%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYN356^5 : 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 : n004.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 08:41:30 AM UTC 2026
% Result : Theorem 3.19s 2.05s
% Output : Refutation 3.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 1
% Syntax : Number of formulae : 4 ( 1 unt; 0 typ; 0 def)
% Number of atoms : 25 ( 0 equ; 0 cnn)
% Maximal formula atoms : 8 ( 6 avg)
% Number of connectives : 71 ( 2 ~; 0 |; 12 &; 48 @)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 5 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 12 ( 0 ^; 12 !; 0 ?; 12 :)
% Comments :
%------------------------------------------------------------------------------
thf(cB_decl,type,
cB: $i ).
thf(cQ_decl,type,
cQ: $i > $i > $o ).
thf(cA_decl,type,
cA: $i ).
thf(cR_decl,type,
cR: $i > $i > $o ).
thf(1,conjecture,
( ( ( cR @ cA @ cB )
& ! [A: $i,B: $i] :
( ( cR @ A @ B )
=> ( ( cR @ B @ A )
& ( cQ @ A @ B ) ) )
& ! [A: $i,B: $i] :
( ( cQ @ A @ B )
=> ( cQ @ A @ A ) ) )
=> ( ( cQ @ cA @ cA )
& ( cQ @ cB @ cB ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cLX2107) ).
thf(2,negated_conjecture,
~ ( ( ( cR @ cA @ cB )
& ! [A: $i,B: $i] :
( ( cR @ A @ B )
=> ( ( cR @ B @ A )
& ( cQ @ A @ B ) ) )
& ! [A: $i,B: $i] :
( ( cQ @ A @ B )
=> ( cQ @ A @ A ) ) )
=> ( ( cQ @ cA @ cA )
& ( cQ @ cB @ cB ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ( ( cR @ cA @ cB )
& ! [A: $i,B: $i] :
( ( cR @ A @ B )
=> ( ( cR @ B @ A )
& ( cQ @ A @ B ) ) )
& ! [A: $i,B: $i] :
( ( cQ @ A @ B )
=> ( cQ @ A @ A ) ) )
=> ( ( cQ @ cA @ cA )
& ( cQ @ cB @ cB ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(16,plain,
$false,
inference(e,[status(thm)],[3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN356^5 : 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
% 0.11/0.22 % Computer : n004.cluster.edu
% 0.11/0.22 % Model : x86_64 x86_64
% 0.11/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.22 % Memory : 8046.5625MB
% 0.11/0.22 % OS : Linux 6.8.0-71-generic
% 0.11/0.22 % CPULimit : 300
% 0.11/0.22 % WCLimit : 300
% 0.11/0.22 % DateTime : Tue Sep 29 16:14:52 UTC 2026
% 0.11/0.22 % CPUTime :
% 0.11/0.22 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
% 0.84/0.78 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.17/0.96 % [INFO] Parsing done (178ms).
% 1.17/0.98 % [INFO] Running in sequential loop mode.
% 1.72/1.37 % [INFO] eprover registered as external prover.
% 1.72/1.38 % [INFO] Scanning for conjecture ...
% 1.91/1.47 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.06/1.51 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.06/1.51 % [INFO] Problem is higher-order (TPTP THF).
% 2.06/1.51 % [INFO] Type checking passed.
% 2.06/1.52 % [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 ...
% 3.19/2.05 % External prover 'e' found a proof!
% 3.19/2.05 % [INFO] Killing All external provers ...
% 3.19/2.05 % Time passed: 1693ms (effective reasoning time: 1062ms)
% 3.19/2.05 % 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)>
% 3.19/2.05 % Axioms used in derivation (0):
% 3.19/2.05 % No. of inferences in proof: 4
% 3.19/2.05 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1693 ms resp. 1062 ms w/o parsing
% 3.19/2.08 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.19/2.08 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------