%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SWV061+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 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 : n012.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 10:54:43 AM UTC 2026
% Result : Theorem 0.12s 0.25s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 15
% Syntax : Number of formulae : 171 ( 123 unt; 0 typ; 0 def)
% Number of atoms : 800 ( 249 equ; 0 cnn)
% Maximal formula atoms : 5 ( 4 avg)
% Number of connectives : 1036 ( 217 ~; 158 |; 12 &; 616 @)
% ( 4 <=>; 29 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 37 ( 34 usr; 14 con; 0-4 aty)
% Number of variables : 242 ( 0 ^; 242 !; 0 ?; 242 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a_select2,type,
a_select2: $i > $i > $i ).
thf(tp_a_select3,type,
a_select3: $i > $i > $i > $i ).
thf(tp_def,type,
def: $i ).
thf(tp_dim,type,
dim: $i > $i > $i ).
thf(tp_geq,type,
geq: $i > $i > $o ).
thf(tp_gt,type,
gt: $i > $i > $o ).
thf(tp_inv,type,
inv: $i > $i ).
thf(tp_leq,type,
leq: $i > $i > $o ).
thf(tp_loopcounter,type,
loopcounter: $i ).
thf(tp_lt,type,
lt: $i > $i > $o ).
thf(tp_minus,type,
minus: $i > $i > $i ).
thf(tp_n0,type,
n0: $i ).
thf(tp_n1,type,
n1: $i ).
thf(tp_n2,type,
n2: $i ).
thf(tp_n3,type,
n3: $i ).
thf(tp_n4,type,
n4: $i ).
thf(tp_n5,type,
n5: $i ).
thf(tp_plus,type,
plus: $i > $i > $i ).
thf(tp_pred,type,
pred: $i > $i ).
thf(tp_succ,type,
succ: $i > $i ).
thf(tp_sum,type,
sum: $i > $i > $i > $i ).
thf(tp_tptp_const_array1,type,
tptp_const_array1: $i > $i > $i ).
thf(tp_tptp_const_array2,type,
tptp_const_array2: $i > $i > $i > $i ).
thf(tp_tptp_float_0_0,type,
tptp_float_0_0: $i ).
thf(tp_tptp_madd,type,
tptp_madd: $i > $i > $i ).
thf(tp_tptp_minus_1,type,
tptp_minus_1: $i ).
thf(tp_tptp_mmul,type,
tptp_mmul: $i > $i > $i ).
thf(tp_tptp_msub,type,
tptp_msub: $i > $i > $i ).
thf(tp_tptp_update2,type,
tptp_update2: $i > $i > $i > $i ).
thf(tp_tptp_update3,type,
tptp_update3: $i > $i > $i > $i > $i ).
thf(tp_trans,type,
trans: $i > $i ).
thf(tp_true,type,
true: $o ).
thf(tp_uniform_int_rnd,type,
uniform_int_rnd: $i > $i > $i ).
thf(tp_use,type,
use: $i ).
thf(17,axiom,
gt @ n3 @ n1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_3_1) ).
thf(18,axiom,
gt @ n2 @ n1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_2_1) ).
thf(19,axiom,
gt @ n5 @ n1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_5_1) ).
thf(20,axiom,
gt @ n4 @ n1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_4_1) ).
thf(23,axiom,
gt @ n1 @ n0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_1_0) ).
thf(28,axiom,
gt @ n1 @ tptp_minus_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_1_tptp_minus_1) ).
thf(34,axiom,
true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ttrue) ).
thf(74,axiom,
! [X: $i] : ( gt @ ( succ @ X ) @ X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_succ) ).
thf(76,axiom,
! [X: $i,Y: $i] :
( ( ( leq @ X @ Y )
& ( X != Y ) )
=> ( gt @ Y @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',leq_gt2) ).
thf(77,axiom,
! [X: $i,Y: $i] :
( ( gt @ Y @ X )
=> ( leq @ X @ Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',leq_gt1) ).
thf(79,axiom,
! [X: $i,Y: $i] :
( ( lt @ X @ Y )
<=> ( gt @ Y @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lt_gt) ).
thf(82,axiom,
! [X: $i] :
~ ( gt @ X @ X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',irreflexivity_gt) ).
thf(83,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( ( gt @ X @ Y )
& ( gt @ Y @ Z ) )
=> ( gt @ X @ Z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity_gt) ).
thf(84,axiom,
! [X: $i,Y: $i] :
( ( gt @ X @ Y )
| ( gt @ Y @ X )
| ( X = Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',totality) ).
thf(85,conjecture,
( true
=> ( ( ~ ( gt @ loopcounter @ n1 )
=> true )
& ( ( gt @ loopcounter @ n1 )
=> true ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cl5_nebula_array_0002) ).
thf(86,negated_conjecture,
( ( true
=> ( ( ~ ( gt @ loopcounter @ n1 )
=> true )
& ( ( gt @ loopcounter @ n1 )
=> true ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[85]) ).
thf(87,plain,
( ( true
=> ( ( ~ ( gt @ loopcounter @ n1 )
=> true )
& ( ( gt @ loopcounter @ n1 )
=> true ) ) )
= $false ),
inference(unfold_def,[status(thm)],[86]) ).
thf(88,plain,
( ( gt @ n3 @ n1 )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(89,plain,
( ( gt @ n2 @ n1 )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(90,plain,
( ( gt @ n5 @ n1 )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(91,plain,
( ( gt @ n4 @ n1 )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(92,plain,
( ( gt @ n1 @ n0 )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(93,plain,
( ( gt @ n1 @ tptp_minus_1 )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(94,plain,
true = $true,
inference(unfold_def,[status(thm)],[34]) ).
thf(95,plain,
( ( ! [X: $i] : ( gt @ ( succ @ X ) @ X ) )
= $true ),
inference(unfold_def,[status(thm)],[74]) ).
thf(96,plain,
( ( ! [X: $i,Y: $i] :
( ( ( leq @ X @ Y )
& ( X != Y ) )
=> ( gt @ Y @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[76]) ).
thf(97,plain,
( ( ! [X: $i,Y: $i] :
( ( gt @ Y @ X )
=> ( leq @ X @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[77]) ).
thf(98,plain,
( ( ! [X: $i,Y: $i] :
( ( lt @ X @ Y )
<=> ( gt @ Y @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[79]) ).
thf(99,plain,
( ( ! [X: $i] :
~ ( gt @ X @ X ) )
= $true ),
inference(unfold_def,[status(thm)],[82]) ).
thf(100,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( ( gt @ X @ Y )
& ( gt @ Y @ Z ) )
=> ( gt @ X @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[83]) ).
thf(101,plain,
( ( ! [X: $i,Y: $i] :
( ( gt @ X @ Y )
| ( gt @ Y @ X )
| ( X = Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[84]) ).
thf(102,plain,
true = $true,
inference(standard_cnf,[status(thm)],[87]) ).
thf(103,plain,
( ( ( ~ ( gt @ loopcounter @ n1 )
=> true )
& ( ( gt @ loopcounter @ n1 )
=> true ) )
= $false ),
inference(standard_cnf,[status(thm)],[87]) ).
thf(104,plain,
( ( ~ ( gt @ loopcounter @ n1 )
=> true )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[103]) ).
thf(105,plain,
( ( ( gt @ loopcounter @ n1 )
=> true )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[103]) ).
thf(106,plain,
( ( ~ ( ~ ( gt @ loopcounter @ n1 )
=> true ) )
= $true ),
inference(polarity_switch,[status(thm)],[104]) ).
thf(107,plain,
( ( ~ ( ( gt @ loopcounter @ n1 )
=> true ) )
= $true ),
inference(polarity_switch,[status(thm)],[105]) ).
thf(108,plain,
( ( ! [X: $i,Y: $i] :
( ( gt @ X @ Y )
| ( gt @ Y @ X )
| ( X = Y ) ) )
= $true ),
inference(copy,[status(thm)],[101]) ).
thf(109,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( ( gt @ X @ Y )
& ( gt @ Y @ Z ) )
=> ( gt @ X @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[100]) ).
thf(110,plain,
( ( ! [X: $i] :
~ ( gt @ X @ X ) )
= $true ),
inference(copy,[status(thm)],[99]) ).
thf(111,plain,
( ( ! [X: $i,Y: $i] :
( ( lt @ X @ Y )
<=> ( gt @ Y @ X ) ) )
= $true ),
inference(copy,[status(thm)],[98]) ).
thf(112,plain,
( ( ! [X: $i,Y: $i] :
( ( gt @ Y @ X )
=> ( leq @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[97]) ).
thf(113,plain,
( ( ! [X: $i,Y: $i] :
( ( ( leq @ X @ Y )
& ( X != Y ) )
=> ( gt @ Y @ X ) ) )
= $true ),
inference(copy,[status(thm)],[96]) ).
thf(114,plain,
( ( ! [X: $i] : ( gt @ ( succ @ X ) @ X ) )
= $true ),
inference(copy,[status(thm)],[95]) ).
thf(115,plain,
true = $true,
inference(copy,[status(thm)],[94]) ).
thf(116,plain,
( ( gt @ n1 @ tptp_minus_1 )
= $true ),
inference(copy,[status(thm)],[93]) ).
thf(117,plain,
( ( gt @ n1 @ n0 )
= $true ),
inference(copy,[status(thm)],[92]) ).
thf(118,plain,
( ( gt @ n4 @ n1 )
= $true ),
inference(copy,[status(thm)],[91]) ).
thf(119,plain,
( ( gt @ n5 @ n1 )
= $true ),
inference(copy,[status(thm)],[90]) ).
thf(120,plain,
( ( gt @ n2 @ n1 )
= $true ),
inference(copy,[status(thm)],[89]) ).
thf(121,plain,
( ( gt @ n3 @ n1 )
= $true ),
inference(copy,[status(thm)],[88]) ).
thf(122,plain,
true = $true,
inference(copy,[status(thm)],[102]) ).
thf(123,plain,
( ( ~ ( ~ ( gt @ loopcounter @ n1 )
=> true ) )
= $true ),
inference(copy,[status(thm)],[106]) ).
thf(124,plain,
( ( ~ ( ~ ~ ( gt @ loopcounter @ n1 )
| true ) )
= $true ),
inference(unfold_def,[status(thm)],[123]) ).
thf(125,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( gt @ SX1 @ SX0 )
| ( leq @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[112]) ).
thf(126,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( leq @ SX0 @ SX1 )
| ~ ( ( SX0 != SX1 ) ) )
| ( gt @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[113]) ).
thf(127,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( gt @ SX0 @ SX1 )
| ~ ( gt @ SX1 @ SX2 ) )
| ( gt @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[109]) ).
thf(128,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( lt @ SX0 @ SX1 )
| ( gt @ SX1 @ SX0 ) )
| ~ ( ~ ( gt @ SX1 @ SX0 )
| ( lt @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[111]) ).
thf(129,plain,
! [SV1: $i] :
( ( ! [SY13: $i] :
( ( gt @ SV1 @ SY13 )
| ( gt @ SY13 @ SV1 )
| ( SV1 = SY13 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[108]) ).
thf(130,plain,
! [SV2: $i] :
( ( ~ ( gt @ SV2 @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[110]) ).
thf(131,plain,
! [SV3: $i] :
( ( gt @ ( succ @ SV3 ) @ SV3 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[114]) ).
thf(132,plain,
( ( ~ ~ ( gt @ loopcounter @ n1 )
| true )
= $false ),
inference(extcnf_not_pos,[status(thm)],[124]) ).
thf(133,plain,
! [SV4: $i] :
( ( ! [SY14: $i] :
( ~ ( gt @ SY14 @ SV4 )
| ( leq @ SV4 @ SY14 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[125]) ).
thf(134,plain,
! [SV5: $i] :
( ( ! [SY15: $i] :
( ~ ~ ( ~ ( leq @ SV5 @ SY15 )
| ~ ( ( SV5 != SY15 ) ) )
| ( gt @ SY15 @ SV5 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[126]) ).
thf(135,plain,
! [SV6: $i] :
( ( ! [SY16: $i,SY17: $i] :
( ~ ~ ( ~ ( gt @ SV6 @ SY16 )
| ~ ( gt @ SY16 @ SY17 ) )
| ( gt @ SV6 @ SY17 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[127]) ).
thf(136,plain,
! [SV7: $i] :
( ( ! [SY18: $i] :
~ ( ~ ( ~ ( lt @ SV7 @ SY18 )
| ( gt @ SY18 @ SV7 ) )
| ~ ( ~ ( gt @ SY18 @ SV7 )
| ( lt @ SV7 @ SY18 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[128]) ).
thf(137,plain,
! [SV8: $i,SV1: $i] :
( ( ( gt @ SV1 @ SV8 )
| ( gt @ SV8 @ SV1 )
| ( SV1 = SV8 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[129]) ).
thf(138,plain,
! [SV2: $i] :
( ( gt @ SV2 @ SV2 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[130]) ).
thf(139,plain,
( ( ~ ~ ( gt @ loopcounter @ n1 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[132]) ).
thf(140,plain,
true = $false,
inference(extcnf_or_neg,[status(thm)],[132]) ).
thf(141,plain,
! [SV4: $i,SV9: $i] :
( ( ~ ( gt @ SV9 @ SV4 )
| ( leq @ SV4 @ SV9 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[133]) ).
thf(142,plain,
! [SV10: $i,SV5: $i] :
( ( ~ ~ ( ~ ( leq @ SV5 @ SV10 )
| ~ ( ( SV5 != SV10 ) ) )
| ( gt @ SV10 @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[134]) ).
thf(143,plain,
! [SV11: $i,SV6: $i] :
( ( ! [SY19: $i] :
( ~ ~ ( ~ ( gt @ SV6 @ SV11 )
| ~ ( gt @ SV11 @ SY19 ) )
| ( gt @ SV6 @ SY19 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[135]) ).
thf(144,plain,
! [SV12: $i,SV7: $i] :
( ( ~ ( ~ ( ~ ( lt @ SV7 @ SV12 )
| ( gt @ SV12 @ SV7 ) )
| ~ ( ~ ( gt @ SV12 @ SV7 )
| ( lt @ SV7 @ SV12 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[136]) ).
thf(145,plain,
! [SV8: $i,SV1: $i] :
( ( ( ( gt @ SV1 @ SV8 )
| ( gt @ SV8 @ SV1 ) )
= $true )
| ( ( SV1 = SV8 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[137]) ).
thf(146,plain,
( ( ~ ( gt @ loopcounter @ n1 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[139]) ).
thf(147,plain,
! [SV4: $i,SV9: $i] :
( ( ( ~ ( gt @ SV9 @ SV4 ) )
= $true )
| ( ( leq @ SV4 @ SV9 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[141]) ).
thf(148,plain,
! [SV10: $i,SV5: $i] :
( ( ( ~ ~ ( ~ ( leq @ SV5 @ SV10 )
| ~ ( ( SV5 != SV10 ) ) ) )
= $true )
| ( ( gt @ SV10 @ SV5 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[142]) ).
thf(149,plain,
! [SV13: $i,SV11: $i,SV6: $i] :
( ( ~ ~ ( ~ ( gt @ SV6 @ SV11 )
| ~ ( gt @ SV11 @ SV13 ) )
| ( gt @ SV6 @ SV13 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[143]) ).
thf(150,plain,
! [SV12: $i,SV7: $i] :
( ( ~ ( ~ ( lt @ SV7 @ SV12 )
| ( gt @ SV12 @ SV7 ) )
| ~ ( ~ ( gt @ SV12 @ SV7 )
| ( lt @ SV7 @ SV12 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[144]) ).
thf(151,plain,
! [SV8: $i,SV1: $i] :
( ( ( gt @ SV1 @ SV8 )
= $true )
| ( ( gt @ SV8 @ SV1 )
= $true )
| ( ( SV1 = SV8 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[145]) ).
thf(152,plain,
( ( gt @ loopcounter @ n1 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[146]) ).
thf(153,plain,
! [SV4: $i,SV9: $i] :
( ( ( gt @ SV9 @ SV4 )
= $false )
| ( ( leq @ SV4 @ SV9 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[147]) ).
thf(154,plain,
! [SV10: $i,SV5: $i] :
( ( ( ~ ( ~ ( leq @ SV5 @ SV10 )
| ~ ( ( SV5 != SV10 ) ) ) )
= $false )
| ( ( gt @ SV10 @ SV5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[148]) ).
thf(155,plain,
! [SV13: $i,SV11: $i,SV6: $i] :
( ( ( ~ ~ ( ~ ( gt @ SV6 @ SV11 )
| ~ ( gt @ SV11 @ SV13 ) ) )
= $true )
| ( ( gt @ SV6 @ SV13 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[149]) ).
thf(156,plain,
! [SV12: $i,SV7: $i] :
( ( ~ ( ~ ( lt @ SV7 @ SV12 )
| ( gt @ SV12 @ SV7 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[150]) ).
thf(157,plain,
! [SV7: $i,SV12: $i] :
( ( ~ ( ~ ( gt @ SV12 @ SV7 )
| ( lt @ SV7 @ SV12 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[150]) ).
thf(158,plain,
! [SV10: $i,SV5: $i] :
( ( ( ~ ( leq @ SV5 @ SV10 )
| ~ ( ( SV5 != SV10 ) ) )
= $true )
| ( ( gt @ SV10 @ SV5 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[154]) ).
thf(159,plain,
! [SV13: $i,SV11: $i,SV6: $i] :
( ( ( ~ ( ~ ( gt @ SV6 @ SV11 )
| ~ ( gt @ SV11 @ SV13 ) ) )
= $false )
| ( ( gt @ SV6 @ SV13 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[155]) ).
thf(160,plain,
! [SV12: $i,SV7: $i] :
( ( ~ ( lt @ SV7 @ SV12 )
| ( gt @ SV12 @ SV7 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[156]) ).
thf(161,plain,
! [SV7: $i,SV12: $i] :
( ( ~ ( gt @ SV12 @ SV7 )
| ( lt @ SV7 @ SV12 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[157]) ).
thf(162,plain,
! [SV10: $i,SV5: $i] :
( ( ( ~ ( leq @ SV5 @ SV10 ) )
= $true )
| ( ( ~ ( ( SV5 != SV10 ) ) )
= $true )
| ( ( gt @ SV10 @ SV5 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[158]) ).
thf(163,plain,
! [SV13: $i,SV11: $i,SV6: $i] :
( ( ( ~ ( gt @ SV6 @ SV11 )
| ~ ( gt @ SV11 @ SV13 ) )
= $true )
| ( ( gt @ SV6 @ SV13 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[159]) ).
thf(164,plain,
! [SV12: $i,SV7: $i] :
( ( ( ~ ( lt @ SV7 @ SV12 ) )
= $true )
| ( ( gt @ SV12 @ SV7 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[160]) ).
thf(165,plain,
! [SV7: $i,SV12: $i] :
( ( ( ~ ( gt @ SV12 @ SV7 ) )
= $true )
| ( ( lt @ SV7 @ SV12 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[161]) ).
thf(166,plain,
! [SV10: $i,SV5: $i] :
( ( ( leq @ SV5 @ SV10 )
= $false )
| ( ( ~ ( ( SV5 != SV10 ) ) )
= $true )
| ( ( gt @ SV10 @ SV5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[162]) ).
thf(167,plain,
! [SV13: $i,SV11: $i,SV6: $i] :
( ( ( ~ ( gt @ SV6 @ SV11 ) )
= $true )
| ( ( ~ ( gt @ SV11 @ SV13 ) )
= $true )
| ( ( gt @ SV6 @ SV13 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[163]) ).
thf(168,plain,
! [SV12: $i,SV7: $i] :
( ( ( lt @ SV7 @ SV12 )
= $false )
| ( ( gt @ SV12 @ SV7 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[164]) ).
thf(169,plain,
! [SV7: $i,SV12: $i] :
( ( ( gt @ SV12 @ SV7 )
= $false )
| ( ( lt @ SV7 @ SV12 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[165]) ).
thf(170,plain,
! [SV10: $i,SV5: $i] :
( ( ( SV5 != SV10 )
= $false )
| ( ( leq @ SV5 @ SV10 )
= $false )
| ( ( gt @ SV10 @ SV5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[166]) ).
thf(171,plain,
! [SV13: $i,SV11: $i,SV6: $i] :
( ( ( gt @ SV6 @ SV11 )
= $false )
| ( ( ~ ( gt @ SV11 @ SV13 ) )
= $true )
| ( ( gt @ SV6 @ SV13 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[167]) ).
thf(172,plain,
! [SV10: $i,SV5: $i] :
( ( ( SV5 = SV10 )
= $true )
| ( ( leq @ SV5 @ SV10 )
= $false )
| ( ( gt @ SV10 @ SV5 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[170]) ).
thf(173,plain,
! [SV6: $i,SV13: $i,SV11: $i] :
( ( ( gt @ SV11 @ SV13 )
= $false )
| ( ( gt @ SV6 @ SV11 )
= $false )
| ( ( gt @ SV6 @ SV13 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[171]) ).
thf(174,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[115,173,172,169,168,153,152,151,140,138,131,122,121,120,119,118,117,116]) ).
thf(175,plain,
( ( ! [X: $i,Y: $i] :
( ( gt @ X @ Y )
| ( gt @ Y @ X )
| ( X = Y ) ) )
= $true ),
inference(copy,[status(thm)],[101]) ).
thf(176,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( ( gt @ X @ Y )
& ( gt @ Y @ Z ) )
=> ( gt @ X @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[100]) ).
thf(177,plain,
( ( ! [X: $i] :
~ ( gt @ X @ X ) )
= $true ),
inference(copy,[status(thm)],[99]) ).
thf(178,plain,
( ( ! [X: $i,Y: $i] :
( ( lt @ X @ Y )
<=> ( gt @ Y @ X ) ) )
= $true ),
inference(copy,[status(thm)],[98]) ).
thf(179,plain,
( ( ! [X: $i,Y: $i] :
( ( gt @ Y @ X )
=> ( leq @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[97]) ).
thf(180,plain,
( ( ! [X: $i,Y: $i] :
( ( ( leq @ X @ Y )
& ( X != Y ) )
=> ( gt @ Y @ X ) ) )
= $true ),
inference(copy,[status(thm)],[96]) ).
thf(181,plain,
( ( ! [X: $i] : ( gt @ ( succ @ X ) @ X ) )
= $true ),
inference(copy,[status(thm)],[95]) ).
thf(182,plain,
true = $true,
inference(copy,[status(thm)],[94]) ).
thf(183,plain,
( ( gt @ n1 @ tptp_minus_1 )
= $true ),
inference(copy,[status(thm)],[93]) ).
thf(184,plain,
( ( gt @ n1 @ n0 )
= $true ),
inference(copy,[status(thm)],[92]) ).
thf(185,plain,
( ( gt @ n4 @ n1 )
= $true ),
inference(copy,[status(thm)],[91]) ).
thf(186,plain,
( ( gt @ n5 @ n1 )
= $true ),
inference(copy,[status(thm)],[90]) ).
thf(187,plain,
( ( gt @ n2 @ n1 )
= $true ),
inference(copy,[status(thm)],[89]) ).
thf(188,plain,
( ( gt @ n3 @ n1 )
= $true ),
inference(copy,[status(thm)],[88]) ).
thf(189,plain,
true = $true,
inference(copy,[status(thm)],[102]) ).
thf(190,plain,
( ( ~ ( ( gt @ loopcounter @ n1 )
=> true ) )
= $true ),
inference(copy,[status(thm)],[107]) ).
thf(191,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( lt @ SX0 @ SX1 )
| ( gt @ SX1 @ SX0 ) )
| ~ ( ~ ( gt @ SX1 @ SX0 )
| ( lt @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[178]) ).
thf(192,plain,
( ( ~ ( ~ ( gt @ loopcounter @ n1 )
| true ) )
= $true ),
inference(unfold_def,[status(thm)],[190]) ).
thf(193,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( gt @ SX1 @ SX0 )
| ( leq @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[179]) ).
thf(194,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( gt @ SX0 @ SX1 )
| ~ ( gt @ SX1 @ SX2 ) )
| ( gt @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[176]) ).
thf(195,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( leq @ SX0 @ SX1 )
| ~ ( ( SX0 != SX1 ) ) )
| ( gt @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[180]) ).
thf(196,plain,
! [SV14: $i] :
( ( ! [SY20: $i] :
( ( gt @ SV14 @ SY20 )
| ( gt @ SY20 @ SV14 )
| ( SV14 = SY20 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[175]) ).
thf(197,plain,
! [SV15: $i] :
( ( ~ ( gt @ SV15 @ SV15 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[177]) ).
thf(198,plain,
! [SV16: $i] :
( ( gt @ ( succ @ SV16 ) @ SV16 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[181]) ).
thf(199,plain,
! [SV17: $i] :
( ( ! [SY21: $i] :
~ ( ~ ( ~ ( lt @ SV17 @ SY21 )
| ( gt @ SY21 @ SV17 ) )
| ~ ( ~ ( gt @ SY21 @ SV17 )
| ( lt @ SV17 @ SY21 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[191]) ).
thf(200,plain,
( ( ~ ( gt @ loopcounter @ n1 )
| true )
= $false ),
inference(extcnf_not_pos,[status(thm)],[192]) ).
thf(201,plain,
! [SV18: $i] :
( ( ! [SY22: $i] :
( ~ ( gt @ SY22 @ SV18 )
| ( leq @ SV18 @ SY22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[193]) ).
thf(202,plain,
! [SV19: $i] :
( ( ! [SY23: $i,SY24: $i] :
( ~ ~ ( ~ ( gt @ SV19 @ SY23 )
| ~ ( gt @ SY23 @ SY24 ) )
| ( gt @ SV19 @ SY24 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[194]) ).
thf(203,plain,
! [SV20: $i] :
( ( ! [SY25: $i] :
( ~ ~ ( ~ ( leq @ SV20 @ SY25 )
| ~ ( ( SV20 != SY25 ) ) )
| ( gt @ SY25 @ SV20 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[195]) ).
thf(204,plain,
! [SV21: $i,SV14: $i] :
( ( ( gt @ SV14 @ SV21 )
| ( gt @ SV21 @ SV14 )
| ( SV14 = SV21 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[196]) ).
thf(205,plain,
! [SV15: $i] :
( ( gt @ SV15 @ SV15 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[197]) ).
thf(206,plain,
! [SV22: $i,SV17: $i] :
( ( ~ ( ~ ( ~ ( lt @ SV17 @ SV22 )
| ( gt @ SV22 @ SV17 ) )
| ~ ( ~ ( gt @ SV22 @ SV17 )
| ( lt @ SV17 @ SV22 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[199]) ).
thf(207,plain,
( ( ~ ( gt @ loopcounter @ n1 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[200]) ).
thf(208,plain,
true = $false,
inference(extcnf_or_neg,[status(thm)],[200]) ).
thf(209,plain,
! [SV18: $i,SV23: $i] :
( ( ~ ( gt @ SV23 @ SV18 )
| ( leq @ SV18 @ SV23 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[201]) ).
thf(210,plain,
! [SV24: $i,SV19: $i] :
( ( ! [SY26: $i] :
( ~ ~ ( ~ ( gt @ SV19 @ SV24 )
| ~ ( gt @ SV24 @ SY26 ) )
| ( gt @ SV19 @ SY26 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[202]) ).
thf(211,plain,
! [SV25: $i,SV20: $i] :
( ( ~ ~ ( ~ ( leq @ SV20 @ SV25 )
| ~ ( ( SV20 != SV25 ) ) )
| ( gt @ SV25 @ SV20 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[203]) ).
thf(212,plain,
! [SV21: $i,SV14: $i] :
( ( ( ( gt @ SV14 @ SV21 )
| ( gt @ SV21 @ SV14 ) )
= $true )
| ( ( SV14 = SV21 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[204]) ).
thf(213,plain,
! [SV22: $i,SV17: $i] :
( ( ~ ( ~ ( lt @ SV17 @ SV22 )
| ( gt @ SV22 @ SV17 ) )
| ~ ( ~ ( gt @ SV22 @ SV17 )
| ( lt @ SV17 @ SV22 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[206]) ).
thf(214,plain,
( ( gt @ loopcounter @ n1 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[207]) ).
thf(215,plain,
! [SV18: $i,SV23: $i] :
( ( ( ~ ( gt @ SV23 @ SV18 ) )
= $true )
| ( ( leq @ SV18 @ SV23 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[209]) ).
thf(216,plain,
! [SV26: $i,SV24: $i,SV19: $i] :
( ( ~ ~ ( ~ ( gt @ SV19 @ SV24 )
| ~ ( gt @ SV24 @ SV26 ) )
| ( gt @ SV19 @ SV26 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[210]) ).
thf(217,plain,
! [SV25: $i,SV20: $i] :
( ( ( ~ ~ ( ~ ( leq @ SV20 @ SV25 )
| ~ ( ( SV20 != SV25 ) ) ) )
= $true )
| ( ( gt @ SV25 @ SV20 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[211]) ).
thf(218,plain,
! [SV21: $i,SV14: $i] :
( ( ( gt @ SV14 @ SV21 )
= $true )
| ( ( gt @ SV21 @ SV14 )
= $true )
| ( ( SV14 = SV21 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[212]) ).
thf(219,plain,
! [SV22: $i,SV17: $i] :
( ( ~ ( ~ ( lt @ SV17 @ SV22 )
| ( gt @ SV22 @ SV17 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[213]) ).
thf(220,plain,
! [SV17: $i,SV22: $i] :
( ( ~ ( ~ ( gt @ SV22 @ SV17 )
| ( lt @ SV17 @ SV22 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[213]) ).
thf(221,plain,
! [SV18: $i,SV23: $i] :
( ( ( gt @ SV23 @ SV18 )
= $false )
| ( ( leq @ SV18 @ SV23 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[215]) ).
thf(222,plain,
! [SV26: $i,SV24: $i,SV19: $i] :
( ( ( ~ ~ ( ~ ( gt @ SV19 @ SV24 )
| ~ ( gt @ SV24 @ SV26 ) ) )
= $true )
| ( ( gt @ SV19 @ SV26 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[216]) ).
thf(223,plain,
! [SV25: $i,SV20: $i] :
( ( ( ~ ( ~ ( leq @ SV20 @ SV25 )
| ~ ( ( SV20 != SV25 ) ) ) )
= $false )
| ( ( gt @ SV25 @ SV20 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[217]) ).
thf(224,plain,
! [SV22: $i,SV17: $i] :
( ( ~ ( lt @ SV17 @ SV22 )
| ( gt @ SV22 @ SV17 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[219]) ).
thf(225,plain,
! [SV17: $i,SV22: $i] :
( ( ~ ( gt @ SV22 @ SV17 )
| ( lt @ SV17 @ SV22 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[220]) ).
thf(226,plain,
! [SV26: $i,SV24: $i,SV19: $i] :
( ( ( ~ ( ~ ( gt @ SV19 @ SV24 )
| ~ ( gt @ SV24 @ SV26 ) ) )
= $false )
| ( ( gt @ SV19 @ SV26 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[222]) ).
thf(227,plain,
! [SV25: $i,SV20: $i] :
( ( ( ~ ( leq @ SV20 @ SV25 )
| ~ ( ( SV20 != SV25 ) ) )
= $true )
| ( ( gt @ SV25 @ SV20 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[223]) ).
thf(228,plain,
! [SV22: $i,SV17: $i] :
( ( ( ~ ( lt @ SV17 @ SV22 ) )
= $true )
| ( ( gt @ SV22 @ SV17 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[224]) ).
thf(229,plain,
! [SV17: $i,SV22: $i] :
( ( ( ~ ( gt @ SV22 @ SV17 ) )
= $true )
| ( ( lt @ SV17 @ SV22 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[225]) ).
thf(230,plain,
! [SV26: $i,SV24: $i,SV19: $i] :
( ( ( ~ ( gt @ SV19 @ SV24 )
| ~ ( gt @ SV24 @ SV26 ) )
= $true )
| ( ( gt @ SV19 @ SV26 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[226]) ).
thf(231,plain,
! [SV25: $i,SV20: $i] :
( ( ( ~ ( leq @ SV20 @ SV25 ) )
= $true )
| ( ( ~ ( ( SV20 != SV25 ) ) )
= $true )
| ( ( gt @ SV25 @ SV20 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[227]) ).
thf(232,plain,
! [SV22: $i,SV17: $i] :
( ( ( lt @ SV17 @ SV22 )
= $false )
| ( ( gt @ SV22 @ SV17 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[228]) ).
thf(233,plain,
! [SV17: $i,SV22: $i] :
( ( ( gt @ SV22 @ SV17 )
= $false )
| ( ( lt @ SV17 @ SV22 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[229]) ).
thf(234,plain,
! [SV26: $i,SV24: $i,SV19: $i] :
( ( ( ~ ( gt @ SV19 @ SV24 ) )
= $true )
| ( ( ~ ( gt @ SV24 @ SV26 ) )
= $true )
| ( ( gt @ SV19 @ SV26 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[230]) ).
thf(235,plain,
! [SV25: $i,SV20: $i] :
( ( ( leq @ SV20 @ SV25 )
= $false )
| ( ( ~ ( ( SV20 != SV25 ) ) )
= $true )
| ( ( gt @ SV25 @ SV20 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[231]) ).
thf(236,plain,
! [SV26: $i,SV24: $i,SV19: $i] :
( ( ( gt @ SV19 @ SV24 )
= $false )
| ( ( ~ ( gt @ SV24 @ SV26 ) )
= $true )
| ( ( gt @ SV19 @ SV26 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[234]) ).
thf(237,plain,
! [SV25: $i,SV20: $i] :
( ( ( SV20 != SV25 )
= $false )
| ( ( leq @ SV20 @ SV25 )
= $false )
| ( ( gt @ SV25 @ SV20 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[235]) ).
thf(238,plain,
! [SV19: $i,SV26: $i,SV24: $i] :
( ( ( gt @ SV24 @ SV26 )
= $false )
| ( ( gt @ SV19 @ SV24 )
= $false )
| ( ( gt @ SV19 @ SV26 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[236]) ).
thf(239,plain,
! [SV25: $i,SV20: $i] :
( ( ( SV20 = SV25 )
= $true )
| ( ( leq @ SV20 @ SV25 )
= $false )
| ( ( gt @ SV25 @ SV20 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[237]) ).
thf(240,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[182,239,238,233,232,221,218,214,208,205,198,189,188,187,186,185,184,183]) ).
thf(241,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[240,174]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWV061+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.03 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.00/0.11 % Computer : n012.cluster.edu
% 0.00/0.11 % Model : x86_64 x86_64
% 0.00/0.11 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.11 % Memory : 8046.5625MB
% 0.00/0.11 % OS : Linux 6.8.0-71-generic
% 0.00/0.11 % CPULimit : 300
% 0.00/0.11 % WCLimit : 300
% 0.00/0.11 % DateTime : Tue Oct 6 16:17:31 UTC 2026
% 0.00/0.12 % CPUTime :
% 0.00/0.12 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.25
% 0.12/0.25 No.of.Axioms: 14
% 0.12/0.25
% 0.12/0.25 Length.of.Defs: 0
% 0.12/0.25
% 0.12/0.25 Contains.Choice.Funs: false
% 0.12/0.25 ....
% 0.12/0.25
% 0.12/0.25 ********************************
% 0.12/0.25 * All subproblems solved! *
% 0.12/0.25 ********************************
% 0.12/0.25 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:15,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:240,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.12/0.25
% 0.12/0.25 %**** Beginning of derivation protocol ****
% 0.12/0.25 % SZS output start CNFRefutation
% See solution above
% 0.12/0.25
% 0.12/0.25 %**** End of derivation protocol ****
% 0.12/0.25 %**** no. of clauses in derivation: 171 ****
% 0.12/0.25 %**** clause counter: 240 ****
% 0.12/0.25
% 0.12/0.25 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:15,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:240,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------