%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYO005^1 : TPTP v9.3.1. Released v3.7.0.
% 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 : n016.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 08:45:00 AM UTC 2026
% Result : Theorem 4.49s 2.58s
% Output : Refutation 4.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 7
% Syntax : Number of formulae : 22 ( 14 unt; 0 typ; 6 def)
% Number of atoms : 33 ( 16 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 107 ( 17 ~; 5 |; 2 &; 68 @)
% ( 0 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 29 ( 29 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 32 ( 4 ^; 24 !; 0 ?; 32 :)
% ( 0 !>; 0 ?*; 0 @-; 4 @+)
% Comments :
%------------------------------------------------------------------------------
thf(leibeq1_decl,type,
leibeq1: $i > $i > $o ).
thf(leibeq2_decl,type,
leibeq2: ( $i > $i ) > ( $i > $i ) > $o ).
thf(sk1_decl,type,
sk1: $i > $i ).
thf(sk2_decl,type,
sk2: $i > $i ).
thf(sk3_decl,type,
sk3: $i ).
thf(sk4_decl,type,
sk4: $i > $o ).
thf(leibeq1_def,definition,
( leibeq1
= ( ^ [A: $i,B: $i] :
! [C: $i > $o] :
( ( C @ A )
=> ( C @ B ) ) ) ) ).
thf(leibeq2_def,definition,
( leibeq2
= ( ^ [A: $i > $i,B: $i > $i] :
! [C: ( $i > $i ) > $o] :
( ( C @ A )
=> ( C @ B ) ) ) ) ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i > $i] :
~ ! [B: $i > $i] :
( ! [C: ( $i > $i ) > $o] :
( ( C @ A )
=> ( C @ B ) )
=> ! [C: $i,D: $i > $o] :
( ( D @ ( A @ C ) )
=> ( D @ ( B @ C ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i > $i] :
~ ( ! [B: ( $i > $i ) > $o] :
( ( B @ sk1 )
=> ( B @ A ) )
=> ! [B: $i,C: $i > $o] :
( ( C @ ( sk1 @ B ) )
=> ( C @ ( A @ B ) ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: $i] :
~ ! [B: $i > $o] :
( ( B @ ( sk1 @ A ) )
=> ( B @ ( sk2 @ A ) ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( @+[A: $i > $o] :
~ ( ( A @ ( sk1 @ sk3 ) )
=> ( A @ ( sk2 @ sk3 ) ) ) ) ) ).
thf(1,conjecture,
! [A: $i > $i,B: $i > $i] :
( ( leibeq2 @ A @ B )
=> ! [C: $i] : ( leibeq1 @ ( A @ C ) @ ( B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj) ).
thf(2,negated_conjecture,
~ ! [A: $i > $i,B: $i > $i] :
( ( leibeq2 @ A @ B )
=> ! [C: $i] : ( leibeq1 @ ( A @ C ) @ ( B @ C ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ! [A: $i > $i,B: $i > $i] :
( ! [C: ( $i > $i ) > $o] :
( ( C @ A )
=> ( C @ B ) )
=> ! [C: $i,D: $i > $o] :
( ( D @ ( A @ C ) )
=> ( D @ ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
! [A: ( $i > $i ) > $o] :
( ( ~ ( A @ sk1 )
| ( A @ sk2 ) )
& ( sk4 @ ( sk1 @ sk3 ) )
& ~ ( sk4 @ ( sk2 @ sk3 ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(6,plain,
sk4 @ ( sk1 @ sk3 ),
inference(cnfConj,[status(thm)],[4]) ).
thf(7,plain,
~ ( sk4 @ ( sk2 @ sk3 ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(12,plain,
( ~ $true
| ( ( sk4 @ ( sk2 @ sk3 ) )
!= ( sk4 @ ( sk1 @ sk3 ) ) ) ),
inference(paramod_ordered,[status(thm)],[6,7]) ).
thf(13,plain,
( ( sk4 @ ( sk2 @ sk3 ) )
!= ( sk4 @ ( sk1 @ sk3 ) ) ),
inference(simp,[status(thm)],[12]) ).
thf(14,plain,
( ( sk2 @ sk3 )
!= ( sk1 @ sk3 ) ),
inference(simp,[status(thm)],[13]) ).
thf(5,plain,
! [A: ( $i > $i ) > $o] :
( ~ ( A @ sk1 )
| ( A @ sk2 ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(8,plain,
( ( sk1 != sk1 )
| ( sk1 = sk2 ) ),
inference(replace_leibeq,[status(thm)],[5:[bind(A,$thf( (=) @ ( $i > $i ) @ sk1 ))]]) ).
thf(9,plain,
( ( sk1 != sk1 )
| ( sk2 = sk1 ) ),
inference(lifteq,[status(thm)],[8]) ).
thf(10,plain,
sk2 = sk1,
inference(simp,[status(thm)],[9]) ).
thf(11,plain,
! [A: $i] :
( ( sk2 @ A )
= ( sk1 @ A ) ),
inference(func_ext,[status(esa)],[10]) ).
thf(19,plain,
( ( sk1 @ sk3 )
!= ( sk1 @ sk3 ) ),
inference(rewrite,[status(thm)],[14,11]) ).
thf(20,plain,
$false,
inference(simp,[status(thm)],[19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO005^1 : TPTP v9.3.1. Released v3.7.0.
% 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
% 0.12/0.25 % Computer : n016.cluster.edu
% 0.12/0.25 % Model : x86_64 x86_64
% 0.12/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.25 % Memory : 8046.5625MB
% 0.12/0.25 % OS : Linux 6.8.0-71-generic
% 0.12/0.25 % CPULimit : 300
% 0.12/0.25 % WCLimit : 300
% 0.12/0.25 % DateTime : Tue Sep 29 16:25:34 UTC 2026
% 0.12/0.25 % CPUTime :
% 0.12/0.25 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
% 1.17/0.98 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.66/1.14 % [INFO] Parsing done (156ms).
% 1.66/1.15 % [INFO] Running in sequential loop mode.
% 2.23/1.58 % [INFO] eprover registered as external prover.
% 2.23/1.59 % [INFO] Scanning for conjecture ...
% 2.66/1.71 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.66/1.74 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.66/1.74 % [INFO] Problem is higher-order (TPTP THF).
% 2.66/1.75 % [INFO] Type checking passed.
% 2.66/1.75 % [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 ...
% 4.49/2.57 % [INFO] Killing All external provers ...
% 4.49/2.58 % Time passed: 2115ms (effective reasoning time: 1421ms)
% 4.49/2.58 % 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)>
% 4.49/2.58 % Axioms used in derivation (0):
% 4.49/2.58 % No. of inferences in proof: 16
% 4.49/2.58 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2115 ms resp. 1421 ms w/o parsing
% 4.77/2.67 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.77/2.67 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------