%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : PUZ107^5 : TPTP v9.3.1. Bugfixed v6.2.0.
% 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 : n010.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 08:20:47 AM UTC 2026
% Result : Theorem 3.69s 1.86s
% Output : Refutation 4.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 10
% Syntax : Number of formulae : 30 ( 16 unt; 0 typ; 9 def)
% Number of atoms : 147 ( 127 equ; 0 cnn)
% Maximal formula atoms : 21 ( 4 avg)
% Number of connectives : 318 ( 47 ~; 29 |; 78 &; 152 @)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 34 ( 34 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 10 usr; 4 con; 0-4 aty)
% Number of variables : 114 ( 15 ^; 60 !; 34 ?; 114 :)
% ( 0 !>; 0 ?*; 0 @-; 5 @+)
% Comments :
%------------------------------------------------------------------------------
thf(c1_decl,type,
c1: $i ).
thf(cCKB_FIN_decl,type,
cCKB_FIN: ( $i > $i > $o ) > $o ).
thf(cCKB_INF_decl,type,
cCKB_INF: ( $i > $i > $o ) > $o ).
thf(cCKB_INJ_decl,type,
cCKB_INJ: ( $i > $i > $i > $i > $o ) > $o ).
thf(cCKB_XPL_decl,type,
cCKB_XPL: ( $i > $i > $i > $i > $o ) > ( $i > $i > $o ) > $i > $i > $o ).
thf(sk1_decl,type,
sk1: $i > $i > $i > $i > $o ).
thf(sk2_decl,type,
sk2: $i ).
thf(sk3_decl,type,
sk3: $i ).
thf(sk4_decl,type,
sk4: $i > $i > $i ).
thf(sk5_decl,type,
sk5: $i > $i > $i ).
thf(cCKB_FIN_def,definition,
( cCKB_FIN
= ( ^ [A: $i > $i > $o] :
~ ( cCKB_INF @ A ) ) ) ).
thf(cCKB_INF_def,definition,
( cCKB_INF
= ( ^ [A: $i > $i > $o] :
? [B: $i > $i > $i > $i > $o,C: $i,D: $i] :
( ( cCKB_INJ @ B )
& ( cCKB_XPL @ B @ A @ C @ D ) ) ) ) ).
thf(cCKB_INJ_def,definition,
( cCKB_INJ
= ( ^ [A: $i > $i > $i > $i > $o] :
! [B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( A @ B @ C @ F @ G )
& ( A @ D @ E @ F @ G ) )
=> ( ( B = D )
& ( C = E ) ) ) ) ) ).
thf(cCKB_XPL_def,definition,
( cCKB_XPL
= ( ^ [A: $i > $i > $i > $i > $o,B: $i > $i > $o,C: $i,D: $i] :
( ( B @ C @ D )
& ! [E: $i,F: $i] :
( ( B @ E @ F )
=> ? [G: $i,H: $i] :
( ( A @ E @ F @ G @ H )
& ( B @ G @ H )
& ~ ( ( G = C )
& ( H = D ) ) ) ) ) ) ) ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i > $i > $i > $i > $o] :
( ! [B: $i,C: $i,D: $i,E: $i] :
( ? [F: $i,G: $i] :
( ( A @ B @ C @ F @ G )
& ( A @ D @ E @ F @ G ) )
=> ( ( B = D )
& ( C = E ) ) )
& ? [B: $i,C: $i] :
( ( B = c1 )
& ( C = c1 )
& ! [D: $i,E: $i] :
( ( ( D = c1 )
& ( E = c1 ) )
=> ? [F: $i,G: $i] :
( ( A @ D @ E @ F @ G )
& ( F = c1 )
& ( G = c1 )
& ~ ( ( F = B )
& ( G = C ) ) ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
? [B: $i] :
( ( A = c1 )
& ( B = c1 )
& ! [C: $i,D: $i] :
( ( ( C = c1 )
& ( D = c1 ) )
=> ? [E: $i,F: $i] :
( ( sk1 @ C @ D @ E @ F )
& ( E = c1 )
& ( F = c1 )
& ~ ( ( E = A )
& ( F = B ) ) ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: $i] :
( ( sk2 = c1 )
& ( A = c1 )
& ! [B: $i,C: $i] :
( ( ( B = c1 )
& ( C = c1 ) )
=> ? [D: $i,E: $i] :
( ( sk1 @ B @ C @ D @ E )
& ( D = c1 )
& ( E = c1 )
& ~ ( ( D = sk2 )
& ( E = A ) ) ) ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
? [D: $i] :
( ( sk1 @ B @ A @ C @ D )
& ( C = c1 )
& ( D = c1 )
& ~ ( ( C = sk2 )
& ( D = sk3 ) ) ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
( ( sk1 @ B @ A @ ( sk4 @ A @ B ) @ C )
& ( ( sk4 @ A @ B )
= c1 )
& ( C = c1 )
& ~ ( ( ( sk4 @ A @ B )
= sk2 )
& ( C = sk3 ) ) ) ) ) ).
thf(1,conjecture,
( cCKB_FIN
@ ^ [A: $i,B: $i] :
( ( A = c1 )
& ( B = c1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cL3000) ).
thf(2,negated_conjecture,
~ ( cCKB_FIN
@ ^ [A: $i,B: $i] :
( ( A = c1 )
& ( B = c1 ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ~ ? [A: $i > $i > $i > $i > $o,B: $i,C: $i] :
( ! [D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
( ( ( A @ D @ E @ H @ I )
& ( A @ F @ G @ H @ I ) )
=> ( ( D = F )
& ( E = G ) ) )
& ( B = c1 )
& ( C = c1 )
& ! [D: $i,E: $i] :
( ( ( D = c1 )
& ( E = c1 ) )
=> ? [F: $i,G: $i] :
( ( A @ D @ E @ F @ G )
& ( F = c1 )
& ( G = c1 )
& ~ ( ( F = B )
& ( G = C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
? [A: $i > $i > $i > $i > $o,B: $i,C: $i] :
( ! [D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
( ( ( A @ D @ E @ H @ I )
& ( A @ F @ G @ H @ I ) )
=> ( ( D = F )
& ( E = G ) ) )
& ( B = c1 )
& ( C = c1 )
& ! [D: $i,E: $i] :
( ( ( D = c1 )
& ( E = c1 ) )
=> ? [F: $i,G: $i] :
( ( A @ D @ E @ F @ G )
& ( F = c1 )
& ( G = c1 )
& ~ ( ( F = B )
& ( G = C ) ) ) ) ),
inference(polarity_switch,[status(thm)],[3]) ).
thf(5,plain,
? [A: $i > $i > $i > $i > $o] :
( ! [B: $i,C: $i,D: $i,E: $i] :
( ? [F: $i,G: $i] :
( ( A @ B @ C @ F @ G )
& ( A @ D @ E @ F @ G ) )
=> ( ( B = D )
& ( C = E ) ) )
& ? [B: $i,C: $i] :
( ( B = c1 )
& ( C = c1 )
& ! [D: $i,E: $i] :
( ( ( D = c1 )
& ( E = c1 ) )
=> ? [F: $i,G: $i] :
( ( A @ D @ E @ F @ G )
& ( F = c1 )
& ( G = c1 )
& ~ ( ( F = B )
& ( G = C ) ) ) ) ) ),
inference(miniscope,[status(thm)],[4]) ).
thf(6,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ~ ( sk1 @ A @ B @ E @ F )
| ~ ( sk1 @ C @ D @ E @ F )
| ( A = C ) )
& ( ~ ( sk1 @ A @ B @ E @ F )
| ~ ( sk1 @ C @ D @ E @ F )
| ( B = D ) )
& ( sk2 = c1 )
& ( sk3 = c1 )
& ( ( G != c1 )
| ( H != c1 )
| ( sk1 @ G @ H @ ( sk4 @ H @ G ) @ ( sk5 @ H @ G ) ) )
& ( ( G != c1 )
| ( H != c1 )
| ( ( sk4 @ H @ G )
= c1 ) )
& ( ( G != c1 )
| ( H != c1 )
| ( ( sk5 @ H @ G )
= c1 ) )
& ( ( G != c1 )
| ( H != c1 )
| ( ( sk4 @ H @ G )
!= sk2 )
| ( ( sk5 @ H @ G )
!= sk3 ) ) ),
inference(cnf,[status(esa)],[5]) ).
thf(11,plain,
! [B: $i,A: $i] :
( ( A != c1 )
| ( B != c1 )
| ( ( sk4 @ B @ A )
!= sk2 )
| ( ( sk5 @ B @ A )
!= sk3 ) ),
inference(cnfConj,[status(thm)],[6]) ).
thf(23,plain,
! [B: $i,A: $i] :
( ( A != c1 )
| ( B != c1 )
| ( ( sk4 @ B @ A )
!= sk2 )
| ( ( sk5 @ B @ A )
!= sk3 ) ),
inference(lifteq,[status(thm)],[11]) ).
thf(24,plain,
( ( ( sk4 @ c1 @ c1 )
!= sk2 )
| ( ( sk5 @ c1 @ c1 )
!= sk3 ) ),
inference(simp,[status(thm)],[23]) ).
thf(9,plain,
! [B: $i,A: $i] :
( ( A != c1 )
| ( B != c1 )
| ( ( sk5 @ B @ A )
= c1 ) ),
inference(cnfConj,[status(thm)],[6]) ).
thf(17,plain,
! [B: $i,A: $i] :
( ( A != c1 )
| ( B != c1 )
| ( ( sk5 @ B @ A )
= c1 ) ),
inference(lifteq,[status(thm)],[9]) ).
thf(18,plain,
( ( sk5 @ c1 @ c1 )
= c1 ),
inference(simp,[status(thm)],[17]) ).
thf(13,plain,
sk3 = c1,
inference(cnfConj,[status(thm)],[6]) ).
thf(19,plain,
sk3 = c1,
inference(lifteq,[status(thm)],[13]) ).
thf(12,plain,
! [B: $i,A: $i] :
( ( A != c1 )
| ( B != c1 )
| ( ( sk4 @ B @ A )
= c1 ) ),
inference(cnfConj,[status(thm)],[6]) ).
thf(20,plain,
! [B: $i,A: $i] :
( ( A != c1 )
| ( B != c1 )
| ( ( sk4 @ B @ A )
= c1 ) ),
inference(lifteq,[status(thm)],[12]) ).
thf(21,plain,
( ( sk4 @ c1 @ c1 )
= c1 ),
inference(simp,[status(thm)],[20]) ).
thf(10,plain,
sk2 = c1,
inference(cnfConj,[status(thm)],[6]) ).
thf(15,plain,
sk2 = c1,
inference(lifteq,[status(thm)],[10]) ).
thf(27,plain,
( ( c1 != c1 )
| ( c1 != c1 ) ),
inference(rewrite,[status(thm)],[24,18,19,21,15]) ).
thf(28,plain,
$false,
inference(simp,[status(thm)],[27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : PUZ107^5 : TPTP v9.3.1. Bugfixed v6.2.0.
% 0.00/0.10 % 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 : n010.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
% 0.24/0.31 % CPULimit : 300
% 0.24/0.31 % WCLimit : 300
% 0.24/0.31 % DateTime : Tue Sep 29 13:23:48 UTC 2026
% 0.24/0.31 % CPUTime :
% 0.24/0.31 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
% 0.92/0.78 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.34/0.94 % [INFO] Parsing done (160ms).
% 1.34/0.95 % [INFO] Running in sequential loop mode.
% 1.96/1.24 % [INFO] eprover registered as external prover.
% 1.96/1.25 % [INFO] Scanning for conjecture ...
% 2.23/1.33 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.23/1.35 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.23/1.35 % [INFO] Problem is higher-order (TPTP THF).
% 2.23/1.35 % [INFO] Type checking passed.
% 2.23/1.35 % [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 ...
% 3.69/1.86 % [INFO] Killing All external provers ...
% 3.69/1.86 % Time passed: 1421ms (effective reasoning time: 901ms)
% 3.69/1.86 % 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)>
% 3.69/1.86 % Axioms used in derivation (0):
% 3.69/1.86 % No. of inferences in proof: 21
% 3.69/1.86 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1421 ms resp. 901 ms w/o parsing
% 4.02/1.94 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.02/1.94 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------