%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NLP264^7 : TPTP v9.3.1. Released v5.5.0.
% 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 : n017.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 08:16:17 AM UTC 2026
% Result : Theorem 4.76s 2.42s
% Output : Refutation 5.07s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NLP264^7 : TPTP v9.3.1. Released v5.5.0.
% 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
% 0.10/0.24 % Computer : n017.cluster.edu
% 0.10/0.24 % Model : x86_64 x86_64
% 0.10/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.24 % Memory : 8046.5625MB
% 0.10/0.24 % OS : Linux 6.8.0-71-generic
% 0.10/0.24 % CPULimit : 300
% 0.10/0.24 % WCLimit : 300
% 0.10/0.24 % DateTime : Tue Sep 29 11:36:51 UTC 2026
% 0.10/0.24 % CPUTime :
% 0.10/0.24 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
% 1.07/0.84 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.91/1.14 % [INFO] Parsing done (291ms).
% 1.91/1.15 % [INFO] Running in sequential loop mode.
% 2.55/1.56 % [INFO] eprover registered as external prover.
% 2.55/1.57 % [INFO] Scanning for conjecture ...
% 3.01/1.74 % [INFO] Found a conjecture (or negated_conjecture) and 15 axioms. Running axiom selection ...
% 3.21/1.81 % [INFO] Axiom selection finished. Selected 15 axioms (removed 0 axioms).
% 3.21/1.82 % [INFO] Problem is higher-order (TPTP THF).
% 3.21/1.82 % [INFO] Type checking passed.
% 3.21/1.83 % [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 ...
% 4.76/2.42 % External prover 'e' found a proof!
% 4.76/2.42 % [INFO] Killing All external provers ...
% 4.76/2.42 % Time passed: 2019ms (effective reasoning time: 1261ms)
% 4.76/2.42 % 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)>
% 4.76/2.42 % Axioms used in derivation (15): law1, law3, existence_of_first_ax, belief1, cumulative_ax, a1, nonempty_ax, a2, law2, belief2, existence_of_ninetyfive_ax, existence_of_second_ax, law4, existence_of_seventy_ax, existence_of_paris_ax
% 4.76/2.42 % No. of inferences in proof: 34
% 4.76/2.42 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2019 ms resp. 1261 ms w/o parsing
% 5.07/2.50 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.07/2.50 thf(mu_type, type, mu: $tType).
% 5.07/2.50 thf(mnot_decl, type, mnot: (($i > $o) > ($i > $o))).
% 5.07/2.50 thf(mor_decl, type, mor: (($i > $o) > (($i > $o) > ($i > $o)))).
% 5.07/2.50 thf(mand_decl, type, mand: (($i > $o) > (($i > $o) > ($i > $o)))).
% 5.07/2.50 thf(mimplies_decl, type, mimplies: (($i > $o) > (($i > $o) > ($i > $o)))).
% 5.07/2.50 thf(exists_in_world_decl, type, exists_in_world: (mu > ($i > $o))).
% 5.07/2.50 thf(mreflexive_decl, type, mreflexive: (($i > ($i > $o)) > $o)).
% 5.07/2.50 thf(mtransitive_decl, type, mtransitive: (($i > ($i > $o)) > $o)).
% 5.07/2.50 thf(mvalid_decl, type, mvalid: (($i > $o) > $o)).
% 5.07/2.50 thf(rel_s4_decl, type, rel_s4: ($i > ($i > $o))).
% 5.07/2.50 thf(mbox_s4_decl, type, mbox_s4: (($i > $o) > ($i > $o))).
% 5.07/2.50 thf(dest_decl, type, dest: (mu > ($i > $o))).
% 5.07/2.50 thf(class_decl, type, class: (mu > ($i > $o))).
% 5.07/2.50 thf(price_decl, type, price: (mu > ($i > $o))).
% 5.07/2.50 thf(first_decl, type, first: mu).
% 5.07/2.50 thf(ninetyfive_decl, type, ninetyfive: mu).
% 5.07/2.50 thf(paris_decl, type, paris: mu).
% 5.07/2.50 thf(second_decl, type, second: mu).
% 5.07/2.50 thf(seventy_decl, type, seventy: mu).
% 5.07/2.50 thf(mnot_def, definition, mnot = (^ [A:($i > $o),B:$i]: ~ (A @ B)) ).
% 5.07/2.50 thf(mor_def, definition, mor = (^ [A:($i > $o),B:($i > $o),C:$i]: ((A @ C) | (B @ C))) ).
% 5.07/2.50 thf(mand_def, definition, mand = (^ [A:($i > $o),B:($i > $o)]: (mnot @ (mor @ (mnot @ A) @ (mnot @ B)))) ).
% 5.07/2.50 thf(mimplies_def, definition, mimplies = (^ [A:($i > $o)]: (mor @ (mnot @ A))) ).
% 5.07/2.50 thf(mreflexive_def, definition, mreflexive = (^ [A:($i > ($i > $o))]: ! [B:$i]: (A @ B @ B)) ).
% 5.07/2.50 thf(mtransitive_def, definition, mtransitive = (^ [A:($i > ($i > $o))]: ! [B:$i,C:$i,D:$i]: (((A @ B @ C) & (A @ C @ D)) => (A @ B @ D))) ).
% 5.07/2.50 thf(mvalid_def, definition, mvalid = ((!) @ $i) ).
% 5.07/2.50 thf(mbox_s4_def, definition, mbox_s4 = (^ [A:($i > $o),B:$i]: ! [C:$i]: (~ (rel_s4 @ B @ C) | (A @ C))) ).
% 5.07/2.50 thf(15,axiom,((mvalid @ (mbox_s4 @ (mnot @ (mand @ (class @ first) @ (class @ second)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',law3)).
% 5.07/2.50 thf(46,plain,((! [A:$i,B:$i]: (~ (rel_s4 @ A @ B) | ~ (class @ first @ B) | ~ (class @ second @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[15])).
% 5.07/2.50 thf(17,axiom,((mreflexive @ rel_s4)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a1)).
% 5.07/2.50 thf(50,plain,((! [A:$i]: (rel_s4 @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[17])).
% 5.07/2.50 thf(13,axiom,((mtransitive @ rel_s4)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a2)).
% 5.07/2.50 thf(42,plain,((! [A:$i,B:$i,C:$i]: (((rel_s4 @ A @ B) & (rel_s4 @ B @ C)) => (rel_s4 @ A @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[13])).
% 5.07/2.50 thf(4,axiom,((! [A:$i]: (exists_in_world @ paris @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_paris_ax)).
% 5.07/2.50 thf(24,plain,((! [A:$i]: (exists_in_world @ paris @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4])).
% 5.07/2.50 thf(6,axiom,((! [A:$i]: (exists_in_world @ first @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_first_ax)).
% 5.07/2.50 thf(28,plain,((! [A:$i]: (exists_in_world @ first @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6])).
% 5.07/2.50 thf(11,axiom,((! [A:$i]: (exists_in_world @ seventy @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_seventy_ax)).
% 5.07/2.50 thf(38,plain,((! [A:$i]: (exists_in_world @ seventy @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[11])).
% 5.07/2.50 thf(8,axiom,((mvalid @ (mbox_s4 @ (mimplies @ (mand @ (dest @ paris) @ (class @ first)) @ (price @ ninetyfive))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',law1)).
% 5.07/2.50 thf(32,plain,((! [A:$i,B:$i]: (~ (rel_s4 @ A @ B) | ~ (dest @ paris @ B) | ~ (class @ first @ B) | (price @ ninetyfive @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8])).
% 5.07/2.50 thf(9,axiom,((mvalid @ (mbox_s4 @ (mimplies @ (mand @ (dest @ paris) @ (class @ second)) @ (price @ seventy))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',law2)).
% 5.07/2.50 thf(34,plain,((! [A:$i,B:$i]: (~ (rel_s4 @ A @ B) | ~ (dest @ paris @ B) | ~ (class @ second @ B) | (price @ seventy @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[9])).
% 5.07/2.50 thf(3,axiom,((! [A:$i]: ? [B:mu]: (exists_in_world @ B @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonempty_ax)).
% 5.07/2.50 thf(22,plain,((! [A:$i]: ? [B:mu]: (exists_in_world @ B @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3])).
% 5.07/2.50 thf(14,axiom,((mvalid @ (mbox_s4 @ (class @ second)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',belief2)).
% 5.07/2.50 thf(44,plain,((! [A:$i,B:$i]: (~ (rel_s4 @ A @ B) | (class @ second @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[14])).
% 5.07/2.50 thf(16,axiom,((mvalid @ (mbox_s4 @ (mnot @ (mand @ (price @ ninetyfive) @ (price @ seventy)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',law4)).
% 5.07/2.50 thf(48,plain,((! [A:$i,B:$i]: (~ (rel_s4 @ A @ B) | ~ (price @ ninetyfive @ B) | ~ (price @ seventy @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[16])).
% 5.07/2.50 thf(1,conjecture,((mvalid @ (mbox_s4 @ (price @ seventy)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con)).
% 5.07/2.50 thf(2,negated_conjecture,((~ (mvalid @ (mbox_s4 @ (price @ seventy))))),inference(neg_conjecture,[status(cth)],[1])).
% 5.07/2.50 thf(18,plain,((~ (! [A:$i,B:$i]: (~ (rel_s4 @ A @ B) | (price @ seventy @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])).
% 5.07/2.50 thf(12,axiom,((mvalid @ (mbox_s4 @ (dest @ paris)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',belief1)).
% 5.07/2.50 thf(40,plain,((! [A:$i,B:$i]: (~ (rel_s4 @ A @ B) | (dest @ paris @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[12])).
% 5.07/2.50 thf(5,axiom,((! [A:$i]: (exists_in_world @ ninetyfive @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_ninetyfive_ax)).
% 5.07/2.50 thf(26,plain,((! [A:$i]: (exists_in_world @ ninetyfive @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5])).
% 5.07/2.50 thf(10,axiom,((! [A:mu,B:$i,C:$i]: (((exists_in_world @ A @ B) & (rel_s4 @ B @ C)) => (exists_in_world @ A @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cumulative_ax)).
% 5.07/2.50 thf(36,plain,((! [A:mu,B:$i,C:$i]: (((exists_in_world @ A @ B) & (rel_s4 @ B @ C)) => (exists_in_world @ A @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[10])).
% 5.07/2.50 thf(7,axiom,((! [A:$i]: (exists_in_world @ second @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_second_ax)).
% 5.07/2.50 thf(30,plain,((! [A:$i]: (exists_in_world @ second @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7])).
% 5.07/2.50 thf(52,plain,(($false)),inference(e,[status(thm)],[46,50,42,24,28,38,32,34,22,44,48,18,40,26,36,30])).
% 5.07/2.50 % SZS output end Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.07/2.50 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------