TSTP Solution File: NUM859+1 by iProver---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : NUM859+1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n022.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 56.53s 8.66s
% Output : CNFRefutation 56.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 23
% Syntax : Number of formulae : 258 ( 20 unt; 0 def)
% Number of atoms : 796 ( 169 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 953 ( 415 ~; 456 |; 57 &)
% ( 14 <=>; 10 =>; 0 <=; 1 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 492 ( 7 sgn 198 !; 22 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : lesseq(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lesseq_ref) ).
fof(f2,axiom,
! [X0,X1,X2] :
( ( lesseq(X1,X2)
& lesseq(X0,X1) )
=> lesseq(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lesseq_trans) ).
fof(f3,axiom,
! [X0,X1] :
( ( lesseq(X1,X0)
& lesseq(X0,X1) )
=> X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lesseq_antisymmetric) ).
fof(f4,axiom,
! [X0,X1] :
( lesseq(X1,X0)
| lesseq(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lesseq_total) ).
fof(f6,axiom,
! [X0,X1] :
( lesseq(X0,X1)
<=> lesseq(summation(X0),summation(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',summation_monotone) ).
fof(f7,axiom,
! [X0,X1] :
( ~ lesseq(X1,X0)
| max(X0,X1) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',max_1) ).
fof(f8,axiom,
! [X0,X1] :
( ~ lesseq(X0,X1)
| max(X0,X1) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',max_2) ).
fof(f9,axiom,
! [X0,X1,X2] :
( ub(X0,X1,X2)
<=> ( lesseq(X1,X2)
& lesseq(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ub) ).
fof(f10,axiom,
! [X0,X1,X3] :
( model_max(X0,X1,X3)
<=> lesseq(max(X0,X1),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',model_max_2) ).
fof(f11,axiom,
! [X0,X1,X3] :
( model_ub(X0,X1,X3)
<=> ? [X2] :
( lesseq(X2,X3)
& ub(X0,X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',model_ub_2) ).
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/sandbox/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/sandbox/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/sandbox/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)
<=> lesseq(max(X0,X1),X2) ),
inference(rectify,[],[f10]) ).
fof(f17,plain,
! [X0,X1,X2] :
( model_ub(X0,X1,X2)
<=> ? [X3] :
( lesseq(X3,X2)
& ub(X0,X1,X3) ) ),
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)
| ~ lesseq(max(X0,X1),X2) )
& ( lesseq(max(X0,X1),X2)
| ~ model_max(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f16]) ).
fof(f32,plain,
! [X0,X1,X2] :
( ( model_ub(X0,X1,X2)
| ! [X3] :
( ~ lesseq(X3,X2)
| ~ ub(X0,X1,X3) ) )
& ( ? [X3] :
( lesseq(X3,X2)
& ub(X0,X1,X3) )
| ~ model_ub(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f17]) ).
fof(f33,plain,
! [X0,X1,X2] :
( ( model_ub(X0,X1,X2)
| ! [X3] :
( ~ lesseq(X3,X2)
| ~ ub(X0,X1,X3) ) )
& ( ? [X4] :
( lesseq(X4,X2)
& ub(X0,X1,X4) )
| ~ model_ub(X0,X1,X2) ) ),
inference(rectify,[],[f32]) ).
fof(f34,plain,
! [X0,X1,X2] :
( ? [X4] :
( lesseq(X4,X2)
& ub(X0,X1,X4) )
=> ( lesseq(sK0(X0,X1,X2),X2)
& ub(X0,X1,sK0(X0,X1,X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f35,plain,
! [X0,X1,X2] :
( ( model_ub(X0,X1,X2)
| ! [X3] :
( ~ lesseq(X3,X2)
| ~ ub(X0,X1,X3) ) )
& ( ( lesseq(sK0(X0,X1,X2),X2)
& ub(X0,X1,sK0(X0,X1,X2)) )
| ~ model_ub(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f33,f34]) ).
fof(f36,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(f37,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,[],[f36]) ).
fof(f38,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,[],[f37]) ).
fof(f39,plain,
! [X0,X1,X2] :
( ? [X3] :
( ~ lesseq(X2,X3)
& model_max(X0,X1,X3) )
=> ( ~ lesseq(X2,sK1(X0,X1,X2))
& model_max(X0,X1,sK1(X0,X1,X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f40,plain,
! [X0,X1,X2] :
( ( minsol_model_max(X0,X1,X2)
| ( ~ lesseq(X2,sK1(X0,X1,X2))
& model_max(X0,X1,sK1(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,[sK1])],[f38,f39]) ).
fof(f41,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(f42,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,[],[f41]) ).
fof(f43,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,[],[f42]) ).
fof(f44,plain,
! [X0,X1,X2] :
( ? [X3] :
( ~ lesseq(X2,X3)
& model_ub(X0,X1,X3) )
=> ( ~ lesseq(X2,sK2(X0,X1,X2))
& model_ub(X0,X1,sK2(X0,X1,X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f45,plain,
! [X0,X1,X2] :
( ( minsol_model_ub(X0,X1,X2)
| ( ~ lesseq(X2,sK2(X0,X1,X2))
& model_ub(X0,X1,sK2(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,[sK2])],[f43,f44]) ).
fof(f46,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(f47,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(sK3,sK4,sK5)
| ~ minsol_model_ub(sK3,sK4,sK5) )
& ( minsol_model_max(sK3,sK4,sK5)
| minsol_model_ub(sK3,sK4,sK5) ) ) ),
introduced(choice_axiom,[]) ).
fof(f48,plain,
( ( ~ minsol_model_max(sK3,sK4,sK5)
| ~ minsol_model_ub(sK3,sK4,sK5) )
& ( minsol_model_max(sK3,sK4,sK5)
| minsol_model_ub(sK3,sK4,sK5) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5])],[f46,f47]) ).
fof(f49,plain,
! [X0] : lesseq(X0,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f50,plain,
! [X2,X0,X1] :
( lesseq(X0,X2)
| ~ lesseq(X1,X2)
| ~ lesseq(X0,X1) ),
inference(cnf_transformation,[],[f21]) ).
fof(f51,plain,
! [X0,X1] :
( X0 = X1
| ~ lesseq(X1,X0)
| ~ lesseq(X0,X1) ),
inference(cnf_transformation,[],[f23]) ).
fof(f52,plain,
! [X0,X1] :
( lesseq(X1,X0)
| lesseq(X0,X1) ),
inference(cnf_transformation,[],[f4]) ).
fof(f56,plain,
! [X0,X1] :
( lesseq(X0,X1)
| ~ lesseq(summation(X0),summation(X1)) ),
inference(cnf_transformation,[],[f28]) ).
fof(f57,plain,
! [X0,X1] :
( ~ lesseq(X1,X0)
| max(X0,X1) = X0 ),
inference(cnf_transformation,[],[f7]) ).
fof(f58,plain,
! [X0,X1] :
( ~ lesseq(X0,X1)
| max(X0,X1) = X1 ),
inference(cnf_transformation,[],[f8]) ).
fof(f59,plain,
! [X2,X0,X1] :
( lesseq(X0,X2)
| ~ ub(X0,X1,X2) ),
inference(cnf_transformation,[],[f30]) ).
fof(f60,plain,
! [X2,X0,X1] :
( lesseq(X1,X2)
| ~ ub(X0,X1,X2) ),
inference(cnf_transformation,[],[f30]) ).
fof(f61,plain,
! [X2,X0,X1] :
( ub(X0,X1,X2)
| ~ lesseq(X1,X2)
| ~ lesseq(X0,X2) ),
inference(cnf_transformation,[],[f30]) ).
fof(f62,plain,
! [X2,X0,X1] :
( lesseq(max(X0,X1),X2)
| ~ model_max(X0,X1,X2) ),
inference(cnf_transformation,[],[f31]) ).
fof(f63,plain,
! [X2,X0,X1] :
( model_max(X0,X1,X2)
| ~ lesseq(max(X0,X1),X2) ),
inference(cnf_transformation,[],[f31]) ).
fof(f64,plain,
! [X2,X0,X1] :
( ub(X0,X1,sK0(X0,X1,X2))
| ~ model_ub(X0,X1,X2) ),
inference(cnf_transformation,[],[f35]) ).
fof(f65,plain,
! [X2,X0,X1] :
( lesseq(sK0(X0,X1,X2),X2)
| ~ model_ub(X0,X1,X2) ),
inference(cnf_transformation,[],[f35]) ).
fof(f66,plain,
! [X2,X3,X0,X1] :
( model_ub(X0,X1,X2)
| ~ lesseq(X3,X2)
| ~ ub(X0,X1,X3) ),
inference(cnf_transformation,[],[f35]) ).
fof(f67,plain,
! [X2,X0,X1] :
( model_max(X0,X1,X2)
| ~ minsol_model_max(X0,X1,X2) ),
inference(cnf_transformation,[],[f40]) ).
fof(f68,plain,
! [X2,X0,X1,X4] :
( lesseq(X2,X4)
| ~ model_max(X0,X1,X4)
| ~ minsol_model_max(X0,X1,X2) ),
inference(cnf_transformation,[],[f40]) ).
fof(f69,plain,
! [X2,X0,X1] :
( minsol_model_max(X0,X1,X2)
| model_max(X0,X1,sK1(X0,X1,X2))
| ~ model_max(X0,X1,X2) ),
inference(cnf_transformation,[],[f40]) ).
fof(f70,plain,
! [X2,X0,X1] :
( minsol_model_max(X0,X1,X2)
| ~ lesseq(X2,sK1(X0,X1,X2))
| ~ model_max(X0,X1,X2) ),
inference(cnf_transformation,[],[f40]) ).
fof(f71,plain,
! [X2,X0,X1] :
( model_ub(X0,X1,X2)
| ~ minsol_model_ub(X0,X1,X2) ),
inference(cnf_transformation,[],[f45]) ).
fof(f72,plain,
! [X2,X0,X1,X4] :
( lesseq(X2,X4)
| ~ model_ub(X0,X1,X4)
| ~ minsol_model_ub(X0,X1,X2) ),
inference(cnf_transformation,[],[f45]) ).
fof(f73,plain,
! [X2,X0,X1] :
( minsol_model_ub(X0,X1,X2)
| model_ub(X0,X1,sK2(X0,X1,X2))
| ~ model_ub(X0,X1,X2) ),
inference(cnf_transformation,[],[f45]) ).
fof(f74,plain,
! [X2,X0,X1] :
( minsol_model_ub(X0,X1,X2)
| ~ lesseq(X2,sK2(X0,X1,X2))
| ~ model_ub(X0,X1,X2) ),
inference(cnf_transformation,[],[f45]) ).
fof(f75,plain,
( minsol_model_max(sK3,sK4,sK5)
| minsol_model_ub(sK3,sK4,sK5) ),
inference(cnf_transformation,[],[f48]) ).
fof(f76,plain,
( ~ minsol_model_max(sK3,sK4,sK5)
| ~ minsol_model_ub(sK3,sK4,sK5) ),
inference(cnf_transformation,[],[f48]) ).
cnf(c_49,plain,
lesseq(X0,X0),
inference(cnf_transformation,[],[f49]) ).
cnf(c_50,plain,
( ~ lesseq(X0,X1)
| ~ lesseq(X1,X2)
| lesseq(X0,X2) ),
inference(cnf_transformation,[],[f50]) ).
cnf(c_51,plain,
( ~ lesseq(X0,X1)
| ~ lesseq(X1,X0)
| X0 = X1 ),
inference(cnf_transformation,[],[f51]) ).
cnf(c_52,plain,
( lesseq(X0,X1)
| lesseq(X1,X0) ),
inference(cnf_transformation,[],[f52]) ).
cnf(c_55,plain,
( ~ lesseq(summation(X0),summation(X1))
| lesseq(X0,X1) ),
inference(cnf_transformation,[],[f56]) ).
cnf(c_57,plain,
( ~ lesseq(X0,X1)
| max(X1,X0) = X1 ),
inference(cnf_transformation,[],[f57]) ).
cnf(c_58,plain,
( ~ lesseq(X0,X1)
| max(X0,X1) = X1 ),
inference(cnf_transformation,[],[f58]) ).
cnf(c_59,plain,
( ~ lesseq(X0,X1)
| ~ lesseq(X2,X1)
| ub(X0,X2,X1) ),
inference(cnf_transformation,[],[f61]) ).
cnf(c_60,plain,
( ~ ub(X0,X1,X2)
| lesseq(X1,X2) ),
inference(cnf_transformation,[],[f60]) ).
cnf(c_61,plain,
( ~ ub(X0,X1,X2)
| lesseq(X0,X2) ),
inference(cnf_transformation,[],[f59]) ).
cnf(c_62,plain,
( ~ lesseq(max(X0,X1),X2)
| model_max(X0,X1,X2) ),
inference(cnf_transformation,[],[f63]) ).
cnf(c_63,plain,
( ~ model_max(X0,X1,X2)
| lesseq(max(X0,X1),X2) ),
inference(cnf_transformation,[],[f62]) ).
cnf(c_64,plain,
( ~ ub(X0,X1,X2)
| ~ lesseq(X2,X3)
| model_ub(X0,X1,X3) ),
inference(cnf_transformation,[],[f66]) ).
cnf(c_65,plain,
( ~ model_ub(X0,X1,X2)
| lesseq(sK0(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f65]) ).
cnf(c_66,plain,
( ~ model_ub(X0,X1,X2)
| ub(X0,X1,sK0(X0,X1,X2)) ),
inference(cnf_transformation,[],[f64]) ).
cnf(c_67,plain,
( ~ lesseq(X0,sK1(X1,X2,X0))
| ~ model_max(X1,X2,X0)
| minsol_model_max(X1,X2,X0) ),
inference(cnf_transformation,[],[f70]) ).
cnf(c_68,plain,
( ~ model_max(X0,X1,X2)
| model_max(X0,X1,sK1(X0,X1,X2))
| minsol_model_max(X0,X1,X2) ),
inference(cnf_transformation,[],[f69]) ).
cnf(c_69,plain,
( ~ model_max(X0,X1,X2)
| ~ minsol_model_max(X0,X1,X3)
| lesseq(X3,X2) ),
inference(cnf_transformation,[],[f68]) ).
cnf(c_70,plain,
( ~ minsol_model_max(X0,X1,X2)
| model_max(X0,X1,X2) ),
inference(cnf_transformation,[],[f67]) ).
cnf(c_71,plain,
( ~ lesseq(X0,sK2(X1,X2,X0))
| ~ model_ub(X1,X2,X0)
| minsol_model_ub(X1,X2,X0) ),
inference(cnf_transformation,[],[f74]) ).
cnf(c_72,plain,
( ~ model_ub(X0,X1,X2)
| model_ub(X0,X1,sK2(X0,X1,X2))
| minsol_model_ub(X0,X1,X2) ),
inference(cnf_transformation,[],[f73]) ).
cnf(c_73,plain,
( ~ model_ub(X0,X1,X2)
| ~ minsol_model_ub(X0,X1,X3)
| lesseq(X3,X2) ),
inference(cnf_transformation,[],[f72]) ).
cnf(c_74,plain,
( ~ minsol_model_ub(X0,X1,X2)
| model_ub(X0,X1,X2) ),
inference(cnf_transformation,[],[f71]) ).
cnf(c_75,negated_conjecture,
( ~ minsol_model_max(sK3,sK4,sK5)
| ~ minsol_model_ub(sK3,sK4,sK5) ),
inference(cnf_transformation,[],[f76]) ).
cnf(c_76,negated_conjecture,
( minsol_model_max(sK3,sK4,sK5)
| minsol_model_ub(sK3,sK4,sK5) ),
inference(cnf_transformation,[],[f75]) ).
cnf(c_77,plain,
lesseq(sK3,sK3),
inference(instantiation,[status(thm)],[c_49]) ).
cnf(c_88,plain,
( ~ lesseq(sK3,sK3)
| sK3 = sK3 ),
inference(instantiation,[status(thm)],[c_51]) ).
cnf(c_103,plain,
X0 = X0,
theory(equality) ).
cnf(c_105,plain,
( X0 != X1
| X2 != X1
| X2 = X0 ),
theory(equality) ).
cnf(c_106,plain,
( X0 != X1
| X2 != X3
| ~ lesseq(X1,X3)
| lesseq(X0,X2) ),
theory(equality) ).
cnf(c_109,plain,
( X0 != X1
| ~ model_ub(X2,X3,X1)
| model_ub(X2,X3,X0) ),
theory(equality) ).
cnf(c_110,plain,
( X0 != X1
| X2 != X3
| X4 != X5
| ~ minsol_model_max(X1,X3,X5)
| minsol_model_max(X0,X2,X4) ),
theory(equality) ).
cnf(c_111,plain,
( X0 != X1
| X2 != X3
| X4 != X5
| ~ minsol_model_ub(X1,X3,X5)
| minsol_model_ub(X0,X2,X4) ),
theory(equality) ).
cnf(c_119,plain,
( ~ lesseq(sK5,sK2(sK3,sK4,sK5))
| ~ model_ub(sK3,sK4,sK5)
| minsol_model_ub(sK3,sK4,sK5) ),
inference(instantiation,[status(thm)],[c_71]) ).
cnf(c_120,plain,
( ~ model_ub(sK3,sK4,sK5)
| model_ub(sK3,sK4,sK2(sK3,sK4,sK5))
| minsol_model_ub(sK3,sK4,sK5) ),
inference(instantiation,[status(thm)],[c_72]) ).
cnf(c_125,plain,
( ~ lesseq(max(X0,X1),max(X0,X1))
| model_max(X0,X1,max(X0,X1)) ),
inference(instantiation,[status(thm)],[c_62]) ).
cnf(c_126,plain,
lesseq(max(X0,X1),max(X0,X1)),
inference(instantiation,[status(thm)],[c_49]) ).
cnf(c_131,plain,
( ~ lesseq(max(X0,X1),X2)
| ~ lesseq(X2,X3)
| lesseq(max(X0,X1),X3) ),
inference(instantiation,[status(thm)],[c_50]) ).
cnf(c_143,plain,
( max(X0,X1) != X2
| X3 != X4
| ~ lesseq(X2,X4)
| lesseq(max(X0,X1),X3) ),
inference(instantiation,[status(thm)],[c_106]) ).
cnf(c_145,plain,
( ~ model_max(sK3,sK4,sK5)
| lesseq(max(sK3,sK4),sK5) ),
inference(instantiation,[status(thm)],[c_63]) ).
cnf(c_146,plain,
( ~ model_max(sK3,sK4,sK5)
| model_max(sK3,sK4,sK1(sK3,sK4,sK5))
| minsol_model_max(sK3,sK4,sK5) ),
inference(instantiation,[status(thm)],[c_68]) ).
cnf(c_147,plain,
( ~ lesseq(sK5,sK1(sK3,sK4,sK5))
| ~ model_max(sK3,sK4,sK5)
| minsol_model_max(sK3,sK4,sK5) ),
inference(instantiation,[status(thm)],[c_67]) ).
cnf(c_154,plain,
( ~ lesseq(X0,sK5)
| ~ lesseq(sK5,X0)
| sK5 = X0 ),
inference(instantiation,[status(thm)],[c_51]) ).
cnf(c_155,plain,
( ~ lesseq(sK3,sK5)
| ~ lesseq(sK5,sK3)
| sK5 = sK3 ),
inference(instantiation,[status(thm)],[c_154]) ).
cnf(c_157,plain,
sK5 = sK5,
inference(instantiation,[status(thm)],[c_103]) ).
cnf(c_159,plain,
( X0 != X1
| sK5 != X1
| sK5 = X0 ),
inference(instantiation,[status(thm)],[c_105]) ).
cnf(c_161,plain,
( ~ lesseq(max(sK3,sK4),sK5)
| model_max(sK3,sK4,sK5) ),
inference(instantiation,[status(thm)],[c_62]) ).
cnf(c_178,plain,
( ~ lesseq(summation(sK5),summation(X0))
| lesseq(sK5,X0) ),
inference(instantiation,[status(thm)],[c_55]) ).
cnf(c_180,plain,
( X0 != X1
| sK5 != X2
| ~ lesseq(X2,X1)
| lesseq(sK5,X0) ),
inference(instantiation,[status(thm)],[c_106]) ).
cnf(c_181,plain,
( ~ lesseq(X0,X1)
| ~ lesseq(sK5,X0)
| lesseq(sK5,X1) ),
inference(instantiation,[status(thm)],[c_50]) ).
cnf(c_184,plain,
( sK3 != sK3
| sK5 != sK3
| ~ lesseq(sK3,sK3)
| lesseq(sK5,sK3) ),
inference(instantiation,[status(thm)],[c_180]) ).
cnf(c_191,plain,
( ~ model_ub(X0,X1,X2)
| ~ minsol_model_ub(X0,X1,sK5)
| lesseq(sK5,X2) ),
inference(instantiation,[status(thm)],[c_73]) ).
cnf(c_192,plain,
( ~ model_max(X0,X1,X2)
| ~ minsol_model_max(X0,X1,sK5)
| lesseq(sK5,X2) ),
inference(instantiation,[status(thm)],[c_69]) ).
cnf(c_198,plain,
sK4 = sK4,
inference(instantiation,[status(thm)],[c_103]) ).
cnf(c_199,plain,
( X0 != X1
| sK4 != X1
| sK4 = X0 ),
inference(instantiation,[status(thm)],[c_105]) ).
cnf(c_218,plain,
( max(sK3,sK4) != X0
| sK5 != X1
| ~ lesseq(X0,X1)
| lesseq(max(sK3,sK4),sK5) ),
inference(instantiation,[status(thm)],[c_143]) ).
cnf(c_237,plain,
( ~ lesseq(summation(sK5),summation(sK5))
| lesseq(sK5,sK5) ),
inference(instantiation,[status(thm)],[c_178]) ).
cnf(c_238,plain,
lesseq(summation(sK5),summation(sK5)),
inference(instantiation,[status(thm)],[c_49]) ).
cnf(c_276,plain,
( X0 != X1
| sK5 != X1
| X0 = sK5 ),
inference(instantiation,[status(thm)],[c_105]) ).
cnf(c_316,plain,
( model_ub(sK3,sK4,sK5)
| minsol_model_max(sK3,sK4,sK5) ),
inference(resolution,[status(thm)],[c_74,c_76]) ).
cnf(c_318,plain,
( ~ lesseq(summation(sK4),summation(X0))
| lesseq(sK4,X0) ),
inference(instantiation,[status(thm)],[c_55]) ).
cnf(c_320,plain,
( X0 != X1
| sK4 != X2
| ~ lesseq(X2,X1)
| lesseq(sK4,X0) ),
inference(instantiation,[status(thm)],[c_106]) ).
cnf(c_329,plain,
( lesseq(X0,sK4)
| lesseq(sK4,X0) ),
inference(instantiation,[status(thm)],[c_52]) ).
cnf(c_330,plain,
( lesseq(sK3,sK4)
| lesseq(sK4,sK3) ),
inference(instantiation,[status(thm)],[c_329]) ).
cnf(c_374,plain,
( model_max(sK3,sK4,sK5)
| model_ub(sK3,sK4,sK5) ),
inference(resolution,[status(thm)],[c_70,c_316]) ).
cnf(c_391,plain,
( ~ model_ub(sK3,sK4,X0)
| minsol_model_max(sK3,sK4,sK5)
| lesseq(sK5,X0) ),
inference(resolution,[status(thm)],[c_73,c_76]) ).
cnf(c_392,plain,
( ~ model_ub(sK3,sK4,sK3)
| minsol_model_max(sK3,sK4,sK5)
| lesseq(sK5,sK3) ),
inference(instantiation,[status(thm)],[c_391]) ).
cnf(c_397,plain,
( X0 != sK4
| sK4 != sK4
| sK4 = X0 ),
inference(instantiation,[status(thm)],[c_199]) ).
cnf(c_403,plain,
( X0 != X1
| sK5 != sK5
| ~ lesseq(sK5,X1)
| lesseq(sK5,X0) ),
inference(instantiation,[status(thm)],[c_180]) ).
cnf(c_415,plain,
( ~ model_ub(sK3,sK4,X0)
| ~ minsol_model_ub(sK3,sK4,sK5)
| lesseq(sK5,X0) ),
inference(instantiation,[status(thm)],[c_191]) ).
cnf(c_500,plain,
( ~ ub(sK3,sK4,X0)
| ~ lesseq(X0,X1)
| model_ub(sK3,sK4,X1) ),
inference(instantiation,[status(thm)],[c_64]) ).
cnf(c_501,plain,
( ~ ub(sK3,sK4,sK3)
| ~ lesseq(sK3,sK3)
| model_ub(sK3,sK4,sK3) ),
inference(instantiation,[status(thm)],[c_500]) ).
cnf(c_504,plain,
( X0 != X1
| ~ model_ub(sK3,sK4,X1)
| model_ub(sK3,sK4,X0) ),
inference(instantiation,[status(thm)],[c_109]) ).
cnf(c_511,plain,
( ~ model_ub(sK3,sK4,X0)
| lesseq(sK5,sK2(sK3,sK4,X0))
| minsol_model_ub(sK3,sK4,X0)
| minsol_model_max(sK3,sK4,sK5) ),
inference(resolution,[status(thm)],[c_72,c_391]) ).
cnf(c_527,plain,
( ~ lesseq(max(X0,X1),sK5)
| ~ lesseq(sK5,max(X0,X1))
| sK5 = max(X0,X1) ),
inference(instantiation,[status(thm)],[c_154]) ).
cnf(c_567,plain,
( X0 != sK3
| X1 != sK4
| X2 != sK5
| minsol_model_max(X0,X1,X2)
| model_ub(sK3,sK4,sK5) ),
inference(resolution,[status(thm)],[c_110,c_316]) ).
cnf(c_579,plain,
( X0 != sK3
| X1 != sK4
| X2 != sK5
| model_max(X0,X1,X2)
| model_ub(sK3,sK4,sK5) ),
inference(resolution,[status(thm)],[c_567,c_70]) ).
cnf(c_585,plain,
( ~ lesseq(X0,sK1(sK3,sK4,sK5))
| ~ lesseq(sK5,X0)
| lesseq(sK5,sK1(sK3,sK4,sK5)) ),
inference(instantiation,[status(thm)],[c_181]) ).
cnf(c_618,plain,
( ~ lesseq(sK4,sK5)
| ~ lesseq(sK5,sK4)
| sK5 = sK4 ),
inference(instantiation,[status(thm)],[c_154]) ).
cnf(c_728,plain,
( ~ lesseq(summation(sK4),summation(sK4))
| lesseq(sK4,sK4) ),
inference(instantiation,[status(thm)],[c_318]) ).
cnf(c_729,plain,
lesseq(summation(sK4),summation(sK4)),
inference(instantiation,[status(thm)],[c_49]) ).
cnf(c_780,plain,
( max(X0,sK4) != sK4
| sK4 != sK4
| sK4 = max(X0,sK4) ),
inference(instantiation,[status(thm)],[c_397]) ).
cnf(c_781,plain,
( ~ lesseq(X0,sK4)
| max(X0,sK4) = sK4 ),
inference(instantiation,[status(thm)],[c_58]) ).
cnf(c_782,plain,
( max(sK3,sK4) != sK4
| sK4 != sK4
| sK4 = max(sK3,sK4) ),
inference(instantiation,[status(thm)],[c_780]) ).
cnf(c_783,plain,
( ~ lesseq(sK3,sK4)
| max(sK3,sK4) = sK4 ),
inference(instantiation,[status(thm)],[c_781]) ).
cnf(c_809,plain,
( ~ model_max(sK3,sK4,X0)
| model_ub(sK3,sK4,sK5)
| lesseq(sK5,X0) ),
inference(resolution,[status(thm)],[c_69,c_316]) ).
cnf(c_873,plain,
( ~ lesseq(X0,X1)
| ~ lesseq(sK4,X1)
| ub(X0,sK4,X1) ),
inference(instantiation,[status(thm)],[c_59]) ).
cnf(c_874,plain,
( ~ lesseq(sK3,sK3)
| ~ lesseq(sK4,sK3)
| ub(sK3,sK4,sK3) ),
inference(instantiation,[status(thm)],[c_873]) ).
cnf(c_898,plain,
( lesseq(summation(X0),summation(X1))
| lesseq(X1,X0) ),
inference(resolution,[status(thm)],[c_55,c_52]) ).
cnf(c_1001,plain,
model_max(X0,X1,max(X0,X1)),
inference(resolution,[status(thm)],[c_62,c_49]) ).
cnf(c_1235,plain,
( X0 != X1
| sK4 != X2
| ~ lesseq(X1,X2)
| lesseq(X0,sK4) ),
inference(instantiation,[status(thm)],[c_106]) ).
cnf(c_1321,plain,
( X0 != sK5
| sK5 != sK5
| ~ lesseq(sK5,sK5)
| lesseq(sK5,X0) ),
inference(instantiation,[status(thm)],[c_403]) ).
cnf(c_1378,plain,
( ~ model_max(X0,sK4,X1)
| ~ minsol_model_max(X0,sK4,sK5)
| lesseq(sK5,X1) ),
inference(instantiation,[status(thm)],[c_192]) ).
cnf(c_1519,plain,
( sK4 != X0
| sK5 != X0
| sK5 = sK4 ),
inference(instantiation,[status(thm)],[c_159]) ).
cnf(c_1520,plain,
( sK4 != sK4
| sK5 != sK4
| sK4 = sK5 ),
inference(instantiation,[status(thm)],[c_397]) ).
cnf(c_1626,plain,
( ~ lesseq(max(sK3,sK4),max(sK3,sK4))
| model_max(sK3,sK4,max(sK3,sK4)) ),
inference(instantiation,[status(thm)],[c_125]) ).
cnf(c_1681,plain,
( sK2(sK3,sK4,sK5) != X0
| sK5 != X1
| ~ lesseq(X1,X0)
| lesseq(sK5,sK2(sK3,sK4,sK5)) ),
inference(instantiation,[status(thm)],[c_180]) ).
cnf(c_1737,plain,
( ~ lesseq(max(sK3,sK4),sK5)
| ~ lesseq(sK5,max(sK3,sK4))
| sK5 = max(sK3,sK4) ),
inference(instantiation,[status(thm)],[c_527]) ).
cnf(c_1756,plain,
( ~ model_max(sK3,sK4,X0)
| lesseq(max(sK3,sK4),X0) ),
inference(instantiation,[status(thm)],[c_63]) ).
cnf(c_1764,plain,
( ~ lesseq(max(sK3,sK4),X0)
| ~ lesseq(X0,X1)
| lesseq(max(sK3,sK4),X1) ),
inference(instantiation,[status(thm)],[c_131]) ).
cnf(c_1890,plain,
( ~ lesseq(sK4,sK3)
| max(sK3,sK4) = sK3 ),
inference(instantiation,[status(thm)],[c_57]) ).
cnf(c_1935,plain,
( max(sK3,sK4) != X0
| sK5 != X0
| max(sK3,sK4) = sK5 ),
inference(instantiation,[status(thm)],[c_276]) ).
cnf(c_1937,plain,
( max(sK3,sK4) != sK3
| sK5 != sK3
| max(sK3,sK4) = sK5 ),
inference(instantiation,[status(thm)],[c_1935]) ).
cnf(c_2200,plain,
( ~ lesseq(X0,X1)
| lesseq(X0,X2)
| lesseq(X2,X1) ),
inference(resolution,[status(thm)],[c_50,c_52]) ).
cnf(c_2203,plain,
( ~ lesseq(X0,max(X1,X2))
| ~ model_max(X1,X2,X3)
| lesseq(X0,X3) ),
inference(resolution,[status(thm)],[c_50,c_63]) ).
cnf(c_2279,plain,
( X0 != X1
| sK4 != max(X2,sK4)
| ~ lesseq(max(X2,sK4),X1)
| lesseq(sK4,X0) ),
inference(instantiation,[status(thm)],[c_320]) ).
cnf(c_2280,plain,
( sK3 != sK3
| sK4 != max(sK3,sK4)
| ~ lesseq(max(sK3,sK4),sK3)
| lesseq(sK4,sK3) ),
inference(instantiation,[status(thm)],[c_2279]) ).
cnf(c_2295,plain,
( max(sK3,sK4) != sK4
| sK5 != X0
| ~ lesseq(sK4,X0)
| lesseq(max(sK3,sK4),sK5) ),
inference(instantiation,[status(thm)],[c_218]) ).
cnf(c_2330,plain,
( ~ lesseq(X0,sK0(X1,X2,X3))
| ~ model_ub(X1,X2,X3)
| lesseq(X0,X3) ),
inference(resolution,[status(thm)],[c_65,c_50]) ).
cnf(c_2797,plain,
( ~ lesseq(X0,sK4)
| ~ lesseq(sK4,sK4)
| ub(X0,sK4,sK4) ),
inference(instantiation,[status(thm)],[c_873]) ).
cnf(c_2798,plain,
( ~ lesseq(sK3,sK4)
| ~ lesseq(sK4,sK4)
| ub(sK3,sK4,sK4) ),
inference(instantiation,[status(thm)],[c_2797]) ).
cnf(c_3554,plain,
( ~ ub(sK3,sK4,X0)
| ~ lesseq(X0,sK4)
| model_ub(sK3,sK4,sK4) ),
inference(instantiation,[status(thm)],[c_500]) ).
cnf(c_4093,plain,
( ~ model_ub(sK3,sK4,sK4)
| ~ minsol_model_ub(sK3,sK4,sK5)
| lesseq(sK5,sK4) ),
inference(instantiation,[status(thm)],[c_415]) ).
cnf(c_4241,plain,
lesseq(max(sK3,sK4),max(sK3,sK4)),
inference(instantiation,[status(thm)],[c_126]) ).
cnf(c_4742,plain,
( ~ model_ub(X0,X1,X2)
| lesseq(X1,sK0(X0,X1,X2)) ),
inference(resolution,[status(thm)],[c_66,c_60]) ).
cnf(c_4743,plain,
( ~ model_ub(X0,X1,X2)
| lesseq(X0,sK0(X0,X1,X2)) ),
inference(resolution,[status(thm)],[c_66,c_61]) ).
cnf(c_5180,plain,
( max(X0,sK4) != X1
| X2 != X1
| X2 = max(X0,sK4) ),
inference(instantiation,[status(thm)],[c_105]) ).
cnf(c_5181,plain,
( max(sK3,sK4) != sK3
| sK3 != sK3
| sK3 = max(sK3,sK4) ),
inference(instantiation,[status(thm)],[c_5180]) ).
cnf(c_6040,plain,
( max(sK3,sK4) != X0
| sK5 != sK5
| ~ lesseq(X0,sK5)
| lesseq(max(sK3,sK4),sK5) ),
inference(instantiation,[status(thm)],[c_218]) ).
cnf(c_6041,plain,
( max(sK3,sK4) != sK3
| sK5 != sK5
| ~ lesseq(sK3,sK5)
| lesseq(max(sK3,sK4),sK5) ),
inference(instantiation,[status(thm)],[c_6040]) ).
cnf(c_6622,plain,
( max(sK3,sK4) != sK4
| sK5 != sK5
| ~ lesseq(sK4,sK5)
| lesseq(max(sK3,sK4),sK5) ),
inference(instantiation,[status(thm)],[c_2295]) ).
cnf(c_7164,plain,
( ~ lesseq(X0,X1)
| ~ lesseq(X1,X3)
| ~ lesseq(X2,X1)
| model_ub(X0,X2,X3) ),
inference(resolution,[status(thm)],[c_64,c_59]) ).
cnf(c_7396,plain,
( X0 != sK5
| model_ub(sK3,sK4,X0)
| model_max(sK3,sK4,sK5) ),
inference(resolution,[status(thm)],[c_109,c_374]) ).
cnf(c_7409,plain,
( X0 != sK5
| model_max(sK3,sK4,sK5)
| minsol_model_max(sK3,sK4,sK5)
| lesseq(sK5,X0) ),
inference(resolution,[status(thm)],[c_7396,c_391]) ).
cnf(c_7412,plain,
( X0 != sK5
| lesseq(sK5,X0) ),
inference(global_subsumption_just,[status(thm)],[c_7409,c_157,c_237,c_238,c_1321]) ).
cnf(c_7424,plain,
( ~ lesseq(X0,sK5)
| lesseq(sK5,max(sK5,X0)) ),
inference(resolution,[status(thm)],[c_7412,c_57]) ).
cnf(c_7688,plain,
( sK5 != X0
| ~ model_ub(sK3,sK4,X0)
| model_ub(sK3,sK4,sK5) ),
inference(instantiation,[status(thm)],[c_504]) ).
cnf(c_7689,plain,
( sK5 != sK3
| ~ model_ub(sK3,sK4,sK3)
| model_ub(sK3,sK4,sK5) ),
inference(instantiation,[status(thm)],[c_7688]) ).
cnf(c_7893,plain,
( sK4 != max(sK3,sK4)
| sK5 != max(sK3,sK4)
| sK5 = sK4 ),
inference(instantiation,[status(thm)],[c_1519]) ).
cnf(c_7899,plain,
( X0 != max(sK3,sK4)
| sK5 != max(sK3,sK4)
| sK5 = X0 ),
inference(instantiation,[status(thm)],[c_159]) ).
cnf(c_7902,plain,
( sK3 != max(sK3,sK4)
| sK5 != max(sK3,sK4)
| sK5 = sK3 ),
inference(instantiation,[status(thm)],[c_7899]) ).
cnf(c_8266,plain,
( ~ model_max(X0,sK4,max(X0,sK4))
| ~ minsol_model_max(X0,sK4,sK5)
| lesseq(sK5,max(X0,sK4)) ),
inference(instantiation,[status(thm)],[c_1378]) ).
cnf(c_8268,plain,
( ~ model_max(sK3,sK4,max(sK3,sK4))
| ~ minsol_model_max(sK3,sK4,sK5)
| lesseq(sK5,max(sK3,sK4)) ),
inference(instantiation,[status(thm)],[c_8266]) ).
cnf(c_8624,plain,
( max(sK3,sK4) != sK5
| sK5 != sK5
| ~ lesseq(sK5,sK5)
| lesseq(sK5,max(sK3,sK4)) ),
inference(instantiation,[status(thm)],[c_1321]) ).
cnf(c_8774,plain,
( ~ model_max(sK3,sK4,sK1(sK3,sK4,sK5))
| lesseq(max(sK3,sK4),sK1(sK3,sK4,sK5)) ),
inference(instantiation,[status(thm)],[c_1756]) ).
cnf(c_9123,plain,
( X0 != sK3
| X1 != sK4
| X2 != sK5
| minsol_model_ub(X0,X1,X2)
| minsol_model_max(sK3,sK4,sK5) ),
inference(resolution,[status(thm)],[c_111,c_76]) ).
cnf(c_9210,plain,
( ~ lesseq(max(X0,X1),sK1(sK3,sK4,sK5))
| ~ lesseq(sK5,max(X0,X1))
| lesseq(sK5,sK1(sK3,sK4,sK5)) ),
inference(instantiation,[status(thm)],[c_585]) ).
cnf(c_9234,plain,
( lesseq(sK5,max(sK3,sK4))
| model_ub(sK3,sK4,sK5) ),
inference(resolution,[status(thm)],[c_1001,c_809]) ).
cnf(c_9268,plain,
( X0 != sK3
| X1 != sK4
| X2 != sK5
| ~ model_ub(X0,X1,X3)
| minsol_model_max(sK3,sK4,sK5)
| lesseq(X2,X3) ),
inference(resolution,[status(thm)],[c_9123,c_73]) ).
cnf(c_9269,plain,
( X0 != sK3
| X1 != sK4
| X2 != sK5
| model_ub(X0,X1,X2)
| minsol_model_max(sK3,sK4,sK5) ),
inference(resolution,[status(thm)],[c_9123,c_74]) ).
cnf(c_9323,plain,
( X0 != sK3
| X1 != sK4
| X2 != sK5
| model_ub(X0,X1,X2)
| model_max(sK3,sK4,sK5) ),
inference(resolution,[status(thm)],[c_9269,c_70]) ).
cnf(c_9510,plain,
( ~ lesseq(max(sK3,sK4),sK5)
| ~ lesseq(sK5,X0)
| lesseq(max(sK3,sK4),X0) ),
inference(instantiation,[status(thm)],[c_1764]) ).
cnf(c_9511,plain,
( ~ lesseq(max(sK3,sK4),sK5)
| ~ lesseq(sK5,sK3)
| lesseq(max(sK3,sK4),sK3) ),
inference(instantiation,[status(thm)],[c_9510]) ).
cnf(c_10382,plain,
( sK5 != sK4
| ~ model_ub(sK3,sK4,sK4)
| model_ub(sK3,sK4,sK5) ),
inference(instantiation,[status(thm)],[c_7688]) ).
cnf(c_10390,plain,
( max(sK3,sK4) != sK4
| sK5 != sK4
| max(sK3,sK4) = sK5 ),
inference(instantiation,[status(thm)],[c_1935]) ).
cnf(c_10453,plain,
( X0 != X1
| sK4 != sK5
| ~ lesseq(X1,sK5)
| lesseq(X0,sK4) ),
inference(instantiation,[status(thm)],[c_1235]) ).
cnf(c_10456,plain,
( sK3 != sK3
| sK4 != sK5
| ~ lesseq(sK3,sK5)
| lesseq(sK3,sK4) ),
inference(instantiation,[status(thm)],[c_10453]) ).
cnf(c_10615,plain,
( ~ ub(sK3,sK4,sK4)
| ~ lesseq(sK4,sK4)
| model_ub(sK3,sK4,sK4) ),
inference(instantiation,[status(thm)],[c_3554]) ).
cnf(c_11780,plain,
( lesseq(summation(X0),X1)
| lesseq(X1,summation(X2))
| lesseq(X2,X0) ),
inference(resolution,[status(thm)],[c_2200,c_898]) ).
cnf(c_12207,plain,
( ~ model_ub(X0,X1,sK2(X2,X3,X4))
| lesseq(sK0(X0,X1,sK2(X2,X3,X4)),sK2(X2,X3,X4)) ),
inference(instantiation,[status(thm)],[c_65]) ).
cnf(c_13454,plain,
sK2(X0,X1,X2) = sK2(X0,X1,X2),
inference(instantiation,[status(thm)],[c_103]) ).
cnf(c_14346,plain,
( ~ model_max(sK5,X0,X1)
| ~ lesseq(X0,sK5)
| lesseq(sK5,X1) ),
inference(resolution,[status(thm)],[c_2203,c_7424]) ).
cnf(c_14415,plain,
( X0 != sK4
| X1 != sK5
| sK5 != sK3
| ~ lesseq(X0,sK5)
| model_ub(sK3,sK4,sK5)
| lesseq(sK5,X1) ),
inference(resolution,[status(thm)],[c_14346,c_579]) ).
cnf(c_15739,plain,
( model_ub(sK3,sK4,sK5)
| sK5 != sK3 ),
inference(global_subsumption_just,[status(thm)],[c_14415,c_77,c_88,c_145,c_184,c_198,c_330,c_374,c_501,c_728,c_729,c_782,c_783,c_874,c_1737,c_1890,c_2280,c_2798,c_5181,c_7689,c_7893,c_7902,c_9234,c_9511,c_10382,c_10615]) ).
cnf(c_15740,plain,
( sK5 != sK3
| model_ub(sK3,sK4,sK5) ),
inference(renaming,[status(thm)],[c_15739]) ).
cnf(c_15741,plain,
model_ub(sK3,sK4,sK5),
inference(global_subsumption_just,[status(thm)],[c_15740,c_77,c_88,c_145,c_198,c_330,c_374,c_728,c_729,c_782,c_783,c_1737,c_1890,c_2798,c_5181,c_7893,c_7902,c_9234,c_10382,c_10615,c_15740]) ).
cnf(c_16177,plain,
( ~ model_ub(X0,X1,X2)
| lesseq(X1,X2) ),
inference(resolution,[status(thm)],[c_2330,c_4742]) ).
cnf(c_16178,plain,
( ~ model_ub(X0,X1,X2)
| lesseq(X0,X2) ),
inference(resolution,[status(thm)],[c_2330,c_4743]) ).
cnf(c_19960,plain,
( ~ lesseq(sK2(sK3,sK4,X0),X1)
| ~ lesseq(X2,sK2(sK3,sK4,X0))
| ~ model_ub(sK3,sK4,X0)
| model_ub(X2,sK5,X1)
| minsol_model_ub(sK3,sK4,X0)
| minsol_model_max(sK3,sK4,sK5) ),
inference(resolution,[status(thm)],[c_7164,c_511]) ).
cnf(c_21117,plain,
( ~ lesseq(sK2(sK3,sK4,X0),X1)
| ~ model_ub(sK3,sK4,X0)
| model_ub(sK5,sK5,X1)
| minsol_model_ub(sK3,sK4,X0)
| minsol_model_max(sK3,sK4,sK5) ),
inference(resolution,[status(thm)],[c_19960,c_511]) ).
cnf(c_28204,plain,
( X0 != sK4
| X1 != sK5
| X2 != sK3
| model_max(sK3,sK4,sK5)
| lesseq(X0,X1) ),
inference(resolution,[status(thm)],[c_16177,c_9323]) ).
cnf(c_28208,plain,
lesseq(sK4,sK5),
inference(resolution,[status(thm)],[c_16177,c_15741]) ).
cnf(c_28957,plain,
lesseq(sK3,sK5),
inference(resolution,[status(thm)],[c_16178,c_15741]) ).
cnf(c_30941,plain,
model_max(sK3,sK4,sK5),
inference(global_subsumption_just,[status(thm)],[c_28204,c_157,c_161,c_330,c_783,c_1890,c_6041,c_6622,c_28208,c_28957]) ).
cnf(c_32221,plain,
( ~ model_ub(sK3,sK4,sK2(sK3,sK4,sK5))
| lesseq(sK0(sK3,sK4,sK2(sK3,sK4,sK5)),sK2(sK3,sK4,sK5)) ),
inference(instantiation,[status(thm)],[c_12207]) ).
cnf(c_32624,plain,
( ~ model_ub(sK3,sK4,X0)
| lesseq(X1,summation(sK2(sK3,sK4,X0)))
| lesseq(summation(X2),X1)
| model_ub(sK5,sK5,X2)
| minsol_model_ub(sK3,sK4,X0)
| minsol_model_max(sK3,sK4,sK5) ),
inference(resolution,[status(thm)],[c_11780,c_21117]) ).
cnf(c_34410,plain,
( X0 != sK5
| sK5 != sK3
| sK5 != sK4
| ~ model_ub(sK3,sK4,X1)
| lesseq(X2,summation(sK2(sK3,sK4,X1)))
| lesseq(summation(X3),X2)
| minsol_model_ub(sK3,sK4,X1)
| minsol_model_max(sK3,sK4,sK5)
| lesseq(X0,X3) ),
inference(resolution,[status(thm)],[c_32624,c_9268]) ).
cnf(c_34809,plain,
( ~ lesseq(max(sK3,sK4),sK1(sK3,sK4,sK5))
| ~ lesseq(sK5,max(sK3,sK4))
| lesseq(sK5,sK1(sK3,sK4,sK5)) ),
inference(instantiation,[status(thm)],[c_9210]) ).
cnf(c_35657,plain,
( minsol_model_max(sK3,sK4,sK5)
| sK5 != sK4 ),
inference(global_subsumption_just,[status(thm)],[c_34410,c_77,c_76,c_88,c_146,c_147,c_155,c_157,c_198,c_237,c_238,c_330,c_392,c_501,c_618,c_728,c_729,c_783,c_874,c_1520,c_1890,c_1937,c_2798,c_4093,c_8624,c_8774,c_10390,c_10456,c_10615,c_28208,c_28957,c_30941,c_34809]) ).
cnf(c_35658,plain,
( sK5 != sK4
| minsol_model_max(sK3,sK4,sK5) ),
inference(renaming,[status(thm)],[c_35657]) ).
cnf(c_35659,plain,
minsol_model_max(sK3,sK4,sK5),
inference(global_subsumption_just,[status(thm)],[c_35658,c_77,c_76,c_146,c_147,c_155,c_157,c_237,c_238,c_330,c_392,c_501,c_618,c_728,c_729,c_874,c_1890,c_1937,c_2798,c_4093,c_8624,c_8774,c_10615,c_28208,c_28957,c_30941,c_34809,c_35658]) ).
cnf(c_37526,plain,
( sK2(sK3,sK4,sK5) != sK2(sK3,sK4,sK5)
| sK5 != X0
| ~ lesseq(X0,sK2(sK3,sK4,sK5))
| lesseq(sK5,sK2(sK3,sK4,sK5)) ),
inference(instantiation,[status(thm)],[c_1681]) ).
cnf(c_37527,plain,
sK2(sK3,sK4,sK5) = sK2(sK3,sK4,sK5),
inference(instantiation,[status(thm)],[c_13454]) ).
cnf(c_37528,plain,
( sK2(sK3,sK4,sK5) != sK2(sK3,sK4,sK5)
| sK5 != sK3
| ~ lesseq(sK3,sK2(sK3,sK4,sK5))
| lesseq(sK5,sK2(sK3,sK4,sK5)) ),
inference(instantiation,[status(thm)],[c_37526]) ).
cnf(c_43084,plain,
( sK2(sK3,sK4,sK5) != X0
| sK5 != X1
| ~ lesseq(X1,X0)
| lesseq(sK5,sK2(sK3,sK4,sK5)) ),
inference(instantiation,[status(thm)],[c_106]) ).
cnf(c_43135,plain,
( ~ lesseq(X0,sK2(sK3,sK4,sK5))
| ~ lesseq(X1,X0)
| lesseq(X1,sK2(sK3,sK4,sK5)) ),
inference(instantiation,[status(thm)],[c_50]) ).
cnf(c_43176,plain,
( sK2(sK3,sK4,sK5) != sK2(sK3,sK4,sK5)
| sK5 != X0
| ~ lesseq(X0,sK2(sK3,sK4,sK5))
| lesseq(sK5,sK2(sK3,sK4,sK5)) ),
inference(instantiation,[status(thm)],[c_43084]) ).
cnf(c_44161,plain,
( ~ lesseq(sK0(sK3,sK4,sK2(sK3,sK4,sK5)),sK2(sK3,sK4,sK5))
| ~ lesseq(X0,sK0(sK3,sK4,sK2(sK3,sK4,sK5)))
| lesseq(X0,sK2(sK3,sK4,sK5)) ),
inference(instantiation,[status(thm)],[c_43135]) ).
cnf(c_44165,plain,
( ~ lesseq(sK0(sK3,sK4,sK2(sK3,sK4,sK5)),sK2(sK3,sK4,sK5))
| ~ lesseq(sK3,sK0(sK3,sK4,sK2(sK3,sK4,sK5)))
| lesseq(sK3,sK2(sK3,sK4,sK5)) ),
inference(instantiation,[status(thm)],[c_44161]) ).
cnf(c_48773,plain,
( ~ ub(X0,X1,sK0(sK3,sK4,sK2(sK3,sK4,sK5)))
| lesseq(X0,sK0(sK3,sK4,sK2(sK3,sK4,sK5))) ),
inference(instantiation,[status(thm)],[c_61]) ).
cnf(c_48777,plain,
( ~ ub(X0,X1,sK0(sK3,sK4,sK2(sK3,sK4,sK5)))
| lesseq(X1,sK0(sK3,sK4,sK2(sK3,sK4,sK5))) ),
inference(instantiation,[status(thm)],[c_60]) ).
cnf(c_48799,plain,
( ~ lesseq(sK0(sK3,sK4,sK2(sK3,sK4,sK5)),sK2(sK3,sK4,sK5))
| ~ lesseq(sK4,sK0(sK3,sK4,sK2(sK3,sK4,sK5)))
| lesseq(sK4,sK2(sK3,sK4,sK5)) ),
inference(instantiation,[status(thm)],[c_44161]) ).
cnf(c_49227,plain,
( ~ model_ub(sK3,sK4,sK2(sK3,sK4,sK5))
| ub(sK3,sK4,sK0(sK3,sK4,sK2(sK3,sK4,sK5))) ),
inference(instantiation,[status(thm)],[c_66]) ).
cnf(c_55967,plain,
( sK2(sK3,sK4,sK5) != sK2(sK3,sK4,sK5)
| sK5 != sK4
| ~ lesseq(sK4,sK2(sK3,sK4,sK5))
| lesseq(sK5,sK2(sK3,sK4,sK5)) ),
inference(instantiation,[status(thm)],[c_43176]) ).
cnf(c_60042,plain,
( ~ ub(sK3,sK4,sK0(sK3,sK4,sK2(sK3,sK4,sK5)))
| lesseq(sK3,sK0(sK3,sK4,sK2(sK3,sK4,sK5))) ),
inference(instantiation,[status(thm)],[c_48773]) ).
cnf(c_60047,plain,
( ~ ub(sK3,sK4,sK0(sK3,sK4,sK2(sK3,sK4,sK5)))
| lesseq(sK4,sK0(sK3,sK4,sK2(sK3,sK4,sK5))) ),
inference(instantiation,[status(thm)],[c_48777]) ).
cnf(c_60048,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_60047,c_60042,c_55967,c_49227,c_48799,c_44165,c_37527,c_37528,c_35659,c_32221,c_30941,c_15741,c_8268,c_7902,c_7893,c_5181,c_4241,c_1890,c_1737,c_1626,c_783,c_782,c_330,c_198,c_145,c_120,c_119,c_88,c_75,c_77]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : NUM859+1 : TPTP v8.1.2. Released v4.1.0.
% 0.09/0.11 % Command : run_iprover %s %d THM
% 0.10/0.31 % Computer : n022.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Thu May 2 19:19:27 EDT 2024
% 0.10/0.31 % CPUTime :
% 0.16/0.41 Running first-order theorem proving
% 0.16/0.41 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 56.53/8.66 % SZS status Started for theBenchmark.p
% 56.53/8.66 % SZS status Theorem for theBenchmark.p
% 56.53/8.66
% 56.53/8.66 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 56.53/8.66
% 56.53/8.66 ------ iProver source info
% 56.53/8.66
% 56.53/8.66 git: date: 2024-05-02 19:28:25 +0000
% 56.53/8.66 git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 56.53/8.66 git: non_committed_changes: false
% 56.53/8.66
% 56.53/8.66 ------ Parsing...
% 56.53/8.66 ------ Clausification by vclausify_rel & Parsing by iProver...
% 56.53/8.66
% 56.53/8.66 ------ Preprocessing... sf_s rm: 1 0s sf_e
% 56.53/8.66
% 56.53/8.66 ------ Preprocessing...
% 56.53/8.66
% 56.53/8.66 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 56.53/8.66 ------ Proving...
% 56.53/8.66 ------ Problem Properties
% 56.53/8.66
% 56.53/8.66
% 56.53/8.66 clauses 28
% 56.53/8.66 conjectures 2
% 56.53/8.66 EPR 14
% 56.53/8.66 Horn 24
% 56.53/8.66 unary 1
% 56.53/8.66 binary 17
% 56.53/8.66 lits 65
% 56.53/8.66 lits eq 3
% 56.53/8.66 fd_pure 0
% 56.53/8.66 fd_pseudo 0
% 56.53/8.66 fd_cond 0
% 56.53/8.66 fd_pseudo_cond 1
% 56.53/8.66 AC symbols 0
% 56.53/8.66
% 56.53/8.66 ------ Input Options Time Limit: Unbounded
% 56.53/8.66
% 56.53/8.66
% 56.53/8.66 ------
% 56.53/8.66 Current options:
% 56.53/8.66 ------
% 56.53/8.66
% 56.53/8.66
% 56.53/8.66
% 56.53/8.66
% 56.53/8.66 ------ Proving...
% 56.53/8.66
% 56.53/8.66
% 56.53/8.66 % SZS status Theorem for theBenchmark.p
% 56.53/8.66
% 56.53/8.66 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 56.53/8.66
% 56.53/8.67
%------------------------------------------------------------------------------