TSTP Solution File: KLE142+2 by LEO-II---1.7.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : KLE142+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n026.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 02:11:32 EDT 2022
% Result : Timeout 299.70s 300.13s
% Output : None
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 26
% Syntax : Number of formulae : 205 ( 172 unt; 8 typ; 0 def)
% Number of atoms : 689 ( 342 equ; 0 cnn)
% Maximal formula atoms : 2 ( 3 avg)
% Number of connectives : 1504 ( 85 ~; 81 |; 7 &;1323 @)
% ( 2 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 410 ( 0 ^ 410 !; 0 ?; 410 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_addition,type,
addition: $i > $i > $i ).
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_star,type,
star: $i > $i ).
thf(tp_strong_iteration,type,
strong_iteration: $i > $i ).
thf(tp_zero,type,
zero: $i ).
thf(1,axiom,
! [A: $i,B: $i] :
( ( leq @ A @ B )
<=> ( ( addition @ A @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',order) ).
thf(3,axiom,
! [A: $i,B: $i,C: $i] :
( ( leq @ C @ ( addition @ ( multiplication @ A @ C ) @ B ) )
=> ( leq @ C @ ( multiplication @ ( strong_iteration @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',infty_coinduction) ).
thf(4,axiom,
! [A: $i] :
( ( strong_iteration @ A )
= ( addition @ ( multiplication @ A @ ( strong_iteration @ A ) ) @ one ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',infty_unfold1) ).
thf(5,axiom,
! [A: $i,B: $i,C: $i] :
( ( leq @ ( addition @ ( multiplication @ C @ A ) @ B ) @ C )
=> ( leq @ ( multiplication @ B @ ( star @ A ) ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',star_induction2) ).
thf(6,axiom,
! [A: $i,B: $i,C: $i] :
( ( leq @ ( addition @ ( multiplication @ A @ C ) @ B ) @ C )
=> ( leq @ ( multiplication @ ( star @ A ) @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',star_induction1) ).
thf(7,axiom,
! [A: $i] :
( ( addition @ one @ ( multiplication @ ( star @ A ) @ A ) )
= ( star @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',star_unfold2) ).
thf(8,axiom,
! [A: $i] :
( ( addition @ one @ ( multiplication @ A @ ( star @ A ) ) )
= ( star @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',star_unfold1) ).
thf(9,axiom,
! [A: $i] :
( ( multiplication @ zero @ A )
= zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_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',distributivity2) ).
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',distributivity1) ).
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',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] :
( ( leq @ ( strong_iteration @ ( strong_iteration @ X0 ) ) @ ( strong_iteration @ one ) )
& ( leq @ ( strong_iteration @ one ) @ ( strong_iteration @ ( strong_iteration @ X0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
thf(20,negated_conjecture,
( ( ! [X0: $i] :
( ( leq @ ( strong_iteration @ ( strong_iteration @ X0 ) ) @ ( strong_iteration @ one ) )
& ( leq @ ( strong_iteration @ one ) @ ( strong_iteration @ ( strong_iteration @ X0 ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[19]) ).
thf(21,plain,
( ( ! [X0: $i] :
( ( leq @ ( strong_iteration @ ( strong_iteration @ X0 ) ) @ ( strong_iteration @ one ) )
& ( leq @ ( strong_iteration @ one ) @ ( strong_iteration @ ( strong_iteration @ X0 ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[20]) ).
thf(22,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( leq @ ( addition @ ( multiplication @ C @ A ) @ B ) @ C )
=> ( leq @ ( multiplication @ B @ ( star @ A ) ) @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(23,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( leq @ ( addition @ ( multiplication @ A @ C ) @ B ) @ C )
=> ( leq @ ( multiplication @ ( star @ A ) @ B ) @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(24,plain,
( ( ! [A: $i] :
( ( addition @ one @ ( multiplication @ ( star @ A ) @ A ) )
= ( star @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(25,plain,
( ( ! [A: $i] :
( ( addition @ one @ ( multiplication @ A @ ( star @ A ) ) )
= ( star @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(26,plain,
( ( ! [A: $i] :
( ( multiplication @ zero @ A )
= zero ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(27,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( multiplication @ ( addition @ A @ B ) @ C )
= ( addition @ ( multiplication @ A @ C ) @ ( multiplication @ B @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(28,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( multiplication @ A @ ( addition @ B @ C ) )
= ( addition @ ( multiplication @ A @ B ) @ ( multiplication @ A @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(29,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(30,plain,
( ( ! [A: $i] :
( ( addition @ A @ A )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(31,plain,
( ( ! [A: $i] :
( ( addition @ A @ zero )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(32,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(33,plain,
( ( ! [A: $i,B: $i] :
( ( addition @ A @ B )
= ( addition @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(34,plain,
( ( ! [A: $i,B: $i] :
( ( leq @ A @ B )
<=> ( ( addition @ A @ B )
= B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(35,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( leq @ C @ ( addition @ ( multiplication @ A @ C ) @ B ) )
=> ( leq @ C @ ( multiplication @ ( strong_iteration @ A ) @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(36,plain,
( ( ! [A: $i] :
( ( strong_iteration @ A )
= ( addition @ ( multiplication @ A @ ( strong_iteration @ A ) ) @ one ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(37,plain,
( ( ! [A: $i] :
( ( multiplication @ one @ A )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(38,plain,
( ( ! [A: $i] :
( ( multiplication @ A @ one )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(39,plain,
( ( ( leq @ ( strong_iteration @ ( strong_iteration @ sK1_X0 ) ) @ ( strong_iteration @ one ) )
& ( leq @ ( strong_iteration @ one ) @ ( strong_iteration @ ( strong_iteration @ sK1_X0 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[21]) ).
thf(40,plain,
( ( leq @ ( strong_iteration @ ( strong_iteration @ sK1_X0 ) ) @ ( strong_iteration @ one ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[39]) ).
thf(41,plain,
( ( leq @ ( strong_iteration @ one ) @ ( strong_iteration @ ( strong_iteration @ sK1_X0 ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[39]) ).
thf(42,plain,
( ( ~ ( leq @ ( strong_iteration @ ( strong_iteration @ sK1_X0 ) ) @ ( strong_iteration @ one ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[40]) ).
thf(43,plain,
( ( ~ ( leq @ ( strong_iteration @ one ) @ ( strong_iteration @ ( strong_iteration @ sK1_X0 ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[41]) ).
thf(44,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( leq @ ( addition @ ( multiplication @ C @ A ) @ B ) @ C )
| ( leq @ ( multiplication @ B @ ( star @ A ) ) @ C ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[22]) ).
thf(45,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( leq @ ( addition @ ( multiplication @ A @ C ) @ B ) @ C )
| ( leq @ ( multiplication @ ( star @ A ) @ B ) @ C ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[23]) ).
thf(46,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)],[34]) ).
thf(47,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( leq @ C @ ( addition @ ( multiplication @ A @ C ) @ B ) )
| ( leq @ C @ ( multiplication @ ( strong_iteration @ A ) @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[35]) ).
thf(48,plain,
( ( ! [A: $i] :
( ( multiplication @ A @ one )
= A ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(49,plain,
( ( ! [A: $i] :
( ( multiplication @ one @ A )
= A ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(50,plain,
( ( ! [A: $i] :
( ( strong_iteration @ A )
= ( addition @ ( multiplication @ A @ ( strong_iteration @ A ) ) @ one ) ) )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(51,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( leq @ C @ ( addition @ ( multiplication @ A @ C ) @ B ) )
| ( leq @ C @ ( multiplication @ ( strong_iteration @ A ) @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(52,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)],[46]) ).
thf(53,plain,
( ( ! [A: $i,B: $i] :
( ( addition @ A @ B )
= ( addition @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(54,plain,
( ( ! [C: $i,B: $i,A: $i] :
( ( addition @ A @ ( addition @ B @ C ) )
= ( addition @ ( addition @ A @ B ) @ C ) ) )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(55,plain,
( ( ! [A: $i] :
( ( addition @ A @ zero )
= A ) )
= $true ),
inference(copy,[status(thm)],[31]) ).
thf(56,plain,
( ( ! [A: $i] :
( ( addition @ A @ A )
= A ) )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(57,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( multiplication @ A @ ( multiplication @ B @ C ) )
= ( multiplication @ ( multiplication @ A @ B ) @ C ) ) )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(58,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( multiplication @ A @ ( addition @ B @ C ) )
= ( addition @ ( multiplication @ A @ B ) @ ( multiplication @ A @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[28]) ).
thf(59,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( multiplication @ ( addition @ A @ B ) @ C )
= ( addition @ ( multiplication @ A @ C ) @ ( multiplication @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(60,plain,
( ( ! [A: $i] :
( ( multiplication @ zero @ A )
= zero ) )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(61,plain,
( ( ! [A: $i] :
( ( addition @ one @ ( multiplication @ A @ ( star @ A ) ) )
= ( star @ A ) ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(62,plain,
( ( ! [A: $i] :
( ( addition @ one @ ( multiplication @ ( star @ A ) @ A ) )
= ( star @ A ) ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(63,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( leq @ ( addition @ ( multiplication @ A @ C ) @ B ) @ C )
| ( leq @ ( multiplication @ ( star @ A ) @ B ) @ C ) ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(64,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( leq @ ( addition @ ( multiplication @ C @ A ) @ B ) @ C )
| ( leq @ ( multiplication @ B @ ( star @ A ) ) @ C ) ) )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(65,plain,
( ( ~ ( leq @ ( strong_iteration @ ( strong_iteration @ sK1_X0 ) ) @ ( strong_iteration @ one ) ) )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(66,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)],[52]) ).
thf(67,plain,
! [SV1: $i] :
( ( ( multiplication @ SV1 @ one )
= SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[48]) ).
thf(68,plain,
! [SV2: $i] :
( ( ( multiplication @ one @ SV2 )
= SV2 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[49]) ).
thf(69,plain,
! [SV3: $i] :
( ( ( strong_iteration @ SV3 )
= ( addition @ ( multiplication @ SV3 @ ( strong_iteration @ SV3 ) ) @ one ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[50]) ).
thf(70,plain,
! [SV4: $i] :
( ( ! [SY248: $i,SY249: $i] :
( ~ ( leq @ SY249 @ ( addition @ ( multiplication @ SV4 @ SY249 ) @ SY248 ) )
| ( leq @ SY249 @ ( multiplication @ ( strong_iteration @ SV4 ) @ SY248 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[51]) ).
thf(71,plain,
! [SV5: $i] :
( ( ! [SY250: $i] :
( ( addition @ SV5 @ SY250 )
= ( addition @ SY250 @ SV5 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[53]) ).
thf(72,plain,
! [SV6: $i] :
( ( ! [SY251: $i,SY252: $i] :
( ( addition @ SY252 @ ( addition @ SY251 @ SV6 ) )
= ( addition @ ( addition @ SY252 @ SY251 ) @ SV6 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[54]) ).
thf(73,plain,
! [SV7: $i] :
( ( ( addition @ SV7 @ zero )
= SV7 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[55]) ).
thf(74,plain,
! [SV8: $i] :
( ( ( addition @ SV8 @ SV8 )
= SV8 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[56]) ).
thf(75,plain,
! [SV9: $i] :
( ( ! [SY253: $i,SY254: $i] :
( ( multiplication @ SV9 @ ( multiplication @ SY253 @ SY254 ) )
= ( multiplication @ ( multiplication @ SV9 @ SY253 ) @ SY254 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[57]) ).
thf(76,plain,
! [SV10: $i] :
( ( ! [SY255: $i,SY256: $i] :
( ( multiplication @ SV10 @ ( addition @ SY255 @ SY256 ) )
= ( addition @ ( multiplication @ SV10 @ SY255 ) @ ( multiplication @ SV10 @ SY256 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[58]) ).
thf(77,plain,
! [SV11: $i] :
( ( ! [SY257: $i,SY258: $i] :
( ( multiplication @ ( addition @ SV11 @ SY257 ) @ SY258 )
= ( addition @ ( multiplication @ SV11 @ SY258 ) @ ( multiplication @ SY257 @ SY258 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[59]) ).
thf(78,plain,
! [SV12: $i] :
( ( ( multiplication @ zero @ SV12 )
= zero )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[60]) ).
thf(79,plain,
! [SV13: $i] :
( ( ( addition @ one @ ( multiplication @ SV13 @ ( star @ SV13 ) ) )
= ( star @ SV13 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[61]) ).
thf(80,plain,
! [SV14: $i] :
( ( ( addition @ one @ ( multiplication @ ( star @ SV14 ) @ SV14 ) )
= ( star @ SV14 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[62]) ).
thf(81,plain,
! [SV15: $i] :
( ( ! [SY259: $i,SY260: $i] :
( ~ ( leq @ ( addition @ ( multiplication @ SV15 @ SY260 ) @ SY259 ) @ SY260 )
| ( leq @ ( multiplication @ ( star @ SV15 ) @ SY259 ) @ SY260 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[63]) ).
thf(82,plain,
! [SV16: $i] :
( ( ! [SY261: $i,SY262: $i] :
( ~ ( leq @ ( addition @ ( multiplication @ SY262 @ SV16 ) @ SY261 ) @ SY262 )
| ( leq @ ( multiplication @ SY261 @ ( star @ SV16 ) ) @ SY262 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[64]) ).
thf(83,plain,
( ( leq @ ( strong_iteration @ ( strong_iteration @ sK1_X0 ) ) @ ( strong_iteration @ one ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[65]) ).
thf(84,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)],[66]) ).
thf(85,plain,
! [SV17: $i,SV4: $i] :
( ( ! [SY263: $i] :
( ~ ( leq @ SY263 @ ( addition @ ( multiplication @ SV4 @ SY263 ) @ SV17 ) )
| ( leq @ SY263 @ ( multiplication @ ( strong_iteration @ SV4 ) @ SV17 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[70]) ).
thf(86,plain,
! [SV18: $i,SV5: $i] :
( ( ( addition @ SV5 @ SV18 )
= ( addition @ SV18 @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(87,plain,
! [SV6: $i,SV19: $i] :
( ( ! [SY264: $i] :
( ( addition @ SY264 @ ( addition @ SV19 @ SV6 ) )
= ( addition @ ( addition @ SY264 @ SV19 ) @ SV6 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[72]) ).
thf(88,plain,
! [SV20: $i,SV9: $i] :
( ( ! [SY265: $i] :
( ( multiplication @ SV9 @ ( multiplication @ SV20 @ SY265 ) )
= ( multiplication @ ( multiplication @ SV9 @ SV20 ) @ SY265 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[75]) ).
thf(89,plain,
! [SV21: $i,SV10: $i] :
( ( ! [SY266: $i] :
( ( multiplication @ SV10 @ ( addition @ SV21 @ SY266 ) )
= ( addition @ ( multiplication @ SV10 @ SV21 ) @ ( multiplication @ SV10 @ SY266 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[76]) ).
thf(90,plain,
! [SV22: $i,SV11: $i] :
( ( ! [SY267: $i] :
( ( multiplication @ ( addition @ SV11 @ SV22 ) @ SY267 )
= ( addition @ ( multiplication @ SV11 @ SY267 ) @ ( multiplication @ SV22 @ SY267 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[77]) ).
thf(91,plain,
! [SV23: $i,SV15: $i] :
( ( ! [SY268: $i] :
( ~ ( leq @ ( addition @ ( multiplication @ SV15 @ SY268 ) @ SV23 ) @ SY268 )
| ( leq @ ( multiplication @ ( star @ SV15 ) @ SV23 ) @ SY268 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[81]) ).
thf(92,plain,
! [SV24: $i,SV16: $i] :
( ( ! [SY269: $i] :
( ~ ( leq @ ( addition @ ( multiplication @ SY269 @ SV16 ) @ SV24 ) @ SY269 )
| ( leq @ ( multiplication @ SV24 @ ( star @ SV16 ) ) @ SY269 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[82]) ).
thf(93,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( addition @ SX0 @ SX1 )
!= SX1 )
| ( leq @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[84]) ).
thf(94,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( leq @ SX0 @ SX1 )
| ( ( addition @ SX0 @ SX1 )
= SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[84]) ).
thf(95,plain,
! [SV17: $i,SV4: $i,SV25: $i] :
( ( ~ ( leq @ SV25 @ ( addition @ ( multiplication @ SV4 @ SV25 ) @ SV17 ) )
| ( leq @ SV25 @ ( multiplication @ ( strong_iteration @ SV4 ) @ SV17 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(96,plain,
! [SV6: $i,SV19: $i,SV26: $i] :
( ( ( addition @ SV26 @ ( addition @ SV19 @ SV6 ) )
= ( addition @ ( addition @ SV26 @ SV19 ) @ SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[87]) ).
thf(97,plain,
! [SV27: $i,SV20: $i,SV9: $i] :
( ( ( multiplication @ SV9 @ ( multiplication @ SV20 @ SV27 ) )
= ( multiplication @ ( multiplication @ SV9 @ SV20 ) @ SV27 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(98,plain,
! [SV28: $i,SV21: $i,SV10: $i] :
( ( ( multiplication @ SV10 @ ( addition @ SV21 @ SV28 ) )
= ( addition @ ( multiplication @ SV10 @ SV21 ) @ ( multiplication @ SV10 @ SV28 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[89]) ).
thf(99,plain,
! [SV29: $i,SV22: $i,SV11: $i] :
( ( ( multiplication @ ( addition @ SV11 @ SV22 ) @ SV29 )
= ( addition @ ( multiplication @ SV11 @ SV29 ) @ ( multiplication @ SV22 @ SV29 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[90]) ).
thf(100,plain,
! [SV23: $i,SV30: $i,SV15: $i] :
( ( ~ ( leq @ ( addition @ ( multiplication @ SV15 @ SV30 ) @ SV23 ) @ SV30 )
| ( leq @ ( multiplication @ ( star @ SV15 ) @ SV23 ) @ SV30 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[91]) ).
thf(101,plain,
! [SV24: $i,SV16: $i,SV31: $i] :
( ( ~ ( leq @ ( addition @ ( multiplication @ SV31 @ SV16 ) @ SV24 ) @ SV31 )
| ( leq @ ( multiplication @ SV24 @ ( star @ SV16 ) ) @ SV31 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[92]) ).
thf(102,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( addition @ SX0 @ SX1 )
!= SX1 )
| ( leq @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[93]) ).
thf(103,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( leq @ SX0 @ SX1 )
| ( ( addition @ SX0 @ SX1 )
= SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[94]) ).
thf(104,plain,
! [SV17: $i,SV4: $i,SV25: $i] :
( ( ( ~ ( leq @ SV25 @ ( addition @ ( multiplication @ SV4 @ SV25 ) @ SV17 ) ) )
= $true )
| ( ( leq @ SV25 @ ( multiplication @ ( strong_iteration @ SV4 ) @ SV17 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[95]) ).
thf(105,plain,
! [SV23: $i,SV30: $i,SV15: $i] :
( ( ( ~ ( leq @ ( addition @ ( multiplication @ SV15 @ SV30 ) @ SV23 ) @ SV30 ) )
= $true )
| ( ( leq @ ( multiplication @ ( star @ SV15 ) @ SV23 ) @ SV30 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[100]) ).
thf(106,plain,
! [SV24: $i,SV16: $i,SV31: $i] :
( ( ( ~ ( leq @ ( addition @ ( multiplication @ SV31 @ SV16 ) @ SV24 ) @ SV31 ) )
= $true )
| ( ( leq @ ( multiplication @ SV24 @ ( star @ SV16 ) ) @ SV31 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[101]) ).
thf(107,plain,
! [SV32: $i] :
( ( ! [SY270: $i] :
( ( ( addition @ SV32 @ SY270 )
!= SY270 )
| ( leq @ SV32 @ SY270 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[102]) ).
thf(108,plain,
! [SV33: $i] :
( ( ! [SY271: $i] :
( ~ ( leq @ SV33 @ SY271 )
| ( ( addition @ SV33 @ SY271 )
= SY271 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[103]) ).
thf(109,plain,
! [SV17: $i,SV4: $i,SV25: $i] :
( ( ( leq @ SV25 @ ( addition @ ( multiplication @ SV4 @ SV25 ) @ SV17 ) )
= $false )
| ( ( leq @ SV25 @ ( multiplication @ ( strong_iteration @ SV4 ) @ SV17 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[104]) ).
thf(110,plain,
! [SV23: $i,SV30: $i,SV15: $i] :
( ( ( leq @ ( addition @ ( multiplication @ SV15 @ SV30 ) @ SV23 ) @ SV30 )
= $false )
| ( ( leq @ ( multiplication @ ( star @ SV15 ) @ SV23 ) @ SV30 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[105]) ).
thf(111,plain,
! [SV24: $i,SV16: $i,SV31: $i] :
( ( ( leq @ ( addition @ ( multiplication @ SV31 @ SV16 ) @ SV24 ) @ SV31 )
= $false )
| ( ( leq @ ( multiplication @ SV24 @ ( star @ SV16 ) ) @ SV31 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[106]) ).
thf(112,plain,
! [SV34: $i,SV32: $i] :
( ( ( ( addition @ SV32 @ SV34 )
!= SV34 )
| ( leq @ SV32 @ SV34 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[107]) ).
thf(113,plain,
! [SV35: $i,SV33: $i] :
( ( ~ ( leq @ SV33 @ SV35 )
| ( ( addition @ SV33 @ SV35 )
= SV35 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[108]) ).
thf(114,plain,
! [SV34: $i,SV32: $i] :
( ( ( ( ( addition @ SV32 @ SV34 )
!= SV34 ) )
= $true )
| ( ( leq @ SV32 @ SV34 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[112]) ).
thf(115,plain,
! [SV35: $i,SV33: $i] :
( ( ( ~ ( leq @ SV33 @ SV35 ) )
= $true )
| ( ( ( addition @ SV33 @ SV35 )
= SV35 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[113]) ).
thf(116,plain,
! [SV34: $i,SV32: $i] :
( ( ( ( addition @ SV32 @ SV34 )
= SV34 )
= $false )
| ( ( leq @ SV32 @ SV34 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[114]) ).
thf(117,plain,
! [SV35: $i,SV33: $i] :
( ( ( leq @ SV33 @ SV35 )
= $false )
| ( ( ( addition @ SV33 @ SV35 )
= SV35 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[115]) ).
thf(118,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[67,117,116,111,110,109,99,98,97,96,86,83,80,79,78,74,73,69,68]) ).
thf(119,plain,
( ( ! [A: $i] :
( ( multiplication @ A @ one )
= A ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(120,plain,
( ( ! [A: $i] :
( ( multiplication @ one @ A )
= A ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(121,plain,
( ( ! [A: $i] :
( ( strong_iteration @ A )
= ( addition @ ( multiplication @ A @ ( strong_iteration @ A ) ) @ one ) ) )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(122,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( leq @ C @ ( addition @ ( multiplication @ A @ C ) @ B ) )
| ( leq @ C @ ( multiplication @ ( strong_iteration @ A ) @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(123,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)],[46]) ).
thf(124,plain,
( ( ! [A: $i,B: $i] :
( ( addition @ A @ B )
= ( addition @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(125,plain,
( ( ! [C: $i,B: $i,A: $i] :
( ( addition @ A @ ( addition @ B @ C ) )
= ( addition @ ( addition @ A @ B ) @ C ) ) )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(126,plain,
( ( ! [A: $i] :
( ( addition @ A @ zero )
= A ) )
= $true ),
inference(copy,[status(thm)],[31]) ).
thf(127,plain,
( ( ! [A: $i] :
( ( addition @ A @ A )
= A ) )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(128,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( multiplication @ A @ ( multiplication @ B @ C ) )
= ( multiplication @ ( multiplication @ A @ B ) @ C ) ) )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(129,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( multiplication @ A @ ( addition @ B @ C ) )
= ( addition @ ( multiplication @ A @ B ) @ ( multiplication @ A @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[28]) ).
thf(130,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( multiplication @ ( addition @ A @ B ) @ C )
= ( addition @ ( multiplication @ A @ C ) @ ( multiplication @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(131,plain,
( ( ! [A: $i] :
( ( multiplication @ zero @ A )
= zero ) )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(132,plain,
( ( ! [A: $i] :
( ( addition @ one @ ( multiplication @ A @ ( star @ A ) ) )
= ( star @ A ) ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(133,plain,
( ( ! [A: $i] :
( ( addition @ one @ ( multiplication @ ( star @ A ) @ A ) )
= ( star @ A ) ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(134,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( leq @ ( addition @ ( multiplication @ A @ C ) @ B ) @ C )
| ( leq @ ( multiplication @ ( star @ A ) @ B ) @ C ) ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(135,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( leq @ ( addition @ ( multiplication @ C @ A ) @ B ) @ C )
| ( leq @ ( multiplication @ B @ ( star @ A ) ) @ C ) ) )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(136,plain,
( ( ~ ( leq @ ( strong_iteration @ one ) @ ( strong_iteration @ ( strong_iteration @ sK1_X0 ) ) ) )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(137,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)],[123]) ).
thf(138,plain,
! [SV36: $i] :
( ( ( multiplication @ SV36 @ one )
= SV36 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[119]) ).
thf(139,plain,
! [SV37: $i] :
( ( ( multiplication @ one @ SV37 )
= SV37 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[120]) ).
thf(140,plain,
! [SV38: $i] :
( ( ( strong_iteration @ SV38 )
= ( addition @ ( multiplication @ SV38 @ ( strong_iteration @ SV38 ) ) @ one ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[121]) ).
thf(141,plain,
! [SV39: $i] :
( ( ! [SY272: $i,SY273: $i] :
( ~ ( leq @ SY273 @ ( addition @ ( multiplication @ SV39 @ SY273 ) @ SY272 ) )
| ( leq @ SY273 @ ( multiplication @ ( strong_iteration @ SV39 ) @ SY272 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[122]) ).
thf(142,plain,
! [SV40: $i] :
( ( ! [SY274: $i] :
( ( addition @ SV40 @ SY274 )
= ( addition @ SY274 @ SV40 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[124]) ).
thf(143,plain,
! [SV41: $i] :
( ( ! [SY275: $i,SY276: $i] :
( ( addition @ SY276 @ ( addition @ SY275 @ SV41 ) )
= ( addition @ ( addition @ SY276 @ SY275 ) @ SV41 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[125]) ).
thf(144,plain,
! [SV42: $i] :
( ( ( addition @ SV42 @ zero )
= SV42 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[126]) ).
thf(145,plain,
! [SV43: $i] :
( ( ( addition @ SV43 @ SV43 )
= SV43 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[127]) ).
thf(146,plain,
! [SV44: $i] :
( ( ! [SY277: $i,SY278: $i] :
( ( multiplication @ SV44 @ ( multiplication @ SY277 @ SY278 ) )
= ( multiplication @ ( multiplication @ SV44 @ SY277 ) @ SY278 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[128]) ).
thf(147,plain,
! [SV45: $i] :
( ( ! [SY279: $i,SY280: $i] :
( ( multiplication @ SV45 @ ( addition @ SY279 @ SY280 ) )
= ( addition @ ( multiplication @ SV45 @ SY279 ) @ ( multiplication @ SV45 @ SY280 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[129]) ).
thf(148,plain,
! [SV46: $i] :
( ( ! [SY281: $i,SY282: $i] :
( ( multiplication @ ( addition @ SV46 @ SY281 ) @ SY282 )
= ( addition @ ( multiplication @ SV46 @ SY282 ) @ ( multiplication @ SY281 @ SY282 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[130]) ).
thf(149,plain,
! [SV47: $i] :
( ( ( multiplication @ zero @ SV47 )
= zero )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[131]) ).
thf(150,plain,
! [SV48: $i] :
( ( ( addition @ one @ ( multiplication @ SV48 @ ( star @ SV48 ) ) )
= ( star @ SV48 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[132]) ).
thf(151,plain,
! [SV49: $i] :
( ( ( addition @ one @ ( multiplication @ ( star @ SV49 ) @ SV49 ) )
= ( star @ SV49 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[133]) ).
thf(152,plain,
! [SV50: $i] :
( ( ! [SY283: $i,SY284: $i] :
( ~ ( leq @ ( addition @ ( multiplication @ SV50 @ SY284 ) @ SY283 ) @ SY284 )
| ( leq @ ( multiplication @ ( star @ SV50 ) @ SY283 ) @ SY284 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[134]) ).
thf(153,plain,
! [SV51: $i] :
( ( ! [SY285: $i,SY286: $i] :
( ~ ( leq @ ( addition @ ( multiplication @ SY286 @ SV51 ) @ SY285 ) @ SY286 )
| ( leq @ ( multiplication @ SY285 @ ( star @ SV51 ) ) @ SY286 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[135]) ).
thf(154,plain,
( ( leq @ ( strong_iteration @ one ) @ ( strong_iteration @ ( strong_iteration @ sK1_X0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[136]) ).
thf(155,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)],[137]) ).
thf(156,plain,
! [SV52: $i,SV39: $i] :
( ( ! [SY287: $i] :
( ~ ( leq @ SY287 @ ( addition @ ( multiplication @ SV39 @ SY287 ) @ SV52 ) )
| ( leq @ SY287 @ ( multiplication @ ( strong_iteration @ SV39 ) @ SV52 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[141]) ).
thf(157,plain,
! [SV53: $i,SV40: $i] :
( ( ( addition @ SV40 @ SV53 )
= ( addition @ SV53 @ SV40 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[142]) ).
thf(158,plain,
! [SV41: $i,SV54: $i] :
( ( ! [SY288: $i] :
( ( addition @ SY288 @ ( addition @ SV54 @ SV41 ) )
= ( addition @ ( addition @ SY288 @ SV54 ) @ SV41 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[143]) ).
thf(159,plain,
! [SV55: $i,SV44: $i] :
( ( ! [SY289: $i] :
( ( multiplication @ SV44 @ ( multiplication @ SV55 @ SY289 ) )
= ( multiplication @ ( multiplication @ SV44 @ SV55 ) @ SY289 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[146]) ).
thf(160,plain,
! [SV56: $i,SV45: $i] :
( ( ! [SY290: $i] :
( ( multiplication @ SV45 @ ( addition @ SV56 @ SY290 ) )
= ( addition @ ( multiplication @ SV45 @ SV56 ) @ ( multiplication @ SV45 @ SY290 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[147]) ).
thf(161,plain,
! [SV57: $i,SV46: $i] :
( ( ! [SY291: $i] :
( ( multiplication @ ( addition @ SV46 @ SV57 ) @ SY291 )
= ( addition @ ( multiplication @ SV46 @ SY291 ) @ ( multiplication @ SV57 @ SY291 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[148]) ).
thf(162,plain,
! [SV58: $i,SV50: $i] :
( ( ! [SY292: $i] :
( ~ ( leq @ ( addition @ ( multiplication @ SV50 @ SY292 ) @ SV58 ) @ SY292 )
| ( leq @ ( multiplication @ ( star @ SV50 ) @ SV58 ) @ SY292 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[152]) ).
thf(163,plain,
! [SV59: $i,SV51: $i] :
( ( ! [SY293: $i] :
( ~ ( leq @ ( addition @ ( multiplication @ SY293 @ SV51 ) @ SV59 ) @ SY293 )
| ( leq @ ( multiplication @ SV59 @ ( star @ SV51 ) ) @ SY293 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[153]) ).
thf(164,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( addition @ SX0 @ SX1 )
!= SX1 )
| ( leq @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[155]) ).
thf(165,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( leq @ SX0 @ SX1 )
| ( ( addition @ SX0 @ SX1 )
= SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[155]) ).
thf(166,plain,
! [SV52: $i,SV39: $i,SV60: $i] :
( ( ~ ( leq @ SV60 @ ( addition @ ( multiplication @ SV39 @ SV60 ) @ SV52 ) )
| ( leq @ SV60 @ ( multiplication @ ( strong_iteration @ SV39 ) @ SV52 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[156]) ).
thf(167,plain,
! [SV41: $i,SV54: $i,SV61: $i] :
( ( ( addition @ SV61 @ ( addition @ SV54 @ SV41 ) )
= ( addition @ ( addition @ SV61 @ SV54 ) @ SV41 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[158]) ).
thf(168,plain,
! [SV62: $i,SV55: $i,SV44: $i] :
( ( ( multiplication @ SV44 @ ( multiplication @ SV55 @ SV62 ) )
= ( multiplication @ ( multiplication @ SV44 @ SV55 ) @ SV62 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[159]) ).
thf(169,plain,
! [SV63: $i,SV56: $i,SV45: $i] :
( ( ( multiplication @ SV45 @ ( addition @ SV56 @ SV63 ) )
= ( addition @ ( multiplication @ SV45 @ SV56 ) @ ( multiplication @ SV45 @ SV63 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[160]) ).
thf(170,plain,
! [SV64: $i,SV57: $i,SV46: $i] :
( ( ( multiplication @ ( addition @ SV46 @ SV57 ) @ SV64 )
= ( addition @ ( multiplication @ SV46 @ SV64 ) @ ( multiplication @ SV57 @ SV64 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[161]) ).
thf(171,plain,
! [SV58: $i,SV65: $i,SV50: $i] :
( ( ~ ( leq @ ( addition @ ( multiplication @ SV50 @ SV65 ) @ SV58 ) @ SV65 )
| ( leq @ ( multiplication @ ( star @ SV50 ) @ SV58 ) @ SV65 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[162]) ).
thf(172,plain,
! [SV59: $i,SV51: $i,SV66: $i] :
( ( ~ ( leq @ ( addition @ ( multiplication @ SV66 @ SV51 ) @ SV59 ) @ SV66 )
| ( leq @ ( multiplication @ SV59 @ ( star @ SV51 ) ) @ SV66 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[163]) ).
thf(173,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( addition @ SX0 @ SX1 )
!= SX1 )
| ( leq @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[164]) ).
thf(174,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( leq @ SX0 @ SX1 )
| ( ( addition @ SX0 @ SX1 )
= SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[165]) ).
thf(175,plain,
! [SV52: $i,SV39: $i,SV60: $i] :
( ( ( ~ ( leq @ SV60 @ ( addition @ ( multiplication @ SV39 @ SV60 ) @ SV52 ) ) )
= $true )
| ( ( leq @ SV60 @ ( multiplication @ ( strong_iteration @ SV39 ) @ SV52 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[166]) ).
thf(176,plain,
! [SV58: $i,SV65: $i,SV50: $i] :
( ( ( ~ ( leq @ ( addition @ ( multiplication @ SV50 @ SV65 ) @ SV58 ) @ SV65 ) )
= $true )
| ( ( leq @ ( multiplication @ ( star @ SV50 ) @ SV58 ) @ SV65 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[171]) ).
thf(177,plain,
! [SV59: $i,SV51: $i,SV66: $i] :
( ( ( ~ ( leq @ ( addition @ ( multiplication @ SV66 @ SV51 ) @ SV59 ) @ SV66 ) )
= $true )
| ( ( leq @ ( multiplication @ SV59 @ ( star @ SV51 ) ) @ SV66 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[172]) ).
thf(178,plain,
! [SV67: $i] :
( ( ! [SY294: $i] :
( ( ( addition @ SV67 @ SY294 )
!= SY294 )
| ( leq @ SV67 @ SY294 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[173]) ).
thf(179,plain,
! [SV68: $i] :
( ( ! [SY295: $i] :
( ~ ( leq @ SV68 @ SY295 )
| ( ( addition @ SV68 @ SY295 )
= SY295 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[174]) ).
thf(180,plain,
! [SV52: $i,SV39: $i,SV60: $i] :
( ( ( leq @ SV60 @ ( addition @ ( multiplication @ SV39 @ SV60 ) @ SV52 ) )
= $false )
| ( ( leq @ SV60 @ ( multiplication @ ( strong_iteration @ SV39 ) @ SV52 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[175]) ).
thf(181,plain,
! [SV58: $i,SV65: $i,SV50: $i] :
( ( ( leq @ ( addition @ ( multiplication @ SV50 @ SV65 ) @ SV58 ) @ SV65 )
= $false )
| ( ( leq @ ( multiplication @ ( star @ SV50 ) @ SV58 ) @ SV65 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[176]) ).
thf(182,plain,
! [SV59: $i,SV51: $i,SV66: $i] :
( ( ( leq @ ( addition @ ( multiplication @ SV66 @ SV51 ) @ SV59 ) @ SV66 )
= $false )
| ( ( leq @ ( multiplication @ SV59 @ ( star @ SV51 ) ) @ SV66 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[177]) ).
thf(183,plain,
! [SV69: $i,SV67: $i] :
( ( ( ( addition @ SV67 @ SV69 )
!= SV69 )
| ( leq @ SV67 @ SV69 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[178]) ).
thf(184,plain,
! [SV70: $i,SV68: $i] :
( ( ~ ( leq @ SV68 @ SV70 )
| ( ( addition @ SV68 @ SV70 )
= SV70 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[179]) ).
thf(185,plain,
! [SV69: $i,SV67: $i] :
( ( ( ( ( addition @ SV67 @ SV69 )
!= SV69 ) )
= $true )
| ( ( leq @ SV67 @ SV69 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[183]) ).
thf(186,plain,
! [SV70: $i,SV68: $i] :
( ( ( ~ ( leq @ SV68 @ SV70 ) )
= $true )
| ( ( ( addition @ SV68 @ SV70 )
= SV70 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[184]) ).
thf(187,plain,
! [SV69: $i,SV67: $i] :
( ( ( ( addition @ SV67 @ SV69 )
= SV69 )
= $false )
| ( ( leq @ SV67 @ SV69 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[185]) ).
thf(188,plain,
! [SV70: $i,SV68: $i] :
( ( ( leq @ SV68 @ SV70 )
= $false )
| ( ( ( addition @ SV68 @ SV70 )
= SV70 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[186]) ).
thf(189,plain,
! [SV71: $i] :
( ( ( multiplication @ SV71 @ one )
= SV71 )
= $true ),
inference(rename,[status(thm)],[138]) ).
thf(190,plain,
! [SV72: $i] :
( ( ( multiplication @ one @ SV72 )
= SV72 )
= $true ),
inference(rename,[status(thm)],[139]) ).
thf(191,plain,
! [SV73: $i] :
( ( ( strong_iteration @ SV73 )
= ( addition @ ( multiplication @ SV73 @ ( strong_iteration @ SV73 ) ) @ one ) )
= $true ),
inference(rename,[status(thm)],[140]) ).
thf(192,plain,
! [SV74: $i] :
( ( ( addition @ SV74 @ zero )
= SV74 )
= $true ),
inference(rename,[status(thm)],[144]) ).
thf(193,plain,
! [SV75: $i] :
( ( ( addition @ SV75 @ SV75 )
= SV75 )
= $true ),
inference(rename,[status(thm)],[145]) ).
thf(194,plain,
! [SV76: $i] :
( ( ( multiplication @ zero @ SV76 )
= zero )
= $true ),
inference(rename,[status(thm)],[149]) ).
thf(195,plain,
! [SV77: $i] :
( ( ( addition @ one @ ( multiplication @ SV77 @ ( star @ SV77 ) ) )
= ( star @ SV77 ) )
= $true ),
inference(rename,[status(thm)],[150]) ).
thf(196,plain,
! [SV78: $i] :
( ( ( addition @ one @ ( multiplication @ ( star @ SV78 ) @ SV78 ) )
= ( star @ SV78 ) )
= $true ),
inference(rename,[status(thm)],[151]) ).
thf(205,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[154,196,195,194,193,192,191,190,189,188,187,182,181,180,170,169,168,167,157]) ).
thf(206,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[205,118]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.14 % Problem : KLE142+2 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.14 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.14/0.36 % Computer : n026.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 600
% 0.14/0.36 % DateTime : Thu Jun 16 09:35:23 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.21/0.37
% 0.21/0.37 No.of.Axioms: 18
% 0.21/0.37
% 0.21/0.37 Length.of.Defs: 0
% 0.21/0.37
% 0.21/0.37 Contains.Choice.Funs: false
% 0.21/0.38 (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).........eprover: CPU time limit exceeded, terminating
% 75.17/75.37 .
% 75.17/75.38 (rf:0,axioms:18,ps:2,u:1,ude:false,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).........eprover: CPU time limit exceeded, terminating
% 150.12/150.46
% 150.12/150.46 (rf:0,axioms:18,ps:3,u:8,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:false,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).........eprover: CPU time limit exceeded, terminating
% 224.59/225.08 ...
% 224.79/225.29 (rf:2,axioms:17,ps:1,u:3,ude:true,rLeibEQ:false,rAndEQ:false,use_choice:false,use_extuni:false,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).........eprover: CPU time limit exceeded, terminating
% 299.70/300.13 .
% 299.81/300.40
% 299.81/300.40 ********************************
% 299.81/300.40 * All subproblems solved! *
% 299.81/300.40 ********************************
% 299.81/300.40 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:2,axioms:17,ps:1,u:3,ude:true,rLeibEQ:false,rAndEQ:false,use_choice:false,use_extuni:false,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:59,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:205,loop_count:10,foatp_calls:2,translation:fof_full)
% 299.81/300.41
% 299.81/300.41 %**** Beginning of derivation protocol ****
% 299.81/300.41 % SZS output start CNFRefutation
% See solution above
% 299.81/300.41
% 299.81/300.41 %**** End of derivation protocol ****
% 299.81/300.41 %**** no. of clauses in derivation: 197 ****
% 299.81/300.41 %**** clause counter: 205 ****
% 299.81/300.41
% 299.81/300.41 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:2,axioms:17,ps:1,u:3,ude:true,rLeibEQ:false,rAndEQ:false,use_choice:false,use_extuni:false,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:59,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:205,loop_count:10,foatp_calls:2,translation:fof_full)
%------------------------------------------------------------------------------