%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYN056+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 : n012.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 09:16:38 AM UTC 2026
% Result : Theorem 1.66s 6.42s
% Output : Refutation 1.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 3
% Syntax : Number of formulae : 8 ( 1 unt; 0 typ; 0 def)
% Number of atoms : 33 ( 0 equ; 0 cnn)
% Maximal formula atoms : 8 ( 4 avg)
% Number of connectives : 59 ( 2 ~; 0 |; 5 &; 32 @)
% ( 4 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 5 ( 4 usr; 1 con; 0-1 aty)
% Number of variables : 18 ( 0 ^; 12 !; 6 ?; 18 :)
% Comments :
%------------------------------------------------------------------------------
thf(big_p_decl,type,
big_p: $i > $o ).
thf(big_r_decl,type,
big_r: $i > $o ).
thf(big_q_decl,type,
big_q: $i > $o ).
thf(big_s_decl,type,
big_s: $i > $o ).
thf(1,conjecture,
( ! [A: $i] :
( ( A @ big_p )
=> ( A @ big_r ) )
<=> ! [A: $i] :
( ( A @ big_q )
=> ( A @ big_s ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pel26) ).
thf(2,negated_conjecture,
~ ( ! [A: $i] :
( ( A @ big_p )
=> ( A @ big_r ) )
<=> ! [A: $i] :
( ( A @ big_q )
=> ( A @ big_s ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(5,plain,
~ ( ( ! [A: $i] :
( ( A @ big_q )
=> ( A @ big_s ) )
=> ! [A: $i] :
( ( A @ big_p )
=> ( A @ big_r ) ) )
& ( ! [A: $i] :
( ( A @ big_p )
=> ( A @ big_r ) )
=> ! [A: $i] :
( ( A @ big_q )
=> ( A @ big_s ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(3,axiom,
( ? [A: $i] : ( A @ big_p )
<=> ? [A: $i] : ( A @ big_q ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pel26_1) ).
thf(14,plain,
( ( ? [A: $i] : ( A @ big_q )
=> ? [A: $i] : ( A @ big_p ) )
& ( ? [A: $i] : ( A @ big_p )
=> ? [A: $i] : ( A @ big_q ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( ( B @ big_q )
& ( A @ big_p ) )
=> ( ( A @ big_r )
<=> ( B @ big_s ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pel26_2) ).
thf(19,plain,
! [A: $i,B: $i] :
( ( ( B @ big_q )
& ( A @ big_p ) )
=> ( ( ( B @ big_s )
=> ( A @ big_r ) )
& ( ( A @ big_r )
=> ( B @ big_s ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(23,plain,
$false,
inference(e,[status(thm)],[5,14,19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SYN056+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % 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
% 0.06/5.54 % Computer : n012.cluster.edu
% 0.06/5.54 % Model : x86_64 x86_64
% 0.06/5.54 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/5.54 % Memory : 8046.5625MB
% 0.06/5.54 % OS : Linux 6.8.0-71-generic
% 0.06/5.55 % CPULimit : 300
% 0.06/5.55 % WCLimit : 300
% 0.06/5.55 % DateTime : Sat Sep 26 17:07:29 UTC 2026
% 0.06/5.55 % CPUTime :
% 0.06/5.55 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
% 0.10/5.83 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.10/5.91 % [INFO] Parsing done (80ms).
% 0.10/5.91 % [INFO] Running in sequential loop mode.
% 0.80/6.09 % [INFO] eprover registered as external prover.
% 0.80/6.09 % [INFO] Scanning for conjecture ...
% 0.98/6.14 % [INFO] Found a conjecture (or negated_conjecture) and 2 axioms. Running axiom selection ...
% 0.98/6.15 % [INFO] Axiom selection finished. Selected 2 axioms (removed 0 axioms).
% 0.98/6.16 % [INFO] Problem is first-order (TPTP FOF).
% 0.98/6.16 % [INFO] Type checking passed.
% 0.98/6.16 % [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 ...
% 1.66/6.42 % External prover 'e' found a proof!
% 1.66/6.42 % [INFO] Killing All external provers ...
% 1.66/6.42 % Time passed: 787ms (effective reasoning time: 502ms)
% 1.66/6.42 % 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)>
% 1.66/6.42 % Axioms used in derivation (2): pel26_1, pel26_2
% 1.66/6.42 % No. of inferences in proof: 8
% 1.66/6.42 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 787 ms resp. 502 ms w/o parsing
% 1.66/6.44 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 1.66/6.44 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------