TSTP Solution File: KLE048+1 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : KLE048+1 : 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 : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sun Jul 17 02:11:06 EDT 2022
% Result : Theorem 52.53s 52.72s
% Output : CNFRefutation 52.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 32
% Syntax : Number of formulae : 205 ( 150 unt; 11 typ; 0 def)
% Number of atoms : 885 ( 429 equ; 0 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 1629 ( 236 ~; 213 |; 16 &;1144 @)
% ( 8 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 12 ( 12 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 11 usr; 5 con; 0-2 aty)
% Number of variables : 428 ( 0 ^ 426 !; 2 ?; 428 :)
% 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_X1,type,
sK2_X1: $i > $i ).
thf(tp_star,type,
star: $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/sandbox2/benchmark/theBenchmark.p',test_4) ).
thf(2,axiom,
! [X0: $i,X1: $i] :
( ( test @ X0 )
=> ( ( ( c @ X0 )
= X1 )
<=> ( complement @ X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',test_2) ).
thf(4,axiom,
! [X0: $i] :
( ( test @ X0 )
<=> ? [X1: $i] : ( complement @ X1 @ X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',test_1) ).
thf(5,axiom,
! [A: $i,B: $i,C: $i] :
( ( leq @ ( addition @ ( multiplication @ A @ B ) @ C ) @ A )
=> ( leq @ ( multiplication @ C @ ( star @ B ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',star_induction_right) ).
thf(6,axiom,
! [A: $i,B: $i,C: $i] :
( ( leq @ ( addition @ ( multiplication @ A @ B ) @ C ) @ B )
=> ( leq @ ( multiplication @ ( star @ A ) @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',star_induction_left) ).
thf(7,axiom,
! [A: $i] : ( leq @ ( addition @ one @ ( multiplication @ ( star @ A ) @ A ) ) @ ( star @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',star_unfold_left) ).
thf(8,axiom,
! [A: $i] : ( leq @ ( addition @ one @ ( multiplication @ A @ ( star @ A ) ) ) @ ( star @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',star_unfold_right) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( leq @ A @ B )
<=> ( ( addition @ A @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',order) ).
thf(10,axiom,
! [A: $i] :
( ( multiplication @ zero @ A )
= zero ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_annihilation) ).
thf(11,axiom,
! [A: $i] :
( ( multiplication @ A @ zero )
= zero ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_annihilation) ).
thf(12,axiom,
! [A: $i,B: $i,C: $i] :
( ( multiplication @ ( addition @ A @ B ) @ C )
= ( addition @ ( multiplication @ A @ C ) @ ( multiplication @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_distributivity) ).
thf(13,axiom,
! [A: $i,B: $i,C: $i] :
( ( multiplication @ A @ ( addition @ B @ C ) )
= ( addition @ ( multiplication @ A @ B ) @ ( multiplication @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_distributivity) ).
thf(14,axiom,
! [A: $i] :
( ( multiplication @ one @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_left_identity) ).
thf(15,axiom,
! [A: $i] :
( ( multiplication @ A @ one )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_right_identity) ).
thf(16,axiom,
! [A: $i,B: $i,C: $i] :
( ( multiplication @ A @ ( multiplication @ B @ C ) )
= ( multiplication @ ( multiplication @ A @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_associativity) ).
thf(17,axiom,
! [A: $i] :
( ( addition @ A @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_idempotence) ).
thf(18,axiom,
! [A: $i] :
( ( addition @ A @ zero )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_identity) ).
thf(19,axiom,
! [C: $i,B: $i,A: $i] :
( ( addition @ A @ ( addition @ B @ C ) )
= ( addition @ ( addition @ A @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_associativity) ).
thf(20,axiom,
! [A: $i,B: $i] :
( ( addition @ A @ B )
= ( addition @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_commutativity) ).
thf(21,conjecture,
! [X0: $i] :
( ( test @ X0 )
=> ( ( star @ X0 )
= one ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
thf(22,negated_conjecture,
( ( ! [X0: $i] :
( ( test @ X0 )
=> ( ( star @ X0 )
= one ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[21]) ).
thf(23,plain,
( ( ! [X0: $i] :
( ( test @ X0 )
=> ( ( star @ X0 )
= one ) ) )
= $false ),
inference(unfold_def,[status(thm)],[22]) ).
thf(24,plain,
( ( ! [X0: $i] :
( ~ ( test @ X0 )
=> ( ( c @ X0 )
= zero ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(25,plain,
( ( ! [X0: $i,X1: $i] :
( ( test @ X0 )
=> ( ( ( c @ X0 )
= X1 )
<=> ( complement @ X0 @ X1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
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)],[3]) ).
thf(27,plain,
( ( ! [X0: $i] :
( ( test @ X0 )
<=> ? [X1: $i] : ( complement @ X1 @ X0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(28,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( leq @ ( addition @ ( multiplication @ A @ B ) @ C ) @ A )
=> ( leq @ ( multiplication @ C @ ( star @ B ) ) @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(29,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( leq @ ( addition @ ( multiplication @ A @ B ) @ C ) @ B )
=> ( leq @ ( multiplication @ ( star @ A ) @ C ) @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(30,plain,
( ( ! [A: $i] : ( leq @ ( addition @ one @ ( multiplication @ ( star @ A ) @ A ) ) @ ( star @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(31,plain,
( ( ! [A: $i] : ( leq @ ( addition @ one @ ( multiplication @ A @ ( star @ A ) ) ) @ ( star @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(32,plain,
( ( ! [A: $i,B: $i] :
( ( leq @ A @ B )
<=> ( ( addition @ A @ B )
= B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(33,plain,
( ( ! [A: $i] :
( ( multiplication @ zero @ A )
= zero ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(34,plain,
( ( ! [A: $i] :
( ( multiplication @ A @ zero )
= zero ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(35,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)],[12]) ).
thf(36,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)],[13]) ).
thf(37,plain,
( ( ! [A: $i] :
( ( multiplication @ one @ A )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(38,plain,
( ( ! [A: $i] :
( ( multiplication @ A @ one )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(39,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( multiplication @ A @ ( multiplication @ B @ C ) )
= ( multiplication @ ( multiplication @ A @ B ) @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(40,plain,
( ( ! [A: $i] :
( ( addition @ A @ A )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(41,plain,
( ( ! [A: $i] :
( ( addition @ A @ zero )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(42,plain,
( ( ! [C: $i,B: $i,A: $i] :
( ( addition @ A @ ( addition @ B @ C ) )
= ( addition @ ( addition @ A @ B ) @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(43,plain,
( ( ! [A: $i,B: $i] :
( ( addition @ A @ B )
= ( addition @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(44,plain,
( ( ( test @ sK1_X0 )
=> ( ( star @ sK1_X0 )
= one ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[23]) ).
thf(45,plain,
( ( test @ sK1_X0 )
= $true ),
inference(standard_cnf,[status(thm)],[44]) ).
thf(46,plain,
( ( ( star @ sK1_X0 )
= one )
= $false ),
inference(standard_cnf,[status(thm)],[44]) ).
thf(47,plain,
( ( ( ( star @ sK1_X0 )
!= one ) )
= $true ),
inference(polarity_switch,[status(thm)],[46]) ).
thf(48,plain,
( ( ! [X0: $i] :
( ( test @ X0 )
| ( ( c @ X0 )
= zero ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[24]) ).
thf(49,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(50,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(51,plain,
( ( ! [X0: $i] :
( ! [X1: $i] :
~ ( complement @ X1 @ X0 )
| ( test @ X0 ) )
& ! [X0: $i] :
( ~ ( test @ X0 )
| ( complement @ ( sK2_X1 @ X0 ) @ X0 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[27]) ).
thf(52,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( leq @ ( addition @ ( multiplication @ A @ B ) @ C ) @ A )
| ( leq @ ( multiplication @ C @ ( star @ B ) ) @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[28]) ).
thf(53,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( leq @ ( addition @ ( multiplication @ A @ B ) @ C ) @ B )
| ( leq @ ( multiplication @ ( star @ A ) @ C ) @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[29]) ).
thf(54,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)],[32]) ).
thf(55,plain,
( ( ! [A: $i,B: $i] :
( ( addition @ A @ B )
= ( addition @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(56,plain,
( ( ! [C: $i,B: $i,A: $i] :
( ( addition @ A @ ( addition @ B @ C ) )
= ( addition @ ( addition @ A @ B ) @ C ) ) )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(57,plain,
( ( ! [A: $i] :
( ( addition @ A @ zero )
= A ) )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(58,plain,
( ( ! [A: $i] :
( ( addition @ A @ A )
= A ) )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(59,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( multiplication @ A @ ( multiplication @ B @ C ) )
= ( multiplication @ ( multiplication @ A @ B ) @ C ) ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(60,plain,
( ( ! [A: $i] :
( ( multiplication @ A @ one )
= A ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(61,plain,
( ( ! [A: $i] :
( ( multiplication @ one @ A )
= A ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(62,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( multiplication @ A @ ( addition @ B @ C ) )
= ( addition @ ( multiplication @ A @ B ) @ ( multiplication @ A @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(63,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( multiplication @ ( addition @ A @ B ) @ C )
= ( addition @ ( multiplication @ A @ C ) @ ( multiplication @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(64,plain,
( ( ! [A: $i] :
( ( multiplication @ A @ zero )
= zero ) )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(65,plain,
( ( ! [A: $i] :
( ( multiplication @ zero @ A )
= zero ) )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(66,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)],[54]) ).
thf(67,plain,
( ( ! [A: $i] : ( leq @ ( addition @ one @ ( multiplication @ A @ ( star @ A ) ) ) @ ( star @ A ) ) )
= $true ),
inference(copy,[status(thm)],[31]) ).
thf(68,plain,
( ( ! [A: $i] : ( leq @ ( addition @ one @ ( multiplication @ ( star @ A ) @ A ) ) @ ( star @ A ) ) )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(69,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( leq @ ( addition @ ( multiplication @ A @ B ) @ C ) @ B )
| ( leq @ ( multiplication @ ( star @ A ) @ C ) @ B ) ) )
= $true ),
inference(copy,[status(thm)],[53]) ).
thf(70,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( leq @ ( addition @ ( multiplication @ A @ B ) @ C ) @ A )
| ( leq @ ( multiplication @ C @ ( star @ B ) ) @ A ) ) )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(71,plain,
( ( ! [X0: $i] :
( ! [X1: $i] :
~ ( complement @ X1 @ X0 )
| ( test @ X0 ) )
& ! [X0: $i] :
( ~ ( test @ X0 )
| ( complement @ ( sK2_X1 @ X0 ) @ X0 ) ) )
= $true ),
inference(copy,[status(thm)],[51]) ).
thf(72,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)],[50]) ).
thf(73,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)],[49]) ).
thf(74,plain,
( ( ! [X0: $i] :
( ( test @ X0 )
| ( ( c @ X0 )
= zero ) ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(75,plain,
( ( test @ sK1_X0 )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(76,plain,
( ( ( ( star @ sK1_X0 )
!= one ) )
= $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)],[66]) ).
thf(78,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)],[72]) ).
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)],[73]) ).
thf(80,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( complement @ SX1 @ SX0 )
| ( test @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( test @ SX0 )
| ( complement @ ( sK2_X1 @ SX0 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[71]) ).
thf(81,plain,
! [SV1: $i] :
( ( ! [SY38: $i] :
( ( addition @ SV1 @ SY38 )
= ( addition @ SY38 @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[55]) ).
thf(82,plain,
! [SV2: $i] :
( ( ! [SY39: $i,SY40: $i] :
( ( addition @ SY40 @ ( addition @ SY39 @ SV2 ) )
= ( addition @ ( addition @ SY40 @ SY39 ) @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[56]) ).
thf(83,plain,
! [SV3: $i] :
( ( ( addition @ SV3 @ zero )
= SV3 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[57]) ).
thf(84,plain,
! [SV4: $i] :
( ( ( addition @ SV4 @ SV4 )
= SV4 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[58]) ).
thf(85,plain,
! [SV5: $i] :
( ( ! [SY41: $i,SY42: $i] :
( ( multiplication @ SV5 @ ( multiplication @ SY41 @ SY42 ) )
= ( multiplication @ ( multiplication @ SV5 @ SY41 ) @ SY42 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[59]) ).
thf(86,plain,
! [SV6: $i] :
( ( ( multiplication @ SV6 @ one )
= SV6 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[60]) ).
thf(87,plain,
! [SV7: $i] :
( ( ( multiplication @ one @ SV7 )
= SV7 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[61]) ).
thf(88,plain,
! [SV8: $i] :
( ( ! [SY43: $i,SY44: $i] :
( ( multiplication @ SV8 @ ( addition @ SY43 @ SY44 ) )
= ( addition @ ( multiplication @ SV8 @ SY43 ) @ ( multiplication @ SV8 @ SY44 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[62]) ).
thf(89,plain,
! [SV9: $i] :
( ( ! [SY45: $i,SY46: $i] :
( ( multiplication @ ( addition @ SV9 @ SY45 ) @ SY46 )
= ( addition @ ( multiplication @ SV9 @ SY46 ) @ ( multiplication @ SY45 @ SY46 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[63]) ).
thf(90,plain,
! [SV10: $i] :
( ( ( multiplication @ SV10 @ zero )
= zero )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[64]) ).
thf(91,plain,
! [SV11: $i] :
( ( ( multiplication @ zero @ SV11 )
= zero )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[65]) ).
thf(92,plain,
! [SV12: $i] :
( ( leq @ ( addition @ one @ ( multiplication @ SV12 @ ( star @ SV12 ) ) ) @ ( star @ SV12 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[67]) ).
thf(93,plain,
! [SV13: $i] :
( ( leq @ ( addition @ one @ ( multiplication @ ( star @ SV13 ) @ SV13 ) ) @ ( star @ SV13 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[68]) ).
thf(94,plain,
! [SV14: $i] :
( ( ! [SY47: $i,SY48: $i] :
( ~ ( leq @ ( addition @ ( multiplication @ SV14 @ SY47 ) @ SY48 ) @ SY47 )
| ( leq @ ( multiplication @ ( star @ SV14 ) @ SY48 ) @ SY47 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[69]) ).
thf(95,plain,
! [SV15: $i] :
( ( ! [SY49: $i,SY50: $i] :
( ~ ( leq @ ( addition @ ( multiplication @ SV15 @ SY49 ) @ SY50 ) @ SV15 )
| ( leq @ ( multiplication @ SY50 @ ( star @ SY49 ) ) @ SV15 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[70]) ).
thf(96,plain,
! [SV16: $i] :
( ( ( test @ SV16 )
| ( ( c @ SV16 )
= zero ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[74]) ).
thf(97,plain,
( ( ( star @ sK1_X0 )
= one )
= $false ),
inference(extcnf_not_pos,[status(thm)],[76]) ).
thf(98,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(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)],[78]) ).
thf(100,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(101,plain,
( ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( complement @ SX1 @ SX0 )
| ( test @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( test @ SX0 )
| ( complement @ ( sK2_X1 @ SX0 ) @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[80]) ).
thf(102,plain,
! [SV17: $i,SV1: $i] :
( ( ( addition @ SV1 @ SV17 )
= ( addition @ SV17 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[81]) ).
thf(103,plain,
! [SV2: $i,SV18: $i] :
( ( ! [SY51: $i] :
( ( addition @ SY51 @ ( addition @ SV18 @ SV2 ) )
= ( addition @ ( addition @ SY51 @ SV18 ) @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[82]) ).
thf(104,plain,
! [SV19: $i,SV5: $i] :
( ( ! [SY52: $i] :
( ( multiplication @ SV5 @ ( multiplication @ SV19 @ SY52 ) )
= ( multiplication @ ( multiplication @ SV5 @ SV19 ) @ SY52 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(105,plain,
! [SV20: $i,SV8: $i] :
( ( ! [SY53: $i] :
( ( multiplication @ SV8 @ ( addition @ SV20 @ SY53 ) )
= ( addition @ ( multiplication @ SV8 @ SV20 ) @ ( multiplication @ SV8 @ SY53 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(106,plain,
! [SV21: $i,SV9: $i] :
( ( ! [SY54: $i] :
( ( multiplication @ ( addition @ SV9 @ SV21 ) @ SY54 )
= ( addition @ ( multiplication @ SV9 @ SY54 ) @ ( multiplication @ SV21 @ SY54 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[89]) ).
thf(107,plain,
! [SV22: $i,SV14: $i] :
( ( ! [SY55: $i] :
( ~ ( leq @ ( addition @ ( multiplication @ SV14 @ SV22 ) @ SY55 ) @ SV22 )
| ( leq @ ( multiplication @ ( star @ SV14 ) @ SY55 ) @ SV22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[94]) ).
thf(108,plain,
! [SV23: $i,SV15: $i] :
( ( ! [SY56: $i] :
( ~ ( leq @ ( addition @ ( multiplication @ SV15 @ SV23 ) @ SY56 ) @ SV15 )
| ( leq @ ( multiplication @ SY56 @ ( star @ SV23 ) ) @ SV15 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[95]) ).
thf(109,plain,
! [SV16: $i] :
( ( ( test @ SV16 )
= $true )
| ( ( ( c @ SV16 )
= zero )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[96]) ).
thf(110,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( addition @ SX0 @ SX1 )
!= SX1 )
| ( leq @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[98]) ).
thf(111,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( leq @ SX0 @ SX1 )
| ( ( addition @ SX0 @ SX1 )
= SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[98]) ).
thf(112,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(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 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[99]) ).
thf(114,plain,
( ( ~ ! [SX0: $i] :
( ~ ( test @ SX0 )
| ! [SX1: $i] :
( ( ( c @ SX0 )
!= SX1 )
| ( complement @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[100]) ).
thf(115,plain,
( ( ~ ! [SX0: $i] :
( ~ ( test @ SX0 )
| ! [SX1: $i] :
( ~ ( complement @ SX0 @ SX1 )
| ( ( c @ SX0 )
= SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[100]) ).
thf(116,plain,
( ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( complement @ SX1 @ SX0 )
| ( test @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[101]) ).
thf(117,plain,
( ( ~ ! [SX0: $i] :
( ~ ( test @ SX0 )
| ( complement @ ( sK2_X1 @ SX0 ) @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[101]) ).
thf(118,plain,
! [SV2: $i,SV18: $i,SV24: $i] :
( ( ( addition @ SV24 @ ( addition @ SV18 @ SV2 ) )
= ( addition @ ( addition @ SV24 @ SV18 ) @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[103]) ).
thf(119,plain,
! [SV25: $i,SV19: $i,SV5: $i] :
( ( ( multiplication @ SV5 @ ( multiplication @ SV19 @ SV25 ) )
= ( multiplication @ ( multiplication @ SV5 @ SV19 ) @ SV25 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[104]) ).
thf(120,plain,
! [SV26: $i,SV20: $i,SV8: $i] :
( ( ( multiplication @ SV8 @ ( addition @ SV20 @ SV26 ) )
= ( addition @ ( multiplication @ SV8 @ SV20 ) @ ( multiplication @ SV8 @ SV26 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[105]) ).
thf(121,plain,
! [SV27: $i,SV21: $i,SV9: $i] :
( ( ( multiplication @ ( addition @ SV9 @ SV21 ) @ SV27 )
= ( addition @ ( multiplication @ SV9 @ SV27 ) @ ( multiplication @ SV21 @ SV27 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[106]) ).
thf(122,plain,
! [SV28: $i,SV22: $i,SV14: $i] :
( ( ~ ( leq @ ( addition @ ( multiplication @ SV14 @ SV22 ) @ SV28 ) @ SV22 )
| ( leq @ ( multiplication @ ( star @ SV14 ) @ SV28 ) @ SV22 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[107]) ).
thf(123,plain,
! [SV29: $i,SV23: $i,SV15: $i] :
( ( ~ ( leq @ ( addition @ ( multiplication @ SV15 @ SV23 ) @ SV29 ) @ SV15 )
| ( leq @ ( multiplication @ SV29 @ ( star @ SV23 ) ) @ SV15 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[108]) ).
thf(124,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( addition @ SX0 @ SX1 )
!= SX1 )
| ( leq @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[110]) ).
thf(125,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( leq @ SX0 @ SX1 )
| ( ( addition @ SX0 @ SX1 )
= SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[111]) ).
thf(126,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)],[112]) ).
thf(127,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)],[113]) ).
thf(128,plain,
( ( ! [SX0: $i] :
( ~ ( test @ SX0 )
| ! [SX1: $i] :
( ( ( c @ SX0 )
!= SX1 )
| ( complement @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[114]) ).
thf(129,plain,
( ( ! [SX0: $i] :
( ~ ( test @ SX0 )
| ! [SX1: $i] :
( ~ ( complement @ SX0 @ SX1 )
| ( ( c @ SX0 )
= SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[115]) ).
thf(130,plain,
( ( ! [SX0: $i] :
( ! [SX1: $i] :
~ ( complement @ SX1 @ SX0 )
| ( test @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[116]) ).
thf(131,plain,
( ( ! [SX0: $i] :
( ~ ( test @ SX0 )
| ( complement @ ( sK2_X1 @ SX0 ) @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[117]) ).
thf(132,plain,
! [SV28: $i,SV22: $i,SV14: $i] :
( ( ( ~ ( leq @ ( addition @ ( multiplication @ SV14 @ SV22 ) @ SV28 ) @ SV22 ) )
= $true )
| ( ( leq @ ( multiplication @ ( star @ SV14 ) @ SV28 ) @ SV22 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[122]) ).
thf(133,plain,
! [SV29: $i,SV23: $i,SV15: $i] :
( ( ( ~ ( leq @ ( addition @ ( multiplication @ SV15 @ SV23 ) @ SV29 ) @ SV15 ) )
= $true )
| ( ( leq @ ( multiplication @ SV29 @ ( star @ SV23 ) ) @ SV15 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[123]) ).
thf(134,plain,
! [SV30: $i] :
( ( ! [SY57: $i] :
( ( ( addition @ SV30 @ SY57 )
!= SY57 )
| ( leq @ SV30 @ SY57 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[124]) ).
thf(135,plain,
! [SV31: $i] :
( ( ! [SY58: $i] :
( ~ ( leq @ SV31 @ SY58 )
| ( ( addition @ SV31 @ SY58 )
= SY58 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[125]) ).
thf(136,plain,
! [SV32: $i] :
( ( ! [SY59: $i] :
( ( ( multiplication @ SV32 @ SY59 )
!= zero )
| ( ( multiplication @ SY59 @ SV32 )
!= zero )
| ( ( addition @ SV32 @ SY59 )
!= one )
| ( complement @ SY59 @ SV32 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[126]) ).
thf(137,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)],[127]) ).
thf(138,plain,
! [SV33: $i] :
( ( ~ ( test @ SV33 )
| ! [SY60: $i] :
( ( ( c @ SV33 )
!= SY60 )
| ( complement @ SV33 @ SY60 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[128]) ).
thf(139,plain,
! [SV34: $i] :
( ( ~ ( test @ SV34 )
| ! [SY61: $i] :
( ~ ( complement @ SV34 @ SY61 )
| ( ( c @ SV34 )
= SY61 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[129]) ).
thf(140,plain,
! [SV35: $i] :
( ( ! [SY62: $i] :
~ ( complement @ SY62 @ SV35 )
| ( test @ SV35 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[130]) ).
thf(141,plain,
! [SV36: $i] :
( ( ~ ( test @ SV36 )
| ( complement @ ( sK2_X1 @ SV36 ) @ SV36 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[131]) ).
thf(142,plain,
! [SV28: $i,SV22: $i,SV14: $i] :
( ( ( leq @ ( addition @ ( multiplication @ SV14 @ SV22 ) @ SV28 ) @ SV22 )
= $false )
| ( ( leq @ ( multiplication @ ( star @ SV14 ) @ SV28 ) @ SV22 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[132]) ).
thf(143,plain,
! [SV29: $i,SV23: $i,SV15: $i] :
( ( ( leq @ ( addition @ ( multiplication @ SV15 @ SV23 ) @ SV29 ) @ SV15 )
= $false )
| ( ( leq @ ( multiplication @ SV29 @ ( star @ SV23 ) ) @ SV15 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[133]) ).
thf(144,plain,
! [SV37: $i,SV30: $i] :
( ( ( ( addition @ SV30 @ SV37 )
!= SV37 )
| ( leq @ SV30 @ SV37 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[134]) ).
thf(145,plain,
! [SV38: $i,SV31: $i] :
( ( ~ ( leq @ SV31 @ SV38 )
| ( ( addition @ SV31 @ SV38 )
= SV38 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[135]) ).
thf(146,plain,
! [SV39: $i,SV32: $i] :
( ( ( ( multiplication @ SV32 @ SV39 )
!= zero )
| ( ( multiplication @ SV39 @ SV32 )
!= zero )
| ( ( addition @ SV32 @ SV39 )
!= one )
| ( complement @ SV39 @ SV32 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[136]) ).
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_or_neg,[status(thm)],[137]) ).
thf(148,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( complement @ SX1 @ SX0 )
| ( ( addition @ SX0 @ SX1 )
= one ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[137]) ).
thf(149,plain,
! [SV33: $i] :
( ( ( ~ ( test @ SV33 ) )
= $true )
| ( ( ! [SY60: $i] :
( ( ( c @ SV33 )
!= SY60 )
| ( complement @ SV33 @ SY60 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[138]) ).
thf(150,plain,
! [SV34: $i] :
( ( ( ~ ( test @ SV34 ) )
= $true )
| ( ( ! [SY61: $i] :
( ~ ( complement @ SV34 @ SY61 )
| ( ( c @ SV34 )
= SY61 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[139]) ).
thf(151,plain,
! [SV35: $i] :
( ( ( ! [SY62: $i] :
~ ( complement @ SY62 @ SV35 ) )
= $true )
| ( ( test @ SV35 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[140]) ).
thf(152,plain,
! [SV36: $i] :
( ( ( ~ ( test @ SV36 ) )
= $true )
| ( ( complement @ ( sK2_X1 @ SV36 ) @ SV36 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[141]) ).
thf(153,plain,
! [SV37: $i,SV30: $i] :
( ( ( ( ( addition @ SV30 @ SV37 )
!= SV37 ) )
= $true )
| ( ( leq @ SV30 @ SV37 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[144]) ).
thf(154,plain,
! [SV38: $i,SV31: $i] :
( ( ( ~ ( leq @ SV31 @ SV38 ) )
= $true )
| ( ( ( addition @ SV31 @ SV38 )
= SV38 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[145]) ).
thf(155,plain,
! [SV39: $i,SV32: $i] :
( ( ( ( ( multiplication @ SV32 @ SV39 )
!= zero )
| ( ( multiplication @ SV39 @ SV32 )
!= zero )
| ( ( addition @ SV32 @ SV39 )
!= one ) )
= $true )
| ( ( complement @ SV39 @ SV32 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[146]) ).
thf(156,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)],[147]) ).
thf(157,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( complement @ SX1 @ SX0 )
| ( ( addition @ SX0 @ SX1 )
= one ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[148]) ).
thf(158,plain,
! [SV33: $i] :
( ( ( test @ SV33 )
= $false )
| ( ( ! [SY60: $i] :
( ( ( c @ SV33 )
!= SY60 )
| ( complement @ SV33 @ SY60 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[149]) ).
thf(159,plain,
! [SV34: $i] :
( ( ( test @ SV34 )
= $false )
| ( ( ! [SY61: $i] :
( ~ ( complement @ SV34 @ SY61 )
| ( ( c @ SV34 )
= SY61 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[150]) ).
thf(160,plain,
! [SV35: $i,SV40: $i] :
( ( ( ~ ( complement @ SV40 @ SV35 ) )
= $true )
| ( ( test @ SV35 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[151]) ).
thf(161,plain,
! [SV36: $i] :
( ( ( test @ SV36 )
= $false )
| ( ( complement @ ( sK2_X1 @ SV36 ) @ SV36 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[152]) ).
thf(162,plain,
! [SV37: $i,SV30: $i] :
( ( ( ( addition @ SV30 @ SV37 )
= SV37 )
= $false )
| ( ( leq @ SV30 @ SV37 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[153]) ).
thf(163,plain,
! [SV38: $i,SV31: $i] :
( ( ( leq @ SV31 @ SV38 )
= $false )
| ( ( ( addition @ SV31 @ SV38 )
= SV38 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[154]) ).
thf(164,plain,
! [SV39: $i,SV32: $i] :
( ( ( ( ( multiplication @ SV32 @ SV39 )
!= zero )
| ( ( multiplication @ SV39 @ SV32 )
!= zero ) )
= $true )
| ( ( ( ( addition @ SV32 @ SV39 )
!= one ) )
= $true )
| ( ( complement @ SV39 @ SV32 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[155]) ).
thf(165,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)],[156]) ).
thf(166,plain,
! [SV41: $i] :
( ( ! [SY63: $i] :
( ~ ( complement @ SY63 @ SV41 )
| ( ( addition @ SV41 @ SY63 )
= one ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[157]) ).
thf(167,plain,
! [SV42: $i,SV33: $i] :
( ( ( ( ( c @ SV33 )
!= SV42 )
| ( complement @ SV33 @ SV42 ) )
= $true )
| ( ( test @ SV33 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[158]) ).
thf(168,plain,
! [SV43: $i,SV34: $i] :
( ( ( ~ ( complement @ SV34 @ SV43 )
| ( ( c @ SV34 )
= SV43 ) )
= $true )
| ( ( test @ SV34 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[159]) ).
thf(169,plain,
! [SV35: $i,SV40: $i] :
( ( ( complement @ SV40 @ SV35 )
= $false )
| ( ( test @ SV35 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[160]) ).
thf(170,plain,
! [SV39: $i,SV32: $i] :
( ( ( ( ( multiplication @ SV32 @ SV39 )
!= zero ) )
= $true )
| ( ( ( ( multiplication @ SV39 @ SV32 )
!= zero ) )
= $true )
| ( ( ( ( addition @ SV32 @ SV39 )
!= one ) )
= $true )
| ( ( complement @ SV39 @ SV32 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[164]) ).
thf(171,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( complement @ SX1 @ SX0 )
| ( ( multiplication @ SX0 @ SX1 )
= zero ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[165]) ).
thf(172,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( complement @ SX1 @ SX0 )
| ( ( multiplication @ SX1 @ SX0 )
= zero ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[165]) ).
thf(173,plain,
! [SV41: $i,SV44: $i] :
( ( ~ ( complement @ SV44 @ SV41 )
| ( ( addition @ SV41 @ SV44 )
= one ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[166]) ).
thf(174,plain,
! [SV42: $i,SV33: $i] :
( ( ( ( ( c @ SV33 )
!= SV42 ) )
= $true )
| ( ( complement @ SV33 @ SV42 )
= $true )
| ( ( test @ SV33 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[167]) ).
thf(175,plain,
! [SV43: $i,SV34: $i] :
( ( ( ~ ( complement @ SV34 @ SV43 ) )
= $true )
| ( ( ( c @ SV34 )
= SV43 )
= $true )
| ( ( test @ SV34 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[168]) ).
thf(176,plain,
! [SV39: $i,SV32: $i] :
( ( ( ( multiplication @ SV32 @ SV39 )
= zero )
= $false )
| ( ( ( ( multiplication @ SV39 @ SV32 )
!= zero ) )
= $true )
| ( ( ( ( addition @ SV32 @ SV39 )
!= one ) )
= $true )
| ( ( complement @ SV39 @ SV32 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[170]) ).
thf(177,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( complement @ SX1 @ SX0 )
| ( ( multiplication @ SX0 @ SX1 )
= zero ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[171]) ).
thf(178,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( complement @ SX1 @ SX0 )
| ( ( multiplication @ SX1 @ SX0 )
= zero ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[172]) ).
thf(179,plain,
! [SV41: $i,SV44: $i] :
( ( ( ~ ( complement @ SV44 @ SV41 ) )
= $true )
| ( ( ( addition @ SV41 @ SV44 )
= one )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[173]) ).
thf(180,plain,
! [SV42: $i,SV33: $i] :
( ( ( ( c @ SV33 )
= SV42 )
= $false )
| ( ( complement @ SV33 @ SV42 )
= $true )
| ( ( test @ SV33 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[174]) ).
thf(181,plain,
! [SV43: $i,SV34: $i] :
( ( ( complement @ SV34 @ SV43 )
= $false )
| ( ( ( c @ SV34 )
= SV43 )
= $true )
| ( ( test @ SV34 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[175]) ).
thf(182,plain,
! [SV32: $i,SV39: $i] :
( ( ( ( multiplication @ SV39 @ SV32 )
= zero )
= $false )
| ( ( ( multiplication @ SV32 @ SV39 )
= zero )
= $false )
| ( ( ( ( addition @ SV32 @ SV39 )
!= one ) )
= $true )
| ( ( complement @ SV39 @ SV32 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[176]) ).
thf(183,plain,
! [SV45: $i] :
( ( ! [SY64: $i] :
( ~ ( complement @ SY64 @ SV45 )
| ( ( multiplication @ SV45 @ SY64 )
= zero ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[177]) ).
thf(184,plain,
! [SV46: $i] :
( ( ! [SY65: $i] :
( ~ ( complement @ SY65 @ SV46 )
| ( ( multiplication @ SY65 @ SV46 )
= zero ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[178]) ).
thf(185,plain,
! [SV41: $i,SV44: $i] :
( ( ( complement @ SV44 @ SV41 )
= $false )
| ( ( ( addition @ SV41 @ SV44 )
= one )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[179]) ).
thf(186,plain,
! [SV39: $i,SV32: $i] :
( ( ( ( addition @ SV32 @ SV39 )
= one )
= $false )
| ( ( ( multiplication @ SV32 @ SV39 )
= zero )
= $false )
| ( ( ( multiplication @ SV39 @ SV32 )
= zero )
= $false )
| ( ( complement @ SV39 @ SV32 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[182]) ).
thf(187,plain,
! [SV45: $i,SV47: $i] :
( ( ~ ( complement @ SV47 @ SV45 )
| ( ( multiplication @ SV45 @ SV47 )
= zero ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[183]) ).
thf(188,plain,
! [SV46: $i,SV48: $i] :
( ( ~ ( complement @ SV48 @ SV46 )
| ( ( multiplication @ SV48 @ SV46 )
= zero ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[184]) ).
thf(189,plain,
! [SV45: $i,SV47: $i] :
( ( ( ~ ( complement @ SV47 @ SV45 ) )
= $true )
| ( ( ( multiplication @ SV45 @ SV47 )
= zero )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[187]) ).
thf(190,plain,
! [SV46: $i,SV48: $i] :
( ( ( ~ ( complement @ SV48 @ SV46 ) )
= $true )
| ( ( ( multiplication @ SV48 @ SV46 )
= zero )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[188]) ).
thf(191,plain,
! [SV45: $i,SV47: $i] :
( ( ( complement @ SV47 @ SV45 )
= $false )
| ( ( ( multiplication @ SV45 @ SV47 )
= zero )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[189]) ).
thf(192,plain,
! [SV46: $i,SV48: $i] :
( ( ( complement @ SV48 @ SV46 )
= $false )
| ( ( ( multiplication @ SV48 @ SV46 )
= zero )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[190]) ).
thf(193,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[75,192,191,186,185,181,180,169,163,162,161,143,142,121,120,119,118,109,102,97,93,92,91,90,87,86,84,83]) ).
thf(194,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[193]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : KLE048+1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.35 % Computer : n012.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Thu Jun 16 12:19:24 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.36
% 0.13/0.36 No.of.Axioms: 20
% 0.13/0.36
% 0.13/0.36 Length.of.Defs: 0
% 0.13/0.36
% 0.13/0.36 Contains.Choice.Funs: false
% 0.13/0.37 .
% 0.13/0.37 (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:600,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:22,loop_count:0,foatp_calls:0,translation:fof_full)...........
% 52.53/52.72
% 52.53/52.72 ********************************
% 52.53/52.72 * All subproblems solved! *
% 52.53/52.72 ********************************
% 52.53/52.72 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:21,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:193,loop_count:0,foatp_calls:1,translation:fof_full)
% 52.57/52.73
% 52.57/52.73 %**** Beginning of derivation protocol ****
% 52.57/52.73 % SZS output start CNFRefutation
% See solution above
% 52.57/52.73
% 52.57/52.73 %**** End of derivation protocol ****
% 52.57/52.73 %**** no. of clauses in derivation: 194 ****
% 52.57/52.73 %**** clause counter: 193 ****
% 52.57/52.73
% 52.57/52.73 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:21,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:193,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------