%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUN025^3 : TPTP v9.3.1. Released v6.4.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:19:49 AM UTC 2026
% Result : Theorem 6.90s 3.19s
% Output : Refutation 7.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 1
% Syntax : Number of formulae : 65 ( 18 unt; 0 typ; 0 def)
% Number of atoms : 345 ( 306 equ; 0 cnn)
% Maximal formula atoms : 10 ( 5 avg)
% Number of connectives : 1043 ( 129 ~; 69 |; 98 &; 718 @)
% ( 0 <=>; 29 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 24 ( 24 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 4 usr; 3 con; 0-3 aty)
% Number of variables : 203 ( 0 ^; 180 !; 23 ?; 203 :)
% Comments :
%------------------------------------------------------------------------------
thf(zero_decl,type,
zero: $i ).
thf(s_decl,type,
s: $i > $i ).
thf(ite_decl,type,
ite: $o > $i > $i > $i ).
thf(h_decl,type,
h: $i > $i ).
thf(1,conjecture,
( ( ! [A: $o,B: $i,C: $i] :
( A
=> ( ( ite @ A @ B @ C )
= B ) )
& ! [A: $o,B: $i,C: $i] :
( ~ A
=> ( ( ite @ A @ B @ C )
= C ) )
& ! [A: $i] :
( ( s @ A )
!= zero )
& ! [A: $i] :
( ( s @ A )
!= A )
& ! [A: $i] :
( ( h @ A )
= ( ite @ ( A = zero ) @ ( s @ zero )
@ ( ite
@ ( A
= ( s @ zero ) )
@ zero
@ ( s @ zero ) ) ) ) )
=> ? [A: $i > $i] :
( ( ( A @ zero )
= ( s @ zero ) )
& ( ( A @ ( s @ zero ) )
= zero )
& ( ( A @ ( s @ ( s @ zero ) ) )
= ( s @ zero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',n10) ).
thf(2,negated_conjecture,
~ ( ( ! [A: $o,B: $i,C: $i] :
( A
=> ( ( ite @ A @ B @ C )
= B ) )
& ! [A: $o,B: $i,C: $i] :
( ~ A
=> ( ( ite @ A @ B @ C )
= C ) )
& ! [A: $i] :
( ( s @ A )
!= zero )
& ! [A: $i] :
( ( s @ A )
!= A )
& ! [A: $i] :
( ( h @ A )
= ( ite @ ( A = zero ) @ ( s @ zero )
@ ( ite
@ ( A
= ( s @ zero ) )
@ zero
@ ( s @ zero ) ) ) ) )
=> ? [A: $i > $i] :
( ( ( A @ zero )
= ( s @ zero ) )
& ( ( A @ ( s @ zero ) )
= zero )
& ( ( A @ ( s @ ( s @ zero ) ) )
= ( s @ zero ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ( ! [A: $o,B: $i,C: $i] :
( A
=> ( ( ite @ A @ B @ C )
= B ) )
& ! [A: $o,B: $i,C: $i] :
( ~ A
=> ( ( ite @ A @ B @ C )
= C ) )
& ! [A: $i] :
( ( s @ A )
!= zero )
& ! [A: $i] :
( ( s @ A )
!= A )
& ! [A: $i] :
( ( h @ A )
= ( ite @ ( A = zero ) @ ( s @ zero )
@ ( ite
@ ( A
= ( s @ zero ) )
@ zero
@ ( s @ zero ) ) ) ) )
=> ? [A: $i > $i] :
( ( ( A @ zero )
= ( s @ zero ) )
& ( ( A @ ( s @ zero ) )
= zero )
& ( ( A @ ( s @ ( s @ zero ) ) )
= ( s @ zero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(6,plain,
~ ( ( ! [A: $i,B: $i] :
( $true
=> ( ( ite @ $true @ A @ B )
= A ) )
& ! [A: $i,B: $i] :
( ~ $false
=> ( ( ite @ $false @ A @ B )
= B ) )
& ! [A: $i] :
( ( s @ A )
!= zero )
& ! [A: $i] :
( ( s @ A )
!= A )
& ! [A: $i] :
( ( h @ A )
= ( ite @ ( A = zero ) @ ( s @ zero )
@ ( ite
@ ( A
= ( s @ zero ) )
@ zero
@ ( s @ zero ) ) ) ) )
=> ? [A: $i > $i] :
( ( ( A @ zero )
= ( s @ zero ) )
& ( ( A @ ( s @ zero ) )
= zero )
& ( ( A @ ( s @ ( s @ zero ) ) )
= ( s @ zero ) ) ) ),
inference(instance,[status(thm)],[3]) ).
thf(7,plain,
~ ( ( ! [A: $i,B: $i] :
( ( ite @ $true @ A @ B )
= A )
& ! [A: $i,B: $i] :
( ( ite @ $false @ A @ B )
= B )
& ! [A: $i] :
( ( s @ A )
!= zero )
& ! [A: $i] :
( ( s @ A )
!= A )
& ! [A: $i] :
( ( h @ A )
= ( ite @ ( A = zero ) @ ( s @ zero )
@ ( ite
@ ( A
= ( s @ zero ) )
@ zero
@ ( s @ zero ) ) ) ) )
=> ? [A: $i > $i] :
( ( ( A @ zero )
= ( s @ zero ) )
& ( ( A @ ( s @ zero ) )
= zero )
& ( ( A @ ( s @ ( s @ zero ) ) )
= ( s @ zero ) ) ) ),
inference(simp,[status(thm)],[6]) ).
thf(19,plain,
~ ( ( ! [A: $i,B: $i] :
( ( ite @ $true @ A @ B )
= A )
& ! [A: $i,B: $i] :
( ( ite @ $false @ A @ B )
= B )
& ~ ? [A: $i] :
( ( s @ A )
= zero )
& ~ ? [A: $i] :
( ( s @ A )
= A )
& ! [A: $i] :
( ( h @ A )
= ( ite @ ( A = zero ) @ ( s @ zero )
@ ( ite
@ ( A
= ( s @ zero ) )
@ zero
@ ( s @ zero ) ) ) ) )
=> ? [A: $i > $i] :
( ( ( A @ zero )
= ( s @ zero ) )
& ( ( A @ ( s @ zero ) )
= zero )
& ( ( A @ ( s @ ( s @ zero ) ) )
= ( s @ zero ) ) ) ),
inference(miniscope,[status(thm)],[7]) ).
thf(20,plain,
! [H: $i > $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( ite @ $true @ A @ B )
= A )
& ( ( ite @ $false @ C @ D )
= D )
& ( ( s @ E )
!= zero )
& ( ( s @ F )
!= F )
& ( ( h @ G )
= ( ite @ ( G = zero ) @ ( s @ zero )
@ ( ite
@ ( G
= ( s @ zero ) )
@ zero
@ ( s @ zero ) ) ) )
& ( ( ( H @ zero )
!= ( s @ zero ) )
| ( ( H @ ( s @ zero ) )
!= zero )
| ( ( H @ ( s @ ( s @ zero ) ) )
!= ( s @ zero ) ) ) ),
inference(cnf,[status(esa)],[19]) ).
thf(22,plain,
! [A: $i] :
( ( h @ A )
= ( ite @ ( A = zero ) @ ( s @ zero )
@ ( ite
@ ( A
= ( s @ zero ) )
@ zero
@ ( s @ zero ) ) ) ),
inference(cnfConj,[status(thm)],[20]) ).
thf(43,plain,
! [A: $i] :
( ( ite @ ( A = zero ) @ ( s @ zero )
@ ( ite
@ ( A
= ( s @ zero ) )
@ zero
@ ( s @ zero ) ) )
= ( h @ A ) ),
inference(lifteq,[status(thm)],[22]) ).
thf(44,plain,
! [A: $i] :
( ( ite @ ( A = zero ) @ ( s @ zero )
@ ( ite
@ ( A
= ( s @ zero ) )
@ zero
@ ( s @ zero ) ) )
= ( h @ A ) ),
inference(simp,[status(thm)],[43]) ).
thf(24,plain,
! [B: $i,A: $i] :
( ( ite @ $false @ A @ B )
= B ),
inference(cnfConj,[status(thm)],[20]) ).
thf(53,plain,
! [B: $i,A: $i] :
( ( ite @ $false @ A @ B )
= B ),
inference(lifteq,[status(thm)],[24]) ).
thf(54,plain,
! [B: $i,A: $i] :
( ( ite @ $false @ A @ B )
= B ),
inference(simp,[status(thm)],[53]) ).
thf(76,plain,
! [C: $i,B: $i,A: $i] :
( ( ( h @ A )
= C )
| ( ( ite @ ( A = zero ) @ ( s @ zero )
@ ( ite
@ ( A
= ( s @ zero ) )
@ zero
@ ( s @ zero ) ) )
!= ( ite @ $false @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[44,54]) ).
thf(80,plain,
! [C: $i,B: $i,A: $i] :
( ( ( h @ A )
= C )
| ( A = zero )
| ( ( s @ zero )
!= B )
| ( ( ite
@ ( A
= ( s @ zero ) )
@ zero
@ ( s @ zero ) )
!= C ) ),
inference(simp,[status(thm)],[76]) ).
thf(84,plain,
! [C: $i,B: $i,A: $i] :
( ( A = zero )
| ( ( h @ A )
= C )
| ( ( s @ zero )
!= B )
| ( ( ite
@ ( A
= ( s @ zero ) )
@ zero
@ ( s @ zero ) )
!= C ) ),
inference(lifteq,[status(thm)],[80]) ).
thf(85,plain,
! [A: $i] :
( ( A = zero )
| ( ( ite
@ ( A
= ( s @ zero ) )
@ zero
@ ( s @ zero ) )
= ( h @ A ) ) ),
inference(simp,[status(thm)],[84]) ).
thf(253,plain,
! [C: $i,B: $i,A: $i] :
( ( A = zero )
| ( ( h @ A )
= C )
| ( ( ite
@ ( A
= ( s @ zero ) )
@ zero
@ ( s @ zero ) )
!= ( ite @ $false @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[85,54]) ).
thf(262,plain,
! [C: $i,B: $i,A: $i] :
( ( A = zero )
| ( ( h @ A )
= C )
| ( A
= ( s @ zero ) )
| ( zero != B )
| ( ( s @ zero )
!= C ) ),
inference(simp,[status(thm)],[253]) ).
thf(278,plain,
! [C: $i,B: $i,A: $i] :
( ( A
= ( s @ zero ) )
| ( A = zero )
| ( ( h @ A )
= C )
| ( zero != B )
| ( ( s @ zero )
!= C ) ),
inference(lifteq,[status(thm)],[262]) ).
thf(279,plain,
! [A: $i] :
( ( A
= ( s @ zero ) )
| ( A = zero )
| ( ( h @ A )
= ( s @ zero ) ) ),
inference(simp,[status(thm)],[278]) ).
thf(25,plain,
! [B: $i,A: $i] :
( ( ite @ $true @ A @ B )
= A ),
inference(cnfConj,[status(thm)],[20]) ).
thf(57,plain,
! [B: $i,A: $i] :
( ( ite @ $true @ A @ B )
= A ),
inference(lifteq,[status(thm)],[25]) ).
thf(92,plain,
! [C: $i,B: $i,A: $i] :
( ( ( h @ A )
= B )
| ( ( ite @ ( A = zero ) @ ( s @ zero )
@ ( ite
@ ( A
= ( s @ zero ) )
@ zero
@ ( s @ zero ) ) )
!= ( ite @ $true @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[44,57]) ).
thf(96,plain,
! [C: $i,B: $i,A: $i] :
( ( ( h @ A )
= B )
| ( A != zero )
| ( ( s @ zero )
!= B )
| ( ( ite
@ ( A
= ( s @ zero ) )
@ zero
@ ( s @ zero ) )
!= C ) ),
inference(simp,[status(thm)],[92]) ).
thf(100,plain,
! [C: $i,B: $i,A: $i] :
( ( A != zero )
| ( ( h @ A )
= B )
| ( ( s @ zero )
!= B )
| ( ( ite
@ ( A
= ( s @ zero ) )
@ zero
@ ( s @ zero ) )
!= C ) ),
inference(lifteq,[status(thm)],[96]) ).
thf(101,plain,
( ( h @ zero )
= ( s @ zero ) ),
inference(simp,[status(thm)],[100]) ).
thf(10,plain,
~ ( ( ! [A: $i,B: $i] :
( $false
=> ( ( ite @ $false @ A @ B )
= A ) )
& ! [A: $i,B: $i] :
( ~ $false
=> ( ( ite @ $false @ A @ B )
= B ) )
& ! [A: $i] :
( ( s @ A )
!= zero )
& ! [A: $i] :
( ( s @ A )
!= A )
& ! [A: $i] :
( ( h @ A )
= ( ite @ ( A = zero ) @ ( s @ zero )
@ ( ite
@ ( A
= ( s @ zero ) )
@ zero
@ ( s @ zero ) ) ) ) )
=> ? [A: $i > $i] :
( ( ( A @ zero )
= ( s @ zero ) )
& ( ( A @ ( s @ zero ) )
= zero )
& ( ( A @ ( s @ ( s @ zero ) ) )
= ( s @ zero ) ) ) ),
inference(instance,[status(thm)],[3]) ).
thf(11,plain,
~ ( ( ! [A: $i,B: $i] :
( ( ite @ $false @ A @ B )
= B )
& ! [A: $i] :
( ( s @ A )
!= zero )
& ! [A: $i] :
( ( s @ A )
!= A )
& ! [A: $i] :
( ( h @ A )
= ( ite @ ( A = zero ) @ ( s @ zero )
@ ( ite
@ ( A
= ( s @ zero ) )
@ zero
@ ( s @ zero ) ) ) ) )
=> ? [A: $i > $i] :
( ( ( A @ zero )
= ( s @ zero ) )
& ( ( A @ ( s @ zero ) )
= zero )
& ( ( A @ ( s @ ( s @ zero ) ) )
= ( s @ zero ) ) ) ),
inference(simp,[status(thm)],[10]) ).
thf(33,plain,
~ ( ( ! [A: $i,B: $i] :
( ( ite @ $false @ A @ B )
= B )
& ~ ? [A: $i] :
( ( s @ A )
= zero )
& ~ ? [A: $i] :
( ( s @ A )
= A )
& ! [A: $i] :
( ( h @ A )
= ( ite @ ( A = zero ) @ ( s @ zero )
@ ( ite
@ ( A
= ( s @ zero ) )
@ zero
@ ( s @ zero ) ) ) ) )
=> ? [A: $i > $i] :
( ( ( A @ zero )
= ( s @ zero ) )
& ( ( A @ ( s @ zero ) )
= zero )
& ( ( A @ ( s @ ( s @ zero ) ) )
= ( s @ zero ) ) ) ),
inference(miniscope,[status(thm)],[11]) ).
thf(34,plain,
! [F: $i > $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( ite @ $false @ A @ B )
= B )
& ( ( s @ C )
!= zero )
& ( ( s @ D )
!= D )
& ( ( h @ E )
= ( ite @ ( E = zero ) @ ( s @ zero )
@ ( ite
@ ( E
= ( s @ zero ) )
@ zero
@ ( s @ zero ) ) ) )
& ( ( ( F @ zero )
!= ( s @ zero ) )
| ( ( F @ ( s @ zero ) )
!= zero )
| ( ( F @ ( s @ ( s @ zero ) ) )
!= ( s @ zero ) ) ) ),
inference(cnf,[status(esa)],[33]) ).
thf(39,plain,
! [A: $i > $i] :
( ( ( A @ zero )
!= ( s @ zero ) )
| ( ( A @ ( s @ zero ) )
!= zero )
| ( ( A @ ( s @ ( s @ zero ) ) )
!= ( s @ zero ) ) ),
inference(cnfConj,[status(thm)],[34]) ).
thf(45,plain,
! [A: $i > $i] :
( ( ( A @ zero )
!= ( s @ zero ) )
| ( ( A @ ( s @ zero ) )
!= zero )
| ( ( A @ ( s @ ( s @ zero ) ) )
!= ( s @ zero ) ) ),
inference(lifteq,[status(thm)],[39]) ).
thf(46,plain,
! [A: $i > $i] :
( ( ( A @ zero )
!= ( s @ zero ) )
| ( ( A @ ( s @ zero ) )
!= zero )
| ( ( A @ ( s @ ( s @ zero ) ) )
!= ( s @ zero ) ) ),
inference(simp,[status(thm)],[45]) ).
thf(135,plain,
! [A: $i > $i] :
( ( ( s @ zero )
!= ( s @ zero ) )
| ( ( A @ ( s @ zero ) )
!= zero )
| ( ( A @ ( s @ ( s @ zero ) ) )
!= ( s @ zero ) )
| ( ( h @ zero )
!= ( A @ zero ) ) ),
inference(paramod_ordered,[status(thm)],[101,46]) ).
thf(136,plain,
! [A: $i > $i] :
( ( ( A @ ( s @ zero ) )
!= zero )
| ( ( A @ ( s @ ( s @ zero ) ) )
!= ( s @ zero ) )
| ( ( h @ zero )
!= ( A @ zero ) ) ),
inference(simp,[status(thm)],[135]) ).
thf(164,plain,
( ( ( h @ ( s @ zero ) )
!= zero )
| ( ( h @ ( s @ ( s @ zero ) ) )
!= ( s @ zero ) ) ),
inference(pre_uni,[status(thm)],[136:[bind(A,$thf( h ))]]) ).
thf(90,plain,
! [C: $i,B: $i,A: $i] :
( ( ( ite @ ( C = zero ) @ ( s @ zero ) @ A )
= ( h @ C ) )
| ( ( ite @ $true @ A @ B )
!= ( ite
@ ( C
= ( s @ zero ) )
@ zero
@ ( s @ zero ) ) ) ),
inference(paramod_ordered,[status(thm)],[57,44]) ).
thf(99,plain,
! [C: $i,B: $i,A: $i] :
( ( ( ite @ ( C = zero ) @ ( s @ zero ) @ A )
= ( h @ C ) )
| ( C
!= ( s @ zero ) )
| ( A != zero )
| ( B
!= ( s @ zero ) ) ),
inference(simp,[status(thm)],[90]) ).
thf(105,plain,
! [C: $i,B: $i,A: $i] :
( ( C
!= ( s @ zero ) )
| ( ( ite @ ( C = zero ) @ ( s @ zero ) @ A )
= ( h @ C ) )
| ( A != zero )
| ( B
!= ( s @ zero ) ) ),
inference(lifteq,[status(thm)],[99]) ).
thf(106,plain,
( ( ite
@ ( ( s @ zero )
= zero )
@ ( s @ zero )
@ zero )
= ( h @ ( s @ zero ) ) ),
inference(simp,[status(thm)],[105]) ).
thf(115,plain,
! [B: $i,A: $i] :
( ( ( h @ ( s @ zero ) )
= B )
| ( ( ite
@ ( ( s @ zero )
= zero )
@ ( s @ zero )
@ zero )
!= ( ite @ $false @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[106,54]) ).
thf(117,plain,
! [B: $i,A: $i] :
( ( ( h @ ( s @ zero ) )
= B )
| ( ( s @ zero )
= zero )
| ( ( s @ zero )
!= A )
| ( zero != B ) ),
inference(simp,[status(thm)],[115]) ).
thf(124,plain,
! [B: $i,A: $i] :
( ( ( s @ zero )
= zero )
| ( ( h @ ( s @ zero ) )
= B )
| ( ( s @ zero )
!= A )
| ( zero != B ) ),
inference(lifteq,[status(thm)],[117]) ).
thf(125,plain,
( ( ( s @ zero )
= zero )
| ( ( h @ ( s @ zero ) )
= zero ) ),
inference(simp,[status(thm)],[124]) ).
thf(8,plain,
~ ( ( ! [A: $i,B: $i] :
( $false
=> ( ( ite @ $false @ A @ B )
= A ) )
& ! [A: $i,B: $i] :
( ~ $true
=> ( ( ite @ $true @ A @ B )
= B ) )
& ! [A: $i] :
( ( s @ A )
!= zero )
& ! [A: $i] :
( ( s @ A )
!= A )
& ! [A: $i] :
( ( h @ A )
= ( ite @ ( A = zero ) @ ( s @ zero )
@ ( ite
@ ( A
= ( s @ zero ) )
@ zero
@ ( s @ zero ) ) ) ) )
=> ? [A: $i > $i] :
( ( ( A @ zero )
= ( s @ zero ) )
& ( ( A @ ( s @ zero ) )
= zero )
& ( ( A @ ( s @ ( s @ zero ) ) )
= ( s @ zero ) ) ) ),
inference(instance,[status(thm)],[3]) ).
thf(9,plain,
~ ( ( ! [A: $i] :
( ( s @ A )
!= zero )
& ! [A: $i] :
( ( s @ A )
!= A )
& ! [A: $i] :
( ( h @ A )
= ( ite @ ( A = zero ) @ ( s @ zero )
@ ( ite
@ ( A
= ( s @ zero ) )
@ zero
@ ( s @ zero ) ) ) ) )
=> ? [A: $i > $i] :
( ( ( A @ zero )
= ( s @ zero ) )
& ( ( A @ ( s @ zero ) )
= zero )
& ( ( A @ ( s @ ( s @ zero ) ) )
= ( s @ zero ) ) ) ),
inference(simp,[status(thm)],[8]) ).
thf(27,plain,
~ ( ( ~ ? [A: $i] :
( ( s @ A )
= zero )
& ~ ? [A: $i] :
( ( s @ A )
= A )
& ! [A: $i] :
( ( h @ A )
= ( ite @ ( A = zero ) @ ( s @ zero )
@ ( ite
@ ( A
= ( s @ zero ) )
@ zero
@ ( s @ zero ) ) ) ) )
=> ? [A: $i > $i] :
( ( ( A @ zero )
= ( s @ zero ) )
& ( ( A @ ( s @ zero ) )
= zero )
& ( ( A @ ( s @ ( s @ zero ) ) )
= ( s @ zero ) ) ) ),
inference(miniscope,[status(thm)],[9]) ).
thf(28,plain,
! [D: $i > $i,C: $i,B: $i,A: $i] :
( ( ( s @ A )
!= zero )
& ( ( s @ B )
!= B )
& ( ( h @ C )
= ( ite @ ( C = zero ) @ ( s @ zero )
@ ( ite
@ ( C
= ( s @ zero ) )
@ zero
@ ( s @ zero ) ) ) )
& ( ( ( D @ zero )
!= ( s @ zero ) )
| ( ( D @ ( s @ zero ) )
!= zero )
| ( ( D @ ( s @ ( s @ zero ) ) )
!= ( s @ zero ) ) ) ),
inference(cnf,[status(esa)],[27]) ).
thf(29,plain,
! [A: $i] :
( ( s @ A )
!= zero ),
inference(cnfConj,[status(thm)],[28]) ).
thf(42,plain,
! [A: $i] :
( ( s @ A )
!= zero ),
inference(lifteq,[status(thm)],[29]) ).
thf(180,plain,
( ( h @ ( s @ zero ) )
= zero ),
inference(simplifyReflect,[status(thm)],[125,42]) ).
thf(307,plain,
( ( zero != zero )
| ( ( h @ ( s @ ( s @ zero ) ) )
!= ( s @ zero ) ) ),
inference(rewrite,[status(thm)],[164,180]) ).
thf(308,plain,
( ( h @ ( s @ ( s @ zero ) ) )
!= ( s @ zero ) ),
inference(simp,[status(thm)],[307]) ).
thf(320,plain,
! [A: $i] :
( ( A
= ( s @ zero ) )
| ( A = zero )
| ( ( s @ zero )
!= ( s @ zero ) )
| ( ( h @ A )
!= ( h @ ( s @ ( s @ zero ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[279,308]) ).
thf(321,plain,
! [A: $i] :
( ( A
= ( s @ zero ) )
| ( A = zero )
| ( ( h @ A )
!= ( h @ ( s @ ( s @ zero ) ) ) ) ),
inference(simp,[status(thm)],[320]) ).
thf(322,plain,
( ( ( s @ ( s @ zero ) )
= ( s @ zero ) )
| ( ( s @ ( s @ zero ) )
= zero ) ),
inference(pattern_uni,[status(thm)],[321:[bind(A,$thf( s @ ( s @ zero ) ))]]) ).
thf(4,plain,
~ ( ( ! [A: $i,B: $i] :
( $true
=> ( ( ite @ $true @ A @ B )
= A ) )
& ! [A: $i,B: $i] :
( ~ $true
=> ( ( ite @ $true @ A @ B )
= B ) )
& ! [A: $i] :
( ( s @ A )
!= zero )
& ! [A: $i] :
( ( s @ A )
!= A )
& ! [A: $i] :
( ( h @ A )
= ( ite @ ( A = zero ) @ ( s @ zero )
@ ( ite
@ ( A
= ( s @ zero ) )
@ zero
@ ( s @ zero ) ) ) ) )
=> ? [A: $i > $i] :
( ( ( A @ zero )
= ( s @ zero ) )
& ( ( A @ ( s @ zero ) )
= zero )
& ( ( A @ ( s @ ( s @ zero ) ) )
= ( s @ zero ) ) ) ),
inference(instance,[status(thm)],[3]) ).
thf(5,plain,
~ ( ( ! [A: $i,B: $i] :
( ( ite @ $true @ A @ B )
= A )
& ! [A: $i] :
( ( s @ A )
!= zero )
& ! [A: $i] :
( ( s @ A )
!= A )
& ! [A: $i] :
( ( h @ A )
= ( ite @ ( A = zero ) @ ( s @ zero )
@ ( ite
@ ( A
= ( s @ zero ) )
@ zero
@ ( s @ zero ) ) ) ) )
=> ? [A: $i > $i] :
( ( ( A @ zero )
= ( s @ zero ) )
& ( ( A @ ( s @ zero ) )
= zero )
& ( ( A @ ( s @ ( s @ zero ) ) )
= ( s @ zero ) ) ) ),
inference(simp,[status(thm)],[4]) ).
thf(12,plain,
~ ( ( ! [A: $i,B: $i] :
( ( ite @ $true @ A @ B )
= A )
& ~ ? [A: $i] :
( ( s @ A )
= zero )
& ~ ? [A: $i] :
( ( s @ A )
= A )
& ! [A: $i] :
( ( h @ A )
= ( ite @ ( A = zero ) @ ( s @ zero )
@ ( ite
@ ( A
= ( s @ zero ) )
@ zero
@ ( s @ zero ) ) ) ) )
=> ? [A: $i > $i] :
( ( ( A @ zero )
= ( s @ zero ) )
& ( ( A @ ( s @ zero ) )
= zero )
& ( ( A @ ( s @ ( s @ zero ) ) )
= ( s @ zero ) ) ) ),
inference(miniscope,[status(thm)],[5]) ).
thf(13,plain,
! [F: $i > $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( ite @ $true @ A @ B )
= A )
& ( ( s @ C )
!= zero )
& ( ( s @ D )
!= D )
& ( ( h @ E )
= ( ite @ ( E = zero ) @ ( s @ zero )
@ ( ite
@ ( E
= ( s @ zero ) )
@ zero
@ ( s @ zero ) ) ) )
& ( ( ( F @ zero )
!= ( s @ zero ) )
| ( ( F @ ( s @ zero ) )
!= zero )
| ( ( F @ ( s @ ( s @ zero ) ) )
!= ( s @ zero ) ) ) ),
inference(cnf,[status(esa)],[12]) ).
thf(14,plain,
! [A: $i] :
( ( s @ A )
!= A ),
inference(cnfConj,[status(thm)],[13]) ).
thf(40,plain,
! [A: $i] :
( ( s @ A )
!= A ),
inference(lifteq,[status(thm)],[14]) ).
thf(41,plain,
! [A: $i] :
( ( s @ A )
!= A ),
inference(simp,[status(thm)],[40]) ).
thf(342,plain,
$false,
inference(simplifyReflect,[status(thm)],[322,41,42]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUN025^3 : TPTP v9.3.1. Released v6.4.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.11/0.22 % Computer : n007.cluster.edu
% 0.11/0.22 % Model : x86_64 x86_64
% 0.11/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.22 % Memory : 8046.5625MB
% 0.11/0.22 % OS : Linux 6.8.0-71-generic
% 0.11/0.22 % CPULimit : 300
% 0.11/0.22 % WCLimit : 300
% 0.11/0.22 % DateTime : Tue Sep 29 13:04:25 UTC 2026
% 0.11/0.22 % CPUTime :
% 0.11/0.22 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.89/0.79 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.23/0.98 % [INFO] Parsing done (188ms).
% 1.23/0.99 % [INFO] Running in sequential loop mode.
% 2.02/1.41 % [INFO] eprover registered as external prover.
% 2.02/1.42 % [INFO] Scanning for conjecture ...
% 2.22/1.52 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.22/1.56 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.22/1.57 % [INFO] Problem is higher-order (TPTP THF).
% 2.22/1.57 % [INFO] Type checking passed.
% 2.22/1.58 % [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 ...
% 6.90/3.18 % [INFO] Killing All external provers ...
% 6.90/3.19 % Time passed: 2824ms (effective reasoning time: 2182ms)
% 6.90/3.19 % 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)>
% 6.90/3.19 % Axioms used in derivation (0):
% 6.90/3.19 % No. of inferences in proof: 65
% 6.90/3.19 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2824 ms resp. 2182 ms w/o parsing
% 7.15/3.27 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 7.15/3.27 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------