TSTP Solution File: KLE007+4 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : KLE007+4 : 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 : n004.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 02:10:47 EDT 2022
% Result : Theorem 6.01s 6.22s
% Output : CNFRefutation 6.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 30
% Syntax : Number of formulae : 343 ( 244 unt; 11 typ; 0 def)
% Number of atoms : 1693 ( 819 equ; 0 cnn)
% Maximal formula atoms : 4 ( 5 avg)
% Number of connectives : 3148 ( 480 ~; 443 |; 37 &;2167 @)
% ( 8 <=>; 13 =>; 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 : 723 ( 0 ^ 721 !; 2 ?; 723 :)
% 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_SY35,type,
sK2_SY35: $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,X1: $i] :
( ( ( test @ X0 )
& ( test @ X1 ) )
=> ( ( c @ ( multiplication @ X0 @ X1 ) )
= ( addition @ ( c @ X0 ) @ ( c @ X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',test_deMorgan2) ).
thf(2,axiom,
! [X0: $i,X1: $i] :
( ( ( test @ X0 )
& ( test @ X1 ) )
=> ( ( c @ ( addition @ X0 @ X1 ) )
= ( multiplication @ ( c @ X0 ) @ ( c @ X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',test_deMorgan1) ).
thf(3,axiom,
! [X0: $i] :
( ~ ( test @ X0 )
=> ( ( c @ X0 )
= zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',test_4) ).
thf(4,axiom,
! [X0: $i,X1: $i] :
( ( test @ X0 )
=> ( ( ( c @ X0 )
= X1 )
<=> ( complement @ X0 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',test_3) ).
thf(5,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(6,axiom,
! [X0: $i] :
( ( test @ X0 )
<=> ? [X1: $i] : ( complement @ X1 @ X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',test_1) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( leq @ A @ B )
<=> ( ( addition @ A @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',order) ).
thf(8,axiom,
! [A: $i] :
( ( multiplication @ zero @ A )
= zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_annihilation) ).
thf(9,axiom,
! [A: $i] :
( ( multiplication @ A @ zero )
= zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_annihilation) ).
thf(10,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(11,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(12,axiom,
! [A: $i] :
( ( multiplication @ one @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_left_identity) ).
thf(13,axiom,
! [A: $i] :
( ( multiplication @ A @ one )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_right_identity) ).
thf(14,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(15,axiom,
! [A: $i] :
( ( addition @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_idempotence) ).
thf(16,axiom,
! [A: $i] :
( ( addition @ A @ zero )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_identity) ).
thf(17,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(18,axiom,
! [A: $i,B: $i] :
( ( addition @ A @ B )
= ( addition @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_commutativity) ).
thf(19,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(20,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)],[19]) ).
thf(21,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)],[20]) ).
thf(22,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( test @ X0 )
& ( test @ X1 ) )
=> ( ( c @ ( multiplication @ X0 @ X1 ) )
= ( addition @ ( c @ X0 ) @ ( c @ X1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(23,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( test @ X0 )
& ( test @ X1 ) )
=> ( ( c @ ( addition @ X0 @ X1 ) )
= ( multiplication @ ( c @ X0 ) @ ( c @ X1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(24,plain,
( ( ! [X0: $i] :
( ~ ( test @ X0 )
=> ( ( c @ X0 )
= zero ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(25,plain,
( ( ! [X0: $i,X1: $i] :
( ( test @ X0 )
=> ( ( ( c @ X0 )
= X1 )
<=> ( complement @ X0 @ X1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(26,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)],[5]) ).
thf(27,plain,
( ( ! [X0: $i] :
( ( test @ X0 )
<=> ? [X1: $i] : ( complement @ X1 @ X0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(28,plain,
( ( ! [A: $i,B: $i] :
( ( leq @ A @ B )
<=> ( ( addition @ A @ B )
= B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(29,plain,
( ( ! [A: $i] :
( ( multiplication @ zero @ A )
= zero ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(30,plain,
( ( ! [A: $i] :
( ( multiplication @ A @ zero )
= zero ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(31,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)],[10]) ).
thf(32,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)],[11]) ).
thf(33,plain,
( ( ! [A: $i] :
( ( multiplication @ one @ A )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(34,plain,
( ( ! [A: $i] :
( ( multiplication @ A @ one )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(35,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( multiplication @ A @ ( multiplication @ B @ C ) )
= ( multiplication @ ( multiplication @ A @ B ) @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(36,plain,
( ( ! [A: $i] :
( ( addition @ A @ A )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(37,plain,
( ( ! [A: $i] :
( ( addition @ A @ zero )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(38,plain,
( ( ! [C: $i,B: $i,A: $i] :
( ( addition @ A @ ( addition @ B @ C ) )
= ( addition @ ( addition @ A @ B ) @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(39,plain,
( ( ! [A: $i,B: $i] :
( ( addition @ A @ B )
= ( addition @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(40,plain,
( ( ! [SY35: $i] :
( ( ( test @ SY35 )
& ( test @ sK1_X0 ) )
=> ( ( leq @ one @ ( addition @ ( multiplication @ ( addition @ sK1_X0 @ ( c @ sK1_X0 ) ) @ SY35 ) @ ( multiplication @ ( addition @ sK1_X0 @ ( c @ sK1_X0 ) ) @ ( c @ SY35 ) ) ) )
& ( leq @ ( addition @ ( multiplication @ ( addition @ sK1_X0 @ ( c @ sK1_X0 ) ) @ SY35 ) @ ( multiplication @ ( addition @ sK1_X0 @ ( c @ sK1_X0 ) ) @ ( c @ SY35 ) ) ) @ one ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[21]) ).
thf(41,plain,
( ( ( ( test @ sK2_SY35 )
& ( test @ sK1_X0 ) )
=> ( ( leq @ one @ ( addition @ ( multiplication @ ( addition @ sK1_X0 @ ( c @ sK1_X0 ) ) @ sK2_SY35 ) @ ( multiplication @ ( addition @ sK1_X0 @ ( c @ sK1_X0 ) ) @ ( c @ sK2_SY35 ) ) ) )
& ( leq @ ( addition @ ( multiplication @ ( addition @ sK1_X0 @ ( c @ sK1_X0 ) ) @ sK2_SY35 ) @ ( multiplication @ ( addition @ sK1_X0 @ ( c @ sK1_X0 ) ) @ ( c @ sK2_SY35 ) ) ) @ one ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[40]) ).
thf(42,plain,
( ( test @ sK2_SY35 )
= $true ),
inference(standard_cnf,[status(thm)],[41]) ).
thf(43,plain,
( ( test @ sK1_X0 )
= $true ),
inference(standard_cnf,[status(thm)],[41]) ).
thf(44,plain,
( ( ( leq @ one @ ( addition @ ( multiplication @ ( addition @ sK1_X0 @ ( c @ sK1_X0 ) ) @ sK2_SY35 ) @ ( multiplication @ ( addition @ sK1_X0 @ ( c @ sK1_X0 ) ) @ ( c @ sK2_SY35 ) ) ) )
& ( leq @ ( addition @ ( multiplication @ ( addition @ sK1_X0 @ ( c @ sK1_X0 ) ) @ sK2_SY35 ) @ ( multiplication @ ( addition @ sK1_X0 @ ( c @ sK1_X0 ) ) @ ( c @ sK2_SY35 ) ) ) @ one ) )
= $false ),
inference(standard_cnf,[status(thm)],[41]) ).
thf(45,plain,
( ( leq @ one @ ( addition @ ( multiplication @ ( addition @ sK1_X0 @ ( c @ sK1_X0 ) ) @ sK2_SY35 ) @ ( multiplication @ ( addition @ sK1_X0 @ ( c @ sK1_X0 ) ) @ ( c @ sK2_SY35 ) ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[44]) ).
thf(46,plain,
( ( leq @ ( addition @ ( multiplication @ ( addition @ sK1_X0 @ ( c @ sK1_X0 ) ) @ sK2_SY35 ) @ ( multiplication @ ( addition @ sK1_X0 @ ( c @ sK1_X0 ) ) @ ( c @ sK2_SY35 ) ) ) @ one )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[44]) ).
thf(47,plain,
( ( ~ ( leq @ one @ ( addition @ ( multiplication @ ( addition @ sK1_X0 @ ( c @ sK1_X0 ) ) @ sK2_SY35 ) @ ( multiplication @ ( addition @ sK1_X0 @ ( c @ sK1_X0 ) ) @ ( c @ sK2_SY35 ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[45]) ).
thf(48,plain,
( ( ~ ( leq @ ( addition @ ( multiplication @ ( addition @ sK1_X0 @ ( c @ sK1_X0 ) ) @ sK2_SY35 ) @ ( multiplication @ ( addition @ sK1_X0 @ ( c @ sK1_X0 ) ) @ ( c @ sK2_SY35 ) ) ) @ one ) )
= $true ),
inference(polarity_switch,[status(thm)],[46]) ).
thf(49,plain,
( ( ! [X0: $i,X1: $i] :
( ~ ( test @ X0 )
| ~ ( test @ X1 )
| ( ( c @ ( multiplication @ X0 @ X1 ) )
= ( addition @ ( c @ X0 ) @ ( c @ X1 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[22]) ).
thf(50,plain,
( ( ! [X0: $i,X1: $i] :
( ~ ( test @ X0 )
| ~ ( test @ X1 )
| ( ( c @ ( addition @ X0 @ X1 ) )
= ( multiplication @ ( c @ X0 ) @ ( c @ X1 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[23]) ).
thf(51,plain,
( ( ! [X0: $i] :
( ( test @ X0 )
| ( ( c @ X0 )
= zero ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[24]) ).
thf(52,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)],[25]) ).
thf(53,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)],[26]) ).
thf(54,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)],[27]) ).
thf(55,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)],[28]) ).
thf(56,plain,
( ( ! [A: $i,B: $i] :
( ( addition @ A @ B )
= ( addition @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(57,plain,
( ( ! [C: $i,B: $i,A: $i] :
( ( addition @ A @ ( addition @ B @ C ) )
= ( addition @ ( addition @ A @ B ) @ C ) ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(58,plain,
( ( ! [A: $i] :
( ( addition @ A @ zero )
= A ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(59,plain,
( ( ! [A: $i] :
( ( addition @ A @ A )
= A ) )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(60,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( multiplication @ A @ ( multiplication @ B @ C ) )
= ( multiplication @ ( multiplication @ A @ B ) @ C ) ) )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(61,plain,
( ( ! [A: $i] :
( ( multiplication @ A @ one )
= A ) )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(62,plain,
( ( ! [A: $i] :
( ( multiplication @ one @ A )
= A ) )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(63,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( multiplication @ A @ ( addition @ B @ C ) )
= ( addition @ ( multiplication @ A @ B ) @ ( multiplication @ A @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(64,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( multiplication @ ( addition @ A @ B ) @ C )
= ( addition @ ( multiplication @ A @ C ) @ ( multiplication @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[31]) ).
thf(65,plain,
( ( ! [A: $i] :
( ( multiplication @ A @ zero )
= zero ) )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(66,plain,
( ( ! [A: $i] :
( ( multiplication @ zero @ A )
= zero ) )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(67,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)],[55]) ).
thf(68,plain,
( ( ! [X0: $i] :
( ! [X1: $i] :
~ ( complement @ X1 @ X0 )
| ( test @ X0 ) )
& ! [X0: $i] :
( ~ ( test @ X0 )
| ( complement @ ( sK3_X1 @ X0 ) @ X0 ) ) )
= $true ),
inference(copy,[status(thm)],[54]) ).
thf(69,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)],[53]) ).
thf(70,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)],[52]) ).
thf(71,plain,
( ( ! [X0: $i] :
( ( test @ X0 )
| ( ( c @ X0 )
= zero ) ) )
= $true ),
inference(copy,[status(thm)],[51]) ).
thf(72,plain,
( ( ! [X0: $i,X1: $i] :
( ~ ( test @ X0 )
| ~ ( test @ X1 )
| ( ( c @ ( addition @ X0 @ X1 ) )
= ( multiplication @ ( c @ X0 ) @ ( c @ X1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(73,plain,
( ( ! [X0: $i,X1: $i] :
( ~ ( test @ X0 )
| ~ ( test @ X1 )
| ( ( c @ ( multiplication @ X0 @ X1 ) )
= ( addition @ ( c @ X0 ) @ ( c @ X1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(74,plain,
( ( test @ sK1_X0 )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(75,plain,
( ( test @ sK2_SY35 )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(76,plain,
( ( ~ ( leq @ one @ ( addition @ ( multiplication @ ( addition @ sK1_X0 @ ( c @ sK1_X0 ) ) @ sK2_SY35 ) @ ( multiplication @ ( addition @ sK1_X0 @ ( c @ sK1_X0 ) ) @ ( c @ sK2_SY35 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(77,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)],[67]) ).
thf(78,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)],[68]) ).
thf(79,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)],[70]) ).
thf(80,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)],[69]) ).
thf(81,plain,
! [SV1: $i] :
( ( ! [SY36: $i] :
( ( addition @ SV1 @ SY36 )
= ( addition @ SY36 @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[56]) ).
thf(82,plain,
! [SV2: $i] :
( ( ! [SY37: $i,SY38: $i] :
( ( addition @ SY38 @ ( addition @ SY37 @ SV2 ) )
= ( addition @ ( addition @ SY38 @ SY37 ) @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[57]) ).
thf(83,plain,
! [SV3: $i] :
( ( ( addition @ SV3 @ zero )
= SV3 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[58]) ).
thf(84,plain,
! [SV4: $i] :
( ( ( addition @ SV4 @ SV4 )
= SV4 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[59]) ).
thf(85,plain,
! [SV5: $i] :
( ( ! [SY39: $i,SY40: $i] :
( ( multiplication @ SV5 @ ( multiplication @ SY39 @ SY40 ) )
= ( multiplication @ ( multiplication @ SV5 @ SY39 ) @ SY40 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[60]) ).
thf(86,plain,
! [SV6: $i] :
( ( ( multiplication @ SV6 @ one )
= SV6 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[61]) ).
thf(87,plain,
! [SV7: $i] :
( ( ( multiplication @ one @ SV7 )
= SV7 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[62]) ).
thf(88,plain,
! [SV8: $i] :
( ( ! [SY41: $i,SY42: $i] :
( ( multiplication @ SV8 @ ( addition @ SY41 @ SY42 ) )
= ( addition @ ( multiplication @ SV8 @ SY41 ) @ ( multiplication @ SV8 @ SY42 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[63]) ).
thf(89,plain,
! [SV9: $i] :
( ( ! [SY43: $i,SY44: $i] :
( ( multiplication @ ( addition @ SV9 @ SY43 ) @ SY44 )
= ( addition @ ( multiplication @ SV9 @ SY44 ) @ ( multiplication @ SY43 @ SY44 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[64]) ).
thf(90,plain,
! [SV10: $i] :
( ( ( multiplication @ SV10 @ zero )
= zero )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[65]) ).
thf(91,plain,
! [SV11: $i] :
( ( ( multiplication @ zero @ SV11 )
= zero )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[66]) ).
thf(92,plain,
! [SV12: $i] :
( ( ( test @ SV12 )
| ( ( c @ SV12 )
= zero ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(93,plain,
! [SV13: $i] :
( ( ! [SY45: $i] :
( ~ ( test @ SV13 )
| ~ ( test @ SY45 )
| ( ( c @ ( addition @ SV13 @ SY45 ) )
= ( multiplication @ ( c @ SV13 ) @ ( c @ SY45 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[72]) ).
thf(94,plain,
! [SV14: $i] :
( ( ! [SY46: $i] :
( ~ ( test @ SV14 )
| ~ ( test @ SY46 )
| ( ( c @ ( multiplication @ SV14 @ SY46 ) )
= ( addition @ ( c @ SV14 ) @ ( c @ SY46 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[73]) ).
thf(95,plain,
( ( leq @ one @ ( addition @ ( multiplication @ ( addition @ sK1_X0 @ ( c @ sK1_X0 ) ) @ sK2_SY35 ) @ ( multiplication @ ( addition @ sK1_X0 @ ( c @ sK1_X0 ) ) @ ( c @ sK2_SY35 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[76]) ).
thf(96,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)],[77]) ).
thf(97,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)],[78]) ).
thf(98,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)],[79]) ).
thf(99,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)],[80]) ).
thf(100,plain,
! [SV15: $i,SV1: $i] :
( ( ( addition @ SV1 @ SV15 )
= ( addition @ SV15 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[81]) ).
thf(101,plain,
! [SV2: $i,SV16: $i] :
( ( ! [SY47: $i] :
( ( addition @ SY47 @ ( addition @ SV16 @ SV2 ) )
= ( addition @ ( addition @ SY47 @ SV16 ) @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[82]) ).
thf(102,plain,
! [SV17: $i,SV5: $i] :
( ( ! [SY48: $i] :
( ( multiplication @ SV5 @ ( multiplication @ SV17 @ SY48 ) )
= ( multiplication @ ( multiplication @ SV5 @ SV17 ) @ SY48 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(103,plain,
! [SV18: $i,SV8: $i] :
( ( ! [SY49: $i] :
( ( multiplication @ SV8 @ ( addition @ SV18 @ SY49 ) )
= ( addition @ ( multiplication @ SV8 @ SV18 ) @ ( multiplication @ SV8 @ SY49 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(104,plain,
! [SV19: $i,SV9: $i] :
( ( ! [SY50: $i] :
( ( multiplication @ ( addition @ SV9 @ SV19 ) @ SY50 )
= ( addition @ ( multiplication @ SV9 @ SY50 ) @ ( multiplication @ SV19 @ SY50 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[89]) ).
thf(105,plain,
! [SV12: $i] :
( ( ( test @ SV12 )
= $true )
| ( ( ( c @ SV12 )
= zero )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[92]) ).
thf(106,plain,
! [SV20: $i,SV13: $i] :
( ( ~ ( test @ SV13 )
| ~ ( test @ SV20 )
| ( ( c @ ( addition @ SV13 @ SV20 ) )
= ( multiplication @ ( c @ SV13 ) @ ( c @ SV20 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[93]) ).
thf(107,plain,
! [SV21: $i,SV14: $i] :
( ( ~ ( test @ SV14 )
| ~ ( test @ SV21 )
| ( ( c @ ( multiplication @ SV14 @ SV21 ) )
= ( addition @ ( c @ SV14 ) @ ( c @ SV21 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[94]) ).
thf(108,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( addition @ SX0 @ SX1 )
!= SX1 )
| ( leq @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[96]) ).
thf(109,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( leq @ SX0 @ SX1 )
| ( ( addition @ SX0 @ SX1 )
= SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[96]) ).
thf(110,plain,
( ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( complement @ SX1 @ SX0 )
| ( test @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[97]) ).
thf(111,plain,
( ( ~ ! [SX0: $i] :
( ~ ( test @ SX0 )
| ( complement @ ( sK3_X1 @ SX0 ) @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[97]) ).
thf(112,plain,
( ( ~ ! [SX0: $i] :
( ~ ( test @ SX0 )
| ! [SX1: $i] :
( ( ( c @ SX0 )
!= SX1 )
| ( complement @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[98]) ).
thf(113,plain,
( ( ~ ! [SX0: $i] :
( ~ ( test @ SX0 )
| ! [SX1: $i] :
( ~ ( complement @ SX0 @ SX1 )
| ( ( c @ SX0 )
= SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[98]) ).
thf(114,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)],[99]) ).
thf(115,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)],[99]) ).
thf(116,plain,
! [SV2: $i,SV16: $i,SV22: $i] :
( ( ( addition @ SV22 @ ( addition @ SV16 @ SV2 ) )
= ( addition @ ( addition @ SV22 @ SV16 ) @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[101]) ).
thf(117,plain,
! [SV23: $i,SV17: $i,SV5: $i] :
( ( ( multiplication @ SV5 @ ( multiplication @ SV17 @ SV23 ) )
= ( multiplication @ ( multiplication @ SV5 @ SV17 ) @ SV23 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[102]) ).
thf(118,plain,
! [SV24: $i,SV18: $i,SV8: $i] :
( ( ( multiplication @ SV8 @ ( addition @ SV18 @ SV24 ) )
= ( addition @ ( multiplication @ SV8 @ SV18 ) @ ( multiplication @ SV8 @ SV24 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[103]) ).
thf(119,plain,
! [SV25: $i,SV19: $i,SV9: $i] :
( ( ( multiplication @ ( addition @ SV9 @ SV19 ) @ SV25 )
= ( addition @ ( multiplication @ SV9 @ SV25 ) @ ( multiplication @ SV19 @ SV25 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[104]) ).
thf(120,plain,
! [SV20: $i,SV13: $i] :
( ( ( ~ ( test @ SV13 )
| ~ ( test @ SV20 ) )
= $true )
| ( ( ( c @ ( addition @ SV13 @ SV20 ) )
= ( multiplication @ ( c @ SV13 ) @ ( c @ SV20 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[106]) ).
thf(121,plain,
! [SV21: $i,SV14: $i] :
( ( ( ~ ( test @ SV14 )
| ~ ( test @ SV21 ) )
= $true )
| ( ( ( c @ ( multiplication @ SV14 @ SV21 ) )
= ( addition @ ( c @ SV14 ) @ ( c @ SV21 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[107]) ).
thf(122,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( addition @ SX0 @ SX1 )
!= SX1 )
| ( leq @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[108]) ).
thf(123,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( leq @ SX0 @ SX1 )
| ( ( addition @ SX0 @ SX1 )
= SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[109]) ).
thf(124,plain,
( ( ! [SX0: $i] :
( ! [SX1: $i] :
~ ( complement @ SX1 @ SX0 )
| ( test @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[110]) ).
thf(125,plain,
( ( ! [SX0: $i] :
( ~ ( test @ SX0 )
| ( complement @ ( sK3_X1 @ SX0 ) @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[111]) ).
thf(126,plain,
( ( ! [SX0: $i] :
( ~ ( test @ SX0 )
| ! [SX1: $i] :
( ( ( c @ SX0 )
!= SX1 )
| ( complement @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[112]) ).
thf(127,plain,
( ( ! [SX0: $i] :
( ~ ( test @ SX0 )
| ! [SX1: $i] :
( ~ ( complement @ SX0 @ SX1 )
| ( ( c @ SX0 )
= SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[113]) ).
thf(128,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)],[114]) ).
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 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( complement @ SX1 @ SX0 )
| ( ( addition @ SX0 @ SX1 )
= one ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[115]) ).
thf(130,plain,
! [SV20: $i,SV13: $i] :
( ( ( ~ ( test @ SV13 ) )
= $true )
| ( ( ~ ( test @ SV20 ) )
= $true )
| ( ( ( c @ ( addition @ SV13 @ SV20 ) )
= ( multiplication @ ( c @ SV13 ) @ ( c @ SV20 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[120]) ).
thf(131,plain,
! [SV21: $i,SV14: $i] :
( ( ( ~ ( test @ SV14 ) )
= $true )
| ( ( ~ ( test @ SV21 ) )
= $true )
| ( ( ( c @ ( multiplication @ SV14 @ SV21 ) )
= ( addition @ ( c @ SV14 ) @ ( c @ SV21 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[121]) ).
thf(132,plain,
! [SV26: $i] :
( ( ! [SY51: $i] :
( ( ( addition @ SV26 @ SY51 )
!= SY51 )
| ( leq @ SV26 @ SY51 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[122]) ).
thf(133,plain,
! [SV27: $i] :
( ( ! [SY52: $i] :
( ~ ( leq @ SV27 @ SY52 )
| ( ( addition @ SV27 @ SY52 )
= SY52 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[123]) ).
thf(134,plain,
! [SV28: $i] :
( ( ! [SY53: $i] :
~ ( complement @ SY53 @ SV28 )
| ( test @ SV28 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[124]) ).
thf(135,plain,
! [SV29: $i] :
( ( ~ ( test @ SV29 )
| ( complement @ ( sK3_X1 @ SV29 ) @ SV29 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[125]) ).
thf(136,plain,
! [SV30: $i] :
( ( ~ ( test @ SV30 )
| ! [SY54: $i] :
( ( ( c @ SV30 )
!= SY54 )
| ( complement @ SV30 @ SY54 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[126]) ).
thf(137,plain,
! [SV31: $i] :
( ( ~ ( test @ SV31 )
| ! [SY55: $i] :
( ~ ( complement @ SV31 @ SY55 )
| ( ( c @ SV31 )
= SY55 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[127]) ).
thf(138,plain,
! [SV32: $i] :
( ( ! [SY56: $i] :
( ( ( multiplication @ SV32 @ SY56 )
!= zero )
| ( ( multiplication @ SY56 @ SV32 )
!= zero )
| ( ( addition @ SV32 @ SY56 )
!= one )
| ( complement @ SY56 @ SV32 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[128]) ).
thf(139,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)],[129]) ).
thf(140,plain,
! [SV20: $i,SV13: $i] :
( ( ( test @ SV13 )
= $false )
| ( ( ~ ( test @ SV20 ) )
= $true )
| ( ( ( c @ ( addition @ SV13 @ SV20 ) )
= ( multiplication @ ( c @ SV13 ) @ ( c @ SV20 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[130]) ).
thf(141,plain,
! [SV21: $i,SV14: $i] :
( ( ( test @ SV14 )
= $false )
| ( ( ~ ( test @ SV21 ) )
= $true )
| ( ( ( c @ ( multiplication @ SV14 @ SV21 ) )
= ( addition @ ( c @ SV14 ) @ ( c @ SV21 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[131]) ).
thf(142,plain,
! [SV33: $i,SV26: $i] :
( ( ( ( addition @ SV26 @ SV33 )
!= SV33 )
| ( leq @ SV26 @ SV33 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[132]) ).
thf(143,plain,
! [SV34: $i,SV27: $i] :
( ( ~ ( leq @ SV27 @ SV34 )
| ( ( addition @ SV27 @ SV34 )
= SV34 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[133]) ).
thf(144,plain,
! [SV28: $i] :
( ( ( ! [SY53: $i] :
~ ( complement @ SY53 @ SV28 ) )
= $true )
| ( ( test @ SV28 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[134]) ).
thf(145,plain,
! [SV29: $i] :
( ( ( ~ ( test @ SV29 ) )
= $true )
| ( ( complement @ ( sK3_X1 @ SV29 ) @ SV29 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[135]) ).
thf(146,plain,
! [SV30: $i] :
( ( ( ~ ( test @ SV30 ) )
= $true )
| ( ( ! [SY54: $i] :
( ( ( c @ SV30 )
!= SY54 )
| ( complement @ SV30 @ SY54 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[136]) ).
thf(147,plain,
! [SV31: $i] :
( ( ( ~ ( test @ SV31 ) )
= $true )
| ( ( ! [SY55: $i] :
( ~ ( complement @ SV31 @ SY55 )
| ( ( c @ SV31 )
= SY55 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[137]) ).
thf(148,plain,
! [SV35: $i,SV32: $i] :
( ( ( ( multiplication @ SV32 @ SV35 )
!= zero )
| ( ( multiplication @ SV35 @ SV32 )
!= zero )
| ( ( addition @ SV32 @ SV35 )
!= one )
| ( complement @ SV35 @ SV32 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[138]) ).
thf(149,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)],[139]) ).
thf(150,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( complement @ SX1 @ SX0 )
| ( ( addition @ SX0 @ SX1 )
= one ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[139]) ).
thf(151,plain,
! [SV13: $i,SV20: $i] :
( ( ( test @ SV20 )
= $false )
| ( ( test @ SV13 )
= $false )
| ( ( ( c @ ( addition @ SV13 @ SV20 ) )
= ( multiplication @ ( c @ SV13 ) @ ( c @ SV20 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[140]) ).
thf(152,plain,
! [SV14: $i,SV21: $i] :
( ( ( test @ SV21 )
= $false )
| ( ( test @ SV14 )
= $false )
| ( ( ( c @ ( multiplication @ SV14 @ SV21 ) )
= ( addition @ ( c @ SV14 ) @ ( c @ SV21 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[141]) ).
thf(153,plain,
! [SV33: $i,SV26: $i] :
( ( ( ( ( addition @ SV26 @ SV33 )
!= SV33 ) )
= $true )
| ( ( leq @ SV26 @ SV33 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[142]) ).
thf(154,plain,
! [SV34: $i,SV27: $i] :
( ( ( ~ ( leq @ SV27 @ SV34 ) )
= $true )
| ( ( ( addition @ SV27 @ SV34 )
= SV34 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[143]) ).
thf(155,plain,
! [SV28: $i,SV36: $i] :
( ( ( ~ ( complement @ SV36 @ SV28 ) )
= $true )
| ( ( test @ SV28 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[144]) ).
thf(156,plain,
! [SV29: $i] :
( ( ( test @ SV29 )
= $false )
| ( ( complement @ ( sK3_X1 @ SV29 ) @ SV29 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[145]) ).
thf(157,plain,
! [SV30: $i] :
( ( ( test @ SV30 )
= $false )
| ( ( ! [SY54: $i] :
( ( ( c @ SV30 )
!= SY54 )
| ( complement @ SV30 @ SY54 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[146]) ).
thf(158,plain,
! [SV31: $i] :
( ( ( test @ SV31 )
= $false )
| ( ( ! [SY55: $i] :
( ~ ( complement @ SV31 @ SY55 )
| ( ( c @ SV31 )
= SY55 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[147]) ).
thf(159,plain,
! [SV35: $i,SV32: $i] :
( ( ( ( ( multiplication @ SV32 @ SV35 )
!= zero )
| ( ( multiplication @ SV35 @ SV32 )
!= zero )
| ( ( addition @ SV32 @ SV35 )
!= one ) )
= $true )
| ( ( complement @ SV35 @ SV32 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[148]) ).
thf(160,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)],[149]) ).
thf(161,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( complement @ SX1 @ SX0 )
| ( ( addition @ SX0 @ SX1 )
= one ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[150]) ).
thf(162,plain,
! [SV33: $i,SV26: $i] :
( ( ( ( addition @ SV26 @ SV33 )
= SV33 )
= $false )
| ( ( leq @ SV26 @ SV33 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[153]) ).
thf(163,plain,
! [SV34: $i,SV27: $i] :
( ( ( leq @ SV27 @ SV34 )
= $false )
| ( ( ( addition @ SV27 @ SV34 )
= SV34 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[154]) ).
thf(164,plain,
! [SV28: $i,SV36: $i] :
( ( ( complement @ SV36 @ SV28 )
= $false )
| ( ( test @ SV28 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[155]) ).
thf(165,plain,
! [SV37: $i,SV30: $i] :
( ( ( ( ( c @ SV30 )
!= SV37 )
| ( complement @ SV30 @ SV37 ) )
= $true )
| ( ( test @ SV30 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[157]) ).
thf(166,plain,
! [SV38: $i,SV31: $i] :
( ( ( ~ ( complement @ SV31 @ SV38 )
| ( ( c @ SV31 )
= SV38 ) )
= $true )
| ( ( test @ SV31 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[158]) ).
thf(167,plain,
! [SV35: $i,SV32: $i] :
( ( ( ( ( multiplication @ SV32 @ SV35 )
!= zero )
| ( ( multiplication @ SV35 @ SV32 )
!= zero ) )
= $true )
| ( ( ( ( addition @ SV32 @ SV35 )
!= one ) )
= $true )
| ( ( complement @ SV35 @ SV32 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[159]) ).
thf(168,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)],[160]) ).
thf(169,plain,
! [SV39: $i] :
( ( ! [SY57: $i] :
( ~ ( complement @ SY57 @ SV39 )
| ( ( addition @ SV39 @ SY57 )
= one ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[161]) ).
thf(170,plain,
! [SV37: $i,SV30: $i] :
( ( ( ( ( c @ SV30 )
!= SV37 ) )
= $true )
| ( ( complement @ SV30 @ SV37 )
= $true )
| ( ( test @ SV30 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[165]) ).
thf(171,plain,
! [SV38: $i,SV31: $i] :
( ( ( ~ ( complement @ SV31 @ SV38 ) )
= $true )
| ( ( ( c @ SV31 )
= SV38 )
= $true )
| ( ( test @ SV31 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[166]) ).
thf(172,plain,
! [SV35: $i,SV32: $i] :
( ( ( ( ( multiplication @ SV32 @ SV35 )
!= zero ) )
= $true )
| ( ( ( ( multiplication @ SV35 @ SV32 )
!= zero ) )
= $true )
| ( ( ( ( addition @ SV32 @ SV35 )
!= one ) )
= $true )
| ( ( complement @ SV35 @ SV32 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[167]) ).
thf(173,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( complement @ SX1 @ SX0 )
| ( ( multiplication @ SX0 @ SX1 )
= zero ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[168]) ).
thf(174,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( complement @ SX1 @ SX0 )
| ( ( multiplication @ SX1 @ SX0 )
= zero ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[168]) ).
thf(175,plain,
! [SV39: $i,SV40: $i] :
( ( ~ ( complement @ SV40 @ SV39 )
| ( ( addition @ SV39 @ SV40 )
= one ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[169]) ).
thf(176,plain,
! [SV37: $i,SV30: $i] :
( ( ( ( c @ SV30 )
= SV37 )
= $false )
| ( ( complement @ SV30 @ SV37 )
= $true )
| ( ( test @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[170]) ).
thf(177,plain,
! [SV38: $i,SV31: $i] :
( ( ( complement @ SV31 @ SV38 )
= $false )
| ( ( ( c @ SV31 )
= SV38 )
= $true )
| ( ( test @ SV31 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[171]) ).
thf(178,plain,
! [SV35: $i,SV32: $i] :
( ( ( ( multiplication @ SV32 @ SV35 )
= zero )
= $false )
| ( ( ( ( multiplication @ SV35 @ SV32 )
!= zero ) )
= $true )
| ( ( ( ( addition @ SV32 @ SV35 )
!= one ) )
= $true )
| ( ( complement @ SV35 @ SV32 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[172]) ).
thf(179,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( complement @ SX1 @ SX0 )
| ( ( multiplication @ SX0 @ SX1 )
= zero ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[173]) ).
thf(180,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( complement @ SX1 @ SX0 )
| ( ( multiplication @ SX1 @ SX0 )
= zero ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[174]) ).
thf(181,plain,
! [SV39: $i,SV40: $i] :
( ( ( ~ ( complement @ SV40 @ SV39 ) )
= $true )
| ( ( ( addition @ SV39 @ SV40 )
= one )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[175]) ).
thf(182,plain,
! [SV32: $i,SV35: $i] :
( ( ( ( multiplication @ SV35 @ SV32 )
= zero )
= $false )
| ( ( ( multiplication @ SV32 @ SV35 )
= zero )
= $false )
| ( ( ( ( addition @ SV32 @ SV35 )
!= one ) )
= $true )
| ( ( complement @ SV35 @ SV32 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[178]) ).
thf(183,plain,
! [SV41: $i] :
( ( ! [SY58: $i] :
( ~ ( complement @ SY58 @ SV41 )
| ( ( multiplication @ SV41 @ SY58 )
= zero ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[179]) ).
thf(184,plain,
! [SV42: $i] :
( ( ! [SY59: $i] :
( ~ ( complement @ SY59 @ SV42 )
| ( ( multiplication @ SY59 @ SV42 )
= zero ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[180]) ).
thf(185,plain,
! [SV39: $i,SV40: $i] :
( ( ( complement @ SV40 @ SV39 )
= $false )
| ( ( ( addition @ SV39 @ SV40 )
= one )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[181]) ).
thf(186,plain,
! [SV35: $i,SV32: $i] :
( ( ( ( addition @ SV32 @ SV35 )
= one )
= $false )
| ( ( ( multiplication @ SV32 @ SV35 )
= zero )
= $false )
| ( ( ( multiplication @ SV35 @ SV32 )
= zero )
= $false )
| ( ( complement @ SV35 @ SV32 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[182]) ).
thf(187,plain,
! [SV41: $i,SV43: $i] :
( ( ~ ( complement @ SV43 @ SV41 )
| ( ( multiplication @ SV41 @ SV43 )
= zero ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[183]) ).
thf(188,plain,
! [SV42: $i,SV44: $i] :
( ( ~ ( complement @ SV44 @ SV42 )
| ( ( multiplication @ SV44 @ SV42 )
= zero ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[184]) ).
thf(189,plain,
! [SV41: $i,SV43: $i] :
( ( ( ~ ( complement @ SV43 @ SV41 ) )
= $true )
| ( ( ( multiplication @ SV41 @ SV43 )
= zero )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[187]) ).
thf(190,plain,
! [SV42: $i,SV44: $i] :
( ( ( ~ ( complement @ SV44 @ SV42 ) )
= $true )
| ( ( ( multiplication @ SV44 @ SV42 )
= zero )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[188]) ).
thf(191,plain,
! [SV41: $i,SV43: $i] :
( ( ( complement @ SV43 @ SV41 )
= $false )
| ( ( ( multiplication @ SV41 @ SV43 )
= zero )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[189]) ).
thf(192,plain,
! [SV42: $i,SV44: $i] :
( ( ( complement @ SV44 @ SV42 )
= $false )
| ( ( ( multiplication @ SV44 @ SV42 )
= zero )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[190]) ).
thf(193,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[74,192,191,186,185,177,176,164,163,162,156,152,151,119,118,117,116,105,100,95,91,90,87,86,84,83,75]) ).
thf(194,plain,
( ( ! [A: $i,B: $i] :
( ( addition @ A @ B )
= ( addition @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(195,plain,
( ( ! [C: $i,B: $i,A: $i] :
( ( addition @ A @ ( addition @ B @ C ) )
= ( addition @ ( addition @ A @ B ) @ C ) ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(196,plain,
( ( ! [A: $i] :
( ( addition @ A @ zero )
= A ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(197,plain,
( ( ! [A: $i] :
( ( addition @ A @ A )
= A ) )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(198,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( multiplication @ A @ ( multiplication @ B @ C ) )
= ( multiplication @ ( multiplication @ A @ B ) @ C ) ) )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(199,plain,
( ( ! [A: $i] :
( ( multiplication @ A @ one )
= A ) )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(200,plain,
( ( ! [A: $i] :
( ( multiplication @ one @ A )
= A ) )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(201,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( multiplication @ A @ ( addition @ B @ C ) )
= ( addition @ ( multiplication @ A @ B ) @ ( multiplication @ A @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(202,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( multiplication @ ( addition @ A @ B ) @ C )
= ( addition @ ( multiplication @ A @ C ) @ ( multiplication @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[31]) ).
thf(203,plain,
( ( ! [A: $i] :
( ( multiplication @ A @ zero )
= zero ) )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(204,plain,
( ( ! [A: $i] :
( ( multiplication @ zero @ A )
= zero ) )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(205,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)],[55]) ).
thf(206,plain,
( ( ! [X0: $i] :
( ! [X1: $i] :
~ ( complement @ X1 @ X0 )
| ( test @ X0 ) )
& ! [X0: $i] :
( ~ ( test @ X0 )
| ( complement @ ( sK3_X1 @ X0 ) @ X0 ) ) )
= $true ),
inference(copy,[status(thm)],[54]) ).
thf(207,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)],[53]) ).
thf(208,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)],[52]) ).
thf(209,plain,
( ( ! [X0: $i] :
( ( test @ X0 )
| ( ( c @ X0 )
= zero ) ) )
= $true ),
inference(copy,[status(thm)],[51]) ).
thf(210,plain,
( ( ! [X0: $i,X1: $i] :
( ~ ( test @ X0 )
| ~ ( test @ X1 )
| ( ( c @ ( addition @ X0 @ X1 ) )
= ( multiplication @ ( c @ X0 ) @ ( c @ X1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(211,plain,
( ( ! [X0: $i,X1: $i] :
( ~ ( test @ X0 )
| ~ ( test @ X1 )
| ( ( c @ ( multiplication @ X0 @ X1 ) )
= ( addition @ ( c @ X0 ) @ ( c @ X1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(212,plain,
( ( test @ sK1_X0 )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(213,plain,
( ( test @ sK2_SY35 )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(214,plain,
( ( ~ ( leq @ ( addition @ ( multiplication @ ( addition @ sK1_X0 @ ( c @ sK1_X0 ) ) @ sK2_SY35 ) @ ( multiplication @ ( addition @ sK1_X0 @ ( c @ sK1_X0 ) ) @ ( c @ sK2_SY35 ) ) ) @ one ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(215,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)],[206]) ).
thf(216,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)],[207]) ).
thf(217,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)],[208]) ).
thf(218,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)],[205]) ).
thf(219,plain,
! [SV45: $i] :
( ( ! [SY60: $i] :
( ( addition @ SV45 @ SY60 )
= ( addition @ SY60 @ SV45 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[194]) ).
thf(220,plain,
! [SV46: $i] :
( ( ! [SY61: $i,SY62: $i] :
( ( addition @ SY62 @ ( addition @ SY61 @ SV46 ) )
= ( addition @ ( addition @ SY62 @ SY61 ) @ SV46 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[195]) ).
thf(221,plain,
! [SV47: $i] :
( ( ( addition @ SV47 @ zero )
= SV47 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[196]) ).
thf(222,plain,
! [SV48: $i] :
( ( ( addition @ SV48 @ SV48 )
= SV48 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[197]) ).
thf(223,plain,
! [SV49: $i] :
( ( ! [SY63: $i,SY64: $i] :
( ( multiplication @ SV49 @ ( multiplication @ SY63 @ SY64 ) )
= ( multiplication @ ( multiplication @ SV49 @ SY63 ) @ SY64 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[198]) ).
thf(224,plain,
! [SV50: $i] :
( ( ( multiplication @ SV50 @ one )
= SV50 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[199]) ).
thf(225,plain,
! [SV51: $i] :
( ( ( multiplication @ one @ SV51 )
= SV51 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[200]) ).
thf(226,plain,
! [SV52: $i] :
( ( ! [SY65: $i,SY66: $i] :
( ( multiplication @ SV52 @ ( addition @ SY65 @ SY66 ) )
= ( addition @ ( multiplication @ SV52 @ SY65 ) @ ( multiplication @ SV52 @ SY66 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[201]) ).
thf(227,plain,
! [SV53: $i] :
( ( ! [SY67: $i,SY68: $i] :
( ( multiplication @ ( addition @ SV53 @ SY67 ) @ SY68 )
= ( addition @ ( multiplication @ SV53 @ SY68 ) @ ( multiplication @ SY67 @ SY68 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[202]) ).
thf(228,plain,
! [SV54: $i] :
( ( ( multiplication @ SV54 @ zero )
= zero )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[203]) ).
thf(229,plain,
! [SV55: $i] :
( ( ( multiplication @ zero @ SV55 )
= zero )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[204]) ).
thf(230,plain,
! [SV56: $i] :
( ( ( test @ SV56 )
| ( ( c @ SV56 )
= zero ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[209]) ).
thf(231,plain,
! [SV57: $i] :
( ( ! [SY69: $i] :
( ~ ( test @ SV57 )
| ~ ( test @ SY69 )
| ( ( c @ ( addition @ SV57 @ SY69 ) )
= ( multiplication @ ( c @ SV57 ) @ ( c @ SY69 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[210]) ).
thf(232,plain,
! [SV58: $i] :
( ( ! [SY70: $i] :
( ~ ( test @ SV58 )
| ~ ( test @ SY70 )
| ( ( c @ ( multiplication @ SV58 @ SY70 ) )
= ( addition @ ( c @ SV58 ) @ ( c @ SY70 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[211]) ).
thf(233,plain,
( ( leq @ ( addition @ ( multiplication @ ( addition @ sK1_X0 @ ( c @ sK1_X0 ) ) @ sK2_SY35 ) @ ( multiplication @ ( addition @ sK1_X0 @ ( c @ sK1_X0 ) ) @ ( c @ sK2_SY35 ) ) ) @ one )
= $false ),
inference(extcnf_not_pos,[status(thm)],[214]) ).
thf(234,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)],[215]) ).
thf(235,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)],[216]) ).
thf(236,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)],[217]) ).
thf(237,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)],[218]) ).
thf(238,plain,
! [SV59: $i,SV45: $i] :
( ( ( addition @ SV45 @ SV59 )
= ( addition @ SV59 @ SV45 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[219]) ).
thf(239,plain,
! [SV46: $i,SV60: $i] :
( ( ! [SY71: $i] :
( ( addition @ SY71 @ ( addition @ SV60 @ SV46 ) )
= ( addition @ ( addition @ SY71 @ SV60 ) @ SV46 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[220]) ).
thf(240,plain,
! [SV61: $i,SV49: $i] :
( ( ! [SY72: $i] :
( ( multiplication @ SV49 @ ( multiplication @ SV61 @ SY72 ) )
= ( multiplication @ ( multiplication @ SV49 @ SV61 ) @ SY72 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[223]) ).
thf(241,plain,
! [SV62: $i,SV52: $i] :
( ( ! [SY73: $i] :
( ( multiplication @ SV52 @ ( addition @ SV62 @ SY73 ) )
= ( addition @ ( multiplication @ SV52 @ SV62 ) @ ( multiplication @ SV52 @ SY73 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[226]) ).
thf(242,plain,
! [SV63: $i,SV53: $i] :
( ( ! [SY74: $i] :
( ( multiplication @ ( addition @ SV53 @ SV63 ) @ SY74 )
= ( addition @ ( multiplication @ SV53 @ SY74 ) @ ( multiplication @ SV63 @ SY74 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[227]) ).
thf(243,plain,
! [SV56: $i] :
( ( ( test @ SV56 )
= $true )
| ( ( ( c @ SV56 )
= zero )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[230]) ).
thf(244,plain,
! [SV64: $i,SV57: $i] :
( ( ~ ( test @ SV57 )
| ~ ( test @ SV64 )
| ( ( c @ ( addition @ SV57 @ SV64 ) )
= ( multiplication @ ( c @ SV57 ) @ ( c @ SV64 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[231]) ).
thf(245,plain,
! [SV65: $i,SV58: $i] :
( ( ~ ( test @ SV58 )
| ~ ( test @ SV65 )
| ( ( c @ ( multiplication @ SV58 @ SV65 ) )
= ( addition @ ( c @ SV58 ) @ ( c @ SV65 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[232]) ).
thf(246,plain,
( ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( complement @ SX1 @ SX0 )
| ( test @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[234]) ).
thf(247,plain,
( ( ~ ! [SX0: $i] :
( ~ ( test @ SX0 )
| ( complement @ ( sK3_X1 @ SX0 ) @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[234]) ).
thf(248,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)],[235]) ).
thf(249,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)],[235]) ).
thf(250,plain,
( ( ~ ! [SX0: $i] :
( ~ ( test @ SX0 )
| ! [SX1: $i] :
( ( ( c @ SX0 )
!= SX1 )
| ( complement @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[236]) ).
thf(251,plain,
( ( ~ ! [SX0: $i] :
( ~ ( test @ SX0 )
| ! [SX1: $i] :
( ~ ( complement @ SX0 @ SX1 )
| ( ( c @ SX0 )
= SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[236]) ).
thf(252,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( addition @ SX0 @ SX1 )
!= SX1 )
| ( leq @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[237]) ).
thf(253,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( leq @ SX0 @ SX1 )
| ( ( addition @ SX0 @ SX1 )
= SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[237]) ).
thf(254,plain,
! [SV46: $i,SV60: $i,SV66: $i] :
( ( ( addition @ SV66 @ ( addition @ SV60 @ SV46 ) )
= ( addition @ ( addition @ SV66 @ SV60 ) @ SV46 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[239]) ).
thf(255,plain,
! [SV67: $i,SV61: $i,SV49: $i] :
( ( ( multiplication @ SV49 @ ( multiplication @ SV61 @ SV67 ) )
= ( multiplication @ ( multiplication @ SV49 @ SV61 ) @ SV67 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[240]) ).
thf(256,plain,
! [SV68: $i,SV62: $i,SV52: $i] :
( ( ( multiplication @ SV52 @ ( addition @ SV62 @ SV68 ) )
= ( addition @ ( multiplication @ SV52 @ SV62 ) @ ( multiplication @ SV52 @ SV68 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[241]) ).
thf(257,plain,
! [SV69: $i,SV63: $i,SV53: $i] :
( ( ( multiplication @ ( addition @ SV53 @ SV63 ) @ SV69 )
= ( addition @ ( multiplication @ SV53 @ SV69 ) @ ( multiplication @ SV63 @ SV69 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[242]) ).
thf(258,plain,
! [SV64: $i,SV57: $i] :
( ( ( ~ ( test @ SV57 )
| ~ ( test @ SV64 ) )
= $true )
| ( ( ( c @ ( addition @ SV57 @ SV64 ) )
= ( multiplication @ ( c @ SV57 ) @ ( c @ SV64 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[244]) ).
thf(259,plain,
! [SV65: $i,SV58: $i] :
( ( ( ~ ( test @ SV58 )
| ~ ( test @ SV65 ) )
= $true )
| ( ( ( c @ ( multiplication @ SV58 @ SV65 ) )
= ( addition @ ( c @ SV58 ) @ ( c @ SV65 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[245]) ).
thf(260,plain,
( ( ! [SX0: $i] :
( ! [SX1: $i] :
~ ( complement @ SX1 @ SX0 )
| ( test @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[246]) ).
thf(261,plain,
( ( ! [SX0: $i] :
( ~ ( test @ SX0 )
| ( complement @ ( sK3_X1 @ SX0 ) @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[247]) ).
thf(262,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)],[248]) ).
thf(263,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)],[249]) ).
thf(264,plain,
( ( ! [SX0: $i] :
( ~ ( test @ SX0 )
| ! [SX1: $i] :
( ( ( c @ SX0 )
!= SX1 )
| ( complement @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[250]) ).
thf(265,plain,
( ( ! [SX0: $i] :
( ~ ( test @ SX0 )
| ! [SX1: $i] :
( ~ ( complement @ SX0 @ SX1 )
| ( ( c @ SX0 )
= SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[251]) ).
thf(266,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( addition @ SX0 @ SX1 )
!= SX1 )
| ( leq @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[252]) ).
thf(267,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( leq @ SX0 @ SX1 )
| ( ( addition @ SX0 @ SX1 )
= SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[253]) ).
thf(268,plain,
! [SV64: $i,SV57: $i] :
( ( ( ~ ( test @ SV57 ) )
= $true )
| ( ( ~ ( test @ SV64 ) )
= $true )
| ( ( ( c @ ( addition @ SV57 @ SV64 ) )
= ( multiplication @ ( c @ SV57 ) @ ( c @ SV64 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[258]) ).
thf(269,plain,
! [SV65: $i,SV58: $i] :
( ( ( ~ ( test @ SV58 ) )
= $true )
| ( ( ~ ( test @ SV65 ) )
= $true )
| ( ( ( c @ ( multiplication @ SV58 @ SV65 ) )
= ( addition @ ( c @ SV58 ) @ ( c @ SV65 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[259]) ).
thf(270,plain,
! [SV70: $i] :
( ( ! [SY75: $i] :
~ ( complement @ SY75 @ SV70 )
| ( test @ SV70 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[260]) ).
thf(271,plain,
! [SV71: $i] :
( ( ~ ( test @ SV71 )
| ( complement @ ( sK3_X1 @ SV71 ) @ SV71 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[261]) ).
thf(272,plain,
! [SV72: $i] :
( ( ! [SY76: $i] :
( ( ( multiplication @ SV72 @ SY76 )
!= zero )
| ( ( multiplication @ SY76 @ SV72 )
!= zero )
| ( ( addition @ SV72 @ SY76 )
!= one )
| ( complement @ SY76 @ SV72 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[262]) ).
thf(273,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)],[263]) ).
thf(274,plain,
! [SV73: $i] :
( ( ~ ( test @ SV73 )
| ! [SY77: $i] :
( ( ( c @ SV73 )
!= SY77 )
| ( complement @ SV73 @ SY77 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[264]) ).
thf(275,plain,
! [SV74: $i] :
( ( ~ ( test @ SV74 )
| ! [SY78: $i] :
( ~ ( complement @ SV74 @ SY78 )
| ( ( c @ SV74 )
= SY78 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[265]) ).
thf(276,plain,
! [SV75: $i] :
( ( ! [SY79: $i] :
( ( ( addition @ SV75 @ SY79 )
!= SY79 )
| ( leq @ SV75 @ SY79 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[266]) ).
thf(277,plain,
! [SV76: $i] :
( ( ! [SY80: $i] :
( ~ ( leq @ SV76 @ SY80 )
| ( ( addition @ SV76 @ SY80 )
= SY80 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[267]) ).
thf(278,plain,
! [SV64: $i,SV57: $i] :
( ( ( test @ SV57 )
= $false )
| ( ( ~ ( test @ SV64 ) )
= $true )
| ( ( ( c @ ( addition @ SV57 @ SV64 ) )
= ( multiplication @ ( c @ SV57 ) @ ( c @ SV64 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[268]) ).
thf(279,plain,
! [SV65: $i,SV58: $i] :
( ( ( test @ SV58 )
= $false )
| ( ( ~ ( test @ SV65 ) )
= $true )
| ( ( ( c @ ( multiplication @ SV58 @ SV65 ) )
= ( addition @ ( c @ SV58 ) @ ( c @ SV65 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[269]) ).
thf(280,plain,
! [SV70: $i] :
( ( ( ! [SY75: $i] :
~ ( complement @ SY75 @ SV70 ) )
= $true )
| ( ( test @ SV70 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[270]) ).
thf(281,plain,
! [SV71: $i] :
( ( ( ~ ( test @ SV71 ) )
= $true )
| ( ( complement @ ( sK3_X1 @ SV71 ) @ SV71 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[271]) ).
thf(282,plain,
! [SV77: $i,SV72: $i] :
( ( ( ( multiplication @ SV72 @ SV77 )
!= zero )
| ( ( multiplication @ SV77 @ SV72 )
!= zero )
| ( ( addition @ SV72 @ SV77 )
!= one )
| ( complement @ SV77 @ SV72 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[272]) ).
thf(283,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)],[273]) ).
thf(284,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( complement @ SX1 @ SX0 )
| ( ( addition @ SX0 @ SX1 )
= one ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[273]) ).
thf(285,plain,
! [SV73: $i] :
( ( ( ~ ( test @ SV73 ) )
= $true )
| ( ( ! [SY77: $i] :
( ( ( c @ SV73 )
!= SY77 )
| ( complement @ SV73 @ SY77 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[274]) ).
thf(286,plain,
! [SV74: $i] :
( ( ( ~ ( test @ SV74 ) )
= $true )
| ( ( ! [SY78: $i] :
( ~ ( complement @ SV74 @ SY78 )
| ( ( c @ SV74 )
= SY78 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[275]) ).
thf(287,plain,
! [SV78: $i,SV75: $i] :
( ( ( ( addition @ SV75 @ SV78 )
!= SV78 )
| ( leq @ SV75 @ SV78 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[276]) ).
thf(288,plain,
! [SV79: $i,SV76: $i] :
( ( ~ ( leq @ SV76 @ SV79 )
| ( ( addition @ SV76 @ SV79 )
= SV79 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[277]) ).
thf(289,plain,
! [SV57: $i,SV64: $i] :
( ( ( test @ SV64 )
= $false )
| ( ( test @ SV57 )
= $false )
| ( ( ( c @ ( addition @ SV57 @ SV64 ) )
= ( multiplication @ ( c @ SV57 ) @ ( c @ SV64 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[278]) ).
thf(290,plain,
! [SV58: $i,SV65: $i] :
( ( ( test @ SV65 )
= $false )
| ( ( test @ SV58 )
= $false )
| ( ( ( c @ ( multiplication @ SV58 @ SV65 ) )
= ( addition @ ( c @ SV58 ) @ ( c @ SV65 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[279]) ).
thf(291,plain,
! [SV70: $i,SV80: $i] :
( ( ( ~ ( complement @ SV80 @ SV70 ) )
= $true )
| ( ( test @ SV70 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[280]) ).
thf(292,plain,
! [SV71: $i] :
( ( ( test @ SV71 )
= $false )
| ( ( complement @ ( sK3_X1 @ SV71 ) @ SV71 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[281]) ).
thf(293,plain,
! [SV77: $i,SV72: $i] :
( ( ( ( ( multiplication @ SV72 @ SV77 )
!= zero )
| ( ( multiplication @ SV77 @ SV72 )
!= zero )
| ( ( addition @ SV72 @ SV77 )
!= one ) )
= $true )
| ( ( complement @ SV77 @ SV72 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[282]) ).
thf(294,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)],[283]) ).
thf(295,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( complement @ SX1 @ SX0 )
| ( ( addition @ SX0 @ SX1 )
= one ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[284]) ).
thf(296,plain,
! [SV73: $i] :
( ( ( test @ SV73 )
= $false )
| ( ( ! [SY77: $i] :
( ( ( c @ SV73 )
!= SY77 )
| ( complement @ SV73 @ SY77 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[285]) ).
thf(297,plain,
! [SV74: $i] :
( ( ( test @ SV74 )
= $false )
| ( ( ! [SY78: $i] :
( ~ ( complement @ SV74 @ SY78 )
| ( ( c @ SV74 )
= SY78 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[286]) ).
thf(298,plain,
! [SV78: $i,SV75: $i] :
( ( ( ( ( addition @ SV75 @ SV78 )
!= SV78 ) )
= $true )
| ( ( leq @ SV75 @ SV78 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[287]) ).
thf(299,plain,
! [SV79: $i,SV76: $i] :
( ( ( ~ ( leq @ SV76 @ SV79 ) )
= $true )
| ( ( ( addition @ SV76 @ SV79 )
= SV79 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[288]) ).
thf(300,plain,
! [SV70: $i,SV80: $i] :
( ( ( complement @ SV80 @ SV70 )
= $false )
| ( ( test @ SV70 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[291]) ).
thf(301,plain,
! [SV77: $i,SV72: $i] :
( ( ( ( ( multiplication @ SV72 @ SV77 )
!= zero )
| ( ( multiplication @ SV77 @ SV72 )
!= zero ) )
= $true )
| ( ( ( ( addition @ SV72 @ SV77 )
!= one ) )
= $true )
| ( ( complement @ SV77 @ SV72 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[293]) ).
thf(302,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)],[294]) ).
thf(303,plain,
! [SV81: $i] :
( ( ! [SY81: $i] :
( ~ ( complement @ SY81 @ SV81 )
| ( ( addition @ SV81 @ SY81 )
= one ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[295]) ).
thf(304,plain,
! [SV82: $i,SV73: $i] :
( ( ( ( ( c @ SV73 )
!= SV82 )
| ( complement @ SV73 @ SV82 ) )
= $true )
| ( ( test @ SV73 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[296]) ).
thf(305,plain,
! [SV83: $i,SV74: $i] :
( ( ( ~ ( complement @ SV74 @ SV83 )
| ( ( c @ SV74 )
= SV83 ) )
= $true )
| ( ( test @ SV74 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[297]) ).
thf(306,plain,
! [SV78: $i,SV75: $i] :
( ( ( ( addition @ SV75 @ SV78 )
= SV78 )
= $false )
| ( ( leq @ SV75 @ SV78 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[298]) ).
thf(307,plain,
! [SV79: $i,SV76: $i] :
( ( ( leq @ SV76 @ SV79 )
= $false )
| ( ( ( addition @ SV76 @ SV79 )
= SV79 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[299]) ).
thf(308,plain,
! [SV77: $i,SV72: $i] :
( ( ( ( ( multiplication @ SV72 @ SV77 )
!= zero ) )
= $true )
| ( ( ( ( multiplication @ SV77 @ SV72 )
!= zero ) )
= $true )
| ( ( ( ( addition @ SV72 @ SV77 )
!= one ) )
= $true )
| ( ( complement @ SV77 @ SV72 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[301]) ).
thf(309,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( complement @ SX1 @ SX0 )
| ( ( multiplication @ SX0 @ SX1 )
= zero ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[302]) ).
thf(310,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( complement @ SX1 @ SX0 )
| ( ( multiplication @ SX1 @ SX0 )
= zero ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[302]) ).
thf(311,plain,
! [SV81: $i,SV84: $i] :
( ( ~ ( complement @ SV84 @ SV81 )
| ( ( addition @ SV81 @ SV84 )
= one ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[303]) ).
thf(312,plain,
! [SV82: $i,SV73: $i] :
( ( ( ( ( c @ SV73 )
!= SV82 ) )
= $true )
| ( ( complement @ SV73 @ SV82 )
= $true )
| ( ( test @ SV73 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[304]) ).
thf(313,plain,
! [SV83: $i,SV74: $i] :
( ( ( ~ ( complement @ SV74 @ SV83 ) )
= $true )
| ( ( ( c @ SV74 )
= SV83 )
= $true )
| ( ( test @ SV74 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[305]) ).
thf(314,plain,
! [SV77: $i,SV72: $i] :
( ( ( ( multiplication @ SV72 @ SV77 )
= zero )
= $false )
| ( ( ( ( multiplication @ SV77 @ SV72 )
!= zero ) )
= $true )
| ( ( ( ( addition @ SV72 @ SV77 )
!= one ) )
= $true )
| ( ( complement @ SV77 @ SV72 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[308]) ).
thf(315,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( complement @ SX1 @ SX0 )
| ( ( multiplication @ SX0 @ SX1 )
= zero ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[309]) ).
thf(316,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( complement @ SX1 @ SX0 )
| ( ( multiplication @ SX1 @ SX0 )
= zero ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[310]) ).
thf(317,plain,
! [SV81: $i,SV84: $i] :
( ( ( ~ ( complement @ SV84 @ SV81 ) )
= $true )
| ( ( ( addition @ SV81 @ SV84 )
= one )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[311]) ).
thf(318,plain,
! [SV82: $i,SV73: $i] :
( ( ( ( c @ SV73 )
= SV82 )
= $false )
| ( ( complement @ SV73 @ SV82 )
= $true )
| ( ( test @ SV73 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[312]) ).
thf(319,plain,
! [SV83: $i,SV74: $i] :
( ( ( complement @ SV74 @ SV83 )
= $false )
| ( ( ( c @ SV74 )
= SV83 )
= $true )
| ( ( test @ SV74 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[313]) ).
thf(320,plain,
! [SV72: $i,SV77: $i] :
( ( ( ( multiplication @ SV77 @ SV72 )
= zero )
= $false )
| ( ( ( multiplication @ SV72 @ SV77 )
= zero )
= $false )
| ( ( ( ( addition @ SV72 @ SV77 )
!= one ) )
= $true )
| ( ( complement @ SV77 @ SV72 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[314]) ).
thf(321,plain,
! [SV85: $i] :
( ( ! [SY82: $i] :
( ~ ( complement @ SY82 @ SV85 )
| ( ( multiplication @ SV85 @ SY82 )
= zero ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[315]) ).
thf(322,plain,
! [SV86: $i] :
( ( ! [SY83: $i] :
( ~ ( complement @ SY83 @ SV86 )
| ( ( multiplication @ SY83 @ SV86 )
= zero ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[316]) ).
thf(323,plain,
! [SV81: $i,SV84: $i] :
( ( ( complement @ SV84 @ SV81 )
= $false )
| ( ( ( addition @ SV81 @ SV84 )
= one )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[317]) ).
thf(324,plain,
! [SV77: $i,SV72: $i] :
( ( ( ( addition @ SV72 @ SV77 )
= one )
= $false )
| ( ( ( multiplication @ SV72 @ SV77 )
= zero )
= $false )
| ( ( ( multiplication @ SV77 @ SV72 )
= zero )
= $false )
| ( ( complement @ SV77 @ SV72 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[320]) ).
thf(325,plain,
! [SV85: $i,SV87: $i] :
( ( ~ ( complement @ SV87 @ SV85 )
| ( ( multiplication @ SV85 @ SV87 )
= zero ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[321]) ).
thf(326,plain,
! [SV86: $i,SV88: $i] :
( ( ~ ( complement @ SV88 @ SV86 )
| ( ( multiplication @ SV88 @ SV86 )
= zero ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[322]) ).
thf(327,plain,
! [SV85: $i,SV87: $i] :
( ( ( ~ ( complement @ SV87 @ SV85 ) )
= $true )
| ( ( ( multiplication @ SV85 @ SV87 )
= zero )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[325]) ).
thf(328,plain,
! [SV86: $i,SV88: $i] :
( ( ( ~ ( complement @ SV88 @ SV86 ) )
= $true )
| ( ( ( multiplication @ SV88 @ SV86 )
= zero )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[326]) ).
thf(329,plain,
! [SV85: $i,SV87: $i] :
( ( ( complement @ SV87 @ SV85 )
= $false )
| ( ( ( multiplication @ SV85 @ SV87 )
= zero )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[327]) ).
thf(330,plain,
! [SV86: $i,SV88: $i] :
( ( ( complement @ SV88 @ SV86 )
= $false )
| ( ( ( multiplication @ SV88 @ SV86 )
= zero )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[328]) ).
thf(331,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[212,330,329,324,323,319,318,307,306,300,292,290,289,257,256,255,254,243,238,233,229,228,225,224,222,221,213]) ).
thf(332,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[331,193]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : KLE007+4 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.34 % Computer : n004.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Thu Jun 16 13:03:53 EDT 2022
% 0.21/0.35 % CPUTime :
% 0.21/0.36
% 0.21/0.36 No.of.Axioms: 18
% 0.21/0.36
% 0.21/0.36 Length.of.Defs: 0
% 0.21/0.36
% 0.21/0.36 Contains.Choice.Funs: false
% 0.21/0.37 (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:600,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:20,loop_count:0,foatp_calls:0,translation:fof_full)..................
% 6.01/6.22
% 6.01/6.22 ********************************
% 6.01/6.22 * All subproblems solved! *
% 6.01/6.22 ********************************
% 6.01/6.22 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:20,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:71,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:331,loop_count:0,foatp_calls:1,translation:fof_full)
% 6.01/6.27
% 6.01/6.27 %**** Beginning of derivation protocol ****
% 6.01/6.27 % SZS output start CNFRefutation
% See solution above
% 6.01/6.27
% 6.01/6.27 %**** End of derivation protocol ****
% 6.01/6.27 %**** no. of clauses in derivation: 332 ****
% 6.01/6.27 %**** clause counter: 331 ****
% 6.01/6.27
% 6.01/6.27 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:20,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:71,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:331,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------