%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LCL691^1 : TPTP v9.3.1. Released v3.7.0.
% 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 : n003.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 08:14:09 AM UTC 2026
% Result : Theorem 4.61s 2.41s
% Output : Refutation 4.61s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL691^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.07 % 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
% 0.10/0.20 % Computer : n003.cluster.edu
% 0.10/0.20 % Model : x86_64 x86_64
% 0.10/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.20 % Memory : 8046.5625MB
% 0.10/0.20 % OS : Linux 6.8.0-71-generic
% 0.10/0.20 % CPULimit : 300
% 0.10/0.20 % WCLimit : 300
% 0.10/0.20 % DateTime : Tue Sep 29 09:40:43 UTC 2026
% 0.10/0.20 % CPUTime :
% 0.10/0.20 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
% 0.88/0.77 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.23/1.03 % [INFO] Parsing done (253ms).
% 1.23/1.05 % [INFO] Running in sequential loop mode.
% 2.20/1.44 % [INFO] eprover registered as external prover.
% 2.20/1.44 % [INFO] Scanning for conjecture ...
% 2.42/1.59 % [INFO] Found a conjecture (or negated_conjecture) and 5 axioms. Running axiom selection ...
% 2.64/1.63 % [INFO] Axiom selection finished. Selected 5 axioms (removed 0 axioms).
% 2.64/1.64 % [INFO] Problem is higher-order (TPTP THF).
% 2.64/1.64 % [INFO] Type checking passed.
% 2.64/1.65 % [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 ...
% 4.61/2.40 % External prover 'e' found a proof!
% 4.61/2.40 % [INFO] Killing All external provers ...
% 4.61/2.40 % Time passed: 2068ms (effective reasoning time: 1350ms)
% 4.61/2.40 % 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)>
% 4.61/2.41 % Axioms used in derivation (5): trans_axiom_i, trans_axiom_r, refl_axiom_r, ax_i_r_commute, refl_axiom_i
% 4.61/2.41 % No. of inferences in proof: 14
% 4.61/2.41 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2068 ms resp. 1350 ms w/o parsing
% 4.61/2.47 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.61/2.47 thf(individuals_type, type, individuals: $tType).
% 4.61/2.47 thf(mnot_decl, type, mnot: (($i > $o) > ($i > $o))).
% 4.61/2.47 thf(mor_decl, type, mor: (($i > $o) > (($i > $o) > ($i > $o)))).
% 4.61/2.47 thf(mimpl_decl, type, mimpl: (($i > $o) > (($i > $o) > ($i > $o)))).
% 4.61/2.47 thf(mbox_decl, type, mbox: (($i > ($i > $o)) > (($i > $o) > ($i > $o)))).
% 4.61/2.47 thf(mvalid_decl, type, mvalid: (($i > $o) > $o)).
% 4.61/2.47 thf(reli_decl, type, reli: ($i > ($i > $o))).
% 4.61/2.47 thf(relr_decl, type, relr: ($i > ($i > $o))).
% 4.61/2.47 thf(cs4_atom_decl, type, cs4_atom: (($i > $o) > ($i > $o))).
% 4.61/2.47 thf(cs4_impl_decl, type, cs4_impl: (($i > $o) > (($i > $o) > ($i > $o)))).
% 4.61/2.47 thf(cs4_box_decl, type, cs4_box: (($i > $o) > ($i > $o))).
% 4.61/2.47 thf(cs4_valid_decl, type, cs4_valid: (($i > $o) > $o)).
% 4.61/2.47 thf(mnot_def, definition, mnot = (^ [A:($i > $o),B:$i]: ~ (A @ B)) ).
% 4.61/2.47 thf(mor_def, definition, mor = (^ [A:($i > $o),B:($i > $o),C:$i]: ((A @ C) | (B @ C))) ).
% 4.61/2.47 thf(mimpl_def, definition, mimpl = (^ [A:($i > $o)]: (mor @ (mnot @ A))) ).
% 4.61/2.47 thf(mbox_def, definition, mbox = (^ [A:($i > ($i > $o)),B:($i > $o),C:$i]: ! [D:$i]: ((A @ C @ D) => (B @ D))) ).
% 4.61/2.47 thf(mvalid_def, definition, mvalid = ((!) @ $i) ).
% 4.61/2.47 thf(cs4_atom_def, definition, cs4_atom = (mbox @ reli) ).
% 4.61/2.47 thf(cs4_impl_def, definition, cs4_impl = (^ [A:($i > $o),B:($i > $o)]: (mbox @ reli @ (mimpl @ A @ B))) ).
% 4.61/2.47 thf(cs4_box_def, definition, cs4_box = (^ [A:($i > $o)]: (mbox @ reli @ (mbox @ relr @ A))) ).
% 4.61/2.47 thf(cs4_valid_def, definition, cs4_valid = (mvalid) ).
% 4.61/2.47 thf(3,axiom,((! [A:($i > $o)]: (mvalid @ (mimpl @ (mbox @ reli @ A) @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',refl_axiom_i)).
% 4.61/2.47 thf(14,plain,((! [A:($i > $o),B:$i]: (~ (! [C:$i]: ((reli @ B @ C) => (A @ C))) | (A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3])).
% 4.61/2.47 thf(4,axiom,((! [A:($i > $o)]: (mvalid @ (mimpl @ (mbox @ relr @ A) @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',refl_axiom_r)).
% 4.61/2.47 thf(20,plain,((! [A:($i > $o),B:$i]: (~ (! [C:$i]: ((relr @ B @ C) => (A @ C))) | (A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4])).
% 4.61/2.47 thf(7,axiom,((! [A:($i > $o)]: (mvalid @ (mimpl @ (mbox @ reli @ (mbox @ relr @ A)) @ (mbox @ relr @ (mbox @ reli @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_i_r_commute)).
% 4.61/2.47 thf(38,plain,((! [A:($i > $o),B:$i]: (~ (! [C:$i]: ((reli @ B @ C) => (! [D:$i]: ((relr @ C @ D) => (A @ D))))) | ! [C:$i]: ((relr @ B @ C) => (! [D:$i]: ((reli @ C @ D) => (A @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7])).
% 4.61/2.47 thf(6,axiom,((! [A:($i > $o)]: (mvalid @ (mimpl @ (mbox @ relr @ A) @ (mbox @ relr @ (mbox @ relr @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',trans_axiom_r)).
% 4.61/2.47 thf(32,plain,((! [A:($i > $o),B:$i]: (~ (! [C:$i]: ((relr @ B @ C) => (A @ C))) | ! [C:$i]: ((relr @ B @ C) => (! [D:$i]: ((relr @ C @ D) => (A @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6])).
% 4.61/2.47 thf(5,axiom,((! [A:($i > $o)]: (mvalid @ (mimpl @ (mbox @ reli @ A) @ (mbox @ reli @ (mbox @ reli @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',trans_axiom_i)).
% 4.61/2.47 thf(26,plain,((! [A:($i > $o),B:$i]: (~ (! [C:$i]: ((reli @ B @ C) => (A @ C))) | ! [C:$i]: ((reli @ B @ C) => (! [D:$i]: ((reli @ C @ D) => (A @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5])).
% 4.61/2.47 thf(1,conjecture,((! [A:($i > $o)]: (cs4_valid @ (cs4_impl @ (cs4_box @ (cs4_atom @ A)) @ (cs4_atom @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',cs4_refl)).
% 4.61/2.47 thf(2,negated_conjecture,((~ (! [A:($i > $o)]: (cs4_valid @ (cs4_impl @ (cs4_box @ (cs4_atom @ A)) @ (cs4_atom @ A)))))),inference(neg_conjecture,[status(cth)],[1])).
% 4.61/2.47 thf(8,plain,((~ (! [A:($i > $o),B:$i,C:$i]: ((reli @ B @ C) => (~ (! [D:$i]: ((reli @ C @ D) => (! [E:$i]: ((relr @ D @ E) => (! [F:$i]: ((reli @ E @ F) => (A @ F))))))) | ! [D:$i]: ((reli @ C @ D) => (A @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])).
% 4.61/2.47 thf(45,plain,(($false)),inference(e,[status(thm)],[14,20,38,32,26,8])).
% 4.61/2.47 % SZS output end Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.61/2.47 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------