%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYO258^5 : 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 : n013.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 3.62s 2.19s
% Output : Refutation 3.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 2
% Syntax : Number of formulae : 9 ( 3 unt; 0 typ; 1 def)
% Number of atoms : 21 ( 1 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 81 ( 6 ~; 2 |; 14 &; 52 @)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 11 ( 11 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 20 ( 1 ^; 11 !; 7 ?; 20 :)
% ( 0 !>; 0 ?*; 0 @-; 1 @+)
% Comments :
%------------------------------------------------------------------------------
thf(a_decl,type,
a: $i ).
thf(cQ_decl,type,
cQ: $i > ( $i > $o ) > $o ).
thf(cP_decl,type,
cP: $i > $i > $o ).
thf(b_decl,type,
b: $i ).
thf(sk1_decl,type,
sk1: ( $i > $o ) > $i ).
thf(sk1_def,definition,
( sk1
= ( ^ [A: $i > $o] :
@+[B: $i] :
~ ( ( A @ B )
=> ( ? [C: $i] :
( ( cP @ B @ C )
& ( cQ @ C @ A ) )
& ( A @ a ) ) ) ) ) ).
thf(1,conjecture,
( ( ( cP @ a @ b )
& ! [A: $i > $o] : ( cQ @ b @ A ) )
=> ? [A: $i > $o] :
! [B: $i] :
( ( A @ B )
=> ( ? [C: $i] :
( ( cP @ B @ C )
& ( cQ @ C @ A ) )
& ( A @ a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cBLEDSOE_FENG_6) ).
thf(2,negated_conjecture,
~ ( ( ( cP @ a @ b )
& ! [A: $i > $o] : ( cQ @ b @ A ) )
=> ? [A: $i > $o] :
! [B: $i] :
( ( A @ B )
=> ( ? [C: $i] :
( ( cP @ B @ C )
& ( cQ @ C @ A ) )
& ( A @ a ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ( ( cP @ a @ b )
& ! [A: $i > $o] : ( cQ @ b @ A ) )
=> ? [A: $i > $o] :
! [B: $i] :
( ( A @ B )
=> ( ? [C: $i] :
( ( cP @ B @ C )
& ( cQ @ C @ A ) )
& ( A @ a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
! [C: $i,B: $i > $o,A: $i > $o] :
( ( cP @ a @ b )
& ( cQ @ b @ A )
& ( B @ ( sk1 @ B ) )
& ( ~ ( cP @ ( sk1 @ B ) @ C )
| ~ ( cQ @ C @ B )
| ~ ( B @ a ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(7,plain,
! [A: $i > $o] : ( A @ ( sk1 @ A ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(9,plain,
! [A: $i > $o] : ( A @ ( sk1 @ A ) ),
inference(simp,[status(thm)],[7]) ).
thf(14,plain,
$false,
inference(prim_subst,[status(thm)],[9:[bind(A,$thf( ^ [B: $i] : $false ))]]) ).
thf(23,plain,
$false,
inference(simp,[status(thm)],[14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO258^5 : 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 : n013.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 16:41:06 UTC 2026
% 0.10/0.22 % CPUTime :
% 0.10/0.22 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
% 0.90/0.79 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.24/0.98 % [INFO] Parsing done (187ms).
% 1.24/0.99 % [INFO] Running in sequential loop mode.
% 2.05/1.40 % [INFO] eprover registered as external prover.
% 2.05/1.41 % [INFO] Scanning for conjecture ...
% 2.23/1.51 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.23/1.54 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.23/1.54 % [INFO] Problem is higher-order (TPTP THF).
% 2.23/1.54 % [INFO] Type checking passed.
% 2.23/1.55 % [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 ...
% 3.62/2.18 % [INFO] Killing All external provers ...
% 3.62/2.19 % Time passed: 1830ms (effective reasoning time: 1185ms)
% 3.62/2.19 % 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)>
% 3.62/2.19 % Axioms used in derivation (0):
% 3.62/2.19 % No. of inferences in proof: 8
% 3.62/2.19 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1830 ms resp. 1185 ms w/o parsing
% 3.93/2.24 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.93/2.24 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------