%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYO270^5 : 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 : n019.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 08:45:30 AM UTC 2026
% Result : Theorem 3.25s 1.89s
% Output : Refutation 3.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 2
% Syntax : Number of formulae : 10 ( 5 unt; 0 typ; 1 def)
% Number of atoms : 26 ( 3 equ; 0 cnn)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 103 ( 8 ~; 1 |; 6 &; 84 @)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 11 ( 11 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 34 ( 2 ^; 25 !; 6 ?; 34 :)
% ( 0 !>; 0 ?*; 0 @-; 1 @+)
% Comments :
%------------------------------------------------------------------------------
thf(h_decl,type,
h: $i > $i ).
thf(g_decl,type,
g: $i > $i ).
thf(cP_decl,type,
cP: $i > $i > $o ).
thf(sk1_decl,type,
sk1: ( $i > $i ) > $i > $i ).
thf(sk1_def,definition,
( sk1
= ( ^ [A: $i > $i,B: $i] :
@+[C: $i] :
~ ( ( ! [D: $i] : ( cP @ D @ ( A @ B ) )
& ( cP @ B @ C ) )
=> ( cP @ C @ ( g @ ( h @ C ) ) ) ) ) ) ).
thf(1,conjecture,
? [A: $i,B: $i > $i] :
! [C: $i] :
( ( ! [D: $i] : ( cP @ D @ ( B @ A ) )
& ( cP @ A @ C ) )
=> ( cP @ C @ ( g @ ( h @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM85) ).
thf(2,negated_conjecture,
~ ? [A: $i,B: $i > $i] :
! [C: $i] :
( ( ! [D: $i] : ( cP @ D @ ( B @ A ) )
& ( cP @ A @ C ) )
=> ( cP @ C @ ( g @ ( h @ C ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ? [A: $i,B: $i > $i] :
! [C: $i] :
( ( ! [D: $i] : ( cP @ D @ ( B @ A ) )
& ( cP @ A @ C ) )
=> ( cP @ C @ ( g @ ( h @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
! [C: $i,B: $i > $i,A: $i] :
( ( cP @ C @ ( B @ A ) )
& ( cP @ A @ ( sk1 @ B @ A ) )
& ~ ( cP @ ( sk1 @ B @ A ) @ ( g @ ( h @ ( sk1 @ B @ A ) ) ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(5,plain,
! [C: $i,B: $i > $i,A: $i] : ( cP @ C @ ( B @ A ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(7,plain,
! [B: $i > $i,A: $i] :
~ ( cP @ ( sk1 @ B @ A ) @ ( g @ ( h @ ( sk1 @ B @ A ) ) ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(8,plain,
! [E: $i > $i,D: $i,C: $i,B: $i > $i,A: $i] :
( ~ $true
| ( ( cP @ C @ ( B @ A ) )
!= ( cP @ ( sk1 @ E @ D ) @ ( g @ ( h @ ( sk1 @ E @ D ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[5,7]) ).
thf(9,plain,
! [E: $i > $i,D: $i,C: $i,B: $i > $i,A: $i] :
( ( cP @ C @ ( B @ A ) )
!= ( cP @ ( sk1 @ E @ D ) @ ( g @ ( h @ ( sk1 @ E @ D ) ) ) ) ),
inference(simp,[status(thm)],[8]) ).
thf(14,plain,
$false,
inference(pre_uni,[status(thm)],[9:[bind(A,$thf( A )),bind(B,$thf( ^ [H: $i] : ( g @ ( h @ ( sk1 @ ( H @ H ) @ ( I @ H ) ) ) ) )),bind(C,$thf( sk1 @ ( H @ A ) @ ( I @ A ) )),bind(D,$thf( I @ A )),bind(E,$thf( H @ A ))]]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO270^5 : 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
% 0.09/0.22 % Computer : n019.cluster.edu
% 0.09/0.22 % Model : x86_64 x86_64
% 0.09/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.22 % Memory : 8046.5625MB
% 0.09/0.22 % OS : Linux 6.8.0-71-generic
% 0.09/0.22 % CPULimit : 300
% 0.09/0.22 % WCLimit : 300
% 0.09/0.22 % DateTime : Tue Sep 29 16:42:17 UTC 2026
% 0.09/0.22 % CPUTime :
% 0.09/0.22 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
% 0.64/0.54 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.99/0.65 % [INFO] Parsing done (114ms).
% 0.99/0.67 % [INFO] Running in sequential loop mode.
% 1.59/1.08 % [INFO] eprover registered as external prover.
% 1.59/1.09 % [INFO] Scanning for conjecture ...
% 1.80/1.18 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 1.91/1.21 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 1.91/1.21 % [INFO] Problem is higher-order (TPTP THF).
% 1.91/1.22 % [INFO] Type checking passed.
% 1.91/1.22 % [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 ...
% 3.25/1.89 % [INFO] Killing All external provers ...
% 3.25/1.89 % Time passed: 1573ms (effective reasoning time: 1213ms)
% 3.25/1.89 % 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)>
% 3.25/1.89 % Axioms used in derivation (0):
% 3.25/1.89 % No. of inferences in proof: 9
% 3.25/1.89 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1573 ms resp. 1213 ms w/o parsing
% 3.54/1.94 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.54/1.94 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------