above
% 1.06/0.89 % (2766336)------------------------------
% 1.06/0.89 % (2766336)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.06/0.89 % (2766336)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.06/0.89 % (2766336)CaDiCaL version: 2.1.3
% 1.06/0.89 % (2766336)Termination reason: Refutation
% 1.06/0.89 % (2766336)Time elapsed: 0.018 s
% 1.06/0.89 % (2766336)Peak memory usage: 88 MB
% 1.06/0.89 % (2766336)Instructions burned: 54 (million)
% 1.06/0.89 % (2766336)------------------------------
% 1.06/0.89 % (2766336)------------------------------
% 1.06/0.89 % (2766327)Success in time 0.272 s
% 1.06/0.89 % Vampire exiting
%------------------------------------------------------------------------------