%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM809^5 : TPTP v9.3.1. Bugfixed v5.2.0.
% 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 : n019.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 8.23s 3.40s
% Output : Refutation 8.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 4
% Syntax : Number of formulae : 43 ( 15 unt; 0 typ; 3 def)
% Number of atoms : 125 ( 53 equ; 7 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 387 ( 65 ~; 44 |; 12 &; 255 @)
% ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 13 ( 13 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 6 usr; 6 con; 0-2 aty)
% Number of variables : 76 ( 16 ^; 54 !; 4 ?; 76 :)
% ( 0 !>; 0 ?*; 0 @-; 2 @+)
% Comments :
%------------------------------------------------------------------------------
thf(c0_decl,type,
c0: $i ).
thf(cS_decl,type,
cS: $i > $i ).
thf(r_decl,type,
r: $i > $i > $o ).
thf(cIND_decl,type,
cIND: $o ).
thf(sk1_decl,type,
sk1: ( $i > $o ) > $i ).
thf(sk2_decl,type,
sk2: $i ).
thf(cIND_def,definition,
( cIND
= ( ! [A: $i > $o] :
( ( ( A @ c0 )
& ! [B: $i] :
( ( A @ B )
=> ( A @ ( cS @ B ) ) ) )
=> ! [B: $i] : ( A @ B ) ) ) ) ).
thf(sk1_def,definition,
( sk1
= ( ^ [A: $i > $o] :
@+[B: $i] :
~ ( ( A @ B )
=> ( A @ ( cS @ B ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ? [B: $i] : ( r @ A @ B ) ) ) ).
thf(1,conjecture,
( ( cIND
& ( r @ c0 @ c0 )
& ! [A: $i,B: $i] :
( ( r @ A @ B )
=> ( r @ ( cS @ A ) @ ( cS @ B ) ) ) )
=> ! [A: $i] :
? [B: $i] : ( r @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM130) ).
thf(2,negated_conjecture,
~ ( ( cIND
& ( r @ c0 @ c0 )
& ! [A: $i,B: $i] :
( ( r @ A @ B )
=> ( r @ ( cS @ A ) @ ( cS @ B ) ) ) )
=> ! [A: $i] :
? [B: $i] : ( r @ A @ B ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ( ! [A: $i > $o] :
( ( ( A @ c0 )
& ! [B: $i] :
( ( A @ B )
=> ( A @ ( cS @ B ) ) ) )
=> ! [B: $i] : ( A @ B ) )
& ( r @ c0 @ c0 )
& ! [A: $i,B: $i] :
( ( r @ A @ B )
=> ( r @ ( cS @ A ) @ ( cS @ B ) ) ) )
=> ! [A: $i] :
? [B: $i] : ( r @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i > $o] :
( ( ~ ( A @ c0 )
| ( A @ ( sk1 @ A ) )
| ( A @ B ) )
& ( ~ ( A @ c0 )
| ~ ( A @ ( cS @ ( sk1 @ A ) ) )
| ( A @ B ) )
& ( r @ c0 @ c0 )
& ( ~ ( r @ C @ D )
| ( r @ ( cS @ C ) @ ( cS @ D ) ) )
& ~ ( r @ sk2 @ E ) ),
inference(cnf,[status(esa)],[3]) ).
thf(5,plain,
r @ c0 @ c0,
inference(cnfConj,[status(thm)],[4]) ).
thf(9,plain,
! [B: $i,A: $i > $o] :
( ~ ( A @ c0 )
| ~ ( A @ ( cS @ ( sk1 @ A ) ) )
| ( A @ B ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(7,plain,
! [A: $i] :
~ ( r @ sk2 @ A ),
inference(cnfConj,[status(thm)],[4]) ).
thf(15,plain,
! [A: $i] :
~ ( r @ sk2 @ A ),
inference(simp,[status(thm)],[7]) ).
thf(58,plain,
! [C: $i,B: $i,A: $i > $o] :
( ~ ( A @ c0 )
| ~ ( A @ ( cS @ ( sk1 @ A ) ) )
| ~ $true
| ( ( A @ B )
!= ( r @ sk2 @ C ) ) ),
inference(paramod_ordered,[status(thm)],[9,15]) ).
thf(59,plain,
! [C: $i,B: $i,A: $i > $o] :
( ~ ( A @ c0 )
| ~ ( A @ ( cS @ ( sk1 @ A ) ) )
| ( ( A @ B )
!= ( r @ sk2 @ C ) ) ),
inference(simp,[status(thm)],[58]) ).
thf(95,plain,
! [A: $i > $i] :
( ~ ( r @ c0 @ ( A @ c0 ) )
| ~ ( r
@ ( cS
@ ( sk1
@ ^ [B: $i] : ( r @ B @ ( A @ B ) ) ) )
@ ( A
@ ( cS
@ ( sk1
@ ^ [B: $i] : ( r @ B @ ( A @ B ) ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[59:[bind(A,$thf( ^ [E: $i] : ( r @ E @ ( E @ E ) ) )),bind(B,$thf( sk2 )),bind(C,$thf( E @ sk2 ))]]) ).
thf(133,plain,
! [A: $i > $i] :
( ~ ( r @ c0 @ ( A @ c0 ) )
| ~ ( r
@ ( cS
@ ( sk1
@ ^ [B: $i] : ( r @ B @ ( A @ B ) ) ) )
@ ( A
@ ( cS
@ ( sk1
@ ^ [B: $i] : ( r @ B @ ( A @ B ) ) ) ) ) ) ),
inference(simp,[status(thm)],[95]) ).
thf(18,plain,
! [A: $i] :
( ~ $true
| ( ( r @ sk2 @ A )
!= ( r @ c0 @ c0 ) ) ),
inference(paramod_ordered,[status(thm)],[5,15]) ).
thf(19,plain,
! [A: $i] :
( ( r @ sk2 @ A )
!= ( r @ c0 @ c0 ) ),
inference(simp,[status(thm)],[18]) ).
thf(20,plain,
! [A: $i] :
( ( sk2 != c0 )
| ( A != c0 ) ),
inference(simp,[status(thm)],[19]) ).
thf(21,plain,
sk2 != c0,
inference(simp,[status(thm)],[20]) ).
thf(364,plain,
! [A: $i > $i] :
( ~ $true
| ~ ( r
@ ( cS
@ ( sk1
@ ^ [B: $i] : ( r @ B @ ( A @ B ) ) ) )
@ ( A
@ ( cS
@ ( sk1
@ ^ [B: $i] : ( r @ B @ ( A @ B ) ) ) ) ) )
| ( ( r @ c0 @ ( A @ c0 ) )
!= ( r @ c0 @ c0 ) ) ),
inference(paramod_ordered,[status(thm)],[5,133]) ).
thf(365,plain,
! [A: $i > $i] :
( ~ ( r
@ ( cS
@ ( sk1
@ ^ [B: $i] : ( r @ B @ ( A @ B ) ) ) )
@ ( A
@ ( cS
@ ( sk1
@ ^ [B: $i] : ( r @ B @ ( A @ B ) ) ) ) ) )
| ( ( r @ c0 @ ( A @ c0 ) )
!= ( r @ c0 @ c0 ) ) ),
inference(simp,[status(thm)],[364]) ).
thf(393,plain,
~ ( r
@ ( cS
@ ( sk1
@ ^ [A: $i] : ( r @ A @ c0 ) ) )
@ c0 ),
inference(pre_uni,[status(thm)],[365:[bind(A,$thf( ^ [B: $i] : c0 ))]]) ).
thf(8,plain,
! [B: $i,A: $i > $o] :
( ~ ( A @ c0 )
| ( A @ ( sk1 @ A ) )
| ( A @ B ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(11,plain,
! [A: $i] :
( ( c0 != c0 )
| ( c0
= ( sk1 @ ( (=) @ $i @ c0 ) ) )
| ( c0 = A ) ),
inference(replace_leibeq,[status(thm)],[8:[bind(A,$thf( (=) @ $i @ c0 ))]]) ).
thf(16,plain,
! [A: $i] :
( ( c0 != c0 )
| ( ( sk1 @ ( (=) @ $i @ c0 ) )
= c0 )
| ( c0 = A ) ),
inference(lifteq,[status(thm)],[11]) ).
thf(17,plain,
! [A: $i] :
( ( ( sk1 @ ( (=) @ $i @ c0 ) )
= c0 )
| ( c0 = A ) ),
inference(simp,[status(thm)],[16]) ).
thf(38,plain,
! [A: $i] :
( ( ( sk1 @ ( (=) @ $i @ c0 ) )
= c0 )
| ( c0 != c0 )
| ( A
!= ( sk1 @ ( (=) @ $i @ c0 ) ) ) ),
inference(eqfactor_ordered,[status(thm)],[17]) ).
thf(39,plain,
( ( sk1 @ ( (=) @ $i @ c0 ) )
= c0 ),
inference(pattern_uni,[status(thm)],[38:[bind(A,$thf( sk1 @ ( (=) @ $i @ c0 ) ))]]) ).
thf(443,plain,
( ~ $true
| ( ( r
@ ( cS
@ ( sk1
@ ^ [A: $i] : ( r @ A @ c0 ) ) )
@ c0 )
!= ( r @ c0 @ c0 ) ) ),
inference(paramod_ordered,[status(thm)],[5,393]) ).
thf(444,plain,
( ( r
@ ( cS
@ ( sk1
@ ^ [A: $i] : ( r @ A @ c0 ) ) )
@ c0 )
!= ( r @ c0 @ c0 ) ),
inference(simp,[status(thm)],[443]) ).
thf(457,plain,
( ( ( cS
@ ( sk1
@ ^ [A: $i] : ( r @ A @ c0 ) ) )
!= c0 )
| ( c0 != c0 ) ),
inference(simp,[status(thm)],[444]) ).
thf(469,plain,
( ( cS
@ ( sk1
@ ^ [A: $i] : ( r @ A @ c0 ) ) )
!= c0 ),
inference(simp,[status(thm)],[457]) ).
thf(394,plain,
~ ( r
@ ( cS
@ ( sk1
@ ^ [A: $i] : ( r @ A @ A ) ) )
@ ( cS
@ ( sk1
@ ^ [A: $i] : ( r @ A @ A ) ) ) ),
inference(pre_uni,[status(thm)],[365:[bind(A,$thf( ^ [B: $i] : B ))]]) ).
thf(146,plain,
! [B: $i,A: $i > $o] :
( ~ ( A @ c0 )
| ~ ( A @ ( cS @ c0 ) )
| ( A @ B )
| ( ( sk1 @ ( (=) @ $i @ c0 ) )
!= ( sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[39,9]) ).
thf(147,plain,
! [A: $i] :
( ( c0 != c0 )
| ( c0
!= ( cS @ c0 ) )
| ( c0 = A ) ),
inference(pattern_uni,[status(thm)],[146:[bind(A,$thf( (=) @ $i @ c0 )),bind(B,$thf( B ))]]) ).
thf(148,plain,
! [A: $i] :
( ( c0 != c0 )
| ( ( cS @ c0 )
!= c0 )
| ( c0 = A ) ),
inference(lifteq,[status(thm)],[147]) ).
thf(149,plain,
! [A: $i] :
( ( ( cS @ c0 )
!= c0 )
| ( c0 = A ) ),
inference(simp,[status(thm)],[148]) ).
thf(150,plain,
! [A: $i] :
( ( ( cS @ c0 )
!= c0 )
| ( r @ A @ c0 )
| ( c0 != c0 ) ),
inference(paramod_ordered,[status(thm)],[149,5]) ).
thf(151,plain,
! [A: $i] :
( ( ( cS @ c0 )
!= c0 )
| ( r @ A @ c0 ) ),
inference(pattern_uni,[status(thm)],[150:[]]) ).
thf(205,plain,
! [B: $i,A: $i] :
( ( ( cS @ c0 )
!= c0 )
| ~ $true
| ( ( r @ A @ c0 )
!= ( r @ sk2 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[151,15]) ).
thf(206,plain,
! [B: $i,A: $i] :
( ( ( cS @ c0 )
!= c0 )
| ( ( r @ A @ c0 )
!= ( r @ sk2 @ B ) ) ),
inference(simp,[status(thm)],[205]) ).
thf(207,plain,
( ( cS @ c0 )
!= c0 ),
inference(pattern_uni,[status(thm)],[206:[bind(A,$thf( sk2 )),bind(B,$thf( c0 ))]]) ).
thf(561,plain,
$false,
inference(e,[status(thm)],[5,133,21,9,393,39,15,469,394,3,8,207]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM809^5 : TPTP v9.3.1. Bugfixed v5.2.0.
% 0.00/0.08 % 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
% 0.11/0.21 % Computer : n019.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 13:01:17 UTC 2026
% 0.11/0.21 % CPUTime :
% 0.11/0.21 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
% 0.89/0.79 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.23/0.97 % [INFO] Parsing done (181ms).
% 1.23/0.98 % [INFO] Running in sequential loop mode.
% 1.84/1.39 % [INFO] eprover registered as external prover.
% 2.03/1.40 % [INFO] Scanning for conjecture ...
% 2.21/1.51 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.21/1.54 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.21/1.54 % [INFO] Problem is higher-order (TPTP THF).
% 2.21/1.55 % [INFO] Type checking passed.
% 2.21/1.55 % [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 ...
% 8.23/3.39 % External prover 'e' found a proof!
% 8.23/3.39 % [INFO] Killing All external provers ...
% 8.23/3.39 % Time passed: 3032ms (effective reasoning time: 2401ms)
% 8.23/3.39 % 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)>
% 8.23/3.39 % Axioms used in derivation (0):
% 8.23/3.39 % No. of inferences in proof: 40
% 8.23/3.40 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3032 ms resp. 2401 ms w/o parsing
% 8.76/3.45 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 8.76/3.45 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------