TSTP Solution File: KLE007+2 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : KLE007+2 : 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 : n010.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 : Sun Jul 17 02:10:46 EDT 2022
% Result : Theorem 2.34s 2.57s
% Output : CNFRefutation 2.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 28
% Syntax : Number of formulae : 309 ( 228 unt; 11 typ; 0 def)
% Number of atoms : 1471 ( 725 equ; 0 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 2726 ( 432 ~; 383 |; 33 &;1861 @)
% ( 8 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 11 ( 11 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 11 usr; 6 con; 0-2 aty)
% Number of variables : 655 ( 0 ^ 653 !; 2 ?; 655 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_addition,type,
addition: $i > $i > $i ).
thf(tp_c,type,
c: $i > $i ).
thf(tp_complement,type,
complement: $i > $i > $o ).
thf(tp_leq,type,
leq: $i > $i > $o ).
thf(tp_multiplication,type,
multiplication: $i > $i > $i ).
thf(tp_one,type,
one: $i ).
thf(tp_sK1_X0,type,
sK1_X0: $i ).
thf(tp_sK2_SY31,type,
sK2_SY31: $i ).
thf(tp_sK3_X1,type,
sK3_X1: $i > $i ).
thf(tp_test,type,
test: $i > $o ).
thf(tp_zero,type,
zero: $i ).
thf(1,axiom,
! [X0: $i] :
( ~ ( test @ X0 )
=> ( ( c @ X0 )
= zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',test_4) ).
thf(2,axiom,
! [X0: $i,X1: $i] :
( ( test @ X0 )
=> ( ( ( c @ X0 )
= X1 )
<=> ( complement @ X0 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',test_3) ).
thf(3,axiom,
! [X0: $i,X1: $i] :
( ( complement @ X1 @ X0 )
<=> ( ( ( multiplication @ X0 @ X1 )
= zero )
& ( ( multiplication @ X1 @ X0 )
= zero )
& ( ( addition @ X0 @ X1 )
= one ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',test_2) ).
thf(4,axiom,
! [X0: $i] :
( ( test @ X0 )
<=> ? [X1: $i] : ( complement @ X1 @ X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',test_1) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( leq @ A @ B )
<=> ( ( addition @ A @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',order) ).
thf(6,axiom,
! [A: $i] :
( ( multiplication @ zero @ A )
= zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_annihilation) ).
thf(7,axiom,
! [A: $i] :
( ( multiplication @ A @ zero )
= zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_annihilation) ).
thf(8,axiom,
! [A: $i,B: $i,C: $i] :
( ( multiplication @ ( addition @ A @ B ) @ C )
= ( addition @ ( multiplication @ A @ C ) @ ( multiplication @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_distributivity) ).
thf(9,axiom,
! [A: $i,B: $i,C: $i] :
( ( multiplication @ A @ ( addition @ B @ C ) )
= ( addition @ ( multiplication @ A @ B ) @ ( multiplication @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_distributivity) ).
thf(10,axiom,
! [A: $i] :
( ( multiplication @ one @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_left_identity) ).
thf(11,axiom,
! [A: $i] :
( ( multiplication @ A @ one )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_right_identity) ).
thf(12,axiom,
! [A: $i,B: $i,C: $i] :
( ( multiplication @ A @ ( multiplication @ B @ C ) )
= ( multiplication @ ( multiplication @ A @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_associativity) ).
thf(13,axiom,
! [A: $i] :
( ( addition @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_idempotence) ).
thf(14,axiom,
! [A: $i] :
( ( addition @ A @ zero )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_identity) ).
thf(15,axiom,
! [C: $i,B: $i,A: $i] :
( ( addition @ A @ ( addition @ B @ C ) )
= ( addition @ ( addition @ A @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_associativity) ).
thf(16,axiom,
! [A: $i,B: $i] :
( ( addition @ A @ B )
= ( addition @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_commutativity) ).
thf(17,conjecture,
! [X0: $i,X1: $i] :
( ( ( test @ X1 )
& ( test @ X0 ) )
=> ( ( leq @ one @ ( addition @ ( multiplication @ ( addition @ X0 @ ( c @ X0 ) ) @ X1 ) @ ( multiplication @ ( addition @ X0 @ ( c @ X0 ) ) @ ( c @ X1 ) ) ) )
& ( leq @ ( addition @ ( multiplication @ ( addition @ X0 @ ( c @ X0 ) ) @ X1 ) @ ( multiplication @ ( addition @ X0 @ ( c @ X0 ) ) @ ( c @ X1 ) ) ) @ one ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
thf(18,negated_conjecture,
( ( ! [X0: $i,X1: $i] :
( ( ( test @ X1 )
& ( test @ X0 ) )
=> ( ( leq @ one @ ( addition @ ( multiplication @ ( addition @ X0 @ ( c @ X0 ) ) @ X1 ) @ ( multiplication @ ( addition @ X0 @ ( c @ X0 ) ) @ ( c @ X1 ) ) ) )
& ( leq @ ( addition @ ( multiplication @ ( addition @ X0 @ ( c @ X0 ) ) @ X1 ) @ ( multiplication @ ( addition @ X0 @ ( c @ X0 ) ) @ ( c @ X1 ) ) ) @ one ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[17]) ).
thf(19,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( test @ X1 )
& ( test @ X0 ) )
=> ( ( leq @ one @ ( addition @ ( multiplication @ ( addition @ X0 @ ( c @ X0 ) ) @ X1 ) @ ( multiplication @ ( addition @ X0 @ ( c @ X0 ) ) @ ( c @ X1 ) ) ) )
& ( leq @ ( addition @ ( multiplication @ ( addition @ X0 @ ( c @ X0 ) ) @ X1 ) @ ( multiplication @ ( addition @ X0 @ ( c @ X0 ) ) @ ( c @ X1 ) ) ) @ one ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[18]) ).
thf(20,plain,
( ( ! [X0: $i] :
( ~ ( test @ X0 )
=> ( ( c @ X0 )
= zero ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(21,plain,
( ( ! [X0: $i,X1: $i] :
( ( test @ X0 )
=> ( ( ( c @ X0 )
= X1 )
<=> ( complement @ X0 @ X1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(22,plain,
( ( ! [X0: $i,X1: $i] :
( ( complement @ X1 @ X0 )
<=> ( ( ( multiplication @ X0 @ X1 )
= zero )
& ( ( multiplication @ X1 @ X0 )
= zero )
& ( ( addition @ X0 @ X1 )
= one ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(23,plain,
( ( ! [X0: $i] :
( ( test @ X0 )
<=> ? [X1: $i] : ( complement @ X1 @ X0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(24,plain,
( ( ! [A: $i,B: $i] :
( ( leq @ A @ B )
<=> ( ( addition @ A @ B )
= B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(25,plain,
( ( ! [A: $i] :
( ( multiplication @ zero @ A )
= zero ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(26,plain,
( ( ! [A: $i] :
( ( multiplication @ A @ zero )
= zero ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(27,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( multiplication @ ( addition @ A @ B ) @ C )
= ( addition @ ( multiplication @ A @ C ) @ ( multiplication @ B @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(28,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( multiplication @ A @ ( addition @ B @ C ) )
= ( addition @ ( multiplication @ A @ B ) @ ( multiplication @ A @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(29,plain,
( ( ! [A: $i] :
( ( multiplication @ one @ A )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(30,plain,
( ( ! [A: $i] :
( ( multiplication @ A @ one )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(31,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( multiplication @ A @ ( multiplication @ B @ C ) )
= ( multiplication @ ( multiplication @ A @ B ) @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(32,plain,
( ( ! [A: $i] :
( ( addition @ A @ A )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(33,plain,
( ( ! [A: $i] :
( ( addition @ A @ zero )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(34,plain,
( ( ! [C: $i,B: $i,A: $i] :
( ( addition @ A @ ( addition @ B @ C ) )
= ( addition @ ( addition @ A @ B ) @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(35,plain,
( ( ! [A: $i,B: $i] :
( ( addition @ A @ B )
= ( addition @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(36,plain,
( ( ! [SY31: $i] :
( ( ( test @ SY31 )
& ( test @ sK1_X0 ) )
=> ( ( leq @ one @ ( addition @ ( multiplication @ ( addition @ sK1_X0 @ ( c @ sK1_X0 ) ) @ SY31 ) @ ( multiplication @ ( addition @ sK1_X0 @ ( c @ sK1_X0 ) ) @ ( c @ SY31 ) ) ) )
& ( leq @ ( addition @ ( multiplication @ ( addition @ sK1_X0 @ ( c @ sK1_X0 ) ) @ SY31 ) @ ( multiplication @ ( addition @ sK1_X0 @ ( c @ sK1_X0 ) ) @ ( c @ SY31 ) ) ) @ one ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[19]) ).
thf(37,plain,
( ( ( ( test @ sK2_SY31 )
& ( test @ sK1_X0 ) )
=> ( ( leq @ one @ ( addition @ ( multiplication @ ( addition @ sK1_X0 @ ( c @ sK1_X0 ) ) @ sK2_SY31 ) @ ( multiplication @ ( addition @ sK1_X0 @ ( c @ sK1_X0 ) ) @ ( c @ sK2_SY31 ) ) ) )
& ( leq @ ( addition @ ( multiplication @ ( addition @ sK1_X0 @ ( c @ sK1_X0 ) ) @ sK2_SY31 ) @ ( multiplication @ ( addition @ sK1_X0 @ ( c @ sK1_X0 ) ) @ ( c @ sK2_SY31 ) ) ) @ one ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[36]) ).
thf(38,plain,
( ( test @ sK2_SY31 )
= $true ),
inference(standard_cnf,[status(thm)],[37]) ).
thf(39,plain,
( ( test @ sK1_X0 )
= $true ),
inference(standard_cnf,[status(thm)],[37]) ).
thf(40,plain,
( ( ( leq @ one @ ( addition @ ( multiplication @ ( addition @ sK1_X0 @ ( c @ sK1_X0 ) ) @ sK2_SY31 ) @ ( multiplication @ ( addition @ sK1_X0 @ ( c @ sK1_X0 ) ) @ ( c @ sK2_SY31 ) ) ) )
& ( leq @ ( addition @ ( multiplication @ ( addition @ sK1_X0 @ ( c @ sK1_X0 ) ) @ sK2_SY31 ) @ ( multiplication @ ( addition @ sK1_X0 @ ( c @ sK1_X0 ) ) @ ( c @ sK2_SY31 ) ) ) @ one ) )
= $false ),
inference(standard_cnf,[status(thm)],[37]) ).
thf(41,plain,
( ( leq @ one @ ( addition @ ( multiplication @ ( addition @ sK1_X0 @ ( c @ sK1_X0 ) ) @ sK2_SY31 ) @ ( multiplication @ ( addition @ sK1_X0 @ ( c @ sK1_X0 ) ) @ ( c @ sK2_SY31 ) ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[40]) ).
thf(42,plain,
( ( leq @ ( addition @ ( multiplication @ ( addition @ sK1_X0 @ ( c @ sK1_X0 ) ) @ sK2_SY31 ) @ ( multiplication @ ( addition @ sK1_X0 @ ( c @ sK1_X0 ) ) @ ( c @ sK2_SY31 ) ) ) @ one )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[40]) ).
thf(43,plain,
( ( ~ ( leq @ one @ ( addition @ ( multiplication @ ( addition @ sK1_X0 @ ( c @ sK1_X0 ) ) @ sK2_SY31 ) @ ( multiplication @ ( addition @ sK1_X0 @ ( c @ sK1_X0 ) ) @ ( c @ sK2_SY31 ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[41]) ).
thf(44,plain,
( ( ~ ( leq @ ( addition @ ( multiplication @ ( addition @ sK1_X0 @ ( c @ sK1_X0 ) ) @ sK2_SY31 ) @ ( multiplication @ ( addition @ sK1_X0 @ ( c @ sK1_X0 ) ) @ ( c @ sK2_SY31 ) ) ) @ one ) )
= $true ),
inference(polarity_switch,[status(thm)],[42]) ).
thf(45,plain,
( ( ! [X0: $i] :
( ( test @ X0 )
| ( ( c @ X0 )
= zero ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[20]) ).
thf(46,plain,
( ( ! [X0: $i] :
( ~ ( test @ X0 )
| ! [X1: $i] :
( ( ( c @ X0 )
!= X1 )
| ( complement @ X0 @ X1 ) ) )
& ! [X0: $i] :
( ~ ( test @ X0 )
| ! [X1: $i] :
( ~ ( complement @ X0 @ X1 )
| ( ( c @ X0 )
= X1 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[21]) ).
thf(47,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( multiplication @ X0 @ X1 )
!= zero )
| ( ( multiplication @ X1 @ X0 )
!= zero )
| ( ( addition @ X0 @ X1 )
!= one )
| ( complement @ X1 @ X0 ) )
& ! [X0: $i,X1: $i] :
( ~ ( complement @ X1 @ X0 )
| ( ( multiplication @ X0 @ X1 )
= zero ) )
& ! [X0: $i,X1: $i] :
( ~ ( complement @ X1 @ X0 )
| ( ( multiplication @ X1 @ X0 )
= zero ) )
& ! [X0: $i,X1: $i] :
( ~ ( complement @ X1 @ X0 )
| ( ( addition @ X0 @ X1 )
= one ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[22]) ).
thf(48,plain,
( ( ! [X0: $i] :
( ! [X1: $i] :
~ ( complement @ X1 @ X0 )
| ( test @ X0 ) )
& ! [X0: $i] :
( ~ ( test @ X0 )
| ( complement @ ( sK3_X1 @ X0 ) @ X0 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[23]) ).
thf(49,plain,
( ( ! [A: $i,B: $i] :
( ( ( addition @ A @ B )
!= B )
| ( leq @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( leq @ A @ B )
| ( ( addition @ A @ B )
= B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[24]) ).
thf(50,plain,
( ( ! [A: $i,B: $i] :
( ( addition @ A @ B )
= ( addition @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(51,plain,
( ( ! [C: $i,B: $i,A: $i] :
( ( addition @ A @ ( addition @ B @ C ) )
= ( addition @ ( addition @ A @ B ) @ C ) ) )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(52,plain,
( ( ! [A: $i] :
( ( addition @ A @ zero )
= A ) )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(53,plain,
( ( ! [A: $i] :
( ( addition @ A @ A )
= A ) )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(54,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( multiplication @ A @ ( multiplication @ B @ C ) )
= ( multiplication @ ( multiplication @ A @ B ) @ C ) ) )
= $true ),
inference(copy,[status(thm)],[31]) ).
thf(55,plain,
( ( ! [A: $i] :
( ( multiplication @ A @ one )
= A ) )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(56,plain,
( ( ! [A: $i] :
( ( multiplication @ one @ A )
= A ) )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(57,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( multiplication @ A @ ( addition @ B @ C ) )
= ( addition @ ( multiplication @ A @ B ) @ ( multiplication @ A @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[28]) ).
thf(58,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( multiplication @ ( addition @ A @ B ) @ C )
= ( addition @ ( multiplication @ A @ C ) @ ( multiplication @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(59,plain,
( ( ! [A: $i] :
( ( multiplication @ A @ zero )
= zero ) )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(60,plain,
( ( ! [A: $i] :
( ( multiplication @ zero @ A )
= zero ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(61,plain,
( ( ! [A: $i,B: $i] :
( ( ( addition @ A @ B )
!= B )
| ( leq @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( leq @ A @ B )
| ( ( addition @ A @ B )
= B ) ) )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(62,plain,
( ( ! [X0: $i] :
( ! [X1: $i] :
~ ( complement @ X1 @ X0 )
| ( test @ X0 ) )
& ! [X0: $i] :
( ~ ( test @ X0 )
| ( complement @ ( sK3_X1 @ X0 ) @ X0 ) ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(63,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( multiplication @ X0 @ X1 )
!= zero )
| ( ( multiplication @ X1 @ X0 )
!= zero )
| ( ( addition @ X0 @ X1 )
!= one )
| ( complement @ X1 @ X0 ) )
& ! [X0: $i,X1: $i] :
( ~ ( complement @ X1 @ X0 )
| ( ( multiplication @ X0 @ X1 )
= zero ) )
& ! [X0: $i,X1: $i] :
( ~ ( complement @ X1 @ X0 )
| ( ( multiplication @ X1 @ X0 )
= zero ) )
& ! [X0: $i,X1: $i] :
( ~ ( complement @ X1 @ X0 )
| ( ( addition @ X0 @ X1 )
= one ) ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(64,plain,
( ( ! [X0: $i] :
( ~ ( test @ X0 )
| ! [X1: $i] :
( ( ( c @ X0 )
!= X1 )
| ( complement @ X0 @ X1 ) ) )
& ! [X0: $i] :
( ~ ( test @ X0 )
| ! [X1: $i] :
( ~ ( complement @ X0 @ X1 )
| ( ( c @ X0 )
= X1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(65,plain,
( ( ! [X0: $i] :
( ( test @ X0 )
| ( ( c @ X0 )
= zero ) ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(66,plain,
( ( test @ sK1_X0 )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(67,plain,
( ( test @ sK2_SY31 )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(68,plain,
( ( ~ ( leq @ one @ ( addition @ ( multiplication @ ( addition @ sK1_X0 @ ( c @ sK1_X0 ) ) @ sK2_SY31 ) @ ( multiplication @ ( addition @ sK1_X0 @ ( c @ sK1_X0 ) ) @ ( c @ sK2_SY31 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(69,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( test @ SX0 )
| ! [SX1: $i] :
( ( ( c @ SX0 )
!= SX1 )
| ( complement @ SX0 @ SX1 ) ) )
| ~ ! [SX0: $i] :
( ~ ( test @ SX0 )
| ! [SX1: $i] :
( ~ ( complement @ SX0 @ SX1 )
| ( ( c @ SX0 )
= SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[64]) ).
thf(70,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( ( addition @ SX0 @ SX1 )
!= SX1 )
| ( leq @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( leq @ SX0 @ SX1 )
| ( ( addition @ SX0 @ SX1 )
= SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[61]) ).
thf(71,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( ( multiplication @ SX0 @ SX1 )
!= zero )
| ( ( multiplication @ SX1 @ SX0 )
!= zero )
| ( ( addition @ SX0 @ SX1 )
!= one )
| ( complement @ SX1 @ SX0 ) )
| ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( complement @ SX1 @ SX0 )
| ( ( multiplication @ SX0 @ SX1 )
= zero ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( complement @ SX1 @ SX0 )
| ( ( multiplication @ SX1 @ SX0 )
= zero ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( complement @ SX1 @ SX0 )
| ( ( addition @ SX0 @ SX1 )
= one ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[63]) ).
thf(72,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( complement @ SX1 @ SX0 )
| ( test @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( test @ SX0 )
| ( complement @ ( sK3_X1 @ SX0 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[62]) ).
thf(73,plain,
! [SV1: $i] :
( ( ! [SY32: $i] :
( ( addition @ SV1 @ SY32 )
= ( addition @ SY32 @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[50]) ).
thf(74,plain,
! [SV2: $i] :
( ( ! [SY33: $i,SY34: $i] :
( ( addition @ SY34 @ ( addition @ SY33 @ SV2 ) )
= ( addition @ ( addition @ SY34 @ SY33 ) @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[51]) ).
thf(75,plain,
! [SV3: $i] :
( ( ( addition @ SV3 @ zero )
= SV3 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[52]) ).
thf(76,plain,
! [SV4: $i] :
( ( ( addition @ SV4 @ SV4 )
= SV4 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[53]) ).
thf(77,plain,
! [SV5: $i] :
( ( ! [SY35: $i,SY36: $i] :
( ( multiplication @ SV5 @ ( multiplication @ SY35 @ SY36 ) )
= ( multiplication @ ( multiplication @ SV5 @ SY35 ) @ SY36 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[54]) ).
thf(78,plain,
! [SV6: $i] :
( ( ( multiplication @ SV6 @ one )
= SV6 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[55]) ).
thf(79,plain,
! [SV7: $i] :
( ( ( multiplication @ one @ SV7 )
= SV7 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[56]) ).
thf(80,plain,
! [SV8: $i] :
( ( ! [SY37: $i,SY38: $i] :
( ( multiplication @ SV8 @ ( addition @ SY37 @ SY38 ) )
= ( addition @ ( multiplication @ SV8 @ SY37 ) @ ( multiplication @ SV8 @ SY38 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[57]) ).
thf(81,plain,
! [SV9: $i] :
( ( ! [SY39: $i,SY40: $i] :
( ( multiplication @ ( addition @ SV9 @ SY39 ) @ SY40 )
= ( addition @ ( multiplication @ SV9 @ SY40 ) @ ( multiplication @ SY39 @ SY40 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[58]) ).
thf(82,plain,
! [SV10: $i] :
( ( ( multiplication @ SV10 @ zero )
= zero )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[59]) ).
thf(83,plain,
! [SV11: $i] :
( ( ( multiplication @ zero @ SV11 )
= zero )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[60]) ).
thf(84,plain,
! [SV12: $i] :
( ( ( test @ SV12 )
| ( ( c @ SV12 )
= zero ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[65]) ).
thf(85,plain,
( ( leq @ one @ ( addition @ ( multiplication @ ( addition @ sK1_X0 @ ( c @ sK1_X0 ) ) @ sK2_SY31 ) @ ( multiplication @ ( addition @ sK1_X0 @ ( c @ sK1_X0 ) ) @ ( c @ sK2_SY31 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[68]) ).
thf(86,plain,
( ( ~ ! [SX0: $i] :
( ~ ( test @ SX0 )
| ! [SX1: $i] :
( ( ( c @ SX0 )
!= SX1 )
| ( complement @ SX0 @ SX1 ) ) )
| ~ ! [SX0: $i] :
( ~ ( test @ SX0 )
| ! [SX1: $i] :
( ~ ( complement @ SX0 @ SX1 )
| ( ( c @ SX0 )
= SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[69]) ).
thf(87,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( addition @ SX0 @ SX1 )
!= SX1 )
| ( leq @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( leq @ SX0 @ SX1 )
| ( ( addition @ SX0 @ SX1 )
= SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[70]) ).
thf(88,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( multiplication @ SX0 @ SX1 )
!= zero )
| ( ( multiplication @ SX1 @ SX0 )
!= zero )
| ( ( addition @ SX0 @ SX1 )
!= one )
| ( complement @ SX1 @ SX0 ) )
| ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( complement @ SX1 @ SX0 )
| ( ( multiplication @ SX0 @ SX1 )
= zero ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( complement @ SX1 @ SX0 )
| ( ( multiplication @ SX1 @ SX0 )
= zero ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( complement @ SX1 @ SX0 )
| ( ( addition @ SX0 @ SX1 )
= one ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[71]) ).
thf(89,plain,
( ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( complement @ SX1 @ SX0 )
| ( test @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( test @ SX0 )
| ( complement @ ( sK3_X1 @ SX0 ) @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[72]) ).
thf(90,plain,
! [SV13: $i,SV1: $i] :
( ( ( addition @ SV1 @ SV13 )
= ( addition @ SV13 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[73]) ).
thf(91,plain,
! [SV2: $i,SV14: $i] :
( ( ! [SY41: $i] :
( ( addition @ SY41 @ ( addition @ SV14 @ SV2 ) )
= ( addition @ ( addition @ SY41 @ SV14 ) @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[74]) ).
thf(92,plain,
! [SV15: $i,SV5: $i] :
( ( ! [SY42: $i] :
( ( multiplication @ SV5 @ ( multiplication @ SV15 @ SY42 ) )
= ( multiplication @ ( multiplication @ SV5 @ SV15 ) @ SY42 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[77]) ).
thf(93,plain,
! [SV16: $i,SV8: $i] :
( ( ! [SY43: $i] :
( ( multiplication @ SV8 @ ( addition @ SV16 @ SY43 ) )
= ( addition @ ( multiplication @ SV8 @ SV16 ) @ ( multiplication @ SV8 @ SY43 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[80]) ).
thf(94,plain,
! [SV17: $i,SV9: $i] :
( ( ! [SY44: $i] :
( ( multiplication @ ( addition @ SV9 @ SV17 ) @ SY44 )
= ( addition @ ( multiplication @ SV9 @ SY44 ) @ ( multiplication @ SV17 @ SY44 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[81]) ).
thf(95,plain,
! [SV12: $i] :
( ( ( test @ SV12 )
= $true )
| ( ( ( c @ SV12 )
= zero )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[84]) ).
thf(96,plain,
( ( ~ ! [SX0: $i] :
( ~ ( test @ SX0 )
| ! [SX1: $i] :
( ( ( c @ SX0 )
!= SX1 )
| ( complement @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[86]) ).
thf(97,plain,
( ( ~ ! [SX0: $i] :
( ~ ( test @ SX0 )
| ! [SX1: $i] :
( ~ ( complement @ SX0 @ SX1 )
| ( ( c @ SX0 )
= SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[86]) ).
thf(98,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( addition @ SX0 @ SX1 )
!= SX1 )
| ( leq @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[87]) ).
thf(99,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( leq @ SX0 @ SX1 )
| ( ( addition @ SX0 @ SX1 )
= SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[87]) ).
thf(100,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( multiplication @ SX0 @ SX1 )
!= zero )
| ( ( multiplication @ SX1 @ SX0 )
!= zero )
| ( ( addition @ SX0 @ SX1 )
!= one )
| ( complement @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[88]) ).
thf(101,plain,
( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( complement @ SX1 @ SX0 )
| ( ( multiplication @ SX0 @ SX1 )
= zero ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( complement @ SX1 @ SX0 )
| ( ( multiplication @ SX1 @ SX0 )
= zero ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( complement @ SX1 @ SX0 )
| ( ( addition @ SX0 @ SX1 )
= one ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[88]) ).
thf(102,plain,
( ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( complement @ SX1 @ SX0 )
| ( test @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[89]) ).
thf(103,plain,
( ( ~ ! [SX0: $i] :
( ~ ( test @ SX0 )
| ( complement @ ( sK3_X1 @ SX0 ) @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[89]) ).
thf(104,plain,
! [SV2: $i,SV14: $i,SV18: $i] :
( ( ( addition @ SV18 @ ( addition @ SV14 @ SV2 ) )
= ( addition @ ( addition @ SV18 @ SV14 ) @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[91]) ).
thf(105,plain,
! [SV19: $i,SV15: $i,SV5: $i] :
( ( ( multiplication @ SV5 @ ( multiplication @ SV15 @ SV19 ) )
= ( multiplication @ ( multiplication @ SV5 @ SV15 ) @ SV19 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[92]) ).
thf(106,plain,
! [SV20: $i,SV16: $i,SV8: $i] :
( ( ( multiplication @ SV8 @ ( addition @ SV16 @ SV20 ) )
= ( addition @ ( multiplication @ SV8 @ SV16 ) @ ( multiplication @ SV8 @ SV20 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[93]) ).
thf(107,plain,
! [SV21: $i,SV17: $i,SV9: $i] :
( ( ( multiplication @ ( addition @ SV9 @ SV17 ) @ SV21 )
= ( addition @ ( multiplication @ SV9 @ SV21 ) @ ( multiplication @ SV17 @ SV21 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[94]) ).
thf(108,plain,
( ( ! [SX0: $i] :
( ~ ( test @ SX0 )
| ! [SX1: $i] :
( ( ( c @ SX0 )
!= SX1 )
| ( complement @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[96]) ).
thf(109,plain,
( ( ! [SX0: $i] :
( ~ ( test @ SX0 )
| ! [SX1: $i] :
( ~ ( complement @ SX0 @ SX1 )
| ( ( c @ SX0 )
= SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[97]) ).
thf(110,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( addition @ SX0 @ SX1 )
!= SX1 )
| ( leq @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[98]) ).
thf(111,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( leq @ SX0 @ SX1 )
| ( ( addition @ SX0 @ SX1 )
= SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[99]) ).
thf(112,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( multiplication @ SX0 @ SX1 )
!= zero )
| ( ( multiplication @ SX1 @ SX0 )
!= zero )
| ( ( addition @ SX0 @ SX1 )
!= one )
| ( complement @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[100]) ).
thf(113,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( complement @ SX1 @ SX0 )
| ( ( multiplication @ SX0 @ SX1 )
= zero ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( complement @ SX1 @ SX0 )
| ( ( multiplication @ SX1 @ SX0 )
= zero ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( complement @ SX1 @ SX0 )
| ( ( addition @ SX0 @ SX1 )
= one ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[101]) ).
thf(114,plain,
( ( ! [SX0: $i] :
( ! [SX1: $i] :
~ ( complement @ SX1 @ SX0 )
| ( test @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[102]) ).
thf(115,plain,
( ( ! [SX0: $i] :
( ~ ( test @ SX0 )
| ( complement @ ( sK3_X1 @ SX0 ) @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[103]) ).
thf(116,plain,
! [SV22: $i] :
( ( ~ ( test @ SV22 )
| ! [SY45: $i] :
( ( ( c @ SV22 )
!= SY45 )
| ( complement @ SV22 @ SY45 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[108]) ).
thf(117,plain,
! [SV23: $i] :
( ( ~ ( test @ SV23 )
| ! [SY46: $i] :
( ~ ( complement @ SV23 @ SY46 )
| ( ( c @ SV23 )
= SY46 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[109]) ).
thf(118,plain,
! [SV24: $i] :
( ( ! [SY47: $i] :
( ( ( addition @ SV24 @ SY47 )
!= SY47 )
| ( leq @ SV24 @ SY47 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[110]) ).
thf(119,plain,
! [SV25: $i] :
( ( ! [SY48: $i] :
( ~ ( leq @ SV25 @ SY48 )
| ( ( addition @ SV25 @ SY48 )
= SY48 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[111]) ).
thf(120,plain,
! [SV26: $i] :
( ( ! [SY49: $i] :
( ( ( multiplication @ SV26 @ SY49 )
!= zero )
| ( ( multiplication @ SY49 @ SV26 )
!= zero )
| ( ( addition @ SV26 @ SY49 )
!= one )
| ( complement @ SY49 @ SV26 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[112]) ).
thf(121,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( complement @ SX1 @ SX0 )
| ( ( multiplication @ SX0 @ SX1 )
= zero ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( complement @ SX1 @ SX0 )
| ( ( multiplication @ SX1 @ SX0 )
= zero ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( complement @ SX1 @ SX0 )
| ( ( addition @ SX0 @ SX1 )
= one ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[113]) ).
thf(122,plain,
! [SV27: $i] :
( ( ! [SY50: $i] :
~ ( complement @ SY50 @ SV27 )
| ( test @ SV27 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[114]) ).
thf(123,plain,
! [SV28: $i] :
( ( ~ ( test @ SV28 )
| ( complement @ ( sK3_X1 @ SV28 ) @ SV28 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[115]) ).
thf(124,plain,
! [SV22: $i] :
( ( ( ~ ( test @ SV22 ) )
= $true )
| ( ( ! [SY45: $i] :
( ( ( c @ SV22 )
!= SY45 )
| ( complement @ SV22 @ SY45 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[116]) ).
thf(125,plain,
! [SV23: $i] :
( ( ( ~ ( test @ SV23 ) )
= $true )
| ( ( ! [SY46: $i] :
( ~ ( complement @ SV23 @ SY46 )
| ( ( c @ SV23 )
= SY46 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[117]) ).
thf(126,plain,
! [SV29: $i,SV24: $i] :
( ( ( ( addition @ SV24 @ SV29 )
!= SV29 )
| ( leq @ SV24 @ SV29 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[118]) ).
thf(127,plain,
! [SV30: $i,SV25: $i] :
( ( ~ ( leq @ SV25 @ SV30 )
| ( ( addition @ SV25 @ SV30 )
= SV30 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[119]) ).
thf(128,plain,
! [SV31: $i,SV26: $i] :
( ( ( ( multiplication @ SV26 @ SV31 )
!= zero )
| ( ( multiplication @ SV31 @ SV26 )
!= zero )
| ( ( addition @ SV26 @ SV31 )
!= one )
| ( complement @ SV31 @ SV26 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[120]) ).
thf(129,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( complement @ SX1 @ SX0 )
| ( ( multiplication @ SX0 @ SX1 )
= zero ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( complement @ SX1 @ SX0 )
| ( ( multiplication @ SX1 @ SX0 )
= zero ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[121]) ).
thf(130,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( complement @ SX1 @ SX0 )
| ( ( addition @ SX0 @ SX1 )
= one ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[121]) ).
thf(131,plain,
! [SV27: $i] :
( ( ( ! [SY50: $i] :
~ ( complement @ SY50 @ SV27 ) )
= $true )
| ( ( test @ SV27 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[122]) ).
thf(132,plain,
! [SV28: $i] :
( ( ( ~ ( test @ SV28 ) )
= $true )
| ( ( complement @ ( sK3_X1 @ SV28 ) @ SV28 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[123]) ).
thf(133,plain,
! [SV22: $i] :
( ( ( test @ SV22 )
= $false )
| ( ( ! [SY45: $i] :
( ( ( c @ SV22 )
!= SY45 )
| ( complement @ SV22 @ SY45 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[124]) ).
thf(134,plain,
! [SV23: $i] :
( ( ( test @ SV23 )
= $false )
| ( ( ! [SY46: $i] :
( ~ ( complement @ SV23 @ SY46 )
| ( ( c @ SV23 )
= SY46 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[125]) ).
thf(135,plain,
! [SV29: $i,SV24: $i] :
( ( ( ( ( addition @ SV24 @ SV29 )
!= SV29 ) )
= $true )
| ( ( leq @ SV24 @ SV29 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[126]) ).
thf(136,plain,
! [SV30: $i,SV25: $i] :
( ( ( ~ ( leq @ SV25 @ SV30 ) )
= $true )
| ( ( ( addition @ SV25 @ SV30 )
= SV30 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[127]) ).
thf(137,plain,
! [SV31: $i,SV26: $i] :
( ( ( ( ( multiplication @ SV26 @ SV31 )
!= zero )
| ( ( multiplication @ SV31 @ SV26 )
!= zero )
| ( ( addition @ SV26 @ SV31 )
!= one ) )
= $true )
| ( ( complement @ SV31 @ SV26 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[128]) ).
thf(138,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( complement @ SX1 @ SX0 )
| ( ( multiplication @ SX0 @ SX1 )
= zero ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( complement @ SX1 @ SX0 )
| ( ( multiplication @ SX1 @ SX0 )
= zero ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[129]) ).
thf(139,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( complement @ SX1 @ SX0 )
| ( ( addition @ SX0 @ SX1 )
= one ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[130]) ).
thf(140,plain,
! [SV27: $i,SV32: $i] :
( ( ( ~ ( complement @ SV32 @ SV27 ) )
= $true )
| ( ( test @ SV27 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[131]) ).
thf(141,plain,
! [SV28: $i] :
( ( ( test @ SV28 )
= $false )
| ( ( complement @ ( sK3_X1 @ SV28 ) @ SV28 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[132]) ).
thf(142,plain,
! [SV33: $i,SV22: $i] :
( ( ( ( ( c @ SV22 )
!= SV33 )
| ( complement @ SV22 @ SV33 ) )
= $true )
| ( ( test @ SV22 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[133]) ).
thf(143,plain,
! [SV34: $i,SV23: $i] :
( ( ( ~ ( complement @ SV23 @ SV34 )
| ( ( c @ SV23 )
= SV34 ) )
= $true )
| ( ( test @ SV23 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[134]) ).
thf(144,plain,
! [SV29: $i,SV24: $i] :
( ( ( ( addition @ SV24 @ SV29 )
= SV29 )
= $false )
| ( ( leq @ SV24 @ SV29 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[135]) ).
thf(145,plain,
! [SV30: $i,SV25: $i] :
( ( ( leq @ SV25 @ SV30 )
= $false )
| ( ( ( addition @ SV25 @ SV30 )
= SV30 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[136]) ).
thf(146,plain,
! [SV31: $i,SV26: $i] :
( ( ( ( ( multiplication @ SV26 @ SV31 )
!= zero )
| ( ( multiplication @ SV31 @ SV26 )
!= zero ) )
= $true )
| ( ( ( ( addition @ SV26 @ SV31 )
!= one ) )
= $true )
| ( ( complement @ SV31 @ SV26 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[137]) ).
thf(147,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( complement @ SX1 @ SX0 )
| ( ( multiplication @ SX0 @ SX1 )
= zero ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( complement @ SX1 @ SX0 )
| ( ( multiplication @ SX1 @ SX0 )
= zero ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[138]) ).
thf(148,plain,
! [SV35: $i] :
( ( ! [SY51: $i] :
( ~ ( complement @ SY51 @ SV35 )
| ( ( addition @ SV35 @ SY51 )
= one ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[139]) ).
thf(149,plain,
! [SV27: $i,SV32: $i] :
( ( ( complement @ SV32 @ SV27 )
= $false )
| ( ( test @ SV27 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[140]) ).
thf(150,plain,
! [SV33: $i,SV22: $i] :
( ( ( ( ( c @ SV22 )
!= SV33 ) )
= $true )
| ( ( complement @ SV22 @ SV33 )
= $true )
| ( ( test @ SV22 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[142]) ).
thf(151,plain,
! [SV34: $i,SV23: $i] :
( ( ( ~ ( complement @ SV23 @ SV34 ) )
= $true )
| ( ( ( c @ SV23 )
= SV34 )
= $true )
| ( ( test @ SV23 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[143]) ).
thf(152,plain,
! [SV31: $i,SV26: $i] :
( ( ( ( ( multiplication @ SV26 @ SV31 )
!= zero ) )
= $true )
| ( ( ( ( multiplication @ SV31 @ SV26 )
!= zero ) )
= $true )
| ( ( ( ( addition @ SV26 @ SV31 )
!= one ) )
= $true )
| ( ( complement @ SV31 @ SV26 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[146]) ).
thf(153,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( complement @ SX1 @ SX0 )
| ( ( multiplication @ SX0 @ SX1 )
= zero ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[147]) ).
thf(154,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( complement @ SX1 @ SX0 )
| ( ( multiplication @ SX1 @ SX0 )
= zero ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[147]) ).
thf(155,plain,
! [SV35: $i,SV36: $i] :
( ( ~ ( complement @ SV36 @ SV35 )
| ( ( addition @ SV35 @ SV36 )
= one ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[148]) ).
thf(156,plain,
! [SV33: $i,SV22: $i] :
( ( ( ( c @ SV22 )
= SV33 )
= $false )
| ( ( complement @ SV22 @ SV33 )
= $true )
| ( ( test @ SV22 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[150]) ).
thf(157,plain,
! [SV34: $i,SV23: $i] :
( ( ( complement @ SV23 @ SV34 )
= $false )
| ( ( ( c @ SV23 )
= SV34 )
= $true )
| ( ( test @ SV23 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[151]) ).
thf(158,plain,
! [SV31: $i,SV26: $i] :
( ( ( ( multiplication @ SV26 @ SV31 )
= zero )
= $false )
| ( ( ( ( multiplication @ SV31 @ SV26 )
!= zero ) )
= $true )
| ( ( ( ( addition @ SV26 @ SV31 )
!= one ) )
= $true )
| ( ( complement @ SV31 @ SV26 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[152]) ).
thf(159,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( complement @ SX1 @ SX0 )
| ( ( multiplication @ SX0 @ SX1 )
= zero ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[153]) ).
thf(160,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( complement @ SX1 @ SX0 )
| ( ( multiplication @ SX1 @ SX0 )
= zero ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[154]) ).
thf(161,plain,
! [SV35: $i,SV36: $i] :
( ( ( ~ ( complement @ SV36 @ SV35 ) )
= $true )
| ( ( ( addition @ SV35 @ SV36 )
= one )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[155]) ).
thf(162,plain,
! [SV26: $i,SV31: $i] :
( ( ( ( multiplication @ SV31 @ SV26 )
= zero )
= $false )
| ( ( ( multiplication @ SV26 @ SV31 )
= zero )
= $false )
| ( ( ( ( addition @ SV26 @ SV31 )
!= one ) )
= $true )
| ( ( complement @ SV31 @ SV26 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[158]) ).
thf(163,plain,
! [SV37: $i] :
( ( ! [SY52: $i] :
( ~ ( complement @ SY52 @ SV37 )
| ( ( multiplication @ SV37 @ SY52 )
= zero ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[159]) ).
thf(164,plain,
! [SV38: $i] :
( ( ! [SY53: $i] :
( ~ ( complement @ SY53 @ SV38 )
| ( ( multiplication @ SY53 @ SV38 )
= zero ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[160]) ).
thf(165,plain,
! [SV35: $i,SV36: $i] :
( ( ( complement @ SV36 @ SV35 )
= $false )
| ( ( ( addition @ SV35 @ SV36 )
= one )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[161]) ).
thf(166,plain,
! [SV31: $i,SV26: $i] :
( ( ( ( addition @ SV26 @ SV31 )
= one )
= $false )
| ( ( ( multiplication @ SV26 @ SV31 )
= zero )
= $false )
| ( ( ( multiplication @ SV31 @ SV26 )
= zero )
= $false )
| ( ( complement @ SV31 @ SV26 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[162]) ).
thf(167,plain,
! [SV37: $i,SV39: $i] :
( ( ~ ( complement @ SV39 @ SV37 )
| ( ( multiplication @ SV37 @ SV39 )
= zero ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[163]) ).
thf(168,plain,
! [SV38: $i,SV40: $i] :
( ( ~ ( complement @ SV40 @ SV38 )
| ( ( multiplication @ SV40 @ SV38 )
= zero ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[164]) ).
thf(169,plain,
! [SV37: $i,SV39: $i] :
( ( ( ~ ( complement @ SV39 @ SV37 ) )
= $true )
| ( ( ( multiplication @ SV37 @ SV39 )
= zero )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[167]) ).
thf(170,plain,
! [SV38: $i,SV40: $i] :
( ( ( ~ ( complement @ SV40 @ SV38 ) )
= $true )
| ( ( ( multiplication @ SV40 @ SV38 )
= zero )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[168]) ).
thf(171,plain,
! [SV37: $i,SV39: $i] :
( ( ( complement @ SV39 @ SV37 )
= $false )
| ( ( ( multiplication @ SV37 @ SV39 )
= zero )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[169]) ).
thf(172,plain,
! [SV38: $i,SV40: $i] :
( ( ( complement @ SV40 @ SV38 )
= $false )
| ( ( ( multiplication @ SV40 @ SV38 )
= zero )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[170]) ).
thf(173,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[66,172,171,166,165,157,156,149,145,144,141,107,106,105,104,95,90,85,83,82,79,78,76,75,67]) ).
thf(174,plain,
( ( ! [A: $i,B: $i] :
( ( addition @ A @ B )
= ( addition @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(175,plain,
( ( ! [C: $i,B: $i,A: $i] :
( ( addition @ A @ ( addition @ B @ C ) )
= ( addition @ ( addition @ A @ B ) @ C ) ) )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(176,plain,
( ( ! [A: $i] :
( ( addition @ A @ zero )
= A ) )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(177,plain,
( ( ! [A: $i] :
( ( addition @ A @ A )
= A ) )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(178,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( multiplication @ A @ ( multiplication @ B @ C ) )
= ( multiplication @ ( multiplication @ A @ B ) @ C ) ) )
= $true ),
inference(copy,[status(thm)],[31]) ).
thf(179,plain,
( ( ! [A: $i] :
( ( multiplication @ A @ one )
= A ) )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(180,plain,
( ( ! [A: $i] :
( ( multiplication @ one @ A )
= A ) )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(181,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( multiplication @ A @ ( addition @ B @ C ) )
= ( addition @ ( multiplication @ A @ B ) @ ( multiplication @ A @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[28]) ).
thf(182,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( multiplication @ ( addition @ A @ B ) @ C )
= ( addition @ ( multiplication @ A @ C ) @ ( multiplication @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(183,plain,
( ( ! [A: $i] :
( ( multiplication @ A @ zero )
= zero ) )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(184,plain,
( ( ! [A: $i] :
( ( multiplication @ zero @ A )
= zero ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(185,plain,
( ( ! [A: $i,B: $i] :
( ( ( addition @ A @ B )
!= B )
| ( leq @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( leq @ A @ B )
| ( ( addition @ A @ B )
= B ) ) )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(186,plain,
( ( ! [X0: $i] :
( ! [X1: $i] :
~ ( complement @ X1 @ X0 )
| ( test @ X0 ) )
& ! [X0: $i] :
( ~ ( test @ X0 )
| ( complement @ ( sK3_X1 @ X0 ) @ X0 ) ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(187,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( multiplication @ X0 @ X1 )
!= zero )
| ( ( multiplication @ X1 @ X0 )
!= zero )
| ( ( addition @ X0 @ X1 )
!= one )
| ( complement @ X1 @ X0 ) )
& ! [X0: $i,X1: $i] :
( ~ ( complement @ X1 @ X0 )
| ( ( multiplication @ X0 @ X1 )
= zero ) )
& ! [X0: $i,X1: $i] :
( ~ ( complement @ X1 @ X0 )
| ( ( multiplication @ X1 @ X0 )
= zero ) )
& ! [X0: $i,X1: $i] :
( ~ ( complement @ X1 @ X0 )
| ( ( addition @ X0 @ X1 )
= one ) ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(188,plain,
( ( ! [X0: $i] :
( ~ ( test @ X0 )
| ! [X1: $i] :
( ( ( c @ X0 )
!= X1 )
| ( complement @ X0 @ X1 ) ) )
& ! [X0: $i] :
( ~ ( test @ X0 )
| ! [X1: $i] :
( ~ ( complement @ X0 @ X1 )
| ( ( c @ X0 )
= X1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(189,plain,
( ( ! [X0: $i] :
( ( test @ X0 )
| ( ( c @ X0 )
= zero ) ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(190,plain,
( ( test @ sK1_X0 )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(191,plain,
( ( test @ sK2_SY31 )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(192,plain,
( ( ~ ( leq @ ( addition @ ( multiplication @ ( addition @ sK1_X0 @ ( c @ sK1_X0 ) ) @ sK2_SY31 ) @ ( multiplication @ ( addition @ sK1_X0 @ ( c @ sK1_X0 ) ) @ ( c @ sK2_SY31 ) ) ) @ one ) )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(193,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( ( addition @ SX0 @ SX1 )
!= SX1 )
| ( leq @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( leq @ SX0 @ SX1 )
| ( ( addition @ SX0 @ SX1 )
= SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[185]) ).
thf(194,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( ( multiplication @ SX0 @ SX1 )
!= zero )
| ( ( multiplication @ SX1 @ SX0 )
!= zero )
| ( ( addition @ SX0 @ SX1 )
!= one )
| ( complement @ SX1 @ SX0 ) )
| ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( complement @ SX1 @ SX0 )
| ( ( multiplication @ SX0 @ SX1 )
= zero ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( complement @ SX1 @ SX0 )
| ( ( multiplication @ SX1 @ SX0 )
= zero ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( complement @ SX1 @ SX0 )
| ( ( addition @ SX0 @ SX1 )
= one ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[187]) ).
thf(195,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( complement @ SX1 @ SX0 )
| ( test @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( test @ SX0 )
| ( complement @ ( sK3_X1 @ SX0 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[186]) ).
thf(196,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( test @ SX0 )
| ! [SX1: $i] :
( ( ( c @ SX0 )
!= SX1 )
| ( complement @ SX0 @ SX1 ) ) )
| ~ ! [SX0: $i] :
( ~ ( test @ SX0 )
| ! [SX1: $i] :
( ~ ( complement @ SX0 @ SX1 )
| ( ( c @ SX0 )
= SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[188]) ).
thf(197,plain,
! [SV41: $i] :
( ( ! [SY54: $i] :
( ( addition @ SV41 @ SY54 )
= ( addition @ SY54 @ SV41 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[174]) ).
thf(198,plain,
! [SV42: $i] :
( ( ! [SY55: $i,SY56: $i] :
( ( addition @ SY56 @ ( addition @ SY55 @ SV42 ) )
= ( addition @ ( addition @ SY56 @ SY55 ) @ SV42 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[175]) ).
thf(199,plain,
! [SV43: $i] :
( ( ( addition @ SV43 @ zero )
= SV43 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[176]) ).
thf(200,plain,
! [SV44: $i] :
( ( ( addition @ SV44 @ SV44 )
= SV44 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[177]) ).
thf(201,plain,
! [SV45: $i] :
( ( ! [SY57: $i,SY58: $i] :
( ( multiplication @ SV45 @ ( multiplication @ SY57 @ SY58 ) )
= ( multiplication @ ( multiplication @ SV45 @ SY57 ) @ SY58 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[178]) ).
thf(202,plain,
! [SV46: $i] :
( ( ( multiplication @ SV46 @ one )
= SV46 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[179]) ).
thf(203,plain,
! [SV47: $i] :
( ( ( multiplication @ one @ SV47 )
= SV47 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[180]) ).
thf(204,plain,
! [SV48: $i] :
( ( ! [SY59: $i,SY60: $i] :
( ( multiplication @ SV48 @ ( addition @ SY59 @ SY60 ) )
= ( addition @ ( multiplication @ SV48 @ SY59 ) @ ( multiplication @ SV48 @ SY60 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[181]) ).
thf(205,plain,
! [SV49: $i] :
( ( ! [SY61: $i,SY62: $i] :
( ( multiplication @ ( addition @ SV49 @ SY61 ) @ SY62 )
= ( addition @ ( multiplication @ SV49 @ SY62 ) @ ( multiplication @ SY61 @ SY62 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[182]) ).
thf(206,plain,
! [SV50: $i] :
( ( ( multiplication @ SV50 @ zero )
= zero )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[183]) ).
thf(207,plain,
! [SV51: $i] :
( ( ( multiplication @ zero @ SV51 )
= zero )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[184]) ).
thf(208,plain,
! [SV52: $i] :
( ( ( test @ SV52 )
| ( ( c @ SV52 )
= zero ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[189]) ).
thf(209,plain,
( ( leq @ ( addition @ ( multiplication @ ( addition @ sK1_X0 @ ( c @ sK1_X0 ) ) @ sK2_SY31 ) @ ( multiplication @ ( addition @ sK1_X0 @ ( c @ sK1_X0 ) ) @ ( c @ sK2_SY31 ) ) ) @ one )
= $false ),
inference(extcnf_not_pos,[status(thm)],[192]) ).
thf(210,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( addition @ SX0 @ SX1 )
!= SX1 )
| ( leq @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( leq @ SX0 @ SX1 )
| ( ( addition @ SX0 @ SX1 )
= SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[193]) ).
thf(211,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( multiplication @ SX0 @ SX1 )
!= zero )
| ( ( multiplication @ SX1 @ SX0 )
!= zero )
| ( ( addition @ SX0 @ SX1 )
!= one )
| ( complement @ SX1 @ SX0 ) )
| ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( complement @ SX1 @ SX0 )
| ( ( multiplication @ SX0 @ SX1 )
= zero ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( complement @ SX1 @ SX0 )
| ( ( multiplication @ SX1 @ SX0 )
= zero ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( complement @ SX1 @ SX0 )
| ( ( addition @ SX0 @ SX1 )
= one ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[194]) ).
thf(212,plain,
( ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( complement @ SX1 @ SX0 )
| ( test @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( test @ SX0 )
| ( complement @ ( sK3_X1 @ SX0 ) @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[195]) ).
thf(213,plain,
( ( ~ ! [SX0: $i] :
( ~ ( test @ SX0 )
| ! [SX1: $i] :
( ( ( c @ SX0 )
!= SX1 )
| ( complement @ SX0 @ SX1 ) ) )
| ~ ! [SX0: $i] :
( ~ ( test @ SX0 )
| ! [SX1: $i] :
( ~ ( complement @ SX0 @ SX1 )
| ( ( c @ SX0 )
= SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[196]) ).
thf(214,plain,
! [SV53: $i,SV41: $i] :
( ( ( addition @ SV41 @ SV53 )
= ( addition @ SV53 @ SV41 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[197]) ).
thf(215,plain,
! [SV42: $i,SV54: $i] :
( ( ! [SY63: $i] :
( ( addition @ SY63 @ ( addition @ SV54 @ SV42 ) )
= ( addition @ ( addition @ SY63 @ SV54 ) @ SV42 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[198]) ).
thf(216,plain,
! [SV55: $i,SV45: $i] :
( ( ! [SY64: $i] :
( ( multiplication @ SV45 @ ( multiplication @ SV55 @ SY64 ) )
= ( multiplication @ ( multiplication @ SV45 @ SV55 ) @ SY64 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[201]) ).
thf(217,plain,
! [SV56: $i,SV48: $i] :
( ( ! [SY65: $i] :
( ( multiplication @ SV48 @ ( addition @ SV56 @ SY65 ) )
= ( addition @ ( multiplication @ SV48 @ SV56 ) @ ( multiplication @ SV48 @ SY65 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[204]) ).
thf(218,plain,
! [SV57: $i,SV49: $i] :
( ( ! [SY66: $i] :
( ( multiplication @ ( addition @ SV49 @ SV57 ) @ SY66 )
= ( addition @ ( multiplication @ SV49 @ SY66 ) @ ( multiplication @ SV57 @ SY66 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[205]) ).
thf(219,plain,
! [SV52: $i] :
( ( ( test @ SV52 )
= $true )
| ( ( ( c @ SV52 )
= zero )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[208]) ).
thf(220,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( addition @ SX0 @ SX1 )
!= SX1 )
| ( leq @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[210]) ).
thf(221,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( leq @ SX0 @ SX1 )
| ( ( addition @ SX0 @ SX1 )
= SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[210]) ).
thf(222,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( multiplication @ SX0 @ SX1 )
!= zero )
| ( ( multiplication @ SX1 @ SX0 )
!= zero )
| ( ( addition @ SX0 @ SX1 )
!= one )
| ( complement @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[211]) ).
thf(223,plain,
( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( complement @ SX1 @ SX0 )
| ( ( multiplication @ SX0 @ SX1 )
= zero ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( complement @ SX1 @ SX0 )
| ( ( multiplication @ SX1 @ SX0 )
= zero ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( complement @ SX1 @ SX0 )
| ( ( addition @ SX0 @ SX1 )
= one ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[211]) ).
thf(224,plain,
( ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( complement @ SX1 @ SX0 )
| ( test @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[212]) ).
thf(225,plain,
( ( ~ ! [SX0: $i] :
( ~ ( test @ SX0 )
| ( complement @ ( sK3_X1 @ SX0 ) @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[212]) ).
thf(226,plain,
( ( ~ ! [SX0: $i] :
( ~ ( test @ SX0 )
| ! [SX1: $i] :
( ( ( c @ SX0 )
!= SX1 )
| ( complement @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[213]) ).
thf(227,plain,
( ( ~ ! [SX0: $i] :
( ~ ( test @ SX0 )
| ! [SX1: $i] :
( ~ ( complement @ SX0 @ SX1 )
| ( ( c @ SX0 )
= SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[213]) ).
thf(228,plain,
! [SV42: $i,SV54: $i,SV58: $i] :
( ( ( addition @ SV58 @ ( addition @ SV54 @ SV42 ) )
= ( addition @ ( addition @ SV58 @ SV54 ) @ SV42 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[215]) ).
thf(229,plain,
! [SV59: $i,SV55: $i,SV45: $i] :
( ( ( multiplication @ SV45 @ ( multiplication @ SV55 @ SV59 ) )
= ( multiplication @ ( multiplication @ SV45 @ SV55 ) @ SV59 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[216]) ).
thf(230,plain,
! [SV60: $i,SV56: $i,SV48: $i] :
( ( ( multiplication @ SV48 @ ( addition @ SV56 @ SV60 ) )
= ( addition @ ( multiplication @ SV48 @ SV56 ) @ ( multiplication @ SV48 @ SV60 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[217]) ).
thf(231,plain,
! [SV61: $i,SV57: $i,SV49: $i] :
( ( ( multiplication @ ( addition @ SV49 @ SV57 ) @ SV61 )
= ( addition @ ( multiplication @ SV49 @ SV61 ) @ ( multiplication @ SV57 @ SV61 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[218]) ).
thf(232,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( addition @ SX0 @ SX1 )
!= SX1 )
| ( leq @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[220]) ).
thf(233,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( leq @ SX0 @ SX1 )
| ( ( addition @ SX0 @ SX1 )
= SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[221]) ).
thf(234,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( multiplication @ SX0 @ SX1 )
!= zero )
| ( ( multiplication @ SX1 @ SX0 )
!= zero )
| ( ( addition @ SX0 @ SX1 )
!= one )
| ( complement @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[222]) ).
thf(235,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( complement @ SX1 @ SX0 )
| ( ( multiplication @ SX0 @ SX1 )
= zero ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( complement @ SX1 @ SX0 )
| ( ( multiplication @ SX1 @ SX0 )
= zero ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( complement @ SX1 @ SX0 )
| ( ( addition @ SX0 @ SX1 )
= one ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[223]) ).
thf(236,plain,
( ( ! [SX0: $i] :
( ! [SX1: $i] :
~ ( complement @ SX1 @ SX0 )
| ( test @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[224]) ).
thf(237,plain,
( ( ! [SX0: $i] :
( ~ ( test @ SX0 )
| ( complement @ ( sK3_X1 @ SX0 ) @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[225]) ).
thf(238,plain,
( ( ! [SX0: $i] :
( ~ ( test @ SX0 )
| ! [SX1: $i] :
( ( ( c @ SX0 )
!= SX1 )
| ( complement @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[226]) ).
thf(239,plain,
( ( ! [SX0: $i] :
( ~ ( test @ SX0 )
| ! [SX1: $i] :
( ~ ( complement @ SX0 @ SX1 )
| ( ( c @ SX0 )
= SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[227]) ).
thf(240,plain,
! [SV62: $i] :
( ( ! [SY67: $i] :
( ( ( addition @ SV62 @ SY67 )
!= SY67 )
| ( leq @ SV62 @ SY67 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[232]) ).
thf(241,plain,
! [SV63: $i] :
( ( ! [SY68: $i] :
( ~ ( leq @ SV63 @ SY68 )
| ( ( addition @ SV63 @ SY68 )
= SY68 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[233]) ).
thf(242,plain,
! [SV64: $i] :
( ( ! [SY69: $i] :
( ( ( multiplication @ SV64 @ SY69 )
!= zero )
| ( ( multiplication @ SY69 @ SV64 )
!= zero )
| ( ( addition @ SV64 @ SY69 )
!= one )
| ( complement @ SY69 @ SV64 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[234]) ).
thf(243,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( complement @ SX1 @ SX0 )
| ( ( multiplication @ SX0 @ SX1 )
= zero ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( complement @ SX1 @ SX0 )
| ( ( multiplication @ SX1 @ SX0 )
= zero ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( complement @ SX1 @ SX0 )
| ( ( addition @ SX0 @ SX1 )
= one ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[235]) ).
thf(244,plain,
! [SV65: $i] :
( ( ! [SY70: $i] :
~ ( complement @ SY70 @ SV65 )
| ( test @ SV65 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[236]) ).
thf(245,plain,
! [SV66: $i] :
( ( ~ ( test @ SV66 )
| ( complement @ ( sK3_X1 @ SV66 ) @ SV66 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[237]) ).
thf(246,plain,
! [SV67: $i] :
( ( ~ ( test @ SV67 )
| ! [SY71: $i] :
( ( ( c @ SV67 )
!= SY71 )
| ( complement @ SV67 @ SY71 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[238]) ).
thf(247,plain,
! [SV68: $i] :
( ( ~ ( test @ SV68 )
| ! [SY72: $i] :
( ~ ( complement @ SV68 @ SY72 )
| ( ( c @ SV68 )
= SY72 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[239]) ).
thf(248,plain,
! [SV69: $i,SV62: $i] :
( ( ( ( addition @ SV62 @ SV69 )
!= SV69 )
| ( leq @ SV62 @ SV69 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[240]) ).
thf(249,plain,
! [SV70: $i,SV63: $i] :
( ( ~ ( leq @ SV63 @ SV70 )
| ( ( addition @ SV63 @ SV70 )
= SV70 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[241]) ).
thf(250,plain,
! [SV71: $i,SV64: $i] :
( ( ( ( multiplication @ SV64 @ SV71 )
!= zero )
| ( ( multiplication @ SV71 @ SV64 )
!= zero )
| ( ( addition @ SV64 @ SV71 )
!= one )
| ( complement @ SV71 @ SV64 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[242]) ).
thf(251,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( complement @ SX1 @ SX0 )
| ( ( multiplication @ SX0 @ SX1 )
= zero ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( complement @ SX1 @ SX0 )
| ( ( multiplication @ SX1 @ SX0 )
= zero ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[243]) ).
thf(252,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( complement @ SX1 @ SX0 )
| ( ( addition @ SX0 @ SX1 )
= one ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[243]) ).
thf(253,plain,
! [SV65: $i] :
( ( ( ! [SY70: $i] :
~ ( complement @ SY70 @ SV65 ) )
= $true )
| ( ( test @ SV65 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[244]) ).
thf(254,plain,
! [SV66: $i] :
( ( ( ~ ( test @ SV66 ) )
= $true )
| ( ( complement @ ( sK3_X1 @ SV66 ) @ SV66 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[245]) ).
thf(255,plain,
! [SV67: $i] :
( ( ( ~ ( test @ SV67 ) )
= $true )
| ( ( ! [SY71: $i] :
( ( ( c @ SV67 )
!= SY71 )
| ( complement @ SV67 @ SY71 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[246]) ).
thf(256,plain,
! [SV68: $i] :
( ( ( ~ ( test @ SV68 ) )
= $true )
| ( ( ! [SY72: $i] :
( ~ ( complement @ SV68 @ SY72 )
| ( ( c @ SV68 )
= SY72 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[247]) ).
thf(257,plain,
! [SV69: $i,SV62: $i] :
( ( ( ( ( addition @ SV62 @ SV69 )
!= SV69 ) )
= $true )
| ( ( leq @ SV62 @ SV69 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[248]) ).
thf(258,plain,
! [SV70: $i,SV63: $i] :
( ( ( ~ ( leq @ SV63 @ SV70 ) )
= $true )
| ( ( ( addition @ SV63 @ SV70 )
= SV70 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[249]) ).
thf(259,plain,
! [SV71: $i,SV64: $i] :
( ( ( ( ( multiplication @ SV64 @ SV71 )
!= zero )
| ( ( multiplication @ SV71 @ SV64 )
!= zero )
| ( ( addition @ SV64 @ SV71 )
!= one ) )
= $true )
| ( ( complement @ SV71 @ SV64 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[250]) ).
thf(260,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( complement @ SX1 @ SX0 )
| ( ( multiplication @ SX0 @ SX1 )
= zero ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( complement @ SX1 @ SX0 )
| ( ( multiplication @ SX1 @ SX0 )
= zero ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[251]) ).
thf(261,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( complement @ SX1 @ SX0 )
| ( ( addition @ SX0 @ SX1 )
= one ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[252]) ).
thf(262,plain,
! [SV65: $i,SV72: $i] :
( ( ( ~ ( complement @ SV72 @ SV65 ) )
= $true )
| ( ( test @ SV65 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[253]) ).
thf(263,plain,
! [SV66: $i] :
( ( ( test @ SV66 )
= $false )
| ( ( complement @ ( sK3_X1 @ SV66 ) @ SV66 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[254]) ).
thf(264,plain,
! [SV67: $i] :
( ( ( test @ SV67 )
= $false )
| ( ( ! [SY71: $i] :
( ( ( c @ SV67 )
!= SY71 )
| ( complement @ SV67 @ SY71 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[255]) ).
thf(265,plain,
! [SV68: $i] :
( ( ( test @ SV68 )
= $false )
| ( ( ! [SY72: $i] :
( ~ ( complement @ SV68 @ SY72 )
| ( ( c @ SV68 )
= SY72 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[256]) ).
thf(266,plain,
! [SV69: $i,SV62: $i] :
( ( ( ( addition @ SV62 @ SV69 )
= SV69 )
= $false )
| ( ( leq @ SV62 @ SV69 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[257]) ).
thf(267,plain,
! [SV70: $i,SV63: $i] :
( ( ( leq @ SV63 @ SV70 )
= $false )
| ( ( ( addition @ SV63 @ SV70 )
= SV70 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[258]) ).
thf(268,plain,
! [SV71: $i,SV64: $i] :
( ( ( ( ( multiplication @ SV64 @ SV71 )
!= zero )
| ( ( multiplication @ SV71 @ SV64 )
!= zero ) )
= $true )
| ( ( ( ( addition @ SV64 @ SV71 )
!= one ) )
= $true )
| ( ( complement @ SV71 @ SV64 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[259]) ).
thf(269,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( complement @ SX1 @ SX0 )
| ( ( multiplication @ SX0 @ SX1 )
= zero ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( complement @ SX1 @ SX0 )
| ( ( multiplication @ SX1 @ SX0 )
= zero ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[260]) ).
thf(270,plain,
! [SV73: $i] :
( ( ! [SY73: $i] :
( ~ ( complement @ SY73 @ SV73 )
| ( ( addition @ SV73 @ SY73 )
= one ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[261]) ).
thf(271,plain,
! [SV65: $i,SV72: $i] :
( ( ( complement @ SV72 @ SV65 )
= $false )
| ( ( test @ SV65 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[262]) ).
thf(272,plain,
! [SV74: $i,SV67: $i] :
( ( ( ( ( c @ SV67 )
!= SV74 )
| ( complement @ SV67 @ SV74 ) )
= $true )
| ( ( test @ SV67 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[264]) ).
thf(273,plain,
! [SV75: $i,SV68: $i] :
( ( ( ~ ( complement @ SV68 @ SV75 )
| ( ( c @ SV68 )
= SV75 ) )
= $true )
| ( ( test @ SV68 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[265]) ).
thf(274,plain,
! [SV71: $i,SV64: $i] :
( ( ( ( ( multiplication @ SV64 @ SV71 )
!= zero ) )
= $true )
| ( ( ( ( multiplication @ SV71 @ SV64 )
!= zero ) )
= $true )
| ( ( ( ( addition @ SV64 @ SV71 )
!= one ) )
= $true )
| ( ( complement @ SV71 @ SV64 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[268]) ).
thf(275,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( complement @ SX1 @ SX0 )
| ( ( multiplication @ SX0 @ SX1 )
= zero ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[269]) ).
thf(276,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( complement @ SX1 @ SX0 )
| ( ( multiplication @ SX1 @ SX0 )
= zero ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[269]) ).
thf(277,plain,
! [SV73: $i,SV76: $i] :
( ( ~ ( complement @ SV76 @ SV73 )
| ( ( addition @ SV73 @ SV76 )
= one ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[270]) ).
thf(278,plain,
! [SV74: $i,SV67: $i] :
( ( ( ( ( c @ SV67 )
!= SV74 ) )
= $true )
| ( ( complement @ SV67 @ SV74 )
= $true )
| ( ( test @ SV67 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[272]) ).
thf(279,plain,
! [SV75: $i,SV68: $i] :
( ( ( ~ ( complement @ SV68 @ SV75 ) )
= $true )
| ( ( ( c @ SV68 )
= SV75 )
= $true )
| ( ( test @ SV68 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[273]) ).
thf(280,plain,
! [SV71: $i,SV64: $i] :
( ( ( ( multiplication @ SV64 @ SV71 )
= zero )
= $false )
| ( ( ( ( multiplication @ SV71 @ SV64 )
!= zero ) )
= $true )
| ( ( ( ( addition @ SV64 @ SV71 )
!= one ) )
= $true )
| ( ( complement @ SV71 @ SV64 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[274]) ).
thf(281,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( complement @ SX1 @ SX0 )
| ( ( multiplication @ SX0 @ SX1 )
= zero ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[275]) ).
thf(282,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( complement @ SX1 @ SX0 )
| ( ( multiplication @ SX1 @ SX0 )
= zero ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[276]) ).
thf(283,plain,
! [SV73: $i,SV76: $i] :
( ( ( ~ ( complement @ SV76 @ SV73 ) )
= $true )
| ( ( ( addition @ SV73 @ SV76 )
= one )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[277]) ).
thf(284,plain,
! [SV74: $i,SV67: $i] :
( ( ( ( c @ SV67 )
= SV74 )
= $false )
| ( ( complement @ SV67 @ SV74 )
= $true )
| ( ( test @ SV67 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[278]) ).
thf(285,plain,
! [SV75: $i,SV68: $i] :
( ( ( complement @ SV68 @ SV75 )
= $false )
| ( ( ( c @ SV68 )
= SV75 )
= $true )
| ( ( test @ SV68 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[279]) ).
thf(286,plain,
! [SV64: $i,SV71: $i] :
( ( ( ( multiplication @ SV71 @ SV64 )
= zero )
= $false )
| ( ( ( multiplication @ SV64 @ SV71 )
= zero )
= $false )
| ( ( ( ( addition @ SV64 @ SV71 )
!= one ) )
= $true )
| ( ( complement @ SV71 @ SV64 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[280]) ).
thf(287,plain,
! [SV77: $i] :
( ( ! [SY74: $i] :
( ~ ( complement @ SY74 @ SV77 )
| ( ( multiplication @ SV77 @ SY74 )
= zero ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[281]) ).
thf(288,plain,
! [SV78: $i] :
( ( ! [SY75: $i] :
( ~ ( complement @ SY75 @ SV78 )
| ( ( multiplication @ SY75 @ SV78 )
= zero ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[282]) ).
thf(289,plain,
! [SV73: $i,SV76: $i] :
( ( ( complement @ SV76 @ SV73 )
= $false )
| ( ( ( addition @ SV73 @ SV76 )
= one )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[283]) ).
thf(290,plain,
! [SV71: $i,SV64: $i] :
( ( ( ( addition @ SV64 @ SV71 )
= one )
= $false )
| ( ( ( multiplication @ SV64 @ SV71 )
= zero )
= $false )
| ( ( ( multiplication @ SV71 @ SV64 )
= zero )
= $false )
| ( ( complement @ SV71 @ SV64 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[286]) ).
thf(291,plain,
! [SV77: $i,SV79: $i] :
( ( ~ ( complement @ SV79 @ SV77 )
| ( ( multiplication @ SV77 @ SV79 )
= zero ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[287]) ).
thf(292,plain,
! [SV78: $i,SV80: $i] :
( ( ~ ( complement @ SV80 @ SV78 )
| ( ( multiplication @ SV80 @ SV78 )
= zero ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[288]) ).
thf(293,plain,
! [SV77: $i,SV79: $i] :
( ( ( ~ ( complement @ SV79 @ SV77 ) )
= $true )
| ( ( ( multiplication @ SV77 @ SV79 )
= zero )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[291]) ).
thf(294,plain,
! [SV78: $i,SV80: $i] :
( ( ( ~ ( complement @ SV80 @ SV78 ) )
= $true )
| ( ( ( multiplication @ SV80 @ SV78 )
= zero )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[292]) ).
thf(295,plain,
! [SV77: $i,SV79: $i] :
( ( ( complement @ SV79 @ SV77 )
= $false )
| ( ( ( multiplication @ SV77 @ SV79 )
= zero )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[293]) ).
thf(296,plain,
! [SV78: $i,SV80: $i] :
( ( ( complement @ SV80 @ SV78 )
= $false )
| ( ( ( multiplication @ SV80 @ SV78 )
= zero )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[294]) ).
thf(297,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[190,296,295,290,289,285,284,271,267,266,263,231,230,229,228,219,214,209,207,206,203,202,200,199,191]) ).
thf(298,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[297,173]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : KLE007+2 : TPTP v8.1.0. Released v4.0.0.
% 0.10/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.34 % Computer : n010.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Thu Jun 16 13:24:23 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.36
% 0.12/0.36 No.of.Axioms: 16
% 0.12/0.36
% 0.12/0.36 Length.of.Defs: 0
% 0.12/0.36
% 0.12/0.36 Contains.Choice.Funs: false
% 0.12/0.37 (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:600,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:18,loop_count:0,foatp_calls:0,translation:fof_full).................
% 2.34/2.57
% 2.34/2.57 ********************************
% 2.34/2.57 * All subproblems solved! *
% 2.34/2.57 ********************************
% 2.34/2.57 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:18,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:297,loop_count:0,foatp_calls:1,translation:fof_full)
% 2.44/2.61
% 2.44/2.61 %**** Beginning of derivation protocol ****
% 2.44/2.61 % SZS output start CNFRefutation
% See solution above
% 2.44/2.61
% 2.44/2.61 %**** End of derivation protocol ****
% 2.44/2.61 %**** no. of clauses in derivation: 298 ****
% 2.44/2.61 %**** clause counter: 297 ****
% 2.44/2.61
% 2.44/2.61 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:18,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:297,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------