%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM860+1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n015.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 : Fri Sep 25 02:27:07 PM UTC 2026
% Result : Theorem 126.14s 32.51s
% Output : CNFRefutation 126.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 42
% Number of leaves : 17
% Syntax : Number of formulae : 279 ( 21 unt; 0 def)
% Number of atoms : 769 ( 89 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 857 ( 367 ~; 429 |; 46 &)
% ( 10 <=>; 4 =>; 0 <=; 1 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% 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 : 486 ( 0 sgn 471 !; 15 ?; 294 :)
% 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,X2] :
( model_max(X0,X1,X2)
<=> lesseq(summation(max(X0,X1)),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',model_max_3) ).
fof(f11,axiom,
! [X0,X1,X2] :
( model_ub(X0,X1,X2)
<=> ? [X3] :
( lesseq(summation(X3),X2)
& ub(X0,X1,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',model_ub_3) ).
fof(f12,axiom,
! [X0,X1,X2] :
( minsol_model_max(X0,X1,X2)
<=> ( ! [X3] :
( model_max(X0,X1,X3)
=> lesseq(X2,X3) )
& model_max(X0,X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',minsol_model_max) ).
fof(f13,axiom,
! [X0,X1,X2] :
( minsol_model_ub(X0,X1,X2)
<=> ( ! [X3] :
( model_ub(X0,X1,X3)
=> lesseq(X2,X3) )
& model_ub(X0,X1,X2) ) ),
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,[status(cth)],[f14]) ).
fof(f16,plain,
! [X0,X1,X2] :
( ~ lesseq(X1,X2)
| ~ lesseq(X0,X1)
| lesseq(X0,X2) ),
inference(ennf_transformation,[],[f2]) ).
fof(f17,plain,
! [X0,X1,X2] :
( ~ lesseq(X1,X2)
| ~ lesseq(X0,X1)
| lesseq(X0,X2) ),
inference(flattening,[],[f16]) ).
fof(f18,plain,
! [X0,X1] :
( ~ lesseq(X1,X0)
| ~ lesseq(X0,X1)
| X0 = X1 ),
inference(ennf_transformation,[],[f3]) ).
fof(f19,plain,
! [X0,X1] :
( ~ lesseq(X1,X0)
| ~ lesseq(X0,X1)
| X0 = X1 ),
inference(flattening,[],[f18]) ).
fof(f20,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(ennf_transformation,[],[f12]) ).
fof(f21,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(ennf_transformation,[],[f13]) ).
fof(f22,plain,
? [X0,X1,X2] :
( minsol_model_ub(X0,X1,X2)
<~> minsol_model_max(X0,X1,X2) ),
inference(ennf_transformation,[],[f15]) ).
fof(f24,plain,
! [X0,X1] :
( ( ~ lesseq(X0,X1)
| lesseq(summation(X0),summation(X1)) )
& ( ~ lesseq(summation(X0),summation(X1))
| lesseq(X0,X1) ) ),
inference(nnf_transformation,[],[f6]) ).
fof(f25,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(f26,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,[],[f25]) ).
fof(f27,plain,
! [X0,X1,X2] :
( ( ~ model_max(X0,X1,X2)
| lesseq(summation(max(X0,X1)),X2) )
& ( ~ lesseq(summation(max(X0,X1)),X2)
| model_max(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f10]) ).
fof(f28,plain,
! [X0,X1,X2] :
( ( ~ model_ub(X0,X1,X2)
| ? [X3] :
( lesseq(summation(X3),X2)
& ub(X0,X1,X3) ) )
& ( ! [X3] :
( ~ lesseq(summation(X3),X2)
| ~ ub(X0,X1,X3) )
| model_ub(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f11]) ).
fof(f29,plain,
! [X0,X1,X2] :
( ( ~ model_ub(X0,X1,X2)
| ? [X4] :
( lesseq(summation(X4),X2)
& ub(X0,X1,X4) ) )
& ( ! [X3] :
( ~ lesseq(summation(X3),X2)
| ~ ub(X0,X1,X3) )
| model_ub(X0,X1,X2) ) ),
inference(rectify,[],[f28]) ).
fof(f30,plain,
! [X0,X1,X2] :
( ( ~ model_ub(X0,X1,X2)
| ( lesseq(summation(sK0(X0,X1,X2)),X2)
& ub(X0,X1,sK0(X0,X1,X2)) ) )
& ( ! [X3] :
( ~ lesseq(summation(X3),X2)
| ~ ub(X0,X1,X3) )
| model_ub(X0,X1,X2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X4,sK0(X0,X1,X2))],[f29]) ).
fof(f31,plain,
! [X0,X1,X2] :
( ( ~ minsol_model_max(X0,X1,X2)
| ( ! [X3] :
( ~ model_max(X0,X1,X3)
| lesseq(X2,X3) )
& model_max(X0,X1,X2) ) )
& ( ? [X3] :
( model_max(X0,X1,X3)
& ~ lesseq(X2,X3) )
| ~ model_max(X0,X1,X2)
| minsol_model_max(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f20]) ).
fof(f32,plain,
! [X0,X1,X2] :
( ( ~ minsol_model_max(X0,X1,X2)
| ( ! [X3] :
( ~ model_max(X0,X1,X3)
| lesseq(X2,X3) )
& model_max(X0,X1,X2) ) )
& ( ? [X3] :
( model_max(X0,X1,X3)
& ~ lesseq(X2,X3) )
| ~ model_max(X0,X1,X2)
| minsol_model_max(X0,X1,X2) ) ),
inference(flattening,[],[f31]) ).
fof(f33,plain,
! [X0,X1,X2] :
( ( ~ minsol_model_max(X0,X1,X2)
| ( ! [X4] :
( ~ model_max(X0,X1,X4)
| lesseq(X2,X4) )
& model_max(X0,X1,X2) ) )
& ( ? [X3] :
( model_max(X0,X1,X3)
& ~ lesseq(X2,X3) )
| ~ model_max(X0,X1,X2)
| minsol_model_max(X0,X1,X2) ) ),
inference(rectify,[],[f32]) ).
fof(f34,plain,
! [X0,X1,X2] :
( ( ~ minsol_model_max(X0,X1,X2)
| ( ! [X4] :
( ~ model_max(X0,X1,X4)
| lesseq(X2,X4) )
& model_max(X0,X1,X2) ) )
& ( ( model_max(X0,X1,sK1(X0,X1,X2))
& ~ lesseq(X2,sK1(X0,X1,X2)) )
| ~ model_max(X0,X1,X2)
| minsol_model_max(X0,X1,X2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X3,sK1(X0,X1,X2))],[f33]) ).
fof(f35,plain,
! [X0,X1,X2] :
( ( ~ minsol_model_ub(X0,X1,X2)
| ( ! [X3] :
( ~ model_ub(X0,X1,X3)
| lesseq(X2,X3) )
& model_ub(X0,X1,X2) ) )
& ( ? [X3] :
( model_ub(X0,X1,X3)
& ~ lesseq(X2,X3) )
| ~ model_ub(X0,X1,X2)
| minsol_model_ub(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f21]) ).
fof(f36,plain,
! [X0,X1,X2] :
( ( ~ minsol_model_ub(X0,X1,X2)
| ( ! [X3] :
( ~ model_ub(X0,X1,X3)
| lesseq(X2,X3) )
& model_ub(X0,X1,X2) ) )
& ( ? [X3] :
( model_ub(X0,X1,X3)
& ~ lesseq(X2,X3) )
| ~ model_ub(X0,X1,X2)
| minsol_model_ub(X0,X1,X2) ) ),
inference(flattening,[],[f35]) ).
fof(f37,plain,
! [X0,X1,X2] :
( ( ~ minsol_model_ub(X0,X1,X2)
| ( ! [X4] :
( ~ model_ub(X0,X1,X4)
| lesseq(X2,X4) )
& model_ub(X0,X1,X2) ) )
& ( ? [X3] :
( model_ub(X0,X1,X3)
& ~ lesseq(X2,X3) )
| ~ model_ub(X0,X1,X2)
| minsol_model_ub(X0,X1,X2) ) ),
inference(rectify,[],[f36]) ).
fof(f38,plain,
! [X0,X1,X2] :
( ( ~ minsol_model_ub(X0,X1,X2)
| ( ! [X4] :
( ~ model_ub(X0,X1,X4)
| lesseq(X2,X4) )
& model_ub(X0,X1,X2) ) )
& ( ( model_ub(X0,X1,sK2(X0,X1,X2))
& ~ lesseq(X2,sK2(X0,X1,X2)) )
| ~ model_ub(X0,X1,X2)
| minsol_model_ub(X0,X1,X2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X3,sK2(X0,X1,X2))],[f37]) ).
fof(f39,plain,
? [X0,X1,X2] :
( ( minsol_model_ub(X0,X1,X2)
| minsol_model_max(X0,X1,X2) )
& ( ~ minsol_model_ub(X0,X1,X2)
| ~ minsol_model_max(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f22]) ).
fof(f40,plain,
( ( minsol_model_ub(sK3,sK4,sK5)
| minsol_model_max(sK3,sK4,sK5) )
& ( ~ minsol_model_ub(sK3,sK4,sK5)
| ~ minsol_model_max(sK3,sK4,sK5) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5]),skolemize(X0,sK3),skolemize(X1,sK4),skolemize(X2,sK5)],[f39]) ).
fof(f41,plain,
! [X0] : lesseq(X0,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f42,plain,
! [X2,X0,X1] :
( ~ lesseq(X1,X2)
| ~ lesseq(X0,X1)
| lesseq(X0,X2) ),
inference(cnf_transformation,[],[f17]) ).
fof(f43,plain,
! [X0,X1] :
( ~ lesseq(X1,X0)
| ~ lesseq(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f19]) ).
fof(f44,plain,
! [X0,X1] :
( lesseq(X1,X0)
| lesseq(X0,X1) ),
inference(cnf_transformation,[],[f4]) ).
fof(f47,plain,
! [X0,X1] :
( ~ lesseq(X0,X1)
| lesseq(summation(X0),summation(X1)) ),
inference(cnf_transformation,[],[f24]) ).
fof(f48,plain,
! [X0,X1] :
( ~ lesseq(summation(X0),summation(X1))
| lesseq(X0,X1) ),
inference(cnf_transformation,[],[f24]) ).
fof(f49,plain,
! [X0,X1] :
( ~ lesseq(X1,X0)
| max(X0,X1) = X0 ),
inference(cnf_transformation,[],[f7]) ).
fof(f50,plain,
! [X0,X1] :
( ~ lesseq(X0,X1)
| max(X0,X1) = X1 ),
inference(cnf_transformation,[],[f8]) ).
fof(f51,plain,
! [X2,X0,X1] :
( ~ ub(X0,X1,X2)
| lesseq(X1,X2) ),
inference(cnf_transformation,[],[f26]) ).
fof(f52,plain,
! [X2,X0,X1] :
( ~ ub(X0,X1,X2)
| lesseq(X0,X2) ),
inference(cnf_transformation,[],[f26]) ).
fof(f53,plain,
! [X2,X0,X1] :
( ~ lesseq(X1,X2)
| ~ lesseq(X0,X2)
| ub(X0,X1,X2) ),
inference(cnf_transformation,[],[f26]) ).
fof(f54,plain,
! [X2,X0,X1] :
( ~ model_max(X0,X1,X2)
| lesseq(summation(max(X0,X1)),X2) ),
inference(cnf_transformation,[],[f27]) ).
fof(f55,plain,
! [X2,X0,X1] :
( ~ lesseq(summation(max(X0,X1)),X2)
| model_max(X0,X1,X2) ),
inference(cnf_transformation,[],[f27]) ).
fof(f56,plain,
! [X2,X0,X1] :
( ~ model_ub(X0,X1,X2)
| lesseq(summation(sK0(X0,X1,X2)),X2) ),
inference(cnf_transformation,[],[f30]) ).
fof(f57,plain,
! [X2,X0,X1] :
( ~ model_ub(X0,X1,X2)
| ub(X0,X1,sK0(X0,X1,X2)) ),
inference(cnf_transformation,[],[f30]) ).
fof(f58,plain,
! [X2,X3,X0,X1] :
( ~ lesseq(summation(X3),X2)
| ~ ub(X0,X1,X3)
| model_ub(X0,X1,X2) ),
inference(cnf_transformation,[],[f30]) ).
fof(f59,plain,
! [X2,X0,X1,X4] :
( ~ minsol_model_max(X0,X1,X2)
| ~ model_max(X0,X1,X4)
| lesseq(X2,X4) ),
inference(cnf_transformation,[],[f34]) ).
fof(f60,plain,
! [X2,X0,X1] :
( ~ minsol_model_max(X0,X1,X2)
| model_max(X0,X1,X2) ),
inference(cnf_transformation,[],[f34]) ).
fof(f61,plain,
! [X2,X0,X1] :
( model_max(X0,X1,sK1(X0,X1,X2))
| ~ model_max(X0,X1,X2)
| minsol_model_max(X0,X1,X2) ),
inference(cnf_transformation,[],[f34]) ).
fof(f62,plain,
! [X2,X0,X1] :
( ~ lesseq(X2,sK1(X0,X1,X2))
| ~ model_max(X0,X1,X2)
| minsol_model_max(X0,X1,X2) ),
inference(cnf_transformation,[],[f34]) ).
fof(f63,plain,
! [X2,X0,X1,X4] :
( ~ minsol_model_ub(X0,X1,X2)
| ~ model_ub(X0,X1,X4)
| lesseq(X2,X4) ),
inference(cnf_transformation,[],[f38]) ).
fof(f64,plain,
! [X2,X0,X1] :
( ~ minsol_model_ub(X0,X1,X2)
| model_ub(X0,X1,X2) ),
inference(cnf_transformation,[],[f38]) ).
fof(f65,plain,
! [X2,X0,X1] :
( model_ub(X0,X1,sK2(X0,X1,X2))
| ~ model_ub(X0,X1,X2)
| minsol_model_ub(X0,X1,X2) ),
inference(cnf_transformation,[],[f38]) ).
fof(f66,plain,
! [X2,X0,X1] :
( ~ lesseq(X2,sK2(X0,X1,X2))
| ~ model_ub(X0,X1,X2)
| minsol_model_ub(X0,X1,X2) ),
inference(cnf_transformation,[],[f38]) ).
fof(f67,plain,
( minsol_model_ub(sK3,sK4,sK5)
| minsol_model_max(sK3,sK4,sK5) ),
inference(cnf_transformation,[],[f40]) ).
fof(f68,plain,
( ~ minsol_model_ub(sK3,sK4,sK5)
| ~ minsol_model_max(sK3,sK4,sK5) ),
inference(cnf_transformation,[],[f40]) ).
tcf(c_49,plain,
! [X0: $i] : lesseq(X0,X0),
inference(cnf_transformation,[],[f41]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i,X2: $i] :
( lesseq(X0,X2)
| ~ lesseq(X1,X2)
| ~ lesseq(X0,X1) ),
inference(cnf_transformation,[],[f42]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ lesseq(X1,X0)
| ~ lesseq(X0,X1) ),
inference(cnf_transformation,[],[f43]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i] :
( lesseq(X1,X0)
| lesseq(X0,X1) ),
inference(cnf_transformation,[],[f44]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i] :
( lesseq(X0,X1)
| ~ lesseq(summation(X0),summation(X1)) ),
inference(cnf_transformation,[],[f48]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i] :
( lesseq(summation(X0),summation(X1))
| ~ lesseq(X0,X1) ),
inference(cnf_transformation,[],[f47]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i] :
( ( max(X1,X0) = X1 )
| ~ lesseq(X0,X1) ),
inference(cnf_transformation,[],[f49]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] :
( ( max(X0,X1) = X1 )
| ~ lesseq(X0,X1) ),
inference(cnf_transformation,[],[f50]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i,X2: $i] :
( ub(X0,X2,X1)
| ~ lesseq(X2,X1)
| ~ lesseq(X0,X1) ),
inference(cnf_transformation,[],[f53]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i,X2: $i] :
( lesseq(X0,X2)
| ~ ub(X0,X1,X2) ),
inference(cnf_transformation,[],[f52]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i,X2: $i] :
( lesseq(X1,X2)
| ~ ub(X0,X1,X2) ),
inference(cnf_transformation,[],[f51]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i,X2: $i] :
( model_max(X0,X1,X2)
| ~ lesseq(summation(max(X0,X1)),X2) ),
inference(cnf_transformation,[],[f55]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i,X2: $i] :
( lesseq(summation(max(X0,X1)),X2)
| ~ model_max(X0,X1,X2) ),
inference(cnf_transformation,[],[f54]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( model_ub(X0,X1,X3)
| ~ lesseq(summation(X2),X3)
| ~ ub(X0,X1,X2) ),
inference(cnf_transformation,[],[f58]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i,X2: $i] :
( ub(X0,X1,sK0(X0,X1,X2))
| ~ model_ub(X0,X1,X2) ),
inference(cnf_transformation,[],[f57]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i,X2: $i] :
( lesseq(summation(sK0(X0,X1,X2)),X2)
| ~ model_ub(X0,X1,X2) ),
inference(cnf_transformation,[],[f56]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i,X2: $i] :
( minsol_model_max(X1,X2,X0)
| ~ model_max(X1,X2,X0)
| ~ lesseq(X0,sK1(X1,X2,X0)) ),
inference(cnf_transformation,[],[f62]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i,X2: $i] :
( minsol_model_max(X0,X1,X2)
| model_max(X0,X1,sK1(X0,X1,X2))
| ~ model_max(X0,X1,X2) ),
inference(cnf_transformation,[],[f61]) ).
tcf(c_69,plain,
! [X0: $i,X1: $i,X2: $i] :
( model_max(X0,X1,X2)
| ~ minsol_model_max(X0,X1,X2) ),
inference(cnf_transformation,[],[f60]) ).
tcf(c_70,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( lesseq(X3,X2)
| ~ minsol_model_max(X0,X1,X3)
| ~ model_max(X0,X1,X2) ),
inference(cnf_transformation,[],[f59]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i,X2: $i] :
( minsol_model_ub(X1,X2,X0)
| ~ model_ub(X1,X2,X0)
| ~ lesseq(X0,sK2(X1,X2,X0)) ),
inference(cnf_transformation,[],[f66]) ).
tcf(c_72,plain,
! [X0: $i,X1: $i,X2: $i] :
( minsol_model_ub(X0,X1,X2)
| model_ub(X0,X1,sK2(X0,X1,X2))
| ~ model_ub(X0,X1,X2) ),
inference(cnf_transformation,[],[f65]) ).
tcf(c_73,plain,
! [X0: $i,X1: $i,X2: $i] :
( model_ub(X0,X1,X2)
| ~ minsol_model_ub(X0,X1,X2) ),
inference(cnf_transformation,[],[f64]) ).
tcf(c_74,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( lesseq(X3,X2)
| ~ minsol_model_ub(X0,X1,X3)
| ~ model_ub(X0,X1,X2) ),
inference(cnf_transformation,[],[f63]) ).
tcf(c_75,negated_conjecture,
( ~ minsol_model_ub(sK3,sK4,sK5)
| ~ minsol_model_max(sK3,sK4,sK5) ),
inference(cnf_transformation,[],[f68]) ).
tcf(c_76,negated_conjecture,
( minsol_model_ub(sK3,sK4,sK5)
| minsol_model_max(sK3,sK4,sK5) ),
inference(cnf_transformation,[],[f67]) ).
tcf(c_77,plain,
lesseq(sK3,sK3),
inference(instantiation,[status(thm)],[c_49]) ).
tcf(c_88,plain,
( ( sK3 = sK3 )
| ~ lesseq(sK3,sK3) ),
inference(instantiation,[status(thm)],[c_51]) ).
tcf(c_102,plain,
( ~ minsol_model_max(sK3,sK4,sK5)
| ~ minsol_model_ub(sK3,sK4,sK5) ),
inference(prop_impl_just,[status(thm)],[c_75]) ).
tcf(c_103,plain,
( ~ minsol_model_ub(sK3,sK4,sK5)
| ~ minsol_model_max(sK3,sK4,sK5) ),
inference(renaming,[status(thm)],[c_102]) ).
tcf(c_104,plain,
( minsol_model_max(sK3,sK4,sK5)
| minsol_model_ub(sK3,sK4,sK5) ),
inference(prop_impl_just,[status(thm)],[c_76]) ).
tcf(c_105,plain,
( minsol_model_ub(sK3,sK4,sK5)
| minsol_model_max(sK3,sK4,sK5) ),
inference(renaming,[status(thm)],[c_104]) ).
tcf(c_128,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ minsol_model_max(X0,X1,X2)
| model_max(X0,X1,X2) ),
inference(prop_impl_just,[status(thm)],[c_69]) ).
tcf(c_129,plain,
! [X0: $i,X1: $i,X2: $i] :
( model_max(X0,X1,X2)
| ~ minsol_model_max(X0,X1,X2) ),
inference(renaming,[status(thm)],[c_128]) ).
tcf(c_134,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ minsol_model_ub(X0,X1,X2)
| model_ub(X0,X1,X2) ),
inference(prop_impl_just,[status(thm)],[c_73]) ).
tcf(c_135,plain,
! [X0: $i,X1: $i,X2: $i] :
( model_ub(X0,X1,X2)
| ~ minsol_model_ub(X0,X1,X2) ),
inference(renaming,[status(thm)],[c_134]) ).
tcf(c_546,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ minsol_model_ub(sK3,sK4,sK5)
| ~ model_max(X1,X2,X0)
| ~ lesseq(X0,sK1(X1,X2,X0))
| ( X2 != sK4 )
| ( X1 != sK3 )
| ( X0 != sK5 ) ),
inference(resolution_lifted,[status(thm)],[c_67,c_103]) ).
tcf(c_547,plain,
( ~ minsol_model_ub(sK3,sK4,sK5)
| ~ model_max(sK3,sK4,sK5)
| ~ lesseq(sK5,sK1(sK3,sK4,sK5)) ),
inference(unflattening,[status(thm)],[c_546]) ).
tcf(c_571,plain,
! [X0: $i,X1: $i,X2: $i] :
( model_max(X0,X1,sK1(X0,X1,X2))
| ~ minsol_model_ub(sK3,sK4,sK5)
| ~ model_max(X0,X1,X2)
| ( X2 != sK5 )
| ( X1 != sK4 )
| ( X0 != sK3 ) ),
inference(resolution_lifted,[status(thm)],[c_68,c_103]) ).
tcf(c_572,plain,
( model_max(sK3,sK4,sK1(sK3,sK4,sK5))
| ~ minsol_model_ub(sK3,sK4,sK5)
| ~ model_max(sK3,sK4,sK5) ),
inference(unflattening,[status(thm)],[c_571]) ).
tcf(c_582,plain,
! [X0: $i,X1: $i,X2: $i] :
( minsol_model_ub(sK3,sK4,sK5)
| model_max(X0,X1,X2)
| ( X2 != sK5 )
| ( X1 != sK4 )
| ( X0 != sK3 ) ),
inference(resolution_lifted,[status(thm)],[c_129,c_105]) ).
tcf(c_583,plain,
( minsol_model_ub(sK3,sK4,sK5)
| model_max(sK3,sK4,sK5) ),
inference(unflattening,[status(thm)],[c_582]) ).
tcf(c_590,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( lesseq(X2,X3)
| minsol_model_ub(sK3,sK4,sK5)
| ~ model_max(X0,X1,X3)
| ( X2 != sK5 )
| ( X1 != sK4 )
| ( X0 != sK3 ) ),
inference(resolution_lifted,[status(thm)],[c_70,c_105]) ).
tcf(c_591,plain,
! [X0: $i] :
( lesseq(sK5,X0)
| minsol_model_ub(sK3,sK4,sK5)
| ~ model_max(sK3,sK4,X0) ),
inference(unflattening,[status(thm)],[c_590]) ).
tcf(c_727,plain,
! [X0: $i,X1: $i,X2: $i] :
( model_max(sK3,sK4,sK5)
| model_ub(X0,X1,X2)
| ( X2 != sK5 )
| ( X1 != sK4 )
| ( X0 != sK3 ) ),
inference(resolution_lifted,[status(thm)],[c_135,c_583]) ).
tcf(c_728,plain,
( model_ub(sK3,sK4,sK5)
| model_max(sK3,sK4,sK5) ),
inference(unflattening,[status(thm)],[c_727]) ).
tcf(c_798,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_801,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( lesseq(X0,X2)
| ~ lesseq(X1,X3)
| ( X2 != X3 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_802,plain,
! [X0: $i,X1: $i] :
( ( summation(X0) = summation(X1) )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_803,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ub(X2,X3,X0)
| ~ ub(X2,X3,X1)
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_1468,plain,
! [X0: $i,X1: $i] :
( model_max(X0,X1,summation(max(X0,X1)))
| ~ lesseq(summation(max(X0,X1)),summation(max(X0,X1))) ),
inference(instantiation,[status(thm)],[c_62]) ).
tcf(c_1469,plain,
! [X0: $i,X1: $i] : lesseq(summation(max(X0,X1)),summation(max(X0,X1))),
inference(instantiation,[status(thm)],[c_49]) ).
tcf(c_1510,plain,
( model_ub(sK3,sK4,sK5)
| model_max(sK3,sK4,sK5) ),
inference(superposition,[status(thm)],[c_583,c_73]) ).
tcf(c_1511,plain,
( lesseq(summation(max(sK3,sK4)),sK5)
| ~ model_max(sK3,sK4,sK5) ),
inference(instantiation,[status(thm)],[c_63]) ).
tcf(c_1515,plain,
! [X0: $i,X1: $i] :
( lesseq(X0,X1)
| ( max(X0,X1) = X0 ) ),
inference(superposition,[status(thm)],[c_52,c_57]) ).
tcf(c_1522,plain,
! [X0: $i] : lesseq(summation(X0),summation(X0)),
inference(instantiation,[status(thm)],[c_49]) ).
tcf(c_1527,plain,
! [X0: $i,X1: $i,X2: $i] :
( lesseq(summation(X0),X2)
| ~ lesseq(X1,X2)
| ~ lesseq(summation(X0),X1) ),
inference(instantiation,[status(thm)],[c_50]) ).
tcf(c_1542,plain,
! [X0: $i,X1: $i] :
( lesseq(X1,X0)
| ( max(X0,X1) = X1 ) ),
inference(superposition,[status(thm)],[c_52,c_58]) ).
tcf(c_1550,plain,
! [X0: $i,X1: $i,X2: $i] :
( lesseq(X2,X1)
| lesseq(X0,X2)
| ~ lesseq(X0,X1) ),
inference(superposition,[status(thm)],[c_52,c_50]) ).
tcf(c_1552,plain,
! [X0: $i,X1: $i,X2: $i] :
( lesseq(summation(X2),X1)
| ~ lesseq(X2,X0)
| ~ lesseq(summation(X0),X1) ),
inference(superposition,[status(thm)],[c_56,c_50]) ).
tcf(c_1554,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( lesseq(summation(max(X0,X1)),X3)
| ~ lesseq(X2,X4)
| ( X3 != X4 )
| ( summation(max(X0,X1)) != X2 ) ),
inference(instantiation,[status(thm)],[c_801]) ).
tcf(c_1567,plain,
! [X0: $i,X1: $i] :
( ( max(X0,X1) = X1 )
| ( max(X0,X1) = X0 ) ),
inference(superposition,[status(thm)],[c_1515,c_58]) ).
tcf(c_1572,plain,
( model_max(sK3,sK4,sK5)
| ~ lesseq(summation(max(sK3,sK4)),sK5) ),
inference(instantiation,[status(thm)],[c_62]) ).
tcf(c_1573,plain,
! [X0: $i,X1: $i] :
( model_ub(X0,X1,sK5)
| ~ lesseq(summation(max(sK3,sK4)),sK5)
| ~ ub(X0,X1,max(sK3,sK4)) ),
inference(instantiation,[status(thm)],[c_64]) ).
tcf(c_1577,plain,
! [X0: $i,X1: $i,X2: $i] :
( lesseq(X2,X1)
| ( max(X0,X2) = X2 )
| ~ lesseq(X0,X1) ),
inference(superposition,[status(thm)],[c_1542,c_50]) ).
tcf(c_1578,plain,
! [X0: $i,X1: $i] :
( ( max(X1,X0) = X0 )
| ( max(X0,X1) = X1 ) ),
inference(superposition,[status(thm)],[c_1542,c_58]) ).
tcf(c_1598,plain,
! [X0: $i,X1: $i,X2: $i] :
( lesseq(X2,summation(X1))
| lesseq(summation(X0),X2)
| ~ lesseq(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_1550]) ).
tcf(c_1605,plain,
! [X0: $i] :
( model_max(sK3,sK4,X0)
| ~ lesseq(summation(max(sK3,sK4)),X0) ),
inference(instantiation,[status(thm)],[c_62]) ).
tcf(c_1668,plain,
! [X0: $i] :
( minsol_model_ub(sK3,sK4,sK5)
| lesseq(sK5,summation(X0))
| ~ model_max(sK3,sK4,summation(X0)) ),
inference(instantiation,[status(thm)],[c_591]) ).
tcf(c_1705,plain,
! [X0: $i,X1: $i] :
( lesseq(summation(max(sK3,sK4)),sK5)
| ~ lesseq(X0,X1)
| ( sK5 != X1 )
| ( summation(max(sK3,sK4)) != X0 ) ),
inference(instantiation,[status(thm)],[c_1554]) ).
tcf(c_1791,plain,
! [X0: $i] :
( lesseq(summation(max(sK3,sK4)),X0)
| ~ model_max(sK3,sK4,X0) ),
inference(instantiation,[status(thm)],[c_63]) ).
tcf(c_1846,plain,
! [X0: $i,X1: $i] :
( ub(X0,X1,max(sK3,sK4))
| ~ lesseq(X1,max(sK3,sK4))
| ~ lesseq(X0,max(sK3,sK4)) ),
inference(instantiation,[status(thm)],[c_59]) ).
tcf(c_1848,plain,
! [X0: $i,X1: $i,X2: $i] :
( ub(X1,X2,max(sK3,sK4))
| ~ ub(X1,X2,X0)
| ( max(sK3,sK4) != X0 ) ),
inference(instantiation,[status(thm)],[c_803]) ).
tcf(c_1855,plain,
sK5 = sK5,
inference(instantiation,[status(thm)],[c_798]) ).
tcf(c_1865,plain,
sK4 = sK4,
inference(instantiation,[status(thm)],[c_798]) ).
tcf(c_1920,plain,
! [X0: $i] :
( lesseq(sK5,sK1(sK3,sK4,sK5))
| ~ lesseq(sK5,X0)
| ~ lesseq(X0,sK1(sK3,sK4,sK5)) ),
inference(instantiation,[status(thm)],[c_50]) ).
tcf(c_2099,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( summation(max(X0,X1)) = summation(X2) )
| ( max(X0,X1) != X2 ) ),
inference(instantiation,[status(thm)],[c_802]) ).
tcf(c_2118,plain,
( minsol_model_ub(sK3,sK4,sK5)
| ~ model_ub(sK3,sK4,sK5)
| ~ lesseq(sK5,sK2(sK3,sK4,sK5)) ),
inference(instantiation,[status(thm)],[c_71]) ).
tcf(c_2119,plain,
( minsol_model_ub(sK3,sK4,sK5)
| model_ub(sK3,sK4,sK2(sK3,sK4,sK5))
| ~ model_ub(sK3,sK4,sK5) ),
inference(instantiation,[status(thm)],[c_72]) ).
tcf(c_2157,plain,
( minsol_model_ub(sK3,sK4,sK5)
| lesseq(sK5,summation(max(sK3,sK4)))
| ~ model_max(sK3,sK4,summation(max(sK3,sK4))) ),
inference(instantiation,[status(thm)],[c_1668]) ).
tcf(c_2158,plain,
( model_max(sK3,sK4,summation(max(sK3,sK4)))
| ~ lesseq(summation(max(sK3,sK4)),summation(max(sK3,sK4))) ),
inference(instantiation,[status(thm)],[c_1468]) ).
tcf(c_2284,plain,
! [X0: $i] :
( lesseq(sK5,X0)
| lesseq(X0,sK5) ),
inference(instantiation,[status(thm)],[c_52]) ).
tcf(c_2416,plain,
! [X0: $i,X1: $i] : model_max(X0,X1,summation(max(X0,X1))),
inference(superposition,[status(thm)],[c_49,c_62]) ).
tcf(c_2426,plain,
! [X0: $i,X1: $i,X2: $i] :
( model_max(X1,X2,X0)
| lesseq(X0,summation(max(X1,X2))) ),
inference(superposition,[status(thm)],[c_52,c_62]) ).
tcf(c_2465,plain,
! [X0: $i] :
( lesseq(sK4,X0)
| ~ lesseq(summation(sK4),summation(X0)) ),
inference(instantiation,[status(thm)],[c_55]) ).
tcf(c_2467,plain,
! [X0: $i,X1: $i,X2: $i] :
( lesseq(sK4,X0)
| ~ lesseq(X2,X1)
| ( sK4 != X2 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_801]) ).
tcf(c_2468,plain,
! [X0: $i,X1: $i] :
( lesseq(sK4,X1)
| ~ lesseq(sK4,X0)
| ~ lesseq(X0,X1) ),
inference(instantiation,[status(thm)],[c_50]) ).
tcf(c_2473,plain,
! [X0: $i,X1: $i] :
( lesseq(sK4,X1)
| ~ ub(X0,sK4,X1) ),
inference(instantiation,[status(thm)],[c_61]) ).
tcf(c_2619,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( lesseq(X3,X2)
| model_max(X0,X1,X3)
| ~ lesseq(summation(max(X0,X1)),X2) ),
inference(superposition,[status(thm)],[c_2426,c_50]) ).
tcf(c_2627,plain,
! [X0: $i,X1: $i,X2: $i] :
( lesseq(X2,X1)
| lesseq(X0,X2)
| ~ lesseq(X0,X1) ),
inference(resolution,[status(thm)],[c_50,c_52]) ).
tcf(c_2742,plain,
! [X0: $i,X1: $i,X2: $i] :
( lesseq(X1,max(sK3,sK4))
| ~ lesseq(X2,X0)
| ( X1 != X2 )
| ( max(sK3,sK4) != X0 ) ),
inference(instantiation,[status(thm)],[c_801]) ).
tcf(c_2746,plain,
( lesseq(sK3,max(sK3,sK4))
| ~ lesseq(sK3,sK3)
| ( sK3 != sK3 )
| ( max(sK3,sK4) != sK3 ) ),
inference(instantiation,[status(thm)],[c_2742]) ).
tcf(c_2864,plain,
! [X0: $i,X1: $i] :
( ub(X0,X1,max(sK3,sK4))
| ~ ub(X0,X1,sK3)
| ( max(sK3,sK4) != sK3 ) ),
inference(instantiation,[status(thm)],[c_1848]) ).
tcf(c_2865,plain,
( ( max(sK3,sK4) = sK3 )
| ~ lesseq(sK4,sK3) ),
inference(instantiation,[status(thm)],[c_57]) ).
tcf(c_2925,plain,
! [X0: $i] :
( ( summation(max(sK3,sK4)) = summation(X0) )
| ( max(sK3,sK4) != X0 ) ),
inference(instantiation,[status(thm)],[c_2099]) ).
tcf(c_2981,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( lesseq(X4,summation(max(X2,X3)))
| ~ minsol_model_ub(X0,X1,X4)
| ~ model_ub(X0,X1,summation(max(X2,X3))) ),
inference(instantiation,[status(thm)],[c_74]) ).
tcf(c_3174,plain,
lesseq(summation(max(sK3,sK4)),summation(max(sK3,sK4))),
inference(instantiation,[status(thm)],[c_1469]) ).
tcf(c_3209,plain,
! [X0: $i,X1: $i,X2: $i] :
( lesseq(max(X0,X1),X2)
| ~ model_max(X0,X1,summation(X2)) ),
inference(superposition,[status(thm)],[c_63,c_55]) ).
tcf(c_3346,plain,
! [X0: $i,X1: $i] : model_max(X0,X1,summation(max(X0,X1))),
inference(resolution,[status(thm)],[c_62,c_49]) ).
tcf(c_3349,plain,
! [X0: $i,X1: $i,X2: $i] :
( model_max(X0,X1,summation(X2))
| ~ lesseq(max(X0,X1),X2) ),
inference(resolution,[status(thm)],[c_62,c_56]) ).
tcf(c_3414,plain,
( lesseq(sK4,sK4)
| ~ lesseq(summation(sK4),summation(sK4)) ),
inference(instantiation,[status(thm)],[c_2465]) ).
tcf(c_3415,plain,
lesseq(summation(sK4),summation(sK4)),
inference(instantiation,[status(thm)],[c_1522]) ).
tcf(c_3455,plain,
! [X0: $i,X1: $i,X2: $i] :
( lesseq(X1,sK0(X0,X1,X2))
| ~ model_ub(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_65,c_61]) ).
tcf(c_3456,plain,
! [X0: $i,X1: $i,X2: $i] :
( lesseq(X0,sK0(X0,X1,X2))
| ~ model_ub(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_65,c_60]) ).
tcf(c_3564,plain,
( lesseq(sK5,sK1(sK3,sK4,sK5))
| ~ lesseq(sK5,summation(max(sK3,sK4)))
| ~ lesseq(summation(max(sK3,sK4)),sK1(sK3,sK4,sK5)) ),
inference(instantiation,[status(thm)],[c_1920]) ).
tcf(c_3565,plain,
( lesseq(summation(max(sK3,sK4)),sK1(sK3,sK4,sK5))
| ~ model_max(sK3,sK4,sK1(sK3,sK4,sK5)) ),
inference(instantiation,[status(thm)],[c_1791]) ).
tcf(c_4066,plain,
( ( summation(max(sK3,sK4)) = summation(sK4) )
| ( max(sK3,sK4) != sK4 ) ),
inference(instantiation,[status(thm)],[c_2925]) ).
tcf(c_4195,plain,
! [X0: $i,X1: $i] :
( ub(X0,sK4,X1)
| ~ lesseq(sK4,X1)
| ~ lesseq(X0,X1) ),
inference(instantiation,[status(thm)],[c_59]) ).
tcf(c_4196,plain,
( ub(sK3,sK4,sK3)
| ~ lesseq(sK4,sK3)
| ~ lesseq(sK3,sK3) ),
inference(instantiation,[status(thm)],[c_4195]) ).
tcf(c_4324,plain,
! [X0: $i] :
( lesseq(summation(max(sK3,sK4)),sK5)
| ~ lesseq(X0,sK5)
| ( sK5 != sK5 )
| ( summation(max(sK3,sK4)) != X0 ) ),
inference(instantiation,[status(thm)],[c_1705]) ).
tcf(c_4971,plain,
! [X0: $i,X1: $i] :
( lesseq(sK4,X0)
| ~ lesseq(sK4,X1)
| ( sK4 != sK4 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_2467]) ).
tcf(c_5007,plain,
! [X0: $i,X1: $i,X2: $i] :
( model_ub(X0,X1,X2)
| ~ lesseq(summation(max(sK3,sK4)),X2)
| ~ ub(X0,X1,max(sK3,sK4)) ),
inference(instantiation,[status(thm)],[c_64]) ).
tcf(c_5207,plain,
! [X0: $i,X1: $i] :
( lesseq(sK5,summation(max(X0,X1)))
| ~ minsol_model_ub(sK3,sK4,sK5)
| ~ model_ub(sK3,sK4,summation(max(X0,X1))) ),
inference(instantiation,[status(thm)],[c_2981]) ).
tcf(c_5376,plain,
! [X0: $i,X1: $i,X2: $i] :
( lesseq(summation(max(X0,X1)),X2)
| ~ lesseq(sK5,X2)
| ~ lesseq(summation(max(X0,X1)),sK5) ),
inference(instantiation,[status(thm)],[c_1527]) ).
tcf(c_6411,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( lesseq(X0,X3)
| ~ model_max(X1,X2,X3)
| ~ lesseq(X0,summation(max(X1,X2))) ),
inference(resolution,[status(thm)],[c_63,c_50]) ).
tcf(c_7269,plain,
( minsol_model_ub(sK3,sK4,sK5)
| lesseq(sK5,summation(max(sK3,sK4))) ),
inference(superposition,[status(thm)],[c_2416,c_591]) ).
tcf(c_7360,plain,
( minsol_model_ub(sK3,sK4,sK5)
| lesseq(sK5,summation(sK4))
| ( max(sK3,sK4) = sK3 ) ),
inference(superposition,[status(thm)],[c_1567,c_7269]) ).
tcf(c_7504,plain,
! [X0: $i] :
( minsol_model_ub(sK3,sK4,sK5)
| lesseq(summation(sK5),X0)
| lesseq(X0,summation(summation(max(sK3,sK4)))) ),
inference(superposition,[status(thm)],[c_7269,c_1598]) ).
tcf(c_9450,plain,
( lesseq(sK5,summation(max(sK3,sK4)))
| ~ minsol_model_ub(sK3,sK4,sK5)
| ~ model_ub(sK3,sK4,summation(max(sK3,sK4))) ),
inference(instantiation,[status(thm)],[c_5207]) ).
tcf(c_10083,plain,
! [X0: $i] :
( model_ub(X0,sK4,sK5)
| ~ lesseq(summation(max(sK3,sK4)),sK5)
| ~ ub(X0,sK4,max(sK3,sK4)) ),
inference(instantiation,[status(thm)],[c_1573]) ).
tcf(c_10084,plain,
( model_ub(sK3,sK4,sK5)
| ~ ub(sK3,sK4,max(sK3,sK4))
| ~ lesseq(summation(max(sK3,sK4)),sK5) ),
inference(instantiation,[status(thm)],[c_10083]) ).
tcf(c_10707,plain,
( minsol_model_ub(sK3,sK4,sK5)
| lesseq(sK5,summation(max(sK3,sK4))) ),
inference(resolution,[status(thm)],[c_3346,c_591]) ).
tcf(c_10915,plain,
! [X0: $i,X1: $i] :
( model_ub(X1,sK4,X0)
| ~ ub(X1,sK4,max(sK3,sK4))
| ~ lesseq(summation(max(sK3,sK4)),X0) ),
inference(instantiation,[status(thm)],[c_5007]) ).
tcf(c_14512,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( lesseq(X3,sK2(X1,X2,X3))
| ~ lesseq(X3,X0)
| ~ lesseq(X0,sK2(X1,X2,X3)) ),
inference(instantiation,[status(thm)],[c_50]) ).
tcf(c_14559,plain,
! [X0: $i] :
( lesseq(summation(max(sK3,sK4)),X0)
| ~ lesseq(sK5,X0)
| ~ lesseq(summation(max(sK3,sK4)),sK5) ),
inference(instantiation,[status(thm)],[c_5376]) ).
tcf(c_14800,plain,
! [X0: $i,X1: $i,X2: $i] :
( lesseq(max(sK3,sK4),X1)
| ~ lesseq(X0,X2)
| ( X1 != X2 )
| ( max(sK3,sK4) != X0 ) ),
inference(instantiation,[status(thm)],[c_801]) ).
tcf(c_14804,plain,
( lesseq(max(sK3,sK4),sK3)
| ~ lesseq(sK3,sK3)
| ( sK3 != sK3 )
| ( max(sK3,sK4) != sK3 ) ),
inference(instantiation,[status(thm)],[c_14800]) ).
tcf(c_15114,plain,
! [X0: $i,X1: $i,X2: $i] :
( lesseq(X2,summation(X1))
| lesseq(summation(X0),X2)
| ~ lesseq(X0,X1) ),
inference(resolution,[status(thm)],[c_2627,c_56]) ).
tcf(c_15751,plain,
! [X0: $i] :
( lesseq(sK4,max(sK3,sK4))
| ~ ub(X0,sK4,max(sK3,sK4)) ),
inference(instantiation,[status(thm)],[c_2473]) ).
tcf(c_15752,plain,
! [X0: $i] :
( ub(X0,sK4,max(sK3,sK4))
| ~ ub(X0,sK4,sK3)
| ( max(sK3,sK4) != sK3 ) ),
inference(instantiation,[status(thm)],[c_2864]) ).
tcf(c_15753,plain,
! [X0: $i] :
( ub(X0,sK4,max(sK3,sK4))
| ~ lesseq(sK4,max(sK3,sK4))
| ~ lesseq(X0,max(sK3,sK4)) ),
inference(instantiation,[status(thm)],[c_1846]) ).
tcf(c_15754,plain,
( lesseq(sK4,max(sK3,sK4))
| ~ ub(sK3,sK4,max(sK3,sK4)) ),
inference(instantiation,[status(thm)],[c_15751]) ).
tcf(c_15755,plain,
( ub(sK3,sK4,max(sK3,sK4))
| ~ lesseq(sK4,max(sK3,sK4))
| ~ lesseq(sK3,max(sK3,sK4)) ),
inference(instantiation,[status(thm)],[c_15753]) ).
tcf(c_15756,plain,
( ub(sK3,sK4,max(sK3,sK4))
| ~ ub(sK3,sK4,sK3)
| ( max(sK3,sK4) != sK3 ) ),
inference(instantiation,[status(thm)],[c_15752]) ).
tcf(c_17693,plain,
( lesseq(summation(max(sK3,sK4)),sK5)
| ~ lesseq(summation(sK4),sK5)
| ( sK5 != sK5 )
| ( summation(max(sK3,sK4)) != summation(sK4) ) ),
inference(instantiation,[status(thm)],[c_4324]) ).
tcf(c_19447,plain,
! [X0: $i] :
( minsol_model_ub(sK3,sK4,sK5)
| lesseq(sK5,summation(X0))
| ~ lesseq(max(sK3,sK4),X0) ),
inference(resolution,[status(thm)],[c_3349,c_591]) ).
tcf(c_19448,plain,
( minsol_model_ub(sK3,sK4,sK5)
| lesseq(sK5,summation(sK3))
| ~ lesseq(max(sK3,sK4),sK3) ),
inference(instantiation,[status(thm)],[c_19447]) ).
tcf(c_22637,plain,
! [X0: $i] :
( lesseq(sK4,X0)
| ~ lesseq(sK4,max(sK3,sK4))
| ~ lesseq(max(sK3,sK4),X0) ),
inference(instantiation,[status(thm)],[c_2468]) ).
tcf(c_22645,plain,
( lesseq(sK4,sK3)
| ~ lesseq(sK4,max(sK3,sK4))
| ~ lesseq(max(sK3,sK4),sK3) ),
inference(instantiation,[status(thm)],[c_22637]) ).
tcf(c_23838,plain,
! [X0: $i] :
( lesseq(sK4,X0)
| ~ lesseq(sK4,sK4)
| ( sK4 != sK4 )
| ( X0 != sK4 ) ),
inference(instantiation,[status(thm)],[c_4971]) ).
tcf(c_25876,plain,
! [X0: $i] :
( model_ub(X0,sK4,summation(max(sK3,sK4)))
| ~ ub(X0,sK4,max(sK3,sK4))
| ~ lesseq(summation(max(sK3,sK4)),summation(max(sK3,sK4))) ),
inference(instantiation,[status(thm)],[c_10915]) ).
tcf(c_25877,plain,
( model_ub(sK3,sK4,summation(max(sK3,sK4)))
| ~ ub(sK3,sK4,max(sK3,sK4))
| ~ lesseq(summation(max(sK3,sK4)),summation(max(sK3,sK4))) ),
inference(instantiation,[status(thm)],[c_25876]) ).
tcf(c_38833,plain,
( lesseq(sK4,max(sK3,sK4))
| ~ lesseq(sK4,sK4)
| ( sK4 != sK4 )
| ( max(sK3,sK4) != sK4 ) ),
inference(instantiation,[status(thm)],[c_23838]) ).
tcf(c_46093,plain,
! [X0: $i] :
( lesseq(sK5,sK2(sK3,sK4,sK5))
| ~ lesseq(sK5,X0)
| ~ lesseq(X0,sK2(sK3,sK4,sK5)) ),
inference(instantiation,[status(thm)],[c_14512]) ).
tcf(c_54434,plain,
( lesseq(summation(sK0(sK3,sK4,sK5)),sK5)
| ~ model_ub(sK3,sK4,sK5) ),
inference(instantiation,[status(thm)],[c_66]) ).
tcf(c_54493,plain,
( lesseq(sK4,sK0(sK3,sK4,sK5))
| ~ model_ub(sK3,sK4,sK5) ),
inference(instantiation,[status(thm)],[c_3455]) ).
tcf(c_54494,plain,
( lesseq(sK3,sK0(sK3,sK4,sK5))
| ~ model_ub(sK3,sK4,sK5) ),
inference(instantiation,[status(thm)],[c_3456]) ).
tcf(c_54798,plain,
! [X0: $i] :
( lesseq(summation(X0),sK5)
| ~ lesseq(X0,sK0(sK3,sK4,sK5))
| ~ lesseq(summation(sK0(sK3,sK4,sK5)),sK5) ),
inference(instantiation,[status(thm)],[c_1552]) ).
tcf(c_54800,plain,
( lesseq(summation(sK3),sK5)
| ~ lesseq(sK3,sK0(sK3,sK4,sK5))
| ~ lesseq(summation(sK0(sK3,sK4,sK5)),sK5) ),
inference(instantiation,[status(thm)],[c_54798]) ).
tcf(c_57577,plain,
! [X0: $i,X1: $i] :
( lesseq(summation(X1),sK5)
| ~ lesseq(X1,X0)
| ~ lesseq(summation(X0),sK5) ),
inference(instantiation,[status(thm)],[c_1552]) ).
tcf(c_58928,plain,
! [X0: $i,X1: $i] :
( lesseq(sK4,X1)
| ( max(X0,sK4) = sK4 )
| ~ lesseq(X0,X1) ),
inference(instantiation,[status(thm)],[c_1577]) ).
tcf(c_58929,plain,
( lesseq(sK4,sK3)
| ( max(sK3,sK4) = sK4 )
| ~ lesseq(sK3,sK3) ),
inference(instantiation,[status(thm)],[c_58928]) ).
tcf(c_60475,plain,
! [X0: $i] :
( ( max(X0,sK4) = sK4 )
| ( max(X0,sK4) = X0 ) ),
inference(instantiation,[status(thm)],[c_1567]) ).
tcf(c_60478,plain,
( ( max(sK3,sK4) = sK4 )
| ( max(sK3,sK4) = sK3 ) ),
inference(instantiation,[status(thm)],[c_60475]) ).
tcf(c_71181,plain,
( lesseq(summation(max(sK3,sK4)),sK5)
| ~ lesseq(summation(sK0(sK3,sK4,sK5)),sK5)
| ~ lesseq(max(sK3,sK4),sK0(sK3,sK4,sK5)) ),
inference(instantiation,[status(thm)],[c_54798]) ).
tcf(c_83377,plain,
! [X0: $i] :
( lesseq(max(sK3,sK4),sK0(sK3,sK4,sK5))
| ~ lesseq(max(sK3,sK4),X0)
| ~ lesseq(X0,sK0(sK3,sK4,sK5)) ),
inference(instantiation,[status(thm)],[c_50]) ).
tcf(c_83380,plain,
( lesseq(max(sK3,sK4),sK0(sK3,sK4,sK5))
| ~ lesseq(max(sK3,sK4),sK3)
| ~ lesseq(sK3,sK0(sK3,sK4,sK5)) ),
inference(instantiation,[status(thm)],[c_83377]) ).
tcf(c_133689,plain,
( lesseq(summation(sK4),sK5)
| ~ lesseq(sK4,sK0(sK3,sK4,sK5))
| ~ lesseq(summation(sK0(sK3,sK4,sK5)),sK5) ),
inference(instantiation,[status(thm)],[c_54798]) ).
tcf(c_133711,plain,
! [X0: $i] :
( lesseq(summation(sK4),sK5)
| ~ lesseq(sK4,X0)
| ~ lesseq(summation(X0),sK5) ),
inference(instantiation,[status(thm)],[c_57577]) ).
tcf(c_133712,plain,
( lesseq(summation(sK4),sK5)
| ~ lesseq(sK4,sK3)
| ~ lesseq(summation(sK3),sK5) ),
inference(instantiation,[status(thm)],[c_133711]) ).
tcf(c_152489,plain,
( lesseq(sK3,sK0(sK3,sK4,sK2(sK3,sK4,sK5)))
| ~ model_ub(sK3,sK4,sK2(sK3,sK4,sK5)) ),
inference(instantiation,[status(thm)],[c_3456]) ).
tcf(c_152490,plain,
( lesseq(sK4,sK0(sK3,sK4,sK2(sK3,sK4,sK5)))
| ~ model_ub(sK3,sK4,sK2(sK3,sK4,sK5)) ),
inference(instantiation,[status(thm)],[c_3455]) ).
tcf(c_152491,plain,
( lesseq(summation(sK0(sK3,sK4,sK2(sK3,sK4,sK5))),sK2(sK3,sK4,sK5))
| ~ model_ub(sK3,sK4,sK2(sK3,sK4,sK5)) ),
inference(instantiation,[status(thm)],[c_66]) ).
tcf(c_178862,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( lesseq(X3,X2)
| model_max(X0,X1,X3)
| ~ model_max(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_63,c_2619]) ).
tcf(c_185804,plain,
! [X0: $i] :
( lesseq(X0,sK5)
| model_ub(sK3,sK4,sK5)
| model_max(sK3,sK4,X0) ),
inference(superposition,[status(thm)],[c_1510,c_178862]) ).
tcf(c_186341,plain,
! [X0: $i] :
( lesseq(X0,sK5)
| model_max(sK3,sK4,X0) ),
inference(global_subsumption_just,[status(thm)],[c_185804,c_77,c_88,c_728,c_1511,c_1572,c_1605,c_1855,c_2284,c_4066,c_14559,c_14804,c_17693,c_54434,c_54493,c_54494,c_60478,c_71181,c_83380,c_133689]) ).
tcf(c_186349,plain,
! [X0: $i] :
( lesseq(summation(X0),sK5)
| lesseq(max(sK3,sK4),X0) ),
inference(superposition,[status(thm)],[c_186341,c_3209]) ).
tcf(c_186356,plain,
! [X0: $i] :
( lesseq(sK4,X0)
| lesseq(summation(X0),sK5)
| ( max(sK4,sK3) = sK3 ) ),
inference(superposition,[status(thm)],[c_1578,c_186349]) ).
tcf(c_216349,plain,
! [X0: $i] :
( minsol_model_ub(sK3,sK4,sK5)
| lesseq(summation(sK5),X0)
| lesseq(X0,summation(summation(max(sK3,sK4)))) ),
inference(resolution,[status(thm)],[c_15114,c_10707]) ).
tcf(c_238374,plain,
! [X0: $i] :
( lesseq(sK4,X0)
| lesseq(summation(X0),sK5) ),
inference(global_subsumption_just,[status(thm)],[c_186356,c_77,c_1865,c_3414,c_3415,c_4196,c_15754,c_15756,c_22637,c_38833,c_58929,c_60478,c_186349]) ).
tcf(c_238376,plain,
( lesseq(sK4,sK3)
| lesseq(summation(sK3),sK5) ),
inference(instantiation,[status(thm)],[c_238374]) ).
tcf(c_241662,plain,
model_max(sK3,sK4,sK5),
inference(global_subsumption_just,[status(thm)],[c_583,c_77,c_88,c_728,c_1572,c_1855,c_4066,c_14804,c_17693,c_54434,c_54493,c_54494,c_60478,c_71181,c_83380,c_133689]) ).
tcf(c_241713,plain,
! [X0: $i,X1: $i,X2: $i] :
( lesseq(X2,X1)
| lesseq(X0,X2)
| ~ lesseq(X0,X1) ),
inference(superposition,[status(thm)],[c_52,c_50]) ).
tcf(c_241851,plain,
! [X0: $i,X1: $i,X2: $i] :
( lesseq(summation(X0),X2)
| ( max(X0,X1) = X1 )
| ~ model_max(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_1567,c_63]) ).
tcf(c_241852,plain,
! [X0: $i,X1: $i,X2: $i] :
( lesseq(summation(X1),X2)
| ( max(X0,X1) = X0 )
| ~ model_max(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_1567,c_63]) ).
tcf(c_241894,plain,
( lesseq(summation(sK3),sK5)
| ( max(sK3,sK4) = sK4 ) ),
inference(superposition,[status(thm)],[c_241662,c_241851]) ).
tcf(c_241904,plain,
( lesseq(summation(sK4),sK5)
| ( max(sK3,sK4) = sK3 ) ),
inference(superposition,[status(thm)],[c_241662,c_241852]) ).
tcf(c_241943,plain,
lesseq(summation(sK3),sK5),
inference(global_subsumption_just,[status(thm)],[c_241894,c_77,c_88,c_728,c_1511,c_1572,c_1855,c_2865,c_4066,c_4196,c_10084,c_14804,c_15756,c_17693,c_54434,c_54493,c_54494,c_54800,c_60478,c_71181,c_83380,c_133689,c_238376]) ).
tcf(c_241947,plain,
! [X0: $i] :
( lesseq(summation(sK3),X0)
| ~ lesseq(sK5,X0) ),
inference(superposition,[status(thm)],[c_241943,c_50]) ).
tcf(c_242036,plain,
! [X0: $i] :
( lesseq(sK3,X0)
| ~ lesseq(sK5,summation(X0)) ),
inference(superposition,[status(thm)],[c_241947,c_55]) ).
tcf(c_242255,plain,
lesseq(summation(sK4),sK5),
inference(global_subsumption_just,[status(thm)],[c_241904,c_77,c_88,c_1865,c_3414,c_3415,c_4196,c_14804,c_15754,c_15756,c_22645,c_38833,c_58929,c_60478,c_133712,c_241904,c_241943]) ).
tcf(c_242259,plain,
! [X0: $i] :
( lesseq(summation(sK4),X0)
| ~ lesseq(sK5,X0) ),
inference(superposition,[status(thm)],[c_242255,c_50]) ).
tcf(c_242326,plain,
! [X0: $i] :
( lesseq(sK4,X0)
| ~ lesseq(sK5,summation(X0)) ),
inference(superposition,[status(thm)],[c_242259,c_55]) ).
tcf(c_245251,plain,
( minsol_model_ub(sK3,sK4,sK5)
| lesseq(sK5,summation(max(sK3,sK4))) ),
inference(superposition,[status(thm)],[c_2416,c_591]) ).
tcf(c_245355,plain,
( minsol_model_ub(sK3,sK4,sK5)
| lesseq(sK4,max(sK3,sK4)) ),
inference(superposition,[status(thm)],[c_245251,c_242326]) ).
tcf(c_245356,plain,
( minsol_model_ub(sK3,sK4,sK5)
| lesseq(sK3,max(sK3,sK4)) ),
inference(superposition,[status(thm)],[c_245251,c_242036]) ).
tcf(c_245359,plain,
lesseq(sK4,max(sK3,sK4)),
inference(global_subsumption_just,[status(thm)],[c_245355,c_77,c_1865,c_3414,c_3415,c_4196,c_15754,c_15756,c_38833,c_58929,c_60478]) ).
tcf(c_245366,plain,
! [X0: $i] :
( lesseq(sK4,X0)
| lesseq(X0,max(sK3,sK4)) ),
inference(superposition,[status(thm)],[c_245359,c_241713]) ).
tcf(c_245370,plain,
( lesseq(sK4,sK3)
| lesseq(sK3,max(sK3,sK4)) ),
inference(instantiation,[status(thm)],[c_245366]) ).
tcf(c_245406,plain,
lesseq(sK3,max(sK3,sK4)),
inference(global_subsumption_just,[status(thm)],[c_245356,c_77,c_88,c_2746,c_2865,c_245370]) ).
tcf(c_266188,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( lesseq(X3,sK2(X1,X2,X3))
| ~ lesseq(X3,X0)
| ~ lesseq(X0,sK2(X1,X2,X3)) ),
inference(instantiation,[status(thm)],[c_50]) ).
tcf(c_298737,plain,
! [X0: $i] :
( lesseq(sK5,sK2(sK3,sK4,sK5))
| ~ lesseq(sK5,X0)
| ~ lesseq(X0,sK2(sK3,sK4,sK5)) ),
inference(instantiation,[status(thm)],[c_266188]) ).
tcf(c_372294,plain,
! [X0: $i] :
( lesseq(sK5,sK2(sK3,sK4,sK5))
| ~ lesseq(sK5,summation(X0))
| ~ lesseq(summation(X0),sK2(sK3,sK4,sK5)) ),
inference(instantiation,[status(thm)],[c_298737]) ).
tcf(c_372296,plain,
( lesseq(sK5,sK2(sK3,sK4,sK5))
| ~ lesseq(sK5,summation(sK3))
| ~ lesseq(summation(sK3),sK2(sK3,sK4,sK5)) ),
inference(instantiation,[status(thm)],[c_372294]) ).
tcf(c_397716,plain,
! [X0: $i] :
( lesseq(X0,summation(summation(max(sK3,sK4))))
| lesseq(summation(sK5),X0) ),
inference(global_subsumption_just,[status(thm)],[c_216349,c_77,c_88,c_547,c_572,c_728,c_1572,c_1855,c_1865,c_2157,c_2158,c_2746,c_2865,c_3174,c_3414,c_3415,c_3564,c_3565,c_4066,c_4196,c_7504,c_9450,c_14804,c_15754,c_15755,c_15756,c_17693,c_25877,c_38833,c_54434,c_54493,c_54494,c_58929,c_60478,c_71181,c_83380,c_133689,c_245370]) ).
tcf(c_397717,plain,
! [X0: $i] :
( lesseq(summation(sK5),X0)
| lesseq(X0,summation(summation(max(sK3,sK4)))) ),
inference(renaming,[status(thm)],[c_397716]) ).
tcf(c_397739,plain,
! [X0: $i] :
( lesseq(summation(sK5),summation(X0))
| lesseq(X0,summation(max(sK3,sK4))) ),
inference(resolution,[status(thm)],[c_397717,c_55]) ).
tcf(c_397770,plain,
! [X0: $i] :
( lesseq(X0,max(sK3,sK4))
| lesseq(summation(sK5),summation(summation(X0))) ),
inference(resolution,[status(thm)],[c_397739,c_55]) ).
tcf(c_398534,plain,
! [X0: $i] :
( lesseq(sK5,summation(X0))
| lesseq(X0,max(sK3,sK4)) ),
inference(resolution,[status(thm)],[c_397770,c_55]) ).
tcf(c_398760,plain,
! [X0: $i,X1: $i] :
( lesseq(X1,X0)
| lesseq(sK5,summation(X1))
| lesseq(X0,max(sK3,sK4)) ),
inference(resolution,[status(thm)],[c_398534,c_2627]) ).
tcf(c_398871,plain,
( lesseq(sK5,summation(max(sK3,sK4)))
| lesseq(max(sK3,sK4),max(sK3,sK4)) ),
inference(factoring,[status(thm)],[c_398760]) ).
tcf(c_446906,plain,
lesseq(sK5,summation(max(sK3,sK4))),
inference(global_subsumption_just,[status(thm)],[c_398871,c_77,c_88,c_1865,c_2157,c_2158,c_2746,c_2865,c_3174,c_3414,c_3415,c_4196,c_9450,c_15754,c_15755,c_15756,c_25877,c_38833,c_58929,c_60478,c_245370]) ).
tcf(c_446933,plain,
! [X0: $i] :
( lesseq(sK5,X0)
| ~ model_max(sK3,sK4,X0) ),
inference(resolution,[status(thm)],[c_446906,c_6411]) ).
tcf(c_447071,plain,
( lesseq(sK5,sK1(sK3,sK4,sK5))
| ~ minsol_model_ub(sK3,sK4,sK5)
| ~ model_max(sK3,sK4,sK5) ),
inference(resolution,[status(thm)],[c_446933,c_572]) ).
tcf(c_558640,plain,
~ minsol_model_ub(sK3,sK4,sK5),
inference(global_subsumption_just,[status(thm)],[c_547,c_77,c_88,c_547,c_728,c_1572,c_1855,c_4066,c_14804,c_17693,c_54434,c_54493,c_54494,c_60478,c_71181,c_83380,c_133689,c_447071]) ).
tcf(c_559402,plain,
! [X0: $i] :
( lesseq(sK5,sK2(sK3,sK4,sK5))
| ~ lesseq(sK5,X0)
| ~ lesseq(X0,sK2(sK3,sK4,sK5)) ),
inference(instantiation,[status(thm)],[c_50]) ).
tcf(c_565048,plain,
! [X0: $i] :
( lesseq(summation(X0),sK2(sK3,sK4,sK5))
| ~ lesseq(X0,sK0(sK3,sK4,sK2(sK3,sK4,sK5)))
| ~ lesseq(summation(sK0(sK3,sK4,sK2(sK3,sK4,sK5))),sK2(sK3,sK4,sK5)) ),
inference(instantiation,[status(thm)],[c_1552]) ).
tcf(c_565050,plain,
( lesseq(summation(sK3),sK2(sK3,sK4,sK5))
| ~ lesseq(sK3,sK0(sK3,sK4,sK2(sK3,sK4,sK5)))
| ~ lesseq(summation(sK0(sK3,sK4,sK2(sK3,sK4,sK5))),sK2(sK3,sK4,sK5)) ),
inference(instantiation,[status(thm)],[c_565048]) ).
tcf(c_565663,plain,
! [X0: $i] :
( ~ lesseq(X0,sK2(sK3,sK4,sK5))
| ~ lesseq(sK5,X0) ),
inference(global_subsumption_just,[status(thm)],[c_559402,c_1511,c_2118,c_10084,c_15755,c_46093,c_241662,c_245359,c_245406,c_558640]) ).
tcf(c_565664,plain,
! [X0: $i] :
( ~ lesseq(sK5,X0)
| ~ lesseq(X0,sK2(sK3,sK4,sK5)) ),
inference(renaming,[status(thm)],[c_565663]) ).
tcf(c_577505,plain,
! [X0: $i] :
( lesseq(summation(X0),sK2(sK3,sK4,sK5))
| ~ lesseq(X0,sK0(sK3,sK4,sK2(sK3,sK4,sK5))) ),
inference(global_subsumption_just,[status(thm)],[c_565048,c_77,c_88,c_547,c_572,c_728,c_1511,c_1572,c_1855,c_1865,c_2119,c_2157,c_2158,c_2746,c_2865,c_3174,c_3414,c_3415,c_3564,c_3565,c_4066,c_4196,c_9450,c_10084,c_14804,c_15754,c_15755,c_15756,c_17693,c_25877,c_38833,c_54434,c_54493,c_54494,c_58929,c_60478,c_71181,c_83380,c_133689,c_152491,c_245370,c_565048]) ).
tcf(c_584181,plain,
! [X0: $i] :
( ~ lesseq(sK5,summation(X0))
| ~ lesseq(summation(X0),sK2(sK3,sK4,sK5)) ),
inference(instantiation,[status(thm)],[c_565664]) ).
tcf(c_646212,plain,
( lesseq(summation(sK4),sK2(sK3,sK4,sK5))
| ~ lesseq(sK4,sK0(sK3,sK4,sK2(sK3,sK4,sK5))) ),
inference(instantiation,[status(thm)],[c_577505]) ).
tcf(c_673931,plain,
( ~ lesseq(sK5,summation(sK4))
| ~ lesseq(summation(sK4),sK2(sK3,sK4,sK5)) ),
inference(instantiation,[status(thm)],[c_584181]) ).
tcf(c_673932,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_673931,c_646212,c_565050,c_558640,c_372296,c_245406,c_245359,c_241662,c_152489,c_152490,c_152491,c_19448,c_15755,c_14804,c_10084,c_7360,c_2119,c_2118,c_1511,c_88,c_77]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM860+1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.07/0.35 % Computer : n015.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.36 % DateTime : Thu Sep 24 05:39:10 UTC 2026
% 0.07/0.36 % CPUTime :
% 0.07/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/0.40 Running first-order theorem proving
% 0.13/0.40 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.41
% 0.13/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.41
% 0.13/0.41 % Detected problem language: tptp
% 0.13/0.42 % Proving...
% 126.14/32.51 % SZS status Started for theBenchmark.p
% 126.14/32.51 % SZS status Theorem for theBenchmark.p
% 126.14/32.51
% 126.14/32.51 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 126.14/32.51
% 126.14/32.51 % ------ iProver source info
% 126.14/32.51
% 126.14/32.51 % git: date: 2026-07-19 20:42:38 +0200
% 126.14/32.51 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 126.14/32.51 % git: non_committed_changes: false
% 126.14/32.51
% 126.14/32.51 % ------ Parsing...
% 126.14/32.51 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 126.14/32.51
% 126.14/32.51 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e %
% 126.14/32.51
% 126.14/32.51 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 126.14/32.51
% 126.14/32.51 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 126.14/32.51 % ------ Proving...
% 126.14/32.51 % ------ Problem Properties
% 126.14/32.51
% 126.14/32.51 %
% 126.14/32.51 % clauses 28
% 126.14/32.51 % conjectures 0
% 126.14/32.51 % EPR 11
% 126.14/32.51 % Horn 23
% 126.14/32.51 % unary 1
% 126.14/32.51 % binary 15
% 126.14/32.51 % lits 69
% 126.14/32.51 % lits eq 3
% 126.14/32.51 % fd_pure 0
% 126.14/32.51 % fd_pseudo 0
% 126.14/32.51 % fd_cond 0
% 126.14/32.51 % fd_pseudo_cond 1
% 126.14/32.51 % AC symbols 0
% 126.14/32.51
% 126.14/32.51 % ------ Input Options Time Limit: Unbounded
% 126.14/32.51
% 126.14/32.51
% 126.14/32.51 % ------
% 126.14/32.51 % Current options:
% 126.14/32.51 % ------
% 126.14/32.51
% 126.14/32.51
% 126.14/32.51 %
% 126.14/32.51
% 126.14/32.51 % ------ Proving...
% 126.14/32.51 %
% 126.14/32.51
% 126.14/32.51 % SZS status Theorem for theBenchmark.p
% 126.14/32.51
% 126.14/32.51 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 126.14/32.52
% 126.14/32.52
%------------------------------------------------------------------------------