%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEV055^5 : 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 : n001.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 08:36:46 AM UTC 2026
% Result : Theorem 7.91s 3.25s
% Output : Refutation 7.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of formulae : 18 ( 10 unt; 0 typ; 4 def)
% Number of atoms : 41 ( 6 equ; 0 cnn)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 304 ( 17 ~; 10 |; 21 &; 215 @)
% ( 0 <=>; 41 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 7 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 42 ( 42 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 106 ( 6 ^; 88 !; 8 ?; 106 :)
% ( 0 !>; 0 ?*; 0 @-; 4 @+)
% Comments :
%------------------------------------------------------------------------------
thf(a_type,type,
a: $tType ).
thf(sk1_decl,type,
sk1: a > a > $o ).
thf(sk2_decl,type,
sk2: ( a > $o ) > a ).
thf(sk3_decl,type,
sk3: a > ( a > $o ) > a ).
thf(sk4_decl,type,
sk4: a > a ).
thf(sk1_def,definition,
( sk1
= ( @+[A: a > a > $o] :
~ ( ( ! [B: a,C: a,D: a] :
( ( ( A @ B @ C )
& ( A @ C @ D ) )
=> ( A @ B @ D ) )
& ? [B: ( a > $o ) > a] :
( ! [C: a > $o,D: a] :
( ( C @ D )
=> ( A @ D @ ( B @ C ) ) )
& ! [C: a > $o,D: a] :
( ! [E: a] :
( ( C @ E )
=> ( A @ E @ D ) )
=> ( A @ ( B @ C ) @ D ) ) ) )
=> ! [B: a > a] :
( ! [C: a,D: a] :
( ( A @ C @ D )
=> ( A @ ( B @ C ) @ ( B @ D ) ) )
=> ? [C: a] : ( A @ C @ ( B @ C ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: ( a > $o ) > a] :
( ! [B: a > $o,C: a] :
( ( B @ C )
=> ( sk1 @ C @ ( A @ B ) ) )
& ! [B: a > $o,C: a] :
( ! [D: a] :
( ( B @ D )
=> ( sk1 @ D @ C ) )
=> ( sk1 @ ( A @ B ) @ C ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( ^ [A: a,B: a > $o] :
@+[C: a] :
~ ( ( B @ C )
=> ( sk1 @ C @ A ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( @+[A: a > a] :
~ ( ! [B: a,C: a] :
( ( sk1 @ B @ C )
=> ( sk1 @ ( A @ B ) @ ( A @ C ) ) )
=> ? [B: a] : ( sk1 @ B @ ( A @ B ) ) ) ) ) ).
thf(1,conjecture,
! [A: a > a > $o,B: ( a > $o ) > a] :
( ( ! [C: a,D: a,E: a] :
( ( ( A @ C @ D )
& ( A @ D @ E ) )
=> ( A @ C @ E ) )
& ! [C: a > $o] :
( ! [D: a] :
( ( C @ D )
=> ( A @ D @ ( B @ C ) ) )
& ! [D: a] :
( ! [E: a] :
( ( C @ E )
=> ( A @ E @ D ) )
=> ( A @ ( B @ C ) @ D ) ) ) )
=> ! [C: a > a] :
( ! [D: a,E: a] :
( ( A @ D @ E )
=> ( A @ ( C @ D ) @ ( C @ E ) ) )
=> ? [D: a] : ( A @ D @ ( C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM402_pme) ).
thf(2,negated_conjecture,
~ ! [A: a > a > $o,B: ( a > $o ) > a] :
( ( ! [C: a,D: a,E: a] :
( ( ( A @ C @ D )
& ( A @ D @ E ) )
=> ( A @ C @ E ) )
& ! [C: a > $o] :
( ! [D: a] :
( ( C @ D )
=> ( A @ D @ ( B @ C ) ) )
& ! [D: a] :
( ! [E: a] :
( ( C @ E )
=> ( A @ E @ D ) )
=> ( A @ ( B @ C ) @ D ) ) ) )
=> ! [C: a > a] :
( ! [D: a,E: a] :
( ( A @ D @ E )
=> ( A @ ( C @ D ) @ ( C @ E ) ) )
=> ? [D: a] : ( A @ D @ ( C @ D ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ! [A: a > a > $o,B: ( a > $o ) > a] :
( ( ! [C: a,D: a,E: a] :
( ( ( A @ C @ D )
& ( A @ D @ E ) )
=> ( A @ C @ E ) )
& ! [C: a > $o] :
( ! [D: a] :
( ( C @ D )
=> ( A @ D @ ( B @ C ) ) )
& ! [D: a] :
( ! [E: a] :
( ( C @ E )
=> ( A @ E @ D ) )
=> ( A @ ( B @ C ) @ D ) ) ) )
=> ! [C: a > a] :
( ! [D: a,E: a] :
( ( A @ D @ E )
=> ( A @ ( C @ D ) @ ( C @ E ) ) )
=> ? [D: a] : ( A @ D @ ( C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
~ ! [A: a > a > $o] :
( ( ! [B: a,C: a,D: a] :
( ( ( A @ B @ C )
& ( A @ C @ D ) )
=> ( A @ B @ D ) )
& ? [B: ( a > $o ) > a] :
( ! [C: a > $o,D: a] :
( ( C @ D )
=> ( A @ D @ ( B @ C ) ) )
& ! [C: a > $o,D: a] :
( ! [E: a] :
( ( C @ E )
=> ( A @ E @ D ) )
=> ( A @ ( B @ C ) @ D ) ) ) )
=> ! [B: a > a] :
( ! [C: a,D: a] :
( ( A @ C @ D )
=> ( A @ ( B @ C ) @ ( B @ D ) ) )
=> ? [C: a] : ( A @ C @ ( B @ C ) ) ) ),
inference(miniscope,[status(thm)],[3]) ).
thf(5,plain,
! [J: a,I: a,H: a,G: a,F: a > $o,E: a,D: a > $o,C: a,B: a,A: a] :
( ( ~ ( sk1 @ A @ B )
| ~ ( sk1 @ B @ C )
| ( sk1 @ A @ C ) )
& ( ~ ( D @ E )
| ( sk1 @ E @ ( sk2 @ D ) ) )
& ( ( F @ ( sk3 @ G @ F ) )
| ( sk1 @ ( sk2 @ F ) @ G ) )
& ( ~ ( sk1 @ ( sk3 @ G @ F ) @ G )
| ( sk1 @ ( sk2 @ F ) @ G ) )
& ( ~ ( sk1 @ H @ I )
| ( sk1 @ ( sk4 @ H ) @ ( sk4 @ I ) ) )
& ~ ( sk1 @ J @ ( sk4 @ J ) ) ),
inference(cnf,[status(esa)],[4]) ).
thf(6,plain,
! [B: a,A: a > $o] :
( ( A @ ( sk3 @ B @ A ) )
| ( sk1 @ ( sk2 @ A ) @ B ) ),
inference(cnfConj,[status(thm)],[5]) ).
thf(13,plain,
! [B: a,A: a > $o] :
( ( A @ ( sk3 @ B @ A ) )
| ( sk1 @ ( sk2 @ A ) @ B ) ),
inference(simp,[status(thm)],[6]) ).
thf(240,plain,
! [A: a] :
( $false
| ( sk1
@ ( sk2
@ ^ [B: a] : $false )
@ A ) ),
inference(prim_subst,[status(thm)],[13:[bind(A,$thf( ^ [C: a] : $false ))]]) ).
thf(270,plain,
! [A: a] :
( sk1
@ ( sk2
@ ^ [B: a] : $false )
@ A ),
inference(simp,[status(thm)],[240]) ).
thf(10,plain,
! [A: a] :
~ ( sk1 @ A @ ( sk4 @ A ) ),
inference(cnfConj,[status(thm)],[5]) ).
thf(12,plain,
! [A: a] :
~ ( sk1 @ A @ ( sk4 @ A ) ),
inference(simp,[status(thm)],[10]) ).
thf(288,plain,
! [B: a,A: a] :
( ~ $true
| ( ( sk1
@ ( sk2
@ ^ [C: a] : $false )
@ A )
!= ( sk1 @ B @ ( sk4 @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[270,12]) ).
thf(289,plain,
! [B: a,A: a] :
( ( sk1
@ ( sk2
@ ^ [C: a] : $false )
@ A )
!= ( sk1 @ B @ ( sk4 @ B ) ) ),
inference(simp,[status(thm)],[288]) ).
thf(290,plain,
$false,
inference(pattern_uni,[status(thm)],[289:[bind(A,$thf( sk4 @ ( sk2 @ ^ [C: a] : $false ) )),bind(B,$thf( sk2 @ ^ [C: a] : $false ))]]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV055^5 : TPTP v9.3.1. Released v4.0.0.
% 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
% 0.10/0.21 % Computer : n001.cluster.edu
% 0.10/0.21 % Model : x86_64 x86_64
% 0.10/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.21 % Memory : 8046.5625MB
% 0.10/0.21 % OS : Linux 6.8.0-71-generic
% 0.10/0.21 % CPULimit : 300
% 0.10/0.21 % WCLimit : 300
% 0.10/0.21 % DateTime : Tue Sep 29 15:11:35 UTC 2026
% 0.10/0.21 % CPUTime :
% 0.10/0.21 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
% 1.06/0.81 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.25/0.99 % [INFO] Parsing done (179ms).
% 1.25/1.00 % [INFO] Running in sequential loop mode.
% 2.05/1.40 % [INFO] eprover registered as external prover.
% 2.05/1.41 % [INFO] Scanning for conjecture ...
% 2.24/1.51 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.24/1.55 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.24/1.55 % [INFO] Problem is higher-order (TPTP THF).
% 2.24/1.56 % [INFO] Type checking passed.
% 2.24/1.56 % [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 ...
% 7.91/3.24 % [INFO] Killing All external provers ...
% 7.91/3.25 % Time passed: 2888ms (effective reasoning time: 2239ms)
% 7.91/3.25 % 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)>
% 7.91/3.25 % Axioms used in derivation (0):
% 7.91/3.25 % No. of inferences in proof: 14
% 7.91/3.25 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2888 ms resp. 2239 ms w/o parsing
% 7.23/3.32 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 7.23/3.32 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------