%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM817^5 : 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 : n014.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 6.55s 3.11s
% Output : Refutation 6.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of formulae : 33 ( 12 unt; 0 typ; 4 def)
% Number of atoms : 59 ( 52 equ; 5 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 266 ( 50 ~; 37 |; 10 &; 154 @)
% ( 0 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 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 : 74 ( 7 ^; 60 !; 5 ?; 74 :)
% ( 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 > $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] :
@+[C: $i] :
~ ( ( A @ C )
=> ( A @ ( cS @ ( cS @ C ) ) ) ) ) ) ).
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 ) ) )
=> ? [A: $i] : ( cODD1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM405) ).
thf(2,negated_conjecture,
~ ( ( ! [A: $i] :
( ( cS @ A )
!= c0 )
& ! [A: $i,B: $i] :
( ( ( cS @ A )
= ( cS @ B ) )
=> ( A = B ) ) )
=> ? [A: $i] : ( cODD1 @ A ) ),
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] :
~ ! [B: $i > $o] :
( ( ( B @ c0 )
& ! [C: $i] :
( ( B @ C )
=> ( B @ ( cS @ ( cS @ C ) ) ) ) )
=> ( B @ A ) ) ),
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,B: $i > $o] :
( ( ( B @ c0 )
& ! [C: $i] :
( ( B @ C )
=> ( B @ ( cS @ ( cS @ C ) ) ) ) )
=> ( B @ A ) ) ),
inference(miniscope,[status(thm)],[3]) ).
thf(5,plain,
! [E: $i > $o,D: $i,C: $i,B: $i,A: $i] :
( ( ( cS @ A )
!= c0 )
& ( ( ( cS @ B )
!= ( cS @ C ) )
| ( B = C ) )
& ( ~ ( E @ c0 )
| ( E @ ( sk1 @ E @ D ) )
| ( E @ D ) )
& ( ~ ( E @ c0 )
| ~ ( E @ ( cS @ ( cS @ ( sk1 @ E @ D ) ) ) )
| ( E @ D ) ) ),
inference(cnf,[status(esa)],[4]) ).
thf(8,plain,
! [B: $i > $o,A: $i] :
( ~ ( B @ c0 )
| ( B @ ( sk1 @ B @ A ) )
| ( B @ A ) ),
inference(cnfConj,[status(thm)],[5]) ).
thf(10,plain,
! [A: $i] :
( ( c0 != c0 )
| ( c0
= ( sk1 @ ( (=) @ $i @ c0 ) @ A ) )
| ( c0 = A ) ),
inference(replace_leibeq,[status(thm)],[8:[bind(A,$thf( A )),bind(B,$thf( (=) @ $i @ c0 ))]]) ).
thf(12,plain,
! [A: $i] :
( ( c0 != c0 )
| ( ( sk1 @ ( (=) @ $i @ c0 ) @ A )
= c0 )
| ( c0 = A ) ),
inference(lifteq,[status(thm)],[10]) ).
thf(13,plain,
! [A: $i] :
( ( ( sk1 @ ( (=) @ $i @ c0 ) @ A )
= c0 )
| ( c0 = A ) ),
inference(simp,[status(thm)],[12]) ).
thf(24,plain,
! [A: $i] :
( ( c0 = A )
| ( ( sk1 @ ( (=) @ $i @ c0 ) @ A )
!= A )
| ( c0 != c0 ) ),
inference(eqfactor_ordered,[status(thm)],[13]) ).
thf(25,plain,
! [A: $i] :
( ( c0 = A )
| ( ( sk1 @ ( (=) @ $i @ c0 ) @ A )
!= A ) ),
inference(simp,[status(thm)],[24]) ).
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(22,plain,
! [B: $i > $o,A: $i] :
( ~ ( B @ c0 )
| ( B @ ( sk1 @ B @ A ) )
| ( B @ A ) ),
inference(simp,[status(thm)],[8]) ).
thf(110,plain,
! [B: $i > $o,A: $i] :
( ~ ~ ( B @ c0 )
| ~ ( B
@ ( sk1
@ ^ [C: $i] :
~ ( B @ C )
@ A ) )
| ~ ( B @ A ) ),
inference(prim_subst,[status(thm)],[22:[bind(A,$thf( A )),bind(B,$thf( ^ [D: $i] : ~ ( C @ D ) ))]]) ).
thf(153,plain,
! [B: $i > $o,A: $i] :
( ( B @ c0 )
| ~ ( B
@ ( sk1
@ ^ [C: $i] :
~ ( B @ C )
@ A ) )
| ~ ( B @ A ) ),
inference(cnf,[status(esa)],[110]) ).
thf(154,plain,
! [B: $i > $o,A: $i] :
( ( B @ c0 )
| ~ ( B
@ ( sk1
@ ^ [C: $i] :
~ ( B @ C )
@ A ) )
| ~ ( B @ A ) ),
inference(simp,[status(thm)],[153]) ).
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(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(9,plain,
! [B: $i > $o,A: $i] :
( ~ ( B @ c0 )
| ~ ( B @ ( cS @ ( cS @ ( sk1 @ B @ A ) ) ) )
| ( B @ A ) ),
inference(cnfConj,[status(thm)],[5]) ).
thf(15,plain,
! [B: $i > $o,A: $i] :
( ~ ( B @ c0 )
| ~ ( B @ ( cS @ ( cS @ ( sk1 @ B @ A ) ) ) )
| ( B @ A ) ),
inference(simp,[status(thm)],[9]) ).
thf(28,plain,
! [B: $i > $o,A: $i] :
( ~ ( B @ c0 )
| ( B @ A )
| ( ( B @ ( cS @ ( cS @ ( sk1 @ B @ A ) ) ) )
!= ( B @ c0 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[15]) ).
thf(44,plain,
! [B: $i > $o,A: $i] :
( ~ ( B @ c0 )
| ( B @ A )
| ( ( B @ ( cS @ ( cS @ ( sk1 @ B @ A ) ) ) )
!= ( B @ c0 ) ) ),
inference(pre_uni,[status(thm)],[28:[]]) ).
thf(45,plain,
! [B: $i > $o,A: $i] :
( ( B @ A )
| ~ ( B @ c0 )
| ( ( B @ ( cS @ ( cS @ ( sk1 @ B @ A ) ) ) )
!= ( B @ c0 ) ) ),
inference(pre_uni,[status(thm)],[44:[]]) ).
thf(305,plain,
$false,
inference(e,[status(thm)],[25,14,13,22,3,154,23,15,45,17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM817^5 : TPTP v9.3.1. Bugfixed v5.2.0.
% 0.00/0.07 % 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
% 0.10/0.19 % Computer : n014.cluster.edu
% 0.10/0.19 % Model : x86_64 x86_64
% 0.10/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.19 % Memory : 8046.5625MB
% 0.10/0.19 % OS : Linux 6.8.0-71-generic
% 0.10/0.19 % CPULimit : 300
% 0.10/0.19 % WCLimit : 300
% 0.10/0.19 % DateTime : Tue Sep 29 13:02:30 UTC 2026
% 0.10/0.19 % CPUTime :
% 0.10/0.19 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
% 0.90/0.77 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.26/0.96 % [INFO] Parsing done (184ms).
% 1.26/0.97 % [INFO] Running in sequential loop mode.
% 1.86/1.37 % [INFO] eprover registered as external prover.
% 1.86/1.38 % [INFO] Scanning for conjecture ...
% 2.07/1.48 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.24/1.52 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.24/1.52 % [INFO] Problem is higher-order (TPTP THF).
% 2.24/1.52 % [INFO] Type checking passed.
% 2.24/1.53 % [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 ...
% 6.55/3.10 % External prover 'e' found a proof!
% 6.55/3.10 % [INFO] Killing All external provers ...
% 6.55/3.11 % Time passed: 2774ms (effective reasoning time: 2124ms)
% 6.55/3.11 % 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)>
% 6.55/3.11 % Axioms used in derivation (0):
% 6.55/3.11 % No. of inferences in proof: 29
% 6.55/3.11 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2774 ms resp. 2124 ms w/o parsing
% 6.94/3.16 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 6.94/3.16 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------