%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SWV148+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 : n006.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 10:55:08 AM UTC 2026
% Result : Theorem 0.57s 0.30s
% Output : CNFRefutation 0.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 9
% Syntax : Number of formulae : 99 ( 60 unt; 0 typ; 0 def)
% Number of atoms : 498 ( 154 equ; 0 cnn)
% Maximal formula atoms : 3 ( 5 avg)
% Number of connectives : 762 ( 153 ~; 106 |; 9 &; 470 @)
% ( 6 <=>; 18 =>; 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 : 38 ( 35 usr; 15 con; 0-4 aty)
% Number of variables : 172 ( 0 ^; 172 !; 0 ?; 172 :)
% 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_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_s_best7,type,
s_best7: $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_float_0_001,type,
tptp_float_0_001: $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(9,axiom,
! [X: $i] :
( ( ( leq @ n0 @ X )
& ( leq @ X @ n0 ) )
=> ( X = n0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',finite_domain_0) ).
thf(43,axiom,
! [X: $i,Y: $i] :
( ( leq @ ( succ @ X ) @ ( succ @ Y ) )
<=> ( leq @ X @ Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',leq_succ_succ) ).
thf(73,axiom,
! [X: $i,Y: $i] :
( ( leq @ X @ Y )
=> ( leq @ X @ ( succ @ Y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',leq_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(78,axiom,
! [X: $i,Y: $i] :
( ( geq @ X @ Y )
<=> ( leq @ Y @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',leq_geq) ).
thf(80,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( ( leq @ X @ Y )
& ( leq @ Y @ Z ) )
=> ( leq @ X @ Z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity_leq) ).
thf(81,axiom,
! [X: $i] : ( leq @ X @ X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_leq) ).
thf(85,conjecture,
( ~ ( leq @ tptp_float_0_001 @ tptp_float_0_001 )
=> ( leq @ s_best7 @ n3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gauss_array_0018) ).
thf(86,negated_conjecture,
( ( ~ ( leq @ tptp_float_0_001 @ tptp_float_0_001 )
=> ( leq @ s_best7 @ n3 ) )
= $false ),
inference(negate_conjecture,[status(cth)],[85]) ).
thf(87,plain,
( ( ~ ( leq @ tptp_float_0_001 @ tptp_float_0_001 )
=> ( leq @ s_best7 @ n3 ) )
= $false ),
inference(unfold_def,[status(thm)],[86]) ).
thf(88,plain,
( ( ! [X: $i] :
( ( ( leq @ n0 @ X )
& ( leq @ X @ n0 ) )
=> ( X = n0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(89,plain,
( ( ! [X: $i,Y: $i] :
( ( leq @ ( succ @ X ) @ ( succ @ Y ) )
<=> ( leq @ X @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[43]) ).
thf(90,plain,
( ( ! [X: $i,Y: $i] :
( ( leq @ X @ Y )
=> ( leq @ X @ ( succ @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[73]) ).
thf(91,plain,
( ( ! [X: $i,Y: $i] :
( ( ( leq @ X @ Y )
& ( X != Y ) )
=> ( gt @ Y @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[76]) ).
thf(92,plain,
( ( ! [X: $i,Y: $i] :
( ( gt @ Y @ X )
=> ( leq @ X @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[77]) ).
thf(93,plain,
( ( ! [X: $i,Y: $i] :
( ( geq @ X @ Y )
<=> ( leq @ Y @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[78]) ).
thf(94,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( ( leq @ X @ Y )
& ( leq @ Y @ Z ) )
=> ( leq @ X @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[80]) ).
thf(95,plain,
( ( ! [X: $i] : ( leq @ X @ X ) )
= $true ),
inference(unfold_def,[status(thm)],[81]) ).
thf(96,plain,
( ( ~ ( leq @ tptp_float_0_001 @ tptp_float_0_001 ) )
= $true ),
inference(standard_cnf,[status(thm)],[87]) ).
thf(97,plain,
( ( leq @ s_best7 @ n3 )
= $false ),
inference(standard_cnf,[status(thm)],[87]) ).
thf(98,plain,
( ( ~ ( leq @ s_best7 @ n3 ) )
= $true ),
inference(polarity_switch,[status(thm)],[97]) ).
thf(99,plain,
( ( ! [X: $i] : ( leq @ X @ X ) )
= $true ),
inference(copy,[status(thm)],[95]) ).
thf(100,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( ( leq @ X @ Y )
& ( leq @ Y @ Z ) )
=> ( leq @ X @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[94]) ).
thf(101,plain,
( ( ! [X: $i,Y: $i] :
( ( geq @ X @ Y )
<=> ( leq @ Y @ X ) ) )
= $true ),
inference(copy,[status(thm)],[93]) ).
thf(102,plain,
( ( ! [X: $i,Y: $i] :
( ( gt @ Y @ X )
=> ( leq @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[92]) ).
thf(103,plain,
( ( ! [X: $i,Y: $i] :
( ( ( leq @ X @ Y )
& ( X != Y ) )
=> ( gt @ Y @ X ) ) )
= $true ),
inference(copy,[status(thm)],[91]) ).
thf(104,plain,
( ( ! [X: $i,Y: $i] :
( ( leq @ X @ Y )
=> ( leq @ X @ ( succ @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[90]) ).
thf(105,plain,
( ( ! [X: $i,Y: $i] :
( ( leq @ ( succ @ X ) @ ( succ @ Y ) )
<=> ( leq @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[89]) ).
thf(106,plain,
( ( ! [X: $i] :
( ( ( leq @ n0 @ X )
& ( leq @ X @ n0 ) )
=> ( X = n0 ) ) )
= $true ),
inference(copy,[status(thm)],[88]) ).
thf(107,plain,
( ( ~ ( leq @ tptp_float_0_001 @ tptp_float_0_001 ) )
= $true ),
inference(copy,[status(thm)],[96]) ).
thf(108,plain,
( ( ~ ( leq @ s_best7 @ n3 ) )
= $true ),
inference(copy,[status(thm)],[98]) ).
thf(109,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( leq @ ( succ @ SX0 ) @ ( succ @ SX1 ) )
| ( leq @ SX0 @ SX1 ) )
| ~ ( ~ ( leq @ SX0 @ SX1 )
| ( leq @ ( succ @ SX0 ) @ ( succ @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[105]) ).
thf(110,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( leq @ SX0 @ SX1 )
| ~ ( leq @ SX1 @ SX2 ) )
| ( leq @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[100]) ).
thf(111,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( geq @ SX0 @ SX1 )
| ( leq @ SX1 @ SX0 ) )
| ~ ( ~ ( leq @ SX1 @ SX0 )
| ( geq @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[101]) ).
thf(112,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ( leq @ n0 @ SX0 )
| ~ ( leq @ SX0 @ n0 ) )
| ( SX0 = n0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[106]) ).
thf(113,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( gt @ SX1 @ SX0 )
| ( leq @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[102]) ).
thf(114,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( leq @ SX0 @ SX1 )
| ~ ( ( SX0 != SX1 ) ) )
| ( gt @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[103]) ).
thf(115,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( leq @ SX0 @ SX1 )
| ( leq @ SX0 @ ( succ @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[104]) ).
thf(116,plain,
! [SV1: $i] :
( ( leq @ SV1 @ SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[99]) ).
thf(117,plain,
( ( leq @ tptp_float_0_001 @ tptp_float_0_001 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[107]) ).
thf(118,plain,
( ( leq @ s_best7 @ n3 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[108]) ).
thf(119,plain,
! [SV2: $i] :
( ( ! [SY15: $i] :
~ ( ~ ( ~ ( leq @ ( succ @ SV2 ) @ ( succ @ SY15 ) )
| ( leq @ SV2 @ SY15 ) )
| ~ ( ~ ( leq @ SV2 @ SY15 )
| ( leq @ ( succ @ SV2 ) @ ( succ @ SY15 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[109]) ).
thf(120,plain,
! [SV3: $i] :
( ( ! [SY16: $i,SY17: $i] :
( ~ ~ ( ~ ( leq @ SV3 @ SY16 )
| ~ ( leq @ SY16 @ SY17 ) )
| ( leq @ SV3 @ SY17 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[110]) ).
thf(121,plain,
! [SV4: $i] :
( ( ! [SY18: $i] :
~ ( ~ ( ~ ( geq @ SV4 @ SY18 )
| ( leq @ SY18 @ SV4 ) )
| ~ ( ~ ( leq @ SY18 @ SV4 )
| ( geq @ SV4 @ SY18 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[111]) ).
thf(122,plain,
! [SV5: $i] :
( ( ~ ~ ( ~ ( leq @ n0 @ SV5 )
| ~ ( leq @ SV5 @ n0 ) )
| ( SV5 = n0 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[112]) ).
thf(123,plain,
! [SV6: $i] :
( ( ! [SY19: $i] :
( ~ ( gt @ SY19 @ SV6 )
| ( leq @ SV6 @ SY19 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[113]) ).
thf(124,plain,
! [SV7: $i] :
( ( ! [SY20: $i] :
( ~ ~ ( ~ ( leq @ SV7 @ SY20 )
| ~ ( ( SV7 != SY20 ) ) )
| ( gt @ SY20 @ SV7 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[114]) ).
thf(125,plain,
! [SV8: $i] :
( ( ! [SY21: $i] :
( ~ ( leq @ SV8 @ SY21 )
| ( leq @ SV8 @ ( succ @ SY21 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[115]) ).
thf(126,plain,
! [SV9: $i,SV2: $i] :
( ( ~ ( ~ ( ~ ( leq @ ( succ @ SV2 ) @ ( succ @ SV9 ) )
| ( leq @ SV2 @ SV9 ) )
| ~ ( ~ ( leq @ SV2 @ SV9 )
| ( leq @ ( succ @ SV2 ) @ ( succ @ SV9 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[119]) ).
thf(127,plain,
! [SV10: $i,SV3: $i] :
( ( ! [SY22: $i] :
( ~ ~ ( ~ ( leq @ SV3 @ SV10 )
| ~ ( leq @ SV10 @ SY22 ) )
| ( leq @ SV3 @ SY22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[120]) ).
thf(128,plain,
! [SV11: $i,SV4: $i] :
( ( ~ ( ~ ( ~ ( geq @ SV4 @ SV11 )
| ( leq @ SV11 @ SV4 ) )
| ~ ( ~ ( leq @ SV11 @ SV4 )
| ( geq @ SV4 @ SV11 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[121]) ).
thf(129,plain,
! [SV5: $i] :
( ( ( ~ ~ ( ~ ( leq @ n0 @ SV5 )
| ~ ( leq @ SV5 @ n0 ) ) )
= $true )
| ( ( SV5 = n0 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[122]) ).
thf(130,plain,
! [SV6: $i,SV12: $i] :
( ( ~ ( gt @ SV12 @ SV6 )
| ( leq @ SV6 @ SV12 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[123]) ).
thf(131,plain,
! [SV13: $i,SV7: $i] :
( ( ~ ~ ( ~ ( leq @ SV7 @ SV13 )
| ~ ( ( SV7 != SV13 ) ) )
| ( gt @ SV13 @ SV7 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[124]) ).
thf(132,plain,
! [SV14: $i,SV8: $i] :
( ( ~ ( leq @ SV8 @ SV14 )
| ( leq @ SV8 @ ( succ @ SV14 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[125]) ).
thf(133,plain,
! [SV9: $i,SV2: $i] :
( ( ~ ( ~ ( leq @ ( succ @ SV2 ) @ ( succ @ SV9 ) )
| ( leq @ SV2 @ SV9 ) )
| ~ ( ~ ( leq @ SV2 @ SV9 )
| ( leq @ ( succ @ SV2 ) @ ( succ @ SV9 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[126]) ).
thf(134,plain,
! [SV15: $i,SV10: $i,SV3: $i] :
( ( ~ ~ ( ~ ( leq @ SV3 @ SV10 )
| ~ ( leq @ SV10 @ SV15 ) )
| ( leq @ SV3 @ SV15 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[127]) ).
thf(135,plain,
! [SV11: $i,SV4: $i] :
( ( ~ ( ~ ( geq @ SV4 @ SV11 )
| ( leq @ SV11 @ SV4 ) )
| ~ ( ~ ( leq @ SV11 @ SV4 )
| ( geq @ SV4 @ SV11 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[128]) ).
thf(136,plain,
! [SV5: $i] :
( ( ( ~ ( ~ ( leq @ n0 @ SV5 )
| ~ ( leq @ SV5 @ n0 ) ) )
= $false )
| ( ( SV5 = n0 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[129]) ).
thf(137,plain,
! [SV6: $i,SV12: $i] :
( ( ( ~ ( gt @ SV12 @ SV6 ) )
= $true )
| ( ( leq @ SV6 @ SV12 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[130]) ).
thf(138,plain,
! [SV13: $i,SV7: $i] :
( ( ( ~ ~ ( ~ ( leq @ SV7 @ SV13 )
| ~ ( ( SV7 != SV13 ) ) ) )
= $true )
| ( ( gt @ SV13 @ SV7 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[131]) ).
thf(139,plain,
! [SV14: $i,SV8: $i] :
( ( ( ~ ( leq @ SV8 @ SV14 ) )
= $true )
| ( ( leq @ SV8 @ ( succ @ SV14 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[132]) ).
thf(140,plain,
! [SV9: $i,SV2: $i] :
( ( ~ ( ~ ( leq @ ( succ @ SV2 ) @ ( succ @ SV9 ) )
| ( leq @ SV2 @ SV9 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[133]) ).
thf(141,plain,
! [SV9: $i,SV2: $i] :
( ( ~ ( ~ ( leq @ SV2 @ SV9 )
| ( leq @ ( succ @ SV2 ) @ ( succ @ SV9 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[133]) ).
thf(142,plain,
! [SV15: $i,SV10: $i,SV3: $i] :
( ( ( ~ ~ ( ~ ( leq @ SV3 @ SV10 )
| ~ ( leq @ SV10 @ SV15 ) ) )
= $true )
| ( ( leq @ SV3 @ SV15 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[134]) ).
thf(143,plain,
! [SV11: $i,SV4: $i] :
( ( ~ ( ~ ( geq @ SV4 @ SV11 )
| ( leq @ SV11 @ SV4 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[135]) ).
thf(144,plain,
! [SV4: $i,SV11: $i] :
( ( ~ ( ~ ( leq @ SV11 @ SV4 )
| ( geq @ SV4 @ SV11 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[135]) ).
thf(145,plain,
! [SV5: $i] :
( ( ( ~ ( leq @ n0 @ SV5 )
| ~ ( leq @ SV5 @ n0 ) )
= $true )
| ( ( SV5 = n0 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[136]) ).
thf(146,plain,
! [SV6: $i,SV12: $i] :
( ( ( gt @ SV12 @ SV6 )
= $false )
| ( ( leq @ SV6 @ SV12 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[137]) ).
thf(147,plain,
! [SV13: $i,SV7: $i] :
( ( ( ~ ( ~ ( leq @ SV7 @ SV13 )
| ~ ( ( SV7 != SV13 ) ) ) )
= $false )
| ( ( gt @ SV13 @ SV7 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[138]) ).
thf(148,plain,
! [SV14: $i,SV8: $i] :
( ( ( leq @ SV8 @ SV14 )
= $false )
| ( ( leq @ SV8 @ ( succ @ SV14 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[139]) ).
thf(149,plain,
! [SV9: $i,SV2: $i] :
( ( ~ ( leq @ ( succ @ SV2 ) @ ( succ @ SV9 ) )
| ( leq @ SV2 @ SV9 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[140]) ).
thf(150,plain,
! [SV9: $i,SV2: $i] :
( ( ~ ( leq @ SV2 @ SV9 )
| ( leq @ ( succ @ SV2 ) @ ( succ @ SV9 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[141]) ).
thf(151,plain,
! [SV15: $i,SV10: $i,SV3: $i] :
( ( ( ~ ( ~ ( leq @ SV3 @ SV10 )
| ~ ( leq @ SV10 @ SV15 ) ) )
= $false )
| ( ( leq @ SV3 @ SV15 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[142]) ).
thf(152,plain,
! [SV11: $i,SV4: $i] :
( ( ~ ( geq @ SV4 @ SV11 )
| ( leq @ SV11 @ SV4 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[143]) ).
thf(153,plain,
! [SV4: $i,SV11: $i] :
( ( ~ ( leq @ SV11 @ SV4 )
| ( geq @ SV4 @ SV11 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[144]) ).
thf(154,plain,
! [SV5: $i] :
( ( ( ~ ( leq @ n0 @ SV5 ) )
= $true )
| ( ( ~ ( leq @ SV5 @ n0 ) )
= $true )
| ( ( SV5 = n0 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[145]) ).
thf(155,plain,
! [SV13: $i,SV7: $i] :
( ( ( ~ ( leq @ SV7 @ SV13 )
| ~ ( ( SV7 != SV13 ) ) )
= $true )
| ( ( gt @ SV13 @ SV7 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[147]) ).
thf(156,plain,
! [SV9: $i,SV2: $i] :
( ( ( ~ ( leq @ ( succ @ SV2 ) @ ( succ @ SV9 ) ) )
= $true )
| ( ( leq @ SV2 @ SV9 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[149]) ).
thf(157,plain,
! [SV9: $i,SV2: $i] :
( ( ( ~ ( leq @ SV2 @ SV9 ) )
= $true )
| ( ( leq @ ( succ @ SV2 ) @ ( succ @ SV9 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[150]) ).
thf(158,plain,
! [SV15: $i,SV10: $i,SV3: $i] :
( ( ( ~ ( leq @ SV3 @ SV10 )
| ~ ( leq @ SV10 @ SV15 ) )
= $true )
| ( ( leq @ SV3 @ SV15 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[151]) ).
thf(159,plain,
! [SV11: $i,SV4: $i] :
( ( ( ~ ( geq @ SV4 @ SV11 ) )
= $true )
| ( ( leq @ SV11 @ SV4 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[152]) ).
thf(160,plain,
! [SV4: $i,SV11: $i] :
( ( ( ~ ( leq @ SV11 @ SV4 ) )
= $true )
| ( ( geq @ SV4 @ SV11 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[153]) ).
thf(161,plain,
! [SV5: $i] :
( ( ( leq @ n0 @ SV5 )
= $false )
| ( ( ~ ( leq @ SV5 @ n0 ) )
= $true )
| ( ( SV5 = n0 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[154]) ).
thf(162,plain,
! [SV13: $i,SV7: $i] :
( ( ( ~ ( leq @ SV7 @ SV13 ) )
= $true )
| ( ( ~ ( ( SV7 != SV13 ) ) )
= $true )
| ( ( gt @ SV13 @ SV7 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[155]) ).
thf(163,plain,
! [SV9: $i,SV2: $i] :
( ( ( leq @ ( succ @ SV2 ) @ ( succ @ SV9 ) )
= $false )
| ( ( leq @ SV2 @ SV9 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[156]) ).
thf(164,plain,
! [SV9: $i,SV2: $i] :
( ( ( leq @ SV2 @ SV9 )
= $false )
| ( ( leq @ ( succ @ SV2 ) @ ( succ @ SV9 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[157]) ).
thf(165,plain,
! [SV15: $i,SV10: $i,SV3: $i] :
( ( ( ~ ( leq @ SV3 @ SV10 ) )
= $true )
| ( ( ~ ( leq @ SV10 @ SV15 ) )
= $true )
| ( ( leq @ SV3 @ SV15 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[158]) ).
thf(166,plain,
! [SV11: $i,SV4: $i] :
( ( ( geq @ SV4 @ SV11 )
= $false )
| ( ( leq @ SV11 @ SV4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[159]) ).
thf(167,plain,
! [SV4: $i,SV11: $i] :
( ( ( leq @ SV11 @ SV4 )
= $false )
| ( ( geq @ SV4 @ SV11 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[160]) ).
thf(168,plain,
! [SV5: $i] :
( ( ( leq @ SV5 @ n0 )
= $false )
| ( ( leq @ n0 @ SV5 )
= $false )
| ( ( SV5 = n0 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[161]) ).
thf(169,plain,
! [SV13: $i,SV7: $i] :
( ( ( leq @ SV7 @ SV13 )
= $false )
| ( ( ~ ( ( SV7 != SV13 ) ) )
= $true )
| ( ( gt @ SV13 @ SV7 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[162]) ).
thf(170,plain,
! [SV15: $i,SV10: $i,SV3: $i] :
( ( ( leq @ SV3 @ SV10 )
= $false )
| ( ( ~ ( leq @ SV10 @ SV15 ) )
= $true )
| ( ( leq @ SV3 @ SV15 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[165]) ).
thf(171,plain,
! [SV13: $i,SV7: $i] :
( ( ( SV7 != SV13 )
= $false )
| ( ( leq @ SV7 @ SV13 )
= $false )
| ( ( gt @ SV13 @ SV7 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[169]) ).
thf(172,plain,
! [SV3: $i,SV15: $i,SV10: $i] :
( ( ( leq @ SV10 @ SV15 )
= $false )
| ( ( leq @ SV3 @ SV10 )
= $false )
| ( ( leq @ SV3 @ SV15 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[170]) ).
thf(173,plain,
! [SV13: $i,SV7: $i] :
( ( ( SV7 = SV13 )
= $true )
| ( ( leq @ SV7 @ SV13 )
= $false )
| ( ( gt @ SV13 @ SV7 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[171]) ).
thf(174,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[116,173,172,168,167,166,164,163,148,146,118,117]) ).
thf(175,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[174]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV148+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 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
% 0.06/0.18 % Computer : n006.cluster.edu
% 0.06/0.18 % Model : x86_64 x86_64
% 0.06/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.18 % Memory : 8046.5625MB
% 0.06/0.18 % OS : Linux 6.8.0-71-generic
% 0.06/0.18 % CPULimit : 300
% 0.06/0.18 % WCLimit : 300
% 0.06/0.18 % DateTime : Tue Oct 6 16:19:52 UTC 2026
% 0.06/0.18 % CPUTime :
% 0.06/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.57/0.30
% 0.57/0.30 No.of.Axioms: 8
% 0.57/0.30
% 0.57/0.30 Length.of.Defs: 0
% 0.57/0.30
% 0.57/0.30 Contains.Choice.Funs: false
% 0.57/0.30 ...
% 0.57/0.30
% 0.57/0.30 ********************************
% 0.57/0.30 * All subproblems solved! *
% 0.57/0.30 ********************************
% 0.57/0.30 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:9,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:174,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.57/0.30
% 0.57/0.30 %**** Beginning of derivation protocol ****
% 0.57/0.30 % SZS output start CNFRefutation
% See solution above
% 0.57/0.30
% 0.57/0.30 %**** End of derivation protocol ****
% 0.57/0.30 %**** no. of clauses in derivation: 99 ****
% 0.57/0.30 %**** clause counter: 174 ****
% 0.57/0.30
% 0.57/0.30 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:9,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:174,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------