%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : KLE142+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 10:26:03 AM UTC 2026
% Result : Theorem 12.49s 2.49s
% Output : CNFRefutation 12.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 19
% Syntax : Number of formulae : 193 ( 168 unt; 0 typ; 0 def)
% Number of atoms : 675 ( 331 equ; 0 cnn)
% Maximal formula atoms : 2 ( 3 avg)
% Number of connectives : 1538 ( 88 ~; 76 |; 4 &;1354 @)
% ( 4 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 393 ( 0 ^; 393 !; 0 ?; 393 :)
% 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(2,axiom,
! [A: $i] :
( ( strong_iteration @ A )
= ( addition @ ( star @ A ) @ ( multiplication @ ( strong_iteration @ A ) @ zero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',isolation) ).
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] :
( ( leq @ A @ B )
<=> ( ( addition @ A @ B )
= B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(23,plain,
( ( ! [A: $i] :
( ( strong_iteration @ A )
= ( addition @ ( star @ A ) @ ( multiplication @ ( strong_iteration @ A ) @ zero ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(24,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(25,plain,
( ( ! [A: $i] :
( ( strong_iteration @ A )
= ( addition @ ( multiplication @ A @ ( strong_iteration @ A ) ) @ one ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(26,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(27,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(28,plain,
( ( ! [A: $i] :
( ( addition @ one @ ( multiplication @ ( star @ A ) @ A ) )
= ( star @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(29,plain,
( ( ! [A: $i] :
( ( addition @ one @ ( multiplication @ A @ ( star @ A ) ) )
= ( star @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(30,plain,
( ( ! [A: $i] :
( ( multiplication @ zero @ A )
= zero ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(31,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( multiplication @ ( addition @ A @ B ) @ C )
= ( addition @ ( multiplication @ A @ C ) @ ( multiplication @ B @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(32,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( multiplication @ A @ ( addition @ B @ C ) )
= ( addition @ ( multiplication @ A @ B ) @ ( multiplication @ A @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(33,plain,
( ( ! [A: $i] :
( ( multiplication @ one @ A )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(34,plain,
( ( ! [A: $i] :
( ( multiplication @ A @ one )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(35,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( multiplication @ A @ ( multiplication @ B @ C ) )
= ( multiplication @ ( multiplication @ A @ B ) @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(36,plain,
( ( ! [A: $i] :
( ( addition @ A @ A )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(37,plain,
( ( ! [A: $i] :
( ( addition @ A @ zero )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(38,plain,
( ( ! [C: $i,B: $i,A: $i] :
( ( addition @ A @ ( addition @ B @ C ) )
= ( addition @ ( addition @ A @ B ) @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(39,plain,
( ( ! [A: $i,B: $i] :
( ( addition @ A @ B )
= ( addition @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(40,plain,
( ( ( 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(41,plain,
( ( leq @ ( strong_iteration @ ( strong_iteration @ sK1_X0 ) ) @ ( strong_iteration @ one ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[40]) ).
thf(42,plain,
( ( leq @ ( strong_iteration @ one ) @ ( strong_iteration @ ( strong_iteration @ sK1_X0 ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[40]) ).
thf(43,plain,
( ( ~ ( leq @ ( strong_iteration @ ( strong_iteration @ sK1_X0 ) ) @ ( strong_iteration @ one ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[41]) ).
thf(44,plain,
( ( ~ ( leq @ ( strong_iteration @ one ) @ ( strong_iteration @ ( strong_iteration @ sK1_X0 ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[42]) ).
thf(45,plain,
( ( ! [A: $i,B: $i] :
( ( addition @ A @ B )
= ( addition @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(46,plain,
( ( ! [C: $i,B: $i,A: $i] :
( ( addition @ A @ ( addition @ B @ C ) )
= ( addition @ ( addition @ A @ B ) @ C ) ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(47,plain,
( ( ! [A: $i] :
( ( addition @ A @ zero )
= A ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(48,plain,
( ( ! [A: $i] :
( ( addition @ A @ A )
= A ) )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(49,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( multiplication @ A @ ( multiplication @ B @ C ) )
= ( multiplication @ ( multiplication @ A @ B ) @ C ) ) )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(50,plain,
( ( ! [A: $i] :
( ( multiplication @ A @ one )
= A ) )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(51,plain,
( ( ! [A: $i] :
( ( multiplication @ one @ A )
= A ) )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(52,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( multiplication @ A @ ( addition @ B @ C ) )
= ( addition @ ( multiplication @ A @ B ) @ ( multiplication @ A @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(53,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( multiplication @ ( addition @ A @ B ) @ C )
= ( addition @ ( multiplication @ A @ C ) @ ( multiplication @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[31]) ).
thf(54,plain,
( ( ! [A: $i] :
( ( multiplication @ zero @ A )
= zero ) )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(55,plain,
( ( ! [A: $i] :
( ( addition @ one @ ( multiplication @ A @ ( star @ A ) ) )
= ( star @ A ) ) )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(56,plain,
( ( ! [A: $i] :
( ( addition @ one @ ( multiplication @ ( star @ A ) @ A ) )
= ( star @ A ) ) )
= $true ),
inference(copy,[status(thm)],[28]) ).
thf(57,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)],[27]) ).
thf(58,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)],[26]) ).
thf(59,plain,
( ( ! [A: $i] :
( ( strong_iteration @ A )
= ( addition @ ( multiplication @ A @ ( strong_iteration @ A ) ) @ one ) ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(60,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)],[24]) ).
thf(61,plain,
( ( ! [A: $i] :
( ( strong_iteration @ A )
= ( addition @ ( star @ A ) @ ( multiplication @ ( strong_iteration @ A ) @ zero ) ) ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(62,plain,
( ( ! [A: $i,B: $i] :
( ( leq @ A @ B )
<=> ( ( addition @ A @ B )
= B ) ) )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(63,plain,
( ( ~ ( leq @ ( strong_iteration @ ( strong_iteration @ sK1_X0 ) ) @ ( strong_iteration @ one ) ) )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(64,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( leq @ ( addition @ ( multiplication @ SX0 @ SX2 ) @ SX1 ) @ SX2 )
| ( leq @ ( multiplication @ ( star @ SX0 ) @ SX1 ) @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[57]) ).
thf(65,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( leq @ ( addition @ ( multiplication @ SX2 @ SX0 ) @ SX1 ) @ SX2 )
| ( leq @ ( multiplication @ SX1 @ ( star @ SX0 ) ) @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[58]) ).
thf(66,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( leq @ SX2 @ ( addition @ ( multiplication @ SX0 @ SX2 ) @ SX1 ) )
| ( leq @ SX2 @ ( multiplication @ ( strong_iteration @ SX0 ) @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[60]) ).
thf(67,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( leq @ SX0 @ SX1 )
| ( ( addition @ SX0 @ SX1 )
= SX1 ) )
| ~ ( ( ( addition @ SX0 @ SX1 )
!= SX1 )
| ( leq @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[62]) ).
thf(68,plain,
! [SV1: $i] :
( ( ! [SY35: $i] :
( ( addition @ SV1 @ SY35 )
= ( addition @ SY35 @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[45]) ).
thf(69,plain,
! [SV2: $i] :
( ( ! [SY36: $i,SY37: $i] :
( ( addition @ SY37 @ ( addition @ SY36 @ SV2 ) )
= ( addition @ ( addition @ SY37 @ SY36 ) @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[46]) ).
thf(70,plain,
! [SV3: $i] :
( ( ( addition @ SV3 @ zero )
= SV3 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[47]) ).
thf(71,plain,
! [SV4: $i] :
( ( ( addition @ SV4 @ SV4 )
= SV4 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[48]) ).
thf(72,plain,
! [SV5: $i] :
( ( ! [SY38: $i,SY39: $i] :
( ( multiplication @ SV5 @ ( multiplication @ SY38 @ SY39 ) )
= ( multiplication @ ( multiplication @ SV5 @ SY38 ) @ SY39 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[49]) ).
thf(73,plain,
! [SV6: $i] :
( ( ( multiplication @ SV6 @ one )
= SV6 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[50]) ).
thf(74,plain,
! [SV7: $i] :
( ( ( multiplication @ one @ SV7 )
= SV7 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[51]) ).
thf(75,plain,
! [SV8: $i] :
( ( ! [SY40: $i,SY41: $i] :
( ( multiplication @ SV8 @ ( addition @ SY40 @ SY41 ) )
= ( addition @ ( multiplication @ SV8 @ SY40 ) @ ( multiplication @ SV8 @ SY41 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[52]) ).
thf(76,plain,
! [SV9: $i] :
( ( ! [SY42: $i,SY43: $i] :
( ( multiplication @ ( addition @ SV9 @ SY42 ) @ SY43 )
= ( addition @ ( multiplication @ SV9 @ SY43 ) @ ( multiplication @ SY42 @ SY43 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[53]) ).
thf(77,plain,
! [SV10: $i] :
( ( ( multiplication @ zero @ SV10 )
= zero )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[54]) ).
thf(78,plain,
! [SV11: $i] :
( ( ( addition @ one @ ( multiplication @ SV11 @ ( star @ SV11 ) ) )
= ( star @ SV11 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[55]) ).
thf(79,plain,
! [SV12: $i] :
( ( ( addition @ one @ ( multiplication @ ( star @ SV12 ) @ SV12 ) )
= ( star @ SV12 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[56]) ).
thf(80,plain,
! [SV13: $i] :
( ( ( strong_iteration @ SV13 )
= ( addition @ ( multiplication @ SV13 @ ( strong_iteration @ SV13 ) ) @ one ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[59]) ).
thf(81,plain,
! [SV14: $i] :
( ( ( strong_iteration @ SV14 )
= ( addition @ ( star @ SV14 ) @ ( multiplication @ ( strong_iteration @ SV14 ) @ zero ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[61]) ).
thf(82,plain,
( ( leq @ ( strong_iteration @ ( strong_iteration @ sK1_X0 ) ) @ ( strong_iteration @ one ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[63]) ).
thf(83,plain,
! [SV15: $i] :
( ( ! [SY44: $i,SY45: $i] :
( ~ ( leq @ ( addition @ ( multiplication @ SV15 @ SY45 ) @ SY44 ) @ SY45 )
| ( leq @ ( multiplication @ ( star @ SV15 ) @ SY44 ) @ SY45 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[64]) ).
thf(84,plain,
! [SV16: $i] :
( ( ! [SY46: $i,SY47: $i] :
( ~ ( leq @ ( addition @ ( multiplication @ SY47 @ SV16 ) @ SY46 ) @ SY47 )
| ( leq @ ( multiplication @ SY46 @ ( star @ SV16 ) ) @ SY47 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[65]) ).
thf(85,plain,
! [SV17: $i] :
( ( ! [SY48: $i,SY49: $i] :
( ~ ( leq @ SY49 @ ( addition @ ( multiplication @ SV17 @ SY49 ) @ SY48 ) )
| ( leq @ SY49 @ ( multiplication @ ( strong_iteration @ SV17 ) @ SY48 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[66]) ).
thf(86,plain,
! [SV18: $i] :
( ( ! [SY50: $i] :
~ ( ~ ( ~ ( leq @ SV18 @ SY50 )
| ( ( addition @ SV18 @ SY50 )
= SY50 ) )
| ~ ( ( ( addition @ SV18 @ SY50 )
!= SY50 )
| ( leq @ SV18 @ SY50 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[67]) ).
thf(87,plain,
! [SV19: $i,SV1: $i] :
( ( ( addition @ SV1 @ SV19 )
= ( addition @ SV19 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[68]) ).
thf(88,plain,
! [SV2: $i,SV20: $i] :
( ( ! [SY51: $i] :
( ( addition @ SY51 @ ( addition @ SV20 @ SV2 ) )
= ( addition @ ( addition @ SY51 @ SV20 ) @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[69]) ).
thf(89,plain,
! [SV21: $i,SV5: $i] :
( ( ! [SY52: $i] :
( ( multiplication @ SV5 @ ( multiplication @ SV21 @ SY52 ) )
= ( multiplication @ ( multiplication @ SV5 @ SV21 ) @ SY52 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[72]) ).
thf(90,plain,
! [SV22: $i,SV8: $i] :
( ( ! [SY53: $i] :
( ( multiplication @ SV8 @ ( addition @ SV22 @ SY53 ) )
= ( addition @ ( multiplication @ SV8 @ SV22 ) @ ( multiplication @ SV8 @ SY53 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[75]) ).
thf(91,plain,
! [SV23: $i,SV9: $i] :
( ( ! [SY54: $i] :
( ( multiplication @ ( addition @ SV9 @ SV23 ) @ SY54 )
= ( addition @ ( multiplication @ SV9 @ SY54 ) @ ( multiplication @ SV23 @ SY54 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[76]) ).
thf(92,plain,
! [SV24: $i,SV15: $i] :
( ( ! [SY55: $i] :
( ~ ( leq @ ( addition @ ( multiplication @ SV15 @ SY55 ) @ SV24 ) @ SY55 )
| ( leq @ ( multiplication @ ( star @ SV15 ) @ SV24 ) @ SY55 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[83]) ).
thf(93,plain,
! [SV25: $i,SV16: $i] :
( ( ! [SY56: $i] :
( ~ ( leq @ ( addition @ ( multiplication @ SY56 @ SV16 ) @ SV25 ) @ SY56 )
| ( leq @ ( multiplication @ SV25 @ ( star @ SV16 ) ) @ SY56 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[84]) ).
thf(94,plain,
! [SV26: $i,SV17: $i] :
( ( ! [SY57: $i] :
( ~ ( leq @ SY57 @ ( addition @ ( multiplication @ SV17 @ SY57 ) @ SV26 ) )
| ( leq @ SY57 @ ( multiplication @ ( strong_iteration @ SV17 ) @ SV26 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(95,plain,
! [SV27: $i,SV18: $i] :
( ( ~ ( ~ ( ~ ( leq @ SV18 @ SV27 )
| ( ( addition @ SV18 @ SV27 )
= SV27 ) )
| ~ ( ( ( addition @ SV18 @ SV27 )
!= SV27 )
| ( leq @ SV18 @ SV27 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[86]) ).
thf(96,plain,
! [SV2: $i,SV20: $i,SV28: $i] :
( ( ( addition @ SV28 @ ( addition @ SV20 @ SV2 ) )
= ( addition @ ( addition @ SV28 @ SV20 ) @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(97,plain,
! [SV29: $i,SV21: $i,SV5: $i] :
( ( ( multiplication @ SV5 @ ( multiplication @ SV21 @ SV29 ) )
= ( multiplication @ ( multiplication @ SV5 @ SV21 ) @ SV29 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[89]) ).
thf(98,plain,
! [SV30: $i,SV22: $i,SV8: $i] :
( ( ( multiplication @ SV8 @ ( addition @ SV22 @ SV30 ) )
= ( addition @ ( multiplication @ SV8 @ SV22 ) @ ( multiplication @ SV8 @ SV30 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[90]) ).
thf(99,plain,
! [SV31: $i,SV23: $i,SV9: $i] :
( ( ( multiplication @ ( addition @ SV9 @ SV23 ) @ SV31 )
= ( addition @ ( multiplication @ SV9 @ SV31 ) @ ( multiplication @ SV23 @ SV31 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[91]) ).
thf(100,plain,
! [SV24: $i,SV32: $i,SV15: $i] :
( ( ~ ( leq @ ( addition @ ( multiplication @ SV15 @ SV32 ) @ SV24 ) @ SV32 )
| ( leq @ ( multiplication @ ( star @ SV15 ) @ SV24 ) @ SV32 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[92]) ).
thf(101,plain,
! [SV25: $i,SV16: $i,SV33: $i] :
( ( ~ ( leq @ ( addition @ ( multiplication @ SV33 @ SV16 ) @ SV25 ) @ SV33 )
| ( leq @ ( multiplication @ SV25 @ ( star @ SV16 ) ) @ SV33 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[93]) ).
thf(102,plain,
! [SV26: $i,SV17: $i,SV34: $i] :
( ( ~ ( leq @ SV34 @ ( addition @ ( multiplication @ SV17 @ SV34 ) @ SV26 ) )
| ( leq @ SV34 @ ( multiplication @ ( strong_iteration @ SV17 ) @ SV26 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[94]) ).
thf(103,plain,
! [SV27: $i,SV18: $i] :
( ( ~ ( ~ ( leq @ SV18 @ SV27 )
| ( ( addition @ SV18 @ SV27 )
= SV27 ) )
| ~ ( ( ( addition @ SV18 @ SV27 )
!= SV27 )
| ( leq @ SV18 @ SV27 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[95]) ).
thf(104,plain,
! [SV24: $i,SV32: $i,SV15: $i] :
( ( ( ~ ( leq @ ( addition @ ( multiplication @ SV15 @ SV32 ) @ SV24 ) @ SV32 ) )
= $true )
| ( ( leq @ ( multiplication @ ( star @ SV15 ) @ SV24 ) @ SV32 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[100]) ).
thf(105,plain,
! [SV25: $i,SV16: $i,SV33: $i] :
( ( ( ~ ( leq @ ( addition @ ( multiplication @ SV33 @ SV16 ) @ SV25 ) @ SV33 ) )
= $true )
| ( ( leq @ ( multiplication @ SV25 @ ( star @ SV16 ) ) @ SV33 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[101]) ).
thf(106,plain,
! [SV26: $i,SV17: $i,SV34: $i] :
( ( ( ~ ( leq @ SV34 @ ( addition @ ( multiplication @ SV17 @ SV34 ) @ SV26 ) ) )
= $true )
| ( ( leq @ SV34 @ ( multiplication @ ( strong_iteration @ SV17 ) @ SV26 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[102]) ).
thf(107,plain,
! [SV27: $i,SV18: $i] :
( ( ~ ( ~ ( leq @ SV18 @ SV27 )
| ( ( addition @ SV18 @ SV27 )
= SV27 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[103]) ).
thf(108,plain,
! [SV27: $i,SV18: $i] :
( ( ~ ( ( ( addition @ SV18 @ SV27 )
!= SV27 )
| ( leq @ SV18 @ SV27 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[103]) ).
thf(109,plain,
! [SV24: $i,SV32: $i,SV15: $i] :
( ( ( leq @ ( addition @ ( multiplication @ SV15 @ SV32 ) @ SV24 ) @ SV32 )
= $false )
| ( ( leq @ ( multiplication @ ( star @ SV15 ) @ SV24 ) @ SV32 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[104]) ).
thf(110,plain,
! [SV25: $i,SV16: $i,SV33: $i] :
( ( ( leq @ ( addition @ ( multiplication @ SV33 @ SV16 ) @ SV25 ) @ SV33 )
= $false )
| ( ( leq @ ( multiplication @ SV25 @ ( star @ SV16 ) ) @ SV33 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[105]) ).
thf(111,plain,
! [SV26: $i,SV17: $i,SV34: $i] :
( ( ( leq @ SV34 @ ( addition @ ( multiplication @ SV17 @ SV34 ) @ SV26 ) )
= $false )
| ( ( leq @ SV34 @ ( multiplication @ ( strong_iteration @ SV17 ) @ SV26 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[106]) ).
thf(112,plain,
! [SV27: $i,SV18: $i] :
( ( ~ ( leq @ SV18 @ SV27 )
| ( ( addition @ SV18 @ SV27 )
= SV27 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[107]) ).
thf(113,plain,
! [SV27: $i,SV18: $i] :
( ( ( ( addition @ SV18 @ SV27 )
!= SV27 )
| ( leq @ SV18 @ SV27 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[108]) ).
thf(114,plain,
! [SV27: $i,SV18: $i] :
( ( ( ~ ( leq @ SV18 @ SV27 ) )
= $true )
| ( ( ( addition @ SV18 @ SV27 )
= SV27 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[112]) ).
thf(115,plain,
! [SV27: $i,SV18: $i] :
( ( ( ( addition @ SV18 @ SV27 )
!= SV27 )
= $true )
| ( ( leq @ SV18 @ SV27 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[113]) ).
thf(116,plain,
! [SV27: $i,SV18: $i] :
( ( ( leq @ SV18 @ SV27 )
= $false )
| ( ( ( addition @ SV18 @ SV27 )
= SV27 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[114]) ).
thf(117,plain,
! [SV27: $i,SV18: $i] :
( ( ( ( addition @ SV18 @ SV27 )
= SV27 )
= $false )
| ( ( leq @ SV18 @ SV27 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[115]) ).
thf(118,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[70,117,116,111,110,109,99,98,97,96,87,82,81,80,79,78,77,74,73,71]) ).
thf(119,plain,
( ( ! [A: $i,B: $i] :
( ( addition @ A @ B )
= ( addition @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(120,plain,
( ( ! [C: $i,B: $i,A: $i] :
( ( addition @ A @ ( addition @ B @ C ) )
= ( addition @ ( addition @ A @ B ) @ C ) ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(121,plain,
( ( ! [A: $i] :
( ( addition @ A @ zero )
= A ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(122,plain,
( ( ! [A: $i] :
( ( addition @ A @ A )
= A ) )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(123,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( multiplication @ A @ ( multiplication @ B @ C ) )
= ( multiplication @ ( multiplication @ A @ B ) @ C ) ) )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(124,plain,
( ( ! [A: $i] :
( ( multiplication @ A @ one )
= A ) )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(125,plain,
( ( ! [A: $i] :
( ( multiplication @ one @ A )
= A ) )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(126,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( multiplication @ A @ ( addition @ B @ C ) )
= ( addition @ ( multiplication @ A @ B ) @ ( multiplication @ A @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(127,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( multiplication @ ( addition @ A @ B ) @ C )
= ( addition @ ( multiplication @ A @ C ) @ ( multiplication @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[31]) ).
thf(128,plain,
( ( ! [A: $i] :
( ( multiplication @ zero @ A )
= zero ) )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(129,plain,
( ( ! [A: $i] :
( ( addition @ one @ ( multiplication @ A @ ( star @ A ) ) )
= ( star @ A ) ) )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(130,plain,
( ( ! [A: $i] :
( ( addition @ one @ ( multiplication @ ( star @ A ) @ A ) )
= ( star @ A ) ) )
= $true ),
inference(copy,[status(thm)],[28]) ).
thf(131,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)],[27]) ).
thf(132,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)],[26]) ).
thf(133,plain,
( ( ! [A: $i] :
( ( strong_iteration @ A )
= ( addition @ ( multiplication @ A @ ( strong_iteration @ A ) ) @ one ) ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(134,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)],[24]) ).
thf(135,plain,
( ( ! [A: $i] :
( ( strong_iteration @ A )
= ( addition @ ( star @ A ) @ ( multiplication @ ( strong_iteration @ A ) @ zero ) ) ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(136,plain,
( ( ! [A: $i,B: $i] :
( ( leq @ A @ B )
<=> ( ( addition @ A @ B )
= B ) ) )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(137,plain,
( ( ~ ( leq @ ( strong_iteration @ one ) @ ( strong_iteration @ ( strong_iteration @ sK1_X0 ) ) ) )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(138,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( leq @ ( addition @ ( multiplication @ SX2 @ SX0 ) @ SX1 ) @ SX2 )
| ( leq @ ( multiplication @ SX1 @ ( star @ SX0 ) ) @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[132]) ).
thf(139,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( leq @ SX2 @ ( addition @ ( multiplication @ SX0 @ SX2 ) @ SX1 ) )
| ( leq @ SX2 @ ( multiplication @ ( strong_iteration @ SX0 ) @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[134]) ).
thf(140,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( leq @ SX0 @ SX1 )
| ( ( addition @ SX0 @ SX1 )
= SX1 ) )
| ~ ( ( ( addition @ SX0 @ SX1 )
!= SX1 )
| ( leq @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[136]) ).
thf(141,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( leq @ ( addition @ ( multiplication @ SX0 @ SX2 ) @ SX1 ) @ SX2 )
| ( leq @ ( multiplication @ ( star @ SX0 ) @ SX1 ) @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[131]) ).
thf(142,plain,
! [SV35: $i] :
( ( ! [SY58: $i] :
( ( addition @ SV35 @ SY58 )
= ( addition @ SY58 @ SV35 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[119]) ).
thf(143,plain,
! [SV36: $i] :
( ( ! [SY59: $i,SY60: $i] :
( ( addition @ SY60 @ ( addition @ SY59 @ SV36 ) )
= ( addition @ ( addition @ SY60 @ SY59 ) @ SV36 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[120]) ).
thf(144,plain,
! [SV37: $i] :
( ( ( addition @ SV37 @ zero )
= SV37 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[121]) ).
thf(145,plain,
! [SV38: $i] :
( ( ( addition @ SV38 @ SV38 )
= SV38 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[122]) ).
thf(146,plain,
! [SV39: $i] :
( ( ! [SY61: $i,SY62: $i] :
( ( multiplication @ SV39 @ ( multiplication @ SY61 @ SY62 ) )
= ( multiplication @ ( multiplication @ SV39 @ SY61 ) @ SY62 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[123]) ).
thf(147,plain,
! [SV40: $i] :
( ( ( multiplication @ SV40 @ one )
= SV40 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[124]) ).
thf(148,plain,
! [SV41: $i] :
( ( ( multiplication @ one @ SV41 )
= SV41 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[125]) ).
thf(149,plain,
! [SV42: $i] :
( ( ! [SY63: $i,SY64: $i] :
( ( multiplication @ SV42 @ ( addition @ SY63 @ SY64 ) )
= ( addition @ ( multiplication @ SV42 @ SY63 ) @ ( multiplication @ SV42 @ SY64 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[126]) ).
thf(150,plain,
! [SV43: $i] :
( ( ! [SY65: $i,SY66: $i] :
( ( multiplication @ ( addition @ SV43 @ SY65 ) @ SY66 )
= ( addition @ ( multiplication @ SV43 @ SY66 ) @ ( multiplication @ SY65 @ SY66 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[127]) ).
thf(151,plain,
! [SV44: $i] :
( ( ( multiplication @ zero @ SV44 )
= zero )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[128]) ).
thf(152,plain,
! [SV45: $i] :
( ( ( addition @ one @ ( multiplication @ SV45 @ ( star @ SV45 ) ) )
= ( star @ SV45 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[129]) ).
thf(153,plain,
! [SV46: $i] :
( ( ( addition @ one @ ( multiplication @ ( star @ SV46 ) @ SV46 ) )
= ( star @ SV46 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[130]) ).
thf(154,plain,
! [SV47: $i] :
( ( ( strong_iteration @ SV47 )
= ( addition @ ( multiplication @ SV47 @ ( strong_iteration @ SV47 ) ) @ one ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[133]) ).
thf(155,plain,
! [SV48: $i] :
( ( ( strong_iteration @ SV48 )
= ( addition @ ( star @ SV48 ) @ ( multiplication @ ( strong_iteration @ SV48 ) @ zero ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[135]) ).
thf(156,plain,
( ( leq @ ( strong_iteration @ one ) @ ( strong_iteration @ ( strong_iteration @ sK1_X0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[137]) ).
thf(157,plain,
! [SV49: $i] :
( ( ! [SY67: $i,SY68: $i] :
( ~ ( leq @ ( addition @ ( multiplication @ SY68 @ SV49 ) @ SY67 ) @ SY68 )
| ( leq @ ( multiplication @ SY67 @ ( star @ SV49 ) ) @ SY68 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[138]) ).
thf(158,plain,
! [SV50: $i] :
( ( ! [SY69: $i,SY70: $i] :
( ~ ( leq @ SY70 @ ( addition @ ( multiplication @ SV50 @ SY70 ) @ SY69 ) )
| ( leq @ SY70 @ ( multiplication @ ( strong_iteration @ SV50 ) @ SY69 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[139]) ).
thf(159,plain,
! [SV51: $i] :
( ( ! [SY71: $i] :
~ ( ~ ( ~ ( leq @ SV51 @ SY71 )
| ( ( addition @ SV51 @ SY71 )
= SY71 ) )
| ~ ( ( ( addition @ SV51 @ SY71 )
!= SY71 )
| ( leq @ SV51 @ SY71 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[140]) ).
thf(160,plain,
! [SV52: $i] :
( ( ! [SY72: $i,SY73: $i] :
( ~ ( leq @ ( addition @ ( multiplication @ SV52 @ SY73 ) @ SY72 ) @ SY73 )
| ( leq @ ( multiplication @ ( star @ SV52 ) @ SY72 ) @ SY73 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[141]) ).
thf(161,plain,
! [SV53: $i,SV35: $i] :
( ( ( addition @ SV35 @ SV53 )
= ( addition @ SV53 @ SV35 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[142]) ).
thf(162,plain,
! [SV36: $i,SV54: $i] :
( ( ! [SY74: $i] :
( ( addition @ SY74 @ ( addition @ SV54 @ SV36 ) )
= ( addition @ ( addition @ SY74 @ SV54 ) @ SV36 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[143]) ).
thf(163,plain,
! [SV55: $i,SV39: $i] :
( ( ! [SY75: $i] :
( ( multiplication @ SV39 @ ( multiplication @ SV55 @ SY75 ) )
= ( multiplication @ ( multiplication @ SV39 @ SV55 ) @ SY75 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[146]) ).
thf(164,plain,
! [SV56: $i,SV42: $i] :
( ( ! [SY76: $i] :
( ( multiplication @ SV42 @ ( addition @ SV56 @ SY76 ) )
= ( addition @ ( multiplication @ SV42 @ SV56 ) @ ( multiplication @ SV42 @ SY76 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[149]) ).
thf(165,plain,
! [SV57: $i,SV43: $i] :
( ( ! [SY77: $i] :
( ( multiplication @ ( addition @ SV43 @ SV57 ) @ SY77 )
= ( addition @ ( multiplication @ SV43 @ SY77 ) @ ( multiplication @ SV57 @ SY77 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[150]) ).
thf(166,plain,
! [SV58: $i,SV49: $i] :
( ( ! [SY78: $i] :
( ~ ( leq @ ( addition @ ( multiplication @ SY78 @ SV49 ) @ SV58 ) @ SY78 )
| ( leq @ ( multiplication @ SV58 @ ( star @ SV49 ) ) @ SY78 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[157]) ).
thf(167,plain,
! [SV59: $i,SV50: $i] :
( ( ! [SY79: $i] :
( ~ ( leq @ SY79 @ ( addition @ ( multiplication @ SV50 @ SY79 ) @ SV59 ) )
| ( leq @ SY79 @ ( multiplication @ ( strong_iteration @ SV50 ) @ SV59 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[158]) ).
thf(168,plain,
! [SV60: $i,SV51: $i] :
( ( ~ ( ~ ( ~ ( leq @ SV51 @ SV60 )
| ( ( addition @ SV51 @ SV60 )
= SV60 ) )
| ~ ( ( ( addition @ SV51 @ SV60 )
!= SV60 )
| ( leq @ SV51 @ SV60 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[159]) ).
thf(169,plain,
! [SV61: $i,SV52: $i] :
( ( ! [SY80: $i] :
( ~ ( leq @ ( addition @ ( multiplication @ SV52 @ SY80 ) @ SV61 ) @ SY80 )
| ( leq @ ( multiplication @ ( star @ SV52 ) @ SV61 ) @ SY80 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[160]) ).
thf(170,plain,
! [SV36: $i,SV54: $i,SV62: $i] :
( ( ( addition @ SV62 @ ( addition @ SV54 @ SV36 ) )
= ( addition @ ( addition @ SV62 @ SV54 ) @ SV36 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[162]) ).
thf(171,plain,
! [SV63: $i,SV55: $i,SV39: $i] :
( ( ( multiplication @ SV39 @ ( multiplication @ SV55 @ SV63 ) )
= ( multiplication @ ( multiplication @ SV39 @ SV55 ) @ SV63 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[163]) ).
thf(172,plain,
! [SV64: $i,SV56: $i,SV42: $i] :
( ( ( multiplication @ SV42 @ ( addition @ SV56 @ SV64 ) )
= ( addition @ ( multiplication @ SV42 @ SV56 ) @ ( multiplication @ SV42 @ SV64 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[164]) ).
thf(173,plain,
! [SV65: $i,SV57: $i,SV43: $i] :
( ( ( multiplication @ ( addition @ SV43 @ SV57 ) @ SV65 )
= ( addition @ ( multiplication @ SV43 @ SV65 ) @ ( multiplication @ SV57 @ SV65 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[165]) ).
thf(174,plain,
! [SV58: $i,SV49: $i,SV66: $i] :
( ( ~ ( leq @ ( addition @ ( multiplication @ SV66 @ SV49 ) @ SV58 ) @ SV66 )
| ( leq @ ( multiplication @ SV58 @ ( star @ SV49 ) ) @ SV66 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[166]) ).
thf(175,plain,
! [SV59: $i,SV50: $i,SV67: $i] :
( ( ~ ( leq @ SV67 @ ( addition @ ( multiplication @ SV50 @ SV67 ) @ SV59 ) )
| ( leq @ SV67 @ ( multiplication @ ( strong_iteration @ SV50 ) @ SV59 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[167]) ).
thf(176,plain,
! [SV60: $i,SV51: $i] :
( ( ~ ( ~ ( leq @ SV51 @ SV60 )
| ( ( addition @ SV51 @ SV60 )
= SV60 ) )
| ~ ( ( ( addition @ SV51 @ SV60 )
!= SV60 )
| ( leq @ SV51 @ SV60 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[168]) ).
thf(177,plain,
! [SV61: $i,SV68: $i,SV52: $i] :
( ( ~ ( leq @ ( addition @ ( multiplication @ SV52 @ SV68 ) @ SV61 ) @ SV68 )
| ( leq @ ( multiplication @ ( star @ SV52 ) @ SV61 ) @ SV68 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[169]) ).
thf(178,plain,
! [SV58: $i,SV49: $i,SV66: $i] :
( ( ( ~ ( leq @ ( addition @ ( multiplication @ SV66 @ SV49 ) @ SV58 ) @ SV66 ) )
= $true )
| ( ( leq @ ( multiplication @ SV58 @ ( star @ SV49 ) ) @ SV66 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[174]) ).
thf(179,plain,
! [SV59: $i,SV50: $i,SV67: $i] :
( ( ( ~ ( leq @ SV67 @ ( addition @ ( multiplication @ SV50 @ SV67 ) @ SV59 ) ) )
= $true )
| ( ( leq @ SV67 @ ( multiplication @ ( strong_iteration @ SV50 ) @ SV59 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[175]) ).
thf(180,plain,
! [SV60: $i,SV51: $i] :
( ( ~ ( ~ ( leq @ SV51 @ SV60 )
| ( ( addition @ SV51 @ SV60 )
= SV60 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[176]) ).
thf(181,plain,
! [SV60: $i,SV51: $i] :
( ( ~ ( ( ( addition @ SV51 @ SV60 )
!= SV60 )
| ( leq @ SV51 @ SV60 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[176]) ).
thf(182,plain,
! [SV61: $i,SV68: $i,SV52: $i] :
( ( ( ~ ( leq @ ( addition @ ( multiplication @ SV52 @ SV68 ) @ SV61 ) @ SV68 ) )
= $true )
| ( ( leq @ ( multiplication @ ( star @ SV52 ) @ SV61 ) @ SV68 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[177]) ).
thf(183,plain,
! [SV58: $i,SV49: $i,SV66: $i] :
( ( ( leq @ ( addition @ ( multiplication @ SV66 @ SV49 ) @ SV58 ) @ SV66 )
= $false )
| ( ( leq @ ( multiplication @ SV58 @ ( star @ SV49 ) ) @ SV66 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[178]) ).
thf(184,plain,
! [SV59: $i,SV50: $i,SV67: $i] :
( ( ( leq @ SV67 @ ( addition @ ( multiplication @ SV50 @ SV67 ) @ SV59 ) )
= $false )
| ( ( leq @ SV67 @ ( multiplication @ ( strong_iteration @ SV50 ) @ SV59 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[179]) ).
thf(185,plain,
! [SV60: $i,SV51: $i] :
( ( ~ ( leq @ SV51 @ SV60 )
| ( ( addition @ SV51 @ SV60 )
= SV60 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[180]) ).
thf(186,plain,
! [SV60: $i,SV51: $i] :
( ( ( ( addition @ SV51 @ SV60 )
!= SV60 )
| ( leq @ SV51 @ SV60 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[181]) ).
thf(187,plain,
! [SV61: $i,SV68: $i,SV52: $i] :
( ( ( leq @ ( addition @ ( multiplication @ SV52 @ SV68 ) @ SV61 ) @ SV68 )
= $false )
| ( ( leq @ ( multiplication @ ( star @ SV52 ) @ SV61 ) @ SV68 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[182]) ).
thf(188,plain,
! [SV60: $i,SV51: $i] :
( ( ( ~ ( leq @ SV51 @ SV60 ) )
= $true )
| ( ( ( addition @ SV51 @ SV60 )
= SV60 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[185]) ).
thf(189,plain,
! [SV60: $i,SV51: $i] :
( ( ( ( addition @ SV51 @ SV60 )
!= SV60 )
= $true )
| ( ( leq @ SV51 @ SV60 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[186]) ).
thf(190,plain,
! [SV60: $i,SV51: $i] :
( ( ( leq @ SV51 @ SV60 )
= $false )
| ( ( ( addition @ SV51 @ SV60 )
= SV60 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[188]) ).
thf(191,plain,
! [SV60: $i,SV51: $i] :
( ( ( ( addition @ SV51 @ SV60 )
= SV60 )
= $false )
| ( ( leq @ SV51 @ SV60 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[189]) ).
thf(192,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[144,191,190,187,184,183,173,172,171,170,161,156,155,154,153,152,151,148,147,145]) ).
thf(193,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[192,118]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE142+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.19 % Computer : n016.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Oct 6 11:41:44 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 12.49/2.49
% 12.49/2.49 No.of.Axioms: 18
% 12.49/2.49
% 12.49/2.49 Length.of.Defs: 0
% 12.49/2.49
% 12.49/2.49 Contains.Choice.Funs: false
% 12.49/2.49 .....
% 12.49/2.49
% 12.49/2.49 ********************************
% 12.49/2.49 * All subproblems solved! *
% 12.49/2.49 ********************************
% 12.49/2.49 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:18,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:298,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:192,loop_count:0,foatp_calls:1,translation:fof_full)
% 12.49/2.49
% 12.49/2.49 %**** Beginning of derivation protocol ****
% 12.49/2.49 % SZS output start CNFRefutation
% See solution above
% 12.49/2.49
% 12.49/2.49 %**** End of derivation protocol ****
% 12.49/2.49 %**** no. of clauses in derivation: 193 ****
% 12.49/2.49 %**** clause counter: 192 ****
% 12.49/2.49
% 12.49/2.49 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:18,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:298,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:192,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------