TSTP Solution File: KLE142+1 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : KLE142+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 : n032.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 : Theorem 261.68s 262.11s
% Output : CNFRefutation 261.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 24
% Syntax : Number of formulae : 105 ( 89 unt; 8 typ; 0 def)
% Number of atoms : 304 ( 176 equ; 0 cnn)
% Maximal formula atoms : 2 ( 3 avg)
% Number of connectives : 624 ( 33 ~; 29 |; 2 &; 556 @)
% ( 2 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 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 : 188 ( 0 ^ 188 !; 0 ?; 188 :)
% 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(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] :
( ( strong_iteration @ ( strong_iteration @ X0 ) )
= ( strong_iteration @ one ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
thf(20,negated_conjecture,
( ( ! [X0: $i] :
( ( strong_iteration @ ( strong_iteration @ X0 ) )
= ( strong_iteration @ one ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[19]) ).
thf(21,plain,
( ( ! [X0: $i] :
( ( strong_iteration @ ( strong_iteration @ X0 ) )
= ( strong_iteration @ one ) ) )
= $false ),
inference(unfold_def,[status(thm)],[20]) ).
thf(22,plain,
( ( ! [A: $i,B: $i] :
( ( leq @ A @ B )
<=> ( ( addition @ A @ B )
= B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(23,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(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] :
( ( strong_iteration @ A )
= ( addition @ ( multiplication @ A @ ( strong_iteration @ A ) ) @ one ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(35,plain,
( ( ! [A: $i] :
( ( multiplication @ one @ A )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(36,plain,
( ( ! [A: $i] :
( ( multiplication @ A @ one )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(37,plain,
( ( ( strong_iteration @ ( strong_iteration @ sK1_X0 ) )
= ( strong_iteration @ one ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[21]) ).
thf(38,plain,
( ( ( ( strong_iteration @ ( strong_iteration @ sK1_X0 ) )
!= ( strong_iteration @ one ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[37]) ).
thf(39,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)],[22]) ).
thf(40,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)],[23]) ).
thf(41,plain,
( ( ! [A: $i] :
( ( multiplication @ A @ one )
= A ) )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(42,plain,
( ( ! [A: $i] :
( ( multiplication @ one @ A )
= A ) )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(43,plain,
( ( ! [A: $i] :
( ( strong_iteration @ A )
= ( addition @ ( multiplication @ A @ ( strong_iteration @ A ) ) @ one ) ) )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(44,plain,
( ( ! [A: $i,B: $i] :
( ( addition @ A @ B )
= ( addition @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(45,plain,
( ( ! [C: $i,B: $i,A: $i] :
( ( addition @ A @ ( addition @ B @ C ) )
= ( addition @ ( addition @ A @ B ) @ C ) ) )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(46,plain,
( ( ! [A: $i] :
( ( addition @ A @ zero )
= A ) )
= $true ),
inference(copy,[status(thm)],[31]) ).
thf(47,plain,
( ( ! [A: $i] :
( ( addition @ A @ A )
= A ) )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(48,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( multiplication @ A @ ( multiplication @ B @ C ) )
= ( multiplication @ ( multiplication @ A @ B ) @ C ) ) )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(49,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(50,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(51,plain,
( ( ! [A: $i] :
( ( multiplication @ zero @ A )
= zero ) )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(52,plain,
( ( ! [A: $i] :
( ( addition @ one @ ( multiplication @ A @ ( star @ A ) ) )
= ( star @ A ) ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(53,plain,
( ( ! [A: $i] :
( ( addition @ one @ ( multiplication @ ( star @ A ) @ A ) )
= ( star @ A ) ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(54,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)],[40]) ).
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(copy,[status(thm)],[39]) ).
thf(56,plain,
( ( ( ( strong_iteration @ ( strong_iteration @ sK1_X0 ) )
!= ( strong_iteration @ one ) ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(57,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)],[55]) ).
thf(58,plain,
! [SV1: $i] :
( ( ( multiplication @ SV1 @ one )
= SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[41]) ).
thf(59,plain,
! [SV2: $i] :
( ( ( multiplication @ one @ SV2 )
= SV2 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[42]) ).
thf(60,plain,
! [SV3: $i] :
( ( ( strong_iteration @ SV3 )
= ( addition @ ( multiplication @ SV3 @ ( strong_iteration @ SV3 ) ) @ one ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[43]) ).
thf(61,plain,
! [SV4: $i] :
( ( ! [SY170: $i] :
( ( addition @ SV4 @ SY170 )
= ( addition @ SY170 @ SV4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[44]) ).
thf(62,plain,
! [SV5: $i] :
( ( ! [SY171: $i,SY172: $i] :
( ( addition @ SY172 @ ( addition @ SY171 @ SV5 ) )
= ( addition @ ( addition @ SY172 @ SY171 ) @ SV5 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[45]) ).
thf(63,plain,
! [SV6: $i] :
( ( ( addition @ SV6 @ zero )
= SV6 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[46]) ).
thf(64,plain,
! [SV7: $i] :
( ( ( addition @ SV7 @ SV7 )
= SV7 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[47]) ).
thf(65,plain,
! [SV8: $i] :
( ( ! [SY173: $i,SY174: $i] :
( ( multiplication @ SV8 @ ( multiplication @ SY173 @ SY174 ) )
= ( multiplication @ ( multiplication @ SV8 @ SY173 ) @ SY174 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[48]) ).
thf(66,plain,
! [SV9: $i] :
( ( ! [SY175: $i,SY176: $i] :
( ( multiplication @ SV9 @ ( addition @ SY175 @ SY176 ) )
= ( addition @ ( multiplication @ SV9 @ SY175 ) @ ( multiplication @ SV9 @ SY176 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[49]) ).
thf(67,plain,
! [SV10: $i] :
( ( ! [SY177: $i,SY178: $i] :
( ( multiplication @ ( addition @ SV10 @ SY177 ) @ SY178 )
= ( addition @ ( multiplication @ SV10 @ SY178 ) @ ( multiplication @ SY177 @ SY178 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[50]) ).
thf(68,plain,
! [SV11: $i] :
( ( ( multiplication @ zero @ SV11 )
= zero )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[51]) ).
thf(69,plain,
! [SV12: $i] :
( ( ( addition @ one @ ( multiplication @ SV12 @ ( star @ SV12 ) ) )
= ( star @ SV12 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[52]) ).
thf(70,plain,
! [SV13: $i] :
( ( ( addition @ one @ ( multiplication @ ( star @ SV13 ) @ SV13 ) )
= ( star @ SV13 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[53]) ).
thf(71,plain,
! [SV14: $i] :
( ( ! [SY179: $i,SY180: $i] :
( ~ ( leq @ SY180 @ ( addition @ ( multiplication @ SV14 @ SY180 ) @ SY179 ) )
| ( leq @ SY180 @ ( multiplication @ ( strong_iteration @ SV14 ) @ SY179 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[54]) ).
thf(72,plain,
( ( ( strong_iteration @ ( strong_iteration @ sK1_X0 ) )
= ( strong_iteration @ one ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[56]) ).
thf(73,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)],[57]) ).
thf(74,plain,
! [SV15: $i,SV4: $i] :
( ( ( addition @ SV4 @ SV15 )
= ( addition @ SV15 @ SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[61]) ).
thf(75,plain,
! [SV5: $i,SV16: $i] :
( ( ! [SY181: $i] :
( ( addition @ SY181 @ ( addition @ SV16 @ SV5 ) )
= ( addition @ ( addition @ SY181 @ SV16 ) @ SV5 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[62]) ).
thf(76,plain,
! [SV17: $i,SV8: $i] :
( ( ! [SY182: $i] :
( ( multiplication @ SV8 @ ( multiplication @ SV17 @ SY182 ) )
= ( multiplication @ ( multiplication @ SV8 @ SV17 ) @ SY182 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[65]) ).
thf(77,plain,
! [SV18: $i,SV9: $i] :
( ( ! [SY183: $i] :
( ( multiplication @ SV9 @ ( addition @ SV18 @ SY183 ) )
= ( addition @ ( multiplication @ SV9 @ SV18 ) @ ( multiplication @ SV9 @ SY183 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[66]) ).
thf(78,plain,
! [SV19: $i,SV10: $i] :
( ( ! [SY184: $i] :
( ( multiplication @ ( addition @ SV10 @ SV19 ) @ SY184 )
= ( addition @ ( multiplication @ SV10 @ SY184 ) @ ( multiplication @ SV19 @ SY184 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[67]) ).
thf(79,plain,
! [SV20: $i,SV14: $i] :
( ( ! [SY185: $i] :
( ~ ( leq @ SY185 @ ( addition @ ( multiplication @ SV14 @ SY185 ) @ SV20 ) )
| ( leq @ SY185 @ ( multiplication @ ( strong_iteration @ SV14 ) @ SV20 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(80,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( addition @ SX0 @ SX1 )
!= SX1 )
| ( leq @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[73]) ).
thf(81,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( leq @ SX0 @ SX1 )
| ( ( addition @ SX0 @ SX1 )
= SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[73]) ).
thf(82,plain,
! [SV5: $i,SV16: $i,SV21: $i] :
( ( ( addition @ SV21 @ ( addition @ SV16 @ SV5 ) )
= ( addition @ ( addition @ SV21 @ SV16 ) @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[75]) ).
thf(83,plain,
! [SV22: $i,SV17: $i,SV8: $i] :
( ( ( multiplication @ SV8 @ ( multiplication @ SV17 @ SV22 ) )
= ( multiplication @ ( multiplication @ SV8 @ SV17 ) @ SV22 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[76]) ).
thf(84,plain,
! [SV23: $i,SV18: $i,SV9: $i] :
( ( ( multiplication @ SV9 @ ( addition @ SV18 @ SV23 ) )
= ( addition @ ( multiplication @ SV9 @ SV18 ) @ ( multiplication @ SV9 @ SV23 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[77]) ).
thf(85,plain,
! [SV24: $i,SV19: $i,SV10: $i] :
( ( ( multiplication @ ( addition @ SV10 @ SV19 ) @ SV24 )
= ( addition @ ( multiplication @ SV10 @ SV24 ) @ ( multiplication @ SV19 @ SV24 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[78]) ).
thf(86,plain,
! [SV20: $i,SV14: $i,SV25: $i] :
( ( ~ ( leq @ SV25 @ ( addition @ ( multiplication @ SV14 @ SV25 ) @ SV20 ) )
| ( leq @ SV25 @ ( multiplication @ ( strong_iteration @ SV14 ) @ SV20 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[79]) ).
thf(87,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( addition @ SX0 @ SX1 )
!= SX1 )
| ( leq @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[80]) ).
thf(88,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( leq @ SX0 @ SX1 )
| ( ( addition @ SX0 @ SX1 )
= SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[81]) ).
thf(89,plain,
! [SV20: $i,SV14: $i,SV25: $i] :
( ( ( ~ ( leq @ SV25 @ ( addition @ ( multiplication @ SV14 @ SV25 ) @ SV20 ) ) )
= $true )
| ( ( leq @ SV25 @ ( multiplication @ ( strong_iteration @ SV14 ) @ SV20 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[86]) ).
thf(90,plain,
! [SV26: $i] :
( ( ! [SY186: $i] :
( ( ( addition @ SV26 @ SY186 )
!= SY186 )
| ( leq @ SV26 @ SY186 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[87]) ).
thf(91,plain,
! [SV27: $i] :
( ( ! [SY187: $i] :
( ~ ( leq @ SV27 @ SY187 )
| ( ( addition @ SV27 @ SY187 )
= SY187 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(92,plain,
! [SV20: $i,SV14: $i,SV25: $i] :
( ( ( leq @ SV25 @ ( addition @ ( multiplication @ SV14 @ SV25 ) @ SV20 ) )
= $false )
| ( ( leq @ SV25 @ ( multiplication @ ( strong_iteration @ SV14 ) @ SV20 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[89]) ).
thf(93,plain,
! [SV28: $i,SV26: $i] :
( ( ( ( addition @ SV26 @ SV28 )
!= SV28 )
| ( leq @ SV26 @ SV28 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[90]) ).
thf(94,plain,
! [SV29: $i,SV27: $i] :
( ( ~ ( leq @ SV27 @ SV29 )
| ( ( addition @ SV27 @ SV29 )
= SV29 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[91]) ).
thf(95,plain,
! [SV28: $i,SV26: $i] :
( ( ( ( ( addition @ SV26 @ SV28 )
!= SV28 ) )
= $true )
| ( ( leq @ SV26 @ SV28 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[93]) ).
thf(96,plain,
! [SV29: $i,SV27: $i] :
( ( ( ~ ( leq @ SV27 @ SV29 ) )
= $true )
| ( ( ( addition @ SV27 @ SV29 )
= SV29 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[94]) ).
thf(97,plain,
! [SV28: $i,SV26: $i] :
( ( ( ( addition @ SV26 @ SV28 )
= SV28 )
= $false )
| ( ( leq @ SV26 @ SV28 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[95]) ).
thf(98,plain,
! [SV29: $i,SV27: $i] :
( ( ( leq @ SV27 @ SV29 )
= $false )
| ( ( ( addition @ SV27 @ SV29 )
= SV29 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[96]) ).
thf(99,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[58,98,97,92,85,84,83,82,74,72,70,69,68,64,63,60,59]) ).
thf(100,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[99]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : KLE142+1 : TPTP v8.1.0. Released v4.0.0.
% 0.10/0.10 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.10/0.30 % Computer : n032.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 600
% 0.10/0.30 % DateTime : Thu Jun 16 15:27:30 EDT 2022
% 0.10/0.30 % CPUTime :
% 0.10/0.31
% 0.10/0.31 No.of.Axioms: 18
% 0.10/0.31
% 0.10/0.31 Length.of.Defs: 0
% 0.10/0.31
% 0.10/0.31 Contains.Choice.Funs: false
% 0.16/0.32 (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
% 148.24/148.48 eprover: CPU time limit exceeded, terminating
% 148.29/148.56 .
% 148.29/148.57 (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
% 186.36/186.65 .eprover: CPU time limit exceeded, terminating
% 224.47/224.73 .
% 224.47/224.73 (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
% 261.56/261.82 ..
% 261.62/261.88 (rf:2,axioms:15,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).....
% 261.68/262.11
% 261.68/262.11 ********************************
% 261.68/262.11 * All subproblems solved! *
% 261.68/262.11 ********************************
% 261.68/262.11 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:2,axioms:15,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:149,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:99,loop_count:0,foatp_calls:1,translation:fof_full)
% 261.68/262.12
% 261.68/262.12 %**** Beginning of derivation protocol ****
% 261.68/262.12 % SZS output start CNFRefutation
% See solution above
% 261.68/262.12
% 261.68/262.12 %**** End of derivation protocol ****
% 261.68/262.12 %**** no. of clauses in derivation: 97 ****
% 261.68/262.12 %**** clause counter: 99 ****
% 261.68/262.12
% 261.68/262.12 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:2,axioms:15,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:149,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:99,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------