%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : PUZ086^1 : TPTP v9.3.1. Released v4.0.0.
% 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 : 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 08:20:45 AM UTC 2026
% Result : Theorem 4.56s 2.44s
% Output : Refutation 4.86s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PUZ086^1 : TPTP v9.3.1. Released v4.0.0.
% 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
% 0.10/0.20 % 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 13:23:43 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
% 0.90/0.79 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.61/1.05 % [INFO] Parsing done (252ms).
% 1.61/1.06 % [INFO] Running in sequential loop mode.
% 2.34/1.45 % [INFO] eprover registered as external prover.
% 2.34/1.46 % [INFO] Scanning for conjecture ...
% 2.78/1.65 % [INFO] Found a conjecture (or negated_conjecture) and 12 axioms. Running axiom selection ...
% 2.78/1.68 % [INFO] Axiom selection finished. Selected 12 axioms (removed 0 axioms).
% 2.78/1.69 % [INFO] Problem is higher-order (TPTP THF).
% 2.78/1.69 % [INFO] Type checking passed.
% 2.96/1.70 % [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 ...
% 4.56/2.44 % External prover 'e' found a proof!
% 4.56/2.44 % [INFO] Killing All external provers ...
% 4.56/2.44 % Time passed: 2086ms (effective reasoning time: 1367ms)
% 4.56/2.44 % 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)>
% 4.56/2.44 % Axioms used in derivation (12): ax_i, trans_peter, ax_c, ax_b, trans_john, ax_ii, ax_a, refl_john, ax_d, refl_wife_peter, trans_wife_peter, refl_peter
% 4.56/2.44 % No. of inferences in proof: 28
% 4.56/2.44 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2086 ms resp. 1367 ms w/o parsing
% 4.86/2.52 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.86/2.52 thf(mu_type, type, mu: $tType).
% 4.86/2.52 thf(mnot_decl, type, mnot: (($i > $o) > ($i > $o))).
% 4.86/2.52 thf(mor_decl, type, mor: (($i > $o) > (($i > $o) > ($i > $o)))).
% 4.86/2.52 thf(mand_decl, type, mand: (($i > $o) > (($i > $o) > ($i > $o)))).
% 4.86/2.52 thf(mimplies_decl, type, mimplies: (($i > $o) > (($i > $o) > ($i > $o)))).
% 4.86/2.52 thf(mforall_prop_decl, type, mforall_prop: ((($i > $o) > ($i > $o)) > ($i > $o))).
% 4.86/2.52 thf(mbox_decl, type, mbox: (($i > ($i > $o)) > (($i > $o) > ($i > $o)))).
% 4.86/2.52 thf(mreflexive_decl, type, mreflexive: (($i > ($i > $o)) > $o)).
% 4.86/2.52 thf(mtransitive_decl, type, mtransitive: (($i > ($i > $o)) > $o)).
% 4.86/2.52 thf(mvalid_decl, type, mvalid: (($i > $o) > $o)).
% 4.86/2.52 thf(peter_decl, type, peter: ($i > ($i > $o))).
% 4.86/2.52 thf(john_decl, type, john: ($i > ($i > $o))).
% 4.86/2.52 thf(wife_decl, type, wife: (($i > ($i > $o)) > ($i > ($i > $o)))).
% 4.86/2.52 thf(time_decl, type, time: ($i > $o)).
% 4.86/2.52 thf(place_decl, type, place: ($i > $o)).
% 4.86/2.52 thf(appointment_decl, type, appointment: ($i > $o)).
% 4.86/2.52 thf(mnot_def, definition, mnot = (^ [A:($i > $o),B:$i]: ~ (A @ B)) ).
% 4.86/2.52 thf(mor_def, definition, mor = (^ [A:($i > $o),B:($i > $o),C:$i]: ((A @ C) | (B @ C))) ).
% 4.86/2.52 thf(mand_def, definition, mand = (^ [A:($i > $o),B:($i > $o)]: (mnot @ (mor @ (mnot @ A) @ (mnot @ B)))) ).
% 4.86/2.52 thf(mimplies_def, definition, mimplies = (^ [A:($i > $o)]: (mor @ (mnot @ A))) ).
% 4.86/2.52 thf(mforall_prop_def, definition, mforall_prop = (^ [A:(($i > $o) > ($i > $o)),B:$i]: ! [C:($i > $o)]: (A @ C @ B)) ).
% 4.86/2.52 thf(mbox_def, definition, mbox = (^ [A:($i > ($i > $o)),B:($i > $o),C:$i]: ! [D:$i]: (~ (A @ C @ D) | (B @ D))) ).
% 4.86/2.52 thf(mreflexive_def, definition, mreflexive = (^ [A:($i > ($i > $o))]: ! [B:$i]: (A @ B @ B)) ).
% 4.86/2.52 thf(mtransitive_def, definition, mtransitive = (^ [A:($i > ($i > $o))]: ! [B:$i,C:$i,D:$i]: (((A @ B @ C) & (A @ C @ D)) => (A @ B @ D))) ).
% 4.86/2.52 thf(mvalid_def, definition, mvalid = ((!) @ $i) ).
% 4.86/2.52 thf(3,axiom,((mreflexive @ peter)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',refl_peter)).
% 4.86/2.52 thf(24,plain,((! [A:$i]: (peter @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3])).
% 4.86/2.52 thf(14,axiom,((mvalid @ (mbox @ peter @ (mbox @ john @ (mimplies @ (mand @ place @ time) @ appointment))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_d)).
% 4.86/2.52 thf(57,plain,((! [A:$i,B:$i]: (~ (peter @ A @ B) | ! [C:$i]: (~ (john @ B @ C) | ~ (place @ C) | ~ (time @ C) | (appointment @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[14])).
% 4.86/2.52 thf(5,axiom,((mreflexive @ (wife @ peter))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',refl_wife_peter)).
% 4.86/2.52 thf(28,plain,((! [A:$i]: (wife @ (peter) @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5])).
% 4.86/2.52 thf(13,axiom,((mvalid @ (mbox @ (wife @ peter) @ (mimplies @ (mbox @ peter @ time) @ (mbox @ john @ time))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_c)).
% 4.86/2.52 thf(53,plain,((! [A:$i,B:$i]: (~ (wife @ (peter) @ A @ B) | ~ (! [C:$i]: (~ (peter @ B @ C) | (time @ C))) | ! [C:$i]: (~ (john @ B @ C) | (time @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[13])).
% 4.86/2.52 thf(11,axiom,((mvalid @ (mbox @ peter @ time))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_a)).
% 4.86/2.52 thf(49,plain,((! [A:$i,B:$i]: (~ (peter @ A @ B) | (time @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[11])).
% 4.86/2.52 thf(10,axiom,((mvalid @ (mforall_prop @ (^ [A:($i > $o)]: (mimplies @ (mbox @ (wife @ peter) @ A) @ (mbox @ peter @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_ii)).
% 4.86/2.52 thf(43,plain,((! [A:$i,B:($i > $o)]: (~ (! [C:$i]: (~ (wife @ (peter) @ A @ C) | (B @ C))) | ! [C:$i]: (~ (peter @ A @ C) | (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[10])).
% 4.86/2.52 thf(4,axiom,((mreflexive @ john)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',refl_john)).
% 4.86/2.52 thf(26,plain,((! [A:$i]: (john @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4])).
% 4.86/2.52 thf(1,conjecture,((mvalid @ (mand @ (mbox @ peter @ (mbox @ john @ appointment)) @ (mbox @ john @ (mbox @ peter @ appointment))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj)).
% 4.86/2.52 thf(2,negated_conjecture,((~ (mvalid @ (mand @ (mbox @ peter @ (mbox @ john @ appointment)) @ (mbox @ john @ (mbox @ peter @ appointment)))))),inference(neg_conjecture,[status(cth)],[1])).
% 4.86/2.52 thf(15,plain,((~ (! [A:$i]: ~ (~ (! [B:$i]: (~ (peter @ A @ B) | ! [C:$i]: (~ (john @ B @ C) | (appointment @ C)))) | ~ (! [B:$i]: (~ (john @ A @ B) | ! [C:$i]: (~ (peter @ B @ C) | (appointment @ C)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])).
% 4.86/2.52 thf(7,axiom,((mtransitive @ john)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',trans_john)).
% 4.86/2.52 thf(32,plain,((! [A:$i,B:$i,C:$i]: (((john @ A @ B) & (john @ B @ C)) => (john @ A @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7])).
% 4.86/2.52 thf(8,axiom,((mtransitive @ (wife @ peter))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',trans_wife_peter)).
% 4.86/2.52 thf(34,plain,((! [A:$i,B:$i,C:$i]: (((wife @ (peter) @ A @ B) & (wife @ (peter) @ B @ C)) => (wife @ (peter) @ A @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8])).
% 4.86/2.52 thf(9,axiom,((mvalid @ (mforall_prop @ (^ [A:($i > $o)]: (mimplies @ (mbox @ peter @ (mbox @ john @ A)) @ (mbox @ john @ (mbox @ peter @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_i)).
% 4.86/2.52 thf(36,plain,((! [A:$i,B:($i > $o)]: (~ (! [C:$i]: (~ (peter @ A @ C) | ! [D:$i]: (~ (john @ C @ D) | (B @ D)))) | ! [C:$i]: (~ (john @ A @ C) | ! [D:$i]: (~ (peter @ C @ D) | (B @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[9])).
% 4.86/2.52 thf(6,axiom,((mtransitive @ peter)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',trans_peter)).
% 4.86/2.52 thf(30,plain,((! [A:$i,B:$i,C:$i]: (((peter @ A @ B) & (peter @ B @ C)) => (peter @ A @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6])).
% 4.86/2.52 thf(12,axiom,((mvalid @ (mbox @ peter @ (mbox @ john @ place)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_b)).
% 4.86/2.52 thf(51,plain,((! [A:$i,B:$i]: (~ (peter @ A @ B) | ! [C:$i]: (~ (john @ B @ C) | (place @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[12])).
% 4.86/2.52 thf(59,plain,(($false)),inference(e,[status(thm)],[24,57,28,53,49,43,26,15,32,34,36,30,51])).
% 4.86/2.52 % SZS output end Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.86/2.52 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------