%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM816^5 : TPTP v9.3.1. Bugfixed v5.2.0.
% 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 : n013.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 08:18:14 AM UTC 2026
% Result : Theorem 6.59s 3.05s
% Output : Refutation 6.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of formulae : 37 ( 14 unt; 0 typ; 4 def)
% Number of atoms : 68 ( 61 equ; 7 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 295 ( 54 ~; 40 |; 10 &; 176 @)
% ( 0 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 17 ( 17 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 53 ( 6 ^; 43 !; 2 ?; 53 :)
% ( 0 !>; 0 ?*; 0 @-; 2 @+)
% Comments :
%------------------------------------------------------------------------------
thf(c0_decl,type,
c0: $i ).
thf(cS_decl,type,
cS: $i > $i ).
thf(cEVEN1_decl,type,
cEVEN1: $i > $o ).
thf(cODD1_decl,type,
cODD1: $i > $o ).
thf(sk1_decl,type,
sk1: ( $i > $o ) > $i ).
thf(sk2_decl,type,
sk2: $i > $i ).
thf(cEVEN1_def,definition,
( cEVEN1
= ( ^ [A: $i] :
! [B: $i > $o] :
( ( ( B @ c0 )
& ! [C: $i] :
( ( B @ C )
=> ( B @ ( cS @ ( cS @ C ) ) ) ) )
=> ( B @ A ) ) ) ) ).
thf(cODD1_def,definition,
( cODD1
= ( ^ [A: $i] :
~ ( cEVEN1 @ A ) ) ) ).
thf(sk1_def,definition,
( sk1
= ( ^ [A: $i > $o] :
@+[B: $i] :
~ ( ( A @ B )
=> ( A @ ( cS @ ( cS @ B ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i > $i] :
! [B: $i] :
( ( A @ ( cS @ B ) )
= B ) ) ) ).
thf(1,conjecture,
( ( ! [A: $i] :
( ( cS @ A )
!= c0 )
& ! [A: $i,B: $i] :
( ( ( cS @ A )
= ( cS @ B ) )
=> ( A = B ) ) )
=> ( cODD1 @ ( cS @ c0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM406) ).
thf(2,negated_conjecture,
~ ( ( ! [A: $i] :
( ( cS @ A )
!= c0 )
& ! [A: $i,B: $i] :
( ( ( cS @ A )
= ( cS @ B ) )
=> ( A = B ) ) )
=> ( cODD1 @ ( cS @ c0 ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ( ! [A: $i] :
( ( cS @ A )
!= c0 )
& ! [A: $i,B: $i] :
( ( ( cS @ A )
= ( cS @ B ) )
=> ( A = B ) ) )
=> ~ ! [A: $i > $o] :
( ( ( A @ c0 )
& ! [B: $i] :
( ( A @ B )
=> ( A @ ( cS @ ( cS @ B ) ) ) ) )
=> ( A @ ( cS @ c0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
~ ( ( ~ ? [A: $i] :
( ( cS @ A )
= c0 )
& ! [A: $i,B: $i] :
( ( ( cS @ A )
= ( cS @ B ) )
=> ( A = B ) ) )
=> ~ ! [A: $i > $o] :
( ( ( A @ c0 )
& ! [B: $i] :
( ( A @ B )
=> ( A @ ( cS @ ( cS @ B ) ) ) ) )
=> ( A @ ( cS @ c0 ) ) ) ),
inference(miniscope,[status(thm)],[3]) ).
thf(5,plain,
! [D: $i > $o,C: $i,B: $i,A: $i] :
( ( ( cS @ A )
!= c0 )
& ( ( ( cS @ B )
!= ( cS @ C ) )
| ( B = C ) )
& ( ~ ( D @ c0 )
| ( D @ ( sk1 @ D ) )
| ( D @ ( cS @ c0 ) ) )
& ( ~ ( D @ c0 )
| ~ ( D @ ( cS @ ( cS @ ( sk1 @ D ) ) ) )
| ( D @ ( cS @ c0 ) ) ) ),
inference(cnf,[status(esa)],[4]) ).
thf(8,plain,
! [A: $i > $o] :
( ~ ( A @ c0 )
| ( A @ ( sk1 @ A ) )
| ( A @ ( cS @ c0 ) ) ),
inference(cnfConj,[status(thm)],[5]) ).
thf(10,plain,
( ( c0 != c0 )
| ( c0
= ( sk1 @ ( (=) @ $i @ c0 ) ) )
| ( c0
= ( cS @ c0 ) ) ),
inference(replace_leibeq,[status(thm)],[8:[bind(A,$thf( (=) @ $i @ c0 ))]]) ).
thf(12,plain,
( ( c0 != c0 )
| ( ( sk1 @ ( (=) @ $i @ c0 ) )
= c0 )
| ( ( cS @ c0 )
= c0 ) ),
inference(lifteq,[status(thm)],[10]) ).
thf(13,plain,
( ( ( sk1 @ ( (=) @ $i @ c0 ) )
= c0 )
| ( ( cS @ c0 )
= c0 ) ),
inference(simp,[status(thm)],[12]) ).
thf(6,plain,
! [A: $i] :
( ( cS @ A )
!= c0 ),
inference(cnfConj,[status(thm)],[5]) ).
thf(14,plain,
! [A: $i] :
( ( cS @ A )
!= c0 ),
inference(lifteq,[status(thm)],[6]) ).
thf(24,plain,
( ( sk1 @ ( (=) @ $i @ c0 ) )
= c0 ),
inference(simplifyReflect,[status(thm)],[13,14]) ).
thf(7,plain,
! [B: $i,A: $i] :
( ( ( cS @ A )
!= ( cS @ B ) )
| ( A = B ) ),
inference(cnfConj,[status(thm)],[5]) ).
thf(16,plain,
! [B: $i,A: $i] :
( ( ( cS @ A )
!= ( cS @ B ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[7]) ).
thf(17,plain,
! [B: $i,A: $i] :
( ( ( cS @ A )
!= ( cS @ B ) )
| ( A = B ) ),
inference(simp,[status(thm)],[16]) ).
thf(22,plain,
! [A: $i > $o] :
( ~ ( A @ c0 )
| ( A @ ( sk1 @ A ) )
| ( A @ ( cS @ c0 ) ) ),
inference(simp,[status(thm)],[8]) ).
thf(111,plain,
! [A: $i > $o] :
( ~ ~ ( A @ c0 )
| ~ ( A
@ ( sk1
@ ^ [B: $i] :
~ ( A @ B ) ) )
| ~ ( A @ ( cS @ c0 ) ) ),
inference(prim_subst,[status(thm)],[22:[bind(A,$thf( ^ [C: $i] : ~ ( B @ C ) ))]]) ).
thf(154,plain,
! [A: $i > $o] :
( ( A @ c0 )
| ~ ( A
@ ( sk1
@ ^ [B: $i] :
~ ( A @ B ) ) )
| ~ ( A @ ( cS @ c0 ) ) ),
inference(cnf,[status(esa)],[111]) ).
thf(155,plain,
! [A: $i > $o] :
( ( A @ c0 )
| ~ ( A
@ ( sk1
@ ^ [B: $i] :
~ ( A @ B ) ) )
| ~ ( A @ ( cS @ c0 ) ) ),
inference(simp,[status(thm)],[154]) ).
thf(9,plain,
! [A: $i > $o] :
( ~ ( A @ c0 )
| ~ ( A @ ( cS @ ( cS @ ( sk1 @ A ) ) ) )
| ( A @ ( cS @ c0 ) ) ),
inference(cnfConj,[status(thm)],[5]) ).
thf(15,plain,
! [A: $i > $o] :
( ~ ( A @ c0 )
| ~ ( A @ ( cS @ ( cS @ ( sk1 @ A ) ) ) )
| ( A @ ( cS @ c0 ) ) ),
inference(simp,[status(thm)],[9]) ).
thf(29,plain,
! [A: $i > $o] :
( ~ ( A @ c0 )
| ( A @ ( cS @ c0 ) )
| ( ( A @ ( cS @ ( cS @ ( sk1 @ A ) ) ) )
!= ( A @ c0 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[15]) ).
thf(43,plain,
! [A: $i > $o] :
( ~ ( A @ c0 )
| ( A @ ( cS @ c0 ) )
| ( ( A @ ( cS @ ( cS @ ( sk1 @ A ) ) ) )
!= ( A @ c0 ) ) ),
inference(pre_uni,[status(thm)],[29:[]]) ).
thf(44,plain,
! [A: $i > $o] :
( ( A @ ( cS @ c0 ) )
| ~ ( A @ c0 )
| ( ( A @ ( cS @ ( cS @ ( sk1 @ A ) ) ) )
!= ( A @ c0 ) ) ),
inference(pre_uni,[status(thm)],[43:[]]) ).
thf(11,plain,
( ( c0 != c0 )
| ( c0
!= ( cS @ ( cS @ ( sk1 @ ( (=) @ $i @ c0 ) ) ) ) )
| ( c0
= ( cS @ c0 ) ) ),
inference(replace_leibeq,[status(thm)],[9:[bind(A,$thf( (=) @ $i @ c0 ))]]) ).
thf(20,plain,
( ( c0 != c0 )
| ( ( cS @ ( cS @ ( sk1 @ ( (=) @ $i @ c0 ) ) ) )
!= c0 )
| ( ( cS @ c0 )
= c0 ) ),
inference(lifteq,[status(thm)],[11]) ).
thf(21,plain,
( ( ( cS @ ( cS @ ( sk1 @ ( (=) @ $i @ c0 ) ) ) )
!= c0 )
| ( ( cS @ c0 )
= c0 ) ),
inference(simp,[status(thm)],[20]) ).
thf(25,plain,
( ( ( cS @ ( cS @ c0 ) )
!= c0 )
| ( ( cS @ c0 )
= c0 ) ),
inference(rewrite,[status(thm)],[21,24]) ).
thf(26,plain,
( ( cS @ ( cS @ c0 ) )
!= c0 ),
inference(simplifyReflect,[status(thm)],[25,14]) ).
thf(18,plain,
? [A: $i > $i] :
! [B: $i] :
( ( A @ ( cS @ B ) )
= B ),
inference(detectInverse,[status(thm)],[17]) ).
thf(19,plain,
! [A: $i] :
( ( sk2 @ ( cS @ A ) )
= A ),
inference(cnf,[status(esa)],[18]) ).
thf(23,plain,
! [A: $i] :
( ( sk2 @ ( cS @ A ) )
= A ),
inference(lifteq,[status(thm)],[19]) ).
thf(324,plain,
$false,
inference(e,[status(thm)],[24,14,17,155,3,15,22,44,26,23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM816^5 : TPTP v9.3.1. Bugfixed v5.2.0.
% 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
% 0.11/0.21 % Computer : n013.cluster.edu
% 0.11/0.21 % Model : x86_64 x86_64
% 0.11/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.21 % Memory : 8046.5625MB
% 0.11/0.21 % OS : Linux 6.8.0-71-generic
% 0.11/0.21 % CPULimit : 300
% 0.11/0.21 % WCLimit : 300
% 0.11/0.21 % DateTime : Tue Sep 29 13:02:01 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
% 0.90/0.79 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.25/0.98 % [INFO] Parsing done (189ms).
% 1.25/0.99 % [INFO] Running in sequential loop mode.
% 2.04/1.40 % [INFO] eprover registered as external prover.
% 2.04/1.41 % [INFO] Scanning for conjecture ...
% 2.23/1.51 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.23/1.54 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.23/1.54 % [INFO] Problem is higher-order (TPTP THF).
% 2.23/1.54 % [INFO] Type checking passed.
% 2.23/1.55 % [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 ...
% 6.59/3.05 % External prover 'e' found a proof!
% 6.59/3.05 % [INFO] Killing All external provers ...
% 6.59/3.05 % Time passed: 2697ms (effective reasoning time: 2051ms)
% 6.59/3.05 % 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)>
% 6.59/3.05 % Axioms used in derivation (0):
% 6.59/3.05 % No. of inferences in proof: 33
% 6.59/3.05 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2697 ms resp. 2051 ms w/o parsing
% 6.59/3.11 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 6.59/3.11 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------