TSTP Solution File: NUM858+1 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : NUM858+1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n012.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 : 600s
% DateTime : Mon Jul 18 11:56:09 EDT 2022
% Result : Theorem 13.55s 13.74s
% Output : CNFRefutation 13.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 28
% Syntax : Number of formulae : 466 ( 293 unt; 14 typ; 0 def)
% Number of atoms : 2644 ( 730 equ; 0 cnn)
% Maximal formula atoms : 4 ( 5 avg)
% Number of connectives : 5897 ( 994 ~; 820 |; 50 &;4001 @)
% ( 20 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 28 ( 28 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 14 usr; 5 con; 0-3 aty)
% Number of variables : 1461 ( 0 ^1461 !; 0 ?;1461 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_lesseq,type,
lesseq: $i > $i > $o ).
thf(tp_max,type,
max: $i > $i > $i ).
thf(tp_minsol_model_max,type,
minsol_model_max: $i > $i > $i > $o ).
thf(tp_minsol_model_ub,type,
minsol_model_ub: $i > $i > $i > $o ).
thf(tp_model_max,type,
model_max: $i > $i > $i > $o ).
thf(tp_model_ub,type,
model_ub: $i > $i > $i > $o ).
thf(tp_sK1_X,type,
sK1_X: $i ).
thf(tp_sK2_SY37,type,
sK2_SY37: $i ).
thf(tp_sK3_SY39,type,
sK3_SY39: $i ).
thf(tp_sK4_Z,type,
sK4_Z: $i > $i > $i > $i ).
thf(tp_sK5_Z,type,
sK5_Z: $i > $i > $i > $i ).
thf(tp_sum,type,
sum: $i > $i > $i ).
thf(tp_summation,type,
summation: $i > $i ).
thf(tp_ub,type,
ub: $i > $i > $i > $o ).
thf(1,axiom,
! [X: $i,Y: $i,N: $i] :
( ( minsol_model_ub @ X @ Y @ N )
<=> ( ( model_ub @ X @ Y @ N )
& ! [Z: $i] :
( ( model_ub @ X @ Y @ Z )
=> ( lesseq @ N @ Z ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',minsol_model_ub) ).
thf(2,axiom,
! [X: $i,Y: $i,N: $i] :
( ( minsol_model_max @ X @ Y @ N )
<=> ( ( model_max @ X @ Y @ N )
& ! [Z: $i] :
( ( model_max @ X @ Y @ Z )
=> ( lesseq @ N @ Z ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',minsol_model_max) ).
thf(3,axiom,
! [X: $i,Y: $i,N: $i] :
( ( model_ub @ X @ Y @ N )
<=> ( ub @ X @ Y @ N ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',model_ub_1) ).
thf(4,axiom,
! [X: $i,Y: $i,N: $i] :
( ( model_max @ X @ Y @ N )
<=> ( N
= ( max @ X @ Y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',model_max_1) ).
thf(5,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( ub @ X @ Y @ Z )
<=> ( ( lesseq @ X @ Z )
& ( lesseq @ Y @ Z ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ub) ).
thf(6,axiom,
! [X: $i,Y: $i] :
( ( ( max @ X @ Y )
= Y )
| ~ ( lesseq @ X @ Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',max_2) ).
thf(7,axiom,
! [X: $i,Y: $i] :
( ( ( max @ X @ Y )
= X )
| ~ ( lesseq @ Y @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',max_1) ).
thf(8,axiom,
! [X: $i,Y: $i] :
( ( lesseq @ X @ Y )
<=> ( lesseq @ ( summation @ X ) @ ( summation @ Y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',summation_monotone) ).
thf(9,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( lesseq @ X @ Y )
<=> ( lesseq @ ( sum @ Z @ X ) @ ( sum @ Z @ Y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_monotone_1) ).
thf(10,axiom,
! [X: $i,Y: $i] :
( ( lesseq @ X @ Y )
| ( lesseq @ Y @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lesseq_total) ).
thf(11,axiom,
! [X: $i,Y: $i] :
( ( ( lesseq @ X @ Y )
& ( lesseq @ Y @ X ) )
=> ( X = Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lesseq_antisymmetric) ).
thf(12,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( ( lesseq @ X @ Y )
& ( lesseq @ Y @ Z ) )
=> ( lesseq @ X @ Z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lesseq_trans) ).
thf(13,axiom,
! [X: $i] : ( lesseq @ X @ X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lesseq_ref) ).
thf(14,conjecture,
! [X: $i,Y: $i,Z: $i] :
( ( minsol_model_ub @ X @ Y @ Z )
<=> ( minsol_model_max @ X @ Y @ Z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',max_is_ub_1) ).
thf(15,negated_conjecture,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( minsol_model_ub @ X @ Y @ Z )
<=> ( minsol_model_max @ X @ Y @ Z ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[14]) ).
thf(16,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( minsol_model_ub @ X @ Y @ Z )
<=> ( minsol_model_max @ X @ Y @ Z ) ) )
= $false ),
inference(unfold_def,[status(thm)],[15]) ).
thf(17,plain,
( ( ! [X: $i,Y: $i,N: $i] :
( ( minsol_model_ub @ X @ Y @ N )
<=> ( ( model_ub @ X @ Y @ N )
& ! [Z: $i] :
( ( model_ub @ X @ Y @ Z )
=> ( lesseq @ N @ Z ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(18,plain,
( ( ! [X: $i,Y: $i,N: $i] :
( ( minsol_model_max @ X @ Y @ N )
<=> ( ( model_max @ X @ Y @ N )
& ! [Z: $i] :
( ( model_max @ X @ Y @ Z )
=> ( lesseq @ N @ Z ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(19,plain,
( ( ! [X: $i,Y: $i,N: $i] :
( ( model_ub @ X @ Y @ N )
<=> ( ub @ X @ Y @ N ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(20,plain,
( ( ! [X: $i,Y: $i,N: $i] :
( ( model_max @ X @ Y @ N )
<=> ( N
= ( max @ X @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(21,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( ub @ X @ Y @ Z )
<=> ( ( lesseq @ X @ Z )
& ( lesseq @ Y @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(22,plain,
( ( ! [X: $i,Y: $i] :
( ( ( max @ X @ Y )
= Y )
| ~ ( lesseq @ X @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(23,plain,
( ( ! [X: $i,Y: $i] :
( ( ( max @ X @ Y )
= X )
| ~ ( lesseq @ Y @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(24,plain,
( ( ! [X: $i,Y: $i] :
( ( lesseq @ X @ Y )
<=> ( lesseq @ ( summation @ X ) @ ( summation @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(25,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( lesseq @ X @ Y )
<=> ( lesseq @ ( sum @ Z @ X ) @ ( sum @ Z @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(26,plain,
( ( ! [X: $i,Y: $i] :
( ( lesseq @ X @ Y )
| ( lesseq @ Y @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(27,plain,
( ( ! [X: $i,Y: $i] :
( ( ( lesseq @ X @ Y )
& ( lesseq @ Y @ X ) )
=> ( X = Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(28,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( ( lesseq @ X @ Y )
& ( lesseq @ Y @ Z ) )
=> ( lesseq @ X @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(29,plain,
( ( ! [X: $i] : ( lesseq @ X @ X ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(30,plain,
( ( ! [SY37: $i,SY38: $i] :
( ( minsol_model_ub @ sK1_X @ SY37 @ SY38 )
<=> ( minsol_model_max @ sK1_X @ SY37 @ SY38 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[16]) ).
thf(31,plain,
( ( ! [SY39: $i] :
( ( minsol_model_ub @ sK1_X @ sK2_SY37 @ SY39 )
<=> ( minsol_model_max @ sK1_X @ sK2_SY37 @ SY39 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[30]) ).
thf(32,plain,
( ( ( minsol_model_ub @ sK1_X @ sK2_SY37 @ sK3_SY39 )
<=> ( minsol_model_max @ sK1_X @ sK2_SY37 @ sK3_SY39 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[31]) ).
thf(33,plain,
( ( ( minsol_model_ub @ sK1_X @ sK2_SY37 @ sK3_SY39 )
=> ( minsol_model_max @ sK1_X @ sK2_SY37 @ sK3_SY39 ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[32]) ).
thf(34,plain,
( ( ( minsol_model_max @ sK1_X @ sK2_SY37 @ sK3_SY39 )
=> ( minsol_model_ub @ sK1_X @ sK2_SY37 @ sK3_SY39 ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[32]) ).
thf(35,plain,
( ( ~ ( ( minsol_model_ub @ sK1_X @ sK2_SY37 @ sK3_SY39 )
=> ( minsol_model_max @ sK1_X @ sK2_SY37 @ sK3_SY39 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[33]) ).
thf(36,plain,
( ( ~ ( ( minsol_model_max @ sK1_X @ sK2_SY37 @ sK3_SY39 )
=> ( minsol_model_ub @ sK1_X @ sK2_SY37 @ sK3_SY39 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[34]) ).
thf(37,plain,
( ( ( minsol_model_ub @ sK1_X @ sK2_SY37 @ sK3_SY39 )
& ~ ( minsol_model_max @ sK1_X @ sK2_SY37 @ sK3_SY39 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[35]) ).
thf(38,plain,
( ( ( minsol_model_max @ sK1_X @ sK2_SY37 @ sK3_SY39 )
& ~ ( minsol_model_ub @ sK1_X @ sK2_SY37 @ sK3_SY39 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[36]) ).
thf(39,plain,
( ( ! [X: $i] :
( ! [Y: $i,N: $i] :
( ( ( model_ub @ X @ Y @ ( sK4_Z @ N @ Y @ X ) )
& ~ ( lesseq @ N @ ( sK4_Z @ N @ Y @ X ) ) )
| ~ ( model_ub @ X @ Y @ N )
| ( minsol_model_ub @ X @ Y @ N ) )
& ! [Y: $i,N: $i] :
( ~ ( minsol_model_ub @ X @ Y @ N )
| ! [Z: $i] :
( ~ ( model_ub @ X @ Y @ Z )
| ( lesseq @ N @ Z ) ) )
& ! [Y: $i,N: $i] :
( ~ ( minsol_model_ub @ X @ Y @ N )
| ( model_ub @ X @ Y @ N ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[17]) ).
thf(40,plain,
( ( ! [X: $i] :
( ! [Y: $i,N: $i] :
( ( ( model_max @ X @ Y @ ( sK5_Z @ N @ Y @ X ) )
& ~ ( lesseq @ N @ ( sK5_Z @ N @ Y @ X ) ) )
| ~ ( model_max @ X @ Y @ N )
| ( minsol_model_max @ X @ Y @ N ) )
& ! [Y: $i,N: $i] :
( ~ ( minsol_model_max @ X @ Y @ N )
| ! [Z: $i] :
( ~ ( model_max @ X @ Y @ Z )
| ( lesseq @ N @ Z ) ) )
& ! [Y: $i,N: $i] :
( ~ ( minsol_model_max @ X @ Y @ N )
| ( model_max @ X @ Y @ N ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[18]) ).
thf(41,plain,
( ( ! [X: $i] :
( ! [Y: $i,N: $i] :
( ~ ( model_ub @ X @ Y @ N )
| ( ub @ X @ Y @ N ) )
& ! [Y: $i,N: $i] :
( ~ ( ub @ X @ Y @ N )
| ( model_ub @ X @ Y @ N ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[19]) ).
thf(42,plain,
( ( ! [X: $i] :
( ! [Y: $i,N: $i] :
( ( N
!= ( max @ X @ Y ) )
| ( model_max @ X @ Y @ N ) )
& ! [Y: $i,N: $i] :
( ~ ( model_max @ X @ Y @ N )
| ( N
= ( max @ X @ Y ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[20]) ).
thf(43,plain,
( ( ! [X: $i] :
( ! [Y: $i,Z: $i] :
( ~ ( lesseq @ X @ Z )
| ~ ( lesseq @ Y @ Z )
| ( ub @ X @ Y @ Z ) )
& ! [Y: $i,Z: $i] :
( ~ ( ub @ X @ Y @ Z )
| ( lesseq @ X @ Z ) )
& ! [Y: $i,Z: $i] :
( ~ ( ub @ X @ Y @ Z )
| ( lesseq @ Y @ Z ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[21]) ).
thf(44,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( lesseq @ X @ Y )
| ( lesseq @ ( summation @ X ) @ ( summation @ Y ) ) )
& ! [X: $i,Y: $i] :
( ~ ( lesseq @ ( summation @ X ) @ ( summation @ Y ) )
| ( lesseq @ X @ Y ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[24]) ).
thf(45,plain,
( ( ! [X: $i] :
( ! [Y: $i] :
( ~ ( lesseq @ X @ Y )
| ! [Z: $i] : ( lesseq @ ( sum @ Z @ X ) @ ( sum @ Z @ Y ) ) )
& ! [Y: $i] :
( ! [Z: $i] :
~ ( lesseq @ ( sum @ Z @ X ) @ ( sum @ Z @ Y ) )
| ( lesseq @ X @ Y ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[25]) ).
thf(46,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( lesseq @ X @ Y )
| ~ ( lesseq @ Y @ X )
| ( X = Y ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[27]) ).
thf(47,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ~ ( lesseq @ X @ Y )
| ~ ( lesseq @ Y @ Z )
| ( lesseq @ X @ Z ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[28]) ).
thf(48,plain,
( ( ! [X: $i] : ( lesseq @ X @ X ) )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(49,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ~ ( lesseq @ X @ Y )
| ~ ( lesseq @ Y @ Z )
| ( lesseq @ X @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(50,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( lesseq @ X @ Y )
| ~ ( lesseq @ Y @ X )
| ( X = Y ) ) )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(51,plain,
( ( ! [X: $i,Y: $i] :
( ( lesseq @ X @ Y )
| ( lesseq @ Y @ X ) ) )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(52,plain,
( ( ! [X: $i] :
( ! [Y: $i] :
( ~ ( lesseq @ X @ Y )
| ! [Z: $i] : ( lesseq @ ( sum @ Z @ X ) @ ( sum @ Z @ Y ) ) )
& ! [Y: $i] :
( ! [Z: $i] :
~ ( lesseq @ ( sum @ Z @ X ) @ ( sum @ Z @ Y ) )
| ( lesseq @ X @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(53,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( lesseq @ X @ Y )
| ( lesseq @ ( summation @ X ) @ ( summation @ Y ) ) )
& ! [X: $i,Y: $i] :
( ~ ( lesseq @ ( summation @ X ) @ ( summation @ Y ) )
| ( lesseq @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(54,plain,
( ( ! [X: $i,Y: $i] :
( ( ( max @ X @ Y )
= X )
| ~ ( lesseq @ Y @ X ) ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(55,plain,
( ( ! [X: $i,Y: $i] :
( ( ( max @ X @ Y )
= Y )
| ~ ( lesseq @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(56,plain,
( ( ! [X: $i] :
( ! [Y: $i,Z: $i] :
( ~ ( lesseq @ X @ Z )
| ~ ( lesseq @ Y @ Z )
| ( ub @ X @ Y @ Z ) )
& ! [Y: $i,Z: $i] :
( ~ ( ub @ X @ Y @ Z )
| ( lesseq @ X @ Z ) )
& ! [Y: $i,Z: $i] :
( ~ ( ub @ X @ Y @ Z )
| ( lesseq @ Y @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(57,plain,
( ( ! [X: $i] :
( ! [Y: $i,N: $i] :
( ( N
!= ( max @ X @ Y ) )
| ( model_max @ X @ Y @ N ) )
& ! [Y: $i,N: $i] :
( ~ ( model_max @ X @ Y @ N )
| ( N
= ( max @ X @ Y ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(58,plain,
( ( ! [X: $i] :
( ! [Y: $i,N: $i] :
( ~ ( model_ub @ X @ Y @ N )
| ( ub @ X @ Y @ N ) )
& ! [Y: $i,N: $i] :
( ~ ( ub @ X @ Y @ N )
| ( model_ub @ X @ Y @ N ) ) ) )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(59,plain,
( ( ! [X: $i] :
( ! [Y: $i,N: $i] :
( ( ( model_max @ X @ Y @ ( sK5_Z @ N @ Y @ X ) )
& ~ ( lesseq @ N @ ( sK5_Z @ N @ Y @ X ) ) )
| ~ ( model_max @ X @ Y @ N )
| ( minsol_model_max @ X @ Y @ N ) )
& ! [Y: $i,N: $i] :
( ~ ( minsol_model_max @ X @ Y @ N )
| ! [Z: $i] :
( ~ ( model_max @ X @ Y @ Z )
| ( lesseq @ N @ Z ) ) )
& ! [Y: $i,N: $i] :
( ~ ( minsol_model_max @ X @ Y @ N )
| ( model_max @ X @ Y @ N ) ) ) )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(60,plain,
( ( ! [X: $i] :
( ! [Y: $i,N: $i] :
( ( ( model_ub @ X @ Y @ ( sK4_Z @ N @ Y @ X ) )
& ~ ( lesseq @ N @ ( sK4_Z @ N @ Y @ X ) ) )
| ~ ( model_ub @ X @ Y @ N )
| ( minsol_model_ub @ X @ Y @ N ) )
& ! [Y: $i,N: $i] :
( ~ ( minsol_model_ub @ X @ Y @ N )
| ! [Z: $i] :
( ~ ( model_ub @ X @ Y @ Z )
| ( lesseq @ N @ Z ) ) )
& ! [Y: $i,N: $i] :
( ~ ( minsol_model_ub @ X @ Y @ N )
| ( model_ub @ X @ Y @ N ) ) ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(61,plain,
( ( ( minsol_model_ub @ sK1_X @ sK2_SY37 @ sK3_SY39 )
& ~ ( minsol_model_max @ sK1_X @ sK2_SY37 @ sK3_SY39 ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(62,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ( SX2
!= ( max @ SX0 @ SX1 ) )
| ( model_max @ SX0 @ SX1 @ SX2 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( model_max @ SX0 @ SX1 @ SX2 )
| ( SX2
= ( max @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[57]) ).
thf(63,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( lesseq @ SX0 @ SX1 )
| ( lesseq @ ( summation @ SX0 ) @ ( summation @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( lesseq @ ( summation @ SX0 ) @ ( summation @ SX1 ) )
| ( lesseq @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[53]) ).
thf(64,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( model_ub @ SX0 @ SX1 @ SX2 )
| ( ub @ SX0 @ SX1 @ SX2 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( ub @ SX0 @ SX1 @ SX2 )
| ( model_ub @ SX0 @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[58]) ).
thf(65,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( lesseq @ SX0 @ SX2 )
| ~ ( lesseq @ SX1 @ SX2 )
| ( ub @ SX0 @ SX1 @ SX2 ) )
| ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ub @ SX0 @ SX1 @ SX2 )
| ( lesseq @ SX0 @ SX2 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( ub @ SX0 @ SX1 @ SX2 )
| ( lesseq @ SX1 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[56]) ).
thf(66,plain,
( ( ~ ( ~ ( minsol_model_ub @ sK1_X @ sK2_SY37 @ sK3_SY39 )
| ~ ~ ( minsol_model_max @ sK1_X @ sK2_SY37 @ sK3_SY39 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[61]) ).
thf(67,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ( model_max @ SX0 @ SX1 @ ( sK5_Z @ SX2 @ SX1 @ SX0 ) )
| ~ ~ ( lesseq @ SX2 @ ( sK5_Z @ SX2 @ SX1 @ SX0 ) ) )
| ~ ( model_max @ SX0 @ SX1 @ SX2 )
| ( minsol_model_max @ SX0 @ SX1 @ SX2 ) )
| ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( minsol_model_max @ SX0 @ SX1 @ SX2 )
| ! [SX3: $i] :
( ~ ( model_max @ SX0 @ SX1 @ SX3 )
| ( lesseq @ SX2 @ SX3 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( minsol_model_max @ SX0 @ SX1 @ SX2 )
| ( model_max @ SX0 @ SX1 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[59]) ).
thf(68,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ( model_ub @ SX0 @ SX1 @ ( sK4_Z @ SX2 @ SX1 @ SX0 ) )
| ~ ~ ( lesseq @ SX2 @ ( sK4_Z @ SX2 @ SX1 @ SX0 ) ) )
| ~ ( model_ub @ SX0 @ SX1 @ SX2 )
| ( minsol_model_ub @ SX0 @ SX1 @ SX2 ) )
| ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( minsol_model_ub @ SX0 @ SX1 @ SX2 )
| ! [SX3: $i] :
( ~ ( model_ub @ SX0 @ SX1 @ SX3 )
| ( lesseq @ SX2 @ SX3 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( minsol_model_ub @ SX0 @ SX1 @ SX2 )
| ( model_ub @ SX0 @ SX1 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[60]) ).
thf(69,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i] :
( ~ ( lesseq @ SX0 @ SX1 )
| ! [SX2: $i] : ( lesseq @ ( sum @ SX2 @ SX0 ) @ ( sum @ SX2 @ SX1 ) ) )
| ~ ! [SX1: $i] :
( ! [SX2: $i] :
~ ( lesseq @ ( sum @ SX2 @ SX0 ) @ ( sum @ SX2 @ SX1 ) )
| ( lesseq @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[52]) ).
thf(70,plain,
! [SV1: $i] :
( ( lesseq @ SV1 @ SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[48]) ).
thf(71,plain,
! [SV2: $i] :
( ( ! [SY40: $i,SY41: $i] :
( ~ ( lesseq @ SV2 @ SY40 )
| ~ ( lesseq @ SY40 @ SY41 )
| ( lesseq @ SV2 @ SY41 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[49]) ).
thf(72,plain,
! [SV3: $i] :
( ( ! [SY42: $i] :
( ~ ( lesseq @ SV3 @ SY42 )
| ~ ( lesseq @ SY42 @ SV3 )
| ( SV3 = SY42 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[50]) ).
thf(73,plain,
! [SV4: $i] :
( ( ! [SY43: $i] :
( ( lesseq @ SV4 @ SY43 )
| ( lesseq @ SY43 @ SV4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[51]) ).
thf(74,plain,
! [SV5: $i] :
( ( ! [SY44: $i] :
( ( ( max @ SV5 @ SY44 )
= SV5 )
| ~ ( lesseq @ SY44 @ SV5 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[54]) ).
thf(75,plain,
! [SV6: $i] :
( ( ! [SY45: $i] :
( ( ( max @ SV6 @ SY45 )
= SY45 )
| ~ ( lesseq @ SV6 @ SY45 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[55]) ).
thf(76,plain,
! [SV7: $i] :
( ( ~ ( ~ ! [SY46: $i,SY47: $i] :
( ( SY47
!= ( max @ SV7 @ SY46 ) )
| ( model_max @ SV7 @ SY46 @ SY47 ) )
| ~ ! [SY48: $i,SY49: $i] :
( ~ ( model_max @ SV7 @ SY48 @ SY49 )
| ( SY49
= ( max @ SV7 @ SY48 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[62]) ).
thf(77,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( lesseq @ SX0 @ SX1 )
| ( lesseq @ ( summation @ SX0 ) @ ( summation @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( lesseq @ ( summation @ SX0 ) @ ( summation @ SX1 ) )
| ( lesseq @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[63]) ).
thf(78,plain,
! [SV8: $i] :
( ( ~ ( ~ ! [SY50: $i,SY51: $i] :
( ~ ( model_ub @ SV8 @ SY50 @ SY51 )
| ( ub @ SV8 @ SY50 @ SY51 ) )
| ~ ! [SY52: $i,SY53: $i] :
( ~ ( ub @ SV8 @ SY52 @ SY53 )
| ( model_ub @ SV8 @ SY52 @ SY53 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[64]) ).
thf(79,plain,
! [SV9: $i] :
( ( ~ ( ~ ! [SY54: $i,SY55: $i] :
( ~ ( lesseq @ SV9 @ SY55 )
| ~ ( lesseq @ SY54 @ SY55 )
| ( ub @ SV9 @ SY54 @ SY55 ) )
| ~ ~ ( ~ ! [SY56: $i,SY57: $i] :
( ~ ( ub @ SV9 @ SY56 @ SY57 )
| ( lesseq @ SV9 @ SY57 ) )
| ~ ! [SY58: $i,SY59: $i] :
( ~ ( ub @ SV9 @ SY58 @ SY59 )
| ( lesseq @ SY58 @ SY59 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[65]) ).
thf(80,plain,
( ( ~ ( minsol_model_ub @ sK1_X @ sK2_SY37 @ sK3_SY39 )
| ~ ~ ( minsol_model_max @ sK1_X @ sK2_SY37 @ sK3_SY39 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[66]) ).
thf(81,plain,
! [SV10: $i] :
( ( ~ ( ~ ! [SY60: $i,SY61: $i] :
( ~ ( ~ ( model_max @ SV10 @ SY60 @ ( sK5_Z @ SY61 @ SY60 @ SV10 ) )
| ~ ~ ( lesseq @ SY61 @ ( sK5_Z @ SY61 @ SY60 @ SV10 ) ) )
| ~ ( model_max @ SV10 @ SY60 @ SY61 )
| ( minsol_model_max @ SV10 @ SY60 @ SY61 ) )
| ~ ~ ( ~ ! [SY62: $i,SY63: $i] :
( ~ ( minsol_model_max @ SV10 @ SY62 @ SY63 )
| ! [SY64: $i] :
( ~ ( model_max @ SV10 @ SY62 @ SY64 )
| ( lesseq @ SY63 @ SY64 ) ) )
| ~ ! [SY65: $i,SY66: $i] :
( ~ ( minsol_model_max @ SV10 @ SY65 @ SY66 )
| ( model_max @ SV10 @ SY65 @ SY66 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[67]) ).
thf(82,plain,
! [SV11: $i] :
( ( ~ ( ~ ! [SY67: $i,SY68: $i] :
( ~ ( ~ ( model_ub @ SV11 @ SY67 @ ( sK4_Z @ SY68 @ SY67 @ SV11 ) )
| ~ ~ ( lesseq @ SY68 @ ( sK4_Z @ SY68 @ SY67 @ SV11 ) ) )
| ~ ( model_ub @ SV11 @ SY67 @ SY68 )
| ( minsol_model_ub @ SV11 @ SY67 @ SY68 ) )
| ~ ~ ( ~ ! [SY69: $i,SY70: $i] :
( ~ ( minsol_model_ub @ SV11 @ SY69 @ SY70 )
| ! [SY71: $i] :
( ~ ( model_ub @ SV11 @ SY69 @ SY71 )
| ( lesseq @ SY70 @ SY71 ) ) )
| ~ ! [SY72: $i,SY73: $i] :
( ~ ( minsol_model_ub @ SV11 @ SY72 @ SY73 )
| ( model_ub @ SV11 @ SY72 @ SY73 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[68]) ).
thf(83,plain,
! [SV12: $i] :
( ( ~ ( ~ ! [SY74: $i] :
( ~ ( lesseq @ SV12 @ SY74 )
| ! [SY75: $i] : ( lesseq @ ( sum @ SY75 @ SV12 ) @ ( sum @ SY75 @ SY74 ) ) )
| ~ ! [SY76: $i] :
( ! [SY77: $i] :
~ ( lesseq @ ( sum @ SY77 @ SV12 ) @ ( sum @ SY77 @ SY76 ) )
| ( lesseq @ SV12 @ SY76 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[69]) ).
thf(84,plain,
! [SV13: $i,SV2: $i] :
( ( ! [SY78: $i] :
( ~ ( lesseq @ SV2 @ SV13 )
| ~ ( lesseq @ SV13 @ SY78 )
| ( lesseq @ SV2 @ SY78 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(85,plain,
! [SV14: $i,SV3: $i] :
( ( ~ ( lesseq @ SV3 @ SV14 )
| ~ ( lesseq @ SV14 @ SV3 )
| ( SV3 = SV14 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[72]) ).
thf(86,plain,
! [SV15: $i,SV4: $i] :
( ( ( lesseq @ SV4 @ SV15 )
| ( lesseq @ SV15 @ SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[73]) ).
thf(87,plain,
! [SV16: $i,SV5: $i] :
( ( ( ( max @ SV5 @ SV16 )
= SV5 )
| ~ ( lesseq @ SV16 @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[74]) ).
thf(88,plain,
! [SV17: $i,SV6: $i] :
( ( ( ( max @ SV6 @ SV17 )
= SV17 )
| ~ ( lesseq @ SV6 @ SV17 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[75]) ).
thf(89,plain,
! [SV7: $i] :
( ( ~ ! [SY46: $i,SY47: $i] :
( ( SY47
!= ( max @ SV7 @ SY46 ) )
| ( model_max @ SV7 @ SY46 @ SY47 ) )
| ~ ! [SY48: $i,SY49: $i] :
( ~ ( model_max @ SV7 @ SY48 @ SY49 )
| ( SY49
= ( max @ SV7 @ SY48 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[76]) ).
thf(90,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( lesseq @ SX0 @ SX1 )
| ( lesseq @ ( summation @ SX0 ) @ ( summation @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[77]) ).
thf(91,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( lesseq @ ( summation @ SX0 ) @ ( summation @ SX1 ) )
| ( lesseq @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[77]) ).
thf(92,plain,
! [SV8: $i] :
( ( ~ ! [SY50: $i,SY51: $i] :
( ~ ( model_ub @ SV8 @ SY50 @ SY51 )
| ( ub @ SV8 @ SY50 @ SY51 ) )
| ~ ! [SY52: $i,SY53: $i] :
( ~ ( ub @ SV8 @ SY52 @ SY53 )
| ( model_ub @ SV8 @ SY52 @ SY53 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[78]) ).
thf(93,plain,
! [SV9: $i] :
( ( ~ ! [SY54: $i,SY55: $i] :
( ~ ( lesseq @ SV9 @ SY55 )
| ~ ( lesseq @ SY54 @ SY55 )
| ( ub @ SV9 @ SY54 @ SY55 ) )
| ~ ~ ( ~ ! [SY56: $i,SY57: $i] :
( ~ ( ub @ SV9 @ SY56 @ SY57 )
| ( lesseq @ SV9 @ SY57 ) )
| ~ ! [SY58: $i,SY59: $i] :
( ~ ( ub @ SV9 @ SY58 @ SY59 )
| ( lesseq @ SY58 @ SY59 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[79]) ).
thf(94,plain,
( ( ~ ( minsol_model_ub @ sK1_X @ sK2_SY37 @ sK3_SY39 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[80]) ).
thf(95,plain,
( ( ~ ~ ( minsol_model_max @ sK1_X @ sK2_SY37 @ sK3_SY39 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[80]) ).
thf(96,plain,
! [SV10: $i] :
( ( ~ ! [SY60: $i,SY61: $i] :
( ~ ( ~ ( model_max @ SV10 @ SY60 @ ( sK5_Z @ SY61 @ SY60 @ SV10 ) )
| ~ ~ ( lesseq @ SY61 @ ( sK5_Z @ SY61 @ SY60 @ SV10 ) ) )
| ~ ( model_max @ SV10 @ SY60 @ SY61 )
| ( minsol_model_max @ SV10 @ SY60 @ SY61 ) )
| ~ ~ ( ~ ! [SY62: $i,SY63: $i] :
( ~ ( minsol_model_max @ SV10 @ SY62 @ SY63 )
| ! [SY64: $i] :
( ~ ( model_max @ SV10 @ SY62 @ SY64 )
| ( lesseq @ SY63 @ SY64 ) ) )
| ~ ! [SY65: $i,SY66: $i] :
( ~ ( minsol_model_max @ SV10 @ SY65 @ SY66 )
| ( model_max @ SV10 @ SY65 @ SY66 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[81]) ).
thf(97,plain,
! [SV11: $i] :
( ( ~ ! [SY67: $i,SY68: $i] :
( ~ ( ~ ( model_ub @ SV11 @ SY67 @ ( sK4_Z @ SY68 @ SY67 @ SV11 ) )
| ~ ~ ( lesseq @ SY68 @ ( sK4_Z @ SY68 @ SY67 @ SV11 ) ) )
| ~ ( model_ub @ SV11 @ SY67 @ SY68 )
| ( minsol_model_ub @ SV11 @ SY67 @ SY68 ) )
| ~ ~ ( ~ ! [SY69: $i,SY70: $i] :
( ~ ( minsol_model_ub @ SV11 @ SY69 @ SY70 )
| ! [SY71: $i] :
( ~ ( model_ub @ SV11 @ SY69 @ SY71 )
| ( lesseq @ SY70 @ SY71 ) ) )
| ~ ! [SY72: $i,SY73: $i] :
( ~ ( minsol_model_ub @ SV11 @ SY72 @ SY73 )
| ( model_ub @ SV11 @ SY72 @ SY73 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[82]) ).
thf(98,plain,
! [SV12: $i] :
( ( ~ ! [SY74: $i] :
( ~ ( lesseq @ SV12 @ SY74 )
| ! [SY75: $i] : ( lesseq @ ( sum @ SY75 @ SV12 ) @ ( sum @ SY75 @ SY74 ) ) )
| ~ ! [SY76: $i] :
( ! [SY77: $i] :
~ ( lesseq @ ( sum @ SY77 @ SV12 ) @ ( sum @ SY77 @ SY76 ) )
| ( lesseq @ SV12 @ SY76 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[83]) ).
thf(99,plain,
! [SV18: $i,SV13: $i,SV2: $i] :
( ( ~ ( lesseq @ SV2 @ SV13 )
| ~ ( lesseq @ SV13 @ SV18 )
| ( lesseq @ SV2 @ SV18 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[84]) ).
thf(100,plain,
! [SV14: $i,SV3: $i] :
( ( ( ~ ( lesseq @ SV3 @ SV14 )
| ~ ( lesseq @ SV14 @ SV3 ) )
= $true )
| ( ( SV3 = SV14 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[85]) ).
thf(101,plain,
! [SV15: $i,SV4: $i] :
( ( ( lesseq @ SV4 @ SV15 )
= $true )
| ( ( lesseq @ SV15 @ SV4 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[86]) ).
thf(102,plain,
! [SV16: $i,SV5: $i] :
( ( ( ( max @ SV5 @ SV16 )
= SV5 )
= $true )
| ( ( ~ ( lesseq @ SV16 @ SV5 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[87]) ).
thf(103,plain,
! [SV17: $i,SV6: $i] :
( ( ( ( max @ SV6 @ SV17 )
= SV17 )
= $true )
| ( ( ~ ( lesseq @ SV6 @ SV17 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[88]) ).
thf(104,plain,
! [SV7: $i] :
( ( ~ ! [SY46: $i,SY47: $i] :
( ( SY47
!= ( max @ SV7 @ SY46 ) )
| ( model_max @ SV7 @ SY46 @ SY47 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[89]) ).
thf(105,plain,
! [SV7: $i] :
( ( ~ ! [SY48: $i,SY49: $i] :
( ~ ( model_max @ SV7 @ SY48 @ SY49 )
| ( SY49
= ( max @ SV7 @ SY48 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[89]) ).
thf(106,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( lesseq @ SX0 @ SX1 )
| ( lesseq @ ( summation @ SX0 ) @ ( summation @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[90]) ).
thf(107,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( lesseq @ ( summation @ SX0 ) @ ( summation @ SX1 ) )
| ( lesseq @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[91]) ).
thf(108,plain,
! [SV8: $i] :
( ( ~ ! [SY50: $i,SY51: $i] :
( ~ ( model_ub @ SV8 @ SY50 @ SY51 )
| ( ub @ SV8 @ SY50 @ SY51 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[92]) ).
thf(109,plain,
! [SV8: $i] :
( ( ~ ! [SY52: $i,SY53: $i] :
( ~ ( ub @ SV8 @ SY52 @ SY53 )
| ( model_ub @ SV8 @ SY52 @ SY53 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[92]) ).
thf(110,plain,
! [SV9: $i] :
( ( ~ ! [SY54: $i,SY55: $i] :
( ~ ( lesseq @ SV9 @ SY55 )
| ~ ( lesseq @ SY54 @ SY55 )
| ( ub @ SV9 @ SY54 @ SY55 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[93]) ).
thf(111,plain,
! [SV9: $i] :
( ( ~ ~ ( ~ ! [SY56: $i,SY57: $i] :
( ~ ( ub @ SV9 @ SY56 @ SY57 )
| ( lesseq @ SV9 @ SY57 ) )
| ~ ! [SY58: $i,SY59: $i] :
( ~ ( ub @ SV9 @ SY58 @ SY59 )
| ( lesseq @ SY58 @ SY59 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[93]) ).
thf(112,plain,
( ( minsol_model_ub @ sK1_X @ sK2_SY37 @ sK3_SY39 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[94]) ).
thf(113,plain,
( ( ~ ( minsol_model_max @ sK1_X @ sK2_SY37 @ sK3_SY39 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[95]) ).
thf(114,plain,
! [SV10: $i] :
( ( ~ ! [SY60: $i,SY61: $i] :
( ~ ( ~ ( model_max @ SV10 @ SY60 @ ( sK5_Z @ SY61 @ SY60 @ SV10 ) )
| ~ ~ ( lesseq @ SY61 @ ( sK5_Z @ SY61 @ SY60 @ SV10 ) ) )
| ~ ( model_max @ SV10 @ SY60 @ SY61 )
| ( minsol_model_max @ SV10 @ SY60 @ SY61 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[96]) ).
thf(115,plain,
! [SV10: $i] :
( ( ~ ~ ( ~ ! [SY62: $i,SY63: $i] :
( ~ ( minsol_model_max @ SV10 @ SY62 @ SY63 )
| ! [SY64: $i] :
( ~ ( model_max @ SV10 @ SY62 @ SY64 )
| ( lesseq @ SY63 @ SY64 ) ) )
| ~ ! [SY65: $i,SY66: $i] :
( ~ ( minsol_model_max @ SV10 @ SY65 @ SY66 )
| ( model_max @ SV10 @ SY65 @ SY66 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[96]) ).
thf(116,plain,
! [SV11: $i] :
( ( ~ ! [SY67: $i,SY68: $i] :
( ~ ( ~ ( model_ub @ SV11 @ SY67 @ ( sK4_Z @ SY68 @ SY67 @ SV11 ) )
| ~ ~ ( lesseq @ SY68 @ ( sK4_Z @ SY68 @ SY67 @ SV11 ) ) )
| ~ ( model_ub @ SV11 @ SY67 @ SY68 )
| ( minsol_model_ub @ SV11 @ SY67 @ SY68 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[97]) ).
thf(117,plain,
! [SV11: $i] :
( ( ~ ~ ( ~ ! [SY69: $i,SY70: $i] :
( ~ ( minsol_model_ub @ SV11 @ SY69 @ SY70 )
| ! [SY71: $i] :
( ~ ( model_ub @ SV11 @ SY69 @ SY71 )
| ( lesseq @ SY70 @ SY71 ) ) )
| ~ ! [SY72: $i,SY73: $i] :
( ~ ( minsol_model_ub @ SV11 @ SY72 @ SY73 )
| ( model_ub @ SV11 @ SY72 @ SY73 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[97]) ).
thf(118,plain,
! [SV12: $i] :
( ( ~ ! [SY74: $i] :
( ~ ( lesseq @ SV12 @ SY74 )
| ! [SY75: $i] : ( lesseq @ ( sum @ SY75 @ SV12 ) @ ( sum @ SY75 @ SY74 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[98]) ).
thf(119,plain,
! [SV12: $i] :
( ( ~ ! [SY76: $i] :
( ! [SY77: $i] :
~ ( lesseq @ ( sum @ SY77 @ SV12 ) @ ( sum @ SY77 @ SY76 ) )
| ( lesseq @ SV12 @ SY76 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[98]) ).
thf(120,plain,
! [SV18: $i,SV13: $i,SV2: $i] :
( ( ( ~ ( lesseq @ SV2 @ SV13 )
| ~ ( lesseq @ SV13 @ SV18 ) )
= $true )
| ( ( lesseq @ SV2 @ SV18 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[99]) ).
thf(121,plain,
! [SV14: $i,SV3: $i] :
( ( ( ~ ( lesseq @ SV3 @ SV14 ) )
= $true )
| ( ( ~ ( lesseq @ SV14 @ SV3 ) )
= $true )
| ( ( SV3 = SV14 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[100]) ).
thf(122,plain,
! [SV5: $i,SV16: $i] :
( ( ( lesseq @ SV16 @ SV5 )
= $false )
| ( ( ( max @ SV5 @ SV16 )
= SV5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[102]) ).
thf(123,plain,
! [SV17: $i,SV6: $i] :
( ( ( lesseq @ SV6 @ SV17 )
= $false )
| ( ( ( max @ SV6 @ SV17 )
= SV17 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[103]) ).
thf(124,plain,
! [SV7: $i] :
( ( ! [SY46: $i,SY47: $i] :
( ( SY47
!= ( max @ SV7 @ SY46 ) )
| ( model_max @ SV7 @ SY46 @ SY47 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[104]) ).
thf(125,plain,
! [SV7: $i] :
( ( ! [SY48: $i,SY49: $i] :
( ~ ( model_max @ SV7 @ SY48 @ SY49 )
| ( SY49
= ( max @ SV7 @ SY48 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[105]) ).
thf(126,plain,
! [SV19: $i] :
( ( ! [SY79: $i] :
( ~ ( lesseq @ SV19 @ SY79 )
| ( lesseq @ ( summation @ SV19 ) @ ( summation @ SY79 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[106]) ).
thf(127,plain,
! [SV20: $i] :
( ( ! [SY80: $i] :
( ~ ( lesseq @ ( summation @ SV20 ) @ ( summation @ SY80 ) )
| ( lesseq @ SV20 @ SY80 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[107]) ).
thf(128,plain,
! [SV8: $i] :
( ( ! [SY50: $i,SY51: $i] :
( ~ ( model_ub @ SV8 @ SY50 @ SY51 )
| ( ub @ SV8 @ SY50 @ SY51 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[108]) ).
thf(129,plain,
! [SV8: $i] :
( ( ! [SY52: $i,SY53: $i] :
( ~ ( ub @ SV8 @ SY52 @ SY53 )
| ( model_ub @ SV8 @ SY52 @ SY53 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[109]) ).
thf(130,plain,
! [SV9: $i] :
( ( ! [SY54: $i,SY55: $i] :
( ~ ( lesseq @ SV9 @ SY55 )
| ~ ( lesseq @ SY54 @ SY55 )
| ( ub @ SV9 @ SY54 @ SY55 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[110]) ).
thf(131,plain,
! [SV9: $i] :
( ( ~ ( ~ ! [SY56: $i,SY57: $i] :
( ~ ( ub @ SV9 @ SY56 @ SY57 )
| ( lesseq @ SV9 @ SY57 ) )
| ~ ! [SY58: $i,SY59: $i] :
( ~ ( ub @ SV9 @ SY58 @ SY59 )
| ( lesseq @ SY58 @ SY59 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[111]) ).
thf(132,plain,
( ( minsol_model_max @ sK1_X @ sK2_SY37 @ sK3_SY39 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[113]) ).
thf(133,plain,
! [SV10: $i] :
( ( ! [SY60: $i,SY61: $i] :
( ~ ( ~ ( model_max @ SV10 @ SY60 @ ( sK5_Z @ SY61 @ SY60 @ SV10 ) )
| ~ ~ ( lesseq @ SY61 @ ( sK5_Z @ SY61 @ SY60 @ SV10 ) ) )
| ~ ( model_max @ SV10 @ SY60 @ SY61 )
| ( minsol_model_max @ SV10 @ SY60 @ SY61 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[114]) ).
thf(134,plain,
! [SV10: $i] :
( ( ~ ( ~ ! [SY62: $i,SY63: $i] :
( ~ ( minsol_model_max @ SV10 @ SY62 @ SY63 )
| ! [SY64: $i] :
( ~ ( model_max @ SV10 @ SY62 @ SY64 )
| ( lesseq @ SY63 @ SY64 ) ) )
| ~ ! [SY65: $i,SY66: $i] :
( ~ ( minsol_model_max @ SV10 @ SY65 @ SY66 )
| ( model_max @ SV10 @ SY65 @ SY66 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[115]) ).
thf(135,plain,
! [SV11: $i] :
( ( ! [SY67: $i,SY68: $i] :
( ~ ( ~ ( model_ub @ SV11 @ SY67 @ ( sK4_Z @ SY68 @ SY67 @ SV11 ) )
| ~ ~ ( lesseq @ SY68 @ ( sK4_Z @ SY68 @ SY67 @ SV11 ) ) )
| ~ ( model_ub @ SV11 @ SY67 @ SY68 )
| ( minsol_model_ub @ SV11 @ SY67 @ SY68 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[116]) ).
thf(136,plain,
! [SV11: $i] :
( ( ~ ( ~ ! [SY69: $i,SY70: $i] :
( ~ ( minsol_model_ub @ SV11 @ SY69 @ SY70 )
| ! [SY71: $i] :
( ~ ( model_ub @ SV11 @ SY69 @ SY71 )
| ( lesseq @ SY70 @ SY71 ) ) )
| ~ ! [SY72: $i,SY73: $i] :
( ~ ( minsol_model_ub @ SV11 @ SY72 @ SY73 )
| ( model_ub @ SV11 @ SY72 @ SY73 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[117]) ).
thf(137,plain,
! [SV12: $i] :
( ( ! [SY74: $i] :
( ~ ( lesseq @ SV12 @ SY74 )
| ! [SY75: $i] : ( lesseq @ ( sum @ SY75 @ SV12 ) @ ( sum @ SY75 @ SY74 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[118]) ).
thf(138,plain,
! [SV12: $i] :
( ( ! [SY76: $i] :
( ! [SY77: $i] :
~ ( lesseq @ ( sum @ SY77 @ SV12 ) @ ( sum @ SY77 @ SY76 ) )
| ( lesseq @ SV12 @ SY76 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[119]) ).
thf(139,plain,
! [SV18: $i,SV13: $i,SV2: $i] :
( ( ( ~ ( lesseq @ SV2 @ SV13 ) )
= $true )
| ( ( ~ ( lesseq @ SV13 @ SV18 ) )
= $true )
| ( ( lesseq @ SV2 @ SV18 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[120]) ).
thf(140,plain,
! [SV14: $i,SV3: $i] :
( ( ( lesseq @ SV3 @ SV14 )
= $false )
| ( ( ~ ( lesseq @ SV14 @ SV3 ) )
= $true )
| ( ( SV3 = SV14 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[121]) ).
thf(141,plain,
! [SV21: $i,SV7: $i] :
( ( ! [SY81: $i] :
( ( SY81
!= ( max @ SV7 @ SV21 ) )
| ( model_max @ SV7 @ SV21 @ SY81 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[124]) ).
thf(142,plain,
! [SV22: $i,SV7: $i] :
( ( ! [SY82: $i] :
( ~ ( model_max @ SV7 @ SV22 @ SY82 )
| ( SY82
= ( max @ SV7 @ SV22 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[125]) ).
thf(143,plain,
! [SV23: $i,SV19: $i] :
( ( ~ ( lesseq @ SV19 @ SV23 )
| ( lesseq @ ( summation @ SV19 ) @ ( summation @ SV23 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[126]) ).
thf(144,plain,
! [SV24: $i,SV20: $i] :
( ( ~ ( lesseq @ ( summation @ SV20 ) @ ( summation @ SV24 ) )
| ( lesseq @ SV20 @ SV24 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[127]) ).
thf(145,plain,
! [SV25: $i,SV8: $i] :
( ( ! [SY83: $i] :
( ~ ( model_ub @ SV8 @ SV25 @ SY83 )
| ( ub @ SV8 @ SV25 @ SY83 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[128]) ).
thf(146,plain,
! [SV26: $i,SV8: $i] :
( ( ! [SY84: $i] :
( ~ ( ub @ SV8 @ SV26 @ SY84 )
| ( model_ub @ SV8 @ SV26 @ SY84 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[129]) ).
thf(147,plain,
! [SV27: $i,SV9: $i] :
( ( ! [SY85: $i] :
( ~ ( lesseq @ SV9 @ SY85 )
| ~ ( lesseq @ SV27 @ SY85 )
| ( ub @ SV9 @ SV27 @ SY85 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[130]) ).
thf(148,plain,
! [SV9: $i] :
( ( ~ ! [SY56: $i,SY57: $i] :
( ~ ( ub @ SV9 @ SY56 @ SY57 )
| ( lesseq @ SV9 @ SY57 ) )
| ~ ! [SY58: $i,SY59: $i] :
( ~ ( ub @ SV9 @ SY58 @ SY59 )
| ( lesseq @ SY58 @ SY59 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[131]) ).
thf(149,plain,
! [SV28: $i,SV10: $i] :
( ( ! [SY86: $i] :
( ~ ( ~ ( model_max @ SV10 @ SV28 @ ( sK5_Z @ SY86 @ SV28 @ SV10 ) )
| ~ ~ ( lesseq @ SY86 @ ( sK5_Z @ SY86 @ SV28 @ SV10 ) ) )
| ~ ( model_max @ SV10 @ SV28 @ SY86 )
| ( minsol_model_max @ SV10 @ SV28 @ SY86 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[133]) ).
thf(150,plain,
! [SV10: $i] :
( ( ~ ! [SY62: $i,SY63: $i] :
( ~ ( minsol_model_max @ SV10 @ SY62 @ SY63 )
| ! [SY64: $i] :
( ~ ( model_max @ SV10 @ SY62 @ SY64 )
| ( lesseq @ SY63 @ SY64 ) ) )
| ~ ! [SY65: $i,SY66: $i] :
( ~ ( minsol_model_max @ SV10 @ SY65 @ SY66 )
| ( model_max @ SV10 @ SY65 @ SY66 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[134]) ).
thf(151,plain,
! [SV29: $i,SV11: $i] :
( ( ! [SY87: $i] :
( ~ ( ~ ( model_ub @ SV11 @ SV29 @ ( sK4_Z @ SY87 @ SV29 @ SV11 ) )
| ~ ~ ( lesseq @ SY87 @ ( sK4_Z @ SY87 @ SV29 @ SV11 ) ) )
| ~ ( model_ub @ SV11 @ SV29 @ SY87 )
| ( minsol_model_ub @ SV11 @ SV29 @ SY87 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[135]) ).
thf(152,plain,
! [SV11: $i] :
( ( ~ ! [SY69: $i,SY70: $i] :
( ~ ( minsol_model_ub @ SV11 @ SY69 @ SY70 )
| ! [SY71: $i] :
( ~ ( model_ub @ SV11 @ SY69 @ SY71 )
| ( lesseq @ SY70 @ SY71 ) ) )
| ~ ! [SY72: $i,SY73: $i] :
( ~ ( minsol_model_ub @ SV11 @ SY72 @ SY73 )
| ( model_ub @ SV11 @ SY72 @ SY73 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[136]) ).
thf(153,plain,
! [SV30: $i,SV12: $i] :
( ( ~ ( lesseq @ SV12 @ SV30 )
| ! [SY88: $i] : ( lesseq @ ( sum @ SY88 @ SV12 ) @ ( sum @ SY88 @ SV30 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[137]) ).
thf(154,plain,
! [SV31: $i,SV12: $i] :
( ( ! [SY89: $i] :
~ ( lesseq @ ( sum @ SY89 @ SV12 ) @ ( sum @ SY89 @ SV31 ) )
| ( lesseq @ SV12 @ SV31 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[138]) ).
thf(155,plain,
! [SV18: $i,SV13: $i,SV2: $i] :
( ( ( lesseq @ SV2 @ SV13 )
= $false )
| ( ( ~ ( lesseq @ SV13 @ SV18 ) )
= $true )
| ( ( lesseq @ SV2 @ SV18 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[139]) ).
thf(156,plain,
! [SV3: $i,SV14: $i] :
( ( ( lesseq @ SV14 @ SV3 )
= $false )
| ( ( lesseq @ SV3 @ SV14 )
= $false )
| ( ( SV3 = SV14 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[140]) ).
thf(157,plain,
! [SV21: $i,SV7: $i,SV32: $i] :
( ( ( SV32
!= ( max @ SV7 @ SV21 ) )
| ( model_max @ SV7 @ SV21 @ SV32 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[141]) ).
thf(158,plain,
! [SV33: $i,SV22: $i,SV7: $i] :
( ( ~ ( model_max @ SV7 @ SV22 @ SV33 )
| ( SV33
= ( max @ SV7 @ SV22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[142]) ).
thf(159,plain,
! [SV23: $i,SV19: $i] :
( ( ( ~ ( lesseq @ SV19 @ SV23 ) )
= $true )
| ( ( lesseq @ ( summation @ SV19 ) @ ( summation @ SV23 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[143]) ).
thf(160,plain,
! [SV24: $i,SV20: $i] :
( ( ( ~ ( lesseq @ ( summation @ SV20 ) @ ( summation @ SV24 ) ) )
= $true )
| ( ( lesseq @ SV20 @ SV24 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[144]) ).
thf(161,plain,
! [SV34: $i,SV25: $i,SV8: $i] :
( ( ~ ( model_ub @ SV8 @ SV25 @ SV34 )
| ( ub @ SV8 @ SV25 @ SV34 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[145]) ).
thf(162,plain,
! [SV35: $i,SV26: $i,SV8: $i] :
( ( ~ ( ub @ SV8 @ SV26 @ SV35 )
| ( model_ub @ SV8 @ SV26 @ SV35 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[146]) ).
thf(163,plain,
! [SV27: $i,SV36: $i,SV9: $i] :
( ( ~ ( lesseq @ SV9 @ SV36 )
| ~ ( lesseq @ SV27 @ SV36 )
| ( ub @ SV9 @ SV27 @ SV36 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[147]) ).
thf(164,plain,
! [SV9: $i] :
( ( ~ ! [SY56: $i,SY57: $i] :
( ~ ( ub @ SV9 @ SY56 @ SY57 )
| ( lesseq @ SV9 @ SY57 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[148]) ).
thf(165,plain,
! [SV9: $i] :
( ( ~ ! [SY58: $i,SY59: $i] :
( ~ ( ub @ SV9 @ SY58 @ SY59 )
| ( lesseq @ SY58 @ SY59 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[148]) ).
thf(166,plain,
! [SV37: $i,SV28: $i,SV10: $i] :
( ( ~ ( ~ ( model_max @ SV10 @ SV28 @ ( sK5_Z @ SV37 @ SV28 @ SV10 ) )
| ~ ~ ( lesseq @ SV37 @ ( sK5_Z @ SV37 @ SV28 @ SV10 ) ) )
| ~ ( model_max @ SV10 @ SV28 @ SV37 )
| ( minsol_model_max @ SV10 @ SV28 @ SV37 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[149]) ).
thf(167,plain,
! [SV10: $i] :
( ( ~ ! [SY62: $i,SY63: $i] :
( ~ ( minsol_model_max @ SV10 @ SY62 @ SY63 )
| ! [SY64: $i] :
( ~ ( model_max @ SV10 @ SY62 @ SY64 )
| ( lesseq @ SY63 @ SY64 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[150]) ).
thf(168,plain,
! [SV10: $i] :
( ( ~ ! [SY65: $i,SY66: $i] :
( ~ ( minsol_model_max @ SV10 @ SY65 @ SY66 )
| ( model_max @ SV10 @ SY65 @ SY66 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[150]) ).
thf(169,plain,
! [SV38: $i,SV29: $i,SV11: $i] :
( ( ~ ( ~ ( model_ub @ SV11 @ SV29 @ ( sK4_Z @ SV38 @ SV29 @ SV11 ) )
| ~ ~ ( lesseq @ SV38 @ ( sK4_Z @ SV38 @ SV29 @ SV11 ) ) )
| ~ ( model_ub @ SV11 @ SV29 @ SV38 )
| ( minsol_model_ub @ SV11 @ SV29 @ SV38 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[151]) ).
thf(170,plain,
! [SV11: $i] :
( ( ~ ! [SY69: $i,SY70: $i] :
( ~ ( minsol_model_ub @ SV11 @ SY69 @ SY70 )
| ! [SY71: $i] :
( ~ ( model_ub @ SV11 @ SY69 @ SY71 )
| ( lesseq @ SY70 @ SY71 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[152]) ).
thf(171,plain,
! [SV11: $i] :
( ( ~ ! [SY72: $i,SY73: $i] :
( ~ ( minsol_model_ub @ SV11 @ SY72 @ SY73 )
| ( model_ub @ SV11 @ SY72 @ SY73 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[152]) ).
thf(172,plain,
! [SV30: $i,SV12: $i] :
( ( ( ~ ( lesseq @ SV12 @ SV30 ) )
= $true )
| ( ( ! [SY88: $i] : ( lesseq @ ( sum @ SY88 @ SV12 ) @ ( sum @ SY88 @ SV30 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[153]) ).
thf(173,plain,
! [SV31: $i,SV12: $i] :
( ( ( ! [SY89: $i] :
~ ( lesseq @ ( sum @ SY89 @ SV12 ) @ ( sum @ SY89 @ SV31 ) ) )
= $true )
| ( ( lesseq @ SV12 @ SV31 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[154]) ).
thf(174,plain,
! [SV2: $i,SV18: $i,SV13: $i] :
( ( ( lesseq @ SV13 @ SV18 )
= $false )
| ( ( lesseq @ SV2 @ SV13 )
= $false )
| ( ( lesseq @ SV2 @ SV18 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[155]) ).
thf(175,plain,
! [SV21: $i,SV7: $i,SV32: $i] :
( ( ( ( SV32
!= ( max @ SV7 @ SV21 ) ) )
= $true )
| ( ( model_max @ SV7 @ SV21 @ SV32 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[157]) ).
thf(176,plain,
! [SV33: $i,SV22: $i,SV7: $i] :
( ( ( ~ ( model_max @ SV7 @ SV22 @ SV33 ) )
= $true )
| ( ( SV33
= ( max @ SV7 @ SV22 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[158]) ).
thf(177,plain,
! [SV23: $i,SV19: $i] :
( ( ( lesseq @ SV19 @ SV23 )
= $false )
| ( ( lesseq @ ( summation @ SV19 ) @ ( summation @ SV23 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[159]) ).
thf(178,plain,
! [SV24: $i,SV20: $i] :
( ( ( lesseq @ ( summation @ SV20 ) @ ( summation @ SV24 ) )
= $false )
| ( ( lesseq @ SV20 @ SV24 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[160]) ).
thf(179,plain,
! [SV34: $i,SV25: $i,SV8: $i] :
( ( ( ~ ( model_ub @ SV8 @ SV25 @ SV34 ) )
= $true )
| ( ( ub @ SV8 @ SV25 @ SV34 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[161]) ).
thf(180,plain,
! [SV35: $i,SV26: $i,SV8: $i] :
( ( ( ~ ( ub @ SV8 @ SV26 @ SV35 ) )
= $true )
| ( ( model_ub @ SV8 @ SV26 @ SV35 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[162]) ).
thf(181,plain,
! [SV27: $i,SV36: $i,SV9: $i] :
( ( ( ~ ( lesseq @ SV9 @ SV36 )
| ~ ( lesseq @ SV27 @ SV36 ) )
= $true )
| ( ( ub @ SV9 @ SV27 @ SV36 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[163]) ).
thf(182,plain,
! [SV9: $i] :
( ( ! [SY56: $i,SY57: $i] :
( ~ ( ub @ SV9 @ SY56 @ SY57 )
| ( lesseq @ SV9 @ SY57 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[164]) ).
thf(183,plain,
! [SV9: $i] :
( ( ! [SY58: $i,SY59: $i] :
( ~ ( ub @ SV9 @ SY58 @ SY59 )
| ( lesseq @ SY58 @ SY59 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[165]) ).
thf(184,plain,
! [SV37: $i,SV28: $i,SV10: $i] :
( ( ( ~ ( ~ ( model_max @ SV10 @ SV28 @ ( sK5_Z @ SV37 @ SV28 @ SV10 ) )
| ~ ~ ( lesseq @ SV37 @ ( sK5_Z @ SV37 @ SV28 @ SV10 ) ) )
| ~ ( model_max @ SV10 @ SV28 @ SV37 ) )
= $true )
| ( ( minsol_model_max @ SV10 @ SV28 @ SV37 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[166]) ).
thf(185,plain,
! [SV10: $i] :
( ( ! [SY62: $i,SY63: $i] :
( ~ ( minsol_model_max @ SV10 @ SY62 @ SY63 )
| ! [SY64: $i] :
( ~ ( model_max @ SV10 @ SY62 @ SY64 )
| ( lesseq @ SY63 @ SY64 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[167]) ).
thf(186,plain,
! [SV10: $i] :
( ( ! [SY65: $i,SY66: $i] :
( ~ ( minsol_model_max @ SV10 @ SY65 @ SY66 )
| ( model_max @ SV10 @ SY65 @ SY66 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[168]) ).
thf(187,plain,
! [SV38: $i,SV29: $i,SV11: $i] :
( ( ( ~ ( ~ ( model_ub @ SV11 @ SV29 @ ( sK4_Z @ SV38 @ SV29 @ SV11 ) )
| ~ ~ ( lesseq @ SV38 @ ( sK4_Z @ SV38 @ SV29 @ SV11 ) ) )
| ~ ( model_ub @ SV11 @ SV29 @ SV38 ) )
= $true )
| ( ( minsol_model_ub @ SV11 @ SV29 @ SV38 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[169]) ).
thf(188,plain,
! [SV11: $i] :
( ( ! [SY69: $i,SY70: $i] :
( ~ ( minsol_model_ub @ SV11 @ SY69 @ SY70 )
| ! [SY71: $i] :
( ~ ( model_ub @ SV11 @ SY69 @ SY71 )
| ( lesseq @ SY70 @ SY71 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[170]) ).
thf(189,plain,
! [SV11: $i] :
( ( ! [SY72: $i,SY73: $i] :
( ~ ( minsol_model_ub @ SV11 @ SY72 @ SY73 )
| ( model_ub @ SV11 @ SY72 @ SY73 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[171]) ).
thf(190,plain,
! [SV30: $i,SV12: $i] :
( ( ( lesseq @ SV12 @ SV30 )
= $false )
| ( ( ! [SY88: $i] : ( lesseq @ ( sum @ SY88 @ SV12 ) @ ( sum @ SY88 @ SV30 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[172]) ).
thf(191,plain,
! [SV31: $i,SV12: $i,SV39: $i] :
( ( ( ~ ( lesseq @ ( sum @ SV39 @ SV12 ) @ ( sum @ SV39 @ SV31 ) ) )
= $true )
| ( ( lesseq @ SV12 @ SV31 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[173]) ).
thf(192,plain,
! [SV21: $i,SV7: $i,SV32: $i] :
( ( ( SV32
= ( max @ SV7 @ SV21 ) )
= $false )
| ( ( model_max @ SV7 @ SV21 @ SV32 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[175]) ).
thf(193,plain,
! [SV33: $i,SV22: $i,SV7: $i] :
( ( ( model_max @ SV7 @ SV22 @ SV33 )
= $false )
| ( ( SV33
= ( max @ SV7 @ SV22 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[176]) ).
thf(194,plain,
! [SV34: $i,SV25: $i,SV8: $i] :
( ( ( model_ub @ SV8 @ SV25 @ SV34 )
= $false )
| ( ( ub @ SV8 @ SV25 @ SV34 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[179]) ).
thf(195,plain,
! [SV35: $i,SV26: $i,SV8: $i] :
( ( ( ub @ SV8 @ SV26 @ SV35 )
= $false )
| ( ( model_ub @ SV8 @ SV26 @ SV35 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[180]) ).
thf(196,plain,
! [SV27: $i,SV36: $i,SV9: $i] :
( ( ( ~ ( lesseq @ SV9 @ SV36 ) )
= $true )
| ( ( ~ ( lesseq @ SV27 @ SV36 ) )
= $true )
| ( ( ub @ SV9 @ SV27 @ SV36 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[181]) ).
thf(197,plain,
! [SV40: $i,SV9: $i] :
( ( ! [SY90: $i] :
( ~ ( ub @ SV9 @ SV40 @ SY90 )
| ( lesseq @ SV9 @ SY90 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[182]) ).
thf(198,plain,
! [SV41: $i,SV9: $i] :
( ( ! [SY91: $i] :
( ~ ( ub @ SV9 @ SV41 @ SY91 )
| ( lesseq @ SV41 @ SY91 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[183]) ).
thf(199,plain,
! [SV37: $i,SV28: $i,SV10: $i] :
( ( ( ~ ( ~ ( model_max @ SV10 @ SV28 @ ( sK5_Z @ SV37 @ SV28 @ SV10 ) )
| ~ ~ ( lesseq @ SV37 @ ( sK5_Z @ SV37 @ SV28 @ SV10 ) ) ) )
= $true )
| ( ( ~ ( model_max @ SV10 @ SV28 @ SV37 ) )
= $true )
| ( ( minsol_model_max @ SV10 @ SV28 @ SV37 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[184]) ).
thf(200,plain,
! [SV42: $i,SV10: $i] :
( ( ! [SY92: $i] :
( ~ ( minsol_model_max @ SV10 @ SV42 @ SY92 )
| ! [SY93: $i] :
( ~ ( model_max @ SV10 @ SV42 @ SY93 )
| ( lesseq @ SY92 @ SY93 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[185]) ).
thf(201,plain,
! [SV43: $i,SV10: $i] :
( ( ! [SY94: $i] :
( ~ ( minsol_model_max @ SV10 @ SV43 @ SY94 )
| ( model_max @ SV10 @ SV43 @ SY94 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[186]) ).
thf(202,plain,
! [SV38: $i,SV29: $i,SV11: $i] :
( ( ( ~ ( ~ ( model_ub @ SV11 @ SV29 @ ( sK4_Z @ SV38 @ SV29 @ SV11 ) )
| ~ ~ ( lesseq @ SV38 @ ( sK4_Z @ SV38 @ SV29 @ SV11 ) ) ) )
= $true )
| ( ( ~ ( model_ub @ SV11 @ SV29 @ SV38 ) )
= $true )
| ( ( minsol_model_ub @ SV11 @ SV29 @ SV38 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[187]) ).
thf(203,plain,
! [SV44: $i,SV11: $i] :
( ( ! [SY95: $i] :
( ~ ( minsol_model_ub @ SV11 @ SV44 @ SY95 )
| ! [SY96: $i] :
( ~ ( model_ub @ SV11 @ SV44 @ SY96 )
| ( lesseq @ SY95 @ SY96 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[188]) ).
thf(204,plain,
! [SV45: $i,SV11: $i] :
( ( ! [SY97: $i] :
( ~ ( minsol_model_ub @ SV11 @ SV45 @ SY97 )
| ( model_ub @ SV11 @ SV45 @ SY97 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[189]) ).
thf(205,plain,
! [SV30: $i,SV12: $i,SV46: $i] :
( ( ( lesseq @ ( sum @ SV46 @ SV12 ) @ ( sum @ SV46 @ SV30 ) )
= $true )
| ( ( lesseq @ SV12 @ SV30 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[190]) ).
thf(206,plain,
! [SV31: $i,SV12: $i,SV39: $i] :
( ( ( lesseq @ ( sum @ SV39 @ SV12 ) @ ( sum @ SV39 @ SV31 ) )
= $false )
| ( ( lesseq @ SV12 @ SV31 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[191]) ).
thf(207,plain,
! [SV27: $i,SV36: $i,SV9: $i] :
( ( ( lesseq @ SV9 @ SV36 )
= $false )
| ( ( ~ ( lesseq @ SV27 @ SV36 ) )
= $true )
| ( ( ub @ SV9 @ SV27 @ SV36 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[196]) ).
thf(208,plain,
! [SV47: $i,SV40: $i,SV9: $i] :
( ( ~ ( ub @ SV9 @ SV40 @ SV47 )
| ( lesseq @ SV9 @ SV47 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[197]) ).
thf(209,plain,
! [SV48: $i,SV41: $i,SV9: $i] :
( ( ~ ( ub @ SV9 @ SV41 @ SV48 )
| ( lesseq @ SV41 @ SV48 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[198]) ).
thf(210,plain,
! [SV37: $i,SV28: $i,SV10: $i] :
( ( ( ~ ( model_max @ SV10 @ SV28 @ ( sK5_Z @ SV37 @ SV28 @ SV10 ) )
| ~ ~ ( lesseq @ SV37 @ ( sK5_Z @ SV37 @ SV28 @ SV10 ) ) )
= $false )
| ( ( ~ ( model_max @ SV10 @ SV28 @ SV37 ) )
= $true )
| ( ( minsol_model_max @ SV10 @ SV28 @ SV37 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[199]) ).
thf(211,plain,
! [SV49: $i,SV42: $i,SV10: $i] :
( ( ~ ( minsol_model_max @ SV10 @ SV42 @ SV49 )
| ! [SY98: $i] :
( ~ ( model_max @ SV10 @ SV42 @ SY98 )
| ( lesseq @ SV49 @ SY98 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[200]) ).
thf(212,plain,
! [SV50: $i,SV43: $i,SV10: $i] :
( ( ~ ( minsol_model_max @ SV10 @ SV43 @ SV50 )
| ( model_max @ SV10 @ SV43 @ SV50 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[201]) ).
thf(213,plain,
! [SV38: $i,SV29: $i,SV11: $i] :
( ( ( ~ ( model_ub @ SV11 @ SV29 @ ( sK4_Z @ SV38 @ SV29 @ SV11 ) )
| ~ ~ ( lesseq @ SV38 @ ( sK4_Z @ SV38 @ SV29 @ SV11 ) ) )
= $false )
| ( ( ~ ( model_ub @ SV11 @ SV29 @ SV38 ) )
= $true )
| ( ( minsol_model_ub @ SV11 @ SV29 @ SV38 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[202]) ).
thf(214,plain,
! [SV51: $i,SV44: $i,SV11: $i] :
( ( ~ ( minsol_model_ub @ SV11 @ SV44 @ SV51 )
| ! [SY99: $i] :
( ~ ( model_ub @ SV11 @ SV44 @ SY99 )
| ( lesseq @ SV51 @ SY99 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[203]) ).
thf(215,plain,
! [SV52: $i,SV45: $i,SV11: $i] :
( ( ~ ( minsol_model_ub @ SV11 @ SV45 @ SV52 )
| ( model_ub @ SV11 @ SV45 @ SV52 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[204]) ).
thf(216,plain,
! [SV9: $i,SV36: $i,SV27: $i] :
( ( ( lesseq @ SV27 @ SV36 )
= $false )
| ( ( lesseq @ SV9 @ SV36 )
= $false )
| ( ( ub @ SV9 @ SV27 @ SV36 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[207]) ).
thf(217,plain,
! [SV47: $i,SV40: $i,SV9: $i] :
( ( ( ~ ( ub @ SV9 @ SV40 @ SV47 ) )
= $true )
| ( ( lesseq @ SV9 @ SV47 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[208]) ).
thf(218,plain,
! [SV48: $i,SV41: $i,SV9: $i] :
( ( ( ~ ( ub @ SV9 @ SV41 @ SV48 ) )
= $true )
| ( ( lesseq @ SV41 @ SV48 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[209]) ).
thf(219,plain,
! [SV37: $i,SV28: $i,SV10: $i] :
( ( ( ~ ( model_max @ SV10 @ SV28 @ ( sK5_Z @ SV37 @ SV28 @ SV10 ) ) )
= $false )
| ( ( ~ ( model_max @ SV10 @ SV28 @ SV37 ) )
= $true )
| ( ( minsol_model_max @ SV10 @ SV28 @ SV37 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[210]) ).
thf(220,plain,
! [SV10: $i,SV28: $i,SV37: $i] :
( ( ( ~ ~ ( lesseq @ SV37 @ ( sK5_Z @ SV37 @ SV28 @ SV10 ) ) )
= $false )
| ( ( ~ ( model_max @ SV10 @ SV28 @ SV37 ) )
= $true )
| ( ( minsol_model_max @ SV10 @ SV28 @ SV37 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[210]) ).
thf(221,plain,
! [SV49: $i,SV42: $i,SV10: $i] :
( ( ( ~ ( minsol_model_max @ SV10 @ SV42 @ SV49 ) )
= $true )
| ( ( ! [SY98: $i] :
( ~ ( model_max @ SV10 @ SV42 @ SY98 )
| ( lesseq @ SV49 @ SY98 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[211]) ).
thf(222,plain,
! [SV50: $i,SV43: $i,SV10: $i] :
( ( ( ~ ( minsol_model_max @ SV10 @ SV43 @ SV50 ) )
= $true )
| ( ( model_max @ SV10 @ SV43 @ SV50 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[212]) ).
thf(223,plain,
! [SV38: $i,SV29: $i,SV11: $i] :
( ( ( ~ ( model_ub @ SV11 @ SV29 @ ( sK4_Z @ SV38 @ SV29 @ SV11 ) ) )
= $false )
| ( ( ~ ( model_ub @ SV11 @ SV29 @ SV38 ) )
= $true )
| ( ( minsol_model_ub @ SV11 @ SV29 @ SV38 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[213]) ).
thf(224,plain,
! [SV11: $i,SV29: $i,SV38: $i] :
( ( ( ~ ~ ( lesseq @ SV38 @ ( sK4_Z @ SV38 @ SV29 @ SV11 ) ) )
= $false )
| ( ( ~ ( model_ub @ SV11 @ SV29 @ SV38 ) )
= $true )
| ( ( minsol_model_ub @ SV11 @ SV29 @ SV38 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[213]) ).
thf(225,plain,
! [SV51: $i,SV44: $i,SV11: $i] :
( ( ( ~ ( minsol_model_ub @ SV11 @ SV44 @ SV51 ) )
= $true )
| ( ( ! [SY99: $i] :
( ~ ( model_ub @ SV11 @ SV44 @ SY99 )
| ( lesseq @ SV51 @ SY99 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[214]) ).
thf(226,plain,
! [SV52: $i,SV45: $i,SV11: $i] :
( ( ( ~ ( minsol_model_ub @ SV11 @ SV45 @ SV52 ) )
= $true )
| ( ( model_ub @ SV11 @ SV45 @ SV52 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[215]) ).
thf(227,plain,
! [SV47: $i,SV40: $i,SV9: $i] :
( ( ( ub @ SV9 @ SV40 @ SV47 )
= $false )
| ( ( lesseq @ SV9 @ SV47 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[217]) ).
thf(228,plain,
! [SV48: $i,SV41: $i,SV9: $i] :
( ( ( ub @ SV9 @ SV41 @ SV48 )
= $false )
| ( ( lesseq @ SV41 @ SV48 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[218]) ).
thf(229,plain,
! [SV37: $i,SV28: $i,SV10: $i] :
( ( ( model_max @ SV10 @ SV28 @ ( sK5_Z @ SV37 @ SV28 @ SV10 ) )
= $true )
| ( ( ~ ( model_max @ SV10 @ SV28 @ SV37 ) )
= $true )
| ( ( minsol_model_max @ SV10 @ SV28 @ SV37 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[219]) ).
thf(230,plain,
! [SV10: $i,SV28: $i,SV37: $i] :
( ( ( ~ ( lesseq @ SV37 @ ( sK5_Z @ SV37 @ SV28 @ SV10 ) ) )
= $true )
| ( ( ~ ( model_max @ SV10 @ SV28 @ SV37 ) )
= $true )
| ( ( minsol_model_max @ SV10 @ SV28 @ SV37 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[220]) ).
thf(231,plain,
! [SV49: $i,SV42: $i,SV10: $i] :
( ( ( minsol_model_max @ SV10 @ SV42 @ SV49 )
= $false )
| ( ( ! [SY98: $i] :
( ~ ( model_max @ SV10 @ SV42 @ SY98 )
| ( lesseq @ SV49 @ SY98 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[221]) ).
thf(232,plain,
! [SV50: $i,SV43: $i,SV10: $i] :
( ( ( minsol_model_max @ SV10 @ SV43 @ SV50 )
= $false )
| ( ( model_max @ SV10 @ SV43 @ SV50 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[222]) ).
thf(233,plain,
! [SV38: $i,SV29: $i,SV11: $i] :
( ( ( model_ub @ SV11 @ SV29 @ ( sK4_Z @ SV38 @ SV29 @ SV11 ) )
= $true )
| ( ( ~ ( model_ub @ SV11 @ SV29 @ SV38 ) )
= $true )
| ( ( minsol_model_ub @ SV11 @ SV29 @ SV38 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[223]) ).
thf(234,plain,
! [SV11: $i,SV29: $i,SV38: $i] :
( ( ( ~ ( lesseq @ SV38 @ ( sK4_Z @ SV38 @ SV29 @ SV11 ) ) )
= $true )
| ( ( ~ ( model_ub @ SV11 @ SV29 @ SV38 ) )
= $true )
| ( ( minsol_model_ub @ SV11 @ SV29 @ SV38 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[224]) ).
thf(235,plain,
! [SV51: $i,SV44: $i,SV11: $i] :
( ( ( minsol_model_ub @ SV11 @ SV44 @ SV51 )
= $false )
| ( ( ! [SY99: $i] :
( ~ ( model_ub @ SV11 @ SV44 @ SY99 )
| ( lesseq @ SV51 @ SY99 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[225]) ).
thf(236,plain,
! [SV52: $i,SV45: $i,SV11: $i] :
( ( ( minsol_model_ub @ SV11 @ SV45 @ SV52 )
= $false )
| ( ( model_ub @ SV11 @ SV45 @ SV52 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[226]) ).
thf(237,plain,
! [SV37: $i,SV28: $i,SV10: $i] :
( ( ( model_max @ SV10 @ SV28 @ SV37 )
= $false )
| ( ( model_max @ SV10 @ SV28 @ ( sK5_Z @ SV37 @ SV28 @ SV10 ) )
= $true )
| ( ( minsol_model_max @ SV10 @ SV28 @ SV37 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[229]) ).
thf(238,plain,
! [SV10: $i,SV28: $i,SV37: $i] :
( ( ( lesseq @ SV37 @ ( sK5_Z @ SV37 @ SV28 @ SV10 ) )
= $false )
| ( ( ~ ( model_max @ SV10 @ SV28 @ SV37 ) )
= $true )
| ( ( minsol_model_max @ SV10 @ SV28 @ SV37 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[230]) ).
thf(239,plain,
! [SV49: $i,SV53: $i,SV42: $i,SV10: $i] :
( ( ( ~ ( model_max @ SV10 @ SV42 @ SV53 )
| ( lesseq @ SV49 @ SV53 ) )
= $true )
| ( ( minsol_model_max @ SV10 @ SV42 @ SV49 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[231]) ).
thf(240,plain,
! [SV38: $i,SV29: $i,SV11: $i] :
( ( ( model_ub @ SV11 @ SV29 @ SV38 )
= $false )
| ( ( model_ub @ SV11 @ SV29 @ ( sK4_Z @ SV38 @ SV29 @ SV11 ) )
= $true )
| ( ( minsol_model_ub @ SV11 @ SV29 @ SV38 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[233]) ).
thf(241,plain,
! [SV11: $i,SV29: $i,SV38: $i] :
( ( ( lesseq @ SV38 @ ( sK4_Z @ SV38 @ SV29 @ SV11 ) )
= $false )
| ( ( ~ ( model_ub @ SV11 @ SV29 @ SV38 ) )
= $true )
| ( ( minsol_model_ub @ SV11 @ SV29 @ SV38 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[234]) ).
thf(242,plain,
! [SV51: $i,SV54: $i,SV44: $i,SV11: $i] :
( ( ( ~ ( model_ub @ SV11 @ SV44 @ SV54 )
| ( lesseq @ SV51 @ SV54 ) )
= $true )
| ( ( minsol_model_ub @ SV11 @ SV44 @ SV51 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[235]) ).
thf(243,plain,
! [SV37: $i,SV28: $i,SV10: $i] :
( ( ( model_max @ SV10 @ SV28 @ SV37 )
= $false )
| ( ( lesseq @ SV37 @ ( sK5_Z @ SV37 @ SV28 @ SV10 ) )
= $false )
| ( ( minsol_model_max @ SV10 @ SV28 @ SV37 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[238]) ).
thf(244,plain,
! [SV49: $i,SV53: $i,SV42: $i,SV10: $i] :
( ( ( ~ ( model_max @ SV10 @ SV42 @ SV53 ) )
= $true )
| ( ( lesseq @ SV49 @ SV53 )
= $true )
| ( ( minsol_model_max @ SV10 @ SV42 @ SV49 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[239]) ).
thf(245,plain,
! [SV38: $i,SV29: $i,SV11: $i] :
( ( ( model_ub @ SV11 @ SV29 @ SV38 )
= $false )
| ( ( lesseq @ SV38 @ ( sK4_Z @ SV38 @ SV29 @ SV11 ) )
= $false )
| ( ( minsol_model_ub @ SV11 @ SV29 @ SV38 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[241]) ).
thf(246,plain,
! [SV51: $i,SV54: $i,SV44: $i,SV11: $i] :
( ( ( ~ ( model_ub @ SV11 @ SV44 @ SV54 ) )
= $true )
| ( ( lesseq @ SV51 @ SV54 )
= $true )
| ( ( minsol_model_ub @ SV11 @ SV44 @ SV51 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[242]) ).
thf(247,plain,
! [SV49: $i,SV53: $i,SV42: $i,SV10: $i] :
( ( ( model_max @ SV10 @ SV42 @ SV53 )
= $false )
| ( ( lesseq @ SV49 @ SV53 )
= $true )
| ( ( minsol_model_max @ SV10 @ SV42 @ SV49 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[244]) ).
thf(248,plain,
! [SV51: $i,SV54: $i,SV44: $i,SV11: $i] :
( ( ( model_ub @ SV11 @ SV44 @ SV54 )
= $false )
| ( ( lesseq @ SV51 @ SV54 )
= $true )
| ( ( minsol_model_ub @ SV11 @ SV44 @ SV51 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[246]) ).
thf(249,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[70,248,247,245,243,240,237,236,232,228,227,216,206,205,195,194,193,192,178,177,174,156,132,123,122,112,101]) ).
thf(250,plain,
( ( ! [X: $i] : ( lesseq @ X @ X ) )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(251,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ~ ( lesseq @ X @ Y )
| ~ ( lesseq @ Y @ Z )
| ( lesseq @ X @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(252,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( lesseq @ X @ Y )
| ~ ( lesseq @ Y @ X )
| ( X = Y ) ) )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(253,plain,
( ( ! [X: $i,Y: $i] :
( ( lesseq @ X @ Y )
| ( lesseq @ Y @ X ) ) )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(254,plain,
( ( ! [X: $i] :
( ! [Y: $i] :
( ~ ( lesseq @ X @ Y )
| ! [Z: $i] : ( lesseq @ ( sum @ Z @ X ) @ ( sum @ Z @ Y ) ) )
& ! [Y: $i] :
( ! [Z: $i] :
~ ( lesseq @ ( sum @ Z @ X ) @ ( sum @ Z @ Y ) )
| ( lesseq @ X @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(255,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( lesseq @ X @ Y )
| ( lesseq @ ( summation @ X ) @ ( summation @ Y ) ) )
& ! [X: $i,Y: $i] :
( ~ ( lesseq @ ( summation @ X ) @ ( summation @ Y ) )
| ( lesseq @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(256,plain,
( ( ! [X: $i,Y: $i] :
( ( ( max @ X @ Y )
= X )
| ~ ( lesseq @ Y @ X ) ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(257,plain,
( ( ! [X: $i,Y: $i] :
( ( ( max @ X @ Y )
= Y )
| ~ ( lesseq @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(258,plain,
( ( ! [X: $i] :
( ! [Y: $i,Z: $i] :
( ~ ( lesseq @ X @ Z )
| ~ ( lesseq @ Y @ Z )
| ( ub @ X @ Y @ Z ) )
& ! [Y: $i,Z: $i] :
( ~ ( ub @ X @ Y @ Z )
| ( lesseq @ X @ Z ) )
& ! [Y: $i,Z: $i] :
( ~ ( ub @ X @ Y @ Z )
| ( lesseq @ Y @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(259,plain,
( ( ! [X: $i] :
( ! [Y: $i,N: $i] :
( ( N
!= ( max @ X @ Y ) )
| ( model_max @ X @ Y @ N ) )
& ! [Y: $i,N: $i] :
( ~ ( model_max @ X @ Y @ N )
| ( N
= ( max @ X @ Y ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(260,plain,
( ( ! [X: $i] :
( ! [Y: $i,N: $i] :
( ~ ( model_ub @ X @ Y @ N )
| ( ub @ X @ Y @ N ) )
& ! [Y: $i,N: $i] :
( ~ ( ub @ X @ Y @ N )
| ( model_ub @ X @ Y @ N ) ) ) )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(261,plain,
( ( ! [X: $i] :
( ! [Y: $i,N: $i] :
( ( ( model_max @ X @ Y @ ( sK5_Z @ N @ Y @ X ) )
& ~ ( lesseq @ N @ ( sK5_Z @ N @ Y @ X ) ) )
| ~ ( model_max @ X @ Y @ N )
| ( minsol_model_max @ X @ Y @ N ) )
& ! [Y: $i,N: $i] :
( ~ ( minsol_model_max @ X @ Y @ N )
| ! [Z: $i] :
( ~ ( model_max @ X @ Y @ Z )
| ( lesseq @ N @ Z ) ) )
& ! [Y: $i,N: $i] :
( ~ ( minsol_model_max @ X @ Y @ N )
| ( model_max @ X @ Y @ N ) ) ) )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(262,plain,
( ( ! [X: $i] :
( ! [Y: $i,N: $i] :
( ( ( model_ub @ X @ Y @ ( sK4_Z @ N @ Y @ X ) )
& ~ ( lesseq @ N @ ( sK4_Z @ N @ Y @ X ) ) )
| ~ ( model_ub @ X @ Y @ N )
| ( minsol_model_ub @ X @ Y @ N ) )
& ! [Y: $i,N: $i] :
( ~ ( minsol_model_ub @ X @ Y @ N )
| ! [Z: $i] :
( ~ ( model_ub @ X @ Y @ Z )
| ( lesseq @ N @ Z ) ) )
& ! [Y: $i,N: $i] :
( ~ ( minsol_model_ub @ X @ Y @ N )
| ( model_ub @ X @ Y @ N ) ) ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(263,plain,
( ( ( minsol_model_max @ sK1_X @ sK2_SY37 @ sK3_SY39 )
& ~ ( minsol_model_ub @ sK1_X @ sK2_SY37 @ sK3_SY39 ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(264,plain,
( ( ~ ( ~ ( minsol_model_max @ sK1_X @ sK2_SY37 @ sK3_SY39 )
| ~ ~ ( minsol_model_ub @ sK1_X @ sK2_SY37 @ sK3_SY39 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[263]) ).
thf(265,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( model_ub @ SX0 @ SX1 @ SX2 )
| ( ub @ SX0 @ SX1 @ SX2 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( ub @ SX0 @ SX1 @ SX2 )
| ( model_ub @ SX0 @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[260]) ).
thf(266,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( lesseq @ SX0 @ SX1 )
| ( lesseq @ ( summation @ SX0 ) @ ( summation @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( lesseq @ ( summation @ SX0 ) @ ( summation @ SX1 ) )
| ( lesseq @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[255]) ).
thf(267,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i] :
( ~ ( lesseq @ SX0 @ SX1 )
| ! [SX2: $i] : ( lesseq @ ( sum @ SX2 @ SX0 ) @ ( sum @ SX2 @ SX1 ) ) )
| ~ ! [SX1: $i] :
( ! [SX2: $i] :
~ ( lesseq @ ( sum @ SX2 @ SX0 ) @ ( sum @ SX2 @ SX1 ) )
| ( lesseq @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[254]) ).
thf(268,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ( model_max @ SX0 @ SX1 @ ( sK5_Z @ SX2 @ SX1 @ SX0 ) )
| ~ ~ ( lesseq @ SX2 @ ( sK5_Z @ SX2 @ SX1 @ SX0 ) ) )
| ~ ( model_max @ SX0 @ SX1 @ SX2 )
| ( minsol_model_max @ SX0 @ SX1 @ SX2 ) )
| ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( minsol_model_max @ SX0 @ SX1 @ SX2 )
| ! [SX3: $i] :
( ~ ( model_max @ SX0 @ SX1 @ SX3 )
| ( lesseq @ SX2 @ SX3 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( minsol_model_max @ SX0 @ SX1 @ SX2 )
| ( model_max @ SX0 @ SX1 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[261]) ).
thf(269,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ( SX2
!= ( max @ SX0 @ SX1 ) )
| ( model_max @ SX0 @ SX1 @ SX2 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( model_max @ SX0 @ SX1 @ SX2 )
| ( SX2
= ( max @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[259]) ).
thf(270,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( lesseq @ SX0 @ SX2 )
| ~ ( lesseq @ SX1 @ SX2 )
| ( ub @ SX0 @ SX1 @ SX2 ) )
| ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ub @ SX0 @ SX1 @ SX2 )
| ( lesseq @ SX0 @ SX2 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( ub @ SX0 @ SX1 @ SX2 )
| ( lesseq @ SX1 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[258]) ).
thf(271,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ( model_ub @ SX0 @ SX1 @ ( sK4_Z @ SX2 @ SX1 @ SX0 ) )
| ~ ~ ( lesseq @ SX2 @ ( sK4_Z @ SX2 @ SX1 @ SX0 ) ) )
| ~ ( model_ub @ SX0 @ SX1 @ SX2 )
| ( minsol_model_ub @ SX0 @ SX1 @ SX2 ) )
| ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( minsol_model_ub @ SX0 @ SX1 @ SX2 )
| ! [SX3: $i] :
( ~ ( model_ub @ SX0 @ SX1 @ SX3 )
| ( lesseq @ SX2 @ SX3 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( minsol_model_ub @ SX0 @ SX1 @ SX2 )
| ( model_ub @ SX0 @ SX1 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[262]) ).
thf(272,plain,
! [SV55: $i] :
( ( lesseq @ SV55 @ SV55 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[250]) ).
thf(273,plain,
! [SV56: $i] :
( ( ! [SY100: $i,SY101: $i] :
( ~ ( lesseq @ SV56 @ SY100 )
| ~ ( lesseq @ SY100 @ SY101 )
| ( lesseq @ SV56 @ SY101 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[251]) ).
thf(274,plain,
! [SV57: $i] :
( ( ! [SY102: $i] :
( ~ ( lesseq @ SV57 @ SY102 )
| ~ ( lesseq @ SY102 @ SV57 )
| ( SV57 = SY102 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[252]) ).
thf(275,plain,
! [SV58: $i] :
( ( ! [SY103: $i] :
( ( lesseq @ SV58 @ SY103 )
| ( lesseq @ SY103 @ SV58 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[253]) ).
thf(276,plain,
! [SV59: $i] :
( ( ! [SY104: $i] :
( ( ( max @ SV59 @ SY104 )
= SV59 )
| ~ ( lesseq @ SY104 @ SV59 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[256]) ).
thf(277,plain,
! [SV60: $i] :
( ( ! [SY105: $i] :
( ( ( max @ SV60 @ SY105 )
= SY105 )
| ~ ( lesseq @ SV60 @ SY105 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[257]) ).
thf(278,plain,
( ( ~ ( minsol_model_max @ sK1_X @ sK2_SY37 @ sK3_SY39 )
| ~ ~ ( minsol_model_ub @ sK1_X @ sK2_SY37 @ sK3_SY39 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[264]) ).
thf(279,plain,
! [SV61: $i] :
( ( ~ ( ~ ! [SY106: $i,SY107: $i] :
( ~ ( model_ub @ SV61 @ SY106 @ SY107 )
| ( ub @ SV61 @ SY106 @ SY107 ) )
| ~ ! [SY108: $i,SY109: $i] :
( ~ ( ub @ SV61 @ SY108 @ SY109 )
| ( model_ub @ SV61 @ SY108 @ SY109 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[265]) ).
thf(280,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( lesseq @ SX0 @ SX1 )
| ( lesseq @ ( summation @ SX0 ) @ ( summation @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( lesseq @ ( summation @ SX0 ) @ ( summation @ SX1 ) )
| ( lesseq @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[266]) ).
thf(281,plain,
! [SV62: $i] :
( ( ~ ( ~ ! [SY110: $i] :
( ~ ( lesseq @ SV62 @ SY110 )
| ! [SY111: $i] : ( lesseq @ ( sum @ SY111 @ SV62 ) @ ( sum @ SY111 @ SY110 ) ) )
| ~ ! [SY112: $i] :
( ! [SY113: $i] :
~ ( lesseq @ ( sum @ SY113 @ SV62 ) @ ( sum @ SY113 @ SY112 ) )
| ( lesseq @ SV62 @ SY112 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[267]) ).
thf(282,plain,
! [SV63: $i] :
( ( ~ ( ~ ! [SY114: $i,SY115: $i] :
( ~ ( ~ ( model_max @ SV63 @ SY114 @ ( sK5_Z @ SY115 @ SY114 @ SV63 ) )
| ~ ~ ( lesseq @ SY115 @ ( sK5_Z @ SY115 @ SY114 @ SV63 ) ) )
| ~ ( model_max @ SV63 @ SY114 @ SY115 )
| ( minsol_model_max @ SV63 @ SY114 @ SY115 ) )
| ~ ~ ( ~ ! [SY116: $i,SY117: $i] :
( ~ ( minsol_model_max @ SV63 @ SY116 @ SY117 )
| ! [SY118: $i] :
( ~ ( model_max @ SV63 @ SY116 @ SY118 )
| ( lesseq @ SY117 @ SY118 ) ) )
| ~ ! [SY119: $i,SY120: $i] :
( ~ ( minsol_model_max @ SV63 @ SY119 @ SY120 )
| ( model_max @ SV63 @ SY119 @ SY120 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[268]) ).
thf(283,plain,
! [SV64: $i] :
( ( ~ ( ~ ! [SY121: $i,SY122: $i] :
( ( SY122
!= ( max @ SV64 @ SY121 ) )
| ( model_max @ SV64 @ SY121 @ SY122 ) )
| ~ ! [SY123: $i,SY124: $i] :
( ~ ( model_max @ SV64 @ SY123 @ SY124 )
| ( SY124
= ( max @ SV64 @ SY123 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[269]) ).
thf(284,plain,
! [SV65: $i] :
( ( ~ ( ~ ! [SY125: $i,SY126: $i] :
( ~ ( lesseq @ SV65 @ SY126 )
| ~ ( lesseq @ SY125 @ SY126 )
| ( ub @ SV65 @ SY125 @ SY126 ) )
| ~ ~ ( ~ ! [SY127: $i,SY128: $i] :
( ~ ( ub @ SV65 @ SY127 @ SY128 )
| ( lesseq @ SV65 @ SY128 ) )
| ~ ! [SY129: $i,SY130: $i] :
( ~ ( ub @ SV65 @ SY129 @ SY130 )
| ( lesseq @ SY129 @ SY130 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[270]) ).
thf(285,plain,
! [SV66: $i] :
( ( ~ ( ~ ! [SY131: $i,SY132: $i] :
( ~ ( ~ ( model_ub @ SV66 @ SY131 @ ( sK4_Z @ SY132 @ SY131 @ SV66 ) )
| ~ ~ ( lesseq @ SY132 @ ( sK4_Z @ SY132 @ SY131 @ SV66 ) ) )
| ~ ( model_ub @ SV66 @ SY131 @ SY132 )
| ( minsol_model_ub @ SV66 @ SY131 @ SY132 ) )
| ~ ~ ( ~ ! [SY133: $i,SY134: $i] :
( ~ ( minsol_model_ub @ SV66 @ SY133 @ SY134 )
| ! [SY135: $i] :
( ~ ( model_ub @ SV66 @ SY133 @ SY135 )
| ( lesseq @ SY134 @ SY135 ) ) )
| ~ ! [SY136: $i,SY137: $i] :
( ~ ( minsol_model_ub @ SV66 @ SY136 @ SY137 )
| ( model_ub @ SV66 @ SY136 @ SY137 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[271]) ).
thf(286,plain,
! [SV67: $i,SV56: $i] :
( ( ! [SY138: $i] :
( ~ ( lesseq @ SV56 @ SV67 )
| ~ ( lesseq @ SV67 @ SY138 )
| ( lesseq @ SV56 @ SY138 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[273]) ).
thf(287,plain,
! [SV68: $i,SV57: $i] :
( ( ~ ( lesseq @ SV57 @ SV68 )
| ~ ( lesseq @ SV68 @ SV57 )
| ( SV57 = SV68 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[274]) ).
thf(288,plain,
! [SV69: $i,SV58: $i] :
( ( ( lesseq @ SV58 @ SV69 )
| ( lesseq @ SV69 @ SV58 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[275]) ).
thf(289,plain,
! [SV70: $i,SV59: $i] :
( ( ( ( max @ SV59 @ SV70 )
= SV59 )
| ~ ( lesseq @ SV70 @ SV59 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[276]) ).
thf(290,plain,
! [SV71: $i,SV60: $i] :
( ( ( ( max @ SV60 @ SV71 )
= SV71 )
| ~ ( lesseq @ SV60 @ SV71 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[277]) ).
thf(291,plain,
( ( ~ ( minsol_model_max @ sK1_X @ sK2_SY37 @ sK3_SY39 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[278]) ).
thf(292,plain,
( ( ~ ~ ( minsol_model_ub @ sK1_X @ sK2_SY37 @ sK3_SY39 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[278]) ).
thf(293,plain,
! [SV61: $i] :
( ( ~ ! [SY106: $i,SY107: $i] :
( ~ ( model_ub @ SV61 @ SY106 @ SY107 )
| ( ub @ SV61 @ SY106 @ SY107 ) )
| ~ ! [SY108: $i,SY109: $i] :
( ~ ( ub @ SV61 @ SY108 @ SY109 )
| ( model_ub @ SV61 @ SY108 @ SY109 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[279]) ).
thf(294,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( lesseq @ SX0 @ SX1 )
| ( lesseq @ ( summation @ SX0 ) @ ( summation @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[280]) ).
thf(295,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( lesseq @ ( summation @ SX0 ) @ ( summation @ SX1 ) )
| ( lesseq @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[280]) ).
thf(296,plain,
! [SV62: $i] :
( ( ~ ! [SY110: $i] :
( ~ ( lesseq @ SV62 @ SY110 )
| ! [SY111: $i] : ( lesseq @ ( sum @ SY111 @ SV62 ) @ ( sum @ SY111 @ SY110 ) ) )
| ~ ! [SY112: $i] :
( ! [SY113: $i] :
~ ( lesseq @ ( sum @ SY113 @ SV62 ) @ ( sum @ SY113 @ SY112 ) )
| ( lesseq @ SV62 @ SY112 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[281]) ).
thf(297,plain,
! [SV63: $i] :
( ( ~ ! [SY114: $i,SY115: $i] :
( ~ ( ~ ( model_max @ SV63 @ SY114 @ ( sK5_Z @ SY115 @ SY114 @ SV63 ) )
| ~ ~ ( lesseq @ SY115 @ ( sK5_Z @ SY115 @ SY114 @ SV63 ) ) )
| ~ ( model_max @ SV63 @ SY114 @ SY115 )
| ( minsol_model_max @ SV63 @ SY114 @ SY115 ) )
| ~ ~ ( ~ ! [SY116: $i,SY117: $i] :
( ~ ( minsol_model_max @ SV63 @ SY116 @ SY117 )
| ! [SY118: $i] :
( ~ ( model_max @ SV63 @ SY116 @ SY118 )
| ( lesseq @ SY117 @ SY118 ) ) )
| ~ ! [SY119: $i,SY120: $i] :
( ~ ( minsol_model_max @ SV63 @ SY119 @ SY120 )
| ( model_max @ SV63 @ SY119 @ SY120 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[282]) ).
thf(298,plain,
! [SV64: $i] :
( ( ~ ! [SY121: $i,SY122: $i] :
( ( SY122
!= ( max @ SV64 @ SY121 ) )
| ( model_max @ SV64 @ SY121 @ SY122 ) )
| ~ ! [SY123: $i,SY124: $i] :
( ~ ( model_max @ SV64 @ SY123 @ SY124 )
| ( SY124
= ( max @ SV64 @ SY123 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[283]) ).
thf(299,plain,
! [SV65: $i] :
( ( ~ ! [SY125: $i,SY126: $i] :
( ~ ( lesseq @ SV65 @ SY126 )
| ~ ( lesseq @ SY125 @ SY126 )
| ( ub @ SV65 @ SY125 @ SY126 ) )
| ~ ~ ( ~ ! [SY127: $i,SY128: $i] :
( ~ ( ub @ SV65 @ SY127 @ SY128 )
| ( lesseq @ SV65 @ SY128 ) )
| ~ ! [SY129: $i,SY130: $i] :
( ~ ( ub @ SV65 @ SY129 @ SY130 )
| ( lesseq @ SY129 @ SY130 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[284]) ).
thf(300,plain,
! [SV66: $i] :
( ( ~ ! [SY131: $i,SY132: $i] :
( ~ ( ~ ( model_ub @ SV66 @ SY131 @ ( sK4_Z @ SY132 @ SY131 @ SV66 ) )
| ~ ~ ( lesseq @ SY132 @ ( sK4_Z @ SY132 @ SY131 @ SV66 ) ) )
| ~ ( model_ub @ SV66 @ SY131 @ SY132 )
| ( minsol_model_ub @ SV66 @ SY131 @ SY132 ) )
| ~ ~ ( ~ ! [SY133: $i,SY134: $i] :
( ~ ( minsol_model_ub @ SV66 @ SY133 @ SY134 )
| ! [SY135: $i] :
( ~ ( model_ub @ SV66 @ SY133 @ SY135 )
| ( lesseq @ SY134 @ SY135 ) ) )
| ~ ! [SY136: $i,SY137: $i] :
( ~ ( minsol_model_ub @ SV66 @ SY136 @ SY137 )
| ( model_ub @ SV66 @ SY136 @ SY137 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[285]) ).
thf(301,plain,
! [SV72: $i,SV67: $i,SV56: $i] :
( ( ~ ( lesseq @ SV56 @ SV67 )
| ~ ( lesseq @ SV67 @ SV72 )
| ( lesseq @ SV56 @ SV72 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[286]) ).
thf(302,plain,
! [SV68: $i,SV57: $i] :
( ( ( ~ ( lesseq @ SV57 @ SV68 )
| ~ ( lesseq @ SV68 @ SV57 ) )
= $true )
| ( ( SV57 = SV68 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[287]) ).
thf(303,plain,
! [SV69: $i,SV58: $i] :
( ( ( lesseq @ SV58 @ SV69 )
= $true )
| ( ( lesseq @ SV69 @ SV58 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[288]) ).
thf(304,plain,
! [SV70: $i,SV59: $i] :
( ( ( ( max @ SV59 @ SV70 )
= SV59 )
= $true )
| ( ( ~ ( lesseq @ SV70 @ SV59 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[289]) ).
thf(305,plain,
! [SV71: $i,SV60: $i] :
( ( ( ( max @ SV60 @ SV71 )
= SV71 )
= $true )
| ( ( ~ ( lesseq @ SV60 @ SV71 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[290]) ).
thf(306,plain,
( ( minsol_model_max @ sK1_X @ sK2_SY37 @ sK3_SY39 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[291]) ).
thf(307,plain,
( ( ~ ( minsol_model_ub @ sK1_X @ sK2_SY37 @ sK3_SY39 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[292]) ).
thf(308,plain,
! [SV61: $i] :
( ( ~ ! [SY106: $i,SY107: $i] :
( ~ ( model_ub @ SV61 @ SY106 @ SY107 )
| ( ub @ SV61 @ SY106 @ SY107 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[293]) ).
thf(309,plain,
! [SV61: $i] :
( ( ~ ! [SY108: $i,SY109: $i] :
( ~ ( ub @ SV61 @ SY108 @ SY109 )
| ( model_ub @ SV61 @ SY108 @ SY109 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[293]) ).
thf(310,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( lesseq @ SX0 @ SX1 )
| ( lesseq @ ( summation @ SX0 ) @ ( summation @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[294]) ).
thf(311,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( lesseq @ ( summation @ SX0 ) @ ( summation @ SX1 ) )
| ( lesseq @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[295]) ).
thf(312,plain,
! [SV62: $i] :
( ( ~ ! [SY110: $i] :
( ~ ( lesseq @ SV62 @ SY110 )
| ! [SY111: $i] : ( lesseq @ ( sum @ SY111 @ SV62 ) @ ( sum @ SY111 @ SY110 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[296]) ).
thf(313,plain,
! [SV62: $i] :
( ( ~ ! [SY112: $i] :
( ! [SY113: $i] :
~ ( lesseq @ ( sum @ SY113 @ SV62 ) @ ( sum @ SY113 @ SY112 ) )
| ( lesseq @ SV62 @ SY112 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[296]) ).
thf(314,plain,
! [SV63: $i] :
( ( ~ ! [SY114: $i,SY115: $i] :
( ~ ( ~ ( model_max @ SV63 @ SY114 @ ( sK5_Z @ SY115 @ SY114 @ SV63 ) )
| ~ ~ ( lesseq @ SY115 @ ( sK5_Z @ SY115 @ SY114 @ SV63 ) ) )
| ~ ( model_max @ SV63 @ SY114 @ SY115 )
| ( minsol_model_max @ SV63 @ SY114 @ SY115 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[297]) ).
thf(315,plain,
! [SV63: $i] :
( ( ~ ~ ( ~ ! [SY116: $i,SY117: $i] :
( ~ ( minsol_model_max @ SV63 @ SY116 @ SY117 )
| ! [SY118: $i] :
( ~ ( model_max @ SV63 @ SY116 @ SY118 )
| ( lesseq @ SY117 @ SY118 ) ) )
| ~ ! [SY119: $i,SY120: $i] :
( ~ ( minsol_model_max @ SV63 @ SY119 @ SY120 )
| ( model_max @ SV63 @ SY119 @ SY120 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[297]) ).
thf(316,plain,
! [SV64: $i] :
( ( ~ ! [SY121: $i,SY122: $i] :
( ( SY122
!= ( max @ SV64 @ SY121 ) )
| ( model_max @ SV64 @ SY121 @ SY122 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[298]) ).
thf(317,plain,
! [SV64: $i] :
( ( ~ ! [SY123: $i,SY124: $i] :
( ~ ( model_max @ SV64 @ SY123 @ SY124 )
| ( SY124
= ( max @ SV64 @ SY123 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[298]) ).
thf(318,plain,
! [SV65: $i] :
( ( ~ ! [SY125: $i,SY126: $i] :
( ~ ( lesseq @ SV65 @ SY126 )
| ~ ( lesseq @ SY125 @ SY126 )
| ( ub @ SV65 @ SY125 @ SY126 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[299]) ).
thf(319,plain,
! [SV65: $i] :
( ( ~ ~ ( ~ ! [SY127: $i,SY128: $i] :
( ~ ( ub @ SV65 @ SY127 @ SY128 )
| ( lesseq @ SV65 @ SY128 ) )
| ~ ! [SY129: $i,SY130: $i] :
( ~ ( ub @ SV65 @ SY129 @ SY130 )
| ( lesseq @ SY129 @ SY130 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[299]) ).
thf(320,plain,
! [SV66: $i] :
( ( ~ ! [SY131: $i,SY132: $i] :
( ~ ( ~ ( model_ub @ SV66 @ SY131 @ ( sK4_Z @ SY132 @ SY131 @ SV66 ) )
| ~ ~ ( lesseq @ SY132 @ ( sK4_Z @ SY132 @ SY131 @ SV66 ) ) )
| ~ ( model_ub @ SV66 @ SY131 @ SY132 )
| ( minsol_model_ub @ SV66 @ SY131 @ SY132 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[300]) ).
thf(321,plain,
! [SV66: $i] :
( ( ~ ~ ( ~ ! [SY133: $i,SY134: $i] :
( ~ ( minsol_model_ub @ SV66 @ SY133 @ SY134 )
| ! [SY135: $i] :
( ~ ( model_ub @ SV66 @ SY133 @ SY135 )
| ( lesseq @ SY134 @ SY135 ) ) )
| ~ ! [SY136: $i,SY137: $i] :
( ~ ( minsol_model_ub @ SV66 @ SY136 @ SY137 )
| ( model_ub @ SV66 @ SY136 @ SY137 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[300]) ).
thf(322,plain,
! [SV72: $i,SV67: $i,SV56: $i] :
( ( ( ~ ( lesseq @ SV56 @ SV67 )
| ~ ( lesseq @ SV67 @ SV72 ) )
= $true )
| ( ( lesseq @ SV56 @ SV72 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[301]) ).
thf(323,plain,
! [SV68: $i,SV57: $i] :
( ( ( ~ ( lesseq @ SV57 @ SV68 ) )
= $true )
| ( ( ~ ( lesseq @ SV68 @ SV57 ) )
= $true )
| ( ( SV57 = SV68 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[302]) ).
thf(324,plain,
! [SV59: $i,SV70: $i] :
( ( ( lesseq @ SV70 @ SV59 )
= $false )
| ( ( ( max @ SV59 @ SV70 )
= SV59 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[304]) ).
thf(325,plain,
! [SV71: $i,SV60: $i] :
( ( ( lesseq @ SV60 @ SV71 )
= $false )
| ( ( ( max @ SV60 @ SV71 )
= SV71 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[305]) ).
thf(326,plain,
( ( minsol_model_ub @ sK1_X @ sK2_SY37 @ sK3_SY39 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[307]) ).
thf(327,plain,
! [SV61: $i] :
( ( ! [SY106: $i,SY107: $i] :
( ~ ( model_ub @ SV61 @ SY106 @ SY107 )
| ( ub @ SV61 @ SY106 @ SY107 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[308]) ).
thf(328,plain,
! [SV61: $i] :
( ( ! [SY108: $i,SY109: $i] :
( ~ ( ub @ SV61 @ SY108 @ SY109 )
| ( model_ub @ SV61 @ SY108 @ SY109 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[309]) ).
thf(329,plain,
! [SV73: $i] :
( ( ! [SY139: $i] :
( ~ ( lesseq @ SV73 @ SY139 )
| ( lesseq @ ( summation @ SV73 ) @ ( summation @ SY139 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[310]) ).
thf(330,plain,
! [SV74: $i] :
( ( ! [SY140: $i] :
( ~ ( lesseq @ ( summation @ SV74 ) @ ( summation @ SY140 ) )
| ( lesseq @ SV74 @ SY140 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[311]) ).
thf(331,plain,
! [SV62: $i] :
( ( ! [SY110: $i] :
( ~ ( lesseq @ SV62 @ SY110 )
| ! [SY111: $i] : ( lesseq @ ( sum @ SY111 @ SV62 ) @ ( sum @ SY111 @ SY110 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[312]) ).
thf(332,plain,
! [SV62: $i] :
( ( ! [SY112: $i] :
( ! [SY113: $i] :
~ ( lesseq @ ( sum @ SY113 @ SV62 ) @ ( sum @ SY113 @ SY112 ) )
| ( lesseq @ SV62 @ SY112 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[313]) ).
thf(333,plain,
! [SV63: $i] :
( ( ! [SY114: $i,SY115: $i] :
( ~ ( ~ ( model_max @ SV63 @ SY114 @ ( sK5_Z @ SY115 @ SY114 @ SV63 ) )
| ~ ~ ( lesseq @ SY115 @ ( sK5_Z @ SY115 @ SY114 @ SV63 ) ) )
| ~ ( model_max @ SV63 @ SY114 @ SY115 )
| ( minsol_model_max @ SV63 @ SY114 @ SY115 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[314]) ).
thf(334,plain,
! [SV63: $i] :
( ( ~ ( ~ ! [SY116: $i,SY117: $i] :
( ~ ( minsol_model_max @ SV63 @ SY116 @ SY117 )
| ! [SY118: $i] :
( ~ ( model_max @ SV63 @ SY116 @ SY118 )
| ( lesseq @ SY117 @ SY118 ) ) )
| ~ ! [SY119: $i,SY120: $i] :
( ~ ( minsol_model_max @ SV63 @ SY119 @ SY120 )
| ( model_max @ SV63 @ SY119 @ SY120 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[315]) ).
thf(335,plain,
! [SV64: $i] :
( ( ! [SY121: $i,SY122: $i] :
( ( SY122
!= ( max @ SV64 @ SY121 ) )
| ( model_max @ SV64 @ SY121 @ SY122 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[316]) ).
thf(336,plain,
! [SV64: $i] :
( ( ! [SY123: $i,SY124: $i] :
( ~ ( model_max @ SV64 @ SY123 @ SY124 )
| ( SY124
= ( max @ SV64 @ SY123 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[317]) ).
thf(337,plain,
! [SV65: $i] :
( ( ! [SY125: $i,SY126: $i] :
( ~ ( lesseq @ SV65 @ SY126 )
| ~ ( lesseq @ SY125 @ SY126 )
| ( ub @ SV65 @ SY125 @ SY126 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[318]) ).
thf(338,plain,
! [SV65: $i] :
( ( ~ ( ~ ! [SY127: $i,SY128: $i] :
( ~ ( ub @ SV65 @ SY127 @ SY128 )
| ( lesseq @ SV65 @ SY128 ) )
| ~ ! [SY129: $i,SY130: $i] :
( ~ ( ub @ SV65 @ SY129 @ SY130 )
| ( lesseq @ SY129 @ SY130 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[319]) ).
thf(339,plain,
! [SV66: $i] :
( ( ! [SY131: $i,SY132: $i] :
( ~ ( ~ ( model_ub @ SV66 @ SY131 @ ( sK4_Z @ SY132 @ SY131 @ SV66 ) )
| ~ ~ ( lesseq @ SY132 @ ( sK4_Z @ SY132 @ SY131 @ SV66 ) ) )
| ~ ( model_ub @ SV66 @ SY131 @ SY132 )
| ( minsol_model_ub @ SV66 @ SY131 @ SY132 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[320]) ).
thf(340,plain,
! [SV66: $i] :
( ( ~ ( ~ ! [SY133: $i,SY134: $i] :
( ~ ( minsol_model_ub @ SV66 @ SY133 @ SY134 )
| ! [SY135: $i] :
( ~ ( model_ub @ SV66 @ SY133 @ SY135 )
| ( lesseq @ SY134 @ SY135 ) ) )
| ~ ! [SY136: $i,SY137: $i] :
( ~ ( minsol_model_ub @ SV66 @ SY136 @ SY137 )
| ( model_ub @ SV66 @ SY136 @ SY137 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[321]) ).
thf(341,plain,
! [SV72: $i,SV67: $i,SV56: $i] :
( ( ( ~ ( lesseq @ SV56 @ SV67 ) )
= $true )
| ( ( ~ ( lesseq @ SV67 @ SV72 ) )
= $true )
| ( ( lesseq @ SV56 @ SV72 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[322]) ).
thf(342,plain,
! [SV68: $i,SV57: $i] :
( ( ( lesseq @ SV57 @ SV68 )
= $false )
| ( ( ~ ( lesseq @ SV68 @ SV57 ) )
= $true )
| ( ( SV57 = SV68 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[323]) ).
thf(343,plain,
! [SV75: $i,SV61: $i] :
( ( ! [SY141: $i] :
( ~ ( model_ub @ SV61 @ SV75 @ SY141 )
| ( ub @ SV61 @ SV75 @ SY141 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[327]) ).
thf(344,plain,
! [SV76: $i,SV61: $i] :
( ( ! [SY142: $i] :
( ~ ( ub @ SV61 @ SV76 @ SY142 )
| ( model_ub @ SV61 @ SV76 @ SY142 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[328]) ).
thf(345,plain,
! [SV77: $i,SV73: $i] :
( ( ~ ( lesseq @ SV73 @ SV77 )
| ( lesseq @ ( summation @ SV73 ) @ ( summation @ SV77 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[329]) ).
thf(346,plain,
! [SV78: $i,SV74: $i] :
( ( ~ ( lesseq @ ( summation @ SV74 ) @ ( summation @ SV78 ) )
| ( lesseq @ SV74 @ SV78 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[330]) ).
thf(347,plain,
! [SV79: $i,SV62: $i] :
( ( ~ ( lesseq @ SV62 @ SV79 )
| ! [SY143: $i] : ( lesseq @ ( sum @ SY143 @ SV62 ) @ ( sum @ SY143 @ SV79 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[331]) ).
thf(348,plain,
! [SV80: $i,SV62: $i] :
( ( ! [SY144: $i] :
~ ( lesseq @ ( sum @ SY144 @ SV62 ) @ ( sum @ SY144 @ SV80 ) )
| ( lesseq @ SV62 @ SV80 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[332]) ).
thf(349,plain,
! [SV81: $i,SV63: $i] :
( ( ! [SY145: $i] :
( ~ ( ~ ( model_max @ SV63 @ SV81 @ ( sK5_Z @ SY145 @ SV81 @ SV63 ) )
| ~ ~ ( lesseq @ SY145 @ ( sK5_Z @ SY145 @ SV81 @ SV63 ) ) )
| ~ ( model_max @ SV63 @ SV81 @ SY145 )
| ( minsol_model_max @ SV63 @ SV81 @ SY145 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[333]) ).
thf(350,plain,
! [SV63: $i] :
( ( ~ ! [SY116: $i,SY117: $i] :
( ~ ( minsol_model_max @ SV63 @ SY116 @ SY117 )
| ! [SY118: $i] :
( ~ ( model_max @ SV63 @ SY116 @ SY118 )
| ( lesseq @ SY117 @ SY118 ) ) )
| ~ ! [SY119: $i,SY120: $i] :
( ~ ( minsol_model_max @ SV63 @ SY119 @ SY120 )
| ( model_max @ SV63 @ SY119 @ SY120 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[334]) ).
thf(351,plain,
! [SV82: $i,SV64: $i] :
( ( ! [SY146: $i] :
( ( SY146
!= ( max @ SV64 @ SV82 ) )
| ( model_max @ SV64 @ SV82 @ SY146 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[335]) ).
thf(352,plain,
! [SV83: $i,SV64: $i] :
( ( ! [SY147: $i] :
( ~ ( model_max @ SV64 @ SV83 @ SY147 )
| ( SY147
= ( max @ SV64 @ SV83 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[336]) ).
thf(353,plain,
! [SV84: $i,SV65: $i] :
( ( ! [SY148: $i] :
( ~ ( lesseq @ SV65 @ SY148 )
| ~ ( lesseq @ SV84 @ SY148 )
| ( ub @ SV65 @ SV84 @ SY148 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[337]) ).
thf(354,plain,
! [SV65: $i] :
( ( ~ ! [SY127: $i,SY128: $i] :
( ~ ( ub @ SV65 @ SY127 @ SY128 )
| ( lesseq @ SV65 @ SY128 ) )
| ~ ! [SY129: $i,SY130: $i] :
( ~ ( ub @ SV65 @ SY129 @ SY130 )
| ( lesseq @ SY129 @ SY130 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[338]) ).
thf(355,plain,
! [SV85: $i,SV66: $i] :
( ( ! [SY149: $i] :
( ~ ( ~ ( model_ub @ SV66 @ SV85 @ ( sK4_Z @ SY149 @ SV85 @ SV66 ) )
| ~ ~ ( lesseq @ SY149 @ ( sK4_Z @ SY149 @ SV85 @ SV66 ) ) )
| ~ ( model_ub @ SV66 @ SV85 @ SY149 )
| ( minsol_model_ub @ SV66 @ SV85 @ SY149 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[339]) ).
thf(356,plain,
! [SV66: $i] :
( ( ~ ! [SY133: $i,SY134: $i] :
( ~ ( minsol_model_ub @ SV66 @ SY133 @ SY134 )
| ! [SY135: $i] :
( ~ ( model_ub @ SV66 @ SY133 @ SY135 )
| ( lesseq @ SY134 @ SY135 ) ) )
| ~ ! [SY136: $i,SY137: $i] :
( ~ ( minsol_model_ub @ SV66 @ SY136 @ SY137 )
| ( model_ub @ SV66 @ SY136 @ SY137 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[340]) ).
thf(357,plain,
! [SV72: $i,SV67: $i,SV56: $i] :
( ( ( lesseq @ SV56 @ SV67 )
= $false )
| ( ( ~ ( lesseq @ SV67 @ SV72 ) )
= $true )
| ( ( lesseq @ SV56 @ SV72 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[341]) ).
thf(358,plain,
! [SV57: $i,SV68: $i] :
( ( ( lesseq @ SV68 @ SV57 )
= $false )
| ( ( lesseq @ SV57 @ SV68 )
= $false )
| ( ( SV57 = SV68 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[342]) ).
thf(359,plain,
! [SV86: $i,SV75: $i,SV61: $i] :
( ( ~ ( model_ub @ SV61 @ SV75 @ SV86 )
| ( ub @ SV61 @ SV75 @ SV86 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[343]) ).
thf(360,plain,
! [SV87: $i,SV76: $i,SV61: $i] :
( ( ~ ( ub @ SV61 @ SV76 @ SV87 )
| ( model_ub @ SV61 @ SV76 @ SV87 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[344]) ).
thf(361,plain,
! [SV77: $i,SV73: $i] :
( ( ( ~ ( lesseq @ SV73 @ SV77 ) )
= $true )
| ( ( lesseq @ ( summation @ SV73 ) @ ( summation @ SV77 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[345]) ).
thf(362,plain,
! [SV78: $i,SV74: $i] :
( ( ( ~ ( lesseq @ ( summation @ SV74 ) @ ( summation @ SV78 ) ) )
= $true )
| ( ( lesseq @ SV74 @ SV78 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[346]) ).
thf(363,plain,
! [SV79: $i,SV62: $i] :
( ( ( ~ ( lesseq @ SV62 @ SV79 ) )
= $true )
| ( ( ! [SY143: $i] : ( lesseq @ ( sum @ SY143 @ SV62 ) @ ( sum @ SY143 @ SV79 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[347]) ).
thf(364,plain,
! [SV80: $i,SV62: $i] :
( ( ( ! [SY144: $i] :
~ ( lesseq @ ( sum @ SY144 @ SV62 ) @ ( sum @ SY144 @ SV80 ) ) )
= $true )
| ( ( lesseq @ SV62 @ SV80 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[348]) ).
thf(365,plain,
! [SV88: $i,SV81: $i,SV63: $i] :
( ( ~ ( ~ ( model_max @ SV63 @ SV81 @ ( sK5_Z @ SV88 @ SV81 @ SV63 ) )
| ~ ~ ( lesseq @ SV88 @ ( sK5_Z @ SV88 @ SV81 @ SV63 ) ) )
| ~ ( model_max @ SV63 @ SV81 @ SV88 )
| ( minsol_model_max @ SV63 @ SV81 @ SV88 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[349]) ).
thf(366,plain,
! [SV63: $i] :
( ( ~ ! [SY116: $i,SY117: $i] :
( ~ ( minsol_model_max @ SV63 @ SY116 @ SY117 )
| ! [SY118: $i] :
( ~ ( model_max @ SV63 @ SY116 @ SY118 )
| ( lesseq @ SY117 @ SY118 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[350]) ).
thf(367,plain,
! [SV63: $i] :
( ( ~ ! [SY119: $i,SY120: $i] :
( ~ ( minsol_model_max @ SV63 @ SY119 @ SY120 )
| ( model_max @ SV63 @ SY119 @ SY120 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[350]) ).
thf(368,plain,
! [SV82: $i,SV64: $i,SV89: $i] :
( ( ( SV89
!= ( max @ SV64 @ SV82 ) )
| ( model_max @ SV64 @ SV82 @ SV89 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[351]) ).
thf(369,plain,
! [SV90: $i,SV83: $i,SV64: $i] :
( ( ~ ( model_max @ SV64 @ SV83 @ SV90 )
| ( SV90
= ( max @ SV64 @ SV83 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[352]) ).
thf(370,plain,
! [SV84: $i,SV91: $i,SV65: $i] :
( ( ~ ( lesseq @ SV65 @ SV91 )
| ~ ( lesseq @ SV84 @ SV91 )
| ( ub @ SV65 @ SV84 @ SV91 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[353]) ).
thf(371,plain,
! [SV65: $i] :
( ( ~ ! [SY127: $i,SY128: $i] :
( ~ ( ub @ SV65 @ SY127 @ SY128 )
| ( lesseq @ SV65 @ SY128 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[354]) ).
thf(372,plain,
! [SV65: $i] :
( ( ~ ! [SY129: $i,SY130: $i] :
( ~ ( ub @ SV65 @ SY129 @ SY130 )
| ( lesseq @ SY129 @ SY130 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[354]) ).
thf(373,plain,
! [SV92: $i,SV85: $i,SV66: $i] :
( ( ~ ( ~ ( model_ub @ SV66 @ SV85 @ ( sK4_Z @ SV92 @ SV85 @ SV66 ) )
| ~ ~ ( lesseq @ SV92 @ ( sK4_Z @ SV92 @ SV85 @ SV66 ) ) )
| ~ ( model_ub @ SV66 @ SV85 @ SV92 )
| ( minsol_model_ub @ SV66 @ SV85 @ SV92 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[355]) ).
thf(374,plain,
! [SV66: $i] :
( ( ~ ! [SY133: $i,SY134: $i] :
( ~ ( minsol_model_ub @ SV66 @ SY133 @ SY134 )
| ! [SY135: $i] :
( ~ ( model_ub @ SV66 @ SY133 @ SY135 )
| ( lesseq @ SY134 @ SY135 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[356]) ).
thf(375,plain,
! [SV66: $i] :
( ( ~ ! [SY136: $i,SY137: $i] :
( ~ ( minsol_model_ub @ SV66 @ SY136 @ SY137 )
| ( model_ub @ SV66 @ SY136 @ SY137 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[356]) ).
thf(376,plain,
! [SV56: $i,SV72: $i,SV67: $i] :
( ( ( lesseq @ SV67 @ SV72 )
= $false )
| ( ( lesseq @ SV56 @ SV67 )
= $false )
| ( ( lesseq @ SV56 @ SV72 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[357]) ).
thf(377,plain,
! [SV86: $i,SV75: $i,SV61: $i] :
( ( ( ~ ( model_ub @ SV61 @ SV75 @ SV86 ) )
= $true )
| ( ( ub @ SV61 @ SV75 @ SV86 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[359]) ).
thf(378,plain,
! [SV87: $i,SV76: $i,SV61: $i] :
( ( ( ~ ( ub @ SV61 @ SV76 @ SV87 ) )
= $true )
| ( ( model_ub @ SV61 @ SV76 @ SV87 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[360]) ).
thf(379,plain,
! [SV77: $i,SV73: $i] :
( ( ( lesseq @ SV73 @ SV77 )
= $false )
| ( ( lesseq @ ( summation @ SV73 ) @ ( summation @ SV77 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[361]) ).
thf(380,plain,
! [SV78: $i,SV74: $i] :
( ( ( lesseq @ ( summation @ SV74 ) @ ( summation @ SV78 ) )
= $false )
| ( ( lesseq @ SV74 @ SV78 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[362]) ).
thf(381,plain,
! [SV79: $i,SV62: $i] :
( ( ( lesseq @ SV62 @ SV79 )
= $false )
| ( ( ! [SY143: $i] : ( lesseq @ ( sum @ SY143 @ SV62 ) @ ( sum @ SY143 @ SV79 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[363]) ).
thf(382,plain,
! [SV80: $i,SV62: $i,SV93: $i] :
( ( ( ~ ( lesseq @ ( sum @ SV93 @ SV62 ) @ ( sum @ SV93 @ SV80 ) ) )
= $true )
| ( ( lesseq @ SV62 @ SV80 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[364]) ).
thf(383,plain,
! [SV88: $i,SV81: $i,SV63: $i] :
( ( ( ~ ( ~ ( model_max @ SV63 @ SV81 @ ( sK5_Z @ SV88 @ SV81 @ SV63 ) )
| ~ ~ ( lesseq @ SV88 @ ( sK5_Z @ SV88 @ SV81 @ SV63 ) ) )
| ~ ( model_max @ SV63 @ SV81 @ SV88 ) )
= $true )
| ( ( minsol_model_max @ SV63 @ SV81 @ SV88 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[365]) ).
thf(384,plain,
! [SV63: $i] :
( ( ! [SY116: $i,SY117: $i] :
( ~ ( minsol_model_max @ SV63 @ SY116 @ SY117 )
| ! [SY118: $i] :
( ~ ( model_max @ SV63 @ SY116 @ SY118 )
| ( lesseq @ SY117 @ SY118 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[366]) ).
thf(385,plain,
! [SV63: $i] :
( ( ! [SY119: $i,SY120: $i] :
( ~ ( minsol_model_max @ SV63 @ SY119 @ SY120 )
| ( model_max @ SV63 @ SY119 @ SY120 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[367]) ).
thf(386,plain,
! [SV82: $i,SV64: $i,SV89: $i] :
( ( ( ( SV89
!= ( max @ SV64 @ SV82 ) ) )
= $true )
| ( ( model_max @ SV64 @ SV82 @ SV89 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[368]) ).
thf(387,plain,
! [SV90: $i,SV83: $i,SV64: $i] :
( ( ( ~ ( model_max @ SV64 @ SV83 @ SV90 ) )
= $true )
| ( ( SV90
= ( max @ SV64 @ SV83 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[369]) ).
thf(388,plain,
! [SV84: $i,SV91: $i,SV65: $i] :
( ( ( ~ ( lesseq @ SV65 @ SV91 )
| ~ ( lesseq @ SV84 @ SV91 ) )
= $true )
| ( ( ub @ SV65 @ SV84 @ SV91 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[370]) ).
thf(389,plain,
! [SV65: $i] :
( ( ! [SY127: $i,SY128: $i] :
( ~ ( ub @ SV65 @ SY127 @ SY128 )
| ( lesseq @ SV65 @ SY128 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[371]) ).
thf(390,plain,
! [SV65: $i] :
( ( ! [SY129: $i,SY130: $i] :
( ~ ( ub @ SV65 @ SY129 @ SY130 )
| ( lesseq @ SY129 @ SY130 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[372]) ).
thf(391,plain,
! [SV92: $i,SV85: $i,SV66: $i] :
( ( ( ~ ( ~ ( model_ub @ SV66 @ SV85 @ ( sK4_Z @ SV92 @ SV85 @ SV66 ) )
| ~ ~ ( lesseq @ SV92 @ ( sK4_Z @ SV92 @ SV85 @ SV66 ) ) )
| ~ ( model_ub @ SV66 @ SV85 @ SV92 ) )
= $true )
| ( ( minsol_model_ub @ SV66 @ SV85 @ SV92 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[373]) ).
thf(392,plain,
! [SV66: $i] :
( ( ! [SY133: $i,SY134: $i] :
( ~ ( minsol_model_ub @ SV66 @ SY133 @ SY134 )
| ! [SY135: $i] :
( ~ ( model_ub @ SV66 @ SY133 @ SY135 )
| ( lesseq @ SY134 @ SY135 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[374]) ).
thf(393,plain,
! [SV66: $i] :
( ( ! [SY136: $i,SY137: $i] :
( ~ ( minsol_model_ub @ SV66 @ SY136 @ SY137 )
| ( model_ub @ SV66 @ SY136 @ SY137 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[375]) ).
thf(394,plain,
! [SV86: $i,SV75: $i,SV61: $i] :
( ( ( model_ub @ SV61 @ SV75 @ SV86 )
= $false )
| ( ( ub @ SV61 @ SV75 @ SV86 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[377]) ).
thf(395,plain,
! [SV87: $i,SV76: $i,SV61: $i] :
( ( ( ub @ SV61 @ SV76 @ SV87 )
= $false )
| ( ( model_ub @ SV61 @ SV76 @ SV87 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[378]) ).
thf(396,plain,
! [SV79: $i,SV62: $i,SV94: $i] :
( ( ( lesseq @ ( sum @ SV94 @ SV62 ) @ ( sum @ SV94 @ SV79 ) )
= $true )
| ( ( lesseq @ SV62 @ SV79 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[381]) ).
thf(397,plain,
! [SV80: $i,SV62: $i,SV93: $i] :
( ( ( lesseq @ ( sum @ SV93 @ SV62 ) @ ( sum @ SV93 @ SV80 ) )
= $false )
| ( ( lesseq @ SV62 @ SV80 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[382]) ).
thf(398,plain,
! [SV88: $i,SV81: $i,SV63: $i] :
( ( ( ~ ( ~ ( model_max @ SV63 @ SV81 @ ( sK5_Z @ SV88 @ SV81 @ SV63 ) )
| ~ ~ ( lesseq @ SV88 @ ( sK5_Z @ SV88 @ SV81 @ SV63 ) ) ) )
= $true )
| ( ( ~ ( model_max @ SV63 @ SV81 @ SV88 ) )
= $true )
| ( ( minsol_model_max @ SV63 @ SV81 @ SV88 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[383]) ).
thf(399,plain,
! [SV95: $i,SV63: $i] :
( ( ! [SY150: $i] :
( ~ ( minsol_model_max @ SV63 @ SV95 @ SY150 )
| ! [SY151: $i] :
( ~ ( model_max @ SV63 @ SV95 @ SY151 )
| ( lesseq @ SY150 @ SY151 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[384]) ).
thf(400,plain,
! [SV96: $i,SV63: $i] :
( ( ! [SY152: $i] :
( ~ ( minsol_model_max @ SV63 @ SV96 @ SY152 )
| ( model_max @ SV63 @ SV96 @ SY152 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[385]) ).
thf(401,plain,
! [SV82: $i,SV64: $i,SV89: $i] :
( ( ( SV89
= ( max @ SV64 @ SV82 ) )
= $false )
| ( ( model_max @ SV64 @ SV82 @ SV89 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[386]) ).
thf(402,plain,
! [SV90: $i,SV83: $i,SV64: $i] :
( ( ( model_max @ SV64 @ SV83 @ SV90 )
= $false )
| ( ( SV90
= ( max @ SV64 @ SV83 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[387]) ).
thf(403,plain,
! [SV84: $i,SV91: $i,SV65: $i] :
( ( ( ~ ( lesseq @ SV65 @ SV91 ) )
= $true )
| ( ( ~ ( lesseq @ SV84 @ SV91 ) )
= $true )
| ( ( ub @ SV65 @ SV84 @ SV91 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[388]) ).
thf(404,plain,
! [SV97: $i,SV65: $i] :
( ( ! [SY153: $i] :
( ~ ( ub @ SV65 @ SV97 @ SY153 )
| ( lesseq @ SV65 @ SY153 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[389]) ).
thf(405,plain,
! [SV98: $i,SV65: $i] :
( ( ! [SY154: $i] :
( ~ ( ub @ SV65 @ SV98 @ SY154 )
| ( lesseq @ SV98 @ SY154 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[390]) ).
thf(406,plain,
! [SV92: $i,SV85: $i,SV66: $i] :
( ( ( ~ ( ~ ( model_ub @ SV66 @ SV85 @ ( sK4_Z @ SV92 @ SV85 @ SV66 ) )
| ~ ~ ( lesseq @ SV92 @ ( sK4_Z @ SV92 @ SV85 @ SV66 ) ) ) )
= $true )
| ( ( ~ ( model_ub @ SV66 @ SV85 @ SV92 ) )
= $true )
| ( ( minsol_model_ub @ SV66 @ SV85 @ SV92 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[391]) ).
thf(407,plain,
! [SV99: $i,SV66: $i] :
( ( ! [SY155: $i] :
( ~ ( minsol_model_ub @ SV66 @ SV99 @ SY155 )
| ! [SY156: $i] :
( ~ ( model_ub @ SV66 @ SV99 @ SY156 )
| ( lesseq @ SY155 @ SY156 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[392]) ).
thf(408,plain,
! [SV100: $i,SV66: $i] :
( ( ! [SY157: $i] :
( ~ ( minsol_model_ub @ SV66 @ SV100 @ SY157 )
| ( model_ub @ SV66 @ SV100 @ SY157 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[393]) ).
thf(409,plain,
! [SV88: $i,SV81: $i,SV63: $i] :
( ( ( ~ ( model_max @ SV63 @ SV81 @ ( sK5_Z @ SV88 @ SV81 @ SV63 ) )
| ~ ~ ( lesseq @ SV88 @ ( sK5_Z @ SV88 @ SV81 @ SV63 ) ) )
= $false )
| ( ( ~ ( model_max @ SV63 @ SV81 @ SV88 ) )
= $true )
| ( ( minsol_model_max @ SV63 @ SV81 @ SV88 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[398]) ).
thf(410,plain,
! [SV101: $i,SV95: $i,SV63: $i] :
( ( ~ ( minsol_model_max @ SV63 @ SV95 @ SV101 )
| ! [SY158: $i] :
( ~ ( model_max @ SV63 @ SV95 @ SY158 )
| ( lesseq @ SV101 @ SY158 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[399]) ).
thf(411,plain,
! [SV102: $i,SV96: $i,SV63: $i] :
( ( ~ ( minsol_model_max @ SV63 @ SV96 @ SV102 )
| ( model_max @ SV63 @ SV96 @ SV102 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[400]) ).
thf(412,plain,
! [SV84: $i,SV91: $i,SV65: $i] :
( ( ( lesseq @ SV65 @ SV91 )
= $false )
| ( ( ~ ( lesseq @ SV84 @ SV91 ) )
= $true )
| ( ( ub @ SV65 @ SV84 @ SV91 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[403]) ).
thf(413,plain,
! [SV103: $i,SV97: $i,SV65: $i] :
( ( ~ ( ub @ SV65 @ SV97 @ SV103 )
| ( lesseq @ SV65 @ SV103 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[404]) ).
thf(414,plain,
! [SV104: $i,SV98: $i,SV65: $i] :
( ( ~ ( ub @ SV65 @ SV98 @ SV104 )
| ( lesseq @ SV98 @ SV104 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[405]) ).
thf(415,plain,
! [SV92: $i,SV85: $i,SV66: $i] :
( ( ( ~ ( model_ub @ SV66 @ SV85 @ ( sK4_Z @ SV92 @ SV85 @ SV66 ) )
| ~ ~ ( lesseq @ SV92 @ ( sK4_Z @ SV92 @ SV85 @ SV66 ) ) )
= $false )
| ( ( ~ ( model_ub @ SV66 @ SV85 @ SV92 ) )
= $true )
| ( ( minsol_model_ub @ SV66 @ SV85 @ SV92 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[406]) ).
thf(416,plain,
! [SV105: $i,SV99: $i,SV66: $i] :
( ( ~ ( minsol_model_ub @ SV66 @ SV99 @ SV105 )
| ! [SY159: $i] :
( ~ ( model_ub @ SV66 @ SV99 @ SY159 )
| ( lesseq @ SV105 @ SY159 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[407]) ).
thf(417,plain,
! [SV106: $i,SV100: $i,SV66: $i] :
( ( ~ ( minsol_model_ub @ SV66 @ SV100 @ SV106 )
| ( model_ub @ SV66 @ SV100 @ SV106 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[408]) ).
thf(418,plain,
! [SV88: $i,SV81: $i,SV63: $i] :
( ( ( ~ ( model_max @ SV63 @ SV81 @ ( sK5_Z @ SV88 @ SV81 @ SV63 ) ) )
= $false )
| ( ( ~ ( model_max @ SV63 @ SV81 @ SV88 ) )
= $true )
| ( ( minsol_model_max @ SV63 @ SV81 @ SV88 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[409]) ).
thf(419,plain,
! [SV63: $i,SV81: $i,SV88: $i] :
( ( ( ~ ~ ( lesseq @ SV88 @ ( sK5_Z @ SV88 @ SV81 @ SV63 ) ) )
= $false )
| ( ( ~ ( model_max @ SV63 @ SV81 @ SV88 ) )
= $true )
| ( ( minsol_model_max @ SV63 @ SV81 @ SV88 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[409]) ).
thf(420,plain,
! [SV101: $i,SV95: $i,SV63: $i] :
( ( ( ~ ( minsol_model_max @ SV63 @ SV95 @ SV101 ) )
= $true )
| ( ( ! [SY158: $i] :
( ~ ( model_max @ SV63 @ SV95 @ SY158 )
| ( lesseq @ SV101 @ SY158 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[410]) ).
thf(421,plain,
! [SV102: $i,SV96: $i,SV63: $i] :
( ( ( ~ ( minsol_model_max @ SV63 @ SV96 @ SV102 ) )
= $true )
| ( ( model_max @ SV63 @ SV96 @ SV102 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[411]) ).
thf(422,plain,
! [SV65: $i,SV91: $i,SV84: $i] :
( ( ( lesseq @ SV84 @ SV91 )
= $false )
| ( ( lesseq @ SV65 @ SV91 )
= $false )
| ( ( ub @ SV65 @ SV84 @ SV91 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[412]) ).
thf(423,plain,
! [SV103: $i,SV97: $i,SV65: $i] :
( ( ( ~ ( ub @ SV65 @ SV97 @ SV103 ) )
= $true )
| ( ( lesseq @ SV65 @ SV103 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[413]) ).
thf(424,plain,
! [SV104: $i,SV98: $i,SV65: $i] :
( ( ( ~ ( ub @ SV65 @ SV98 @ SV104 ) )
= $true )
| ( ( lesseq @ SV98 @ SV104 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[414]) ).
thf(425,plain,
! [SV92: $i,SV85: $i,SV66: $i] :
( ( ( ~ ( model_ub @ SV66 @ SV85 @ ( sK4_Z @ SV92 @ SV85 @ SV66 ) ) )
= $false )
| ( ( ~ ( model_ub @ SV66 @ SV85 @ SV92 ) )
= $true )
| ( ( minsol_model_ub @ SV66 @ SV85 @ SV92 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[415]) ).
thf(426,plain,
! [SV66: $i,SV85: $i,SV92: $i] :
( ( ( ~ ~ ( lesseq @ SV92 @ ( sK4_Z @ SV92 @ SV85 @ SV66 ) ) )
= $false )
| ( ( ~ ( model_ub @ SV66 @ SV85 @ SV92 ) )
= $true )
| ( ( minsol_model_ub @ SV66 @ SV85 @ SV92 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[415]) ).
thf(427,plain,
! [SV105: $i,SV99: $i,SV66: $i] :
( ( ( ~ ( minsol_model_ub @ SV66 @ SV99 @ SV105 ) )
= $true )
| ( ( ! [SY159: $i] :
( ~ ( model_ub @ SV66 @ SV99 @ SY159 )
| ( lesseq @ SV105 @ SY159 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[416]) ).
thf(428,plain,
! [SV106: $i,SV100: $i,SV66: $i] :
( ( ( ~ ( minsol_model_ub @ SV66 @ SV100 @ SV106 ) )
= $true )
| ( ( model_ub @ SV66 @ SV100 @ SV106 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[417]) ).
thf(429,plain,
! [SV88: $i,SV81: $i,SV63: $i] :
( ( ( model_max @ SV63 @ SV81 @ ( sK5_Z @ SV88 @ SV81 @ SV63 ) )
= $true )
| ( ( ~ ( model_max @ SV63 @ SV81 @ SV88 ) )
= $true )
| ( ( minsol_model_max @ SV63 @ SV81 @ SV88 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[418]) ).
thf(430,plain,
! [SV63: $i,SV81: $i,SV88: $i] :
( ( ( ~ ( lesseq @ SV88 @ ( sK5_Z @ SV88 @ SV81 @ SV63 ) ) )
= $true )
| ( ( ~ ( model_max @ SV63 @ SV81 @ SV88 ) )
= $true )
| ( ( minsol_model_max @ SV63 @ SV81 @ SV88 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[419]) ).
thf(431,plain,
! [SV101: $i,SV95: $i,SV63: $i] :
( ( ( minsol_model_max @ SV63 @ SV95 @ SV101 )
= $false )
| ( ( ! [SY158: $i] :
( ~ ( model_max @ SV63 @ SV95 @ SY158 )
| ( lesseq @ SV101 @ SY158 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[420]) ).
thf(432,plain,
! [SV102: $i,SV96: $i,SV63: $i] :
( ( ( minsol_model_max @ SV63 @ SV96 @ SV102 )
= $false )
| ( ( model_max @ SV63 @ SV96 @ SV102 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[421]) ).
thf(433,plain,
! [SV103: $i,SV97: $i,SV65: $i] :
( ( ( ub @ SV65 @ SV97 @ SV103 )
= $false )
| ( ( lesseq @ SV65 @ SV103 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[423]) ).
thf(434,plain,
! [SV104: $i,SV98: $i,SV65: $i] :
( ( ( ub @ SV65 @ SV98 @ SV104 )
= $false )
| ( ( lesseq @ SV98 @ SV104 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[424]) ).
thf(435,plain,
! [SV92: $i,SV85: $i,SV66: $i] :
( ( ( model_ub @ SV66 @ SV85 @ ( sK4_Z @ SV92 @ SV85 @ SV66 ) )
= $true )
| ( ( ~ ( model_ub @ SV66 @ SV85 @ SV92 ) )
= $true )
| ( ( minsol_model_ub @ SV66 @ SV85 @ SV92 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[425]) ).
thf(436,plain,
! [SV66: $i,SV85: $i,SV92: $i] :
( ( ( ~ ( lesseq @ SV92 @ ( sK4_Z @ SV92 @ SV85 @ SV66 ) ) )
= $true )
| ( ( ~ ( model_ub @ SV66 @ SV85 @ SV92 ) )
= $true )
| ( ( minsol_model_ub @ SV66 @ SV85 @ SV92 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[426]) ).
thf(437,plain,
! [SV105: $i,SV99: $i,SV66: $i] :
( ( ( minsol_model_ub @ SV66 @ SV99 @ SV105 )
= $false )
| ( ( ! [SY159: $i] :
( ~ ( model_ub @ SV66 @ SV99 @ SY159 )
| ( lesseq @ SV105 @ SY159 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[427]) ).
thf(438,plain,
! [SV106: $i,SV100: $i,SV66: $i] :
( ( ( minsol_model_ub @ SV66 @ SV100 @ SV106 )
= $false )
| ( ( model_ub @ SV66 @ SV100 @ SV106 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[428]) ).
thf(439,plain,
! [SV88: $i,SV81: $i,SV63: $i] :
( ( ( model_max @ SV63 @ SV81 @ SV88 )
= $false )
| ( ( model_max @ SV63 @ SV81 @ ( sK5_Z @ SV88 @ SV81 @ SV63 ) )
= $true )
| ( ( minsol_model_max @ SV63 @ SV81 @ SV88 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[429]) ).
thf(440,plain,
! [SV63: $i,SV81: $i,SV88: $i] :
( ( ( lesseq @ SV88 @ ( sK5_Z @ SV88 @ SV81 @ SV63 ) )
= $false )
| ( ( ~ ( model_max @ SV63 @ SV81 @ SV88 ) )
= $true )
| ( ( minsol_model_max @ SV63 @ SV81 @ SV88 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[430]) ).
thf(441,plain,
! [SV101: $i,SV107: $i,SV95: $i,SV63: $i] :
( ( ( ~ ( model_max @ SV63 @ SV95 @ SV107 )
| ( lesseq @ SV101 @ SV107 ) )
= $true )
| ( ( minsol_model_max @ SV63 @ SV95 @ SV101 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[431]) ).
thf(442,plain,
! [SV92: $i,SV85: $i,SV66: $i] :
( ( ( model_ub @ SV66 @ SV85 @ SV92 )
= $false )
| ( ( model_ub @ SV66 @ SV85 @ ( sK4_Z @ SV92 @ SV85 @ SV66 ) )
= $true )
| ( ( minsol_model_ub @ SV66 @ SV85 @ SV92 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[435]) ).
thf(443,plain,
! [SV66: $i,SV85: $i,SV92: $i] :
( ( ( lesseq @ SV92 @ ( sK4_Z @ SV92 @ SV85 @ SV66 ) )
= $false )
| ( ( ~ ( model_ub @ SV66 @ SV85 @ SV92 ) )
= $true )
| ( ( minsol_model_ub @ SV66 @ SV85 @ SV92 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[436]) ).
thf(444,plain,
! [SV105: $i,SV108: $i,SV99: $i,SV66: $i] :
( ( ( ~ ( model_ub @ SV66 @ SV99 @ SV108 )
| ( lesseq @ SV105 @ SV108 ) )
= $true )
| ( ( minsol_model_ub @ SV66 @ SV99 @ SV105 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[437]) ).
thf(445,plain,
! [SV88: $i,SV81: $i,SV63: $i] :
( ( ( model_max @ SV63 @ SV81 @ SV88 )
= $false )
| ( ( lesseq @ SV88 @ ( sK5_Z @ SV88 @ SV81 @ SV63 ) )
= $false )
| ( ( minsol_model_max @ SV63 @ SV81 @ SV88 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[440]) ).
thf(446,plain,
! [SV101: $i,SV107: $i,SV95: $i,SV63: $i] :
( ( ( ~ ( model_max @ SV63 @ SV95 @ SV107 ) )
= $true )
| ( ( lesseq @ SV101 @ SV107 )
= $true )
| ( ( minsol_model_max @ SV63 @ SV95 @ SV101 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[441]) ).
thf(447,plain,
! [SV92: $i,SV85: $i,SV66: $i] :
( ( ( model_ub @ SV66 @ SV85 @ SV92 )
= $false )
| ( ( lesseq @ SV92 @ ( sK4_Z @ SV92 @ SV85 @ SV66 ) )
= $false )
| ( ( minsol_model_ub @ SV66 @ SV85 @ SV92 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[443]) ).
thf(448,plain,
! [SV105: $i,SV108: $i,SV99: $i,SV66: $i] :
( ( ( ~ ( model_ub @ SV66 @ SV99 @ SV108 ) )
= $true )
| ( ( lesseq @ SV105 @ SV108 )
= $true )
| ( ( minsol_model_ub @ SV66 @ SV99 @ SV105 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[444]) ).
thf(449,plain,
! [SV101: $i,SV107: $i,SV95: $i,SV63: $i] :
( ( ( model_max @ SV63 @ SV95 @ SV107 )
= $false )
| ( ( lesseq @ SV101 @ SV107 )
= $true )
| ( ( minsol_model_max @ SV63 @ SV95 @ SV101 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[446]) ).
thf(450,plain,
! [SV105: $i,SV108: $i,SV99: $i,SV66: $i] :
( ( ( model_ub @ SV66 @ SV99 @ SV108 )
= $false )
| ( ( lesseq @ SV105 @ SV108 )
= $true )
| ( ( minsol_model_ub @ SV66 @ SV99 @ SV105 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[448]) ).
thf(451,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[272,450,449,447,445,442,439,438,434,433,432,422,402,401,397,396,395,394,380,379,376,358,326,325,324,306,303]) ).
thf(452,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[451,249]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM858+1 : TPTP v8.1.0. Released v4.1.0.
% 0.07/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.34 % Computer : n012.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Wed Jul 6 14:21:45 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35
% 0.13/0.35 No.of.Axioms: 13
% 0.13/0.35
% 0.13/0.35 Length.of.Defs: 0
% 0.13/0.35
% 0.13/0.35 Contains.Choice.Funs: false
% 0.13/0.36 (rf:0,axioms:13,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:600,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:15,loop_count:0,foatp_calls:0,translation:fof_full).............................
% 13.55/13.74
% 13.55/13.74 ********************************
% 13.55/13.74 * All subproblems solved! *
% 13.55/13.74 ********************************
% 13.55/13.74 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:13,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:451,loop_count:0,foatp_calls:1,translation:fof_full)
% 13.55/13.83
% 13.55/13.83 %**** Beginning of derivation protocol ****
% 13.55/13.83 % SZS output start CNFRefutation
% See solution above
% 13.55/13.83
% 13.55/13.83 %**** End of derivation protocol ****
% 13.55/13.83 %**** no. of clauses in derivation: 452 ****
% 13.55/13.83 %**** clause counter: 451 ****
% 13.55/13.83
% 13.55/13.83 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:13,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:451,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------