TSTP Solution File: SWV488+3 by LEO-II---1.7.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SWV488+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n007.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 : Wed Jul 20 20:13:03 EDT 2022
% Result : Theorem 2.58s 2.79s
% Output : CNFRefutation 2.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 25
% Syntax : Number of formulae : 227 ( 122 unt; 12 typ; 0 def)
% Number of atoms : 2029 ( 716 equ; 0 cnn)
% Maximal formula atoms : 17 ( 9 avg)
% Number of connectives : 3773 ( 645 ~; 772 |; 50 &;2272 @)
% ( 6 <=>; 28 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 12 usr; 9 con; 0-2 aty)
% Number of variables : 613 ( 0 ^ 611 !; 2 ?; 613 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $i > $i > $i ).
thf(tp_int_leq,type,
int_leq: $i > $i > $o ).
thf(tp_int_less,type,
int_less: $i > $i > $o ).
thf(tp_int_one,type,
int_one: $i ).
thf(tp_int_zero,type,
int_zero: $i ).
thf(tp_n,type,
n: $i ).
thf(tp_plus,type,
plus: $i > $i > $i ).
thf(tp_real_one,type,
real_one: $i ).
thf(tp_real_zero,type,
real_zero: $i ).
thf(tp_sK1_I,type,
sK1_I: $i ).
thf(tp_sK2_SY29,type,
sK2_SY29: $i ).
thf(tp_sK3_K,type,
sK3_K: $i > $i > $i ).
thf(1,axiom,
real_zero != real_one,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',real_constants) ).
thf(2,axiom,
! [I: $i] :
( ( int_less @ int_zero @ I )
<=> ( int_leq @ int_one @ I ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',one_successor_of_zero) ).
thf(3,axiom,
! [I: $i,J: $i] :
( ( int_less @ I @ J )
<=> ? [K: $i] :
( ( ( plus @ I @ K )
= J )
& ( int_less @ int_zero @ K ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',plus_and_inverse) ).
thf(4,axiom,
! [I1: $i,J1: $i,I2: $i,J2: $i] :
( ( ( int_less @ I1 @ J1 )
& ( int_leq @ I2 @ J2 ) )
=> ( int_leq @ ( plus @ I1 @ I2 ) @ ( plus @ J1 @ J2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',plus_and_order1) ).
thf(5,axiom,
! [I: $i] :
( ( plus @ I @ int_zero )
= I ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',plus_zero) ).
thf(6,axiom,
! [I: $i,J: $i] :
( ( plus @ I @ J )
= ( plus @ J @ I ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',plus_commutative) ).
thf(7,axiom,
int_less @ int_zero @ int_one,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',int_zero_one) ).
thf(8,axiom,
! [I: $i,J: $i] :
( ( int_less @ I @ J )
| ( int_leq @ J @ I ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',int_less_total) ).
thf(9,axiom,
! [I: $i,J: $i] :
( ( int_less @ I @ J )
=> ( I != J ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',int_less_irreflexive) ).
thf(10,axiom,
! [I: $i,J: $i,K: $i] :
( ( ( int_less @ I @ J )
& ( int_less @ J @ K ) )
=> ( int_less @ I @ K ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',int_less_transitive) ).
thf(11,axiom,
! [I: $i,J: $i] :
( ( int_leq @ I @ J )
<=> ( ( int_less @ I @ J )
| ( I = J ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',int_leq) ).
thf(12,axiom,
! [I: $i,J: $i] :
( ( ( int_leq @ int_one @ I )
& ( int_leq @ I @ n )
& ( int_leq @ int_one @ J )
& ( int_leq @ J @ n ) )
=> ( ! [C: $i] :
( ( ( int_less @ int_zero @ C )
& ( I
= ( plus @ J @ C ) ) )
=> ! [K: $i] :
( ( ( int_leq @ int_one @ K )
& ( int_leq @ K @ J ) )
=> ( ( a @ ( plus @ K @ C ) @ K )
= real_zero ) ) )
& ! [K: $i] :
( ( ( int_leq @ int_one @ K )
& ( int_leq @ K @ J ) )
=> ( ( a @ K @ K )
= real_one ) )
& ! [C: $i] :
( ( ( int_less @ int_zero @ C )
& ( J
= ( plus @ I @ C ) ) )
=> ! [K: $i] :
( ( ( int_leq @ int_one @ K )
& ( int_leq @ K @ I ) )
=> ( ( a @ K @ ( plus @ K @ C ) )
= real_zero ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qii) ).
thf(13,conjecture,
! [I: $i,J: $i] :
( ( ( int_leq @ int_one @ J )
& ( int_leq @ J @ I )
& ( int_leq @ I @ n ) )
=> ( ( I = J )
=> ( ( a @ I @ J )
!= real_zero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',uti) ).
thf(14,negated_conjecture,
( ( ! [I: $i,J: $i] :
( ( ( int_leq @ int_one @ J )
& ( int_leq @ J @ I )
& ( int_leq @ I @ n ) )
=> ( ( I = J )
=> ( ( a @ I @ J )
!= real_zero ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[13]) ).
thf(15,plain,
( ( ! [I: $i,J: $i] :
( ( ( int_leq @ int_one @ J )
& ( int_leq @ J @ I )
& ( int_leq @ I @ n ) )
=> ( ( I = J )
=> ( ( a @ I @ J )
!= real_zero ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[14]) ).
thf(16,plain,
( ( ( real_zero != real_one ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(17,plain,
( ( ! [I: $i] :
( ( int_less @ int_zero @ I )
<=> ( int_leq @ int_one @ I ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(18,plain,
( ( ! [I: $i,J: $i] :
( ( int_less @ I @ J )
<=> ? [K: $i] :
( ( ( plus @ I @ K )
= J )
& ( int_less @ int_zero @ K ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(19,plain,
( ( ! [I1: $i,J1: $i,I2: $i,J2: $i] :
( ( ( int_less @ I1 @ J1 )
& ( int_leq @ I2 @ J2 ) )
=> ( int_leq @ ( plus @ I1 @ I2 ) @ ( plus @ J1 @ J2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(20,plain,
( ( ! [I: $i] :
( ( plus @ I @ int_zero )
= I ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(21,plain,
( ( ! [I: $i,J: $i] :
( ( plus @ I @ J )
= ( plus @ J @ I ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(22,plain,
( ( int_less @ int_zero @ int_one )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(23,plain,
( ( ! [I: $i,J: $i] :
( ( int_less @ I @ J )
| ( int_leq @ J @ I ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(24,plain,
( ( ! [I: $i,J: $i] :
( ( int_less @ I @ J )
=> ( I != J ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(25,plain,
( ( ! [I: $i,J: $i,K: $i] :
( ( ( int_less @ I @ J )
& ( int_less @ J @ K ) )
=> ( int_less @ I @ K ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(26,plain,
( ( ! [I: $i,J: $i] :
( ( int_leq @ I @ J )
<=> ( ( int_less @ I @ J )
| ( I = J ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(27,plain,
( ( ! [I: $i,J: $i] :
( ( ( int_leq @ int_one @ I )
& ( int_leq @ I @ n )
& ( int_leq @ int_one @ J )
& ( int_leq @ J @ n ) )
=> ( ! [C: $i] :
( ( ( int_less @ int_zero @ C )
& ( I
= ( plus @ J @ C ) ) )
=> ! [K: $i] :
( ( ( int_leq @ int_one @ K )
& ( int_leq @ K @ J ) )
=> ( ( a @ ( plus @ K @ C ) @ K )
= real_zero ) ) )
& ! [K: $i] :
( ( ( int_leq @ int_one @ K )
& ( int_leq @ K @ J ) )
=> ( ( a @ K @ K )
= real_one ) )
& ! [C: $i] :
( ( ( int_less @ int_zero @ C )
& ( J
= ( plus @ I @ C ) ) )
=> ! [K: $i] :
( ( ( int_leq @ int_one @ K )
& ( int_leq @ K @ I ) )
=> ( ( a @ K @ ( plus @ K @ C ) )
= real_zero ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(28,plain,
( ( ! [SY29: $i] :
( ( ( int_leq @ int_one @ SY29 )
& ( int_leq @ SY29 @ sK1_I )
& ( int_leq @ sK1_I @ n ) )
=> ( ( sK1_I = SY29 )
=> ( ( a @ sK1_I @ SY29 )
!= real_zero ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[15]) ).
thf(29,plain,
( ( ( ( int_leq @ int_one @ sK2_SY29 )
& ( int_leq @ sK2_SY29 @ sK1_I )
& ( int_leq @ sK1_I @ n ) )
=> ( ( sK1_I = sK2_SY29 )
=> ( ( a @ sK1_I @ sK2_SY29 )
!= real_zero ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[28]) ).
thf(30,plain,
( ( int_leq @ int_one @ sK2_SY29 )
= $true ),
inference(standard_cnf,[status(thm)],[29]) ).
thf(31,plain,
( ( int_leq @ sK2_SY29 @ sK1_I )
= $true ),
inference(standard_cnf,[status(thm)],[29]) ).
thf(32,plain,
( ( int_leq @ sK1_I @ n )
= $true ),
inference(standard_cnf,[status(thm)],[29]) ).
thf(33,plain,
( ( sK1_I = sK2_SY29 )
= $true ),
inference(standard_cnf,[status(thm)],[29]) ).
thf(34,plain,
( ( ( ( a @ sK1_I @ sK2_SY29 )
!= real_zero ) )
= $false ),
inference(standard_cnf,[status(thm)],[29]) ).
thf(35,plain,
( ( ~ ( ( ( a @ sK1_I @ sK2_SY29 )
!= real_zero ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[34]) ).
thf(36,plain,
( ( ( a @ sK1_I @ sK2_SY29 )
= real_zero )
= $true ),
inference(extcnf_combined,[status(esa)],[35]) ).
thf(37,plain,
( ( ( real_zero != real_one ) )
= $true ),
inference(extcnf_combined,[status(esa)],[16]) ).
thf(38,plain,
( ( ! [I: $i] :
( ~ ( int_leq @ int_one @ I )
| ( int_less @ int_zero @ I ) )
& ! [I: $i] :
( ~ ( int_less @ int_zero @ I )
| ( int_leq @ int_one @ I ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[17]) ).
thf(39,plain,
( ( ! [I: $i,J: $i] :
( ! [K: $i] :
( ( ( plus @ I @ K )
!= J )
| ~ ( int_less @ int_zero @ K ) )
| ( int_less @ I @ J ) )
& ! [I: $i,J: $i] :
( ~ ( int_less @ I @ J )
| ( ( ( plus @ I @ ( sK3_K @ J @ I ) )
= J )
& ( int_less @ int_zero @ ( sK3_K @ J @ I ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[18]) ).
thf(40,plain,
( ( ! [I1: $i,J1: $i,I2: $i,J2: $i] :
( ~ ( int_leq @ I2 @ J2 )
| ~ ( int_less @ I1 @ J1 )
| ( int_leq @ ( plus @ I1 @ I2 ) @ ( plus @ J1 @ J2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[19]) ).
thf(41,plain,
( ( ! [I: $i,J: $i] :
( ( int_leq @ J @ I )
| ( int_less @ I @ J ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[23]) ).
thf(42,plain,
( ( ! [I: $i,J: $i] :
( ~ ( int_less @ I @ J )
| ( I != J ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[24]) ).
thf(43,plain,
( ( ! [I: $i,J: $i,K: $i] :
( ~ ( int_less @ I @ J )
| ~ ( int_less @ J @ K )
| ( int_less @ I @ K ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[25]) ).
thf(44,plain,
( ( ! [I: $i,J: $i] :
( ~ ( int_leq @ I @ J )
| ( I = J )
| ( int_less @ I @ J ) )
& ! [I: $i,J: $i] :
( ( I != J )
| ( int_leq @ I @ J ) )
& ! [I: $i,J: $i] :
( ~ ( int_less @ I @ J )
| ( int_leq @ I @ J ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[26]) ).
thf(45,plain,
( ( ! [I: $i,J: $i] :
( ~ ( int_leq @ int_one @ I )
| ~ ( int_leq @ I @ n )
| ~ ( int_leq @ int_one @ J )
| ~ ( int_leq @ J @ n )
| ! [C: $i] :
( ( J
!= ( plus @ I @ C ) )
| ~ ( int_less @ int_zero @ C )
| ! [K: $i] :
( ~ ( int_leq @ int_one @ K )
| ~ ( int_leq @ K @ I )
| ( ( a @ K @ ( plus @ K @ C ) )
= real_zero ) ) ) )
& ! [I: $i,J: $i] :
( ~ ( int_leq @ int_one @ I )
| ~ ( int_leq @ I @ n )
| ~ ( int_leq @ int_one @ J )
| ~ ( int_leq @ J @ n )
| ! [C: $i] :
( ( I
!= ( plus @ J @ C ) )
| ~ ( int_less @ int_zero @ C )
| ! [K: $i] :
( ~ ( int_leq @ int_one @ K )
| ~ ( int_leq @ K @ J )
| ( ( a @ ( plus @ K @ C ) @ K )
= real_zero ) ) ) )
& ! [I: $i,J: $i] :
( ~ ( int_leq @ int_one @ I )
| ~ ( int_leq @ I @ n )
| ~ ( int_leq @ int_one @ J )
| ~ ( int_leq @ J @ n )
| ! [K: $i] :
( ~ ( int_leq @ int_one @ K )
| ~ ( int_leq @ K @ J )
| ( ( a @ K @ K )
= real_one ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[27]) ).
thf(46,plain,
( ( ! [I: $i,J: $i] :
( ~ ( int_leq @ int_one @ I )
| ~ ( int_leq @ I @ n )
| ~ ( int_leq @ int_one @ J )
| ~ ( int_leq @ J @ n )
| ! [C: $i] :
( ( J
!= ( plus @ I @ C ) )
| ~ ( int_less @ int_zero @ C )
| ! [K: $i] :
( ~ ( int_leq @ int_one @ K )
| ~ ( int_leq @ K @ I )
| ( ( a @ K @ ( plus @ K @ C ) )
= real_zero ) ) ) )
& ! [I: $i,J: $i] :
( ~ ( int_leq @ int_one @ I )
| ~ ( int_leq @ I @ n )
| ~ ( int_leq @ int_one @ J )
| ~ ( int_leq @ J @ n )
| ! [C: $i] :
( ( I
!= ( plus @ J @ C ) )
| ~ ( int_less @ int_zero @ C )
| ! [K: $i] :
( ~ ( int_leq @ int_one @ K )
| ~ ( int_leq @ K @ J )
| ( ( a @ ( plus @ K @ C ) @ K )
= real_zero ) ) ) )
& ! [I: $i,J: $i] :
( ~ ( int_leq @ int_one @ I )
| ~ ( int_leq @ I @ n )
| ~ ( int_leq @ int_one @ J )
| ~ ( int_leq @ J @ n )
| ! [K: $i] :
( ~ ( int_leq @ int_one @ K )
| ~ ( int_leq @ K @ J )
| ( ( a @ K @ K )
= real_one ) ) ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(47,plain,
( ( ! [I: $i,J: $i] :
( ~ ( int_leq @ I @ J )
| ( I = J )
| ( int_less @ I @ J ) )
& ! [I: $i,J: $i] :
( ( I != J )
| ( int_leq @ I @ J ) )
& ! [I: $i,J: $i] :
( ~ ( int_less @ I @ J )
| ( int_leq @ I @ J ) ) )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(48,plain,
( ( ! [I: $i,J: $i,K: $i] :
( ~ ( int_less @ I @ J )
| ~ ( int_less @ J @ K )
| ( int_less @ I @ K ) ) )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(49,plain,
( ( ! [I: $i,J: $i] :
( ~ ( int_less @ I @ J )
| ( I != J ) ) )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(50,plain,
( ( ! [I: $i,J: $i] :
( ( int_leq @ J @ I )
| ( int_less @ I @ J ) ) )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(51,plain,
( ( int_less @ int_zero @ int_one )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(52,plain,
( ( ! [I: $i,J: $i] :
( ( plus @ I @ J )
= ( plus @ J @ I ) ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(53,plain,
( ( ! [I: $i] :
( ( plus @ I @ int_zero )
= I ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(54,plain,
( ( ! [I1: $i,J1: $i,I2: $i,J2: $i] :
( ~ ( int_leq @ I2 @ J2 )
| ~ ( int_less @ I1 @ J1 )
| ( int_leq @ ( plus @ I1 @ I2 ) @ ( plus @ J1 @ J2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(55,plain,
( ( ! [I: $i,J: $i] :
( ! [K: $i] :
( ( ( plus @ I @ K )
!= J )
| ~ ( int_less @ int_zero @ K ) )
| ( int_less @ I @ J ) )
& ! [I: $i,J: $i] :
( ~ ( int_less @ I @ J )
| ( ( ( plus @ I @ ( sK3_K @ J @ I ) )
= J )
& ( int_less @ int_zero @ ( sK3_K @ J @ I ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(56,plain,
( ( ! [I: $i] :
( ~ ( int_leq @ int_one @ I )
| ( int_less @ int_zero @ I ) )
& ! [I: $i] :
( ~ ( int_less @ int_zero @ I )
| ( int_leq @ int_one @ I ) ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(57,plain,
( ( ( real_zero != real_one ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(58,plain,
( ( sK1_I = sK2_SY29 )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(59,plain,
( ( int_leq @ sK1_I @ n )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(60,plain,
( ( int_leq @ sK2_SY29 @ sK1_I )
= $true ),
inference(copy,[status(thm)],[31]) ).
thf(61,plain,
( ( int_leq @ int_one @ sK2_SY29 )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(62,plain,
( ( ( a @ sK1_I @ sK2_SY29 )
= real_zero )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(63,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( int_leq @ int_one @ SX0 )
| ~ ( int_leq @ SX0 @ n )
| ~ ( int_leq @ int_one @ SX1 )
| ~ ( int_leq @ SX1 @ n )
| ! [SX2: $i] :
( ( SX1
!= ( plus @ SX0 @ SX2 ) )
| ~ ( int_less @ int_zero @ SX2 )
| ! [SX3: $i] :
( ~ ( int_leq @ int_one @ SX3 )
| ~ ( int_leq @ SX3 @ SX0 )
| ( ( a @ SX3 @ ( plus @ SX3 @ SX2 ) )
= real_zero ) ) ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( int_leq @ int_one @ SX0 )
| ~ ( int_leq @ SX0 @ n )
| ~ ( int_leq @ int_one @ SX1 )
| ~ ( int_leq @ SX1 @ n )
| ! [SX2: $i] :
( ( SX0
!= ( plus @ SX1 @ SX2 ) )
| ~ ( int_less @ int_zero @ SX2 )
| ! [SX3: $i] :
( ~ ( int_leq @ int_one @ SX3 )
| ~ ( int_leq @ SX3 @ SX1 )
| ( ( a @ ( plus @ SX3 @ SX2 ) @ SX3 )
= real_zero ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( int_leq @ int_one @ SX0 )
| ~ ( int_leq @ SX0 @ n )
| ~ ( int_leq @ int_one @ SX1 )
| ~ ( int_leq @ SX1 @ n )
| ! [SX2: $i] :
( ~ ( int_leq @ int_one @ SX2 )
| ~ ( int_leq @ SX2 @ SX1 )
| ( ( a @ SX2 @ SX2 )
= real_one ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[46]) ).
thf(64,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( int_leq @ SX0 @ SX1 )
| ( SX0 = SX1 )
| ( int_less @ SX0 @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( int_leq @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( int_less @ SX0 @ SX1 )
| ( int_leq @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[47]) ).
thf(65,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( int_leq @ int_one @ SX0 )
| ( int_less @ int_zero @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( int_less @ int_zero @ SX0 )
| ( int_leq @ int_one @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[56]) ).
thf(66,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ( ( plus @ SX0 @ SX2 )
!= SX1 )
| ~ ( int_less @ int_zero @ SX2 ) )
| ( int_less @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( int_less @ SX0 @ SX1 )
| ~ ( ( ( plus @ SX0 @ ( sK3_K @ SX1 @ SX0 ) )
!= SX1 )
| ~ ( int_less @ int_zero @ ( sK3_K @ SX1 @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[55]) ).
thf(67,plain,
! [SV1: $i] :
( ( ! [SY30: $i,SY31: $i] :
( ~ ( int_less @ SV1 @ SY30 )
| ~ ( int_less @ SY30 @ SY31 )
| ( int_less @ SV1 @ SY31 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[48]) ).
thf(68,plain,
! [SV2: $i] :
( ( ! [SY32: $i] :
( ~ ( int_less @ SV2 @ SY32 )
| ( SV2 != SY32 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[49]) ).
thf(69,plain,
! [SV3: $i] :
( ( ! [SY33: $i] :
( ( int_leq @ SY33 @ SV3 )
| ( int_less @ SV3 @ SY33 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[50]) ).
thf(70,plain,
! [SV4: $i] :
( ( ! [SY34: $i] :
( ( plus @ SV4 @ SY34 )
= ( plus @ SY34 @ SV4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[52]) ).
thf(71,plain,
! [SV5: $i] :
( ( ( plus @ SV5 @ int_zero )
= SV5 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[53]) ).
thf(72,plain,
! [SV6: $i] :
( ( ! [SY35: $i,SY36: $i,SY37: $i] :
( ~ ( int_leq @ SY36 @ SY37 )
| ~ ( int_less @ SV6 @ SY35 )
| ( int_leq @ ( plus @ SV6 @ SY36 ) @ ( plus @ SY35 @ SY37 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[54]) ).
thf(73,plain,
( ( real_zero = real_one )
= $false ),
inference(extcnf_not_pos,[status(thm)],[57]) ).
thf(74,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( int_leq @ int_one @ SX0 )
| ~ ( int_leq @ SX0 @ n )
| ~ ( int_leq @ int_one @ SX1 )
| ~ ( int_leq @ SX1 @ n )
| ! [SX2: $i] :
( ( SX1
!= ( plus @ SX0 @ SX2 ) )
| ~ ( int_less @ int_zero @ SX2 )
| ! [SX3: $i] :
( ~ ( int_leq @ int_one @ SX3 )
| ~ ( int_leq @ SX3 @ SX0 )
| ( ( a @ SX3 @ ( plus @ SX3 @ SX2 ) )
= real_zero ) ) ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( int_leq @ int_one @ SX0 )
| ~ ( int_leq @ SX0 @ n )
| ~ ( int_leq @ int_one @ SX1 )
| ~ ( int_leq @ SX1 @ n )
| ! [SX2: $i] :
( ( SX0
!= ( plus @ SX1 @ SX2 ) )
| ~ ( int_less @ int_zero @ SX2 )
| ! [SX3: $i] :
( ~ ( int_leq @ int_one @ SX3 )
| ~ ( int_leq @ SX3 @ SX1 )
| ( ( a @ ( plus @ SX3 @ SX2 ) @ SX3 )
= real_zero ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( int_leq @ int_one @ SX0 )
| ~ ( int_leq @ SX0 @ n )
| ~ ( int_leq @ int_one @ SX1 )
| ~ ( int_leq @ SX1 @ n )
| ! [SX2: $i] :
( ~ ( int_leq @ int_one @ SX2 )
| ~ ( int_leq @ SX2 @ SX1 )
| ( ( a @ SX2 @ SX2 )
= real_one ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[63]) ).
thf(75,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( int_leq @ SX0 @ SX1 )
| ( SX0 = SX1 )
| ( int_less @ SX0 @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( int_leq @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( int_less @ SX0 @ SX1 )
| ( int_leq @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[64]) ).
thf(76,plain,
( ( ~ ! [SX0: $i] :
( ~ ( int_leq @ int_one @ SX0 )
| ( int_less @ int_zero @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( int_less @ int_zero @ SX0 )
| ( int_leq @ int_one @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[65]) ).
thf(77,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ( ( plus @ SX0 @ SX2 )
!= SX1 )
| ~ ( int_less @ int_zero @ SX2 ) )
| ( int_less @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( int_less @ SX0 @ SX1 )
| ~ ( ( ( plus @ SX0 @ ( sK3_K @ SX1 @ SX0 ) )
!= SX1 )
| ~ ( int_less @ int_zero @ ( sK3_K @ SX1 @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[66]) ).
thf(78,plain,
! [SV7: $i,SV1: $i] :
( ( ! [SY38: $i] :
( ~ ( int_less @ SV1 @ SV7 )
| ~ ( int_less @ SV7 @ SY38 )
| ( int_less @ SV1 @ SY38 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[67]) ).
thf(79,plain,
! [SV8: $i,SV2: $i] :
( ( ~ ( int_less @ SV2 @ SV8 )
| ( SV2 != SV8 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[68]) ).
thf(80,plain,
! [SV3: $i,SV9: $i] :
( ( ( int_leq @ SV9 @ SV3 )
| ( int_less @ SV3 @ SV9 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[69]) ).
thf(81,plain,
! [SV10: $i,SV4: $i] :
( ( ( plus @ SV4 @ SV10 )
= ( plus @ SV10 @ SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[70]) ).
thf(82,plain,
! [SV11: $i,SV6: $i] :
( ( ! [SY39: $i,SY40: $i] :
( ~ ( int_leq @ SY39 @ SY40 )
| ~ ( int_less @ SV6 @ SV11 )
| ( int_leq @ ( plus @ SV6 @ SY39 ) @ ( plus @ SV11 @ SY40 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[72]) ).
thf(83,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( int_leq @ int_one @ SX0 )
| ~ ( int_leq @ SX0 @ n )
| ~ ( int_leq @ int_one @ SX1 )
| ~ ( int_leq @ SX1 @ n )
| ! [SX2: $i] :
( ( SX1
!= ( plus @ SX0 @ SX2 ) )
| ~ ( int_less @ int_zero @ SX2 )
| ! [SX3: $i] :
( ~ ( int_leq @ int_one @ SX3 )
| ~ ( int_leq @ SX3 @ SX0 )
| ( ( a @ SX3 @ ( plus @ SX3 @ SX2 ) )
= real_zero ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[74]) ).
thf(84,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( int_leq @ int_one @ SX0 )
| ~ ( int_leq @ SX0 @ n )
| ~ ( int_leq @ int_one @ SX1 )
| ~ ( int_leq @ SX1 @ n )
| ! [SX2: $i] :
( ( SX0
!= ( plus @ SX1 @ SX2 ) )
| ~ ( int_less @ int_zero @ SX2 )
| ! [SX3: $i] :
( ~ ( int_leq @ int_one @ SX3 )
| ~ ( int_leq @ SX3 @ SX1 )
| ( ( a @ ( plus @ SX3 @ SX2 ) @ SX3 )
= real_zero ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( int_leq @ int_one @ SX0 )
| ~ ( int_leq @ SX0 @ n )
| ~ ( int_leq @ int_one @ SX1 )
| ~ ( int_leq @ SX1 @ n )
| ! [SX2: $i] :
( ~ ( int_leq @ int_one @ SX2 )
| ~ ( int_leq @ SX2 @ SX1 )
| ( ( a @ SX2 @ SX2 )
= real_one ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[74]) ).
thf(85,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( int_leq @ SX0 @ SX1 )
| ( SX0 = SX1 )
| ( int_less @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[75]) ).
thf(86,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( int_leq @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( int_less @ SX0 @ SX1 )
| ( int_leq @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[75]) ).
thf(87,plain,
( ( ~ ! [SX0: $i] :
( ~ ( int_leq @ int_one @ SX0 )
| ( int_less @ int_zero @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[76]) ).
thf(88,plain,
( ( ~ ! [SX0: $i] :
( ~ ( int_less @ int_zero @ SX0 )
| ( int_leq @ int_one @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[76]) ).
thf(89,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ( ( plus @ SX0 @ SX2 )
!= SX1 )
| ~ ( int_less @ int_zero @ SX2 ) )
| ( int_less @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[77]) ).
thf(90,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( int_less @ SX0 @ SX1 )
| ~ ( ( ( plus @ SX0 @ ( sK3_K @ SX1 @ SX0 ) )
!= SX1 )
| ~ ( int_less @ int_zero @ ( sK3_K @ SX1 @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[77]) ).
thf(91,plain,
! [SV12: $i,SV7: $i,SV1: $i] :
( ( ~ ( int_less @ SV1 @ SV7 )
| ~ ( int_less @ SV7 @ SV12 )
| ( int_less @ SV1 @ SV12 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[78]) ).
thf(92,plain,
! [SV8: $i,SV2: $i] :
( ( ( ~ ( int_less @ SV2 @ SV8 ) )
= $true )
| ( ( ( SV2 != SV8 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[79]) ).
thf(93,plain,
! [SV3: $i,SV9: $i] :
( ( ( int_leq @ SV9 @ SV3 )
= $true )
| ( ( int_less @ SV3 @ SV9 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[80]) ).
thf(94,plain,
! [SV11: $i,SV6: $i,SV13: $i] :
( ( ! [SY41: $i] :
( ~ ( int_leq @ SV13 @ SY41 )
| ~ ( int_less @ SV6 @ SV11 )
| ( int_leq @ ( plus @ SV6 @ SV13 ) @ ( plus @ SV11 @ SY41 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[82]) ).
thf(95,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( int_leq @ int_one @ SX0 )
| ~ ( int_leq @ SX0 @ n )
| ~ ( int_leq @ int_one @ SX1 )
| ~ ( int_leq @ SX1 @ n )
| ! [SX2: $i] :
( ( SX1
!= ( plus @ SX0 @ SX2 ) )
| ~ ( int_less @ int_zero @ SX2 )
| ! [SX3: $i] :
( ~ ( int_leq @ int_one @ SX3 )
| ~ ( int_leq @ SX3 @ SX0 )
| ( ( a @ SX3 @ ( plus @ SX3 @ SX2 ) )
= real_zero ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[83]) ).
thf(96,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( int_leq @ int_one @ SX0 )
| ~ ( int_leq @ SX0 @ n )
| ~ ( int_leq @ int_one @ SX1 )
| ~ ( int_leq @ SX1 @ n )
| ! [SX2: $i] :
( ( SX0
!= ( plus @ SX1 @ SX2 ) )
| ~ ( int_less @ int_zero @ SX2 )
| ! [SX3: $i] :
( ~ ( int_leq @ int_one @ SX3 )
| ~ ( int_leq @ SX3 @ SX1 )
| ( ( a @ ( plus @ SX3 @ SX2 ) @ SX3 )
= real_zero ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( int_leq @ int_one @ SX0 )
| ~ ( int_leq @ SX0 @ n )
| ~ ( int_leq @ int_one @ SX1 )
| ~ ( int_leq @ SX1 @ n )
| ! [SX2: $i] :
( ~ ( int_leq @ int_one @ SX2 )
| ~ ( int_leq @ SX2 @ SX1 )
| ( ( a @ SX2 @ SX2 )
= real_one ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[84]) ).
thf(97,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( int_leq @ SX0 @ SX1 )
| ( SX0 = SX1 )
| ( int_less @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[85]) ).
thf(98,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( int_leq @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( int_less @ SX0 @ SX1 )
| ( int_leq @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[86]) ).
thf(99,plain,
( ( ! [SX0: $i] :
( ~ ( int_leq @ int_one @ SX0 )
| ( int_less @ int_zero @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[87]) ).
thf(100,plain,
( ( ! [SX0: $i] :
( ~ ( int_less @ int_zero @ SX0 )
| ( int_leq @ int_one @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[88]) ).
thf(101,plain,
( ( ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ( ( plus @ SX0 @ SX2 )
!= SX1 )
| ~ ( int_less @ int_zero @ SX2 ) )
| ( int_less @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[89]) ).
thf(102,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( int_less @ SX0 @ SX1 )
| ~ ( ( ( plus @ SX0 @ ( sK3_K @ SX1 @ SX0 ) )
!= SX1 )
| ~ ( int_less @ int_zero @ ( sK3_K @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[90]) ).
thf(103,plain,
! [SV12: $i,SV7: $i,SV1: $i] :
( ( ( ~ ( int_less @ SV1 @ SV7 )
| ~ ( int_less @ SV7 @ SV12 ) )
= $true )
| ( ( int_less @ SV1 @ SV12 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[91]) ).
thf(104,plain,
! [SV8: $i,SV2: $i] :
( ( ( int_less @ SV2 @ SV8 )
= $false )
| ( ( ( SV2 != SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[92]) ).
thf(105,plain,
! [SV11: $i,SV6: $i,SV14: $i,SV13: $i] :
( ( ~ ( int_leq @ SV13 @ SV14 )
| ~ ( int_less @ SV6 @ SV11 )
| ( int_leq @ ( plus @ SV6 @ SV13 ) @ ( plus @ SV11 @ SV14 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[94]) ).
thf(106,plain,
! [SV15: $i] :
( ( ! [SY42: $i] :
( ~ ( int_leq @ int_one @ SV15 )
| ~ ( int_leq @ SV15 @ n )
| ~ ( int_leq @ int_one @ SY42 )
| ~ ( int_leq @ SY42 @ n )
| ! [SY43: $i] :
( ( SY42
!= ( plus @ SV15 @ SY43 ) )
| ~ ( int_less @ int_zero @ SY43 )
| ! [SY44: $i] :
( ~ ( int_leq @ int_one @ SY44 )
| ~ ( int_leq @ SY44 @ SV15 )
| ( ( a @ SY44 @ ( plus @ SY44 @ SY43 ) )
= real_zero ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[95]) ).
thf(107,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( int_leq @ int_one @ SX0 )
| ~ ( int_leq @ SX0 @ n )
| ~ ( int_leq @ int_one @ SX1 )
| ~ ( int_leq @ SX1 @ n )
| ! [SX2: $i] :
( ( SX0
!= ( plus @ SX1 @ SX2 ) )
| ~ ( int_less @ int_zero @ SX2 )
| ! [SX3: $i] :
( ~ ( int_leq @ int_one @ SX3 )
| ~ ( int_leq @ SX3 @ SX1 )
| ( ( a @ ( plus @ SX3 @ SX2 ) @ SX3 )
= real_zero ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( int_leq @ int_one @ SX0 )
| ~ ( int_leq @ SX0 @ n )
| ~ ( int_leq @ int_one @ SX1 )
| ~ ( int_leq @ SX1 @ n )
| ! [SX2: $i] :
( ~ ( int_leq @ int_one @ SX2 )
| ~ ( int_leq @ SX2 @ SX1 )
| ( ( a @ SX2 @ SX2 )
= real_one ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[96]) ).
thf(108,plain,
! [SV16: $i] :
( ( ! [SY45: $i] :
( ~ ( int_leq @ SV16 @ SY45 )
| ( SV16 = SY45 )
| ( int_less @ SV16 @ SY45 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[97]) ).
thf(109,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( int_leq @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( int_less @ SX0 @ SX1 )
| ( int_leq @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[98]) ).
thf(110,plain,
! [SV17: $i] :
( ( ~ ( int_leq @ int_one @ SV17 )
| ( int_less @ int_zero @ SV17 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[99]) ).
thf(111,plain,
! [SV18: $i] :
( ( ~ ( int_less @ int_zero @ SV18 )
| ( int_leq @ int_one @ SV18 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[100]) ).
thf(112,plain,
! [SV19: $i] :
( ( ! [SY46: $i] :
( ! [SY47: $i] :
( ( ( plus @ SV19 @ SY47 )
!= SY46 )
| ~ ( int_less @ int_zero @ SY47 ) )
| ( int_less @ SV19 @ SY46 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[101]) ).
thf(113,plain,
! [SV20: $i] :
( ( ! [SY48: $i] :
( ~ ( int_less @ SV20 @ SY48 )
| ~ ( ( ( plus @ SV20 @ ( sK3_K @ SY48 @ SV20 ) )
!= SY48 )
| ~ ( int_less @ int_zero @ ( sK3_K @ SY48 @ SV20 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[102]) ).
thf(114,plain,
! [SV12: $i,SV7: $i,SV1: $i] :
( ( ( ~ ( int_less @ SV1 @ SV7 ) )
= $true )
| ( ( ~ ( int_less @ SV7 @ SV12 ) )
= $true )
| ( ( int_less @ SV1 @ SV12 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[103]) ).
thf(115,plain,
! [SV8: $i,SV2: $i] :
( ( ( SV2 = SV8 )
= $false )
| ( ( int_less @ SV2 @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[104]) ).
thf(116,plain,
! [SV11: $i,SV6: $i,SV14: $i,SV13: $i] :
( ( ( ~ ( int_leq @ SV13 @ SV14 )
| ~ ( int_less @ SV6 @ SV11 ) )
= $true )
| ( ( int_leq @ ( plus @ SV6 @ SV13 ) @ ( plus @ SV11 @ SV14 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[105]) ).
thf(117,plain,
! [SV21: $i,SV15: $i] :
( ( ~ ( int_leq @ int_one @ SV15 )
| ~ ( int_leq @ SV15 @ n )
| ~ ( int_leq @ int_one @ SV21 )
| ~ ( int_leq @ SV21 @ n )
| ! [SY49: $i] :
( ( SV21
!= ( plus @ SV15 @ SY49 ) )
| ~ ( int_less @ int_zero @ SY49 )
| ! [SY44: $i] :
( ~ ( int_leq @ int_one @ SY44 )
| ~ ( int_leq @ SY44 @ SV15 )
| ( ( a @ SY44 @ ( plus @ SY44 @ SY49 ) )
= real_zero ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[106]) ).
thf(118,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( int_leq @ int_one @ SX0 )
| ~ ( int_leq @ SX0 @ n )
| ~ ( int_leq @ int_one @ SX1 )
| ~ ( int_leq @ SX1 @ n )
| ! [SX2: $i] :
( ( SX0
!= ( plus @ SX1 @ SX2 ) )
| ~ ( int_less @ int_zero @ SX2 )
| ! [SX3: $i] :
( ~ ( int_leq @ int_one @ SX3 )
| ~ ( int_leq @ SX3 @ SX1 )
| ( ( a @ ( plus @ SX3 @ SX2 ) @ SX3 )
= real_zero ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[107]) ).
thf(119,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( int_leq @ int_one @ SX0 )
| ~ ( int_leq @ SX0 @ n )
| ~ ( int_leq @ int_one @ SX1 )
| ~ ( int_leq @ SX1 @ n )
| ! [SX2: $i] :
( ~ ( int_leq @ int_one @ SX2 )
| ~ ( int_leq @ SX2 @ SX1 )
| ( ( a @ SX2 @ SX2 )
= real_one ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[107]) ).
thf(120,plain,
! [SV22: $i,SV16: $i] :
( ( ~ ( int_leq @ SV16 @ SV22 )
| ( SV16 = SV22 )
| ( int_less @ SV16 @ SV22 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[108]) ).
thf(121,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( int_leq @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[109]) ).
thf(122,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( int_less @ SX0 @ SX1 )
| ( int_leq @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[109]) ).
thf(123,plain,
! [SV17: $i] :
( ( ( ~ ( int_leq @ int_one @ SV17 ) )
= $true )
| ( ( int_less @ int_zero @ SV17 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[110]) ).
thf(124,plain,
! [SV18: $i] :
( ( ( ~ ( int_less @ int_zero @ SV18 ) )
= $true )
| ( ( int_leq @ int_one @ SV18 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[111]) ).
thf(125,plain,
! [SV23: $i,SV19: $i] :
( ( ! [SY51: $i] :
( ( ( plus @ SV19 @ SY51 )
!= SV23 )
| ~ ( int_less @ int_zero @ SY51 ) )
| ( int_less @ SV19 @ SV23 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[112]) ).
thf(126,plain,
! [SV24: $i,SV20: $i] :
( ( ~ ( int_less @ SV20 @ SV24 )
| ~ ( ( ( plus @ SV20 @ ( sK3_K @ SV24 @ SV20 ) )
!= SV24 )
| ~ ( int_less @ int_zero @ ( sK3_K @ SV24 @ SV20 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[113]) ).
thf(127,plain,
! [SV12: $i,SV7: $i,SV1: $i] :
( ( ( int_less @ SV1 @ SV7 )
= $false )
| ( ( ~ ( int_less @ SV7 @ SV12 ) )
= $true )
| ( ( int_less @ SV1 @ SV12 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[114]) ).
thf(128,plain,
! [SV11: $i,SV6: $i,SV14: $i,SV13: $i] :
( ( ( ~ ( int_leq @ SV13 @ SV14 ) )
= $true )
| ( ( ~ ( int_less @ SV6 @ SV11 ) )
= $true )
| ( ( int_leq @ ( plus @ SV6 @ SV13 ) @ ( plus @ SV11 @ SV14 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[116]) ).
thf(129,plain,
! [SV21: $i,SV15: $i] :
( ( ( ~ ( int_leq @ int_one @ SV15 )
| ~ ( int_leq @ SV15 @ n )
| ~ ( int_leq @ int_one @ SV21 )
| ~ ( int_leq @ SV21 @ n ) )
= $true )
| ( ( ! [SY49: $i] :
( ( SV21
!= ( plus @ SV15 @ SY49 ) )
| ~ ( int_less @ int_zero @ SY49 )
| ! [SY44: $i] :
( ~ ( int_leq @ int_one @ SY44 )
| ~ ( int_leq @ SY44 @ SV15 )
| ( ( a @ SY44 @ ( plus @ SY44 @ SY49 ) )
= real_zero ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[117]) ).
thf(130,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( int_leq @ int_one @ SX0 )
| ~ ( int_leq @ SX0 @ n )
| ~ ( int_leq @ int_one @ SX1 )
| ~ ( int_leq @ SX1 @ n )
| ! [SX2: $i] :
( ( SX0
!= ( plus @ SX1 @ SX2 ) )
| ~ ( int_less @ int_zero @ SX2 )
| ! [SX3: $i] :
( ~ ( int_leq @ int_one @ SX3 )
| ~ ( int_leq @ SX3 @ SX1 )
| ( ( a @ ( plus @ SX3 @ SX2 ) @ SX3 )
= real_zero ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[118]) ).
thf(131,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( int_leq @ int_one @ SX0 )
| ~ ( int_leq @ SX0 @ n )
| ~ ( int_leq @ int_one @ SX1 )
| ~ ( int_leq @ SX1 @ n )
| ! [SX2: $i] :
( ~ ( int_leq @ int_one @ SX2 )
| ~ ( int_leq @ SX2 @ SX1 )
| ( ( a @ SX2 @ SX2 )
= real_one ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[119]) ).
thf(132,plain,
! [SV22: $i,SV16: $i] :
( ( ( ~ ( int_leq @ SV16 @ SV22 ) )
= $true )
| ( ( ( SV16 = SV22 )
| ( int_less @ SV16 @ SV22 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[120]) ).
thf(133,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( int_leq @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[121]) ).
thf(134,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( int_less @ SX0 @ SX1 )
| ( int_leq @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[122]) ).
thf(135,plain,
! [SV17: $i] :
( ( ( int_leq @ int_one @ SV17 )
= $false )
| ( ( int_less @ int_zero @ SV17 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[123]) ).
thf(136,plain,
! [SV18: $i] :
( ( ( int_less @ int_zero @ SV18 )
= $false )
| ( ( int_leq @ int_one @ SV18 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[124]) ).
thf(137,plain,
! [SV23: $i,SV19: $i] :
( ( ( ! [SY51: $i] :
( ( ( plus @ SV19 @ SY51 )
!= SV23 )
| ~ ( int_less @ int_zero @ SY51 ) ) )
= $true )
| ( ( int_less @ SV19 @ SV23 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[125]) ).
thf(138,plain,
! [SV24: $i,SV20: $i] :
( ( ( ~ ( int_less @ SV20 @ SV24 ) )
= $true )
| ( ( ~ ( ( ( plus @ SV20 @ ( sK3_K @ SV24 @ SV20 ) )
!= SV24 )
| ~ ( int_less @ int_zero @ ( sK3_K @ SV24 @ SV20 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[126]) ).
thf(139,plain,
! [SV1: $i,SV12: $i,SV7: $i] :
( ( ( int_less @ SV7 @ SV12 )
= $false )
| ( ( int_less @ SV1 @ SV7 )
= $false )
| ( ( int_less @ SV1 @ SV12 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[127]) ).
thf(140,plain,
! [SV11: $i,SV6: $i,SV14: $i,SV13: $i] :
( ( ( int_leq @ SV13 @ SV14 )
= $false )
| ( ( ~ ( int_less @ SV6 @ SV11 ) )
= $true )
| ( ( int_leq @ ( plus @ SV6 @ SV13 ) @ ( plus @ SV11 @ SV14 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[128]) ).
thf(141,plain,
! [SV21: $i,SV15: $i] :
( ( ( ~ ( int_leq @ int_one @ SV15 )
| ~ ( int_leq @ SV15 @ n )
| ~ ( int_leq @ int_one @ SV21 ) )
= $true )
| ( ( ~ ( int_leq @ SV21 @ n ) )
= $true )
| ( ( ! [SY49: $i] :
( ( SV21
!= ( plus @ SV15 @ SY49 ) )
| ~ ( int_less @ int_zero @ SY49 )
| ! [SY44: $i] :
( ~ ( int_leq @ int_one @ SY44 )
| ~ ( int_leq @ SY44 @ SV15 )
| ( ( a @ SY44 @ ( plus @ SY44 @ SY49 ) )
= real_zero ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[129]) ).
thf(142,plain,
! [SV25: $i] :
( ( ! [SY52: $i] :
( ~ ( int_leq @ int_one @ SV25 )
| ~ ( int_leq @ SV25 @ n )
| ~ ( int_leq @ int_one @ SY52 )
| ~ ( int_leq @ SY52 @ n )
| ! [SY53: $i] :
( ( SV25
!= ( plus @ SY52 @ SY53 ) )
| ~ ( int_less @ int_zero @ SY53 )
| ! [SX3: $i] :
( ~ ( int_leq @ int_one @ SX3 )
| ~ ( int_leq @ SX3 @ SY52 )
| ( ( a @ ( plus @ SX3 @ SY53 ) @ SX3 )
= real_zero ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[130]) ).
thf(143,plain,
! [SV26: $i] :
( ( ! [SY55: $i] :
( ~ ( int_leq @ int_one @ SV26 )
| ~ ( int_leq @ SV26 @ n )
| ~ ( int_leq @ int_one @ SY55 )
| ~ ( int_leq @ SY55 @ n )
| ! [SX2: $i] :
( ~ ( int_leq @ int_one @ SX2 )
| ~ ( int_leq @ SX2 @ SY55 )
| ( ( a @ SX2 @ SX2 )
= real_one ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[131]) ).
thf(144,plain,
! [SV22: $i,SV16: $i] :
( ( ( int_leq @ SV16 @ SV22 )
= $false )
| ( ( ( SV16 = SV22 )
| ( int_less @ SV16 @ SV22 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[132]) ).
thf(145,plain,
! [SV27: $i] :
( ( ! [SY57: $i] :
( ( SV27 != SY57 )
| ( int_leq @ SV27 @ SY57 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[133]) ).
thf(146,plain,
! [SV28: $i] :
( ( ! [SY58: $i] :
( ~ ( int_less @ SV28 @ SY58 )
| ( int_leq @ SV28 @ SY58 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[134]) ).
thf(147,plain,
! [SV23: $i,SV29: $i,SV19: $i] :
( ( ( ( ( plus @ SV19 @ SV29 )
!= SV23 )
| ~ ( int_less @ int_zero @ SV29 ) )
= $true )
| ( ( int_less @ SV19 @ SV23 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[137]) ).
thf(148,plain,
! [SV24: $i,SV20: $i] :
( ( ( int_less @ SV20 @ SV24 )
= $false )
| ( ( ~ ( ( ( plus @ SV20 @ ( sK3_K @ SV24 @ SV20 ) )
!= SV24 )
| ~ ( int_less @ int_zero @ ( sK3_K @ SV24 @ SV20 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[138]) ).
thf(149,plain,
! [SV14: $i,SV13: $i,SV11: $i,SV6: $i] :
( ( ( int_less @ SV6 @ SV11 )
= $false )
| ( ( int_leq @ SV13 @ SV14 )
= $false )
| ( ( int_leq @ ( plus @ SV6 @ SV13 ) @ ( plus @ SV11 @ SV14 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[140]) ).
thf(150,plain,
! [SV21: $i,SV15: $i] :
( ( ( ~ ( int_leq @ int_one @ SV15 )
| ~ ( int_leq @ SV15 @ n ) )
= $true )
| ( ( ~ ( int_leq @ int_one @ SV21 ) )
= $true )
| ( ( ~ ( int_leq @ SV21 @ n ) )
= $true )
| ( ( ! [SY49: $i] :
( ( SV21
!= ( plus @ SV15 @ SY49 ) )
| ~ ( int_less @ int_zero @ SY49 )
| ! [SY44: $i] :
( ~ ( int_leq @ int_one @ SY44 )
| ~ ( int_leq @ SY44 @ SV15 )
| ( ( a @ SY44 @ ( plus @ SY44 @ SY49 ) )
= real_zero ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[141]) ).
thf(151,plain,
! [SV30: $i,SV25: $i] :
( ( ~ ( int_leq @ int_one @ SV25 )
| ~ ( int_leq @ SV25 @ n )
| ~ ( int_leq @ int_one @ SV30 )
| ~ ( int_leq @ SV30 @ n )
| ! [SY59: $i] :
( ( SV25
!= ( plus @ SV30 @ SY59 ) )
| ~ ( int_less @ int_zero @ SY59 )
| ! [SY60: $i] :
( ~ ( int_leq @ int_one @ SY60 )
| ~ ( int_leq @ SY60 @ SV30 )
| ( ( a @ ( plus @ SY60 @ SY59 ) @ SY60 )
= real_zero ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[142]) ).
thf(152,plain,
! [SV31: $i,SV26: $i] :
( ( ~ ( int_leq @ int_one @ SV26 )
| ~ ( int_leq @ SV26 @ n )
| ~ ( int_leq @ int_one @ SV31 )
| ~ ( int_leq @ SV31 @ n )
| ! [SY61: $i] :
( ~ ( int_leq @ int_one @ SY61 )
| ~ ( int_leq @ SY61 @ SV31 )
| ( ( a @ SY61 @ SY61 )
= real_one ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[143]) ).
thf(153,plain,
! [SV22: $i,SV16: $i] :
( ( ( SV16 = SV22 )
= $true )
| ( ( int_less @ SV16 @ SV22 )
= $true )
| ( ( int_leq @ SV16 @ SV22 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[144]) ).
thf(154,plain,
! [SV32: $i,SV27: $i] :
( ( ( SV27 != SV32 )
| ( int_leq @ SV27 @ SV32 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[145]) ).
thf(155,plain,
! [SV33: $i,SV28: $i] :
( ( ~ ( int_less @ SV28 @ SV33 )
| ( int_leq @ SV28 @ SV33 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[146]) ).
thf(156,plain,
! [SV23: $i,SV29: $i,SV19: $i] :
( ( ( ( ( plus @ SV19 @ SV29 )
!= SV23 ) )
= $true )
| ( ( ~ ( int_less @ int_zero @ SV29 ) )
= $true )
| ( ( int_less @ SV19 @ SV23 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[147]) ).
thf(157,plain,
! [SV24: $i,SV20: $i] :
( ( ( ( ( plus @ SV20 @ ( sK3_K @ SV24 @ SV20 ) )
!= SV24 )
| ~ ( int_less @ int_zero @ ( sK3_K @ SV24 @ SV20 ) ) )
= $false )
| ( ( int_less @ SV20 @ SV24 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[148]) ).
thf(158,plain,
! [SV21: $i,SV15: $i] :
( ( ( ~ ( int_leq @ int_one @ SV15 ) )
= $true )
| ( ( ~ ( int_leq @ SV15 @ n ) )
= $true )
| ( ( ~ ( int_leq @ int_one @ SV21 ) )
= $true )
| ( ( ~ ( int_leq @ SV21 @ n ) )
= $true )
| ( ( ! [SY49: $i] :
( ( SV21
!= ( plus @ SV15 @ SY49 ) )
| ~ ( int_less @ int_zero @ SY49 )
| ! [SY44: $i] :
( ~ ( int_leq @ int_one @ SY44 )
| ~ ( int_leq @ SY44 @ SV15 )
| ( ( a @ SY44 @ ( plus @ SY44 @ SY49 ) )
= real_zero ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[150]) ).
thf(159,plain,
! [SV30: $i,SV25: $i] :
( ( ( ~ ( int_leq @ int_one @ SV25 )
| ~ ( int_leq @ SV25 @ n )
| ~ ( int_leq @ int_one @ SV30 )
| ~ ( int_leq @ SV30 @ n ) )
= $true )
| ( ( ! [SY59: $i] :
( ( SV25
!= ( plus @ SV30 @ SY59 ) )
| ~ ( int_less @ int_zero @ SY59 )
| ! [SY60: $i] :
( ~ ( int_leq @ int_one @ SY60 )
| ~ ( int_leq @ SY60 @ SV30 )
| ( ( a @ ( plus @ SY60 @ SY59 ) @ SY60 )
= real_zero ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[151]) ).
thf(160,plain,
! [SV31: $i,SV26: $i] :
( ( ( ~ ( int_leq @ int_one @ SV26 )
| ~ ( int_leq @ SV26 @ n )
| ~ ( int_leq @ int_one @ SV31 )
| ~ ( int_leq @ SV31 @ n ) )
= $true )
| ( ( ! [SY61: $i] :
( ~ ( int_leq @ int_one @ SY61 )
| ~ ( int_leq @ SY61 @ SV31 )
| ( ( a @ SY61 @ SY61 )
= real_one ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[152]) ).
thf(161,plain,
! [SV32: $i,SV27: $i] :
( ( ( ( SV27 != SV32 ) )
= $true )
| ( ( int_leq @ SV27 @ SV32 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[154]) ).
thf(162,plain,
! [SV33: $i,SV28: $i] :
( ( ( ~ ( int_less @ SV28 @ SV33 ) )
= $true )
| ( ( int_leq @ SV28 @ SV33 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[155]) ).
thf(163,plain,
! [SV23: $i,SV29: $i,SV19: $i] :
( ( ( ( plus @ SV19 @ SV29 )
= SV23 )
= $false )
| ( ( ~ ( int_less @ int_zero @ SV29 ) )
= $true )
| ( ( int_less @ SV19 @ SV23 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[156]) ).
thf(164,plain,
! [SV24: $i,SV20: $i] :
( ( ( ( ( plus @ SV20 @ ( sK3_K @ SV24 @ SV20 ) )
!= SV24 ) )
= $false )
| ( ( int_less @ SV20 @ SV24 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[157]) ).
thf(165,plain,
! [SV20: $i,SV24: $i] :
( ( ( ~ ( int_less @ int_zero @ ( sK3_K @ SV24 @ SV20 ) ) )
= $false )
| ( ( int_less @ SV20 @ SV24 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[157]) ).
thf(166,plain,
! [SV21: $i,SV15: $i] :
( ( ( int_leq @ int_one @ SV15 )
= $false )
| ( ( ~ ( int_leq @ SV15 @ n ) )
= $true )
| ( ( ~ ( int_leq @ int_one @ SV21 ) )
= $true )
| ( ( ~ ( int_leq @ SV21 @ n ) )
= $true )
| ( ( ! [SY49: $i] :
( ( SV21
!= ( plus @ SV15 @ SY49 ) )
| ~ ( int_less @ int_zero @ SY49 )
| ! [SY44: $i] :
( ~ ( int_leq @ int_one @ SY44 )
| ~ ( int_leq @ SY44 @ SV15 )
| ( ( a @ SY44 @ ( plus @ SY44 @ SY49 ) )
= real_zero ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[158]) ).
thf(167,plain,
! [SV30: $i,SV25: $i] :
( ( ( ~ ( int_leq @ int_one @ SV25 )
| ~ ( int_leq @ SV25 @ n )
| ~ ( int_leq @ int_one @ SV30 ) )
= $true )
| ( ( ~ ( int_leq @ SV30 @ n ) )
= $true )
| ( ( ! [SY59: $i] :
( ( SV25
!= ( plus @ SV30 @ SY59 ) )
| ~ ( int_less @ int_zero @ SY59 )
| ! [SY60: $i] :
( ~ ( int_leq @ int_one @ SY60 )
| ~ ( int_leq @ SY60 @ SV30 )
| ( ( a @ ( plus @ SY60 @ SY59 ) @ SY60 )
= real_zero ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[159]) ).
thf(168,plain,
! [SV31: $i,SV26: $i] :
( ( ( ~ ( int_leq @ int_one @ SV26 )
| ~ ( int_leq @ SV26 @ n )
| ~ ( int_leq @ int_one @ SV31 ) )
= $true )
| ( ( ~ ( int_leq @ SV31 @ n ) )
= $true )
| ( ( ! [SY61: $i] :
( ~ ( int_leq @ int_one @ SY61 )
| ~ ( int_leq @ SY61 @ SV31 )
| ( ( a @ SY61 @ SY61 )
= real_one ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[160]) ).
thf(169,plain,
! [SV32: $i,SV27: $i] :
( ( ( SV27 = SV32 )
= $false )
| ( ( int_leq @ SV27 @ SV32 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[161]) ).
thf(170,plain,
! [SV33: $i,SV28: $i] :
( ( ( int_less @ SV28 @ SV33 )
= $false )
| ( ( int_leq @ SV28 @ SV33 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[162]) ).
thf(171,plain,
! [SV23: $i,SV19: $i,SV29: $i] :
( ( ( int_less @ int_zero @ SV29 )
= $false )
| ( ( ( plus @ SV19 @ SV29 )
= SV23 )
= $false )
| ( ( int_less @ SV19 @ SV23 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[163]) ).
thf(172,plain,
! [SV24: $i,SV20: $i] :
( ( ( ( plus @ SV20 @ ( sK3_K @ SV24 @ SV20 ) )
= SV24 )
= $true )
| ( ( int_less @ SV20 @ SV24 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[164]) ).
thf(173,plain,
! [SV20: $i,SV24: $i] :
( ( ( int_less @ int_zero @ ( sK3_K @ SV24 @ SV20 ) )
= $true )
| ( ( int_less @ SV20 @ SV24 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[165]) ).
thf(174,plain,
! [SV21: $i,SV15: $i] :
( ( ( int_leq @ SV15 @ n )
= $false )
| ( ( int_leq @ int_one @ SV15 )
= $false )
| ( ( ~ ( int_leq @ int_one @ SV21 ) )
= $true )
| ( ( ~ ( int_leq @ SV21 @ n ) )
= $true )
| ( ( ! [SY49: $i] :
( ( SV21
!= ( plus @ SV15 @ SY49 ) )
| ~ ( int_less @ int_zero @ SY49 )
| ! [SY44: $i] :
( ~ ( int_leq @ int_one @ SY44 )
| ~ ( int_leq @ SY44 @ SV15 )
| ( ( a @ SY44 @ ( plus @ SY44 @ SY49 ) )
= real_zero ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[166]) ).
thf(175,plain,
! [SV30: $i,SV25: $i] :
( ( ( ~ ( int_leq @ int_one @ SV25 )
| ~ ( int_leq @ SV25 @ n ) )
= $true )
| ( ( ~ ( int_leq @ int_one @ SV30 ) )
= $true )
| ( ( ~ ( int_leq @ SV30 @ n ) )
= $true )
| ( ( ! [SY59: $i] :
( ( SV25
!= ( plus @ SV30 @ SY59 ) )
| ~ ( int_less @ int_zero @ SY59 )
| ! [SY60: $i] :
( ~ ( int_leq @ int_one @ SY60 )
| ~ ( int_leq @ SY60 @ SV30 )
| ( ( a @ ( plus @ SY60 @ SY59 ) @ SY60 )
= real_zero ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[167]) ).
thf(176,plain,
! [SV31: $i,SV26: $i] :
( ( ( ~ ( int_leq @ int_one @ SV26 )
| ~ ( int_leq @ SV26 @ n ) )
= $true )
| ( ( ~ ( int_leq @ int_one @ SV31 ) )
= $true )
| ( ( ~ ( int_leq @ SV31 @ n ) )
= $true )
| ( ( ! [SY61: $i] :
( ~ ( int_leq @ int_one @ SY61 )
| ~ ( int_leq @ SY61 @ SV31 )
| ( ( a @ SY61 @ SY61 )
= real_one ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[168]) ).
thf(177,plain,
! [SV15: $i,SV21: $i] :
( ( ( int_leq @ int_one @ SV21 )
= $false )
| ( ( int_leq @ int_one @ SV15 )
= $false )
| ( ( int_leq @ SV15 @ n )
= $false )
| ( ( ~ ( int_leq @ SV21 @ n ) )
= $true )
| ( ( ! [SY49: $i] :
( ( SV21
!= ( plus @ SV15 @ SY49 ) )
| ~ ( int_less @ int_zero @ SY49 )
| ! [SY44: $i] :
( ~ ( int_leq @ int_one @ SY44 )
| ~ ( int_leq @ SY44 @ SV15 )
| ( ( a @ SY44 @ ( plus @ SY44 @ SY49 ) )
= real_zero ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[174]) ).
thf(178,plain,
! [SV30: $i,SV25: $i] :
( ( ( ~ ( int_leq @ int_one @ SV25 ) )
= $true )
| ( ( ~ ( int_leq @ SV25 @ n ) )
= $true )
| ( ( ~ ( int_leq @ int_one @ SV30 ) )
= $true )
| ( ( ~ ( int_leq @ SV30 @ n ) )
= $true )
| ( ( ! [SY59: $i] :
( ( SV25
!= ( plus @ SV30 @ SY59 ) )
| ~ ( int_less @ int_zero @ SY59 )
| ! [SY60: $i] :
( ~ ( int_leq @ int_one @ SY60 )
| ~ ( int_leq @ SY60 @ SV30 )
| ( ( a @ ( plus @ SY60 @ SY59 ) @ SY60 )
= real_zero ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[175]) ).
thf(179,plain,
! [SV31: $i,SV26: $i] :
( ( ( ~ ( int_leq @ int_one @ SV26 ) )
= $true )
| ( ( ~ ( int_leq @ SV26 @ n ) )
= $true )
| ( ( ~ ( int_leq @ int_one @ SV31 ) )
= $true )
| ( ( ~ ( int_leq @ SV31 @ n ) )
= $true )
| ( ( ! [SY61: $i] :
( ~ ( int_leq @ int_one @ SY61 )
| ~ ( int_leq @ SY61 @ SV31 )
| ( ( a @ SY61 @ SY61 )
= real_one ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[176]) ).
thf(180,plain,
! [SV15: $i,SV21: $i] :
( ( ( int_leq @ SV21 @ n )
= $false )
| ( ( int_leq @ SV15 @ n )
= $false )
| ( ( int_leq @ int_one @ SV15 )
= $false )
| ( ( int_leq @ int_one @ SV21 )
= $false )
| ( ( ! [SY49: $i] :
( ( SV21
!= ( plus @ SV15 @ SY49 ) )
| ~ ( int_less @ int_zero @ SY49 )
| ! [SY44: $i] :
( ~ ( int_leq @ int_one @ SY44 )
| ~ ( int_leq @ SY44 @ SV15 )
| ( ( a @ SY44 @ ( plus @ SY44 @ SY49 ) )
= real_zero ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[177]) ).
thf(181,plain,
! [SV30: $i,SV25: $i] :
( ( ( int_leq @ int_one @ SV25 )
= $false )
| ( ( ~ ( int_leq @ SV25 @ n ) )
= $true )
| ( ( ~ ( int_leq @ int_one @ SV30 ) )
= $true )
| ( ( ~ ( int_leq @ SV30 @ n ) )
= $true )
| ( ( ! [SY59: $i] :
( ( SV25
!= ( plus @ SV30 @ SY59 ) )
| ~ ( int_less @ int_zero @ SY59 )
| ! [SY60: $i] :
( ~ ( int_leq @ int_one @ SY60 )
| ~ ( int_leq @ SY60 @ SV30 )
| ( ( a @ ( plus @ SY60 @ SY59 ) @ SY60 )
= real_zero ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[178]) ).
thf(182,plain,
! [SV31: $i,SV26: $i] :
( ( ( int_leq @ int_one @ SV26 )
= $false )
| ( ( ~ ( int_leq @ SV26 @ n ) )
= $true )
| ( ( ~ ( int_leq @ int_one @ SV31 ) )
= $true )
| ( ( ~ ( int_leq @ SV31 @ n ) )
= $true )
| ( ( ! [SY61: $i] :
( ~ ( int_leq @ int_one @ SY61 )
| ~ ( int_leq @ SY61 @ SV31 )
| ( ( a @ SY61 @ SY61 )
= real_one ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[179]) ).
thf(183,plain,
! [SV34: $i,SV15: $i,SV21: $i] :
( ( ( ( SV21
!= ( plus @ SV15 @ SV34 ) )
| ~ ( int_less @ int_zero @ SV34 )
| ! [SY62: $i] :
( ~ ( int_leq @ int_one @ SY62 )
| ~ ( int_leq @ SY62 @ SV15 )
| ( ( a @ SY62 @ ( plus @ SY62 @ SV34 ) )
= real_zero ) ) )
= $true )
| ( ( int_leq @ int_one @ SV21 )
= $false )
| ( ( int_leq @ int_one @ SV15 )
= $false )
| ( ( int_leq @ SV15 @ n )
= $false )
| ( ( int_leq @ SV21 @ n )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[180]) ).
thf(184,plain,
! [SV30: $i,SV25: $i] :
( ( ( int_leq @ SV25 @ n )
= $false )
| ( ( int_leq @ int_one @ SV25 )
= $false )
| ( ( ~ ( int_leq @ int_one @ SV30 ) )
= $true )
| ( ( ~ ( int_leq @ SV30 @ n ) )
= $true )
| ( ( ! [SY59: $i] :
( ( SV25
!= ( plus @ SV30 @ SY59 ) )
| ~ ( int_less @ int_zero @ SY59 )
| ! [SY60: $i] :
( ~ ( int_leq @ int_one @ SY60 )
| ~ ( int_leq @ SY60 @ SV30 )
| ( ( a @ ( plus @ SY60 @ SY59 ) @ SY60 )
= real_zero ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[181]) ).
thf(185,plain,
! [SV31: $i,SV26: $i] :
( ( ( int_leq @ SV26 @ n )
= $false )
| ( ( int_leq @ int_one @ SV26 )
= $false )
| ( ( ~ ( int_leq @ int_one @ SV31 ) )
= $true )
| ( ( ~ ( int_leq @ SV31 @ n ) )
= $true )
| ( ( ! [SY61: $i] :
( ~ ( int_leq @ int_one @ SY61 )
| ~ ( int_leq @ SY61 @ SV31 )
| ( ( a @ SY61 @ SY61 )
= real_one ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[182]) ).
thf(186,plain,
! [SV34: $i,SV15: $i,SV21: $i] :
( ( ( ( SV21
!= ( plus @ SV15 @ SV34 ) )
| ~ ( int_less @ int_zero @ SV34 ) )
= $true )
| ( ( ! [SY62: $i] :
( ~ ( int_leq @ int_one @ SY62 )
| ~ ( int_leq @ SY62 @ SV15 )
| ( ( a @ SY62 @ ( plus @ SY62 @ SV34 ) )
= real_zero ) ) )
= $true )
| ( ( int_leq @ int_one @ SV21 )
= $false )
| ( ( int_leq @ int_one @ SV15 )
= $false )
| ( ( int_leq @ SV15 @ n )
= $false )
| ( ( int_leq @ SV21 @ n )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[183]) ).
thf(187,plain,
! [SV25: $i,SV30: $i] :
( ( ( int_leq @ int_one @ SV30 )
= $false )
| ( ( int_leq @ int_one @ SV25 )
= $false )
| ( ( int_leq @ SV25 @ n )
= $false )
| ( ( ~ ( int_leq @ SV30 @ n ) )
= $true )
| ( ( ! [SY59: $i] :
( ( SV25
!= ( plus @ SV30 @ SY59 ) )
| ~ ( int_less @ int_zero @ SY59 )
| ! [SY60: $i] :
( ~ ( int_leq @ int_one @ SY60 )
| ~ ( int_leq @ SY60 @ SV30 )
| ( ( a @ ( plus @ SY60 @ SY59 ) @ SY60 )
= real_zero ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[184]) ).
thf(188,plain,
! [SV26: $i,SV31: $i] :
( ( ( int_leq @ int_one @ SV31 )
= $false )
| ( ( int_leq @ int_one @ SV26 )
= $false )
| ( ( int_leq @ SV26 @ n )
= $false )
| ( ( ~ ( int_leq @ SV31 @ n ) )
= $true )
| ( ( ! [SY61: $i] :
( ~ ( int_leq @ int_one @ SY61 )
| ~ ( int_leq @ SY61 @ SV31 )
| ( ( a @ SY61 @ SY61 )
= real_one ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[185]) ).
thf(189,plain,
! [SV34: $i,SV15: $i,SV21: $i] :
( ( ( ( SV21
!= ( plus @ SV15 @ SV34 ) ) )
= $true )
| ( ( ~ ( int_less @ int_zero @ SV34 ) )
= $true )
| ( ( ! [SY62: $i] :
( ~ ( int_leq @ int_one @ SY62 )
| ~ ( int_leq @ SY62 @ SV15 )
| ( ( a @ SY62 @ ( plus @ SY62 @ SV34 ) )
= real_zero ) ) )
= $true )
| ( ( int_leq @ int_one @ SV21 )
= $false )
| ( ( int_leq @ int_one @ SV15 )
= $false )
| ( ( int_leq @ SV15 @ n )
= $false )
| ( ( int_leq @ SV21 @ n )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[186]) ).
thf(190,plain,
! [SV25: $i,SV30: $i] :
( ( ( int_leq @ SV30 @ n )
= $false )
| ( ( int_leq @ SV25 @ n )
= $false )
| ( ( int_leq @ int_one @ SV25 )
= $false )
| ( ( int_leq @ int_one @ SV30 )
= $false )
| ( ( ! [SY59: $i] :
( ( SV25
!= ( plus @ SV30 @ SY59 ) )
| ~ ( int_less @ int_zero @ SY59 )
| ! [SY60: $i] :
( ~ ( int_leq @ int_one @ SY60 )
| ~ ( int_leq @ SY60 @ SV30 )
| ( ( a @ ( plus @ SY60 @ SY59 ) @ SY60 )
= real_zero ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[187]) ).
thf(191,plain,
! [SV26: $i,SV31: $i] :
( ( ( int_leq @ SV31 @ n )
= $false )
| ( ( int_leq @ SV26 @ n )
= $false )
| ( ( int_leq @ int_one @ SV26 )
= $false )
| ( ( int_leq @ int_one @ SV31 )
= $false )
| ( ( ! [SY61: $i] :
( ~ ( int_leq @ int_one @ SY61 )
| ~ ( int_leq @ SY61 @ SV31 )
| ( ( a @ SY61 @ SY61 )
= real_one ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[188]) ).
thf(192,plain,
! [SV34: $i,SV15: $i,SV21: $i] :
( ( ( SV21
= ( plus @ SV15 @ SV34 ) )
= $false )
| ( ( ~ ( int_less @ int_zero @ SV34 ) )
= $true )
| ( ( ! [SY62: $i] :
( ~ ( int_leq @ int_one @ SY62 )
| ~ ( int_leq @ SY62 @ SV15 )
| ( ( a @ SY62 @ ( plus @ SY62 @ SV34 ) )
= real_zero ) ) )
= $true )
| ( ( int_leq @ int_one @ SV21 )
= $false )
| ( ( int_leq @ int_one @ SV15 )
= $false )
| ( ( int_leq @ SV15 @ n )
= $false )
| ( ( int_leq @ SV21 @ n )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[189]) ).
thf(193,plain,
! [SV35: $i,SV30: $i,SV25: $i] :
( ( ( ( SV25
!= ( plus @ SV30 @ SV35 ) )
| ~ ( int_less @ int_zero @ SV35 )
| ! [SY63: $i] :
( ~ ( int_leq @ int_one @ SY63 )
| ~ ( int_leq @ SY63 @ SV30 )
| ( ( a @ ( plus @ SY63 @ SV35 ) @ SY63 )
= real_zero ) ) )
= $true )
| ( ( int_leq @ int_one @ SV30 )
= $false )
| ( ( int_leq @ int_one @ SV25 )
= $false )
| ( ( int_leq @ SV25 @ n )
= $false )
| ( ( int_leq @ SV30 @ n )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[190]) ).
thf(194,plain,
! [SV26: $i,SV31: $i,SV36: $i] :
( ( ( ~ ( int_leq @ int_one @ SV36 )
| ~ ( int_leq @ SV36 @ SV31 )
| ( ( a @ SV36 @ SV36 )
= real_one ) )
= $true )
| ( ( int_leq @ int_one @ SV31 )
= $false )
| ( ( int_leq @ int_one @ SV26 )
= $false )
| ( ( int_leq @ SV26 @ n )
= $false )
| ( ( int_leq @ SV31 @ n )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[191]) ).
thf(195,plain,
! [SV15: $i,SV21: $i,SV34: $i] :
( ( ( int_less @ int_zero @ SV34 )
= $false )
| ( ( SV21
= ( plus @ SV15 @ SV34 ) )
= $false )
| ( ( ! [SY62: $i] :
( ~ ( int_leq @ int_one @ SY62 )
| ~ ( int_leq @ SY62 @ SV15 )
| ( ( a @ SY62 @ ( plus @ SY62 @ SV34 ) )
= real_zero ) ) )
= $true )
| ( ( int_leq @ int_one @ SV21 )
= $false )
| ( ( int_leq @ int_one @ SV15 )
= $false )
| ( ( int_leq @ SV15 @ n )
= $false )
| ( ( int_leq @ SV21 @ n )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[192]) ).
thf(196,plain,
! [SV35: $i,SV30: $i,SV25: $i] :
( ( ( ( SV25
!= ( plus @ SV30 @ SV35 ) )
| ~ ( int_less @ int_zero @ SV35 ) )
= $true )
| ( ( ! [SY63: $i] :
( ~ ( int_leq @ int_one @ SY63 )
| ~ ( int_leq @ SY63 @ SV30 )
| ( ( a @ ( plus @ SY63 @ SV35 ) @ SY63 )
= real_zero ) ) )
= $true )
| ( ( int_leq @ int_one @ SV30 )
= $false )
| ( ( int_leq @ int_one @ SV25 )
= $false )
| ( ( int_leq @ SV25 @ n )
= $false )
| ( ( int_leq @ SV30 @ n )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[193]) ).
thf(197,plain,
! [SV26: $i,SV31: $i,SV36: $i] :
( ( ( ~ ( int_leq @ int_one @ SV36 )
| ~ ( int_leq @ SV36 @ SV31 ) )
= $true )
| ( ( ( a @ SV36 @ SV36 )
= real_one )
= $true )
| ( ( int_leq @ int_one @ SV31 )
= $false )
| ( ( int_leq @ int_one @ SV26 )
= $false )
| ( ( int_leq @ SV26 @ n )
= $false )
| ( ( int_leq @ SV31 @ n )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[194]) ).
thf(198,plain,
! [SV21: $i,SV34: $i,SV15: $i,SV37: $i] :
( ( ( ~ ( int_leq @ int_one @ SV37 )
| ~ ( int_leq @ SV37 @ SV15 )
| ( ( a @ SV37 @ ( plus @ SV37 @ SV34 ) )
= real_zero ) )
= $true )
| ( ( SV21
= ( plus @ SV15 @ SV34 ) )
= $false )
| ( ( int_less @ int_zero @ SV34 )
= $false )
| ( ( int_leq @ int_one @ SV21 )
= $false )
| ( ( int_leq @ int_one @ SV15 )
= $false )
| ( ( int_leq @ SV15 @ n )
= $false )
| ( ( int_leq @ SV21 @ n )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[195]) ).
thf(199,plain,
! [SV35: $i,SV30: $i,SV25: $i] :
( ( ( ( SV25
!= ( plus @ SV30 @ SV35 ) ) )
= $true )
| ( ( ~ ( int_less @ int_zero @ SV35 ) )
= $true )
| ( ( ! [SY63: $i] :
( ~ ( int_leq @ int_one @ SY63 )
| ~ ( int_leq @ SY63 @ SV30 )
| ( ( a @ ( plus @ SY63 @ SV35 ) @ SY63 )
= real_zero ) ) )
= $true )
| ( ( int_leq @ int_one @ SV30 )
= $false )
| ( ( int_leq @ int_one @ SV25 )
= $false )
| ( ( int_leq @ SV25 @ n )
= $false )
| ( ( int_leq @ SV30 @ n )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[196]) ).
thf(200,plain,
! [SV26: $i,SV31: $i,SV36: $i] :
( ( ( ~ ( int_leq @ int_one @ SV36 ) )
= $true )
| ( ( ~ ( int_leq @ SV36 @ SV31 ) )
= $true )
| ( ( ( a @ SV36 @ SV36 )
= real_one )
= $true )
| ( ( int_leq @ int_one @ SV31 )
= $false )
| ( ( int_leq @ int_one @ SV26 )
= $false )
| ( ( int_leq @ SV26 @ n )
= $false )
| ( ( int_leq @ SV31 @ n )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[197]) ).
thf(201,plain,
! [SV21: $i,SV34: $i,SV15: $i,SV37: $i] :
( ( ( ~ ( int_leq @ int_one @ SV37 )
| ~ ( int_leq @ SV37 @ SV15 ) )
= $true )
| ( ( ( a @ SV37 @ ( plus @ SV37 @ SV34 ) )
= real_zero )
= $true )
| ( ( SV21
= ( plus @ SV15 @ SV34 ) )
= $false )
| ( ( int_less @ int_zero @ SV34 )
= $false )
| ( ( int_leq @ int_one @ SV21 )
= $false )
| ( ( int_leq @ int_one @ SV15 )
= $false )
| ( ( int_leq @ SV15 @ n )
= $false )
| ( ( int_leq @ SV21 @ n )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[198]) ).
thf(202,plain,
! [SV35: $i,SV30: $i,SV25: $i] :
( ( ( SV25
= ( plus @ SV30 @ SV35 ) )
= $false )
| ( ( ~ ( int_less @ int_zero @ SV35 ) )
= $true )
| ( ( ! [SY63: $i] :
( ~ ( int_leq @ int_one @ SY63 )
| ~ ( int_leq @ SY63 @ SV30 )
| ( ( a @ ( plus @ SY63 @ SV35 ) @ SY63 )
= real_zero ) ) )
= $true )
| ( ( int_leq @ int_one @ SV30 )
= $false )
| ( ( int_leq @ int_one @ SV25 )
= $false )
| ( ( int_leq @ SV25 @ n )
= $false )
| ( ( int_leq @ SV30 @ n )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[199]) ).
thf(203,plain,
! [SV26: $i,SV31: $i,SV36: $i] :
( ( ( int_leq @ int_one @ SV36 )
= $false )
| ( ( ~ ( int_leq @ SV36 @ SV31 ) )
= $true )
| ( ( ( a @ SV36 @ SV36 )
= real_one )
= $true )
| ( ( int_leq @ int_one @ SV31 )
= $false )
| ( ( int_leq @ int_one @ SV26 )
= $false )
| ( ( int_leq @ SV26 @ n )
= $false )
| ( ( int_leq @ SV31 @ n )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[200]) ).
thf(204,plain,
! [SV21: $i,SV34: $i,SV15: $i,SV37: $i] :
( ( ( ~ ( int_leq @ int_one @ SV37 ) )
= $true )
| ( ( ~ ( int_leq @ SV37 @ SV15 ) )
= $true )
| ( ( ( a @ SV37 @ ( plus @ SV37 @ SV34 ) )
= real_zero )
= $true )
| ( ( SV21
= ( plus @ SV15 @ SV34 ) )
= $false )
| ( ( int_less @ int_zero @ SV34 )
= $false )
| ( ( int_leq @ int_one @ SV21 )
= $false )
| ( ( int_leq @ int_one @ SV15 )
= $false )
| ( ( int_leq @ SV15 @ n )
= $false )
| ( ( int_leq @ SV21 @ n )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[201]) ).
thf(205,plain,
! [SV30: $i,SV25: $i,SV35: $i] :
( ( ( int_less @ int_zero @ SV35 )
= $false )
| ( ( SV25
= ( plus @ SV30 @ SV35 ) )
= $false )
| ( ( ! [SY63: $i] :
( ~ ( int_leq @ int_one @ SY63 )
| ~ ( int_leq @ SY63 @ SV30 )
| ( ( a @ ( plus @ SY63 @ SV35 ) @ SY63 )
= real_zero ) ) )
= $true )
| ( ( int_leq @ int_one @ SV30 )
= $false )
| ( ( int_leq @ int_one @ SV25 )
= $false )
| ( ( int_leq @ SV25 @ n )
= $false )
| ( ( int_leq @ SV30 @ n )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[202]) ).
thf(206,plain,
! [SV26: $i,SV31: $i,SV36: $i] :
( ( ( int_leq @ SV36 @ SV31 )
= $false )
| ( ( int_leq @ int_one @ SV36 )
= $false )
| ( ( ( a @ SV36 @ SV36 )
= real_one )
= $true )
| ( ( int_leq @ int_one @ SV31 )
= $false )
| ( ( int_leq @ int_one @ SV26 )
= $false )
| ( ( int_leq @ SV26 @ n )
= $false )
| ( ( int_leq @ SV31 @ n )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[203]) ).
thf(207,plain,
! [SV21: $i,SV34: $i,SV15: $i,SV37: $i] :
( ( ( int_leq @ int_one @ SV37 )
= $false )
| ( ( ~ ( int_leq @ SV37 @ SV15 ) )
= $true )
| ( ( ( a @ SV37 @ ( plus @ SV37 @ SV34 ) )
= real_zero )
= $true )
| ( ( SV21
= ( plus @ SV15 @ SV34 ) )
= $false )
| ( ( int_less @ int_zero @ SV34 )
= $false )
| ( ( int_leq @ int_one @ SV21 )
= $false )
| ( ( int_leq @ int_one @ SV15 )
= $false )
| ( ( int_leq @ SV15 @ n )
= $false )
| ( ( int_leq @ SV21 @ n )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[204]) ).
thf(208,plain,
! [SV25: $i,SV35: $i,SV30: $i,SV38: $i] :
( ( ( ~ ( int_leq @ int_one @ SV38 )
| ~ ( int_leq @ SV38 @ SV30 )
| ( ( a @ ( plus @ SV38 @ SV35 ) @ SV38 )
= real_zero ) )
= $true )
| ( ( SV25
= ( plus @ SV30 @ SV35 ) )
= $false )
| ( ( int_less @ int_zero @ SV35 )
= $false )
| ( ( int_leq @ int_one @ SV30 )
= $false )
| ( ( int_leq @ int_one @ SV25 )
= $false )
| ( ( int_leq @ SV25 @ n )
= $false )
| ( ( int_leq @ SV30 @ n )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[205]) ).
thf(209,plain,
! [SV21: $i,SV34: $i,SV15: $i,SV37: $i] :
( ( ( int_leq @ SV37 @ SV15 )
= $false )
| ( ( int_leq @ int_one @ SV37 )
= $false )
| ( ( ( a @ SV37 @ ( plus @ SV37 @ SV34 ) )
= real_zero )
= $true )
| ( ( SV21
= ( plus @ SV15 @ SV34 ) )
= $false )
| ( ( int_less @ int_zero @ SV34 )
= $false )
| ( ( int_leq @ int_one @ SV21 )
= $false )
| ( ( int_leq @ int_one @ SV15 )
= $false )
| ( ( int_leq @ SV15 @ n )
= $false )
| ( ( int_leq @ SV21 @ n )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[207]) ).
thf(210,plain,
! [SV25: $i,SV35: $i,SV30: $i,SV38: $i] :
( ( ( ~ ( int_leq @ int_one @ SV38 )
| ~ ( int_leq @ SV38 @ SV30 ) )
= $true )
| ( ( ( a @ ( plus @ SV38 @ SV35 ) @ SV38 )
= real_zero )
= $true )
| ( ( SV25
= ( plus @ SV30 @ SV35 ) )
= $false )
| ( ( int_less @ int_zero @ SV35 )
= $false )
| ( ( int_leq @ int_one @ SV30 )
= $false )
| ( ( int_leq @ int_one @ SV25 )
= $false )
| ( ( int_leq @ SV25 @ n )
= $false )
| ( ( int_leq @ SV30 @ n )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[208]) ).
thf(211,plain,
! [SV25: $i,SV35: $i,SV30: $i,SV38: $i] :
( ( ( ~ ( int_leq @ int_one @ SV38 ) )
= $true )
| ( ( ~ ( int_leq @ SV38 @ SV30 ) )
= $true )
| ( ( ( a @ ( plus @ SV38 @ SV35 ) @ SV38 )
= real_zero )
= $true )
| ( ( SV25
= ( plus @ SV30 @ SV35 ) )
= $false )
| ( ( int_less @ int_zero @ SV35 )
= $false )
| ( ( int_leq @ int_one @ SV30 )
= $false )
| ( ( int_leq @ int_one @ SV25 )
= $false )
| ( ( int_leq @ SV25 @ n )
= $false )
| ( ( int_leq @ SV30 @ n )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[210]) ).
thf(212,plain,
! [SV25: $i,SV35: $i,SV30: $i,SV38: $i] :
( ( ( int_leq @ int_one @ SV38 )
= $false )
| ( ( ~ ( int_leq @ SV38 @ SV30 ) )
= $true )
| ( ( ( a @ ( plus @ SV38 @ SV35 ) @ SV38 )
= real_zero )
= $true )
| ( ( SV25
= ( plus @ SV30 @ SV35 ) )
= $false )
| ( ( int_less @ int_zero @ SV35 )
= $false )
| ( ( int_leq @ int_one @ SV30 )
= $false )
| ( ( int_leq @ int_one @ SV25 )
= $false )
| ( ( int_leq @ SV25 @ n )
= $false )
| ( ( int_leq @ SV30 @ n )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[211]) ).
thf(213,plain,
! [SV25: $i,SV35: $i,SV30: $i,SV38: $i] :
( ( ( int_leq @ SV38 @ SV30 )
= $false )
| ( ( int_leq @ int_one @ SV38 )
= $false )
| ( ( ( a @ ( plus @ SV38 @ SV35 ) @ SV38 )
= real_zero )
= $true )
| ( ( SV25
= ( plus @ SV30 @ SV35 ) )
= $false )
| ( ( int_less @ int_zero @ SV35 )
= $false )
| ( ( int_leq @ int_one @ SV30 )
= $false )
| ( ( int_leq @ int_one @ SV25 )
= $false )
| ( ( int_leq @ SV25 @ n )
= $false )
| ( ( int_leq @ SV30 @ n )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[212]) ).
thf(214,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[51,213,209,206,173,172,171,170,169,153,149,139,136,135,115,93,81,73,71,62,61,60,59,58]) ).
thf(215,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[214]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWV488+3 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.14/0.35 % Computer : n007.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Thu Jun 16 00:20:11 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.36
% 0.14/0.36 No.of.Axioms: 12
% 0.14/0.36
% 0.14/0.36 Length.of.Defs: 0
% 0.14/0.36
% 0.14/0.36 Contains.Choice.Funs: false
% 0.20/0.37 (rf:0,axioms:12,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:14,loop_count:0,foatp_calls:0,translation:fof_full)................
% 2.58/2.79
% 2.58/2.79 ********************************
% 2.58/2.79 * All subproblems solved! *
% 2.58/2.79 ********************************
% 2.58/2.79 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:16,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:214,loop_count:0,foatp_calls:1,translation:fof_full)
% 2.65/2.82
% 2.65/2.82 %**** Beginning of derivation protocol ****
% 2.65/2.82 % SZS output start CNFRefutation
% See solution above
% 2.65/2.82
% 2.65/2.82 %**** End of derivation protocol ****
% 2.65/2.82 %**** no. of clauses in derivation: 215 ****
% 2.65/2.82 %**** clause counter: 214 ****
% 2.65/2.82
% 2.65/2.82 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:16,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:214,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------