%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : AGT028^2 : 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 : n018.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 5.17s 2.67s
% Output : Refutation 5.51s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : AGT028^2 : TPTP v9.3.1. Released v5.2.0.
% 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
% 0.11/0.22 % Computer : n018.cluster.edu
% 0.11/0.22 % Model : x86_64 x86_64
% 0.11/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.22 % Memory : 8046.5625MB
% 0.11/0.22 % OS : Linux 6.8.0-71-generic
% 0.11/0.22 % CPULimit : 300
% 0.11/0.22 % WCLimit : 300
% 0.11/0.22 % DateTime : Tue Sep 29 17:31:49 UTC 2026
% 0.11/0.22 % CPUTime :
% 0.11/0.22 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
% 1.05/0.80 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.51/1.10 % [INFO] Parsing done (292ms).
% 1.51/1.11 % [INFO] Running in sequential loop mode.
% 2.57/1.50 % [INFO] eprover registered as external prover.
% 2.57/1.51 % [INFO] Scanning for conjecture ...
% 2.99/1.70 % [INFO] Found a conjecture (or negated_conjecture) and 21 axioms. Running axiom selection ...
% 2.99/1.77 % [INFO] Axiom selection finished. Selected 21 axioms (removed 0 axioms).
% 3.20/1.80 % [INFO] Problem is higher-order (TPTP THF).
% 3.20/1.80 % [INFO] Type checking passed.
% 3.20/1.81 % [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 ...
% 5.17/2.66 % External prover 'e' found a proof!
% 5.17/2.66 % [INFO] Killing All external provers ...
% 5.17/2.66 % Time passed: 2304ms (effective reasoning time: 1545ms)
% 5.17/2.66 % 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)>
% 5.17/2.67 % Axioms used in derivation (21): axiom_r2_3, axiom_r3_1, axiom_r4_2, axiom_r3_5, axiom_r1, axiom_r4_1, axiom_r4_4, axiom_r2_1, axiom_r4_3, axiom_r3_3, axiom_a9, axiom_r2_2, axiom_a6, axiom_r2_5, axiom_r3_4, axiom_r5, axiom_a7, axiom_a8, axiom_r4_5, axiom_r3_2, axiom_r2_4
% 5.17/2.67 % No. of inferences in proof: 46
% 5.17/2.67 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2304 ms resp. 1545 ms w/o parsing
% 5.51/2.77 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.51/2.77 thf(mu_type, type, mu: $tType).
% 5.51/2.77 thf(mnot_decl, type, mnot: (($i > $o) > ($i > $o))).
% 5.51/2.77 thf(mor_decl, type, mor: (($i > $o) > (($i > $o) > ($i > $o)))).
% 5.51/2.77 thf(mimplies_decl, type, mimplies: (($i > $o) > (($i > $o) > ($i > $o)))).
% 5.51/2.77 thf(mforall_ind_decl, type, mforall_ind: ((mu > ($i > $o)) > ($i > $o))).
% 5.51/2.77 thf(mexists_ind_decl, type, mexists_ind: ((mu > ($i > $o)) > ($i > $o))).
% 5.51/2.77 thf(mbox_decl, type, mbox: (($i > ($i > $o)) > (($i > $o) > ($i > $o)))).
% 5.51/2.77 thf(mdia_decl, type, mdia: (($i > ($i > $o)) > (($i > $o) > ($i > $o)))).
% 5.51/2.77 thf(mvalid_decl, type, mvalid: (($i > $o) > $o)).
% 5.51/2.77 thf(r1_decl, type, r1: ($i > ($i > $o))).
% 5.51/2.77 thf(r2_decl, type, r2: ($i > ($i > $o))).
% 5.51/2.77 thf(r3_decl, type, r3: ($i > ($i > $o))).
% 5.51/2.77 thf(r4_decl, type, r4: ($i > ($i > $o))).
% 5.51/2.77 thf(r5_decl, type, r5: ($i > ($i > $o))).
% 5.51/2.77 thf(john_decl, type, john: mu).
% 5.51/2.77 thf(tom_decl, type, tom: mu).
% 5.51/2.77 thf(peter_decl, type, peter: mu).
% 5.51/2.77 thf(mike_decl, type, mike: mu).
% 5.51/2.77 thf(good_in_maths_decl, type, good_in_maths: (mu > ($i > $o))).
% 5.51/2.77 thf(maths_teacher_decl, type, maths_teacher: (mu > ($i > $o))).
% 5.51/2.77 thf(mathematician_decl, type, mathematician: (mu > ($i > $o))).
% 5.51/2.77 thf(maths_student_decl, type, maths_student: (mu > ($i > $o))).
% 5.51/2.77 thf(good_in_physics_decl, type, good_in_physics: (mu > ($i > $o))).
% 5.51/2.77 thf(physics_student_decl, type, physics_student: (mu > ($i > $o))).
% 5.51/2.77 thf(mnot_def, definition, mnot = (^ [A:($i > $o),B:$i]: ~ (A @ B)) ).
% 5.51/2.77 thf(mor_def, definition, mor = (^ [A:($i > $o),B:($i > $o),C:$i]: ((A @ C) | (B @ C))) ).
% 5.51/2.77 thf(mimplies_def, definition, mimplies = (^ [A:($i > $o)]: (mor @ (mnot @ A))) ).
% 5.51/2.77 thf(mforall_ind_def, definition, mforall_ind = (^ [A:(mu > ($i > $o)),B:$i]: ! [C:mu]: (A @ C @ B)) ).
% 5.51/2.77 thf(mexists_ind_def, definition, mexists_ind = (^ [A:(mu > ($i > $o))]: (mnot @ (mforall_ind @ (^ [B:mu]: (mnot @ (A @ B)))))) ).
% 5.51/2.77 thf(mbox_def, definition, mbox = (^ [A:($i > ($i > $o)),B:($i > $o),C:$i]: ! [D:$i]: (~ (A @ C @ D) | (B @ D))) ).
% 5.51/2.77 thf(mdia_def, definition, mdia = (^ [A:($i > ($i > $o)),B:($i > $o)]: (mnot @ (mbox @ A @ (mnot @ B)))) ).
% 5.51/2.77 thf(mvalid_def, definition, mvalid = ((!) @ $i) ).
% 5.51/2.77 thf(13,axiom,((mvalid @ (mbox @ r5 @ (maths_student @ peter)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_a8)).
% 5.51/2.77 thf(69,plain,((! [A:$i,B:$i]: (~ (r5 @ A @ B) | (maths_student @ peter @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[13])).
% 5.51/2.77 thf(19,axiom,((mvalid @ (mforall_ind @ (^ [A:mu]: (mbox @ r3 @ (mimplies @ (physics_student @ A) @ (mdia @ r5 @ (good_in_physics @ A)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_r4_5)).
% 5.51/2.77 thf(85,plain,((! [A:$i,B:mu,C:$i]: (~ (r3 @ A @ C) | ~ (physics_student @ B @ C) | ~ (! [D:$i]: (~ (r5 @ C @ D) | ~ (good_in_physics @ B @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[19])).
% 5.51/2.77 thf(4,axiom,((mvalid @ (mforall_ind @ (^ [A:mu]: (mbox @ r3 @ (mimplies @ (maths_student @ A) @ (mdia @ r3 @ (good_in_maths @ A)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_r3_3)).
% 5.51/2.77 thf(33,plain,((! [A:$i,B:mu,C:$i]: (~ (r3 @ A @ C) | ~ (maths_student @ B @ C) | ~ (! [D:$i]: (~ (r3 @ C @ D) | ~ (good_in_maths @ B @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4])).
% 5.51/2.77 thf(9,axiom,((mvalid @ (mforall_ind @ (^ [A:mu]: (mbox @ r5 @ (mimplies @ (mbox @ r3 @ (mathematician @ A)) @ (mbox @ r3 @ (good_in_maths @ A)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_r2_3)).
% 5.51/2.77 thf(53,plain,((! [A:$i,B:mu,C:$i]: (~ (r5 @ A @ C) | ~ (! [D:$i]: (~ (r3 @ C @ D) | (mathematician @ B @ D))) | ! [D:$i]: (~ (r3 @ C @ D) | (good_in_maths @ B @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[9])).
% 5.51/2.77 thf(16,axiom,((mvalid @ (maths_teacher @ john))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_a6)).
% 5.51/2.77 thf(77,plain,((! [A:$i]: (maths_teacher @ john @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[16])).
% 5.51/2.77 thf(6,axiom,((mvalid @ (mforall_ind @ (^ [A:mu]: (mbox @ r3 @ (mimplies @ (maths_student @ A) @ (mdia @ r5 @ (good_in_maths @ A)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_r3_5)).
% 5.51/2.77 thf(41,plain,((! [A:$i,B:mu,C:$i]: (~ (r3 @ A @ C) | ~ (maths_student @ B @ C) | ~ (! [D:$i]: (~ (r5 @ C @ D) | ~ (good_in_maths @ B @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6])).
% 5.51/2.77 thf(7,axiom,((mvalid @ (mforall_ind @ (^ [A:mu]: (mbox @ r5 @ (mimplies @ (mbox @ r1 @ (mathematician @ A)) @ (mbox @ r1 @ (good_in_maths @ A)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_r2_1)).
% 5.51/2.77 thf(45,plain,((! [A:$i,B:mu,C:$i]: (~ (r5 @ A @ C) | ~ (! [D:$i]: (~ (r1 @ C @ D) | (mathematician @ B @ D))) | ! [D:$i]: (~ (r1 @ C @ D) | (good_in_maths @ B @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7])).
% 5.51/2.77 thf(23,axiom,((mvalid @ (mforall_ind @ (^ [A:mu]: (mbox @ r5 @ (mimplies @ (mbox @ r4 @ (mathematician @ A)) @ (mbox @ r4 @ (good_in_maths @ A)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_r2_4)).
% 5.51/2.77 thf(99,plain,((! [A:$i,B:mu,C:$i]: (~ (r5 @ A @ C) | ~ (! [D:$i]: (~ (r4 @ C @ D) | (mathematician @ B @ D))) | ! [D:$i]: (~ (r4 @ C @ D) | (good_in_maths @ B @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[23])).
% 5.51/2.77 thf(15,axiom,((mvalid @ (mbox @ r2 @ (mathematician @ tom)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_a7)).
% 5.51/2.77 thf(75,plain,((! [A:$i,B:$i]: (~ (r2 @ A @ B) | (mathematician @ tom @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[15])).
% 5.51/2.77 thf(17,axiom,((mvalid @ (mforall_ind @ (^ [A:mu]: (mbox @ r3 @ (mimplies @ (maths_student @ A) @ (mdia @ r1 @ (good_in_maths @ A)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_r3_1)).
% 5.51/2.77 thf(79,plain,((! [A:$i,B:mu,C:$i]: (~ (r3 @ A @ C) | ~ (maths_student @ B @ C) | ~ (! [D:$i]: (~ (r1 @ C @ D) | ~ (good_in_maths @ B @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[17])).
% 5.51/2.77 thf(18,axiom,((mvalid @ (mbox @ r5 @ (physics_student @ mike)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_a9)).
% 5.51/2.77 thf(83,plain,((! [A:$i,B:$i]: (~ (r5 @ A @ B) | (physics_student @ mike @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[18])).
% 5.51/2.77 thf(1,conjecture,((mvalid @ (mexists_ind @ (^ [A:mu]: (mbox @ r4 @ (good_in_maths @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj)).
% 5.51/2.77 thf(2,negated_conjecture,((~ (mvalid @ (mexists_ind @ (^ [A:mu]: (mbox @ r4 @ (good_in_maths @ A))))))),inference(neg_conjecture,[status(cth)],[1])).
% 5.51/2.77 thf(24,plain,((~ (! [A:$i]: ~ (! [B:mu]: ~ (! [C:$i]: (~ (r4 @ A @ C) | (good_in_maths @ B @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])).
% 5.51/2.77 thf(5,axiom,((mvalid @ (mforall_ind @ (^ [A:mu]: (mbox @ r3 @ (mimplies @ (physics_student @ A) @ (mdia @ r2 @ (good_in_physics @ A)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_r4_2)).
% 5.51/2.77 thf(37,plain,((! [A:$i,B:mu,C:$i]: (~ (r3 @ A @ C) | ~ (physics_student @ B @ C) | ~ (! [D:$i]: (~ (r2 @ C @ D) | ~ (good_in_physics @ B @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5])).
% 5.51/2.77 thf(21,axiom,((mvalid @ (mforall_ind @ (^ [A:mu]: (mbox @ r5 @ (mimplies @ (mbox @ r5 @ (mathematician @ A)) @ (mbox @ r5 @ (good_in_maths @ A)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_r2_5)).
% 5.51/2.77 thf(93,plain,((! [A:$i,B:mu,C:$i]: (~ (r5 @ A @ C) | ~ (! [D:$i]: (~ (r5 @ C @ D) | (mathematician @ B @ D))) | ! [D:$i]: (~ (r5 @ C @ D) | (good_in_maths @ B @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[21])).
% 5.51/2.77 thf(10,axiom,((mvalid @ (mforall_ind @ (^ [A:mu]: (mbox @ r2 @ (mimplies @ (good_in_physics @ A) @ (mdia @ r2 @ (good_in_maths @ A)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_r5)).
% 5.51/2.77 thf(57,plain,((! [A:$i,B:mu,C:$i]: (~ (r2 @ A @ C) | ~ (good_in_physics @ B @ C) | ~ (! [D:$i]: (~ (r2 @ C @ D) | ~ (good_in_maths @ B @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[10])).
% 5.51/2.77 thf(3,axiom,((mvalid @ (mforall_ind @ (^ [A:mu]: (mbox @ r3 @ (mimplies @ (physics_student @ A) @ (mdia @ r1 @ (good_in_physics @ A)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_r4_1)).
% 5.51/2.77 thf(29,plain,((! [A:$i,B:mu,C:$i]: (~ (r3 @ A @ C) | ~ (physics_student @ B @ C) | ~ (! [D:$i]: (~ (r1 @ C @ D) | ~ (good_in_physics @ B @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3])).
% 5.51/2.77 thf(11,axiom,((mvalid @ (mforall_ind @ (^ [A:mu]: (mbox @ r5 @ (mimplies @ (mbox @ r2 @ (mathematician @ A)) @ (mbox @ r2 @ (good_in_maths @ A)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_r2_2)).
% 5.51/2.77 thf(61,plain,((! [A:$i,B:mu,C:$i]: (~ (r5 @ A @ C) | ~ (! [D:$i]: (~ (r2 @ C @ D) | (mathematician @ B @ D))) | ! [D:$i]: (~ (r2 @ C @ D) | (good_in_maths @ B @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[11])).
% 5.51/2.77 thf(20,axiom,((mvalid @ (mforall_ind @ (^ [A:mu]: (mbox @ r3 @ (mimplies @ (physics_student @ A) @ (mdia @ r4 @ (good_in_physics @ A)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_r4_4)).
% 5.51/2.77 thf(89,plain,((! [A:$i,B:mu,C:$i]: (~ (r3 @ A @ C) | ~ (physics_student @ B @ C) | ~ (! [D:$i]: (~ (r4 @ C @ D) | ~ (good_in_physics @ B @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[20])).
% 5.51/2.77 thf(12,axiom,((mvalid @ (mforall_ind @ (^ [A:mu]: (mbox @ r3 @ (mimplies @ (physics_student @ A) @ (mdia @ r3 @ (good_in_physics @ A)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_r4_3)).
% 5.51/2.77 thf(65,plain,((! [A:$i,B:mu,C:$i]: (~ (r3 @ A @ C) | ~ (physics_student @ B @ C) | ~ (! [D:$i]: (~ (r3 @ C @ D) | ~ (good_in_physics @ B @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[12])).
% 5.51/2.77 thf(22,axiom,((mvalid @ (mforall_ind @ (^ [A:mu]: (mimplies @ (maths_teacher @ A) @ (mbox @ r4 @ (good_in_maths @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_r1)).
% 5.51/2.77 thf(97,plain,((! [A:$i,B:mu]: (~ (maths_teacher @ B @ A) | ! [C:$i]: (~ (r4 @ A @ C) | (good_in_maths @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[22])).
% 5.51/2.77 thf(14,axiom,((mvalid @ (mforall_ind @ (^ [A:mu]: (mbox @ r3 @ (mimplies @ (maths_student @ A) @ (mdia @ r4 @ (good_in_maths @ A)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_r3_4)).
% 5.51/2.77 thf(71,plain,((! [A:$i,B:mu,C:$i]: (~ (r3 @ A @ C) | ~ (maths_student @ B @ C) | ~ (! [D:$i]: (~ (r4 @ C @ D) | ~ (good_in_maths @ B @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[14])).
% 5.51/2.77 thf(8,axiom,((mvalid @ (mforall_ind @ (^ [A:mu]: (mbox @ r3 @ (mimplies @ (maths_student @ A) @ (mdia @ r2 @ (good_in_maths @ A)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_r3_2)).
% 5.51/2.77 thf(49,plain,((! [A:$i,B:mu,C:$i]: (~ (r3 @ A @ C) | ~ (maths_student @ B @ C) | ~ (! [D:$i]: (~ (r2 @ C @ D) | ~ (good_in_maths @ B @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8])).
% 5.51/2.77 thf(103,plain,(($false)),inference(e,[status(thm)],[69,85,33,53,77,41,45,99,75,79,83,24,37,93,57,29,61,89,65,97,71,49])).
% 5.51/2.77 % SZS output end Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.51/2.77 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------