%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : KLE005+1 : 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 : n007.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 10:25:45 AM UTC 2026
% Result : Theorem 0.07s 0.25s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 9
% Syntax : Number of formulae : 86 ( 47 unt; 0 typ; 0 def)
% Number of atoms : 494 ( 280 equ; 0 cnn)
% Maximal formula atoms : 4 ( 5 avg)
% Number of connectives : 784 ( 216 ~; 136 |; 6 &; 414 @)
% ( 6 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 128 ( 0 ^; 128 !; 0 ?; 128 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_addition,type,
addition: $i > $i > $i ).
thf(tp_c,type,
c: $i > $i ).
thf(tp_complement,type,
complement: $i > $i > $o ).
thf(tp_leq,type,
leq: $i > $i > $o ).
thf(tp_multiplication,type,
multiplication: $i > $i > $i ).
thf(tp_one,type,
one: $i ).
thf(tp_test,type,
test: $i > $o ).
thf(tp_zero,type,
zero: $i ).
thf(1,axiom,
! [X0: $i] :
( ~ ( test @ X0 )
=> ( ( c @ X0 )
= zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',test_4) ).
thf(2,axiom,
! [X0: $i,X1: $i] :
( ( test @ X0 )
=> ( ( ( c @ X0 )
= X1 )
<=> ( complement @ X0 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',test_3) ).
thf(3,axiom,
! [X0: $i,X1: $i] :
( ( complement @ X1 @ X0 )
<=> ( ( ( multiplication @ X0 @ X1 )
= zero )
& ( ( multiplication @ X1 @ X0 )
= zero )
& ( ( addition @ X0 @ X1 )
= one ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',test_2) ).
thf(6,axiom,
! [A: $i] :
( ( multiplication @ zero @ A )
= zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_annihilation) ).
thf(7,axiom,
! [A: $i] :
( ( multiplication @ A @ zero )
= zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_annihilation) ).
thf(10,axiom,
! [A: $i] :
( ( multiplication @ one @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_left_identity) ).
thf(11,axiom,
! [A: $i] :
( ( multiplication @ A @ one )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_right_identity) ).
thf(14,axiom,
! [A: $i] :
( ( addition @ A @ zero )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_identity) ).
thf(17,conjecture,
( ( c @ one )
= zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
thf(18,negated_conjecture,
( ( ( c @ one )
= zero )
= $false ),
inference(negate_conjecture,[status(cth)],[17]) ).
thf(19,plain,
( ( ( c @ one )
= zero )
= $false ),
inference(unfold_def,[status(thm)],[18]) ).
thf(20,plain,
( ( ! [X0: $i] :
( ~ ( test @ X0 )
=> ( ( c @ X0 )
= zero ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(21,plain,
( ( ! [X0: $i,X1: $i] :
( ( test @ X0 )
=> ( ( ( c @ X0 )
= X1 )
<=> ( complement @ X0 @ X1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(22,plain,
( ( ! [X0: $i,X1: $i] :
( ( complement @ X1 @ X0 )
<=> ( ( ( multiplication @ X0 @ X1 )
= zero )
& ( ( multiplication @ X1 @ X0 )
= zero )
& ( ( addition @ X0 @ X1 )
= one ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(23,plain,
( ( ! [A: $i] :
( ( multiplication @ zero @ A )
= zero ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(24,plain,
( ( ! [A: $i] :
( ( multiplication @ A @ zero )
= zero ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(25,plain,
( ( ! [A: $i] :
( ( multiplication @ one @ A )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(26,plain,
( ( ! [A: $i] :
( ( multiplication @ A @ one )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(27,plain,
( ( ! [A: $i] :
( ( addition @ A @ zero )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(28,plain,
( ( ( c @ one )
!= zero )
= $true ),
inference(polarity_switch,[status(thm)],[19]) ).
thf(29,plain,
( ( ! [A: $i] :
( ( addition @ A @ zero )
= A ) )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(30,plain,
( ( ! [A: $i] :
( ( multiplication @ A @ one )
= A ) )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(31,plain,
( ( ! [A: $i] :
( ( multiplication @ one @ A )
= A ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(32,plain,
( ( ! [A: $i] :
( ( multiplication @ A @ zero )
= zero ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(33,plain,
( ( ! [A: $i] :
( ( multiplication @ zero @ A )
= zero ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(34,plain,
( ( ! [X0: $i,X1: $i] :
( ( complement @ X1 @ X0 )
<=> ( ( ( multiplication @ X0 @ X1 )
= zero )
& ( ( multiplication @ X1 @ X0 )
= zero )
& ( ( addition @ X0 @ X1 )
= one ) ) ) )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(35,plain,
( ( ! [X0: $i,X1: $i] :
( ( test @ X0 )
=> ( ( ( c @ X0 )
= X1 )
<=> ( complement @ X0 @ X1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(36,plain,
( ( ! [X0: $i] :
( ~ ( test @ X0 )
=> ( ( c @ X0 )
= zero ) ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(37,plain,
( ( ( c @ one )
!= zero )
= $true ),
inference(copy,[status(thm)],[28]) ).
thf(38,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( test @ SX0 )
| ~ ( ~ ( ( ( c @ SX0 )
!= SX1 )
| ( complement @ SX0 @ SX1 ) )
| ~ ( ~ ( complement @ SX0 @ SX1 )
| ( ( c @ SX0 )
= SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[35]) ).
thf(39,plain,
( ( ! [SX0: $i] :
( ~ ~ ( test @ SX0 )
| ( ( c @ SX0 )
= zero ) ) )
= $true ),
inference(unfold_def,[status(thm)],[36]) ).
thf(40,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( complement @ SX1 @ SX0 )
| ~ ( ~ ~ ( ( ( multiplication @ SX0 @ SX1 )
!= zero )
| ( ( multiplication @ SX1 @ SX0 )
!= zero ) )
| ( ( addition @ SX0 @ SX1 )
!= one ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( ( multiplication @ SX0 @ SX1 )
!= zero )
| ( ( multiplication @ SX1 @ SX0 )
!= zero ) )
| ( ( addition @ SX0 @ SX1 )
!= one ) )
| ( complement @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[34]) ).
thf(41,plain,
! [SV1: $i] :
( ( ( addition @ SV1 @ zero )
= SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[29]) ).
thf(42,plain,
! [SV2: $i] :
( ( ( multiplication @ SV2 @ one )
= SV2 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[30]) ).
thf(43,plain,
! [SV3: $i] :
( ( ( multiplication @ one @ SV3 )
= SV3 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[31]) ).
thf(44,plain,
! [SV4: $i] :
( ( ( multiplication @ SV4 @ zero )
= zero )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[32]) ).
thf(45,plain,
! [SV5: $i] :
( ( ( multiplication @ zero @ SV5 )
= zero )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[33]) ).
thf(46,plain,
( ( ( c @ one )
= zero )
= $false ),
inference(extcnf_not_pos,[status(thm)],[37]) ).
thf(47,plain,
! [SV6: $i] :
( ( ! [SY10: $i] :
( ~ ( test @ SV6 )
| ~ ( ~ ( ( ( c @ SV6 )
!= SY10 )
| ( complement @ SV6 @ SY10 ) )
| ~ ( ~ ( complement @ SV6 @ SY10 )
| ( ( c @ SV6 )
= SY10 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[38]) ).
thf(48,plain,
! [SV7: $i] :
( ( ~ ~ ( test @ SV7 )
| ( ( c @ SV7 )
= zero ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[39]) ).
thf(49,plain,
! [SV8: $i] :
( ( ! [SY11: $i] :
~ ( ~ ( ~ ( complement @ SY11 @ SV8 )
| ~ ( ~ ~ ( ( ( multiplication @ SV8 @ SY11 )
!= zero )
| ( ( multiplication @ SY11 @ SV8 )
!= zero ) )
| ( ( addition @ SV8 @ SY11 )
!= one ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( ( multiplication @ SV8 @ SY11 )
!= zero )
| ( ( multiplication @ SY11 @ SV8 )
!= zero ) )
| ( ( addition @ SV8 @ SY11 )
!= one ) )
| ( complement @ SY11 @ SV8 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[40]) ).
thf(50,plain,
! [SV9: $i,SV6: $i] :
( ( ~ ( test @ SV6 )
| ~ ( ~ ( ( ( c @ SV6 )
!= SV9 )
| ( complement @ SV6 @ SV9 ) )
| ~ ( ~ ( complement @ SV6 @ SV9 )
| ( ( c @ SV6 )
= SV9 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[47]) ).
thf(51,plain,
! [SV7: $i] :
( ( ( ~ ~ ( test @ SV7 ) )
= $true )
| ( ( ( c @ SV7 )
= zero )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[48]) ).
thf(52,plain,
! [SV8: $i,SV10: $i] :
( ( ~ ( ~ ( ~ ( complement @ SV10 @ SV8 )
| ~ ( ~ ~ ( ( ( multiplication @ SV8 @ SV10 )
!= zero )
| ( ( multiplication @ SV10 @ SV8 )
!= zero ) )
| ( ( addition @ SV8 @ SV10 )
!= one ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( ( multiplication @ SV8 @ SV10 )
!= zero )
| ( ( multiplication @ SV10 @ SV8 )
!= zero ) )
| ( ( addition @ SV8 @ SV10 )
!= one ) )
| ( complement @ SV10 @ SV8 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[49]) ).
thf(53,plain,
! [SV9: $i,SV6: $i] :
( ( ( ~ ( test @ SV6 ) )
= $true )
| ( ( ~ ( ~ ( ( ( c @ SV6 )
!= SV9 )
| ( complement @ SV6 @ SV9 ) )
| ~ ( ~ ( complement @ SV6 @ SV9 )
| ( ( c @ SV6 )
= SV9 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[50]) ).
thf(54,plain,
! [SV7: $i] :
( ( ( ~ ( test @ SV7 ) )
= $false )
| ( ( ( c @ SV7 )
= zero )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[51]) ).
thf(55,plain,
! [SV8: $i,SV10: $i] :
( ( ~ ( ~ ( complement @ SV10 @ SV8 )
| ~ ( ~ ~ ( ( ( multiplication @ SV8 @ SV10 )
!= zero )
| ( ( multiplication @ SV10 @ SV8 )
!= zero ) )
| ( ( addition @ SV8 @ SV10 )
!= one ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( ( multiplication @ SV8 @ SV10 )
!= zero )
| ( ( multiplication @ SV10 @ SV8 )
!= zero ) )
| ( ( addition @ SV8 @ SV10 )
!= one ) )
| ( complement @ SV10 @ SV8 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[52]) ).
thf(56,plain,
! [SV9: $i,SV6: $i] :
( ( ( test @ SV6 )
= $false )
| ( ( ~ ( ~ ( ( ( c @ SV6 )
!= SV9 )
| ( complement @ SV6 @ SV9 ) )
| ~ ( ~ ( complement @ SV6 @ SV9 )
| ( ( c @ SV6 )
= SV9 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[53]) ).
thf(57,plain,
! [SV7: $i] :
( ( ( test @ SV7 )
= $true )
| ( ( ( c @ SV7 )
= zero )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[54]) ).
thf(58,plain,
! [SV8: $i,SV10: $i] :
( ( ~ ( ~ ( complement @ SV10 @ SV8 )
| ~ ( ~ ~ ( ( ( multiplication @ SV8 @ SV10 )
!= zero )
| ( ( multiplication @ SV10 @ SV8 )
!= zero ) )
| ( ( addition @ SV8 @ SV10 )
!= one ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[55]) ).
thf(59,plain,
! [SV10: $i,SV8: $i] :
( ( ~ ( ~ ~ ( ~ ~ ( ( ( multiplication @ SV8 @ SV10 )
!= zero )
| ( ( multiplication @ SV10 @ SV8 )
!= zero ) )
| ( ( addition @ SV8 @ SV10 )
!= one ) )
| ( complement @ SV10 @ SV8 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[55]) ).
thf(60,plain,
! [SV9: $i,SV6: $i] :
( ( ( ~ ( ( ( c @ SV6 )
!= SV9 )
| ( complement @ SV6 @ SV9 ) )
| ~ ( ~ ( complement @ SV6 @ SV9 )
| ( ( c @ SV6 )
= SV9 ) ) )
= $false )
| ( ( test @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[56]) ).
thf(61,plain,
! [SV8: $i,SV10: $i] :
( ( ~ ( complement @ SV10 @ SV8 )
| ~ ( ~ ~ ( ( ( multiplication @ SV8 @ SV10 )
!= zero )
| ( ( multiplication @ SV10 @ SV8 )
!= zero ) )
| ( ( addition @ SV8 @ SV10 )
!= one ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[58]) ).
thf(62,plain,
! [SV10: $i,SV8: $i] :
( ( ~ ~ ( ~ ~ ( ( ( multiplication @ SV8 @ SV10 )
!= zero )
| ( ( multiplication @ SV10 @ SV8 )
!= zero ) )
| ( ( addition @ SV8 @ SV10 )
!= one ) )
| ( complement @ SV10 @ SV8 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[59]) ).
thf(63,plain,
! [SV9: $i,SV6: $i] :
( ( ( ~ ( ( ( c @ SV6 )
!= SV9 )
| ( complement @ SV6 @ SV9 ) ) )
= $false )
| ( ( test @ SV6 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[60]) ).
thf(64,plain,
! [SV9: $i,SV6: $i] :
( ( ( ~ ( ~ ( complement @ SV6 @ SV9 )
| ( ( c @ SV6 )
= SV9 ) ) )
= $false )
| ( ( test @ SV6 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[60]) ).
thf(65,plain,
! [SV8: $i,SV10: $i] :
( ( ( ~ ( complement @ SV10 @ SV8 ) )
= $true )
| ( ( ~ ( ~ ~ ( ( ( multiplication @ SV8 @ SV10 )
!= zero )
| ( ( multiplication @ SV10 @ SV8 )
!= zero ) )
| ( ( addition @ SV8 @ SV10 )
!= one ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[61]) ).
thf(66,plain,
! [SV10: $i,SV8: $i] :
( ( ( ~ ~ ( ~ ~ ( ( ( multiplication @ SV8 @ SV10 )
!= zero )
| ( ( multiplication @ SV10 @ SV8 )
!= zero ) )
| ( ( addition @ SV8 @ SV10 )
!= one ) ) )
= $true )
| ( ( complement @ SV10 @ SV8 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[62]) ).
thf(67,plain,
! [SV9: $i,SV6: $i] :
( ( ( ( ( c @ SV6 )
!= SV9 )
| ( complement @ SV6 @ SV9 ) )
= $true )
| ( ( test @ SV6 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[63]) ).
thf(68,plain,
! [SV9: $i,SV6: $i] :
( ( ( ~ ( complement @ SV6 @ SV9 )
| ( ( c @ SV6 )
= SV9 ) )
= $true )
| ( ( test @ SV6 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[64]) ).
thf(69,plain,
! [SV8: $i,SV10: $i] :
( ( ( complement @ SV10 @ SV8 )
= $false )
| ( ( ~ ( ~ ~ ( ( ( multiplication @ SV8 @ SV10 )
!= zero )
| ( ( multiplication @ SV10 @ SV8 )
!= zero ) )
| ( ( addition @ SV8 @ SV10 )
!= one ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[65]) ).
thf(70,plain,
! [SV10: $i,SV8: $i] :
( ( ( ~ ( ~ ~ ( ( ( multiplication @ SV8 @ SV10 )
!= zero )
| ( ( multiplication @ SV10 @ SV8 )
!= zero ) )
| ( ( addition @ SV8 @ SV10 )
!= one ) ) )
= $false )
| ( ( complement @ SV10 @ SV8 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[66]) ).
thf(71,plain,
! [SV9: $i,SV6: $i] :
( ( ( ( c @ SV6 )
!= SV9 )
= $true )
| ( ( complement @ SV6 @ SV9 )
= $true )
| ( ( test @ SV6 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[67]) ).
thf(72,plain,
! [SV9: $i,SV6: $i] :
( ( ( ~ ( complement @ SV6 @ SV9 ) )
= $true )
| ( ( ( c @ SV6 )
= SV9 )
= $true )
| ( ( test @ SV6 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[68]) ).
thf(73,plain,
! [SV10: $i,SV8: $i] :
( ( ( ~ ~ ( ( ( multiplication @ SV8 @ SV10 )
!= zero )
| ( ( multiplication @ SV10 @ SV8 )
!= zero ) )
| ( ( addition @ SV8 @ SV10 )
!= one ) )
= $false )
| ( ( complement @ SV10 @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[69]) ).
thf(74,plain,
! [SV10: $i,SV8: $i] :
( ( ( ~ ~ ( ( ( multiplication @ SV8 @ SV10 )
!= zero )
| ( ( multiplication @ SV10 @ SV8 )
!= zero ) )
| ( ( addition @ SV8 @ SV10 )
!= one ) )
= $true )
| ( ( complement @ SV10 @ SV8 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[70]) ).
thf(75,plain,
! [SV9: $i,SV6: $i] :
( ( ( ( c @ SV6 )
= SV9 )
= $false )
| ( ( complement @ SV6 @ SV9 )
= $true )
| ( ( test @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[71]) ).
thf(76,plain,
! [SV9: $i,SV6: $i] :
( ( ( complement @ SV6 @ SV9 )
= $false )
| ( ( ( c @ SV6 )
= SV9 )
= $true )
| ( ( test @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[72]) ).
thf(77,plain,
! [SV10: $i,SV8: $i] :
( ( ( ~ ~ ( ( ( multiplication @ SV8 @ SV10 )
!= zero )
| ( ( multiplication @ SV10 @ SV8 )
!= zero ) ) )
= $false )
| ( ( complement @ SV10 @ SV8 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[73]) ).
thf(78,plain,
! [SV10: $i,SV8: $i] :
( ( ( ( addition @ SV8 @ SV10 )
!= one )
= $false )
| ( ( complement @ SV10 @ SV8 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[73]) ).
thf(79,plain,
! [SV10: $i,SV8: $i] :
( ( ( ~ ~ ( ( ( multiplication @ SV8 @ SV10 )
!= zero )
| ( ( multiplication @ SV10 @ SV8 )
!= zero ) ) )
= $true )
| ( ( ( addition @ SV8 @ SV10 )
!= one )
= $true )
| ( ( complement @ SV10 @ SV8 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[74]) ).
thf(80,plain,
! [SV10: $i,SV8: $i] :
( ( ( ~ ( ( ( multiplication @ SV8 @ SV10 )
!= zero )
| ( ( multiplication @ SV10 @ SV8 )
!= zero ) ) )
= $true )
| ( ( complement @ SV10 @ SV8 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[77]) ).
thf(81,plain,
! [SV10: $i,SV8: $i] :
( ( ( ( addition @ SV8 @ SV10 )
= one )
= $true )
| ( ( complement @ SV10 @ SV8 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[78]) ).
thf(82,plain,
! [SV10: $i,SV8: $i] :
( ( ( ~ ( ( ( multiplication @ SV8 @ SV10 )
!= zero )
| ( ( multiplication @ SV10 @ SV8 )
!= zero ) ) )
= $false )
| ( ( ( addition @ SV8 @ SV10 )
!= one )
= $true )
| ( ( complement @ SV10 @ SV8 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[79]) ).
thf(83,plain,
! [SV10: $i,SV8: $i] :
( ( ( ( ( multiplication @ SV8 @ SV10 )
!= zero )
| ( ( multiplication @ SV10 @ SV8 )
!= zero ) )
= $false )
| ( ( complement @ SV10 @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[80]) ).
thf(84,plain,
! [SV10: $i,SV8: $i] :
( ( ( ( ( multiplication @ SV8 @ SV10 )
!= zero )
| ( ( multiplication @ SV10 @ SV8 )
!= zero ) )
= $true )
| ( ( ( addition @ SV8 @ SV10 )
!= one )
= $true )
| ( ( complement @ SV10 @ SV8 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[82]) ).
thf(85,plain,
! [SV10: $i,SV8: $i] :
( ( ( ( multiplication @ SV8 @ SV10 )
!= zero )
= $false )
| ( ( complement @ SV10 @ SV8 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[83]) ).
thf(86,plain,
! [SV8: $i,SV10: $i] :
( ( ( ( multiplication @ SV10 @ SV8 )
!= zero )
= $false )
| ( ( complement @ SV10 @ SV8 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[83]) ).
thf(87,plain,
! [SV10: $i,SV8: $i] :
( ( ( ( multiplication @ SV8 @ SV10 )
!= zero )
= $true )
| ( ( ( multiplication @ SV10 @ SV8 )
!= zero )
= $true )
| ( ( ( addition @ SV8 @ SV10 )
!= one )
= $true )
| ( ( complement @ SV10 @ SV8 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[84]) ).
thf(88,plain,
! [SV10: $i,SV8: $i] :
( ( ( ( multiplication @ SV8 @ SV10 )
= zero )
= $true )
| ( ( complement @ SV10 @ SV8 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[85]) ).
thf(89,plain,
! [SV8: $i,SV10: $i] :
( ( ( ( multiplication @ SV10 @ SV8 )
= zero )
= $true )
| ( ( complement @ SV10 @ SV8 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[86]) ).
thf(90,plain,
! [SV10: $i,SV8: $i] :
( ( ( ( multiplication @ SV8 @ SV10 )
= zero )
= $false )
| ( ( ( multiplication @ SV10 @ SV8 )
!= zero )
= $true )
| ( ( ( addition @ SV8 @ SV10 )
!= one )
= $true )
| ( ( complement @ SV10 @ SV8 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[87]) ).
thf(91,plain,
! [SV8: $i,SV10: $i] :
( ( ( ( multiplication @ SV10 @ SV8 )
= zero )
= $false )
| ( ( ( multiplication @ SV8 @ SV10 )
= zero )
= $false )
| ( ( ( addition @ SV8 @ SV10 )
!= one )
= $true )
| ( ( complement @ SV10 @ SV8 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[90]) ).
thf(92,plain,
! [SV10: $i,SV8: $i] :
( ( ( ( addition @ SV8 @ SV10 )
= one )
= $false )
| ( ( ( multiplication @ SV8 @ SV10 )
= zero )
= $false )
| ( ( ( multiplication @ SV10 @ SV8 )
= zero )
= $false )
| ( ( complement @ SV10 @ SV8 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[91]) ).
thf(93,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[41,92,89,88,81,76,75,57,46,45,44,43,42]) ).
thf(94,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[93]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KLE005+1 : 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
% 0.07/0.18 % Computer : n007.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Oct 6 11:28:45 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.25
% 0.07/0.25 No.of.Axioms: 8
% 0.07/0.25
% 0.07/0.25 Length.of.Defs: 0
% 0.07/0.25
% 0.07/0.25 Contains.Choice.Funs: false
% 0.07/0.25 ..
% 0.07/0.25
% 0.07/0.25 ********************************
% 0.07/0.25 * All subproblems solved! *
% 0.07/0.25 ********************************
% 0.07/0.25 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:8,ps:0,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:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:93,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.07/0.25
% 0.07/0.25 %**** Beginning of derivation protocol ****
% 0.07/0.25 % SZS output start CNFRefutation
% See solution above
% 0.07/0.25
% 0.07/0.25 %**** End of derivation protocol ****
% 0.07/0.25 %**** no. of clauses in derivation: 86 ****
% 0.07/0.25 %**** clause counter: 93 ****
% 0.07/0.25
% 0.07/0.25 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:8,ps:0,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:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:93,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------