%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : GRA014+1 : TPTP v9.3.1. Released v3.2.0.
% 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 : 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 07:18:22 AM UTC 2026
% Result : Theorem 2.94s 1.81s
% Output : Refutation 2.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 6
% Syntax : Number of formulae : 14 ( 4 unt; 0 typ; 0 def)
% Number of atoms : 42 ( 0 equ; 0 cnn)
% Maximal formula atoms : 5 ( 3 avg)
% Number of connectives : 98 ( 2 ~; 2 |; 18 &; 68 @)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 22 ( 0 ^; 22 !; 0 ?; 22 :)
% Comments :
%------------------------------------------------------------------------------
thf(goal_decl,type,
goal: $o ).
thf(red_decl,type,
red: $i > $i > $o ).
thf(green_decl,type,
green: $i > $i > $o ).
thf(less_than_decl,type,
less_than: $i > $i > $o ).
thf(n1_decl,type,
n1: $i ).
thf(n2_decl,type,
n2: $i ).
thf(n3_decl,type,
n3: $i ).
thf(n4_decl,type,
n4: $i ).
thf(n5_decl,type,
n5: $i ).
thf(n6_decl,type,
n6: $i ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ less_than ) )
=> ( ( B @ ( A @ green ) )
| ( B @ ( A @ red ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',partition) ).
thf(24,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ less_than ) )
=> ( ( B @ ( A @ green ) )
| ( B @ ( A @ red ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(3,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ red ) )
& ( C @ ( B @ red ) )
& ( B @ ( A @ red ) ) )
=> goal ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',red_clique) ).
thf(9,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ red ) )
& ( C @ ( B @ red ) )
& ( B @ ( A @ red ) ) )
=> goal ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(6,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ less_than ) )
& ( B @ ( A @ less_than ) ) )
=> ( C @ ( A @ less_than ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less_than_transitive) ).
thf(22,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ less_than ) )
& ( B @ ( A @ less_than ) ) )
=> ( C @ ( A @ less_than ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(4,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ green ) )
& ( C @ ( B @ green ) )
& ( B @ ( A @ green ) ) )
=> goal ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',green_clique) ).
thf(12,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ green ) )
& ( C @ ( B @ green ) )
& ( B @ ( A @ green ) ) )
=> goal ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(1,conjecture,
goal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal_to_be_proved) ).
thf(2,negated_conjecture,
~ goal,
inference(neg_conjecture,[status(cth)],[1]) ).
thf(8,plain,
~ goal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(5,axiom,
( ( n6 @ ( n5 @ less_than ) )
& ( n5 @ ( n4 @ less_than ) )
& ( n4 @ ( n3 @ less_than ) )
& ( n3 @ ( n2 @ less_than ) )
& ( n2 @ ( n1 @ less_than ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ordering) ).
thf(15,plain,
( ( n6 @ ( n5 @ less_than ) )
& ( n5 @ ( n4 @ less_than ) )
& ( n4 @ ( n3 @ less_than ) )
& ( n3 @ ( n2 @ less_than ) )
& ( n2 @ ( n1 @ less_than ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(37,plain,
$false,
inference(e,[status(thm)],[24,9,22,12,8,15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : GRA014+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % 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
% 0.06/0.32 % Computer : n012.cluster.edu
% 0.06/0.32 % Model : x86_64 x86_64
% 0.06/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.32 % Memory : 8046.5625MB
% 0.06/0.32 % OS : Linux 6.8.0-71-generic
% 0.06/0.32 % CPULimit : 300
% 0.06/0.32 % WCLimit : 300
% 0.06/0.32 % DateTime : Fri Sep 25 13:48:36 UTC 2026
% 0.06/0.33 % CPUTime :
% 0.06/0.33 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
% 0.60/0.76 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.96/0.90 % [INFO] Parsing done (144ms).
% 0.96/0.91 % [INFO] Running in sequential loop mode.
% 1.46/1.20 % [INFO] eprover registered as external prover.
% 1.46/1.20 % [INFO] Scanning for conjecture ...
% 1.46/1.26 % [INFO] Found a conjecture (or negated_conjecture) and 5 axioms. Running axiom selection ...
% 1.46/1.28 % [INFO] Axiom selection finished. Selected 5 axioms (removed 0 axioms).
% 1.64/1.30 % [INFO] Problem is first-order (TPTP FOF).
% 1.64/1.31 % [INFO] Type checking passed.
% 1.64/1.31 % [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 ...
% 2.94/1.81 % External prover 'e' found a proof!
% 2.94/1.81 % [INFO] Killing All external provers ...
% 2.94/1.81 % Time passed: 1388ms (effective reasoning time: 890ms)
% 2.94/1.81 % 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)>
% 2.94/1.81 % Axioms used in derivation (5): red_clique, less_than_transitive, partition, green_clique, ordering
% 2.94/1.81 % No. of inferences in proof: 14
% 2.94/1.81 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1388 ms resp. 890 ms w/o parsing
% 2.94/1.84 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.94/1.84 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------