%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYO364^5 : 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 : n020.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 08:45:39 AM UTC 2026
% Result : Theorem 5.10s 2.66s
% Output : Refutation 5.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 2
% Syntax : Number of formulae : 22 ( 11 unt; 0 typ; 1 def)
% Number of atoms : 28 ( 17 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 174 ( 20 ~; 9 |; 6 &; 126 @)
% ( 0 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 26 ( 26 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 38 ( 0 ^; 37 !; 0 ?; 38 :)
% ( 0 !>; 0 ?*; 0 @-; 1 @+)
% Comments :
%------------------------------------------------------------------------------
thf(a_type,type,
a: $tType ).
thf(j_decl,type,
j: a > a ).
thf(g_decl,type,
g: ( a > a ) > a > a ).
thf(h_decl,type,
h: a > a ).
thf(f_decl,type,
f: ( a > a ) > a > a ).
thf(sk1_decl,type,
sk1: ( a > a ) > $o ).
thf(sk2_decl,type,
sk2: a ).
thf(sk1_def,definition,
( sk1
= ( @+[A: ( a > a ) > $o] :
~ ( ( A @ ( f @ h ) )
=> ( A @ ( g @ j ) ) ) ) ) ).
thf(1,conjecture,
( ( ! [A: a > a,B: a,C: a > $o] :
( ( C @ ( f @ A @ B ) )
=> ( C @ ( g @ A @ B ) ) )
& ! [A: a,B: a > $o] :
( ( B @ ( h @ A ) )
=> ( B @ ( j @ A ) ) ) )
=> ! [A: ( a > a ) > $o] :
( ( A @ ( f @ h ) )
=> ( A @ ( g @ j ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cEDEC_pme) ).
thf(2,negated_conjecture,
~ ( ( ! [A: a > a,B: a,C: a > $o] :
( ( C @ ( f @ A @ B ) )
=> ( C @ ( g @ A @ B ) ) )
& ! [A: a,B: a > $o] :
( ( B @ ( h @ A ) )
=> ( B @ ( j @ A ) ) ) )
=> ! [A: ( a > a ) > $o] :
( ( A @ ( f @ h ) )
=> ( A @ ( g @ j ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ( ! [A: a > a,B: a,C: a > $o] :
( ( C @ ( f @ A @ B ) )
=> ( C @ ( g @ A @ B ) ) )
& ! [A: a,B: a > $o] :
( ( B @ ( h @ A ) )
=> ( B @ ( j @ A ) ) ) )
=> ! [A: ( a > a ) > $o] :
( ( A @ ( f @ h ) )
=> ( A @ ( g @ j ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
! [E: a > $o,D: a,C: a > $o,B: a,A: a > a] :
( ( ~ ( C @ ( f @ A @ B ) )
| ( C @ ( g @ A @ B ) ) )
& ( ~ ( E @ ( h @ D ) )
| ( E @ ( j @ D ) ) )
& ( sk1 @ ( f @ h ) )
& ~ ( sk1 @ ( g @ j ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(7,plain,
sk1 @ ( f @ h ),
inference(cnfConj,[status(thm)],[4]) ).
thf(8,plain,
~ ( sk1 @ ( g @ j ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(16,plain,
( ~ $true
| ( ( sk1 @ ( f @ h ) )
!= ( sk1 @ ( g @ j ) ) ) ),
inference(paramod_ordered,[status(thm)],[7,8]) ).
thf(17,plain,
( ( sk1 @ ( f @ h ) )
!= ( sk1 @ ( g @ j ) ) ),
inference(simp,[status(thm)],[16]) ).
thf(18,plain,
( ( f @ h )
!= ( g @ j ) ),
inference(simp,[status(thm)],[17]) ).
thf(19,plain,
( ( f @ h @ sk2 )
!= ( g @ j @ sk2 ) ),
inference(func_ext,[status(esa)],[18]) ).
thf(6,plain,
! [B: a > $o,A: a] :
( ~ ( B @ ( h @ A ) )
| ( B @ ( j @ A ) ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(10,plain,
! [A: a] :
( ( ( h @ A )
!= ( h @ A ) )
| ( ( h @ A )
= ( j @ A ) ) ),
inference(replace_leibeq,[status(thm)],[6:[bind(A,$thf( A )),bind(B,$thf( (=) @ a @ ( h @ A ) ))]]) ).
thf(11,plain,
! [A: a] :
( ( ( h @ A )
!= ( h @ A ) )
| ( ( h @ A )
= ( j @ A ) ) ),
inference(lifteq,[status(thm)],[10]) ).
thf(12,plain,
! [A: a] :
( ( h @ A )
= ( j @ A ) ),
inference(simp,[status(thm)],[11]) ).
thf(67,plain,
( ( f @ j @ sk2 )
!= ( g @ j @ sk2 ) ),
inference(rewrite,[status(thm)],[19,12]) ).
thf(5,plain,
! [C: a > $o,B: a,A: a > a] :
( ~ ( C @ ( f @ A @ B ) )
| ( C @ ( g @ A @ B ) ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(9,plain,
! [B: a,A: a > a] :
( ( ( f @ A @ B )
!= ( f @ A @ B ) )
| ( ( f @ A @ B )
= ( g @ A @ B ) ) ),
inference(replace_leibeq,[status(thm)],[5:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( (=) @ a @ ( f @ A @ B ) ))]]) ).
thf(14,plain,
! [B: a,A: a > a] :
( ( ( f @ A @ B )
!= ( f @ A @ B ) )
| ( ( f @ A @ B )
= ( g @ A @ B ) ) ),
inference(lifteq,[status(thm)],[9]) ).
thf(15,plain,
! [B: a,A: a > a] :
( ( f @ A @ B )
= ( g @ A @ B ) ),
inference(simp,[status(thm)],[14]) ).
thf(96,plain,
( ( g @ j @ sk2 )
!= ( g @ j @ sk2 ) ),
inference(rewrite,[status(thm)],[67,15]) ).
thf(97,plain,
$false,
inference(simp,[status(thm)],[96]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO364^5 : 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
% 0.11/0.21 % Computer : n020.cluster.edu
% 0.11/0.21 % Model : x86_64 x86_64
% 0.11/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.21 % Memory : 8046.5625MB
% 0.11/0.21 % OS : Linux 6.8.0-71-generic
% 0.11/0.21 % CPULimit : 300
% 0.11/0.21 % WCLimit : 300
% 0.11/0.21 % DateTime : Tue Sep 29 16:50:04 UTC 2026
% 0.11/0.21 % CPUTime :
% 0.11/0.21 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
% 0.88/0.79 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.24/0.99 % [INFO] Parsing done (192ms).
% 1.24/1.00 % [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 ...
% 2.24/1.54 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.24/1.54 % [INFO] Problem is higher-order (TPTP THF).
% 2.24/1.55 % [INFO] Type checking passed.
% 2.24/1.55 % [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 ...
% 5.10/2.66 % [INFO] Killing All external provers ...
% 5.10/2.66 % Time passed: 2295ms (effective reasoning time: 1650ms)
% 5.10/2.66 % 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)>
% 5.10/2.66 % Axioms used in derivation (0):
% 5.10/2.66 % No. of inferences in proof: 21
% 5.10/2.66 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2295 ms resp. 1650 ms w/o parsing
% 5.51/2.71 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 5.51/2.71 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------