%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYN055^5 : 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 08:41:30 AM UTC 2026
% Result : Theorem 3.26s 2.04s
% Output : Refutation 3.26s
% 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 : 40 ( 0 equ; 0 cnn)
% Maximal formula atoms : 13 ( 10 avg)
% Number of connectives : 80 ( 5 ~; 3 |; 21 &; 39 @)
% ( 0 <=>; 12 =>; 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 : 6 ( 5 usr; 1 con; 0-1 aty)
% Number of variables : 18 ( 0 ^; 9 !; 9 ?; 18 :)
% Comments :
%------------------------------------------------------------------------------
thf(cP_decl,type,
cP: $i > $o ).
thf(cQ_decl,type,
cQ: $i > $o ).
thf(cR_decl,type,
cR: $i > $o ).
thf(cF_decl,type,
cF: $i > $o ).
thf(cG_decl,type,
cG: $i > $o ).
thf(1,conjecture,
( ( ? [A: $i] : ( cP @ A )
& ! [A: $i] :
( ( cF @ A )
=> ( ~ ( cG @ A )
& ( cR @ A ) ) )
& ! [A: $i] :
( ( cP @ A )
=> ( ( cG @ A )
& ( cF @ A ) ) )
& ( ! [A: $i] :
( ( cP @ A )
=> ( cQ @ A ) )
| ? [A: $i] :
( ( cP @ A )
& ( cR @ A ) ) ) )
=> ? [A: $i] :
( ( cQ @ A )
& ( cP @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cPELL25) ).
thf(2,negated_conjecture,
~ ( ( ? [A: $i] : ( cP @ A )
& ! [A: $i] :
( ( cF @ A )
=> ( ~ ( cG @ A )
& ( cR @ A ) ) )
& ! [A: $i] :
( ( cP @ A )
=> ( ( cG @ A )
& ( cF @ A ) ) )
& ( ! [A: $i] :
( ( cP @ A )
=> ( cQ @ A ) )
| ? [A: $i] :
( ( cP @ A )
& ( cR @ A ) ) ) )
=> ? [A: $i] :
( ( cQ @ A )
& ( cP @ A ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ( ? [A: $i] : ( cP @ A )
& ! [A: $i] :
( ( cF @ A )
=> ( ~ ( cG @ A )
& ( cR @ A ) ) )
& ! [A: $i] :
( ( cP @ A )
=> ( ( cG @ A )
& ( cF @ A ) ) )
& ( ! [A: $i] :
( ( cP @ A )
=> ( cQ @ A ) )
| ? [A: $i] :
( ( cP @ A )
& ( cR @ A ) ) ) )
=> ? [A: $i] :
( ( cQ @ A )
& ( cP @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(18,plain,
$false,
inference(e,[status(thm)],[3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN055^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % 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 : n020.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 16:15:04 UTC 2026
% 0.10/0.21 % CPUTime :
% 0.10/0.21 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
% 0.85/0.78 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.17/0.96 % [INFO] Parsing done (168ms).
% 1.17/0.97 % [INFO] Running in sequential loop mode.
% 1.70/1.36 % [INFO] eprover registered as external prover.
% 1.70/1.37 % [INFO] Scanning for conjecture ...
% 1.89/1.47 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.05/1.50 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.05/1.51 % [INFO] Problem is higher-order (TPTP THF).
% 2.05/1.51 % [INFO] Type checking passed.
% 2.05/1.52 % [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 ...
% 3.26/2.04 % External prover 'e' found a proof!
% 3.26/2.04 % [INFO] Killing All external provers ...
% 3.26/2.04 % Time passed: 1689ms (effective reasoning time: 1064ms)
% 3.26/2.04 % 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)>
% 3.26/2.04 % Axioms used in derivation (0):
% 3.26/2.04 % No. of inferences in proof: 4
% 3.26/2.04 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1689 ms resp. 1064 ms w/o parsing
% 3.26/2.08 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.26/2.08 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------