%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LCL584^1 : TPTP v9.3.1. Released v3.6.0.
% 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 : n006.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 : Wed Sep 30 08:14:05 AM UTC 2026
% Result : Theorem 4.09s 2.19s
% Output : Refutation 4.30s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL584^1 : TPTP v9.3.1. Released v3.6.0.
% 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
% 0.10/0.21 % Computer : n006.cluster.edu
% 0.10/0.21 % Model : x86_64 x86_64
% 0.10/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.21 % Memory : 8046.5625MB
% 0.10/0.21 % OS : Linux 6.8.0-71-generic
% 0.10/0.21 % CPULimit : 300
% 0.10/0.21 % WCLimit : 300
% 0.10/0.21 % DateTime : Tue Sep 29 08:56:39 UTC 2026
% 0.10/0.21 % CPUTime :
% 0.10/0.21 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
% 0.92/0.78 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.27/1.02 % [INFO] Parsing done (237ms).
% 1.27/1.03 % [INFO] Running in sequential loop mode.
% 2.34/1.43 % [INFO] eprover registered as external prover.
% 2.34/1.43 % [INFO] Scanning for conjecture ...
% 2.55/1.56 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.55/1.59 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.55/1.59 % [INFO] Problem is higher-order (TPTP THF).
% 2.55/1.59 % [INFO] Type checking passed.
% 2.55/1.59 % [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 ...
% 4.09/2.18 % External prover 'e' found a proof!
% 4.09/2.18 % [INFO] Killing All external provers ...
% 4.09/2.18 % Time passed: 1835ms (effective reasoning time: 1144ms)
% 4.09/2.18 % 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)>
% 4.09/2.19 % Axioms used in derivation (0):
% 4.09/2.19 % No. of inferences in proof: 4
% 4.09/2.19 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1835 ms resp. 1144 ms w/o parsing
% 4.30/2.25 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.30/2.25 thf(individuals_type, type, individuals: $tType).
% 4.30/2.25 thf(mnot_decl, type, mnot: (($i > $o) > ($i > $o))).
% 4.30/2.25 thf(mor_decl, type, mor: (($i > $o) > (($i > $o) > ($i > $o)))).
% 4.30/2.25 thf(mand_decl, type, mand: (($i > $o) > (($i > $o) > ($i > $o)))).
% 4.30/2.25 thf(mimpl_decl, type, mimpl: (($i > $o) > (($i > $o) > ($i > $o)))).
% 4.30/2.25 thf(miff_decl, type, miff: (($i > $o) > (($i > $o) > ($i > $o)))).
% 4.30/2.25 thf(mbox_decl, type, mbox: (($i > ($i > $o)) > (($i > $o) > ($i > $o)))).
% 4.30/2.25 thf(mvalid_decl, type, mvalid: (($i > $o) > $o)).
% 4.30/2.25 thf(a_decl, type, a: ($i > $o)).
% 4.30/2.25 thf(b_decl, type, b: ($i > $o)).
% 4.30/2.25 thf(r_decl, type, r: ($i > ($i > $o))).
% 4.30/2.25 thf(mnot_def, definition, mnot = (^ [A:($i > $o),B:$i]: ~ (A @ B)) ).
% 4.30/2.25 thf(mor_def, definition, mor = (^ [A:($i > $o),B:($i > $o),C:$i]: ((A @ C) | (B @ C))) ).
% 4.30/2.25 thf(mand_def, definition, mand = (^ [A:($i > $o),B:($i > $o),C:$i]: ((A @ C) & (B @ C))) ).
% 4.30/2.25 thf(mimpl_def, definition, mimpl = (^ [A:($i > $o)]: (mor @ (mnot @ A))) ).
% 4.30/2.25 thf(miff_def, definition, miff = (^ [A:($i > $o),B:($i > $o)]: (mand @ (mimpl @ A @ B) @ (mimpl @ B @ A))) ).
% 4.30/2.25 thf(mbox_def, definition, mbox = (^ [A:($i > ($i > $o)),B:($i > $o),C:$i]: ! [D:$i]: ((A @ C @ D) => (B @ D))) ).
% 4.30/2.25 thf(mvalid_def, definition, mvalid = ((!) @ $i) ).
% 4.30/2.25 thf(1,conjecture,((mvalid @ (miff @ (mbox @ r @ (mand @ a @ b)) @ (mand @ (mbox @ r @ a) @ (mbox @ r @ b))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm)).
% 4.30/2.25 thf(2,negated_conjecture,((~ (mvalid @ (miff @ (mbox @ r @ (mand @ a @ b)) @ (mand @ (mbox @ r @ a) @ (mbox @ r @ b)))))),inference(neg_conjecture,[status(cth)],[1])).
% 4.30/2.25 thf(3,plain,((~ (! [A:$i]: ((~ (! [B:$i]: ((r @ A @ B) => ((a @ B) & (b @ B)))) | (! [B:$i]: ((r @ A @ B) => (a @ B)) & ! [B:$i]: ((r @ A @ B) => (b @ B)))) & (~ (! [B:$i]: ((r @ A @ B) => (a @ B)) & ! [B:$i]: ((r @ A @ B) => (b @ B))) | ! [B:$i]: ((r @ A @ B) => ((a @ B) & (b @ B)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])).
% 4.30/2.25 thf(18,plain,(($false)),inference(e,[status(thm)],[3])).
% 4.30/2.25 % SZS output end Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.30/2.25 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------