%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYN371+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 09:17:23 AM UTC 2026
% Result : Theorem 3.21s 2.28s
% Output : Refutation 3.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 2
% Syntax : Number of formulae : 11 ( 6 unt; 0 typ; 1 def)
% Number of atoms : 27 ( 1 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 71 ( 8 ~; 1 |; 2 &; 48 @)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 5 ( 2 usr; 3 con; 0-2 aty)
% Number of variables : 22 ( 0 ^; 14 !; 7 ?; 22 :)
% ( 0 !>; 0 ?*; 0 @-; 1 @+)
% Comments :
%------------------------------------------------------------------------------
thf(big_r_decl,type,
big_r: $i > $i > $o ).
thf(sk1_decl,type,
sk1: $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ( A @ ( A @ big_r ) ) ) ) ).
thf(1,conjecture,
( ( ? [A: $i] : ( A @ ( A @ big_r ) )
=> ! [A: $i] : ( A @ ( A @ big_r ) ) )
=> ? [A: $i] :
! [B: $i] :
( ( A @ ( A @ big_r ) )
=> ( B @ ( B @ big_r ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x2122) ).
thf(2,negated_conjecture,
~ ( ( ? [A: $i] : ( A @ ( A @ big_r ) )
=> ! [A: $i] : ( A @ ( A @ big_r ) ) )
=> ? [A: $i] :
! [B: $i] :
( ( A @ ( A @ big_r ) )
=> ( B @ ( B @ big_r ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ( ? [A: $i] : ( A @ ( A @ big_r ) )
=> ! [A: $i] : ( A @ ( A @ big_r ) ) )
=> ? [A: $i] :
! [B: $i] :
( ( A @ ( A @ big_r ) )
=> ( B @ ( B @ big_r ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
~ ( ( ? [A: $i] : ( A @ ( A @ big_r ) )
=> ! [A: $i] : ( A @ ( A @ big_r ) ) )
=> ( ! [A: $i] : ( A @ ( A @ big_r ) )
=> ! [A: $i] : ( A @ ( A @ big_r ) ) ) ),
inference(miniscope,[status(thm)],[3]) ).
thf(5,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( sk1 @ ( sk1 @ big_r ) )
& ( C @ ( C @ big_r ) )
& ( ( B @ ( B @ big_r ) )
| ~ ( A @ ( A @ big_r ) ) ) ),
inference(cnf,[status(esa)],[4]) ).
thf(8,plain,
~ ( sk1 @ ( sk1 @ big_r ) ),
inference(cnfConj,[status(thm)],[5]) ).
thf(7,plain,
! [A: $i] : ( A @ ( A @ big_r ) ),
inference(cnfConj,[status(thm)],[5]) ).
thf(9,plain,
! [A: $i] : ( A @ ( A @ big_r ) ),
inference(simp,[status(thm)],[7]) ).
thf(10,plain,
~ $true,
inference(rewrite,[status(thm)],[8,9]) ).
thf(11,plain,
$false,
inference(simp,[status(thm)],[10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN371+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
% 0.14/0.42 % Computer : n016.cluster.edu
% 0.14/0.42 % Model : x86_64 x86_64
% 0.14/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.42 % Memory : 8046.5625MB
% 0.14/0.42 % OS : Linux 6.8.0-71-generic
% 0.14/0.42 % CPULimit : 300
% 0.14/0.42 % WCLimit : 300
% 0.14/0.42 % DateTime : Sat Sep 26 17:44:02 UTC 2026
% 0.14/0.42 % CPUTime :
% 0.14/0.42 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
% 0.88/1.00 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.28/1.18 % [INFO] Parsing done (176ms).
% 1.40/1.20 % [INFO] Running in sequential loop mode.
% 1.99/1.61 % [INFO] eprover registered as external prover.
% 1.99/1.62 % [INFO] Scanning for conjecture ...
% 2.16/1.70 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.16/1.74 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.16/1.74 % [INFO] Problem is first-order (TPTP FOF).
% 2.16/1.74 % [INFO] Type checking passed.
% 2.16/1.75 % [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 ...
% 3.21/2.27 % [INFO] Killing All external provers ...
% 3.21/2.27 % Time passed: 1708ms (effective reasoning time: 1065ms)
% 3.21/2.27 % 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)>
% 3.21/2.27 % Axioms used in derivation (0):
% 3.21/2.27 % No. of inferences in proof: 10
% 3.21/2.28 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1708 ms resp. 1065 ms w/o parsing
% 3.52/2.32 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.52/2.32 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------