%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYO259^5 : 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 : 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 08:45:29 AM UTC 2026
% Result : Theorem 4.73s 2.16s
% Output : Refutation 4.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 17 ( 8 unt; 0 typ; 4 def)
% Number of atoms : 33 ( 6 equ; 0 cnn)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 181 ( 38 ~; 38 |; 19 &; 86 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 35 ( 35 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 5 usr; 5 con; 0-2 aty)
% Number of variables : 54 ( 4 ^; 32 !; 14 ?; 54 :)
% ( 0 !>; 0 ?*; 0 @-; 4 @+)
% Comments :
%------------------------------------------------------------------------------
thf(sk1_decl,type,
sk1: $i ).
thf(sk2_decl,type,
sk2: $i ).
thf(sk3_decl,type,
sk3: $i ).
thf(sk4_decl,type,
sk4: $i > $o ).
thf(sk5_decl,type,
sk5: ( $i > $o ) > ( $i > $o ) > $o ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ! [B: $i,C: $i,D: $i > $o] :
? [E: $i > $o,F: $i > $o] :
( ( ( F @ A )
| ( E @ A ) )
& ( ( D @ B )
| ( F @ B ) )
& ( ( E @ C )
| ~ ( D @ C ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ! [B: $i,C: $i > $o] :
? [D: $i > $o,E: $i > $o] :
( ( ( E @ sk1 )
| ( D @ sk1 ) )
& ( ( C @ A )
| ( E @ A ) )
& ( ( D @ B )
| ~ ( C @ B ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: $i] :
~ ! [B: $i > $o] :
? [C: $i > $o,D: $i > $o] :
( ( ( D @ sk1 )
| ( C @ sk1 ) )
& ( ( B @ sk2 )
| ( D @ sk2 ) )
& ( ( C @ A )
| ~ ( B @ A ) ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( @+[A: $i > $o] :
~ ? [B: $i > $o,C: $i > $o] :
( ( ( C @ sk1 )
| ( B @ sk1 ) )
& ( ( A @ sk2 )
| ( C @ sk2 ) )
& ( ( B @ sk3 )
| ~ ( A @ sk3 ) ) ) ) ) ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i,D: $i > $o] :
? [E: $i > $o,F: $i > $o] :
( ( ( F @ A )
| ( E @ A ) )
& ( ( D @ B )
| ( F @ B ) )
& ( ( E @ C )
| ~ ( D @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM125B) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i,D: $i > $o] :
? [E: $i > $o,F: $i > $o] :
( ( ( F @ A )
| ( E @ A ) )
& ( ( D @ B )
| ( F @ B ) )
& ( ( E @ C )
| ~ ( D @ C ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ! [A: $i,B: $i,C: $i,D: $i > $o] :
? [E: $i > $o,F: $i > $o] :
( ( ( F @ A )
| ( E @ A ) )
& ( ( D @ B )
| ( F @ B ) )
& ( ( E @ C )
| ~ ( D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
! [B: $i > $o,A: $i > $o] :
( ( ~ ( B @ sk1 )
| ~ ( sk5 @ B @ A ) )
& ( ~ ( A @ sk1 )
| ~ ( sk5 @ B @ A ) )
& ( ( sk5 @ B @ A )
| ~ ( sk4 @ sk2 )
| ~ ( A @ sk3 ) )
& ( ( sk5 @ B @ A )
| ~ ( sk4 @ sk2 )
| ( sk4 @ sk3 ) )
& ( ( sk5 @ B @ A )
| ~ ( B @ sk2 )
| ~ ( A @ sk3 ) )
& ( ( sk5 @ B @ A )
| ~ ( B @ sk2 )
| ( sk4 @ sk3 ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(10,plain,
! [B: $i > $o,A: $i > $o] :
( ~ ( B @ sk1 )
| ~ ( sk5 @ B @ A ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(6,plain,
! [B: $i > $o,A: $i > $o] :
( ~ ( A @ sk1 )
| ~ ( sk5 @ B @ A ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(14,plain,
! [A: $i > $o] :
( ~ $true
| ~ ( sk5 @ A
@ ^ [B: $i] : $true ) ),
inference(prim_subst,[status(thm)],[6:[bind(A,$thf( ^ [C: $i] : $true ))]]) ).
thf(24,plain,
! [A: $i > $o] :
~ ( sk5 @ A
@ ^ [B: $i] : $true ),
inference(simp,[status(thm)],[14]) ).
thf(32,plain,
! [A: $i > $o] :
( ~ $true
| ~ ( sk5
@ ^ [B: $i] : $true
@ A ) ),
inference(prim_subst,[status(thm)],[10:[bind(A,$thf( A )),bind(B,$thf( ^ [C: $i] : $true ))]]) ).
thf(34,plain,
! [A: $i > $o] :
~ ( sk5
@ ^ [B: $i] : $true
@ A ),
inference(simp,[status(thm)],[32]) ).
thf(11,plain,
! [B: $i > $o,A: $i > $o] :
( ~ ( A @ sk1 )
| ( ( sk5 @ B @ A )
!= ( A @ sk1 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[6]) ).
thf(17,plain,
! [B: $i > $o,A: $i > $o] :
( ~ ( A @ sk1 )
| ( ( sk5 @ B @ A )
!= ( A @ sk1 ) ) ),
inference(simp,[status(thm)],[11]) ).
thf(115,plain,
$false,
inference(e,[status(thm)],[10,24,6,3,34,17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO259^5 : 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
% 0.09/0.20 % Computer : n010.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % 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 16:42:03 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
% 0.86/0.77 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.20/0.95 % [INFO] Parsing done (183ms).
% 1.20/0.97 % [INFO] Running in sequential loop mode.
% 1.78/1.36 % [INFO] eprover registered as external prover.
% 1.78/1.36 % [INFO] Scanning for conjecture ...
% 2.01/1.40 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.01/1.42 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.01/1.42 % [INFO] Problem is higher-order (TPTP THF).
% 2.01/1.43 % [INFO] Type checking passed.
% 2.01/1.43 % [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 ...
% 4.73/2.15 % External prover 'e' found a proof!
% 4.73/2.15 % [INFO] Killing All external provers ...
% 4.73/2.15 % Time passed: 1815ms (effective reasoning time: 1179ms)
% 4.73/2.15 % 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)>
% 4.73/2.15 % Axioms used in derivation (0):
% 4.73/2.15 % No. of inferences in proof: 13
% 4.73/2.16 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1815 ms resp. 1179 ms w/o parsing
% 4.99/2.21 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.99/2.21 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------