%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : AGT032^2 : TPTP v9.3.1. Released v5.2.0.
% 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 : 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 : Wed Sep 30 07:44:34 AM UTC 2026
% Result : Theorem 3.27s 1.54s
% Output : Refutation 3.53s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : AGT032^2 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.04 % 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
% 0.00/0.11 % Computer : n012.cluster.edu
% 0.00/0.11 % Model : x86_64 x86_64
% 0.00/0.11 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.11 % Memory : 8046.5625MB
% 0.00/0.11 % OS : Linux 6.8.0-71-generic
% 0.00/0.11 % CPULimit : 300
% 0.00/0.11 % WCLimit : 300
% 0.00/0.11 % DateTime : Tue Sep 29 17:30:09 UTC 2026
% 0.00/0.11 % CPUTime :
% 0.04/0.11 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
% 0.40/0.38 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.56/0.52 % [INFO] Parsing done (134ms).
% 0.56/0.53 % [INFO] Running in sequential loop mode.
% 1.12/0.73 % [INFO] eprover registered as external prover.
% 1.12/0.73 % [INFO] Scanning for conjecture ...
% 1.37/0.87 % [INFO] Found a conjecture (or negated_conjecture) and 18 axioms. Running axiom selection ...
% 1.58/0.93 % [INFO] Axiom selection finished. Selected 18 axioms (removed 0 axioms).
% 1.58/0.95 % [INFO] Problem is higher-order (TPTP THF).
% 1.58/0.95 % [INFO] Type checking passed.
% 1.58/0.95 % [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 ...
% 3.27/1.54 % External prover 'e' found a proof!
% 3.27/1.54 % [INFO] Killing All external provers ...
% 3.27/1.54 % Time passed: 1353ms (effective reasoning time: 1008ms)
% 3.27/1.54 % 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)>
% 3.27/1.54 % Axioms used in derivation (18): axiom_a1_4, axiom_a3_3, axiom_user_communication_3, axiom_a2_2, axiom_a3_4, axiom_a1_1, axiom_user_communication_4, axiom_a2_3, axiom_a1_2, axiom_a2_5, axiom_user_communication_2, axiom_a1_3, axiom_a3_2, axiom_a2_1, axiom_user_communication_1, axiom_a2_4, axiom_user_communication_5, axiom_a3_1
% 3.27/1.54 % No. of inferences in proof: 40
% 3.27/1.54 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1353 ms resp. 1008 ms w/o parsing
% 3.53/1.63 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.53/1.63 thf(mu_type, type, mu: $tType).
% 3.53/1.63 thf(mnot_decl, type, mnot: (($i > $o) > ($i > $o))).
% 3.53/1.63 thf(mor_decl, type, mor: (($i > $o) > (($i > $o) > ($i > $o)))).
% 3.53/1.63 thf(mand_decl, type, mand: (($i > $o) > (($i > $o) > ($i > $o)))).
% 3.53/1.63 thf(mimplies_decl, type, mimplies: (($i > $o) > (($i > $o) > ($i > $o)))).
% 3.53/1.63 thf(mforall_ind_decl, type, mforall_ind: ((mu > ($i > $o)) > ($i > $o))).
% 3.53/1.63 thf(mexists_ind_decl, type, mexists_ind: ((mu > ($i > $o)) > ($i > $o))).
% 3.53/1.63 thf(mbox_decl, type, mbox: (($i > ($i > $o)) > (($i > $o) > ($i > $o)))).
% 3.53/1.63 thf(mdia_decl, type, mdia: (($i > ($i > $o)) > (($i > $o) > ($i > $o)))).
% 3.53/1.63 thf(mvalid_decl, type, mvalid: (($i > $o) > $o)).
% 3.53/1.63 thf(a1_decl, type, a1: ($i > ($i > $o))).
% 3.53/1.63 thf(a2_decl, type, a2: ($i > ($i > $o))).
% 3.53/1.63 thf(a3_decl, type, a3: ($i > ($i > $o))).
% 3.53/1.63 thf(jan_decl, type, jan: mu).
% 3.53/1.63 thf(piotr_decl, type, piotr: mu).
% 3.53/1.63 thf(cola_decl, type, cola: mu).
% 3.53/1.63 thf(pepsi_decl, type, pepsi: mu).
% 3.53/1.63 thf(beer_decl, type, beer: mu).
% 3.53/1.63 thf(likes_decl, type, likes: (mu > (mu > ($i > $o)))).
% 3.53/1.63 thf(very_much_likes_decl, type, very_much_likes: (mu > (mu > ($i > $o)))).
% 3.53/1.63 thf(possibly_likes_decl, type, possibly_likes: (mu > (mu > ($i > $o)))).
% 3.53/1.63 thf(mnot_def, definition, mnot = (^ [A:($i > $o),B:$i]: ~ (A @ B)) ).
% 3.53/1.63 thf(mor_def, definition, mor = (^ [A:($i > $o),B:($i > $o),C:$i]: ((A @ C) | (B @ C))) ).
% 3.53/1.63 thf(mand_def, definition, mand = (^ [A:($i > $o),B:($i > $o)]: (mnot @ (mor @ (mnot @ A) @ (mnot @ B)))) ).
% 3.53/1.63 thf(mimplies_def, definition, mimplies = (^ [A:($i > $o)]: (mor @ (mnot @ A))) ).
% 3.53/1.63 thf(mforall_ind_def, definition, mforall_ind = (^ [A:(mu > ($i > $o)),B:$i]: ! [C:mu]: (A @ C @ B)) ).
% 3.53/1.63 thf(mexists_ind_def, definition, mexists_ind = (^ [A:(mu > ($i > $o))]: (mnot @ (mforall_ind @ (^ [B:mu]: (mnot @ (A @ B)))))) ).
% 3.53/1.63 thf(mbox_def, definition, mbox = (^ [A:($i > ($i > $o)),B:($i > $o),C:$i]: ! [D:$i]: (~ (A @ C @ D) | (B @ D))) ).
% 3.53/1.63 thf(mdia_def, definition, mdia = (^ [A:($i > ($i > $o)),B:($i > $o)]: (mnot @ (mbox @ A @ (mnot @ B)))) ).
% 3.53/1.63 thf(mvalid_def, definition, mvalid = ((!) @ $i) ).
% 3.53/1.63 thf(15,axiom,((mvalid @ (mforall_ind @ (^ [A:mu]: (mbox @ a1 @ (mimplies @ (mdia @ a1 @ (likes @ A @ cola)) @ (likes @ A @ pepsi))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_a1_4)).
% 3.53/1.63 thf(56,plain,((! [A:$i,B:mu,C:$i]: (~ (a1 @ A @ C) | ! [D:$i]: (~ (a1 @ C @ D) | ~ (likes @ B @ cola @ D)) | (likes @ B @ pepsi @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[15])).
% 3.53/1.63 thf(13,axiom,((mvalid @ (mbox @ a2 @ (likes @ jan @ pepsi)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_a2_1)).
% 3.53/1.63 thf(52,plain,((! [A:$i,B:$i]: (~ (a2 @ A @ B) | (likes @ jan @ pepsi @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[13])).
% 3.53/1.63 thf(10,axiom,((mvalid @ (mbox @ a1 @ (likes @ piotr @ beer)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_a2_3)).
% 3.53/1.63 thf(46,plain,((! [A:$i,B:$i]: (~ (a1 @ A @ B) | (likes @ piotr @ beer @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[10])).
% 3.53/1.63 thf(17,axiom,((mvalid @ (mforall_ind @ (^ [A:mu]: (mforall_ind @ (^ [B:mu]: (mbox @ a3 @ (mimplies @ (mand @ (likes @ A @ B) @ (mand @ (mbox @ a1 @ (likes @ A @ B)) @ (mbox @ a2 @ (likes @ A @ B)))) @ (very_much_likes @ A @ B))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_a3_4)).
% 3.53/1.63 thf(60,plain,((! [A:$i,B:mu,C:mu,D:$i]: (~ (a3 @ A @ D) | ~ (likes @ B @ C @ D) | ~ (! [E:$i]: (~ (a1 @ D @ E) | (likes @ B @ C @ E))) | ~ (! [E:$i]: (~ (a2 @ D @ E) | (likes @ B @ C @ E))) | (very_much_likes @ B @ C @ D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[17])).
% 3.53/1.63 thf(9,axiom,((mvalid @ (mforall_ind @ (^ [A:mu]: (mforall_ind @ (^ [B:mu]: (mimplies @ (mdia @ a1 @ (likes @ A @ B)) @ (possibly_likes @ A @ B)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_user_communication_3)).
% 3.53/1.63 thf(44,plain,((! [A:$i,B:mu,C:mu]: (! [D:$i]: (~ (a1 @ A @ D) | ~ (likes @ B @ C @ D)) | (possibly_likes @ B @ C @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[9])).
% 3.53/1.63 thf(14,axiom,((mvalid @ (mforall_ind @ (^ [A:mu]: (mforall_ind @ (^ [B:mu]: (mimplies @ (mdia @ a3 @ (likes @ A @ B)) @ (possibly_likes @ A @ B)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_user_communication_5)).
% 3.53/1.63 thf(54,plain,((! [A:$i,B:mu,C:mu]: (! [D:$i]: (~ (a3 @ A @ D) | ~ (likes @ B @ C @ D)) | (possibly_likes @ B @ C @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[14])).
% 3.53/1.63 thf(8,axiom,((mvalid @ (mdia @ a1 @ (likes @ piotr @ beer)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_a3_3)).
% 3.53/1.63 thf(39,plain,((! [A:$i]: ~ (! [B:$i]: (~ (a1 @ A @ B) | ~ (likes @ piotr @ beer @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8])).
% 3.53/1.63 thf(18,axiom,((mvalid @ (mbox @ a3 @ (likes @ jan @ cola)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_a3_1)).
% 3.53/1.63 thf(66,plain,((! [A:$i,B:$i]: (~ (a3 @ A @ B) | (likes @ jan @ cola @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[18])).
% 3.53/1.63 thf(6,axiom,((mvalid @ (mbox @ a1 @ (likes @ jan @ cola)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_a1_1)).
% 3.53/1.63 thf(35,plain,((! [A:$i,B:$i]: (~ (a1 @ A @ B) | (likes @ jan @ cola @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6])).
% 3.53/1.63 thf(11,axiom,((mvalid @ (mforall_ind @ (^ [A:mu]: (mbox @ a1 @ (mimplies @ (mdia @ a1 @ (likes @ A @ pepsi)) @ (likes @ A @ cola))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_a1_3)).
% 3.53/1.63 thf(48,plain,((! [A:$i,B:mu,C:$i]: (~ (a1 @ A @ C) | ! [D:$i]: (~ (a1 @ C @ D) | ~ (likes @ B @ pepsi @ D)) | (likes @ B @ cola @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[11])).
% 3.53/1.63 thf(12,axiom,((mvalid @ (mforall_ind @ (^ [A:mu]: (mbox @ a2 @ (mimplies @ (likes @ A @ pepsi) @ (likes @ A @ cola))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_a2_4)).
% 3.53/1.63 thf(50,plain,((! [A:$i,B:mu,C:$i]: (~ (a2 @ A @ C) | ~ (likes @ B @ pepsi @ C) | (likes @ B @ cola @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[12])).
% 3.53/1.63 thf(16,axiom,((mvalid @ (mbox @ a1 @ (likes @ piotr @ pepsi)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_a1_2)).
% 3.53/1.63 thf(58,plain,((! [A:$i,B:$i]: (~ (a1 @ A @ B) | (likes @ piotr @ pepsi @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[16])).
% 3.53/1.63 thf(5,axiom,((mvalid @ (mdia @ a3 @ (likes @ piotr @ pepsi)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_a3_2)).
% 3.53/1.63 thf(30,plain,((! [A:$i]: ~ (! [B:$i]: (~ (a3 @ A @ B) | ~ (likes @ piotr @ pepsi @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5])).
% 3.53/1.63 thf(19,axiom,((mvalid @ (mforall_ind @ (^ [A:mu]: (mbox @ a2 @ (mimplies @ (likes @ A @ cola) @ (likes @ A @ pepsi))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_a2_5)).
% 3.53/1.63 thf(68,plain,((! [A:$i,B:mu,C:$i]: (~ (a2 @ A @ C) | ~ (likes @ B @ cola @ C) | (likes @ B @ pepsi @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[19])).
% 3.53/1.63 thf(3,axiom,((mvalid @ (mforall_ind @ (^ [A:mu]: (mforall_ind @ (^ [B:mu]: (mimplies @ (mbox @ a3 @ (very_much_likes @ A @ B)) @ (very_much_likes @ A @ B)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_user_communication_1)).
% 3.53/1.63 thf(24,plain,((! [A:$i,B:mu,C:mu]: (~ (! [D:$i]: (~ (a3 @ A @ D) | (very_much_likes @ B @ C @ D))) | (very_much_likes @ B @ C @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3])).
% 3.53/1.63 thf(7,axiom,((mvalid @ (mforall_ind @ (^ [A:mu]: (mforall_ind @ (^ [B:mu]: (mimplies @ (mdia @ a3 @ (very_much_likes @ A @ B)) @ (likes @ A @ B)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_user_communication_2)).
% 3.53/1.63 thf(37,plain,((! [A:$i,B:mu,C:mu]: (! [D:$i]: (~ (a3 @ A @ D) | ~ (very_much_likes @ B @ C @ D)) | (likes @ B @ C @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7])).
% 3.53/1.63 thf(4,axiom,((mvalid @ (mbox @ a1 @ (likes @ piotr @ cola)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_a2_2)).
% 3.53/1.63 thf(28,plain,((! [A:$i,B:$i]: (~ (a1 @ A @ B) | (likes @ piotr @ cola @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4])).
% 3.53/1.63 thf(20,axiom,((mvalid @ (mforall_ind @ (^ [A:mu]: (mforall_ind @ (^ [B:mu]: (mimplies @ (mdia @ a2 @ (likes @ A @ B)) @ (possibly_likes @ A @ B)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_user_communication_4)).
% 3.53/1.63 thf(70,plain,((! [A:$i,B:mu,C:mu]: (! [D:$i]: (~ (a2 @ A @ D) | ~ (likes @ B @ C @ D)) | (possibly_likes @ B @ C @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[20])).
% 3.53/1.63 thf(1,conjecture,((mvalid @ (mexists_ind @ (^ [A:mu]: (mexists_ind @ (likes @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj)).
% 3.53/1.63 thf(2,negated_conjecture,((~ (mvalid @ (mexists_ind @ (^ [A:mu]: (mexists_ind @ (likes @ A))))))),inference(neg_conjecture,[status(cth)],[1])).
% 3.53/1.63 thf(21,plain,((~ (! [A:$i]: ~ (! [B:mu,C:mu]: ~ (likes @ B @ C @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])).
% 3.53/1.63 thf(80,plain,(($false)),inference(e,[status(thm)],[56,52,46,60,44,54,39,66,35,48,50,58,30,68,24,37,28,70,21])).
% 3.53/1.63 % SZS output end Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.53/1.63 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------