TSTP Solution File: NUM858+1 by iProver---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : NUM858+1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 3 02:50:58 EDT 2024
% Result : Theorem 69.29s 10.26s
% Output : CNFRefutation 69.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 22
% Syntax : Number of formulae : 268 ( 18 unt; 0 def)
% Number of atoms : 802 ( 203 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 964 ( 430 ~; 462 |; 48 &)
% ( 14 <=>; 9 =>; 0 <=; 1 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 482 ( 11 sgn 184 !; 17 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : lesseq(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lesseq_ref) ).
fof(f2,axiom,
! [X0,X1,X2] :
( ( lesseq(X1,X2)
& lesseq(X0,X1) )
=> lesseq(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lesseq_trans) ).
fof(f3,axiom,
! [X0,X1] :
( ( lesseq(X1,X0)
& lesseq(X0,X1) )
=> X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lesseq_antisymmetric) ).
fof(f4,axiom,
! [X0,X1] :
( lesseq(X1,X0)
| lesseq(X0,X1) ),
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] :
( ~ lesseq(X1,X0)
| max(X0,X1) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',max_1) ).
fof(f8,axiom,
! [X0,X1] :
( ~ lesseq(X0,X1)
| max(X0,X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',max_2) ).
fof(f9,axiom,
! [X0,X1,X2] :
( ub(X0,X1,X2)
<=> ( lesseq(X1,X2)
& lesseq(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ub) ).
fof(f10,axiom,
! [X0,X1,X3] :
( model_max(X0,X1,X3)
<=> max(X0,X1) = X3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',model_max_1) ).
fof(f11,axiom,
! [X0,X1,X3] :
( model_ub(X0,X1,X3)
<=> ub(X0,X1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',model_ub_1) ).
fof(f12,axiom,
! [X0,X1,X3] :
( minsol_model_max(X0,X1,X3)
<=> ( ! [X2] :
( model_max(X0,X1,X2)
=> lesseq(X3,X2) )
& model_max(X0,X1,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',minsol_model_max) ).
fof(f13,axiom,
! [X0,X1,X3] :
( minsol_model_ub(X0,X1,X3)
<=> ( ! [X2] :
( model_ub(X0,X1,X2)
=> lesseq(X3,X2) )
& model_ub(X0,X1,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,[],[f14]) ).
fof(f16,plain,
! [X0,X1,X2] :
( model_max(X0,X1,X2)
<=> max(X0,X1) = X2 ),
inference(rectify,[],[f10]) ).
fof(f17,plain,
! [X0,X1,X2] :
( model_ub(X0,X1,X2)
<=> ub(X0,X1,X2) ),
inference(rectify,[],[f11]) ).
fof(f18,plain,
! [X0,X1,X2] :
( minsol_model_max(X0,X1,X2)
<=> ( ! [X3] :
( model_max(X0,X1,X3)
=> lesseq(X2,X3) )
& model_max(X0,X1,X2) ) ),
inference(rectify,[],[f12]) ).
fof(f19,plain,
! [X0,X1,X2] :
( minsol_model_ub(X0,X1,X2)
<=> ( ! [X3] :
( model_ub(X0,X1,X3)
=> lesseq(X2,X3) )
& model_ub(X0,X1,X2) ) ),
inference(rectify,[],[f13]) ).
fof(f20,plain,
! [X0,X1,X2] :
( lesseq(X0,X2)
| ~ lesseq(X1,X2)
| ~ lesseq(X0,X1) ),
inference(ennf_transformation,[],[f2]) ).
fof(f21,plain,
! [X0,X1,X2] :
( lesseq(X0,X2)
| ~ lesseq(X1,X2)
| ~ lesseq(X0,X1) ),
inference(flattening,[],[f20]) ).
fof(f22,plain,
! [X0,X1] :
( X0 = X1
| ~ lesseq(X1,X0)
| ~ lesseq(X0,X1) ),
inference(ennf_transformation,[],[f3]) ).
fof(f23,plain,
! [X0,X1] :
( X0 = X1
| ~ lesseq(X1,X0)
| ~ lesseq(X0,X1) ),
inference(flattening,[],[f22]) ).
fof(f24,plain,
! [X0,X1,X2] :
( minsol_model_max(X0,X1,X2)
<=> ( ! [X3] :
( lesseq(X2,X3)
| ~ model_max(X0,X1,X3) )
& model_max(X0,X1,X2) ) ),
inference(ennf_transformation,[],[f18]) ).
fof(f25,plain,
! [X0,X1,X2] :
( minsol_model_ub(X0,X1,X2)
<=> ( ! [X3] :
( lesseq(X2,X3)
| ~ model_ub(X0,X1,X3) )
& model_ub(X0,X1,X2) ) ),
inference(ennf_transformation,[],[f19]) ).
fof(f26,plain,
? [X0,X1,X2] :
( minsol_model_ub(X0,X1,X2)
<~> minsol_model_max(X0,X1,X2) ),
inference(ennf_transformation,[],[f15]) ).
fof(f28,plain,
! [X0,X1] :
( ( lesseq(X0,X1)
| ~ lesseq(summation(X0),summation(X1)) )
& ( lesseq(summation(X0),summation(X1))
| ~ lesseq(X0,X1) ) ),
inference(nnf_transformation,[],[f6]) ).
fof(f29,plain,
! [X0,X1,X2] :
( ( ub(X0,X1,X2)
| ~ lesseq(X1,X2)
| ~ lesseq(X0,X2) )
& ( ( lesseq(X1,X2)
& lesseq(X0,X2) )
| ~ ub(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f9]) ).
fof(f30,plain,
! [X0,X1,X2] :
( ( ub(X0,X1,X2)
| ~ lesseq(X1,X2)
| ~ lesseq(X0,X2) )
& ( ( lesseq(X1,X2)
& lesseq(X0,X2) )
| ~ ub(X0,X1,X2) ) ),
inference(flattening,[],[f29]) ).
fof(f31,plain,
! [X0,X1,X2] :
( ( model_max(X0,X1,X2)
| max(X0,X1) != X2 )
& ( max(X0,X1) = X2
| ~ model_max(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f16]) ).
fof(f32,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,[],[f17]) ).
fof(f33,plain,
! [X0,X1,X2] :
( ( minsol_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) )
& model_max(X0,X1,X2) )
| ~ minsol_model_max(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f24]) ).
fof(f34,plain,
! [X0,X1,X2] :
( ( minsol_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) )
& model_max(X0,X1,X2) )
| ~ minsol_model_max(X0,X1,X2) ) ),
inference(flattening,[],[f33]) ).
fof(f35,plain,
! [X0,X1,X2] :
( ( minsol_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) )
& model_max(X0,X1,X2) )
| ~ minsol_model_max(X0,X1,X2) ) ),
inference(rectify,[],[f34]) ).
fof(f36,plain,
! [X0,X1,X2] :
( ? [X3] :
( ~ lesseq(X2,X3)
& model_max(X0,X1,X3) )
=> ( ~ lesseq(X2,sK0(X0,X1,X2))
& model_max(X0,X1,sK0(X0,X1,X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f37,plain,
! [X0,X1,X2] :
( ( minsol_model_max(X0,X1,X2)
| ( ~ lesseq(X2,sK0(X0,X1,X2))
& model_max(X0,X1,sK0(X0,X1,X2)) )
| ~ model_max(X0,X1,X2) )
& ( ( ! [X4] :
( lesseq(X2,X4)
| ~ model_max(X0,X1,X4) )
& model_max(X0,X1,X2) )
| ~ minsol_model_max(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f35,f36]) ).
fof(f38,plain,
! [X0,X1,X2] :
( ( minsol_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) )
& model_ub(X0,X1,X2) )
| ~ minsol_model_ub(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f25]) ).
fof(f39,plain,
! [X0,X1,X2] :
( ( minsol_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) )
& model_ub(X0,X1,X2) )
| ~ minsol_model_ub(X0,X1,X2) ) ),
inference(flattening,[],[f38]) ).
fof(f40,plain,
! [X0,X1,X2] :
( ( minsol_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) )
& model_ub(X0,X1,X2) )
| ~ minsol_model_ub(X0,X1,X2) ) ),
inference(rectify,[],[f39]) ).
fof(f41,plain,
! [X0,X1,X2] :
( ? [X3] :
( ~ lesseq(X2,X3)
& model_ub(X0,X1,X3) )
=> ( ~ lesseq(X2,sK1(X0,X1,X2))
& model_ub(X0,X1,sK1(X0,X1,X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f42,plain,
! [X0,X1,X2] :
( ( minsol_model_ub(X0,X1,X2)
| ( ~ lesseq(X2,sK1(X0,X1,X2))
& model_ub(X0,X1,sK1(X0,X1,X2)) )
| ~ model_ub(X0,X1,X2) )
& ( ( ! [X4] :
( lesseq(X2,X4)
| ~ model_ub(X0,X1,X4) )
& model_ub(X0,X1,X2) )
| ~ minsol_model_ub(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f40,f41]) ).
fof(f43,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,[],[f26]) ).
fof(f44,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) ) )
=> ( ( ~ minsol_model_max(sK2,sK3,sK4)
| ~ minsol_model_ub(sK2,sK3,sK4) )
& ( minsol_model_max(sK2,sK3,sK4)
| minsol_model_ub(sK2,sK3,sK4) ) ) ),
introduced(choice_axiom,[]) ).
fof(f45,plain,
( ( ~ minsol_model_max(sK2,sK3,sK4)
| ~ minsol_model_ub(sK2,sK3,sK4) )
& ( minsol_model_max(sK2,sK3,sK4)
| minsol_model_ub(sK2,sK3,sK4) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4])],[f43,f44]) ).
fof(f46,plain,
! [X0] : lesseq(X0,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f47,plain,
! [X2,X0,X1] :
( lesseq(X0,X2)
| ~ lesseq(X1,X2)
| ~ lesseq(X0,X1) ),
inference(cnf_transformation,[],[f21]) ).
fof(f48,plain,
! [X0,X1] :
( X0 = X1
| ~ lesseq(X1,X0)
| ~ lesseq(X0,X1) ),
inference(cnf_transformation,[],[f23]) ).
fof(f49,plain,
! [X0,X1] :
( lesseq(X1,X0)
| lesseq(X0,X1) ),
inference(cnf_transformation,[],[f4]) ).
fof(f53,plain,
! [X0,X1] :
( lesseq(X0,X1)
| ~ lesseq(summation(X0),summation(X1)) ),
inference(cnf_transformation,[],[f28]) ).
fof(f54,plain,
! [X0,X1] :
( ~ lesseq(X1,X0)
| max(X0,X1) = X0 ),
inference(cnf_transformation,[],[f7]) ).
fof(f55,plain,
! [X0,X1] :
( ~ lesseq(X0,X1)
| max(X0,X1) = X1 ),
inference(cnf_transformation,[],[f8]) ).
fof(f56,plain,
! [X2,X0,X1] :
( lesseq(X0,X2)
| ~ ub(X0,X1,X2) ),
inference(cnf_transformation,[],[f30]) ).
fof(f57,plain,
! [X2,X0,X1] :
( lesseq(X1,X2)
| ~ ub(X0,X1,X2) ),
inference(cnf_transformation,[],[f30]) ).
fof(f58,plain,
! [X2,X0,X1] :
( ub(X0,X1,X2)
| ~ lesseq(X1,X2)
| ~ lesseq(X0,X2) ),
inference(cnf_transformation,[],[f30]) ).
fof(f59,plain,
! [X2,X0,X1] :
( max(X0,X1) = X2
| ~ model_max(X0,X1,X2) ),
inference(cnf_transformation,[],[f31]) ).
fof(f60,plain,
! [X2,X0,X1] :
( model_max(X0,X1,X2)
| max(X0,X1) != X2 ),
inference(cnf_transformation,[],[f31]) ).
fof(f61,plain,
! [X2,X0,X1] :
( ub(X0,X1,X2)
| ~ model_ub(X0,X1,X2) ),
inference(cnf_transformation,[],[f32]) ).
fof(f62,plain,
! [X2,X0,X1] :
( model_ub(X0,X1,X2)
| ~ ub(X0,X1,X2) ),
inference(cnf_transformation,[],[f32]) ).
fof(f63,plain,
! [X2,X0,X1] :
( model_max(X0,X1,X2)
| ~ minsol_model_max(X0,X1,X2) ),
inference(cnf_transformation,[],[f37]) ).
fof(f64,plain,
! [X2,X0,X1,X4] :
( lesseq(X2,X4)
| ~ model_max(X0,X1,X4)
| ~ minsol_model_max(X0,X1,X2) ),
inference(cnf_transformation,[],[f37]) ).
fof(f65,plain,
! [X2,X0,X1] :
( minsol_model_max(X0,X1,X2)
| model_max(X0,X1,sK0(X0,X1,X2))
| ~ model_max(X0,X1,X2) ),
inference(cnf_transformation,[],[f37]) ).
fof(f66,plain,
! [X2,X0,X1] :
( minsol_model_max(X0,X1,X2)
| ~ lesseq(X2,sK0(X0,X1,X2))
| ~ model_max(X0,X1,X2) ),
inference(cnf_transformation,[],[f37]) ).
fof(f67,plain,
! [X2,X0,X1] :
( model_ub(X0,X1,X2)
| ~ minsol_model_ub(X0,X1,X2) ),
inference(cnf_transformation,[],[f42]) ).
fof(f68,plain,
! [X2,X0,X1,X4] :
( lesseq(X2,X4)
| ~ model_ub(X0,X1,X4)
| ~ minsol_model_ub(X0,X1,X2) ),
inference(cnf_transformation,[],[f42]) ).
fof(f69,plain,
! [X2,X0,X1] :
( minsol_model_ub(X0,X1,X2)
| model_ub(X0,X1,sK1(X0,X1,X2))
| ~ model_ub(X0,X1,X2) ),
inference(cnf_transformation,[],[f42]) ).
fof(f70,plain,
! [X2,X0,X1] :
( minsol_model_ub(X0,X1,X2)
| ~ lesseq(X2,sK1(X0,X1,X2))
| ~ model_ub(X0,X1,X2) ),
inference(cnf_transformation,[],[f42]) ).
fof(f71,plain,
( minsol_model_max(sK2,sK3,sK4)
| minsol_model_ub(sK2,sK3,sK4) ),
inference(cnf_transformation,[],[f45]) ).
fof(f72,plain,
( ~ minsol_model_max(sK2,sK3,sK4)
| ~ minsol_model_ub(sK2,sK3,sK4) ),
inference(cnf_transformation,[],[f45]) ).
fof(f73,plain,
! [X0,X1] : model_max(X0,X1,max(X0,X1)),
inference(equality_resolution,[],[f60]) ).
cnf(c_49,plain,
lesseq(X0,X0),
inference(cnf_transformation,[],[f46]) ).
cnf(c_50,plain,
( ~ lesseq(X0,X1)
| ~ lesseq(X1,X2)
| lesseq(X0,X2) ),
inference(cnf_transformation,[],[f47]) ).
cnf(c_51,plain,
( ~ lesseq(X0,X1)
| ~ lesseq(X1,X0)
| X0 = X1 ),
inference(cnf_transformation,[],[f48]) ).
cnf(c_52,plain,
( lesseq(X0,X1)
| lesseq(X1,X0) ),
inference(cnf_transformation,[],[f49]) ).
cnf(c_55,plain,
( ~ lesseq(summation(X0),summation(X1))
| lesseq(X0,X1) ),
inference(cnf_transformation,[],[f53]) ).
cnf(c_57,plain,
( ~ lesseq(X0,X1)
| max(X1,X0) = X1 ),
inference(cnf_transformation,[],[f54]) ).
cnf(c_58,plain,
( ~ lesseq(X0,X1)
| max(X0,X1) = X1 ),
inference(cnf_transformation,[],[f55]) ).
cnf(c_59,plain,
( ~ lesseq(X0,X1)
| ~ lesseq(X2,X1)
| ub(X0,X2,X1) ),
inference(cnf_transformation,[],[f58]) ).
cnf(c_60,plain,
( ~ ub(X0,X1,X2)
| lesseq(X1,X2) ),
inference(cnf_transformation,[],[f57]) ).
cnf(c_61,plain,
( ~ ub(X0,X1,X2)
| lesseq(X0,X2) ),
inference(cnf_transformation,[],[f56]) ).
cnf(c_62,plain,
model_max(X0,X1,max(X0,X1)),
inference(cnf_transformation,[],[f73]) ).
cnf(c_63,plain,
( ~ model_max(X0,X1,X2)
| max(X0,X1) = X2 ),
inference(cnf_transformation,[],[f59]) ).
cnf(c_64,plain,
( ~ ub(X0,X1,X2)
| model_ub(X0,X1,X2) ),
inference(cnf_transformation,[],[f62]) ).
cnf(c_65,plain,
( ~ model_ub(X0,X1,X2)
| ub(X0,X1,X2) ),
inference(cnf_transformation,[],[f61]) ).
cnf(c_66,plain,
( ~ lesseq(X0,sK0(X1,X2,X0))
| ~ model_max(X1,X2,X0)
| minsol_model_max(X1,X2,X0) ),
inference(cnf_transformation,[],[f66]) ).
cnf(c_67,plain,
( ~ model_max(X0,X1,X2)
| model_max(X0,X1,sK0(X0,X1,X2))
| minsol_model_max(X0,X1,X2) ),
inference(cnf_transformation,[],[f65]) ).
cnf(c_68,plain,
( ~ model_max(X0,X1,X2)
| ~ minsol_model_max(X0,X1,X3)
| lesseq(X3,X2) ),
inference(cnf_transformation,[],[f64]) ).
cnf(c_69,plain,
( ~ minsol_model_max(X0,X1,X2)
| model_max(X0,X1,X2) ),
inference(cnf_transformation,[],[f63]) ).
cnf(c_70,plain,
( ~ lesseq(X0,sK1(X1,X2,X0))
| ~ model_ub(X1,X2,X0)
| minsol_model_ub(X1,X2,X0) ),
inference(cnf_transformation,[],[f70]) ).
cnf(c_71,plain,
( ~ model_ub(X0,X1,X2)
| model_ub(X0,X1,sK1(X0,X1,X2))
| minsol_model_ub(X0,X1,X2) ),
inference(cnf_transformation,[],[f69]) ).
cnf(c_72,plain,
( ~ model_ub(X0,X1,X2)
| ~ minsol_model_ub(X0,X1,X3)
| lesseq(X3,X2) ),
inference(cnf_transformation,[],[f68]) ).
cnf(c_73,plain,
( ~ minsol_model_ub(X0,X1,X2)
| model_ub(X0,X1,X2) ),
inference(cnf_transformation,[],[f67]) ).
cnf(c_74,negated_conjecture,
( ~ minsol_model_max(sK2,sK3,sK4)
| ~ minsol_model_ub(sK2,sK3,sK4) ),
inference(cnf_transformation,[],[f72]) ).
cnf(c_75,negated_conjecture,
( minsol_model_max(sK2,sK3,sK4)
| minsol_model_ub(sK2,sK3,sK4) ),
inference(cnf_transformation,[],[f71]) ).
cnf(c_76,plain,
lesseq(sK2,sK2),
inference(instantiation,[status(thm)],[c_49]) ).
cnf(c_87,plain,
( ~ lesseq(sK2,sK2)
| sK2 = sK2 ),
inference(instantiation,[status(thm)],[c_51]) ).
cnf(c_96,plain,
( model_ub(X0,X1,X2)
| ~ ub(X0,X1,X2) ),
inference(prop_impl_just,[status(thm)],[c_64]) ).
cnf(c_97,plain,
( ~ ub(X0,X1,X2)
| model_ub(X0,X1,X2) ),
inference(renaming,[status(thm)],[c_96]) ).
cnf(c_100,plain,
( ~ minsol_model_ub(sK2,sK3,sK4)
| ~ minsol_model_max(sK2,sK3,sK4) ),
inference(prop_impl_just,[status(thm)],[c_74]) ).
cnf(c_101,plain,
( ~ minsol_model_max(sK2,sK3,sK4)
| ~ minsol_model_ub(sK2,sK3,sK4) ),
inference(renaming,[status(thm)],[c_100]) ).
cnf(c_102,plain,
( minsol_model_ub(sK2,sK3,sK4)
| minsol_model_max(sK2,sK3,sK4) ),
inference(prop_impl_just,[status(thm)],[c_75]) ).
cnf(c_103,plain,
( minsol_model_max(sK2,sK3,sK4)
| minsol_model_ub(sK2,sK3,sK4) ),
inference(renaming,[status(thm)],[c_102]) ).
cnf(c_110,plain,
( lesseq(X0,X2)
| ~ model_ub(X0,X1,X2) ),
inference(prop_impl_just,[status(thm)],[c_61,c_65]) ).
cnf(c_111,plain,
( ~ model_ub(X0,X1,X2)
| lesseq(X0,X2) ),
inference(renaming,[status(thm)],[c_110]) ).
cnf(c_116,plain,
( lesseq(X1,X2)
| ~ model_ub(X0,X1,X2) ),
inference(prop_impl_just,[status(thm)],[c_60,c_65]) ).
cnf(c_117,plain,
( ~ model_ub(X0,X1,X2)
| lesseq(X1,X2) ),
inference(renaming,[status(thm)],[c_116]) ).
cnf(c_124,plain,
( model_max(X0,X1,X2)
| ~ minsol_model_max(X0,X1,X2) ),
inference(prop_impl_just,[status(thm)],[c_69]) ).
cnf(c_125,plain,
( ~ minsol_model_max(X0,X1,X2)
| model_max(X0,X1,X2) ),
inference(renaming,[status(thm)],[c_124]) ).
cnf(c_383,plain,
( X0 != X1
| X2 != X3
| X4 != X5
| ~ lesseq(X0,X2)
| ~ lesseq(X4,X2)
| model_ub(X1,X5,X3) ),
inference(resolution_lifted,[status(thm)],[c_59,c_97]) ).
cnf(c_384,plain,
( ~ lesseq(X0,X1)
| ~ lesseq(X2,X1)
| model_ub(X0,X2,X1) ),
inference(unflattening,[status(thm)],[c_383]) ).
cnf(c_417,plain,
( X0 != sK4
| X1 != sK2
| X2 != sK3
| ~ lesseq(X0,sK0(X1,X2,X0))
| ~ model_max(X1,X2,X0)
| ~ minsol_model_ub(sK2,sK3,sK4) ),
inference(resolution_lifted,[status(thm)],[c_66,c_101]) ).
cnf(c_418,plain,
( ~ lesseq(sK4,sK0(sK2,sK3,sK4))
| ~ model_max(sK2,sK3,sK4)
| ~ minsol_model_ub(sK2,sK3,sK4) ),
inference(unflattening,[status(thm)],[c_417]) ).
cnf(c_442,plain,
( X0 != sK2
| X1 != sK3
| X2 != sK4
| ~ model_max(X0,X1,X2)
| ~ minsol_model_ub(sK2,sK3,sK4)
| model_max(X0,X1,sK0(X0,X1,X2)) ),
inference(resolution_lifted,[status(thm)],[c_67,c_101]) ).
cnf(c_443,plain,
( ~ model_max(sK2,sK3,sK4)
| ~ minsol_model_ub(sK2,sK3,sK4)
| model_max(sK2,sK3,sK0(sK2,sK3,sK4)) ),
inference(unflattening,[status(thm)],[c_442]) ).
cnf(c_453,plain,
( X0 != sK2
| X1 != sK3
| X2 != sK4
| model_max(X0,X1,X2)
| minsol_model_ub(sK2,sK3,sK4) ),
inference(resolution_lifted,[status(thm)],[c_125,c_103]) ).
cnf(c_454,plain,
( model_max(sK2,sK3,sK4)
| minsol_model_ub(sK2,sK3,sK4) ),
inference(unflattening,[status(thm)],[c_453]) ).
cnf(c_461,plain,
( X0 != sK2
| X1 != sK3
| X2 != sK4
| ~ model_max(X0,X1,X3)
| minsol_model_ub(sK2,sK3,sK4)
| lesseq(X2,X3) ),
inference(resolution_lifted,[status(thm)],[c_68,c_103]) ).
cnf(c_462,plain,
( ~ model_max(sK2,sK3,X0)
| minsol_model_ub(sK2,sK3,sK4)
| lesseq(sK4,X0) ),
inference(unflattening,[status(thm)],[c_461]) ).
cnf(c_679,plain,
( lesseq(X0,X2)
| ~ model_ub(X0,X1,X2) ),
inference(prop_impl_just,[status(thm)],[c_111]) ).
cnf(c_680,plain,
( ~ model_ub(X0,X1,X2)
| lesseq(X0,X2) ),
inference(renaming,[status(thm)],[c_679]) ).
cnf(c_685,plain,
( lesseq(X1,X2)
| ~ model_ub(X0,X1,X2) ),
inference(prop_impl_just,[status(thm)],[c_117]) ).
cnf(c_686,plain,
( ~ model_ub(X0,X1,X2)
| lesseq(X1,X2) ),
inference(renaming,[status(thm)],[c_685]) ).
cnf(c_701,plain,
( minsol_model_ub(sK2,sK3,sK4)
| model_max(sK2,sK3,sK4) ),
inference(prop_impl_just,[status(thm)],[c_454]) ).
cnf(c_702,plain,
( model_max(sK2,sK3,sK4)
| minsol_model_ub(sK2,sK3,sK4) ),
inference(renaming,[status(thm)],[c_701]) ).
cnf(c_1119,plain,
X0 = X0,
theory(equality) ).
cnf(c_1121,plain,
( X0 != X1
| X2 != X1
| X2 = X0 ),
theory(equality) ).
cnf(c_1122,plain,
( X0 != X1
| X2 != X3
| ~ lesseq(X1,X3)
| lesseq(X0,X2) ),
theory(equality) ).
cnf(c_1123,plain,
( X0 != X1
| X2 != X3
| X4 != X5
| ~ model_max(X1,X3,X5)
| model_max(X0,X2,X4) ),
theory(equality) ).
cnf(c_1124,plain,
( X0 != X1
| ~ model_ub(X2,X3,X1)
| model_ub(X2,X3,X0) ),
theory(equality) ).
cnf(c_1126,plain,
( X0 != X1
| X2 != X3
| X4 != X5
| ~ minsol_model_ub(X1,X3,X5)
| minsol_model_ub(X0,X2,X4) ),
theory(equality) ).
cnf(c_1928,plain,
( ~ model_ub(sK2,sK3,sK4)
| model_ub(sK2,sK3,sK1(sK2,sK3,sK4))
| minsol_model_ub(sK2,sK3,sK4) ),
inference(instantiation,[status(thm)],[c_71]) ).
cnf(c_1929,plain,
( sK2 != X0
| sK3 != X1
| sK4 != X2
| ~ minsol_model_ub(X0,X1,X2)
| minsol_model_ub(sK2,sK3,sK4) ),
inference(instantiation,[status(thm)],[c_1126]) ).
cnf(c_1948,plain,
model_max(sK2,sK3,max(sK2,sK3)),
inference(instantiation,[status(thm)],[c_62]) ).
cnf(c_1949,plain,
( ~ model_max(sK2,sK3,max(sK2,sK3))
| lesseq(sK4,max(sK2,sK3))
| minsol_model_ub(sK2,sK3,sK4) ),
inference(instantiation,[status(thm)],[c_462]) ).
cnf(c_1994,plain,
( X0 != X1
| X2 != X3
| X4 != max(X1,X3)
| ~ model_max(X1,X3,max(X1,X3))
| model_max(X0,X2,X4) ),
inference(instantiation,[status(thm)],[c_1123]) ).
cnf(c_2032,plain,
( ~ lesseq(sK2,sK4)
| ~ lesseq(sK3,sK4)
| model_ub(sK2,sK3,sK4) ),
inference(instantiation,[status(thm)],[c_384]) ).
cnf(c_2033,plain,
( ~ minsol_model_ub(sK2,sK3,sK4)
| model_ub(sK2,sK3,sK4) ),
inference(instantiation,[status(thm)],[c_73]) ).
cnf(c_2042,plain,
( sK2 != X0
| sK3 != X1
| sK4 != sK4
| ~ minsol_model_ub(X0,X1,sK4)
| minsol_model_ub(sK2,sK3,sK4) ),
inference(instantiation,[status(thm)],[c_1929]) ).
cnf(c_2043,plain,
sK4 = sK4,
inference(instantiation,[status(thm)],[c_1119]) ).
cnf(c_2045,plain,
( X0 != X1
| sK4 != X1
| sK4 = X0 ),
inference(instantiation,[status(thm)],[c_1121]) ).
cnf(c_2076,plain,
( max(X0,X1) != X2
| X3 != X2
| X3 = max(X0,X1) ),
inference(instantiation,[status(thm)],[c_1121]) ).
cnf(c_2238,plain,
( ~ lesseq(summation(X0),summation(sK4))
| lesseq(X0,sK4) ),
inference(instantiation,[status(thm)],[c_55]) ).
cnf(c_2240,plain,
( X0 != X1
| sK4 != X2
| ~ lesseq(X1,X2)
| lesseq(X0,sK4) ),
inference(instantiation,[status(thm)],[c_1122]) ).
cnf(c_2241,plain,
( ~ lesseq(X0,X1)
| ~ lesseq(X1,sK4)
| lesseq(X0,sK4) ),
inference(instantiation,[status(thm)],[c_50]) ).
cnf(c_2248,plain,
( lesseq(X0,sK4)
| lesseq(sK4,X0) ),
inference(instantiation,[status(thm)],[c_52]) ).
cnf(c_2324,plain,
( X0 != sK4
| sK4 != sK4
| sK4 = X0 ),
inference(instantiation,[status(thm)],[c_2045]) ).
cnf(c_2326,plain,
( ~ lesseq(X0,sK3)
| ~ lesseq(sK3,X0)
| sK3 = X0 ),
inference(instantiation,[status(thm)],[c_51]) ).
cnf(c_2329,plain,
sK3 = sK3,
inference(instantiation,[status(thm)],[c_1119]) ).
cnf(c_2331,plain,
( X0 != X1
| sK3 != X1
| sK3 = X0 ),
inference(instantiation,[status(thm)],[c_1121]) ).
cnf(c_2402,plain,
( model_max(sK2,sK3,sK4)
| model_ub(sK2,sK3,sK4) ),
inference(resolution,[status(thm)],[c_73,c_702]) ).
cnf(c_2403,plain,
( sK2 != X0
| sK3 != X1
| sK4 != max(X0,X1)
| ~ model_max(X0,X1,max(X0,X1))
| model_max(sK2,sK3,sK4) ),
inference(instantiation,[status(thm)],[c_1994]) ).
cnf(c_2405,plain,
( X0 != max(X1,X2)
| sK2 != X1
| sK3 != X2
| ~ model_max(X1,X2,max(X1,X2))
| model_max(sK2,sK3,X0) ),
inference(instantiation,[status(thm)],[c_1994]) ).
cnf(c_2454,plain,
( ~ model_ub(sK2,sK3,X0)
| model_max(sK2,sK3,sK4)
| lesseq(sK4,X0) ),
inference(resolution,[status(thm)],[c_72,c_702]) ).
cnf(c_2491,plain,
( ~ lesseq(summation(sK4),summation(sK4))
| lesseq(sK4,sK4) ),
inference(instantiation,[status(thm)],[c_2238]) ).
cnf(c_2492,plain,
lesseq(summation(sK4),summation(sK4)),
inference(instantiation,[status(thm)],[c_49]) ).
cnf(c_2677,plain,
( ~ lesseq(X0,sK4)
| ~ lesseq(sK4,X0)
| X0 = sK4 ),
inference(instantiation,[status(thm)],[c_51]) ).
cnf(c_2678,plain,
( ~ lesseq(sK2,sK4)
| ~ lesseq(sK4,sK2)
| sK2 = sK4 ),
inference(instantiation,[status(thm)],[c_2677]) ).
cnf(c_2679,plain,
( max(sK4,X0) != sK4
| sK4 != sK4
| sK4 = max(sK4,X0) ),
inference(instantiation,[status(thm)],[c_2324]) ).
cnf(c_2680,plain,
( ~ lesseq(X0,sK4)
| max(sK4,X0) = sK4 ),
inference(instantiation,[status(thm)],[c_57]) ).
cnf(c_2683,plain,
( max(X0,sK4) != sK4
| sK4 != sK4
| sK4 = max(X0,sK4) ),
inference(instantiation,[status(thm)],[c_2324]) ).
cnf(c_2684,plain,
( ~ lesseq(X0,sK4)
| max(X0,sK4) = sK4 ),
inference(instantiation,[status(thm)],[c_58]) ).
cnf(c_2685,plain,
( max(sK2,sK4) != sK4
| sK4 != sK4
| sK4 = max(sK2,sK4) ),
inference(instantiation,[status(thm)],[c_2683]) ).
cnf(c_2686,plain,
( ~ lesseq(sK2,sK4)
| max(sK2,sK4) = sK4 ),
inference(instantiation,[status(thm)],[c_2684]) ).
cnf(c_2687,plain,
( max(X0,X1) != sK4
| sK4 != sK4
| sK4 = max(X0,X1) ),
inference(instantiation,[status(thm)],[c_2324]) ).
cnf(c_2688,plain,
( ~ model_max(X0,X1,sK4)
| max(X0,X1) = sK4 ),
inference(instantiation,[status(thm)],[c_63]) ).
cnf(c_2692,plain,
( X0 != X1
| sK4 != X1
| X0 = sK4 ),
inference(instantiation,[status(thm)],[c_1121]) ).
cnf(c_2851,plain,
( ~ lesseq(X0,X1)
| ~ lesseq(X1,sK3)
| lesseq(X0,sK3) ),
inference(instantiation,[status(thm)],[c_50]) ).
cnf(c_2858,plain,
( lesseq(X0,sK3)
| lesseq(sK3,X0) ),
inference(instantiation,[status(thm)],[c_52]) ).
cnf(c_2859,plain,
( lesseq(sK2,sK3)
| lesseq(sK3,sK2) ),
inference(instantiation,[status(thm)],[c_2858]) ).
cnf(c_2860,plain,
( ~ minsol_model_ub(X0,X1,X2)
| ~ model_ub(X0,X1,sK3)
| lesseq(X2,sK3) ),
inference(instantiation,[status(thm)],[c_72]) ).
cnf(c_2863,plain,
( ~ lesseq(sK3,sK4)
| ~ lesseq(sK4,sK3)
| sK3 = sK4 ),
inference(instantiation,[status(thm)],[c_2326]) ).
cnf(c_2864,plain,
( lesseq(sK3,sK4)
| lesseq(sK4,sK3) ),
inference(instantiation,[status(thm)],[c_2248]) ).
cnf(c_3085,plain,
( ~ model_ub(X0,X1,X2)
| lesseq(X1,sK1(X0,X1,X2))
| minsol_model_ub(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_71,c_686]) ).
cnf(c_3221,plain,
( ~ model_ub(X0,X1,X1)
| minsol_model_ub(X0,X1,X1) ),
inference(superposition,[status(thm)],[c_3085,c_70]) ).
cnf(c_3671,plain,
( ~ lesseq(X0,X1)
| ~ lesseq(X1,X1)
| minsol_model_ub(X0,X1,X1) ),
inference(superposition,[status(thm)],[c_384,c_3221]) ).
cnf(c_3673,plain,
( ~ lesseq(X0,X1)
| minsol_model_ub(X0,X1,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3671,c_49]) ).
cnf(c_3942,plain,
( X0 != sK3
| sK3 != sK3
| sK3 = X0 ),
inference(instantiation,[status(thm)],[c_2331]) ).
cnf(c_4021,plain,
( X0 != X1
| sK4 != sK4
| ~ lesseq(X1,sK4)
| lesseq(X0,sK4) ),
inference(instantiation,[status(thm)],[c_2240]) ).
cnf(c_4041,plain,
( X0 != max(X1,sK3)
| sK2 != X1
| sK3 != sK3
| ~ model_max(X1,sK3,max(X1,sK3))
| model_max(sK2,sK3,X0) ),
inference(instantiation,[status(thm)],[c_2405]) ).
cnf(c_4052,plain,
( ~ lesseq(sK4,sK1(sK2,sK3,sK4))
| ~ model_ub(sK2,sK3,sK4)
| minsol_model_ub(sK2,sK3,sK4) ),
inference(instantiation,[status(thm)],[c_70]) ).
cnf(c_4067,plain,
( ~ lesseq(sK2,X0)
| ~ lesseq(sK3,X0)
| model_ub(sK2,sK3,X0) ),
inference(instantiation,[status(thm)],[c_384]) ).
cnf(c_4071,plain,
( X0 != X1
| ~ model_ub(sK2,sK3,X1)
| model_ub(sK2,sK3,X0) ),
inference(instantiation,[status(thm)],[c_1124]) ).
cnf(c_4309,plain,
( ~ lesseq(X0,sK3)
| ~ lesseq(sK3,sK4)
| lesseq(X0,sK4) ),
inference(instantiation,[status(thm)],[c_2241]) ).
cnf(c_4335,plain,
( ~ lesseq(X0,max(sK2,sK3))
| ~ lesseq(max(sK2,sK3),sK4)
| lesseq(X0,sK4) ),
inference(instantiation,[status(thm)],[c_2241]) ).
cnf(c_4336,plain,
( ~ lesseq(max(sK2,sK3),sK4)
| ~ lesseq(sK2,max(sK2,sK3))
| lesseq(sK2,sK4) ),
inference(instantiation,[status(thm)],[c_4335]) ).
cnf(c_4534,plain,
( ~ lesseq(sK3,sK4)
| max(sK4,sK3) = sK4 ),
inference(instantiation,[status(thm)],[c_2680]) ).
cnf(c_4689,plain,
( max(X0,sK3) != sK3
| sK3 != sK3
| sK3 = max(X0,sK3) ),
inference(instantiation,[status(thm)],[c_3942]) ).
cnf(c_4690,plain,
( ~ lesseq(X0,sK3)
| max(X0,sK3) = sK3 ),
inference(instantiation,[status(thm)],[c_58]) ).
cnf(c_4691,plain,
( max(sK2,sK3) != sK3
| sK3 != sK3
| sK3 = max(sK2,sK3) ),
inference(instantiation,[status(thm)],[c_4689]) ).
cnf(c_4692,plain,
( ~ lesseq(sK2,sK3)
| max(sK2,sK3) = sK3 ),
inference(instantiation,[status(thm)],[c_4690]) ).
cnf(c_4708,plain,
( ~ lesseq(X0,X1)
| ~ lesseq(sK3,X0)
| lesseq(sK3,X1) ),
inference(instantiation,[status(thm)],[c_50]) ).
cnf(c_4952,plain,
( ~ lesseq(sK2,sK3)
| ~ lesseq(sK3,sK3)
| model_ub(sK2,sK3,sK3) ),
inference(instantiation,[status(thm)],[c_4067]) ).
cnf(c_4953,plain,
lesseq(sK3,sK3),
inference(instantiation,[status(thm)],[c_49]) ).
cnf(c_5207,plain,
( ~ model_max(sK2,sK3,sK4)
| max(sK2,sK3) = sK4 ),
inference(instantiation,[status(thm)],[c_2688]) ).
cnf(c_5266,plain,
( X0 != sK4
| model_ub(sK2,sK3,X0)
| model_max(sK2,sK3,sK4) ),
inference(resolution,[status(thm)],[c_1124,c_2402]) ).
cnf(c_5345,plain,
( X0 != sK4
| sK4 != sK4
| ~ lesseq(sK4,sK4)
| lesseq(X0,sK4) ),
inference(instantiation,[status(thm)],[c_4021]) ).
cnf(c_5347,plain,
( X0 != max(sK2,sK3)
| sK4 != sK4
| ~ lesseq(max(sK2,sK3),sK4)
| lesseq(X0,sK4) ),
inference(instantiation,[status(thm)],[c_4021]) ).
cnf(c_5348,plain,
( sK2 != max(sK2,sK3)
| sK4 != sK4
| ~ lesseq(max(sK2,sK3),sK4)
| lesseq(sK2,sK4) ),
inference(instantiation,[status(thm)],[c_5347]) ).
cnf(c_5592,plain,
( ~ lesseq(X0,sK4)
| ~ lesseq(sK4,sK3)
| lesseq(X0,sK3) ),
inference(instantiation,[status(thm)],[c_2851]) ).
cnf(c_5593,plain,
( ~ lesseq(sK2,sK4)
| ~ lesseq(sK4,sK3)
| lesseq(sK2,sK3) ),
inference(instantiation,[status(thm)],[c_5592]) ).
cnf(c_6018,plain,
( max(X0,sK3) != X1
| X2 != X1
| X2 = max(X0,sK3) ),
inference(instantiation,[status(thm)],[c_2076]) ).
cnf(c_6019,plain,
( max(sK2,sK3) != sK2
| sK2 != sK2
| sK2 = max(sK2,sK3) ),
inference(instantiation,[status(thm)],[c_6018]) ).
cnf(c_6441,plain,
( model_max(sK2,sK3,sK4)
| lesseq(sK2,sK4) ),
inference(resolution,[status(thm)],[c_680,c_2402]) ).
cnf(c_6585,plain,
( model_max(sK2,sK3,sK4)
| lesseq(sK3,sK4) ),
inference(resolution,[status(thm)],[c_686,c_2402]) ).
cnf(c_6586,plain,
( X0 != sK4
| model_max(sK2,sK3,sK4)
| lesseq(sK3,X0) ),
inference(resolution,[status(thm)],[c_686,c_5266]) ).
cnf(c_6698,plain,
( ~ minsol_model_ub(sK2,sK3,X0)
| ~ model_ub(sK2,sK3,sK3)
| lesseq(X0,sK3) ),
inference(instantiation,[status(thm)],[c_2860]) ).
cnf(c_6806,plain,
( ~ model_ub(X0,X1,sK1(X2,X3,X4))
| lesseq(X0,sK1(X2,X3,X4)) ),
inference(instantiation,[status(thm)],[c_680]) ).
cnf(c_7007,plain,
( ~ lesseq(X0,sK4)
| ~ lesseq(sK4,X0)
| model_max(sK2,sK3,sK4)
| lesseq(sK3,X0) ),
inference(resolution,[status(thm)],[c_6586,c_51]) ).
cnf(c_7411,plain,
( max(sK2,sK3) != sK4
| sK4 != sK4
| sK4 = max(sK2,sK3) ),
inference(instantiation,[status(thm)],[c_2687]) ).
cnf(c_7488,plain,
( max(sK2,sK3) != X0
| X1 != X2
| ~ lesseq(X2,X0)
| lesseq(X1,max(sK2,sK3)) ),
inference(instantiation,[status(thm)],[c_1122]) ).
cnf(c_7492,plain,
( max(sK2,sK3) != sK2
| sK2 != sK2
| ~ lesseq(sK2,sK2)
| lesseq(sK2,max(sK2,sK3)) ),
inference(instantiation,[status(thm)],[c_7488]) ).
cnf(c_7498,plain,
( ~ model_ub(X0,X1,max(sK2,sK3))
| ~ minsol_model_ub(X0,X1,X2)
| lesseq(X2,max(sK2,sK3)) ),
inference(instantiation,[status(thm)],[c_72]) ).
cnf(c_7756,plain,
( ~ model_ub(sK2,sK3,sK1(X0,X1,X2))
| lesseq(sK2,sK1(X0,X1,X2)) ),
inference(instantiation,[status(thm)],[c_6806]) ).
cnf(c_7889,plain,
( max(sK2,sK3) != sK4
| sK4 != sK4
| ~ lesseq(sK4,sK4)
| lesseq(max(sK2,sK3),sK4) ),
inference(instantiation,[status(thm)],[c_5345]) ).
cnf(c_8735,plain,
( max(sK4,sK3) != sK4
| sK4 != sK4
| sK4 = max(sK4,sK3) ),
inference(instantiation,[status(thm)],[c_2679]) ).
cnf(c_8736,plain,
( sK2 != sK4
| sK3 != sK3
| sK4 != max(sK4,sK3)
| ~ model_max(sK4,sK3,max(sK4,sK3))
| model_max(sK2,sK3,sK4) ),
inference(instantiation,[status(thm)],[c_4041]) ).
cnf(c_8824,plain,
( sK2 != X0
| sK3 != sK4
| sK4 != max(X0,sK4)
| ~ model_max(X0,sK4,max(X0,sK4))
| model_max(sK2,sK3,sK4) ),
inference(instantiation,[status(thm)],[c_2403]) ).
cnf(c_8825,plain,
( sK2 != sK2
| sK3 != sK4
| sK4 != max(sK2,sK4)
| ~ model_max(sK2,sK4,max(sK2,sK4))
| model_max(sK2,sK3,sK4) ),
inference(instantiation,[status(thm)],[c_8824]) ).
cnf(c_8962,plain,
( ~ lesseq(sK2,X0)
| ~ lesseq(sK3,X0)
| model_max(sK2,sK3,sK4)
| lesseq(sK4,X0) ),
inference(resolution,[status(thm)],[c_384,c_2454]) ).
cnf(c_8963,plain,
( ~ lesseq(sK2,sK2)
| ~ lesseq(sK3,sK2)
| model_max(sK2,sK3,sK4)
| lesseq(sK4,sK2) ),
inference(instantiation,[status(thm)],[c_8962]) ).
cnf(c_9304,plain,
( sK3 != max(sK2,sK3)
| sK4 != sK4
| ~ lesseq(max(sK2,sK3),sK4)
| lesseq(sK3,sK4) ),
inference(instantiation,[status(thm)],[c_5347]) ).
cnf(c_9512,plain,
( ~ lesseq(X0,X1)
| ~ lesseq(sK4,X0)
| lesseq(sK4,X1) ),
inference(instantiation,[status(thm)],[c_50]) ).
cnf(c_9650,plain,
( ~ model_ub(sK2,sK3,sK3)
| ~ minsol_model_ub(sK2,sK3,sK4)
| lesseq(sK4,sK3) ),
inference(instantiation,[status(thm)],[c_6698]) ).
cnf(c_9840,plain,
( ~ lesseq(sK4,X0)
| model_max(sK2,sK3,sK4)
| lesseq(sK3,X0) ),
inference(global_subsumption_just,[status(thm)],[c_7007,c_2858,c_4309,c_6585,c_7007]) ).
cnf(c_9865,plain,
( model_max(sK2,sK3,sK4)
| lesseq(X0,sK4)
| lesseq(sK3,X0) ),
inference(resolution,[status(thm)],[c_9840,c_52]) ).
cnf(c_10182,plain,
( ~ lesseq(X0,X1)
| model_max(sK2,sK3,sK4)
| lesseq(X0,sK4)
| lesseq(sK3,X1) ),
inference(resolution,[status(thm)],[c_9865,c_50]) ).
cnf(c_10281,plain,
( X0 != sK4
| ~ model_ub(sK2,sK3,sK4)
| model_ub(sK2,sK3,X0) ),
inference(instantiation,[status(thm)],[c_4071]) ).
cnf(c_10321,plain,
( ~ lesseq(sK4,X0)
| ~ lesseq(sK3,sK4)
| lesseq(sK3,X0) ),
inference(instantiation,[status(thm)],[c_4708]) ).
cnf(c_11707,plain,
( ~ lesseq(sK3,X0)
| max(X0,sK3) = X0 ),
inference(instantiation,[status(thm)],[c_57]) ).
cnf(c_11708,plain,
( ~ lesseq(sK3,sK2)
| max(sK2,sK3) = sK2 ),
inference(instantiation,[status(thm)],[c_11707]) ).
cnf(c_11711,plain,
( ~ model_max(X0,sK3,X1)
| max(X0,sK3) = X1 ),
inference(instantiation,[status(thm)],[c_63]) ).
cnf(c_12433,plain,
( ~ lesseq(X0,X1)
| lesseq(X0,sK4)
| lesseq(sK3,X1) ),
inference(global_subsumption_just,[status(thm)],[c_10182,c_76,c_87,c_2043,c_2248,c_2329,c_2491,c_2492,c_2859,c_2864,c_4691,c_4692,c_4708,c_5207,c_5348,c_5593,c_6019,c_6585,c_7889,c_9304,c_10321,c_11708]) ).
cnf(c_12435,plain,
( ~ lesseq(sK2,sK2)
| lesseq(sK2,sK4)
| lesseq(sK3,sK2) ),
inference(instantiation,[status(thm)],[c_12433]) ).
cnf(c_12450,plain,
( lesseq(X0,X1)
| lesseq(X1,sK4)
| lesseq(sK3,X0) ),
inference(resolution,[status(thm)],[c_12433,c_52]) ).
cnf(c_12845,plain,
( lesseq(sK3,sK4)
| lesseq(sK4,sK3) ),
inference(factoring,[status(thm)],[c_12450]) ).
cnf(c_13206,plain,
lesseq(sK3,sK4),
inference(global_subsumption_just,[status(thm)],[c_12845,c_76,c_87,c_2043,c_2329,c_2491,c_2492,c_2859,c_2864,c_4691,c_4692,c_5207,c_5348,c_5593,c_6019,c_6585,c_7889,c_9304,c_11708]) ).
cnf(c_14406,plain,
model_max(sK4,sK3,max(sK4,sK3)),
inference(instantiation,[status(thm)],[c_62]) ).
cnf(c_15650,plain,
( max(X0,sK3) != sK4
| ~ model_ub(sK2,sK3,sK4)
| model_ub(sK2,sK3,max(X0,sK3)) ),
inference(instantiation,[status(thm)],[c_10281]) ).
cnf(c_15651,plain,
( max(sK2,sK3) != sK4
| ~ model_ub(sK2,sK3,sK4)
| model_ub(sK2,sK3,max(sK2,sK3)) ),
inference(instantiation,[status(thm)],[c_15650]) ).
cnf(c_16985,plain,
( sK3 != X0
| sK4 != X0
| sK3 = sK4 ),
inference(instantiation,[status(thm)],[c_2692]) ).
cnf(c_18653,plain,
( ~ lesseq(X0,sK1(sK2,sK3,sK4))
| ~ lesseq(sK4,X0)
| lesseq(sK4,sK1(sK2,sK3,sK4)) ),
inference(instantiation,[status(thm)],[c_9512]) ).
cnf(c_18654,plain,
( ~ lesseq(sK2,sK1(sK2,sK3,sK4))
| ~ lesseq(sK4,sK2)
| lesseq(sK4,sK1(sK2,sK3,sK4)) ),
inference(instantiation,[status(thm)],[c_18653]) ).
cnf(c_21952,plain,
( ~ model_ub(sK2,sK3,sK1(sK2,sK3,sK4))
| lesseq(sK2,sK1(sK2,sK3,sK4)) ),
inference(instantiation,[status(thm)],[c_7756]) ).
cnf(c_23053,plain,
( ~ model_ub(X0,sK3,max(sK2,sK3))
| ~ minsol_model_ub(X0,sK3,X1)
| lesseq(X1,max(sK2,sK3)) ),
inference(instantiation,[status(thm)],[c_7498]) ).
cnf(c_25786,plain,
( sK2 != X0
| sK3 != sK4
| sK4 != sK4
| ~ minsol_model_ub(X0,sK4,sK4)
| minsol_model_ub(sK2,sK3,sK4) ),
inference(instantiation,[status(thm)],[c_2042]) ).
cnf(c_25793,plain,
( sK2 != sK2
| sK3 != sK4
| sK4 != sK4
| ~ minsol_model_ub(sK2,sK4,sK4)
| minsol_model_ub(sK2,sK3,sK4) ),
inference(instantiation,[status(thm)],[c_25786]) ).
cnf(c_38115,plain,
( sK3 != max(X0,sK3)
| sK4 != max(X0,sK3)
| sK3 = sK4 ),
inference(instantiation,[status(thm)],[c_16985]) ).
cnf(c_38116,plain,
( sK3 != max(sK2,sK3)
| sK4 != max(sK2,sK3)
| sK3 = sK4 ),
inference(instantiation,[status(thm)],[c_38115]) ).
cnf(c_42920,plain,
model_max(X0,sK4,max(X0,sK4)),
inference(instantiation,[status(thm)],[c_62]) ).
cnf(c_42921,plain,
model_max(sK2,sK4,max(sK2,sK4)),
inference(instantiation,[status(thm)],[c_42920]) ).
cnf(c_46790,plain,
( ~ lesseq(max(X0,sK3),X1)
| ~ lesseq(sK4,max(X0,sK3))
| lesseq(sK4,X1) ),
inference(instantiation,[status(thm)],[c_9512]) ).
cnf(c_46797,plain,
( ~ lesseq(max(sK2,sK3),sK2)
| ~ lesseq(sK4,max(sK2,sK3))
| lesseq(sK4,sK2) ),
inference(instantiation,[status(thm)],[c_46790]) ).
cnf(c_48322,plain,
( ~ model_ub(X0,sK3,max(sK2,sK3))
| ~ minsol_model_ub(X0,sK3,sK4)
| lesseq(sK4,max(sK2,sK3)) ),
inference(instantiation,[status(thm)],[c_23053]) ).
cnf(c_48323,plain,
( ~ model_ub(sK2,sK3,max(sK2,sK3))
| ~ minsol_model_ub(sK2,sK3,sK4)
| lesseq(sK4,max(sK2,sK3)) ),
inference(instantiation,[status(thm)],[c_48322]) ).
cnf(c_50455,plain,
( ~ model_max(sK2,sK3,sK0(sK2,sK3,sK4))
| max(sK2,sK3) = sK0(sK2,sK3,sK4) ),
inference(instantiation,[status(thm)],[c_11711]) ).
cnf(c_53749,plain,
( max(sK2,sK3) != X0
| X1 != X2
| ~ lesseq(X0,X2)
| lesseq(max(sK2,sK3),X1) ),
inference(instantiation,[status(thm)],[c_1122]) ).
cnf(c_53753,plain,
( max(sK2,sK3) != sK2
| sK2 != sK2
| ~ lesseq(sK2,sK2)
| lesseq(max(sK2,sK3),sK2) ),
inference(instantiation,[status(thm)],[c_53749]) ).
cnf(c_67466,plain,
( sK0(sK2,sK3,sK4) != X0
| sK4 != X1
| ~ lesseq(X1,X0)
| lesseq(sK4,sK0(sK2,sK3,sK4)) ),
inference(instantiation,[status(thm)],[c_1122]) ).
cnf(c_67542,plain,
( sK0(sK2,sK3,sK4) != X0
| sK4 != sK4
| ~ lesseq(sK4,X0)
| lesseq(sK4,sK0(sK2,sK3,sK4)) ),
inference(instantiation,[status(thm)],[c_67466]) ).
cnf(c_67704,plain,
( ~ lesseq(sK0(sK2,sK3,sK4),X0)
| ~ lesseq(X0,sK0(sK2,sK3,sK4))
| sK0(sK2,sK3,sK4) = X0 ),
inference(instantiation,[status(thm)],[c_51]) ).
cnf(c_67707,plain,
( sK0(sK2,sK3,sK4) != X0
| X1 != X0
| sK0(sK2,sK3,sK4) = X1 ),
inference(instantiation,[status(thm)],[c_1121]) ).
cnf(c_67798,plain,
lesseq(sK0(sK2,sK3,sK4),sK0(sK2,sK3,sK4)),
inference(instantiation,[status(thm)],[c_49]) ).
cnf(c_67860,plain,
( ~ lesseq(X0,sK4)
| minsol_model_ub(X0,sK4,sK4) ),
inference(instantiation,[status(thm)],[c_3673]) ).
cnf(c_67861,plain,
( ~ lesseq(sK2,sK4)
| minsol_model_ub(sK2,sK4,sK4) ),
inference(instantiation,[status(thm)],[c_67860]) ).
cnf(c_68370,plain,
( ~ lesseq(sK0(sK2,sK3,sK4),sK0(sK2,sK3,sK4))
| sK0(sK2,sK3,sK4) = sK0(sK2,sK3,sK4) ),
inference(instantiation,[status(thm)],[c_67704]) ).
cnf(c_68526,plain,
( sK0(sK2,sK3,sK4) != sK0(sK2,sK3,sK4)
| X0 != sK0(sK2,sK3,sK4)
| sK0(sK2,sK3,sK4) = X0 ),
inference(instantiation,[status(thm)],[c_67707]) ).
cnf(c_70072,plain,
( sK0(sK2,sK3,sK4) != sK0(sK2,sK3,sK4)
| max(X0,X1) != sK0(sK2,sK3,sK4)
| sK0(sK2,sK3,sK4) = max(X0,X1) ),
inference(instantiation,[status(thm)],[c_68526]) ).
cnf(c_97042,plain,
( sK0(sK2,sK3,sK4) != sK0(sK2,sK3,sK4)
| max(sK2,sK3) != sK0(sK2,sK3,sK4)
| sK0(sK2,sK3,sK4) = max(sK2,sK3) ),
inference(instantiation,[status(thm)],[c_70072]) ).
cnf(c_108182,plain,
( sK0(sK2,sK3,sK4) != max(sK2,sK3)
| sK4 != sK4
| ~ lesseq(sK4,max(sK2,sK3))
| lesseq(sK4,sK0(sK2,sK3,sK4)) ),
inference(instantiation,[status(thm)],[c_67542]) ).
cnf(c_109708,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_108182,c_97042,c_68370,c_67861,c_67798,c_53753,c_50455,c_48323,c_46797,c_42921,c_38116,c_25793,c_21952,c_18654,c_15651,c_14406,c_13206,c_12435,c_11708,c_9650,c_8963,c_8825,c_8736,c_8735,c_7889,c_7492,c_7411,c_6441,c_5207,c_4953,c_4952,c_4692,c_4691,c_4534,c_4336,c_4052,c_2863,c_2859,c_2686,c_2685,c_2678,c_2492,c_2491,c_2329,c_2043,c_2033,c_2032,c_1949,c_1948,c_1928,c_454,c_443,c_418,c_87,c_76]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : NUM858+1 : TPTP v8.1.2. Released v4.1.0.
% 0.06/0.13 % Command : run_iprover %s %d THM
% 0.13/0.34 % Computer : n005.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu May 2 19:31:26 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.19/0.47 Running first-order theorem proving
% 0.19/0.47 Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 69.29/10.26 % SZS status Started for theBenchmark.p
% 69.29/10.26 % SZS status Theorem for theBenchmark.p
% 69.29/10.26
% 69.29/10.26 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 69.29/10.26
% 69.29/10.26 ------ iProver source info
% 69.29/10.26
% 69.29/10.26 git: date: 2024-05-02 19:28:25 +0000
% 69.29/10.26 git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 69.29/10.26 git: non_committed_changes: false
% 69.29/10.26
% 69.29/10.26 ------ Parsing...
% 69.29/10.26 ------ Clausification by vclausify_rel & Parsing by iProver...
% 69.29/10.26
% 69.29/10.26 ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e
% 69.29/10.26
% 69.29/10.26 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 69.29/10.26
% 69.29/10.26 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 69.29/10.26 ------ Proving...
% 69.29/10.26 ------ Problem Properties
% 69.29/10.26
% 69.29/10.26
% 69.29/10.26 clauses 25
% 69.29/10.26 conjectures 0
% 69.29/10.26 EPR 11
% 69.29/10.26 Horn 20
% 69.29/10.26 unary 2
% 69.29/10.26 binary 12
% 69.29/10.26 lits 61
% 69.29/10.26 lits eq 4
% 69.29/10.26 fd_pure 0
% 69.29/10.26 fd_pseudo 0
% 69.29/10.26 fd_cond 0
% 69.29/10.26 fd_pseudo_cond 2
% 69.29/10.26 AC symbols 0
% 69.29/10.26
% 69.29/10.26 ------ Input Options Time Limit: Unbounded
% 69.29/10.26
% 69.29/10.26
% 69.29/10.26 ------
% 69.29/10.26 Current options:
% 69.29/10.26 ------
% 69.29/10.26
% 69.29/10.26
% 69.29/10.26
% 69.29/10.26
% 69.29/10.26 ------ Proving...
% 69.29/10.26
% 69.29/10.26
% 69.29/10.26 % SZS status Theorem for theBenchmark.p
% 69.29/10.26
% 69.29/10.26 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 69.29/10.26
% 69.29/10.26
%------------------------------------------------------------------------------