%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SWV107+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 : n001.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 10:54:52 AM UTC 2026
% Result : Theorem 0.56s 0.31s
% Output : CNFRefutation 0.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 28
% Syntax : Number of formulae : 164 ( 121 unt; 0 typ; 0 def)
% Number of atoms : 800 ( 345 equ; 0 cnn)
% Maximal formula atoms : 10 ( 4 avg)
% Number of connectives : 983 ( 113 ~; 181 |; 18 &; 632 @)
% ( 3 <=>; 36 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 2 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 : 100 ( 0 ^; 100 !; 0 ?; 100 :)
% 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_n6,type,
n6: $i ).
thf(tp_n999,type,
n999: $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(1,axiom,
( ( succ @ ( succ @ ( succ @ n0 ) ) )
= n3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_3) ).
thf(2,axiom,
( ( succ @ ( succ @ n0 ) )
= n2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_2) ).
thf(3,axiom,
( ( succ @ n0 )
= n1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_1) ).
thf(4,axiom,
( ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ n0 ) ) ) ) ) )
= n6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_6) ).
thf(7,axiom,
! [X: $i] :
( ( ( leq @ n0 @ X )
& ( leq @ X @ n3 ) )
=> ( ( X = n0 )
| ( X = n1 )
| ( X = n2 )
| ( X = n3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',finite_domain_3) ).
thf(8,axiom,
! [X: $i] :
( ( ( leq @ n0 @ X )
& ( leq @ X @ n2 ) )
=> ( ( X = n0 )
| ( X = n1 )
| ( X = n2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',finite_domain_2) ).
thf(9,axiom,
! [X: $i] :
( ( ( leq @ n0 @ X )
& ( leq @ X @ n1 ) )
=> ( ( X = n0 )
| ( X = n1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',finite_domain_1) ).
thf(10,axiom,
! [X: $i] :
( ( ( leq @ n0 @ X )
& ( leq @ X @ n0 ) )
=> ( X = n0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',finite_domain_0) ).
thf(14,axiom,
gt @ n999 @ n3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_999_3) ).
thf(15,axiom,
gt @ n6 @ n3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_6_3) ).
thf(18,axiom,
gt @ n3 @ n2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_3_2) ).
thf(19,axiom,
gt @ n999 @ n2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_999_2) ).
thf(20,axiom,
gt @ n6 @ n2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_6_2) ).
thf(23,axiom,
gt @ n3 @ n1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_3_1) ).
thf(24,axiom,
gt @ n2 @ n1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_2_1) ).
thf(25,axiom,
gt @ n999 @ n1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_999_1) ).
thf(26,axiom,
gt @ n6 @ n1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_6_1) ).
thf(29,axiom,
gt @ n3 @ n0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_3_0) ).
thf(30,axiom,
gt @ n2 @ n0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_2_0) ).
thf(31,axiom,
gt @ n1 @ n0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_1_0) ).
thf(32,axiom,
gt @ n999 @ n0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_999_0) ).
thf(33,axiom,
gt @ n6 @ n0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_6_0) ).
thf(44,axiom,
gt @ n999 @ n6,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_999_6) ).
thf(51,axiom,
true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ttrue) ).
thf(58,axiom,
! [X: $i,Y: $i] :
( ( leq @ ( minus @ X @ Y ) @ X )
=> ( leq @ n0 @ Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',leq_minus) ).
thf(63,axiom,
! [X: $i] :
( ( minus @ X @ n1 )
= ( pred @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pred_minus_1) ).
thf(95,axiom,
! [X: $i,Y: $i] :
( ( geq @ X @ Y )
<=> ( leq @ Y @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',leq_geq) ).
thf(102,conjecture,
( ( geq @ ( minus @ n3 @ n1 ) @ n0 )
=> ( ( geq @ ( minus @ n6 @ n1 ) @ n0 )
=> ( ( ( geq @ n2 @ n0 )
& ( geq @ ( minus @ n999 @ n1 ) @ n0 ) )
=> ( ( geq @ ( minus @ n6 @ n1 ) @ n0 )
=> ( ( geq @ ( minus @ n6 @ n1 ) @ n0 )
=> ( ( geq @ ( minus @ n6 @ n1 ) @ n0 )
=> ( ( ( geq @ ( minus @ n3 @ n1 ) @ n0 )
& ( geq @ ( minus @ n999 @ n1 ) @ n0 ) )
=> true ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quaternion_ds1_inuse_0019) ).
thf(103,negated_conjecture,
( ( ( geq @ ( minus @ n3 @ n1 ) @ n0 )
=> ( ( geq @ ( minus @ n6 @ n1 ) @ n0 )
=> ( ( ( geq @ n2 @ n0 )
& ( geq @ ( minus @ n999 @ n1 ) @ n0 ) )
=> ( ( geq @ ( minus @ n6 @ n1 ) @ n0 )
=> ( ( geq @ ( minus @ n6 @ n1 ) @ n0 )
=> ( ( geq @ ( minus @ n6 @ n1 ) @ n0 )
=> ( ( ( geq @ ( minus @ n3 @ n1 ) @ n0 )
& ( geq @ ( minus @ n999 @ n1 ) @ n0 ) )
=> true ) ) ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[102]) ).
thf(104,plain,
( ( ( geq @ ( minus @ n3 @ n1 ) @ n0 )
=> ( ( geq @ ( minus @ n6 @ n1 ) @ n0 )
=> ( ( ( geq @ n2 @ n0 )
& ( geq @ ( minus @ n999 @ n1 ) @ n0 ) )
=> ( ( geq @ ( minus @ n6 @ n1 ) @ n0 )
=> ( ( geq @ ( minus @ n6 @ n1 ) @ n0 )
=> ( ( geq @ ( minus @ n6 @ n1 ) @ n0 )
=> ( ( ( geq @ ( minus @ n3 @ n1 ) @ n0 )
& ( geq @ ( minus @ n999 @ n1 ) @ n0 ) )
=> true ) ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[103]) ).
thf(105,plain,
( ( ( succ @ ( succ @ ( succ @ n0 ) ) )
= n3 )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(106,plain,
( ( ( succ @ ( succ @ n0 ) )
= n2 )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(107,plain,
( ( ( succ @ n0 )
= n1 )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(108,plain,
( ( ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ n0 ) ) ) ) ) )
= n6 )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(109,plain,
( ( ! [X: $i] :
( ( ( leq @ n0 @ X )
& ( leq @ X @ n3 ) )
=> ( ( X = n0 )
| ( X = n1 )
| ( X = n2 )
| ( X = n3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(110,plain,
( ( ! [X: $i] :
( ( ( leq @ n0 @ X )
& ( leq @ X @ n2 ) )
=> ( ( X = n0 )
| ( X = n1 )
| ( X = n2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(111,plain,
( ( ! [X: $i] :
( ( ( leq @ n0 @ X )
& ( leq @ X @ n1 ) )
=> ( ( X = n0 )
| ( X = n1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(112,plain,
( ( ! [X: $i] :
( ( ( leq @ n0 @ X )
& ( leq @ X @ n0 ) )
=> ( X = n0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(113,plain,
( ( gt @ n999 @ n3 )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(114,plain,
( ( gt @ n6 @ n3 )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(115,plain,
( ( gt @ n3 @ n2 )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(116,plain,
( ( gt @ n999 @ n2 )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(117,plain,
( ( gt @ n6 @ n2 )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(118,plain,
( ( gt @ n3 @ n1 )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(119,plain,
( ( gt @ n2 @ n1 )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(120,plain,
( ( gt @ n999 @ n1 )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(121,plain,
( ( gt @ n6 @ n1 )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(122,plain,
( ( gt @ n3 @ n0 )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(123,plain,
( ( gt @ n2 @ n0 )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(124,plain,
( ( gt @ n1 @ n0 )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(125,plain,
( ( gt @ n999 @ n0 )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(126,plain,
( ( gt @ n6 @ n0 )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(127,plain,
( ( gt @ n999 @ n6 )
= $true ),
inference(unfold_def,[status(thm)],[44]) ).
thf(128,plain,
true = $true,
inference(unfold_def,[status(thm)],[51]) ).
thf(129,plain,
( ( ! [X: $i,Y: $i] :
( ( leq @ ( minus @ X @ Y ) @ X )
=> ( leq @ n0 @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[58]) ).
thf(130,plain,
( ( ! [X: $i] :
( ( minus @ X @ n1 )
= ( pred @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[63]) ).
thf(131,plain,
( ( ! [X: $i,Y: $i] :
( ( geq @ X @ Y )
<=> ( leq @ Y @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[95]) ).
thf(132,plain,
( ( geq @ ( minus @ n3 @ n1 ) @ n0 )
= $true ),
inference(standard_cnf,[status(thm)],[104]) ).
thf(133,plain,
( ( geq @ ( minus @ n6 @ n1 ) @ n0 )
= $true ),
inference(standard_cnf,[status(thm)],[104]) ).
thf(134,plain,
( ( geq @ n2 @ n0 )
= $true ),
inference(standard_cnf,[status(thm)],[104]) ).
thf(135,plain,
( ( geq @ ( minus @ n999 @ n1 ) @ n0 )
= $true ),
inference(standard_cnf,[status(thm)],[104]) ).
thf(136,plain,
( ( geq @ ( minus @ n6 @ n1 ) @ n0 )
= $true ),
inference(standard_cnf,[status(thm)],[104]) ).
thf(137,plain,
( ( geq @ ( minus @ n6 @ n1 ) @ n0 )
= $true ),
inference(standard_cnf,[status(thm)],[104]) ).
thf(138,plain,
( ( geq @ ( minus @ n6 @ n1 ) @ n0 )
= $true ),
inference(standard_cnf,[status(thm)],[104]) ).
thf(139,plain,
( ( geq @ ( minus @ n3 @ n1 ) @ n0 )
= $true ),
inference(standard_cnf,[status(thm)],[104]) ).
thf(140,plain,
( ( geq @ ( minus @ n999 @ n1 ) @ n0 )
= $true ),
inference(standard_cnf,[status(thm)],[104]) ).
thf(141,plain,
true = $false,
inference(standard_cnf,[status(thm)],[104]) ).
thf(142,plain,
( ( ~ true ) = $true ),
inference(polarity_switch,[status(thm)],[141]) ).
thf(143,plain,
( ( ! [X: $i,Y: $i] :
( ( geq @ X @ Y )
<=> ( leq @ Y @ X ) ) )
= $true ),
inference(copy,[status(thm)],[131]) ).
thf(144,plain,
( ( ! [X: $i] :
( ( minus @ X @ n1 )
= ( pred @ X ) ) )
= $true ),
inference(copy,[status(thm)],[130]) ).
thf(145,plain,
( ( ! [X: $i,Y: $i] :
( ( leq @ ( minus @ X @ Y ) @ X )
=> ( leq @ n0 @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[129]) ).
thf(146,plain,
true = $true,
inference(copy,[status(thm)],[128]) ).
thf(147,plain,
( ( gt @ n999 @ n6 )
= $true ),
inference(copy,[status(thm)],[127]) ).
thf(148,plain,
( ( gt @ n6 @ n0 )
= $true ),
inference(copy,[status(thm)],[126]) ).
thf(149,plain,
( ( gt @ n999 @ n0 )
= $true ),
inference(copy,[status(thm)],[125]) ).
thf(150,plain,
( ( gt @ n1 @ n0 )
= $true ),
inference(copy,[status(thm)],[124]) ).
thf(151,plain,
( ( gt @ n2 @ n0 )
= $true ),
inference(copy,[status(thm)],[123]) ).
thf(152,plain,
( ( gt @ n3 @ n0 )
= $true ),
inference(copy,[status(thm)],[122]) ).
thf(153,plain,
( ( gt @ n6 @ n1 )
= $true ),
inference(copy,[status(thm)],[121]) ).
thf(154,plain,
( ( gt @ n999 @ n1 )
= $true ),
inference(copy,[status(thm)],[120]) ).
thf(155,plain,
( ( gt @ n2 @ n1 )
= $true ),
inference(copy,[status(thm)],[119]) ).
thf(156,plain,
( ( gt @ n3 @ n1 )
= $true ),
inference(copy,[status(thm)],[118]) ).
thf(157,plain,
( ( gt @ n6 @ n2 )
= $true ),
inference(copy,[status(thm)],[117]) ).
thf(158,plain,
( ( gt @ n999 @ n2 )
= $true ),
inference(copy,[status(thm)],[116]) ).
thf(159,plain,
( ( gt @ n3 @ n2 )
= $true ),
inference(copy,[status(thm)],[115]) ).
thf(160,plain,
( ( gt @ n6 @ n3 )
= $true ),
inference(copy,[status(thm)],[114]) ).
thf(161,plain,
( ( gt @ n999 @ n3 )
= $true ),
inference(copy,[status(thm)],[113]) ).
thf(162,plain,
( ( ! [X: $i] :
( ( ( leq @ n0 @ X )
& ( leq @ X @ n0 ) )
=> ( X = n0 ) ) )
= $true ),
inference(copy,[status(thm)],[112]) ).
thf(163,plain,
( ( ! [X: $i] :
( ( ( leq @ n0 @ X )
& ( leq @ X @ n1 ) )
=> ( ( X = n0 )
| ( X = n1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[111]) ).
thf(164,plain,
( ( ! [X: $i] :
( ( ( leq @ n0 @ X )
& ( leq @ X @ n2 ) )
=> ( ( X = n0 )
| ( X = n1 )
| ( X = n2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[110]) ).
thf(165,plain,
( ( ! [X: $i] :
( ( ( leq @ n0 @ X )
& ( leq @ X @ n3 ) )
=> ( ( X = n0 )
| ( X = n1 )
| ( X = n2 )
| ( X = n3 ) ) ) )
= $true ),
inference(copy,[status(thm)],[109]) ).
thf(166,plain,
( ( ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ n0 ) ) ) ) ) )
= n6 )
= $true ),
inference(copy,[status(thm)],[108]) ).
thf(167,plain,
( ( ( succ @ n0 )
= n1 )
= $true ),
inference(copy,[status(thm)],[107]) ).
thf(168,plain,
( ( ( succ @ ( succ @ n0 ) )
= n2 )
= $true ),
inference(copy,[status(thm)],[106]) ).
thf(169,plain,
( ( ( succ @ ( succ @ ( succ @ n0 ) ) )
= n3 )
= $true ),
inference(copy,[status(thm)],[105]) ).
thf(170,plain,
( ( geq @ ( minus @ n999 @ n1 ) @ n0 )
= $true ),
inference(copy,[status(thm)],[140]) ).
thf(171,plain,
( ( geq @ ( minus @ n3 @ n1 ) @ n0 )
= $true ),
inference(copy,[status(thm)],[139]) ).
thf(172,plain,
( ( geq @ ( minus @ n6 @ n1 ) @ n0 )
= $true ),
inference(copy,[status(thm)],[138]) ).
thf(173,plain,
( ( geq @ ( minus @ n6 @ n1 ) @ n0 )
= $true ),
inference(copy,[status(thm)],[137]) ).
thf(174,plain,
( ( geq @ ( minus @ n6 @ n1 ) @ n0 )
= $true ),
inference(copy,[status(thm)],[136]) ).
thf(175,plain,
( ( geq @ ( minus @ n999 @ n1 ) @ n0 )
= $true ),
inference(copy,[status(thm)],[135]) ).
thf(176,plain,
( ( geq @ n2 @ n0 )
= $true ),
inference(copy,[status(thm)],[134]) ).
thf(177,plain,
( ( geq @ ( minus @ n6 @ n1 ) @ n0 )
= $true ),
inference(copy,[status(thm)],[133]) ).
thf(178,plain,
( ( geq @ ( minus @ n3 @ n1 ) @ n0 )
= $true ),
inference(copy,[status(thm)],[132]) ).
thf(179,plain,
( ( ~ true ) = $true ),
inference(copy,[status(thm)],[142]) ).
thf(180,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ( leq @ n0 @ SX0 )
| ~ ( leq @ SX0 @ n1 ) )
| ( SX0 = n0 )
| ( SX0 = n1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[163]) ).
thf(181,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ( leq @ n0 @ SX0 )
| ~ ( leq @ SX0 @ n3 ) )
| ( SX0 = n0 )
| ( SX0 = n1 )
| ( SX0 = n2 )
| ( SX0 = n3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[165]) ).
thf(182,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ( leq @ n0 @ SX0 )
| ~ ( leq @ SX0 @ n2 ) )
| ( SX0 = n0 )
| ( SX0 = n1 )
| ( SX0 = n2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[164]) ).
thf(183,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ( leq @ n0 @ SX0 )
| ~ ( leq @ SX0 @ n0 ) )
| ( SX0 = n0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[162]) ).
thf(184,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( geq @ SX0 @ SX1 )
| ( leq @ SX1 @ SX0 ) )
| ~ ( ~ ( leq @ SX1 @ SX0 )
| ( geq @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[143]) ).
thf(185,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( leq @ ( minus @ SX0 @ SX1 ) @ SX0 )
| ( leq @ n0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[145]) ).
thf(186,plain,
! [SV1: $i] :
( ( ( minus @ SV1 @ n1 )
= ( pred @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[144]) ).
thf(187,plain,
true = $false,
inference(extcnf_not_pos,[status(thm)],[179]) ).
thf(188,plain,
! [SV2: $i] :
( ( ~ ~ ( ~ ( leq @ n0 @ SV2 )
| ~ ( leq @ SV2 @ n1 ) )
| ( SV2 = n0 )
| ( SV2 = n1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[180]) ).
thf(189,plain,
! [SV3: $i] :
( ( ~ ~ ( ~ ( leq @ n0 @ SV3 )
| ~ ( leq @ SV3 @ n3 ) )
| ( SV3 = n0 )
| ( SV3 = n1 )
| ( SV3 = n2 )
| ( SV3 = n3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[181]) ).
thf(190,plain,
! [SV4: $i] :
( ( ~ ~ ( ~ ( leq @ n0 @ SV4 )
| ~ ( leq @ SV4 @ n2 ) )
| ( SV4 = n0 )
| ( SV4 = n1 )
| ( SV4 = n2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[182]) ).
thf(191,plain,
! [SV5: $i] :
( ( ~ ~ ( ~ ( leq @ n0 @ SV5 )
| ~ ( leq @ SV5 @ n0 ) )
| ( SV5 = n0 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[183]) ).
thf(192,plain,
! [SV6: $i] :
( ( ! [SY9: $i] :
~ ( ~ ( ~ ( geq @ SV6 @ SY9 )
| ( leq @ SY9 @ SV6 ) )
| ~ ( ~ ( leq @ SY9 @ SV6 )
| ( geq @ SV6 @ SY9 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[184]) ).
thf(193,plain,
! [SV7: $i] :
( ( ! [SY10: $i] :
( ~ ( leq @ ( minus @ SV7 @ SY10 ) @ SV7 )
| ( leq @ n0 @ SY10 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[185]) ).
thf(194,plain,
! [SV2: $i] :
( ( ( ~ ~ ( ~ ( leq @ n0 @ SV2 )
| ~ ( leq @ SV2 @ n1 ) ) )
= $true )
| ( ( ( SV2 = n0 )
| ( SV2 = n1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[188]) ).
thf(195,plain,
! [SV3: $i] :
( ( ( ~ ~ ( ~ ( leq @ n0 @ SV3 )
| ~ ( leq @ SV3 @ n3 ) ) )
= $true )
| ( ( ( SV3 = n0 )
| ( SV3 = n1 )
| ( SV3 = n2 )
| ( SV3 = n3 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[189]) ).
thf(196,plain,
! [SV4: $i] :
( ( ( ~ ~ ( ~ ( leq @ n0 @ SV4 )
| ~ ( leq @ SV4 @ n2 ) ) )
= $true )
| ( ( ( SV4 = n0 )
| ( SV4 = n1 )
| ( SV4 = n2 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[190]) ).
thf(197,plain,
! [SV5: $i] :
( ( ( ~ ~ ( ~ ( leq @ n0 @ SV5 )
| ~ ( leq @ SV5 @ n0 ) ) )
= $true )
| ( ( SV5 = n0 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[191]) ).
thf(198,plain,
! [SV8: $i,SV6: $i] :
( ( ~ ( ~ ( ~ ( geq @ SV6 @ SV8 )
| ( leq @ SV8 @ SV6 ) )
| ~ ( ~ ( leq @ SV8 @ SV6 )
| ( geq @ SV6 @ SV8 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[192]) ).
thf(199,plain,
! [SV9: $i,SV7: $i] :
( ( ~ ( leq @ ( minus @ SV7 @ SV9 ) @ SV7 )
| ( leq @ n0 @ SV9 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[193]) ).
thf(200,plain,
! [SV2: $i] :
( ( ( ~ ( ~ ( leq @ n0 @ SV2 )
| ~ ( leq @ SV2 @ n1 ) ) )
= $false )
| ( ( ( SV2 = n0 )
| ( SV2 = n1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[194]) ).
thf(201,plain,
! [SV3: $i] :
( ( ( ~ ( ~ ( leq @ n0 @ SV3 )
| ~ ( leq @ SV3 @ n3 ) ) )
= $false )
| ( ( ( SV3 = n0 )
| ( SV3 = n1 )
| ( SV3 = n2 )
| ( SV3 = n3 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[195]) ).
thf(202,plain,
! [SV4: $i] :
( ( ( ~ ( ~ ( leq @ n0 @ SV4 )
| ~ ( leq @ SV4 @ n2 ) ) )
= $false )
| ( ( ( SV4 = n0 )
| ( SV4 = n1 )
| ( SV4 = n2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[196]) ).
thf(203,plain,
! [SV5: $i] :
( ( ( ~ ( ~ ( leq @ n0 @ SV5 )
| ~ ( leq @ SV5 @ n0 ) ) )
= $false )
| ( ( SV5 = n0 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[197]) ).
thf(204,plain,
! [SV8: $i,SV6: $i] :
( ( ~ ( ~ ( geq @ SV6 @ SV8 )
| ( leq @ SV8 @ SV6 ) )
| ~ ( ~ ( leq @ SV8 @ SV6 )
| ( geq @ SV6 @ SV8 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[198]) ).
thf(205,plain,
! [SV9: $i,SV7: $i] :
( ( ( ~ ( leq @ ( minus @ SV7 @ SV9 ) @ SV7 ) )
= $true )
| ( ( leq @ n0 @ SV9 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[199]) ).
thf(206,plain,
! [SV2: $i] :
( ( ( ~ ( leq @ n0 @ SV2 )
| ~ ( leq @ SV2 @ n1 ) )
= $true )
| ( ( ( SV2 = n0 )
| ( SV2 = n1 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[200]) ).
thf(207,plain,
! [SV3: $i] :
( ( ( ~ ( leq @ n0 @ SV3 )
| ~ ( leq @ SV3 @ n3 ) )
= $true )
| ( ( ( SV3 = n0 )
| ( SV3 = n1 )
| ( SV3 = n2 )
| ( SV3 = n3 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[201]) ).
thf(208,plain,
! [SV4: $i] :
( ( ( ~ ( leq @ n0 @ SV4 )
| ~ ( leq @ SV4 @ n2 ) )
= $true )
| ( ( ( SV4 = n0 )
| ( SV4 = n1 )
| ( SV4 = n2 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[202]) ).
thf(209,plain,
! [SV5: $i] :
( ( ( ~ ( leq @ n0 @ SV5 )
| ~ ( leq @ SV5 @ n0 ) )
= $true )
| ( ( SV5 = n0 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[203]) ).
thf(210,plain,
! [SV8: $i,SV6: $i] :
( ( ~ ( ~ ( geq @ SV6 @ SV8 )
| ( leq @ SV8 @ SV6 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[204]) ).
thf(211,plain,
! [SV6: $i,SV8: $i] :
( ( ~ ( ~ ( leq @ SV8 @ SV6 )
| ( geq @ SV6 @ SV8 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[204]) ).
thf(212,plain,
! [SV9: $i,SV7: $i] :
( ( ( leq @ ( minus @ SV7 @ SV9 ) @ SV7 )
= $false )
| ( ( leq @ n0 @ SV9 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[205]) ).
thf(213,plain,
! [SV2: $i] :
( ( ( ~ ( leq @ n0 @ SV2 ) )
= $true )
| ( ( ~ ( leq @ SV2 @ n1 ) )
= $true )
| ( ( ( SV2 = n0 )
| ( SV2 = n1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[206]) ).
thf(214,plain,
! [SV3: $i] :
( ( ( ~ ( leq @ n0 @ SV3 ) )
= $true )
| ( ( ~ ( leq @ SV3 @ n3 ) )
= $true )
| ( ( ( SV3 = n0 )
| ( SV3 = n1 )
| ( SV3 = n2 )
| ( SV3 = n3 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[207]) ).
thf(215,plain,
! [SV4: $i] :
( ( ( ~ ( leq @ n0 @ SV4 ) )
= $true )
| ( ( ~ ( leq @ SV4 @ n2 ) )
= $true )
| ( ( ( SV4 = n0 )
| ( SV4 = n1 )
| ( SV4 = n2 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[208]) ).
thf(216,plain,
! [SV5: $i] :
( ( ( ~ ( leq @ n0 @ SV5 ) )
= $true )
| ( ( ~ ( leq @ SV5 @ n0 ) )
= $true )
| ( ( SV5 = n0 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[209]) ).
thf(217,plain,
! [SV8: $i,SV6: $i] :
( ( ~ ( geq @ SV6 @ SV8 )
| ( leq @ SV8 @ SV6 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[210]) ).
thf(218,plain,
! [SV6: $i,SV8: $i] :
( ( ~ ( leq @ SV8 @ SV6 )
| ( geq @ SV6 @ SV8 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[211]) ).
thf(219,plain,
! [SV2: $i] :
( ( ( leq @ n0 @ SV2 )
= $false )
| ( ( ~ ( leq @ SV2 @ n1 ) )
= $true )
| ( ( ( SV2 = n0 )
| ( SV2 = n1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[213]) ).
thf(220,plain,
! [SV3: $i] :
( ( ( leq @ n0 @ SV3 )
= $false )
| ( ( ~ ( leq @ SV3 @ n3 ) )
= $true )
| ( ( ( SV3 = n0 )
| ( SV3 = n1 )
| ( SV3 = n2 )
| ( SV3 = n3 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[214]) ).
thf(221,plain,
! [SV4: $i] :
( ( ( leq @ n0 @ SV4 )
= $false )
| ( ( ~ ( leq @ SV4 @ n2 ) )
= $true )
| ( ( ( SV4 = n0 )
| ( SV4 = n1 )
| ( SV4 = n2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[215]) ).
thf(222,plain,
! [SV5: $i] :
( ( ( leq @ n0 @ SV5 )
= $false )
| ( ( ~ ( leq @ SV5 @ n0 ) )
= $true )
| ( ( SV5 = n0 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[216]) ).
thf(223,plain,
! [SV8: $i,SV6: $i] :
( ( ( ~ ( geq @ SV6 @ SV8 ) )
= $true )
| ( ( leq @ SV8 @ SV6 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[217]) ).
thf(224,plain,
! [SV6: $i,SV8: $i] :
( ( ( ~ ( leq @ SV8 @ SV6 ) )
= $true )
| ( ( geq @ SV6 @ SV8 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[218]) ).
thf(225,plain,
! [SV2: $i] :
( ( ( leq @ SV2 @ n1 )
= $false )
| ( ( leq @ n0 @ SV2 )
= $false )
| ( ( ( SV2 = n0 )
| ( SV2 = n1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[219]) ).
thf(226,plain,
! [SV3: $i] :
( ( ( leq @ SV3 @ n3 )
= $false )
| ( ( leq @ n0 @ SV3 )
= $false )
| ( ( ( SV3 = n0 )
| ( SV3 = n1 )
| ( SV3 = n2 )
| ( SV3 = n3 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[220]) ).
thf(227,plain,
! [SV4: $i] :
( ( ( leq @ SV4 @ n2 )
= $false )
| ( ( leq @ n0 @ SV4 )
= $false )
| ( ( ( SV4 = n0 )
| ( SV4 = n1 )
| ( SV4 = n2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[221]) ).
thf(228,plain,
! [SV5: $i] :
( ( ( leq @ SV5 @ n0 )
= $false )
| ( ( leq @ n0 @ SV5 )
= $false )
| ( ( SV5 = n0 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[222]) ).
thf(229,plain,
! [SV8: $i,SV6: $i] :
( ( ( geq @ SV6 @ SV8 )
= $false )
| ( ( leq @ SV8 @ SV6 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[223]) ).
thf(230,plain,
! [SV6: $i,SV8: $i] :
( ( ( leq @ SV8 @ SV6 )
= $false )
| ( ( geq @ SV6 @ SV8 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[224]) ).
thf(231,plain,
! [SV2: $i] :
( ( ( SV2 = n0 )
= $true )
| ( ( SV2 = n1 )
= $true )
| ( ( leq @ n0 @ SV2 )
= $false )
| ( ( leq @ SV2 @ n1 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[225]) ).
thf(232,plain,
! [SV3: $i] :
( ( ( ( SV3 = n0 )
| ( SV3 = n1 )
| ( SV3 = n2 ) )
= $true )
| ( ( SV3 = n3 )
= $true )
| ( ( leq @ n0 @ SV3 )
= $false )
| ( ( leq @ SV3 @ n3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[226]) ).
thf(233,plain,
! [SV4: $i] :
( ( ( ( SV4 = n0 )
| ( SV4 = n1 ) )
= $true )
| ( ( SV4 = n2 )
= $true )
| ( ( leq @ n0 @ SV4 )
= $false )
| ( ( leq @ SV4 @ n2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[227]) ).
thf(234,plain,
! [SV3: $i] :
( ( ( ( SV3 = n0 )
| ( SV3 = n1 ) )
= $true )
| ( ( SV3 = n2 )
= $true )
| ( ( SV3 = n3 )
= $true )
| ( ( leq @ n0 @ SV3 )
= $false )
| ( ( leq @ SV3 @ n3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[232]) ).
thf(235,plain,
! [SV4: $i] :
( ( ( SV4 = n0 )
= $true )
| ( ( SV4 = n1 )
= $true )
| ( ( SV4 = n2 )
= $true )
| ( ( leq @ n0 @ SV4 )
= $false )
| ( ( leq @ SV4 @ n2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[233]) ).
thf(236,plain,
! [SV3: $i] :
( ( ( SV3 = n0 )
= $true )
| ( ( SV3 = n1 )
= $true )
| ( ( SV3 = n2 )
= $true )
| ( ( SV3 = n3 )
= $true )
| ( ( leq @ n0 @ SV3 )
= $false )
| ( ( leq @ SV3 @ n3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[234]) ).
thf(237,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[146,236,235,231,230,229,228,212,187,186,178,177,176,175,174,173,172,171,170,169,168,167,166,161,160,159,158,157,156,155,154,153,152,151,150,149,148,147]) ).
thf(238,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[237]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV107+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
% 0.07/0.17 % Computer : n001.cluster.edu
% 0.07/0.17 % Model : x86_64 x86_64
% 0.07/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.17 % Memory : 8046.5625MB
% 0.07/0.17 % OS : Linux 6.8.0-71-generic
% 0.07/0.17 % CPULimit : 300
% 0.07/0.17 % WCLimit : 300
% 0.07/0.17 % DateTime : Tue Oct 6 16:25:32 UTC 2026
% 0.07/0.17 % CPUTime :
% 0.07/0.17 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.56/0.31
% 0.56/0.31 No.of.Axioms: 27
% 0.56/0.31
% 0.56/0.31 Length.of.Defs: 0
% 0.56/0.31
% 0.56/0.31 Contains.Choice.Funs: false
% 0.56/0.31 ....
% 0.56/0.31
% 0.56/0.31 ********************************
% 0.56/0.31 * All subproblems solved! *
% 0.56/0.31 ********************************
% 0.56/0.31 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:36,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:237,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.56/0.31
% 0.56/0.31 %**** Beginning of derivation protocol ****
% 0.56/0.31 % SZS output start CNFRefutation
% See solution above
% 0.56/0.31
% 0.56/0.31 %**** End of derivation protocol ****
% 0.56/0.31 %**** no. of clauses in derivation: 164 ****
% 0.56/0.31 %**** clause counter: 237 ****
% 0.56/0.31
% 0.56/0.31 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:36,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:237,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------