%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : DAT284^1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 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 Sep 30 07:48:12 AM UTC 2026
% Result : Theorem 30.79s 8.73s
% Output : Refutation 25.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 11
% Syntax : Number of formulae : 67 ( 50 unt; 0 typ; 3 def)
% Number of atoms : 126 ( 84 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 479 ( 38 ~; 15 |; 11 &; 415 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 33 ( 33 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 11 usr; 6 con; 0-5 aty)
% Number of variables : 181 ( 19 ^; 151 !; 8 ?; 181 :)
% ( 0 !>; 0 ?*; 0 @-; 3 @+)
% Comments :
%------------------------------------------------------------------------------
thf('type/nums/num_type',type,
'type/nums/num': $tType ).
thf(skt1_type,type,
skt1: $tType ).
thf('const/nums/SUC_decl',type,
'const/nums/SUC': 'type/nums/num' > 'type/nums/num' ).
thf('const/nums/_0_decl',type,
'const/nums/_0': 'type/nums/num' ).
thf('const/ind_types/NIL_decl',type,
'const/ind_types/NIL':
!>[TA: $tType] : ( 'type/ind_types/list' @ TA ) ).
thf('const/ind_types/CONS_decl',type,
'const/ind_types/CONS':
!>[TA: $tType] : ( TA > ( 'type/ind_types/list' @ TA ) > ( 'type/ind_types/list' @ TA ) ) ).
thf('const/arith/+_decl',type,
'const/arith/+': 'type/nums/num' > 'type/nums/num' > 'type/nums/num' ).
thf('const/arith/<=_decl',type,
'const/arith/<=': 'type/nums/num' > 'type/nums/num' > $o ).
thf('const/arith/<_decl',type,
'const/arith/<': 'type/nums/num' > 'type/nums/num' > $o ).
thf(sk1_decl,type,
sk1: skt1 ).
thf(sk2_decl,type,
sk2: 'type/ind_types/list' @ skt1 ).
thf(sk3_decl,type,
sk3:
!>[TA: $tType,TB: $tType] : ( ( TB > ( 'type/ind_types/list' @ TB ) > TA > TA ) > TA > ( 'type/ind_types/list' @ TB ) > TA ) ).
thf(sk1_def,definition,
( sk1
= ( @+[A: skt1] :
~ ! [B: 'type/ind_types/list' @ skt1] :
( ( 'const/ind_types/CONS' @ skt1 @ A @ B )
!= ( 'const/ind_types/NIL' @ skt1 ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: 'type/ind_types/list' @ skt1] :
~ ( ( ( 'const/ind_types/CONS' @ skt1 @ sk1 @ A )
!= ( 'const/ind_types/NIL' @ skt1 ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( ^ [TA: $tType,TB: $tType,A: TB > ( 'type/ind_types/list' @ TB ) > TA > TA,B: TA] :
@+[C: ( 'type/ind_types/list' @ TB ) > TA] :
( ( ( C @ ( 'const/ind_types/NIL' @ TB ) )
= B )
& ! [D: TB,E: 'type/ind_types/list' @ TB] :
( ( C @ ( 'const/ind_types/CONS' @ TB @ D @ E ) )
= ( A @ D @ E @ ( C @ E ) ) ) ) ) ) ).
thf(12,axiom,
! [A: 'type/nums/num',B: 'type/nums/num'] :
( ( ( 'const/arith/<=' @ A @ B )
& ( 'const/arith/<=' @ B @ A ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/arith/LE_ANTISYM_') ).
thf(44,plain,
! [A: 'type/nums/num',B: 'type/nums/num'] :
( ( ( 'const/arith/<=' @ A @ B )
& ( 'const/arith/<=' @ B @ A ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(45,plain,
! [B: 'type/nums/num',A: 'type/nums/num'] :
( ( ( 'const/arith/<=' @ A @ B )
& ( 'const/arith/<=' @ B @ A ) )
= ( A = B ) ),
inference(cnf,[status(esa)],[44]) ).
thf(46,plain,
! [B: 'type/nums/num',A: 'type/nums/num'] :
( ( ( 'const/arith/<=' @ A @ B )
& ( 'const/arith/<=' @ B @ A ) )
= ( A = B ) ),
inference(lifteq,[status(thm)],[45]) ).
thf(850,plain,
! [B: 'type/nums/num',A: 'type/nums/num'] :
( ( ( 'const/arith/<=' @ A @ B )
& ( 'const/arith/<=' @ B @ A ) )
| ( A != B ) ),
inference(bool_ext,[status(thm)],[46]) ).
thf(856,plain,
! [B: 'type/nums/num',A: 'type/nums/num'] :
( ( A != B )
| ( ( 'const/arith/<=' @ A @ B )
& ( 'const/arith/<=' @ B @ A ) ) ),
inference(lifteq,[status(thm)],[850]) ).
thf(864,plain,
! [B: 'type/nums/num',A: 'type/nums/num'] :
( ( ( A != B )
| ( 'const/arith/<=' @ A @ B ) )
& ( ( A != B )
| ( 'const/arith/<=' @ B @ A ) ) ),
inference(cnf,[status(esa)],[856]) ).
thf(865,plain,
! [B: 'type/nums/num',A: 'type/nums/num'] :
( ( A != B )
| ( 'const/arith/<=' @ A @ B ) ),
inference(cnfConj,[status(thm)],[864]) ).
thf(867,plain,
! [A: 'type/nums/num'] : ( 'const/arith/<=' @ A @ A ),
inference(simp,[status(thm)],[865]) ).
thf(3,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA > ( 'type/ind_types/list' @ TA ) > TB > TB] :
? [C: ( 'type/ind_types/list' @ TA ) > TB] :
( ( ( C @ ( 'const/ind_types/NIL' @ TA ) )
= A )
& ! [D: TA,E: 'type/ind_types/list' @ TA] :
( ( C @ ( 'const/ind_types/CONS' @ TA @ D @ E ) )
= ( B @ D @ E @ ( C @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/ind_types/list_RECURSION_') ).
thf(16,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA > ( 'type/ind_types/list' @ TA ) > TB > TB] :
? [C: ( 'type/ind_types/list' @ TA ) > TB] :
( ( ( C @ ( 'const/ind_types/NIL' @ TA ) )
= A )
& ! [D: TA,E: 'type/ind_types/list' @ TA] :
( ( C @ ( 'const/ind_types/CONS' @ TA @ D @ E ) )
= ( B @ D @ E @ ( C @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(17,plain,
! [TA: $tType,TB: $tType,D: 'type/ind_types/list' @ TB,C: TB,B: TB > ( 'type/ind_types/list' @ TB ) > TA > TA,A: TA] :
( ( ( sk3 @ TB @ TA @ B @ A @ ( 'const/ind_types/NIL' @ TB ) )
= A )
& ( ( sk3 @ TB @ TA @ B @ A @ ( 'const/ind_types/CONS' @ TB @ C @ D ) )
= ( B @ C @ D @ ( sk3 @ TB @ TA @ B @ A @ D ) ) ) ),
inference(cnf,[status(esa)],[16]) ).
thf(18,plain,
! [TA: $tType,TB: $tType,B: TB > ( 'type/ind_types/list' @ TB ) > TA > TA,A: TA] :
( ( sk3 @ TB @ TA @ B @ A @ ( 'const/ind_types/NIL' @ TB ) )
= A ),
inference(cnfConj,[status(thm)],[17]) ).
thf(20,plain,
! [TA: $tType,TB: $tType,B: TB > ( 'type/ind_types/list' @ TB ) > TA > TA,A: TA] :
( ( sk3 @ TB @ TA @ B @ A @ ( 'const/ind_types/NIL' @ TB ) )
= A ),
inference(lifteq,[status(thm)],[18]) ).
thf(1,conjecture,
! [TA: $tType,A: TA,B: 'type/ind_types/list' @ TA] :
( ( 'const/ind_types/CONS' @ TA @ A @ B )
!= ( 'const/ind_types/NIL' @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/lists/NOT_CONS_NIL_') ).
thf(2,negated_conjecture,
~ ! [TA: $tType,A: TA,B: 'type/ind_types/list' @ TA] :
( ( 'const/ind_types/CONS' @ TA @ A @ B )
!= ( 'const/ind_types/NIL' @ TA ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(13,plain,
~ ! [TA: $tType,A: TA,B: 'type/ind_types/list' @ TA] :
( ( 'const/ind_types/CONS' @ TA @ A @ B )
!= ( 'const/ind_types/NIL' @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(14,plain,
( ( 'const/ind_types/CONS' @ skt1 @ sk1 @ sk2 )
= ( 'const/ind_types/NIL' @ skt1 ) ),
inference(cnf,[status(esa)],[13]) ).
thf(15,plain,
( ( 'const/ind_types/CONS' @ skt1 @ sk1 @ sk2 )
= ( 'const/ind_types/NIL' @ skt1 ) ),
inference(lifteq,[status(thm)],[14]) ).
thf(19,plain,
! [TA: $tType,TB: $tType,D: 'type/ind_types/list' @ TB,C: TB,B: TB > ( 'type/ind_types/list' @ TB ) > TA > TA,A: TA] :
( ( sk3 @ TB @ TA @ B @ A @ ( 'const/ind_types/CONS' @ TB @ C @ D ) )
= ( B @ C @ D @ ( sk3 @ TB @ TA @ B @ A @ D ) ) ),
inference(cnfConj,[status(thm)],[17]) ).
thf(21,plain,
! [TA: $tType,TB: $tType,D: 'type/ind_types/list' @ TB,C: TB,B: TB > ( 'type/ind_types/list' @ TB ) > TA > TA,A: TA] :
( ( sk3 @ TB @ TA @ B @ A @ ( 'const/ind_types/CONS' @ TB @ C @ D ) )
= ( B @ C @ D @ ( sk3 @ TB @ TA @ B @ A @ D ) ) ),
inference(lifteq,[status(thm)],[19]) ).
thf(5,axiom,
( ( 'const/arith/+' @ 'const/nums/_0' @ 'const/nums/_0' )
= 'const/nums/_0' ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/calc_num/ARITH_11') ).
thf(24,plain,
( ( 'const/arith/+' @ 'const/nums/_0' @ 'const/nums/_0' )
= 'const/nums/_0' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(25,plain,
( ( 'const/arith/+' @ 'const/nums/_0' @ 'const/nums/_0' )
= 'const/nums/_0' ),
inference(lifteq,[status(thm)],[24]) ).
thf(84,plain,
! [TB: $tType,D: 'type/ind_types/list' @ TB,C: TB,B: TB > ( 'type/ind_types/list' @ TB ) > 'type/nums/num' > 'type/nums/num',A: 'type/nums/num'] :
( ( ( 'const/arith/+' @ ( sk3 @ TB @ 'type/nums/num' @ B @ A @ ( 'const/ind_types/CONS' @ TB @ C @ D ) ) @ 'const/nums/_0' )
= 'const/nums/_0' )
| ( ( B @ C @ D @ ( sk3 @ TB @ 'type/nums/num' @ B @ A @ D ) )
!= 'const/nums/_0' ) ),
inference(paramod_ordered,[status(thm)],[21,25]) ).
thf(96,plain,
! [TB: $tType,C: 'type/ind_types/list' @ TB,B: TB,A: 'type/nums/num'] :
( ( 'const/arith/+'
@ ( sk3 @ TB @ 'type/nums/num'
@ ^ [D: TB,E: 'type/ind_types/list' @ TB,F: 'type/nums/num'] : 'const/nums/_0'
@ A
@ ( 'const/ind_types/CONS' @ TB @ B @ C ) )
@ 'const/nums/_0' )
= 'const/nums/_0' ),
inference(pre_uni,[status(thm)],[84:[bind(A,$thf( A )),bind(B,$thf( ^ [E: TB] : ^ [F: 'type/ind_types/list' @ TB] : ^ [G: 'type/nums/num'] : 'const/nums/_0' ))]]) ).
thf(125,plain,
! [TA: $tType,C: 'type/ind_types/list' @ TA,B: TA,A: 'type/nums/num'] :
( ( 'const/arith/+'
@ ( sk3 @ TA @ 'type/nums/num'
@ ^ [D: TA,E: 'type/ind_types/list' @ TA,F: 'type/nums/num'] : 'const/nums/_0'
@ A
@ ( 'const/ind_types/CONS' @ TA @ B @ C ) )
@ 'const/nums/_0' )
= 'const/nums/_0' ),
inference(simp,[status(thm)],[96]) ).
thf(494,plain,
! [C: 'type/ind_types/list' @ skt1,B: skt1,A: 'type/nums/num'] :
( ( ( 'const/arith/+'
@ ( sk3 @ skt1 @ 'type/nums/num'
@ ^ [D: skt1,E: 'type/ind_types/list' @ skt1,F: 'type/nums/num'] : 'const/nums/_0'
@ A
@ ( 'const/ind_types/NIL' @ skt1 ) )
@ 'const/nums/_0' )
= 'const/nums/_0' )
| ( ( 'const/ind_types/CONS' @ skt1 @ sk1 @ sk2 )
!= ( 'const/ind_types/CONS' @ skt1 @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[15,125]) ).
thf(495,plain,
! [A: 'type/nums/num'] :
( ( 'const/arith/+'
@ ( sk3 @ skt1 @ 'type/nums/num'
@ ^ [B: skt1,C: 'type/ind_types/list' @ skt1,D: 'type/nums/num'] : 'const/nums/_0'
@ A
@ ( 'const/ind_types/NIL' @ skt1 ) )
@ 'const/nums/_0' )
= 'const/nums/_0' ),
inference(pattern_uni,[status(thm)],[494:[bind(A,$thf( A )),bind(B,$thf( sk1 )),bind(C,$thf( sk2 ))]]) ).
thf(527,plain,
! [TB: $tType,C: 'type/nums/num',B: TB > ( 'type/ind_types/list' @ TB ) > 'type/nums/num' > 'type/nums/num',A: 'type/nums/num'] :
( ( ( 'const/arith/+' @ A @ 'const/nums/_0' )
= 'const/nums/_0' )
| ( ( sk3 @ TB @ 'type/nums/num' @ B @ A @ ( 'const/ind_types/NIL' @ TB ) )
!= ( sk3 @ skt1 @ 'type/nums/num'
@ ^ [D: skt1,E: 'type/ind_types/list' @ skt1,F: 'type/nums/num'] : 'const/nums/_0'
@ C
@ ( 'const/ind_types/NIL' @ skt1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[20,495]) ).
thf(528,plain,
! [A: 'type/nums/num'] :
( ( 'const/arith/+' @ A @ 'const/nums/_0' )
= 'const/nums/_0' ),
inference(pattern_uni,[status(thm)],[527:[bind(A,$thf( A )),bind(B,$thf( ^ [D: skt1] : ^ [E: 'type/ind_types/list' @ skt1] : ^ [F: 'type/nums/num'] : 'const/nums/_0' )),bind(C,$thf( A )),bind_type(TA,$thf( TA )),bind_type(TB,$thf( skt1 ))]]) ).
thf(8,axiom,
! [A: 'type/nums/num',B: 'type/nums/num'] :
( ( 'const/arith/<' @ A @ B )
= ( ? [C: 'type/nums/num'] :
( B
= ( 'const/arith/+' @ A @ ( 'const/nums/SUC' @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/arith/LT_EXISTS_') ).
thf(32,plain,
! [A: 'type/nums/num',B: 'type/nums/num'] :
( ( 'const/arith/<' @ A @ B )
= ( ? [C: 'type/nums/num'] :
( B
= ( 'const/arith/+' @ A @ ( 'const/nums/SUC' @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(33,plain,
! [B: 'type/nums/num',A: 'type/nums/num'] :
( ( 'const/arith/<' @ A @ B )
= ( ? [C: 'type/nums/num'] :
( B
= ( 'const/arith/+' @ A @ ( 'const/nums/SUC' @ C ) ) ) ) ),
inference(cnf,[status(esa)],[32]) ).
thf(34,plain,
! [B: 'type/nums/num',A: 'type/nums/num'] :
( ( 'const/arith/<' @ A @ B )
= ( ? [C: 'type/nums/num'] :
( B
= ( 'const/arith/+' @ A @ ( 'const/nums/SUC' @ C ) ) ) ) ),
inference(lifteq,[status(thm)],[33]) ).
thf(9,axiom,
! [A: 'type/nums/num',B: 'type/nums/num'] :
( ( ~ ( 'const/arith/<=' @ A @ B ) )
= ( 'const/arith/<' @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/arith/NOT_LE_') ).
thf(35,plain,
! [A: 'type/nums/num',B: 'type/nums/num'] :
( ( ~ ( 'const/arith/<=' @ A @ B ) )
= ( 'const/arith/<' @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(36,plain,
! [B: 'type/nums/num',A: 'type/nums/num'] :
( ( ~ ( 'const/arith/<=' @ A @ B ) )
= ( 'const/arith/<' @ B @ A ) ),
inference(cnf,[status(esa)],[35]) ).
thf(37,plain,
! [B: 'type/nums/num',A: 'type/nums/num'] :
( ( 'const/arith/<' @ B @ A )
= ( ~ ( 'const/arith/<=' @ A @ B ) ) ),
inference(lifteq,[status(thm)],[36]) ).
thf(7,axiom,
! [A: 'type/nums/num',B: 'type/nums/num'] :
( ( 'const/arith/+' @ A @ ( 'const/nums/SUC' @ B ) )
= ( 'const/nums/SUC' @ ( 'const/arith/+' @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/arith/ADD_SUC_') ).
thf(29,plain,
! [A: 'type/nums/num',B: 'type/nums/num'] :
( ( 'const/arith/+' @ A @ ( 'const/nums/SUC' @ B ) )
= ( 'const/nums/SUC' @ ( 'const/arith/+' @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(30,plain,
! [B: 'type/nums/num',A: 'type/nums/num'] :
( ( 'const/arith/+' @ A @ ( 'const/nums/SUC' @ B ) )
= ( 'const/nums/SUC' @ ( 'const/arith/+' @ A @ B ) ) ),
inference(cnf,[status(esa)],[29]) ).
thf(31,plain,
! [B: 'type/nums/num',A: 'type/nums/num'] :
( ( 'const/arith/+' @ A @ ( 'const/nums/SUC' @ B ) )
= ( 'const/nums/SUC' @ ( 'const/arith/+' @ A @ B ) ) ),
inference(lifteq,[status(thm)],[30]) ).
thf(659,plain,
! [B: 'type/nums/num',A: 'type/nums/num'] :
( ( ~ ( 'const/arith/<=' @ B @ A ) )
= ( ? [C: 'type/nums/num'] :
( B
= ( 'const/nums/SUC' @ ( 'const/arith/+' @ A @ C ) ) ) ) ),
inference(rewrite,[status(thm)],[34,37,31]) ).
thf(661,plain,
! [B: 'type/nums/num',A: 'type/nums/num'] :
( ~ ( 'const/arith/<=' @ B @ A )
| ~ ? [C: 'type/nums/num'] :
( B
= ( 'const/nums/SUC' @ ( 'const/arith/+' @ A @ C ) ) ) ),
inference(bool_ext,[status(thm)],[659]) ).
thf(682,plain,
! [C: 'type/nums/num',B: 'type/nums/num',A: 'type/nums/num'] :
( ~ ( 'const/arith/<=' @ B @ A )
| ( B
!= ( 'const/nums/SUC' @ ( 'const/arith/+' @ A @ C ) ) ) ),
inference(cnf,[status(esa)],[661]) ).
thf(683,plain,
! [C: 'type/nums/num',B: 'type/nums/num',A: 'type/nums/num'] :
( ( B
!= ( 'const/nums/SUC' @ ( 'const/arith/+' @ A @ C ) ) )
| ~ ( 'const/arith/<=' @ B @ A ) ),
inference(lifteq,[status(thm)],[682]) ).
thf(684,plain,
! [B: 'type/nums/num',A: 'type/nums/num'] :
~ ( 'const/arith/<=' @ ( 'const/nums/SUC' @ ( 'const/arith/+' @ A @ B ) ) @ A ),
inference(simp,[status(thm)],[683]) ).
thf(725,plain,
! [C: 'type/nums/num',B: 'type/nums/num',A: 'type/nums/num'] :
( ~ ( 'const/arith/<=' @ ( 'const/nums/SUC' @ 'const/nums/_0' ) @ B )
| ( ( 'const/arith/+' @ A @ 'const/nums/_0' )
!= ( 'const/arith/+' @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[528,684]) ).
thf(726,plain,
! [A: 'type/nums/num'] :
~ ( 'const/arith/<=' @ ( 'const/nums/SUC' @ 'const/nums/_0' ) @ A ),
inference(pattern_uni,[status(thm)],[725:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( 'const/nums/_0' ))]]) ).
thf(6,axiom,
! [A: 'type/nums/num',B: 'type/nums/num'] :
( ( 'const/arith/+' @ A @ B )
= ( 'const/arith/+' @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/arith/ADD_SYM_') ).
thf(26,plain,
! [A: 'type/nums/num',B: 'type/nums/num'] :
( ( 'const/arith/+' @ A @ B )
= ( 'const/arith/+' @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(27,plain,
! [B: 'type/nums/num',A: 'type/nums/num'] :
( ( 'const/arith/+' @ A @ B )
= ( 'const/arith/+' @ B @ A ) ),
inference(cnf,[status(esa)],[26]) ).
thf(28,plain,
! [B: 'type/nums/num',A: 'type/nums/num'] :
( ( 'const/arith/+' @ A @ B )
= ( 'const/arith/+' @ B @ A ) ),
inference(lifteq,[status(thm)],[27]) ).
thf(597,plain,
! [C: 'type/nums/num',B: 'type/nums/num',A: 'type/nums/num'] :
( ( ( 'const/arith/+' @ C @ B )
= 'const/nums/_0' )
| ( ( 'const/arith/+' @ A @ 'const/nums/_0' )
!= ( 'const/arith/+' @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[528,28]) ).
thf(598,plain,
! [A: 'type/nums/num'] :
( ( 'const/arith/+' @ 'const/nums/_0' @ A )
= 'const/nums/_0' ),
inference(pattern_uni,[status(thm)],[597:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( 'const/nums/_0' ))]]) ).
thf(636,plain,
! [C: 'type/nums/num',B: 'type/nums/num',A: 'type/nums/num'] :
( ( ( 'const/nums/SUC' @ ( 'const/arith/+' @ B @ C ) )
= 'const/nums/_0' )
| ( ( 'const/arith/+' @ 'const/nums/_0' @ A )
!= ( 'const/arith/+' @ B @ ( 'const/nums/SUC' @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[598,31]) ).
thf(637,plain,
! [A: 'type/nums/num'] :
( ( 'const/nums/SUC' @ ( 'const/arith/+' @ 'const/nums/_0' @ A ) )
= 'const/nums/_0' ),
inference(pattern_uni,[status(thm)],[636:[bind(A,$thf( 'const/nums/SUC' @ D )),bind(B,$thf( 'const/nums/_0' )),bind(C,$thf( D ))]]) ).
thf(653,plain,
! [A: 'type/nums/num'] :
( ( 'const/nums/SUC' @ ( 'const/arith/+' @ 'const/nums/_0' @ A ) )
= 'const/nums/_0' ),
inference(simp,[status(thm)],[637]) ).
thf(690,plain,
( ( 'const/nums/SUC' @ 'const/nums/_0' )
= 'const/nums/_0' ),
inference(rewrite,[status(thm)],[653,598]) ).
thf(748,plain,
! [A: 'type/nums/num'] :
~ ( 'const/arith/<=' @ 'const/nums/_0' @ A ),
inference(rewrite,[status(thm)],[726,690]) ).
thf(890,plain,
! [B: 'type/nums/num',A: 'type/nums/num'] :
( ~ $true
| ( ( 'const/arith/<=' @ A @ A )
!= ( 'const/arith/<=' @ 'const/nums/_0' @ B ) ) ),
inference(paramod_ordered,[status(thm)],[867,748]) ).
thf(891,plain,
! [B: 'type/nums/num',A: 'type/nums/num'] :
( ( 'const/arith/<=' @ A @ A )
!= ( 'const/arith/<=' @ 'const/nums/_0' @ B ) ),
inference(simp,[status(thm)],[890]) ).
thf(892,plain,
$false,
inference(pattern_uni,[status(thm)],[891:[bind(A,$thf( 'const/nums/_0' )),bind(B,$thf( 'const/nums/_0' ))]]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : DAT284^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.11 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.24/0.28 % Computer : n001.cluster.edu
% 0.24/0.28 % Model : x86_64 x86_64
% 0.24/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.24/0.28 % Memory : 8046.5625MB
% 0.24/0.28 % OS : Linux 6.8.0-71-generic
% 0.24/0.28 % CPULimit : 300
% 0.24/0.28 % WCLimit : 300
% 0.24/0.28 % DateTime : Tue Sep 29 18:25:36 UTC 2026
% 0.24/0.29 % CPUTime :
% 0.24/0.29 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 1.34/1.10 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.79/1.39 % [INFO] Parsing done (282ms).
% 2.07/1.41 % [INFO] Running in sequential loop mode.
% 2.97/1.92 % [INFO] eprover registered as external prover.
% 2.97/1.93 % [INFO] Scanning for conjecture ...
% 3.24/2.06 % [INFO] Found a conjecture (or negated_conjecture) and 10 axioms. Running axiom selection ...
% 3.24/2.12 % [INFO] Axiom selection finished. Selected 10 axioms (removed 0 axioms).
% 3.45/2.16 % [INFO] Problem is higher-order (TPTP THF).
% 3.45/2.16 % [INFO] Type checking passed.
% 3.45/2.17 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 30.79/8.72 % [INFO] Killing All external provers ...
% 30.79/8.72 % Time passed: 8226ms (effective reasoning time: 7299ms)
% 30.79/8.72 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 30.79/8.73 % Axioms used in derivation (7): thm/calc_num/ARITH_11, thm/arith/LT_EXISTS_, thm/arith/ADD_SUC_, thm/arith/LE_ANTISYM_, thm/arith/NOT_LE_, thm/arith/ADD_SYM_, thm/ind_types/list_RECURSION_
% 30.79/8.73 % No. of inferences in proof: 64
% 30.79/8.73 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 8226 ms resp. 7299 ms w/o parsing
% 25.51/8.83 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 25.51/8.83 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------