%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYN359+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 : n016.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 09:17:21 AM UTC 2026
% Result : Theorem 2.17s 1.33s
% Output : Refutation 2.17s
% 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 : 22 ( 0 equ; 0 cnn)
% Maximal formula atoms : 7 ( 5 avg)
% Number of connectives : 53 ( 2 ~; 0 |; 9 &; 33 @)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 3 ( 2 usr; 1 con; 0-2 aty)
% Number of variables : 21 ( 0 ^; 9 !; 12 ?; 21 :)
% Comments :
%------------------------------------------------------------------------------
thf(big_r_decl,type,
big_r: $i > $o ).
thf(big_q_decl,type,
big_q: $i > $i > $o ).
thf(1,conjecture,
( ( ! [A: $i,B: $i] :
( ( B @ ( A @ big_q ) )
=> ( A @ ( A @ big_q ) ) )
& ! [A: $i] :
( ( A @ big_r )
=> ? [B: $i] : ( B @ ( A @ big_q ) ) )
& ? [A: $i] : ( A @ big_r ) )
=> ? [A: $i,B: $i] :
( ( B @ big_r )
& ( B @ ( A @ big_q ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x2110) ).
thf(2,negated_conjecture,
~ ( ( ! [A: $i,B: $i] :
( ( B @ ( A @ big_q ) )
=> ( A @ ( A @ big_q ) ) )
& ! [A: $i] :
( ( A @ big_r )
=> ? [B: $i] : ( B @ ( A @ big_q ) ) )
& ? [A: $i] : ( A @ big_r ) )
=> ? [A: $i,B: $i] :
( ( B @ big_r )
& ( B @ ( A @ big_q ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ( ! [A: $i,B: $i] :
( ( B @ ( A @ big_q ) )
=> ( A @ ( A @ big_q ) ) )
& ! [A: $i] :
( ( A @ big_r )
=> ? [B: $i] : ( B @ ( A @ big_q ) ) )
& ? [A: $i] : ( A @ big_r ) )
=> ? [A: $i,B: $i] :
( ( B @ big_r )
& ( B @ ( A @ big_q ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(15,plain,
$false,
inference(e,[status(thm)],[3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN359+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.07 % 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
% 0.12/0.39 % Computer : n016.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Sat Sep 26 17:43:15 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 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
% 0.60/0.69 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.73/0.77 % [INFO] Parsing done (87ms).
% 0.73/0.78 % [INFO] Running in sequential loop mode.
% 1.13/0.97 % [INFO] eprover registered as external prover.
% 1.13/0.97 % [INFO] Scanning for conjecture ...
% 1.13/1.02 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 1.43/1.03 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 1.43/1.03 % [INFO] Problem is first-order (TPTP FOF).
% 1.43/1.04 % [INFO] Type checking passed.
% 1.43/1.04 % [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 ...
% 2.17/1.32 % External prover 'e' found a proof!
% 2.17/1.32 % [INFO] Killing All external provers ...
% 2.17/1.33 % Time passed: 846ms (effective reasoning time: 541ms)
% 2.17/1.33 % 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)>
% 2.17/1.33 % Axioms used in derivation (0):
% 2.17/1.33 % No. of inferences in proof: 4
% 2.17/1.33 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 846 ms resp. 541 ms w/o parsing
% 2.17/1.34 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 2.17/1.34 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------