%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM827^5 : TPTP v9.3.1. Bugfixed v5.3.0.
% 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 : n004.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 08:18:15 AM UTC 2026
% Result : Theorem 80.10s 21.23s
% Output : Refutation 69.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 6
% Syntax : Number of formulae : 102 ( 24 unt; 0 typ; 5 def)
% Number of atoms : 274 ( 264 equ; 0 cnn)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 1267 ( 202 ~; 144 |; 12 &; 901 @)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 59 ( 59 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 416 ( 283 ^; 131 !; 0 ?; 416 :)
% ( 0 !>; 0 ?*; 0 @-; 2 @+)
% Comments :
%------------------------------------------------------------------------------
thf(n_type,type,
n: $tType ).
thf(c0_decl,type,
c0: n ).
thf(cS_decl,type,
cS: n > n ).
thf(c_plus_decl,type,
c_plus: n > n > n ).
thf(cPA_1_decl,type,
cPA_1: $o ).
thf(cPA_2_decl,type,
cPA_2: $o ).
thf(cPA_IND_EQ_decl,type,
cPA_IND_EQ: $o ).
thf(sk1_decl,type,
sk1: ( n > n ) > ( n > n ) > n ).
thf(sk2_decl,type,
sk2: n ).
thf(cPA_1_def,definition,
( cPA_1
= ( ! [A: n] :
( ( c_plus @ A @ c0 )
= A ) ) ) ).
thf(cPA_2_def,definition,
( cPA_2
= ( ! [A: n,B: n] :
( ( c_plus @ A @ ( cS @ B ) )
= ( cS @ ( c_plus @ A @ B ) ) ) ) ) ).
thf(cPA_IND_EQ_def,definition,
( cPA_IND_EQ
= ( ! [A: n > n,B: n > n] :
( ( ( ( A @ c0 )
= ( B @ c0 ) )
& ! [C: n] :
( ( ( A @ C )
= ( B @ C ) )
=> ( ( A @ ( cS @ C ) )
= ( B @ ( cS @ C ) ) ) ) )
=> ! [C: n] :
( ( A @ C )
= ( B @ C ) ) ) ) ) ).
thf(sk1_def,definition,
( sk1
= ( ^ [A: n > n,B: n > n] :
@+[C: n] :
~ ( ( ( B @ C )
= ( A @ C ) )
=> ( ( B @ ( cS @ C ) )
= ( A @ ( cS @ C ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: n] :
( ( c_plus @ A @ c0 )
!= ( c_plus @ c0 @ A ) ) ) ) ).
thf(1,conjecture,
( ( cPA_1
& cPA_2
& cPA_IND_EQ )
=> ! [A: n] :
( ( c_plus @ A @ c0 )
= ( c_plus @ c0 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cPA_THM2) ).
thf(2,negated_conjecture,
~ ( ( cPA_1
& cPA_2
& cPA_IND_EQ )
=> ! [A: n] :
( ( c_plus @ A @ c0 )
= ( c_plus @ c0 @ A ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ( ! [A: n] :
( ( c_plus @ A @ c0 )
= A )
& ! [A: n,B: n] :
( ( c_plus @ A @ ( cS @ B ) )
= ( cS @ ( c_plus @ A @ B ) ) )
& ! [A: n > n,B: n > n] :
( ( ( ( A @ c0 )
= ( B @ c0 ) )
& ! [C: n] :
( ( ( A @ C )
= ( B @ C ) )
=> ( ( A @ ( cS @ C ) )
= ( B @ ( cS @ C ) ) ) ) )
=> ! [C: n] :
( ( A @ C )
= ( B @ C ) ) ) )
=> ! [A: n] :
( ( c_plus @ A @ c0 )
= ( c_plus @ c0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
! [F: n,E: n > n,D: n > n,C: n,B: n,A: n] :
( ( ( c_plus @ A @ c0 )
= A )
& ( ( c_plus @ B @ ( cS @ C ) )
= ( cS @ ( c_plus @ B @ C ) ) )
& ( ( ( D @ c0 )
!= ( E @ c0 ) )
| ( ( D @ ( sk1 @ E @ D ) )
= ( E @ ( sk1 @ E @ D ) ) )
| ( ( D @ F )
= ( E @ F ) ) )
& ( ( ( D @ c0 )
!= ( E @ c0 ) )
| ( ( D @ ( cS @ ( sk1 @ E @ D ) ) )
!= ( E @ ( cS @ ( sk1 @ E @ D ) ) ) )
| ( ( D @ F )
= ( E @ F ) ) )
& ( ( c_plus @ sk2 @ c0 )
!= ( c_plus @ c0 @ sk2 ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(7,plain,
! [B: n,A: n] :
( ( c_plus @ A @ ( cS @ B ) )
= ( cS @ ( c_plus @ A @ B ) ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(14,plain,
! [B: n,A: n] :
( ( c_plus @ A @ ( cS @ B ) )
= ( cS @ ( c_plus @ A @ B ) ) ),
inference(lifteq,[status(thm)],[7]) ).
thf(15,plain,
! [B: n,A: n] :
( ( c_plus @ A @ ( cS @ B ) )
= ( cS @ ( c_plus @ A @ B ) ) ),
inference(simp,[status(thm)],[14]) ).
thf(6,plain,
( ( c_plus @ sk2 @ c0 )
!= ( c_plus @ c0 @ sk2 ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(12,plain,
( ( c_plus @ sk2 @ c0 )
!= ( c_plus @ c0 @ sk2 ) ),
inference(lifteq,[status(thm)],[6]) ).
thf(9,plain,
! [A: n] :
( ( c_plus @ A @ c0 )
= A ),
inference(cnfConj,[status(thm)],[4]) ).
thf(13,plain,
! [A: n] :
( ( c_plus @ A @ c0 )
= A ),
inference(lifteq,[status(thm)],[9]) ).
thf(20,plain,
( ( c_plus @ c0 @ sk2 )
!= sk2 ),
inference(rewrite,[status(thm)],[12,13]) ).
thf(127,plain,
! [B: n,A: n] :
( ( ( cS @ ( c_plus @ A @ B ) )
!= sk2 )
| ( ( c_plus @ A @ ( cS @ B ) )
!= ( c_plus @ c0 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[15,20]) ).
thf(137,plain,
! [B: n,A: n] :
( ( ( cS @ ( c_plus @ A @ B ) )
!= sk2 )
| ( A != c0 )
| ( ( cS @ B )
!= sk2 ) ),
inference(simp,[status(thm)],[127]) ).
thf(175,plain,
! [A: n] :
( ( ( cS @ ( c_plus @ c0 @ A ) )
!= sk2 )
| ( ( cS @ A )
!= sk2 ) ),
inference(simp,[status(thm)],[137]) ).
thf(198,plain,
! [C: n,B: n,A: n] :
( ( ( cS @ ( cS @ ( c_plus @ A @ B ) ) )
!= sk2 )
| ( ( cS @ C )
!= sk2 )
| ( ( c_plus @ A @ ( cS @ B ) )
!= ( c_plus @ c0 @ C ) ) ),
inference(paramod_ordered,[status(thm)],[15,175]) ).
thf(199,plain,
! [A: n] :
( ( ( cS @ ( cS @ ( c_plus @ c0 @ A ) ) )
!= sk2 )
| ( ( cS @ ( cS @ A ) )
!= sk2 ) ),
inference(pattern_uni,[status(thm)],[198:[bind(A,$thf( c0 )),bind(B,$thf( D )),bind(C,$thf( cS @ D ))]]) ).
thf(225,plain,
! [A: n] :
( ( ( cS @ ( cS @ ( c_plus @ c0 @ A ) ) )
!= sk2 )
| ( ( cS @ ( cS @ A ) )
!= sk2 ) ),
inference(simp,[status(thm)],[199]) ).
thf(1195,plain,
! [C: n,B: n,A: n] :
( ( ( cS @ ( cS @ ( cS @ ( c_plus @ A @ B ) ) ) )
!= sk2 )
| ( ( cS @ ( cS @ C ) )
!= sk2 )
| ( ( c_plus @ A @ ( cS @ B ) )
!= ( c_plus @ c0 @ C ) ) ),
inference(paramod_ordered,[status(thm)],[15,225]) ).
thf(1196,plain,
! [A: n] :
( ( ( cS @ ( cS @ ( cS @ ( c_plus @ c0 @ A ) ) ) )
!= sk2 )
| ( ( cS @ ( cS @ ( cS @ A ) ) )
!= sk2 ) ),
inference(pattern_uni,[status(thm)],[1195:[bind(A,$thf( c0 )),bind(B,$thf( D )),bind(C,$thf( cS @ D ))]]) ).
thf(1337,plain,
! [A: n] :
( ( ( cS @ ( cS @ ( cS @ ( c_plus @ c0 @ A ) ) ) )
!= sk2 )
| ( ( cS @ ( cS @ ( cS @ A ) ) )
!= sk2 ) ),
inference(simp,[status(thm)],[1196]) ).
thf(5,plain,
! [C: n,B: n > n,A: n > n] :
( ( ( A @ c0 )
!= ( B @ c0 ) )
| ( ( A @ ( sk1 @ B @ A ) )
= ( B @ ( sk1 @ B @ A ) ) )
| ( ( A @ C )
= ( B @ C ) ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(10,plain,
! [C: n,B: n > n,A: n > n] :
( ( ( A @ c0 )
!= ( B @ c0 ) )
| ( ( A @ ( sk1 @ B @ A ) )
= ( B @ ( sk1 @ B @ A ) ) )
| ( ( A @ C )
= ( B @ C ) ) ),
inference(lifteq,[status(thm)],[5]) ).
thf(11,plain,
! [C: n,B: n > n,A: n > n] :
( ( ( A @ c0 )
!= ( B @ c0 ) )
| ( ( A @ ( sk1 @ B @ A ) )
= ( B @ ( sk1 @ B @ A ) ) )
| ( ( A @ C )
= ( B @ C ) ) ),
inference(simp,[status(thm)],[10]) ).
thf(18,plain,
( ( sk2 != c0 )
| ( sk2 != c0 ) ),
inference(simp,[status(thm)],[12]) ).
thf(19,plain,
sk2 != c0,
inference(simp,[status(thm)],[18]) ).
thf(326,plain,
! [C: n,B: n > n,A: n > n] :
( ( ( A @ c0 )
!= ( B @ c0 ) )
| ( ( A @ ( sk1 @ B @ A ) )
= ( B @ ( sk1 @ B @ A ) ) )
| ( ( A @ C )
!= c0 )
| ( ( B @ C )
!= sk2 ) ),
inference(paramod_ordered,[status(thm)],[11,19]) ).
thf(635,plain,
! [A: n > n] :
( ( ( A @ c0 )
!= c0 )
| ( ( A
@ ( sk1
@ ^ [B: n] : B
@ A ) )
= ( sk1
@ ^ [B: n] : B
@ A ) )
| ( ( A @ sk2 )
!= c0 ) ),
inference(pre_uni,[status(thm)],[326:[bind(A,$thf( A )),bind(B,$thf( ^ [D: n] : D )),bind(C,$thf( sk2 ))]]) ).
thf(636,plain,
( ( sk1
@ ^ [A: n] : A
@ ^ [A: n] : c0 )
= c0 ),
inference(pre_uni,[status(thm)],[635:[bind(A,$thf( ^ [B: n] : c0 ))]]) ).
thf(8,plain,
! [C: n,B: n > n,A: n > n] :
( ( ( A @ c0 )
!= ( B @ c0 ) )
| ( ( A @ ( cS @ ( sk1 @ B @ A ) ) )
!= ( B @ ( cS @ ( sk1 @ B @ A ) ) ) )
| ( ( A @ C )
= ( B @ C ) ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(16,plain,
! [C: n,B: n > n,A: n > n] :
( ( ( A @ c0 )
!= ( B @ c0 ) )
| ( ( A @ ( cS @ ( sk1 @ B @ A ) ) )
!= ( B @ ( cS @ ( sk1 @ B @ A ) ) ) )
| ( ( A @ C )
= ( B @ C ) ) ),
inference(lifteq,[status(thm)],[8]) ).
thf(17,plain,
! [C: n,B: n > n,A: n > n] :
( ( ( A @ c0 )
!= ( B @ c0 ) )
| ( ( A @ ( cS @ ( sk1 @ B @ A ) ) )
!= ( B @ ( cS @ ( sk1 @ B @ A ) ) ) )
| ( ( A @ C )
= ( B @ C ) ) ),
inference(simp,[status(thm)],[16]) ).
thf(28,plain,
! [C: n,B: n > n,A: n > n] :
( ( ( A @ c0 )
!= ( B @ c0 ) )
| ( ( A @ ( cS @ ( sk1 @ B @ A ) ) )
!= ( B @ ( cS @ ( sk1 @ B @ A ) ) ) )
| ( ( A @ C )
!= c0 )
| ( ( B @ C )
!= sk2 ) ),
inference(paramod_ordered,[status(thm)],[17,19]) ).
thf(76,plain,
! [A: n > n] :
( ( ( A @ c0 )
!= c0 )
| ( ( A
@ ( cS
@ ( sk1
@ ^ [B: n] : B
@ A ) ) )
!= ( cS
@ ( sk1
@ ^ [B: n] : B
@ A ) ) )
| ( ( A @ sk2 )
!= c0 ) ),
inference(pre_uni,[status(thm)],[28:[bind(A,$thf( A )),bind(B,$thf( ^ [D: n] : D )),bind(C,$thf( sk2 ))]]) ).
thf(4511,plain,
! [A: n > n] :
( ( c0 != c0 )
| ( ( A
@ ( cS
@ ( sk1
@ ^ [B: n] : B
@ A ) ) )
!= ( cS
@ ( sk1
@ ^ [B: n] : B
@ A ) ) )
| ( ( A @ sk2 )
!= c0 )
| ( ( sk1
@ ^ [B: n] : B
@ ^ [B: n] : c0 )
!= ( A @ c0 ) ) ),
inference(paramod_ordered,[status(thm)],[636,76]) ).
thf(4512,plain,
! [A: n > n] :
( ( ( A
@ ( cS
@ ( sk1
@ ^ [B: n] : B
@ A ) ) )
!= ( cS
@ ( sk1
@ ^ [B: n] : B
@ A ) ) )
| ( ( A @ sk2 )
!= c0 )
| ( ( sk1
@ ^ [B: n] : B
@ ^ [B: n] : c0 )
!= ( A @ c0 ) ) ),
inference(simp,[status(thm)],[4511]) ).
thf(4599,plain,
( ( ( sk1
@ ^ [A: n] : A
@ ^ [A: n] :
( cS
@ ( sk1
@ ^ [B: n] : B
@ ^ [B: n] :
( sk1
@ ^ [C: n] : C
@ ^ [C: n] : B ) ) ) )
!= ( cS
@ ( sk1
@ ^ [A: n] : A
@ ^ [A: n] :
( sk1
@ ^ [B: n] : B
@ ^ [B: n] : A ) ) ) )
| ( ( sk1
@ ^ [A: n] : A
@ ^ [A: n] : sk2 )
!= c0 ) ),
inference(pre_uni,[status(thm)],[4512:[bind(A,$thf( ^ [B: n] : ( sk1 @ ^ [C: n] : C @ ^ [C: n] : B ) ))]]) ).
thf(6497,plain,
( ( ( sk1
@ ^ [A: n] : A
@ ^ [A: n] :
( cS
@ ( sk1
@ ^ [B: n] : B
@ ^ [B: n] :
( sk1
@ ^ [C: n] : C
@ ^ [C: n] : B ) ) ) )
!= ( cS
@ ( sk1
@ ^ [A: n] : A
@ ^ [A: n] :
( sk1
@ ^ [B: n] : B
@ ^ [B: n] : A ) ) ) )
| ( c0 != c0 )
| ( ( sk1
@ ^ [A: n] : A
@ ^ [A: n] : sk2 )
!= ( sk1
@ ^ [A: n] : A
@ ^ [A: n] : c0 ) ) ),
inference(paramod_ordered,[status(thm)],[636,4599]) ).
thf(6498,plain,
( ( ( sk1
@ ^ [A: n] : A
@ ^ [A: n] :
( cS
@ ( sk1
@ ^ [B: n] : B
@ ^ [B: n] :
( sk1
@ ^ [C: n] : C
@ ^ [C: n] : B ) ) ) )
!= ( cS
@ ( sk1
@ ^ [A: n] : A
@ ^ [A: n] :
( sk1
@ ^ [B: n] : B
@ ^ [B: n] : A ) ) ) )
| ( ( sk1
@ ^ [A: n] : A
@ ^ [A: n] : sk2 )
!= ( sk1
@ ^ [A: n] : A
@ ^ [A: n] : c0 ) ) ),
inference(simp,[status(thm)],[6497]) ).
thf(6552,plain,
( ( ( sk1
@ ^ [A: n] : A
@ ^ [A: n] :
( cS
@ ( sk1
@ ^ [B: n] : B
@ ^ [B: n] :
( sk1
@ ^ [C: n] : C
@ ^ [C: n] : B ) ) ) )
!= ( cS
@ ( sk1
@ ^ [A: n] : A
@ ^ [A: n] :
( sk1
@ ^ [B: n] : B
@ ^ [B: n] : A ) ) ) )
| ( ( ^ [A: n] : A )
!= ( ^ [A: n] : A ) )
| ( ( ^ [A: n] : sk2 )
!= ( ^ [A: n] : c0 ) ) ),
inference(simp,[status(thm)],[6498]) ).
thf(6643,plain,
( ( ( sk1
@ ^ [A: n] : A
@ ^ [A: n] :
( cS
@ ( sk1
@ ^ [B: n] : B
@ ^ [B: n] :
( sk1
@ ^ [C: n] : C
@ ^ [C: n] : B ) ) ) )
!= ( cS
@ ( sk1
@ ^ [A: n] : A
@ ^ [A: n] :
( sk1
@ ^ [B: n] : B
@ ^ [B: n] : A ) ) ) )
| ( ( ^ [A: n] : sk2 )
!= ( ^ [A: n] : c0 ) ) ),
inference(simp,[status(thm)],[6552]) ).
thf(33,plain,
! [C: n,B: n > n,A: n > n] :
( ( ( A @ c0 )
!= ( B @ c0 ) )
| ( ( A @ ( cS @ ( sk1 @ B @ A ) ) )
!= ( B @ ( cS @ ( sk1 @ B @ A ) ) ) )
| ( ( c_plus @ ( A @ C ) @ sk2 )
!= sk2 )
| ( ( B @ C )
!= c0 ) ),
inference(paramod_ordered,[status(thm)],[17,20]) ).
thf(74,plain,
! [A: n > n] :
( ( ( A @ c0 )
!= c0 )
| ( ( A
@ ( cS
@ ( sk1
@ ^ [B: n] : B
@ A ) ) )
!= ( cS
@ ( sk1
@ ^ [B: n] : B
@ A ) ) )
| ( ( c_plus @ ( A @ c0 ) @ sk2 )
!= sk2 ) ),
inference(pre_uni,[status(thm)],[33:[bind(A,$thf( A )),bind(B,$thf( ^ [D: n] : D )),bind(C,$thf( c0 ))]]) ).
thf(188,plain,
! [B: n,A: n] :
( ( ( cS @ A )
!= sk2 )
| ( ( cS @ B )
!= sk2 )
| ( ( c_plus @ A @ c0 )
!= ( c_plus @ c0 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[13,175]) ).
thf(189,plain,
( ( ( cS @ c0 )
!= sk2 )
| ( ( cS @ c0 )
!= sk2 ) ),
inference(pattern_uni,[status(thm)],[188:[bind(A,$thf( c0 )),bind(B,$thf( c0 ))]]) ).
thf(248,plain,
( ( cS @ c0 )
!= sk2 ),
inference(simp,[status(thm)],[189]) ).
thf(200,plain,
! [A: n] :
( ( ( cS @ A )
!= sk2 )
| ( ( cS @ ( c_plus @ c0 @ A ) )
!= ( cS @ A ) )
| ( sk2 != sk2 ) ),
inference(eqfactor_ordered,[status(thm)],[175]) ).
thf(224,plain,
! [A: n] :
( ( ( cS @ A )
!= sk2 )
| ( ( c_plus @ c0 @ A )
!= A ) ),
inference(simp,[status(thm)],[200]) ).
thf(325,plain,
! [C: n,B: n > n,A: n > n] :
( ( ( A @ c0 )
!= ( B @ c0 ) )
| ( ( A @ ( sk1 @ B @ A ) )
= ( B @ ( sk1 @ B @ A ) ) )
| ( ( B @ C )
!= c0 )
| ( ( A @ C )
!= sk2 ) ),
inference(paramod_ordered,[status(thm)],[11,19]) ).
thf(425,plain,
! [A: n > n] :
( ( ( A @ c0 )
!= c0 )
| ( ( A
@ ( sk1 @ A
@ ^ [B: n] : B ) )
= ( sk1 @ A
@ ^ [B: n] : B ) )
| ( ( A @ sk2 )
!= c0 ) ),
inference(pre_uni,[status(thm)],[325:[bind(A,$thf( ^ [D: n] : D )),bind(B,$thf( B )),bind(C,$thf( sk2 ))]]) ).
thf(426,plain,
( ( sk1
@ ^ [A: n] : c0
@ ^ [A: n] : A )
= c0 ),
inference(pre_uni,[status(thm)],[425:[bind(A,$thf( ^ [B: n] : c0 ))]]) ).
thf(41,plain,
! [C: n,B: n > n,A: n > n] :
( ( ( A @ c0 )
!= ( B @ c0 ) )
| ( ( A @ C )
= ( B @ C ) )
| ( ( A @ ( cS @ ( sk1 @ B @ A ) ) )
!= ( A @ c0 ) )
| ( ( B @ ( cS @ ( sk1 @ B @ A ) ) )
!= ( B @ c0 ) ) ),
inference(eqfactor_ordered,[status(thm)],[17]) ).
thf(47,plain,
! [C: n,B: n > n,A: n > n] :
( ( ( A @ c0 )
!= ( B @ c0 ) )
| ( ( A @ C )
= ( B @ C ) )
| ( ( A @ ( cS @ ( sk1 @ B @ A ) ) )
!= ( A @ c0 ) )
| ( ( B @ ( cS @ ( sk1 @ B @ A ) ) )
!= ( B @ c0 ) ) ),
inference(pre_uni,[status(thm)],[41:[]]) ).
thf(48,plain,
! [C: n,B: n > n,A: n > n] :
( ( ( A @ C )
= ( B @ C ) )
| ( ( A @ c0 )
!= ( B @ c0 ) )
| ( ( A @ ( cS @ ( sk1 @ B @ A ) ) )
!= ( A @ c0 ) )
| ( ( B @ ( cS @ ( sk1 @ B @ A ) ) )
!= ( B @ c0 ) ) ),
inference(pre_uni,[status(thm)],[47:[]]) ).
thf(1181,plain,
! [B: n,A: n] :
( ( ( cS @ ( cS @ A ) )
!= sk2 )
| ( ( cS @ ( cS @ B ) )
!= sk2 )
| ( ( c_plus @ A @ c0 )
!= ( c_plus @ c0 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[13,225]) ).
thf(1182,plain,
( ( ( cS @ ( cS @ c0 ) )
!= sk2 )
| ( ( cS @ ( cS @ c0 ) )
!= sk2 ) ),
inference(pattern_uni,[status(thm)],[1181:[bind(A,$thf( c0 )),bind(B,$thf( c0 ))]]) ).
thf(1336,plain,
( ( cS @ ( cS @ c0 ) )
!= sk2 ),
inference(simp,[status(thm)],[1182]) ).
thf(32,plain,
! [C: n,B: n > n,A: n > n] :
( ( ( A @ c0 )
!= ( B @ c0 ) )
| ( ( A @ ( cS @ ( sk1 @ B @ A ) ) )
!= ( B @ ( cS @ ( sk1 @ B @ A ) ) ) )
| ( ( A @ C )
!= sk2 )
| ( ( B @ C )
!= ( c_plus @ c0 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[17,20]) ).
thf(84,plain,
! [A: n > n] :
( ( ( A @ c0 )
!= ( c_plus @ c0 @ c0 ) )
| ( ( A @ ( cS @ ( sk1 @ ( c_plus @ c0 ) @ A ) ) )
!= ( c_plus @ c0 @ ( cS @ ( sk1 @ ( c_plus @ c0 ) @ A ) ) ) )
| ( ( A @ sk2 )
!= sk2 ) ),
inference(pre_uni,[status(thm)],[32:[bind(A,$thf( A )),bind(B,$thf( c_plus @ c0 )),bind(C,$thf( sk2 ))]]) ).
thf(8336,plain,
! [A: n > n] :
( ( ( A @ c0 )
!= c0 )
| ( ( A @ ( cS @ ( sk1 @ ( c_plus @ c0 ) @ A ) ) )
!= ( cS @ ( c_plus @ c0 @ ( sk1 @ ( c_plus @ c0 ) @ A ) ) ) )
| ( ( A @ sk2 )
!= sk2 ) ),
inference(rewrite,[status(thm)],[84,13,15]) ).
thf(857,plain,
! [C: n,B: n > n,A: n > n] :
( ( ( A @ c0 )
!= ( B @ c0 ) )
| ( ( A @ C )
= ( B @ C ) )
| ( ( A @ ( sk1 @ B @ A ) )
= c0 )
| ( ( B @ ( sk1 @ B @ A ) )
!= ( sk1
@ ^ [D: n] : c0
@ ^ [D: n] : D ) ) ),
inference(paramod_ordered,[status(thm)],[11,426]) ).
thf(897,plain,
! [B: n,A: n > n] :
( ( ( A @ c0 )
!= ( sk1
@ ^ [C: n] : c0
@ ^ [C: n] : C ) )
| ( ( A @ B )
= ( sk1
@ ^ [C: n] : c0
@ ^ [C: n] : C ) )
| ( ( A
@ ( sk1
@ ^ [C: n] :
( sk1
@ ^ [D: n] : c0
@ ^ [D: n] : D )
@ A ) )
= c0 ) ),
inference(pre_uni,[status(thm)],[857:[bind(A,$thf( A )),bind(B,$thf( ^ [D: n] : ( sk1 @ ^ [E: n] : c0 @ ^ [E: n] : E ) )),bind(C,$thf( C ))]]) ).
thf(899,plain,
! [A: n] :
( ( ( sk1
@ ^ [B: n] :
( sk1
@ ^ [C: n] :
( sk1
@ ^ [D: n] : c0
@ ^ [D: n] : D )
@ ^ [C: n] :
( sk1
@ ^ [D: n] : C
@ ^ [D: n] : D ) )
@ ^ [B: n] : B )
= c0 )
| ( ( sk1
@ ^ [B: n] : A
@ ^ [B: n] : B )
= ( sk1
@ ^ [B: n] : c0
@ ^ [B: n] : B ) ) ),
inference(pre_uni,[status(thm)],[897:[bind(A,$thf( ^ [C: n] : ( sk1 @ ^ [D: n] : C @ ^ [D: n] : D ) )),bind(B,$thf( B ))]]) ).
thf(967,plain,
! [A: n] :
( ( ( sk1
@ ^ [B: n] :
( sk1
@ ^ [C: n] :
( sk1
@ ^ [D: n] : c0
@ ^ [D: n] : D )
@ ^ [C: n] :
( sk1
@ ^ [D: n] : C
@ ^ [D: n] : D ) )
@ ^ [B: n] : B )
= c0 )
| ( ( sk1
@ ^ [B: n] : A
@ ^ [B: n] : B )
= ( sk1
@ ^ [B: n] : c0
@ ^ [B: n] : B ) ) ),
inference(simp,[status(thm)],[899]) ).
thf(7548,plain,
! [A: n] :
( ( ( sk1
@ ^ [B: n] :
( sk1
@ ^ [C: n] : c0
@ ^ [C: n] :
( sk1
@ ^ [D: n] : C
@ ^ [D: n] : D ) )
@ ^ [B: n] : B )
= c0 )
| ( ( sk1
@ ^ [B: n] : A
@ ^ [B: n] : B )
= c0 ) ),
inference(rewrite,[status(thm)],[967,426]) ).
thf(7640,plain,
! [A: n] :
( ( ( sk1
@ ^ [B: n] : A
@ ^ [B: n] : B )
= c0 )
| ( ( sk1
@ ^ [B: n] :
( sk1
@ ^ [C: n] : c0
@ ^ [C: n] :
( sk1
@ ^ [D: n] : C
@ ^ [D: n] : D ) )
@ ^ [B: n] : B )
!= ( sk1
@ ^ [B: n] : A
@ ^ [B: n] : B ) )
| ( c0 != c0 ) ),
inference(eqfactor_ordered,[status(thm)],[7548]) ).
thf(7680,plain,
( ( sk1
@ ^ [A: n] :
( sk1
@ ^ [B: n] : c0
@ ^ [B: n] :
( sk1
@ ^ [C: n] : B
@ ^ [C: n] : C ) )
@ ^ [A: n] : A )
= c0 ),
inference(pattern_uni,[status(thm)],[7640:[bind(A,$thf( sk1 @ ^ [B: n] : c0 @ ^ [B: n] : ( sk1 @ ^ [C: n] : B @ ^ [C: n] : C ) ))]]) ).
thf(4513,plain,
! [A: n > n] :
( ( ( A @ c0 )
!= c0 )
| ( ( A @ ( cS @ c0 ) )
!= ( cS
@ ( sk1
@ ^ [B: n] : B
@ A ) ) )
| ( ( A @ sk2 )
!= c0 )
| ( ( sk1
@ ^ [B: n] : B
@ ^ [B: n] : c0 )
!= ( sk1
@ ^ [B: n] : B
@ A ) ) ),
inference(paramod_ordered,[status(thm)],[636,76]) ).
thf(4514,plain,
( ( c0 != c0 )
| ( ( cS
@ ( sk1
@ ^ [A: n] : A
@ ^ [A: n] : c0 ) )
!= c0 )
| ( c0 != c0 ) ),
inference(pattern_uni,[status(thm)],[4513:[bind(A,$thf( ^ [B: n] : c0 ))]]) ).
thf(4737,plain,
( ( cS
@ ( sk1
@ ^ [A: n] : A
@ ^ [A: n] : c0 ) )
!= c0 ),
inference(simp,[status(thm)],[4514]) ).
thf(4777,plain,
( ( cS @ c0 )
!= c0 ),
inference(rewrite,[status(thm)],[4737,636]) ).
thf(1221,plain,
! [A: n] :
( ( ( cS @ ( cS @ A ) )
!= sk2 )
| ( ( cS @ ( cS @ ( c_plus @ c0 @ A ) ) )
!= ( cS @ ( cS @ A ) ) )
| ( sk2 != sk2 ) ),
inference(eqfactor_ordered,[status(thm)],[225]) ).
thf(1246,plain,
! [A: n] :
( ( ( cS @ ( cS @ A ) )
!= sk2 )
| ( ( cS @ ( c_plus @ c0 @ A ) )
!= ( cS @ A ) ) ),
inference(simp,[status(thm)],[1221]) ).
thf(81,plain,
! [A: n > n] :
( ( ( A @ c0 )
!= c0 )
| ( ( A
@ ( cS
@ ( sk1
@ ^ [B: n] : B
@ A ) ) )
!= ( cS
@ ( sk1
@ ^ [B: n] : B
@ A ) ) )
| ( ( A @ ( c_plus @ c0 @ sk2 ) )
!= sk2 ) ),
inference(pre_uni,[status(thm)],[32:[bind(A,$thf( A )),bind(B,$thf( ^ [D: n] : D )),bind(C,$thf( c_plus @ c0 @ sk2 ))]]) ).
thf(4485,plain,
! [A: n > n] :
( ( c0 != c0 )
| ( ( A
@ ( cS
@ ( sk1
@ ^ [B: n] : B
@ A ) ) )
!= ( cS
@ ( sk1
@ ^ [B: n] : B
@ A ) ) )
| ( ( A @ sk2 )
!= c0 )
| ( ( sk1
@ ^ [B: n] : c0
@ ^ [B: n] : B )
!= ( A @ c0 ) ) ),
inference(paramod_ordered,[status(thm)],[426,76]) ).
thf(4486,plain,
! [A: n > n] :
( ( ( A
@ ( cS
@ ( sk1
@ ^ [B: n] : B
@ A ) ) )
!= ( cS
@ ( sk1
@ ^ [B: n] : B
@ A ) ) )
| ( ( A @ sk2 )
!= c0 )
| ( ( sk1
@ ^ [B: n] : c0
@ ^ [B: n] : B )
!= ( A @ c0 ) ) ),
inference(simp,[status(thm)],[4485]) ).
thf(4601,plain,
( ( ( sk1
@ ^ [A: n] :
( cS
@ ( sk1
@ ^ [B: n] : B
@ ^ [B: n] :
( sk1
@ ^ [C: n] : B
@ ^ [C: n] : C ) ) )
@ ^ [A: n] : A )
!= ( cS
@ ( sk1
@ ^ [A: n] : A
@ ^ [A: n] :
( sk1
@ ^ [B: n] : A
@ ^ [B: n] : B ) ) ) )
| ( ( sk1
@ ^ [A: n] : sk2
@ ^ [A: n] : A )
!= c0 ) ),
inference(pre_uni,[status(thm)],[4486:[bind(A,$thf( ^ [B: n] : ( sk1 @ ^ [C: n] : B @ ^ [C: n] : C ) ))]]) ).
thf(42,plain,
! [C: n,B: n > n,A: n > n] :
( ( ( A @ c0 )
!= ( B @ c0 ) )
| ( ( A @ C )
= ( B @ C ) )
| ( ( A @ ( cS @ ( sk1 @ B @ A ) ) )
!= ( B @ c0 ) )
| ( ( B @ ( cS @ ( sk1 @ B @ A ) ) )
!= ( A @ c0 ) ) ),
inference(eqfactor_ordered,[status(thm)],[17]) ).
thf(65,plain,
! [C: n,B: n > n,A: n > n] :
( ( ( A @ c0 )
!= ( B @ c0 ) )
| ( ( A @ C )
= ( B @ C ) )
| ( ( A @ ( cS @ ( sk1 @ B @ A ) ) )
!= ( B @ c0 ) )
| ( ( B @ ( cS @ ( sk1 @ B @ A ) ) )
!= ( A @ c0 ) ) ),
inference(pre_uni,[status(thm)],[42:[]]) ).
thf(66,plain,
! [C: n,B: n > n,A: n > n] :
( ( ( A @ C )
= ( B @ C ) )
| ( ( A @ c0 )
!= ( B @ c0 ) )
| ( ( A @ ( cS @ ( sk1 @ B @ A ) ) )
!= ( B @ c0 ) )
| ( ( B @ ( cS @ ( sk1 @ B @ A ) ) )
!= ( A @ c0 ) ) ),
inference(pre_uni,[status(thm)],[65:[]]) ).
thf(6473,plain,
( ( ( sk1
@ ^ [A: n] : A
@ ^ [A: n] :
( cS
@ ( sk1
@ ^ [B: n] : B
@ ^ [B: n] :
( sk1
@ ^ [C: n] : C
@ ^ [C: n] : B ) ) ) )
!= ( cS
@ ( sk1
@ ^ [A: n] : A
@ ^ [A: n] :
( sk1
@ ^ [B: n] : B
@ ^ [B: n] : A ) ) ) )
| ( c0 != c0 )
| ( ( sk1
@ ^ [A: n] : c0
@ ^ [A: n] : A )
!= ( sk1
@ ^ [A: n] : A
@ ^ [A: n] : sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[426,4599]) ).
thf(6474,plain,
( ( ( sk1
@ ^ [A: n] : A
@ ^ [A: n] :
( cS
@ ( sk1
@ ^ [B: n] : B
@ ^ [B: n] :
( sk1
@ ^ [C: n] : C
@ ^ [C: n] : B ) ) ) )
!= ( cS
@ ( sk1
@ ^ [A: n] : A
@ ^ [A: n] :
( sk1
@ ^ [B: n] : B
@ ^ [B: n] : A ) ) ) )
| ( ( sk1
@ ^ [A: n] : c0
@ ^ [A: n] : A )
!= ( sk1
@ ^ [A: n] : A
@ ^ [A: n] : sk2 ) ) ),
inference(simp,[status(thm)],[6473]) ).
thf(6553,plain,
( ( ( sk1
@ ^ [A: n] : A
@ ^ [A: n] :
( cS
@ ( sk1
@ ^ [B: n] : B
@ ^ [B: n] :
( sk1
@ ^ [C: n] : C
@ ^ [C: n] : B ) ) ) )
!= ( cS
@ ( sk1
@ ^ [A: n] : A
@ ^ [A: n] :
( sk1
@ ^ [B: n] : B
@ ^ [B: n] : A ) ) ) )
| ( ( ^ [A: n] : c0 )
!= ( ^ [A: n] : A ) )
| ( ( ^ [A: n] : A )
!= ( ^ [A: n] : sk2 ) ) ),
inference(simp,[status(thm)],[6474]) ).
thf(223,plain,
! [A: n] :
( ( ( cS @ A )
!= sk2 )
| ( ( cS @ ( c_plus @ c0 @ A ) )
!= ( cS @ A ) ) ),
inference(simp,[status(thm)],[200]) ).
thf(6909,plain,
( ( ( sk1
@ ^ [A: n] :
( cS
@ ( sk1
@ ^ [B: n] : B
@ ^ [B: n] :
( sk1
@ ^ [C: n] : B
@ ^ [C: n] : C ) ) )
@ ^ [A: n] : A )
!= ( cS
@ ( sk1
@ ^ [A: n] : A
@ ^ [A: n] :
( sk1
@ ^ [B: n] : A
@ ^ [B: n] : B ) ) ) )
| ( c0 != c0 )
| ( ( sk1
@ ^ [A: n] : A
@ ^ [A: n] : c0 )
!= ( sk1
@ ^ [A: n] : sk2
@ ^ [A: n] : A ) ) ),
inference(paramod_ordered,[status(thm)],[636,4601]) ).
thf(6910,plain,
( ( ( sk1
@ ^ [A: n] :
( cS
@ ( sk1
@ ^ [B: n] : B
@ ^ [B: n] :
( sk1
@ ^ [C: n] : B
@ ^ [C: n] : C ) ) )
@ ^ [A: n] : A )
!= ( cS
@ ( sk1
@ ^ [A: n] : A
@ ^ [A: n] :
( sk1
@ ^ [B: n] : A
@ ^ [B: n] : B ) ) ) )
| ( ( sk1
@ ^ [A: n] : A
@ ^ [A: n] : c0 )
!= ( sk1
@ ^ [A: n] : sk2
@ ^ [A: n] : A ) ) ),
inference(simp,[status(thm)],[6909]) ).
thf(7016,plain,
( ( ( sk1
@ ^ [A: n] :
( cS
@ ( sk1
@ ^ [B: n] : B
@ ^ [B: n] :
( sk1
@ ^ [C: n] : B
@ ^ [C: n] : C ) ) )
@ ^ [A: n] : A )
!= ( cS
@ ( sk1
@ ^ [A: n] : A
@ ^ [A: n] :
( sk1
@ ^ [B: n] : A
@ ^ [B: n] : B ) ) ) )
| ( ( ^ [A: n] : A )
!= ( ^ [A: n] : sk2 ) )
| ( ( ^ [A: n] : c0 )
!= ( ^ [A: n] : A ) ) ),
inference(simp,[status(thm)],[6910]) ).
thf(4488,plain,
! [A: n > n] :
( ( ( A @ c0 )
!= c0 )
| ( ( cS
@ ( sk1
@ ^ [B: n] : B
@ A ) )
!= c0 )
| ( ( A @ sk2 )
!= c0 )
| ( ( sk1
@ ^ [B: n] : c0
@ ^ [B: n] : B )
!= ( A
@ ( cS
@ ( sk1
@ ^ [B: n] : B
@ A ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[426,76]) ).
thf(4654,plain,
( ( ( sk1
@ ^ [A: n] : c0
@ ^ [A: n] : A )
!= c0 )
| ( ( cS
@ ( sk1
@ ^ [A: n] : A
@ ^ [A: n] :
( sk1
@ ^ [B: n] : c0
@ ^ [B: n] : B ) ) )
!= c0 )
| ( ( sk1
@ ^ [A: n] : c0
@ ^ [A: n] : A )
!= c0 ) ),
inference(pre_uni,[status(thm)],[4488:[bind(A,$thf( ^ [B: n] : ( sk1 @ ^ [C: n] : c0 @ ^ [C: n] : C ) ))]]) ).
thf(4714,plain,
( ( ( sk1
@ ^ [A: n] : c0
@ ^ [A: n] : A )
!= c0 )
| ( ( cS
@ ( sk1
@ ^ [A: n] : A
@ ^ [A: n] :
( sk1
@ ^ [B: n] : c0
@ ^ [B: n] : B ) ) )
!= c0 ) ),
inference(simp,[status(thm)],[4654]) ).
thf(4875,plain,
( ( c0 != c0 )
| ( ( cS
@ ( sk1
@ ^ [A: n] : A
@ ^ [A: n] : c0 ) )
!= c0 ) ),
inference(rewrite,[status(thm)],[4714,426]) ).
thf(4876,plain,
( ( cS
@ ( sk1
@ ^ [A: n] : A
@ ^ [A: n] : c0 ) )
!= c0 ),
inference(simp,[status(thm)],[4875]) ).
thf(83,plain,
! [A: n > n] :
( ( ( A @ c0 )
!= ( c_plus @ c0 @ sk2 ) )
| ( ( A
@ ( cS
@ ( sk1
@ ^ [B: n] : ( c_plus @ B @ sk2 )
@ A ) ) )
!= ( c_plus
@ ( cS
@ ( sk1
@ ^ [B: n] : ( c_plus @ B @ sk2 )
@ A ) )
@ sk2 ) )
| ( ( A @ c0 )
!= sk2 ) ),
inference(pre_uni,[status(thm)],[32:[bind(A,$thf( A )),bind(B,$thf( ^ [D: n] : ( c_plus @ D @ sk2 ) )),bind(C,$thf( c0 ))]]) ).
thf(2128,plain,
! [B: n,A: n] :
( ( ( cS @ ( cS @ ( cS @ A ) ) )
!= sk2 )
| ( ( cS @ ( cS @ ( cS @ B ) ) )
!= sk2 )
| ( ( c_plus @ A @ c0 )
!= ( c_plus @ c0 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[13,1337]) ).
thf(2129,plain,
( ( ( cS @ ( cS @ ( cS @ c0 ) ) )
!= sk2 )
| ( ( cS @ ( cS @ ( cS @ c0 ) ) )
!= sk2 ) ),
inference(pattern_uni,[status(thm)],[2128:[bind(A,$thf( c0 )),bind(B,$thf( c0 ))]]) ).
thf(2438,plain,
( ( cS @ ( cS @ ( cS @ c0 ) ) )
!= sk2 ),
inference(simp,[status(thm)],[2129]) ).
thf(9257,plain,
$false,
inference(e,[status(thm)],[1337,6643,20,74,248,224,225,426,48,1336,8336,7680,4777,13,1246,17,4599,81,4601,76,66,6553,636,223,3,11,175,7016,19,4876,15,83,2438]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : NUM827^5 : TPTP v9.3.1. Bugfixed v5.3.0.
% 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
% 0.24/0.30 % Computer : n004.cluster.edu
% 0.24/0.30 % Model : x86_64 x86_64
% 0.24/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.24/0.30 % Memory : 8046.5625MB
% 0.24/0.30 % OS : Linux 6.8.0-71-generic
% 0.24/0.30 % CPULimit : 300
% 0.24/0.30 % WCLimit : 300
% 0.24/0.30 % DateTime : Tue Sep 29 13:03:07 UTC 2026
% 0.24/0.30 % CPUTime :
% 0.24/0.30 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
% 1.13/1.02 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.64/1.24 % [INFO] Parsing done (215ms).
% 1.64/1.26 % [INFO] Running in sequential loop mode.
% 2.40/1.74 % [INFO] eprover registered as external prover.
% 2.40/1.75 % [INFO] Scanning for conjecture ...
% 2.59/1.87 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.78/1.91 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.78/1.91 % [INFO] Problem is higher-order (TPTP THF).
% 2.78/1.92 % [INFO] Type checking passed.
% 2.78/1.92 % [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 ...
% 80.10/21.22 % External prover 'e' found a proof!
% 80.10/21.22 % [INFO] Killing All external provers ...
% 80.10/21.22 % Time passed: 20717ms (effective reasoning time: 19957ms)
% 80.10/21.23 % 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)>
% 80.10/21.23 % Axioms used in derivation (0):
% 80.10/21.23 % No. of inferences in proof: 97
% 80.10/21.23 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 20717 ms resp. 19957 ms w/o parsing
% 69.57/21.38 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 69.57/21.39 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------