%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU967^5 : TPTP v9.3.1. Released v4.0.0.
% 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 : 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 08:29:39 AM UTC 2026
% Result : Theorem 2.70s 1.22s
% Output : Refutation 2.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 11 ( 4 unt; 0 typ; 2 def)
% Number of atoms : 16 ( 2 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 263 ( 18 ~; 7 |; 18 &; 220 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 11 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 86 ( 86 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 6 usr; 1 con; 0-2 aty)
% Number of variables : 132 ( 56 ^; 12 !; 62 ?; 132 :)
% ( 0 !>; 0 ?*; 0 @-; 2 @+)
% Comments :
%------------------------------------------------------------------------------
thf(cY_0_decl,type,
cY_0: ( ( $i > $i ) > $o ) > $i ).
thf(cG_0_decl,type,
cG_0: ( ( $i > $i ) > $o ) > $i > $i ).
thf(cP_0_decl,type,
cP_0: $i > $o ).
thf(cH_0_decl,type,
cH_0: ( ( $i > $i ) > $o ) > $i > $i ).
thf(sk1_decl,type,
sk1: ( ( $i > $i ) > $i > $o ) > $i ).
thf(sk2_decl,type,
sk2: ( ( $i > $i ) > $i > $o ) > $i ).
thf(sk1_def,definition,
( sk1
= ( ^ [A: ( $i > $i ) > $i > $o] :
@+[B: $i] :
( A
@ ( cG_0
@ ^ [C: $i > $i] :
? [D: $i] : ( A @ C @ D ) )
@ B ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( ^ [A: ( $i > $i ) > $i > $o] :
@+[B: $i] :
( A
@ ( cH_0
@ ^ [C: $i > $i] :
? [D: $i] : ( A @ C @ D ) )
@ B ) ) ) ).
thf(1,conjecture,
~ ! [A: ( $i > $i ) > $i > $o] :
( ? [B: $i] :
( A
@ ( cG_0
@ ^ [C: $i > $i] :
? [D: $i] : ( A @ C @ D ) )
@ B )
& ? [B: $i] :
( A
@ ( cH_0
@ ^ [C: $i > $i] :
? [D: $i] : ( A @ C @ D ) )
@ B )
& ( ~ ? [B: $i] :
( A
@ ^ [C: $i] :
( cG_0
@ ^ [D: $i > $i] :
? [E: $i] : ( A @ D @ E )
@ ( cH_0
@ ^ [D: $i > $i] :
? [E: $i] : ( A @ D @ E )
@ C ) )
@ B )
| ( ( cP_0
@ ( cY_0
@ ^ [B: $i > $i] :
? [C: $i] : ( A @ B @ C ) ) )
& ~ ( cP_0
@ ( cG_0
@ ^ [B: $i > $i] :
? [C: $i] : ( A @ B @ C )
@ ( cY_0
@ ^ [B: $i > $i] :
? [C: $i] : ( A @ B @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cBUGWFFA_pme) ).
thf(2,negated_conjecture,
~ ~ ! [A: ( $i > $i ) > $i > $o] :
( ? [B: $i] :
( A
@ ( cG_0
@ ^ [C: $i > $i] :
? [D: $i] : ( A @ C @ D ) )
@ B )
& ? [B: $i] :
( A
@ ( cH_0
@ ^ [C: $i > $i] :
? [D: $i] : ( A @ C @ D ) )
@ B )
& ( ~ ? [B: $i] :
( A
@ ^ [C: $i] :
( cG_0
@ ^ [D: $i > $i] :
? [E: $i] : ( A @ D @ E )
@ ( cH_0
@ ^ [D: $i > $i] :
? [E: $i] : ( A @ D @ E )
@ C ) )
@ B )
| ( ( cP_0
@ ( cY_0
@ ^ [B: $i > $i] :
? [C: $i] : ( A @ B @ C ) ) )
& ~ ( cP_0
@ ( cG_0
@ ^ [B: $i > $i] :
? [C: $i] : ( A @ B @ C )
@ ( cY_0
@ ^ [B: $i > $i] :
? [C: $i] : ( A @ B @ C ) ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ~ ! [A: ( $i > $i ) > $i > $o] :
( ? [B: $i] :
( A
@ ( cG_0
@ ^ [C: $i > $i] :
? [D: $i] : ( A @ C @ D ) )
@ B )
& ? [B: $i] :
( A
@ ( cH_0
@ ^ [C: $i > $i] :
? [D: $i] : ( A @ C @ D ) )
@ B )
& ( ~ ? [B: $i] :
( A
@ ^ [C: $i] :
( cG_0
@ ^ [D: $i > $i] :
? [E: $i] : ( A @ D @ E )
@ ( cH_0
@ ^ [D: $i > $i] :
? [E: $i] : ( A @ D @ E )
@ C ) )
@ B )
| ( ( cP_0
@ ( cY_0
@ ^ [B: $i > $i] :
? [C: $i] : ( A @ B @ C ) ) )
& ~ ( cP_0
@ ( cG_0
@ ^ [B: $i > $i] :
? [C: $i] : ( A @ B @ C )
@ ( cY_0
@ ^ [B: $i > $i] :
? [C: $i] : ( A @ B @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
! [A: ( $i > $i ) > $i > $o] :
( ? [B: $i] :
( A
@ ( cG_0
@ ^ [C: $i > $i] :
? [D: $i] : ( A @ C @ D ) )
@ B )
& ? [B: $i] :
( A
@ ( cH_0
@ ^ [C: $i > $i] :
? [D: $i] : ( A @ C @ D ) )
@ B )
& ( ~ ? [B: $i] :
( A
@ ^ [C: $i] :
( cG_0
@ ^ [D: $i > $i] :
? [E: $i] : ( A @ D @ E )
@ ( cH_0
@ ^ [D: $i > $i] :
? [E: $i] : ( A @ D @ E )
@ C ) )
@ B )
| ( ( cP_0
@ ( cY_0
@ ^ [B: $i > $i] :
? [C: $i] : ( A @ B @ C ) ) )
& ~ ( cP_0
@ ( cG_0
@ ^ [B: $i > $i] :
? [C: $i] : ( A @ B @ C )
@ ( cY_0
@ ^ [B: $i > $i] :
? [C: $i] : ( A @ B @ C ) ) ) ) ) ) ),
inference(polarity_switch,[status(thm)],[3]) ).
thf(5,plain,
( ! [A: ( $i > $i ) > $i > $o] :
? [B: $i] :
( A
@ ( cG_0
@ ^ [C: $i > $i] :
? [D: $i] : ( A @ C @ D ) )
@ B )
& ! [A: ( $i > $i ) > $i > $o] :
? [B: $i] :
( A
@ ( cH_0
@ ^ [C: $i > $i] :
? [D: $i] : ( A @ C @ D ) )
@ B )
& ! [A: ( $i > $i ) > $i > $o] :
( ~ ? [B: $i] :
( A
@ ^ [C: $i] :
( cG_0
@ ^ [D: $i > $i] :
? [E: $i] : ( A @ D @ E )
@ ( cH_0
@ ^ [D: $i > $i] :
? [E: $i] : ( A @ D @ E )
@ C ) )
@ B )
| ( ( cP_0
@ ( cY_0
@ ^ [B: $i > $i] :
? [C: $i] : ( A @ B @ C ) ) )
& ~ ( cP_0
@ ( cG_0
@ ^ [B: $i > $i] :
? [C: $i] : ( A @ B @ C )
@ ( cY_0
@ ^ [B: $i > $i] :
? [C: $i] : ( A @ B @ C ) ) ) ) ) ) ),
inference(miniscope,[status(thm)],[4]) ).
thf(6,plain,
! [D: $i,C: ( $i > $i ) > $i > $o,B: ( $i > $i ) > $i > $o,A: ( $i > $i ) > $i > $o] :
( ( A
@ ( cG_0
@ ^ [E: $i > $i] :
? [F: $i] : ( A @ E @ F ) )
@ ( sk1 @ A ) )
& ( B
@ ( cH_0
@ ^ [E: $i > $i] :
? [F: $i] : ( B @ E @ F ) )
@ ( sk2 @ B ) )
& ( ~ ( C
@ ^ [E: $i] :
( cG_0
@ ^ [F: $i > $i] :
? [G: $i] : ( C @ F @ G )
@ ( cH_0
@ ^ [F: $i > $i] :
? [G: $i] : ( C @ F @ G )
@ E ) )
@ D )
| ( cP_0
@ ( cY_0
@ ^ [E: $i > $i] :
? [F: $i] : ( C @ E @ F ) ) ) )
& ( ~ ( C
@ ^ [E: $i] :
( cG_0
@ ^ [F: $i > $i] :
? [G: $i] : ( C @ F @ G )
@ ( cH_0
@ ^ [F: $i > $i] :
? [G: $i] : ( C @ F @ G )
@ E ) )
@ D )
| ~ ( cP_0
@ ( cG_0
@ ^ [E: $i > $i] :
? [F: $i] : ( C @ E @ F )
@ ( cY_0
@ ^ [E: $i > $i] :
? [F: $i] : ( C @ E @ F ) ) ) ) ) ),
inference(cnf,[status(esa)],[5]) ).
thf(7,plain,
! [A: ( $i > $i ) > $i > $o] :
( A
@ ( cG_0
@ ^ [B: $i > $i] :
? [C: $i] : ( A @ B @ C ) )
@ ( sk1 @ A ) ),
inference(cnfConj,[status(thm)],[6]) ).
thf(18,plain,
$false,
inference(prim_subst,[status(thm)],[7:[bind(A,$thf( ^ [B: $i > $i] : ^ [C: $i] : $false ))]]) ).
thf(22,plain,
$false,
inference(simp,[status(thm)],[18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU967^5 : TPTP v9.3.1. Released v4.0.0.
% 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
% 0.09/0.19 % Computer : n004.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 14:53:17 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 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
% 0.67/0.50 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.90/0.60 % [INFO] Parsing done (98ms).
% 0.90/0.61 % [INFO] Running in sequential loop mode.
% 1.25/0.79 % [INFO] eprover registered as external prover.
% 1.47/0.80 % [INFO] Scanning for conjecture ...
% 1.47/0.85 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 1.47/0.87 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 1.47/0.87 % [INFO] Problem is higher-order (TPTP THF).
% 1.47/0.87 % [INFO] Type checking passed.
% 1.47/0.87 % [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 ...
% 2.70/1.21 % [INFO] Killing All external provers ...
% 2.70/1.22 % Time passed: 920ms (effective reasoning time: 605ms)
% 2.70/1.22 % 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)>
% 2.70/1.22 % Axioms used in derivation (0):
% 2.70/1.22 % No. of inferences in proof: 9
% 2.70/1.22 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 920 ms resp. 605 ms w/o parsing
% 2.70/1.28 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.70/1.28 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------