%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYN084+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n018.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 : Sun Sep 27 09:16:47 AM UTC 2026
% Result : Theorem 3.47s 2.32s
% Output : Refutation 3.47s
% 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 : 41 ( 0 equ; 0 cnn)
% Maximal formula atoms : 20 ( 10 avg)
% Number of connectives : 123 ( 14 ~; 16 |; 9 &; 72 @)
% ( 2 <=>; 10 =>; 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 : 4 ( 3 usr; 2 con; 0-1 aty)
% Number of variables : 8 ( 0 ^; 8 !; 0 ?; 8 :)
% Comments :
%------------------------------------------------------------------------------
thf(big_p_decl,type,
big_p: $i > $o ).
thf(a_decl,type,
a: $i ).
thf(f_decl,type,
f: $i > $i ).
thf(1,conjecture,
( ! [A: $i] :
( ( ( ( A @ big_p )
=> ( A @ f @ big_p ) )
& ( a @ big_p ) )
=> ( A @ f @ f @ big_p ) )
<=> ! [A: $i] :
( ( ( A @ f @ f @ big_p )
| ~ ( A @ f @ big_p )
| ~ ( a @ big_p ) )
& ( ( A @ f @ f @ big_p )
| ( A @ big_p )
| ~ ( a @ big_p ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pel62) ).
thf(2,negated_conjecture,
~ ( ! [A: $i] :
( ( ( ( A @ big_p )
=> ( A @ f @ big_p ) )
& ( a @ big_p ) )
=> ( A @ f @ f @ big_p ) )
<=> ! [A: $i] :
( ( ( A @ f @ f @ big_p )
| ~ ( A @ f @ big_p )
| ~ ( a @ big_p ) )
& ( ( A @ f @ f @ big_p )
| ( A @ big_p )
| ~ ( a @ big_p ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ( ! [A: $i] :
( ( ( A @ f @ f @ big_p )
| ~ ( A @ f @ big_p )
| ~ ( a @ big_p ) )
& ( ( A @ f @ f @ big_p )
| ( A @ big_p )
| ~ ( a @ big_p ) ) )
=> ! [A: $i] :
( ( ( ( A @ big_p )
=> ( A @ f @ big_p ) )
& ( a @ big_p ) )
=> ( A @ f @ f @ big_p ) ) )
& ( ! [A: $i] :
( ( ( ( A @ big_p )
=> ( A @ f @ big_p ) )
& ( a @ big_p ) )
=> ( A @ f @ f @ big_p ) )
=> ! [A: $i] :
( ( ( A @ f @ f @ big_p )
| ~ ( A @ f @ big_p )
| ~ ( a @ big_p ) )
& ( ( A @ f @ f @ big_p )
| ( A @ big_p )
| ~ ( a @ big_p ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(21,plain,
$false,
inference(e,[status(thm)],[3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN084+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.13/0.39 % Computer : n018.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Sat Sep 26 17:12:37 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.13/0.40 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.89/0.99 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.27/1.17 % [INFO] Parsing done (180ms).
% 1.27/1.18 % [INFO] Running in sequential loop mode.
% 1.84/1.59 % [INFO] eprover registered as external prover.
% 2.04/1.60 % [INFO] Scanning for conjecture ...
% 2.21/1.70 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.21/1.74 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.21/1.74 % [INFO] Problem is first-order (TPTP FOF).
% 2.21/1.75 % [INFO] Type checking passed.
% 2.21/1.75 % [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 ...
% 3.47/2.31 % External prover 'e' found a proof!
% 3.47/2.31 % [INFO] Killing All external provers ...
% 3.47/2.31 % Time passed: 1772ms (effective reasoning time: 1123ms)
% 3.47/2.31 % 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)>
% 3.47/2.32 % Axioms used in derivation (0):
% 3.47/2.32 % No. of inferences in proof: 4
% 3.47/2.32 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1772 ms resp. 1123 ms w/o parsing
% 3.47/2.35 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.47/2.35 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------