%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : AGT030^1 : 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 : n001.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 33.23s 7.95s
% Output : Refutation 33.98s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : AGT030^1 : 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
% 0.12/0.22 % Computer : n001.cluster.edu
% 0.12/0.22 % Model : x86_64 x86_64
% 0.12/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.22 % Memory : 8046.5625MB
% 0.12/0.22 % OS : Linux 6.8.0-71-generic
% 0.12/0.22 % CPULimit : 300
% 0.12/0.22 % WCLimit : 300
% 0.12/0.22 % DateTime : Tue Sep 29 17:35:29 UTC 2026
% 0.12/0.23 % CPUTime :
% 0.12/0.23 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
% 0.86/0.79 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.56/1.08 % [INFO] Parsing done (285ms).
% 1.56/1.09 % [INFO] Running in sequential loop mode.
% 2.37/1.49 % [INFO] eprover registered as external prover.
% 2.55/1.50 % [INFO] Scanning for conjecture ...
% 2.73/1.69 % [INFO] Found a conjecture (or negated_conjecture) and 66 axioms. Running axiom selection ...
% 2.93/1.78 % [INFO] Axiom selection finished. Selected 66 axioms (removed 0 axioms).
% 3.16/1.83 % [INFO] Problem is higher-order (TPTP THF).
% 3.16/1.84 % [INFO] Type checking passed.
% 3.16/1.84 % [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 ...
% 33.23/7.95 % External prover 'e' found a proof!
% 33.23/7.95 % [INFO] Killing All external provers ...
% 33.23/7.95 % Time passed: 7585ms (effective reasoning time: 6852ms)
% 33.23/7.95 % 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)>
% 33.23/7.95 % Axioms used in derivation (66): axiom_I_for_r4_r1, axiom_4s_for_r1_r1, axiom_4s_for_r5_r1, axiom_r4_4, axiom_4s_for_r3_r1, axiom_4s_for_r5_r2, axiom_4s_for_r3_r2, axiom_4s_for_r3_r4, axiom_5_for_r5, axiom_r2_3, axiom_I_for_r45r1, axiom_D_for_r5, axiom_I_for_r5_r3, axiom_4s_for_r4_r3, axiom_4s_for_r5_r5, axiom_r3_1, axiom_D_for_r2, axiom_r4_2, axiom_4s_for_r5_r4, axiom_4s_for_r4_r2, axiom_4s_for_r1_r4, axiom_4s_for_r2_r1, axiom_4s_for_r3_r3, axiom_4s_for_r4_r4, axiom_4s_for_r2_r5, axiom_r3_5, axiom_I_for_r4_r2, axiom_D_for_r4, axiom_I_for_r2_r1, axiom_4s_for_r2_r2, axiom_r1, axiom_a6, axiom_I_for_r3_r1, axiom_r2_2, axiom_I_for_r5_r4, axiom_r4_1, axiom_4s_for_r5_r3, axiom_r2_5, axiom_r3_4, axiom_5_for_r3, axiom_5_for_r2, axiom_I_for_r4_r3, axiom_r5, axiom_4s_for_r1_r5, axiom_D_for_r3, axiom_a7, axiom_a8, axiom_4s_for_r1_r2, axiom_r4_5, axiom_I_for_r3_r2, axiom_4s_for_r2_r4, axiom_4s_for_r3_r5, axiom_r2_1, axiom_5_for_r4, axiom_r3_2, axiom_r2_4, axiom_5_for_r1, axiom_4s_for_r2_r3, axiom_I_for_r5_r2, axiom_r4_3, axiom_4s_for_r4_r5, axiom_4s_for_r1_r3, axiom_r3_3, axiom_4s_for_r4_r1, axiom_D_for_r1, axiom_a9
% 33.23/7.95 % No. of inferences in proof: 227
% 33.23/7.95 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 7585 ms resp. 6852 ms w/o parsing
% 33.98/8.04 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 33.98/8.04 thf(mu_type, type, mu: $tType).
% 33.98/8.04 thf(mnot_decl, type, mnot: (($i > $o) > ($i > $o))).
% 33.98/8.04 thf(mor_decl, type, mor: (($i > $o) > (($i > $o) > ($i > $o)))).
% 33.98/8.04 thf(mimplies_decl, type, mimplies: (($i > $o) > (($i > $o) > ($i > $o)))).
% 33.98/8.04 thf(mforall_ind_decl, type, mforall_ind: ((mu > ($i > $o)) > ($i > $o))).
% 33.98/8.04 thf(mforall_prop_decl, type, mforall_prop: ((($i > $o) > ($i > $o)) > ($i > $o))).
% 33.98/8.04 thf(mexists_ind_decl, type, mexists_ind: ((mu > ($i > $o)) > ($i > $o))).
% 33.98/8.04 thf(mbox_decl, type, mbox: (($i > ($i > $o)) > (($i > $o) > ($i > $o)))).
% 33.98/8.04 thf(mdia_decl, type, mdia: (($i > ($i > $o)) > (($i > $o) > ($i > $o)))).
% 33.98/8.04 thf(mvalid_decl, type, mvalid: (($i > $o) > $o)).
% 33.98/8.04 thf(r1_decl, type, r1: ($i > ($i > $o))).
% 33.98/8.04 thf(r2_decl, type, r2: ($i > ($i > $o))).
% 33.98/8.04 thf(r3_decl, type, r3: ($i > ($i > $o))).
% 33.98/8.04 thf(r4_decl, type, r4: ($i > ($i > $o))).
% 33.98/8.04 thf(r5_decl, type, r5: ($i > ($i > $o))).
% 33.98/8.04 thf(john_decl, type, john: mu).
% 33.98/8.04 thf(tom_decl, type, tom: mu).
% 33.98/8.04 thf(peter_decl, type, peter: mu).
% 33.98/8.04 thf(mike_decl, type, mike: mu).
% 33.98/8.04 thf(good_in_maths_decl, type, good_in_maths: (mu > ($i > $o))).
% 33.98/8.04 thf(maths_teacher_decl, type, maths_teacher: (mu > ($i > $o))).
% 33.98/8.04 thf(mathematician_decl, type, mathematician: (mu > ($i > $o))).
% 33.98/8.04 thf(maths_student_decl, type, maths_student: (mu > ($i > $o))).
% 33.98/8.04 thf(good_in_physics_decl, type, good_in_physics: (mu > ($i > $o))).
% 33.98/8.04 thf(physics_student_decl, type, physics_student: (mu > ($i > $o))).
% 33.98/8.04 thf(sk1_decl, type, sk1: $i).
% 33.98/8.04 thf(sk2_decl, type, sk2: ($i > (mu > ($i > $i)))).
% 33.98/8.04 thf(sk3_decl, type, sk3: (($i > $o) > ($i > $i))).
% 33.98/8.04 thf(sk4_decl, type, sk4: (($i > $o) > ($i > $i))).
% 33.98/8.04 thf(sk5_decl, type, sk5: (($i > $o) > ($i > $i))).
% 33.98/8.04 thf(sk18_decl, type, sk18: (($i > $o) > ($i > $i))).
% 33.98/8.04 thf(sk19_decl, type, sk19: (($i > $o) > ($i > $i))).
% 33.98/8.04 thf(sk25_decl, type, sk25: (($i > $o) > ($i > $i))).
% 33.98/8.04 thf(sk26_decl, type, sk26: (($i > $o) > ($i > $i))).
% 33.98/8.04 thf(mnot_def, definition, mnot = (^ [A:($i > $o),B:$i]: ~ (A @ B)) ).
% 33.98/8.04 thf(mor_def, definition, mor = (^ [A:($i > $o),B:($i > $o),C:$i]: ((A @ C) | (B @ C))) ).
% 33.98/8.04 thf(mimplies_def, definition, mimplies = (^ [A:($i > $o)]: (mor @ (mnot @ A))) ).
% 33.98/8.04 thf(mforall_ind_def, definition, mforall_ind = (^ [A:(mu > ($i > $o)),B:$i]: ! [C:mu]: (A @ C @ B)) ).
% 33.98/8.04 thf(mforall_prop_def, definition, mforall_prop = (^ [A:(($i > $o) > ($i > $o)),B:$i]: ! [C:($i > $o)]: (A @ C @ B)) ).
% 33.98/8.04 thf(mexists_ind_def, definition, mexists_ind = (^ [A:(mu > ($i > $o))]: (mnot @ (mforall_ind @ (^ [B:mu]: (mnot @ (A @ B)))))) ).
% 33.98/8.04 thf(mbox_def, definition, mbox = (^ [A:($i > ($i > $o)),B:($i > $o),C:$i]: ! [D:$i]: (~ (A @ C @ D) | (B @ D))) ).
% 33.98/8.04 thf(mdia_def, definition, mdia = (^ [A:($i > ($i > $o)),B:($i > $o)]: (mnot @ (mbox @ A @ (mnot @ B)))) ).
% 33.98/8.04 thf(mvalid_def, definition, mvalid = ((!) @ $i) ).
% 33.98/8.04 thf(sk1_def, definition, sk1 = (@+ [A:$i]: ! [B:mu,C:$i]: (~ (r1 @ A @ C) | ~ (good_in_maths @ B @ C))) ).
% 33.98/8.04 thf(sk2_def, definition, sk2 = (^ [A:$i,B:mu,C:$i]: (@+ [D:$i]: ~ (~ (r2 @ A @ D) | ~ (good_in_maths @ B @ D)))) ).
% 33.98/8.04 thf(sk3_def, definition, sk3 = (^ [A:($i > $o),B:$i]: (@+ [C:$i]: ~ (~ (r1 @ B @ C) | (A @ C)))) ).
% 33.98/8.04 thf(sk4_def, definition, sk4 = (^ [A:($i > $o),B:$i]: (@+ [C:$i]: ~ (~ (r2 @ B @ C) | (A @ C)))) ).
% 33.98/8.04 thf(sk5_def, definition, sk5 = (^ [A:($i > $o),B:$i]: (@+ [C:$i]: ~ (~ (r2 @ B @ C) | ~ (A @ C)))) ).
% 33.98/8.04 thf(sk18_def, definition, sk18 = (^ [A:($i > $o),B:$i]: (@+ [C:$i]: ~ (~ (r4 @ B @ C) | (A @ C)))) ).
% 33.98/8.04 thf(sk19_def, definition, sk19 = (^ [A:($i > $o),B:$i]: (@+ [C:$i]: ~ (~ (r4 @ B @ C) | ~ (A @ C)))) ).
% 33.98/8.04 thf(sk25_def, definition, sk25 = (^ [A:($i > $o),B:$i]: (@+ [C:$i]: ~ (~ (r1 @ B @ C) | (A @ C)))) ).
% 33.98/8.04 thf(sk26_def, definition, sk26 = (^ [A:($i > $o),B:$i]: (@+ [C:$i]: ~ (~ (r1 @ B @ C) | ~ (A @ C)))) ).
% 33.98/8.04 thf(30,axiom,((mvalid @ (maths_teacher @ john))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_a6)).
% 33.98/8.04 thf(228,plain,((! [A:$i]: (maths_teacher @ john @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[30])).
% 33.98/8.04 thf(229,plain,(! [A:$i] : ((maths_teacher @ john @ A))),inference(cnf,[status(esa)],[228])).
% 33.98/8.04 thf(26,axiom,((mvalid @ (mforall_prop @ (^ [A:($i > $o)]: (mimplies @ (mbox @ r2 @ A) @ (mbox @ r1 @ (mbox @ r2 @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4s_for_r2_r1)).
% 33.98/8.04 thf(204,plain,((! [A:$i,B:($i > $o)]: (~ (! [C:$i]: (~ (r2 @ A @ C) | (B @ C))) | ! [C:$i]: (~ (r1 @ A @ C) | ! [D:$i]: (~ (r2 @ C @ D) | (B @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[26])).
% 33.98/8.04 thf(58,axiom,((mvalid @ (mforall_prop @ (^ [A:($i > $o)]: (mimplies @ (mbox @ r5 @ A) @ (mbox @ r2 @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_I_for_r5_r2)).
% 33.98/8.04 thf(374,plain,((! [A:$i,B:($i > $o)]: (~ (! [C:$i]: (~ (r5 @ A @ C) | (B @ C))) | ! [C:$i]: (~ (r2 @ A @ C) | (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[58])).
% 33.98/8.04 thf(22,axiom,((mvalid @ (mforall_prop @ (^ [A:($i > $o)]: (mimplies @ (mbox @ r1 @ A) @ (mbox @ r5 @ (mbox @ r1 @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4s_for_r1_r5)).
% 33.98/8.04 thf(182,plain,((! [A:$i,B:($i > $o)]: (~ (! [C:$i]: (~ (r1 @ A @ C) | (B @ C))) | ! [C:$i]: (~ (r5 @ A @ C) | ! [D:$i]: (~ (r1 @ C @ D) | (B @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[22])).
% 33.98/8.04 thf(1,conjecture,((mvalid @ (mexists_ind @ (^ [A:mu]: (mdia @ r1 @ (good_in_maths @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj)).
% 33.98/8.04 thf(2,negated_conjecture,((~ (mvalid @ (mexists_ind @ (^ [A:mu]: (mdia @ r1 @ (good_in_maths @ A))))))),inference(neg_conjecture,[status(cth)],[1])).
% 33.98/8.04 thf(69,plain,((~ (! [A:$i]: ~ (! [B:mu,C:$i]: (~ (r1 @ A @ C) | ~ (good_in_maths @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])).
% 33.98/8.04 thf(4,axiom,((mvalid @ (mforall_prop @ (^ [A:($i > $o)]: (mimplies @ (mbox @ r1 @ A) @ (mbox @ r3 @ (mbox @ r1 @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4s_for_r1_r3)).
% 33.98/8.04 thf(76,plain,((! [A:$i,B:($i > $o)]: (~ (! [C:$i]: (~ (r1 @ A @ C) | (B @ C))) | ! [C:$i]: (~ (r3 @ A @ C) | ! [D:$i]: (~ (r1 @ C @ D) | (B @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4])).
% 33.98/8.04 thf(77,plain,(! [D:$i,C:$i,B:($i > $o),A:$i] : ((((r1 @ A @ (sk3 @ (B) @ A)) | ~ (r3 @ A @ C) | ~ (r1 @ C @ D) | (B @ D)) & (~ (B @ (sk3 @ (B) @ A)) | ~ (r3 @ A @ C) | ~ (r1 @ C @ D) | (B @ D))))),inference(cnf,[status(esa)],[76])).
% 33.98/8.04 thf(78,plain,(! [D:$i,C:$i,B:($i > $o),A:$i] : ((r1 @ A @ (sk3 @ (B) @ A)) | (~ (r3 @ A @ C)) | (~ (r1 @ C @ D)) | (B @ D))),inference(cnfConj,[status(thm)],[77])).
% 33.98/8.04 thf(70,plain,((~ (~ (? [A:$i]: ! [B:mu,C:$i]: (~ (r1 @ A @ C) | ~ (good_in_maths @ B @ C)))))),inference(miniscope,[status(thm)],[69])).
% 33.98/8.04 thf(71,plain,(! [B:$i,A:mu] : ((~ (r1 @ sk1 @ B)) | (~ (good_in_maths @ A @ B)))),inference(cnf,[status(esa)],[70])).
% 33.98/8.04 thf(1710,plain,(! [F:$i,E:mu,D:$i,C:$i,B:($i > $o),A:$i] : ((~ (r3 @ A @ C)) | (~ (r1 @ C @ D)) | (B @ D) | ~ (($true)) | (~ (good_in_maths @ E @ F)) | ((r1 @ A @ (sk3 @ (B) @ A)) != (r1 @ sk1 @ F)))),inference(paramod_ordered,[status(thm)],[78,71])).
% 33.98/8.04 thf(1711,plain,(! [F:$i,E:mu,D:$i,C:$i,B:($i > $o),A:$i] : ((~ (r3 @ A @ C)) | (~ (r1 @ C @ D)) | (B @ D) | (~ (good_in_maths @ E @ F)) | ((r1 @ A @ (sk3 @ (B) @ A)) != (r1 @ sk1 @ F)))),inference(simp,[status(thm)],[1710])).
% 33.98/8.05 thf(1712,plain,(! [D:($i > $o),C:mu,B:$i,A:$i] : ((~ (r3 @ sk1 @ A)) | (~ (r1 @ A @ B)) | (D @ B) | (~ (good_in_maths @ C @ (sk3 @ (D) @ sk1))))),inference(pattern_uni,[status(thm)],[1711:[bind(A, $thf(sk1)),bind(B, $thf(G)),bind(C, $thf(C)),bind(D, $thf(D)),bind(E, $thf(E)),bind(F, $thf(sk3 @ (G) @ sk1))]])).
% 33.98/8.05 thf(2072,plain,(! [D:($i > $o),C:mu,B:$i,A:$i] : ((~ (r3 @ sk1 @ A)) | (~ (r1 @ A @ B)) | (D @ B) | (~ (good_in_maths @ C @ (sk3 @ (D) @ sk1))))),inference(simp,[status(thm)],[1712])).
% 33.98/8.05 thf(54,axiom,((mvalid @ (mforall_ind @ (^ [A:mu]: (mbox @ r5 @ (mimplies @ (mbox @ r5 @ (mathematician @ A)) @ (mbox @ r5 @ (good_in_maths @ A)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_r2_5)).
% 33.98/8.05 thf(352,plain,((! [A:$i,B:mu,C:$i]: (~ (r5 @ A @ C) | ~ (! [D:$i]: (~ (r5 @ C @ D) | (mathematician @ B @ D))) | ! [D:$i]: (~ (r5 @ C @ D) | (good_in_maths @ B @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[54])).
% 33.98/8.05 thf(45,axiom,((mvalid @ (mforall_prop @ (^ [A:($i > $o)]: (mimplies @ (mnot @ (mbox @ r1 @ A)) @ (mbox @ r1 @ (mnot @ (mbox @ r1 @ A)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_5_for_r1)).
% 33.98/8.05 thf(308,plain,((! [A:$i,B:($i > $o)]: (! [C:$i]: (~ (r1 @ A @ C) | (B @ C)) | ! [C:$i]: (~ (r1 @ A @ C) | ~ (! [D:$i]: (~ (r1 @ C @ D) | (B @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[45])).
% 33.98/8.05 thf(11,axiom,((mvalid @ (mforall_prop @ (^ [A:($i > $o)]: (mimplies @ (mbox @ r5 @ A) @ (mbox @ r3 @ (mbox @ r5 @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4s_for_r5_r3)).
% 33.98/8.05 thf(120,plain,((! [A:$i,B:($i > $o)]: (~ (! [C:$i]: (~ (r5 @ A @ C) | (B @ C))) | ! [C:$i]: (~ (r3 @ A @ C) | ! [D:$i]: (~ (r5 @ C @ D) | (B @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[11])).
% 33.98/8.05 thf(79,plain,(! [D:$i,C:$i,B:($i > $o),A:$i] : ((~ (B @ (sk3 @ (B) @ A))) | (~ (r3 @ A @ C)) | (~ (r1 @ C @ D)) | (B @ D))),inference(cnfConj,[status(thm)],[77])).
% 33.98/8.05 thf(432,plain,(! [F:$i,E:mu,D:$i,C:$i,B:($i > $o),A:$i] : ((~ (B @ (sk3 @ (B) @ A))) | (~ (r3 @ A @ C)) | (~ (r1 @ C @ D)) | ~ (($true)) | (~ (good_in_maths @ E @ F)) | ((B @ D) != (r1 @ sk1 @ F)))),inference(paramod_ordered,[status(thm)],[79,71])).
% 33.98/8.05 thf(433,plain,(! [F:$i,E:mu,D:$i,C:$i,B:($i > $o),A:$i] : ((~ (B @ (sk3 @ (B) @ A))) | (~ (r3 @ A @ C)) | (~ (r1 @ C @ D)) | (~ (good_in_maths @ E @ F)) | ((B @ D) != (r1 @ sk1 @ F)))),inference(simp,[status(thm)],[432])).
% 33.98/8.05 thf(481,plain,(! [E:($i > $i),D:mu,C:$i,B:$i,A:$i] : ((~ (r1 @ sk1 @ (E @ (sk3 @ (^ [F:$i]: (r1 @ sk1 @ (E @ F))) @ A)))) | (~ (r3 @ A @ B)) | (~ (r1 @ B @ C)) | (~ (good_in_maths @ D @ (E @ C))))),inference(pre_uni,[status(thm)],[433:[bind(A, $thf(A)),bind(B, $thf(^ [H:$i]: (r1 @ sk1 @ (H @ H)))),bind(C, $thf(C)),bind(D, $thf(D)),bind(E, $thf(E)),bind(F, $thf(H @ D))]])).
% 33.98/8.05 thf(519,plain,(! [E:($i > $i),D:mu,C:$i,B:$i,A:$i] : ((~ (r1 @ sk1 @ (E @ (sk3 @ (^ [F:$i]: (r1 @ sk1 @ (E @ F))) @ A)))) | (~ (r3 @ A @ B)) | (~ (r1 @ B @ C)) | (~ (good_in_maths @ D @ (E @ C))))),inference(simp,[status(thm)],[481])).
% 33.98/8.05 thf(537,plain,(! [E:($i > $i),D:mu,C:$i,B:$i,A:$i] : ((~ (r1 @ sk1 @ (E @ (sk3 @ (^ [F:$i]: (r1 @ sk1 @ (E @ F))) @ A)))) | (~ (r3 @ A @ B)) | (~ (good_in_maths @ D @ (E @ C))) | ((r1 @ B @ C) != (r1 @ sk1 @ (E @ (sk3 @ (^ [F:$i]: (r1 @ sk1 @ (E @ F))) @ A)))) | ~ (($true)))),inference(eqfactor_ordered,[status(thm)],[519])).
% 33.98/8.05 thf(539,plain,(! [C:($i > $i),B:mu,A:$i] : ((~ (r1 @ sk1 @ (C @ (sk3 @ (^ [D:$i]: (r1 @ sk1 @ (C @ D))) @ A)))) | (~ (r3 @ A @ sk1)) | (~ (good_in_maths @ B @ (C @ (C @ (sk3 @ (^ [D:$i]: (r1 @ sk1 @ (C @ D))) @ A))))))),inference(pre_uni,[status(thm)],[537:[bind(A, $thf(A)),bind(B, $thf(sk1)),bind(C, $thf(E @ (sk3 @ (^ [F:$i]: (r1 @ sk1 @ (E @ F))) @ A)))]])).
% 33.98/8.05 thf(550,plain,(! [C:($i > $i),B:mu,A:$i] : ((~ (r1 @ sk1 @ (C @ (sk3 @ (^ [D:$i]: (r1 @ sk1 @ (C @ D))) @ A)))) | (~ (r3 @ A @ sk1)) | (~ (good_in_maths @ B @ (C @ (C @ (sk3 @ (^ [D:$i]: (r1 @ sk1 @ (C @ D))) @ A))))))),inference(simp,[status(thm)],[539])).
% 33.98/8.05 thf(51,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)).
% 33.98/8.05 thf(340,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)],[51])).
% 33.98/8.05 thf(41,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)).
% 33.98/8.05 thf(288,plain,((! [A:$i,B:mu,C:$i]: (~ (r3 @ A @ C) | ~ (physics_student @ B @ C) | ~ (! [D:$i]: (~ (r5 @ C @ D) | ~ (good_in_physics @ B @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[41])).
% 33.98/8.05 thf(47,axiom,((mvalid @ (mforall_prop @ (^ [A:($i > $o)]: (mimplies @ (mbox @ r3 @ A) @ (mbox @ r2 @ (mbox @ r3 @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4s_for_r3_r2)).
% 33.98/8.05 thf(320,plain,((! [A:$i,B:($i > $o)]: (~ (! [C:$i]: (~ (r3 @ A @ C) | (B @ C))) | ! [C:$i]: (~ (r2 @ A @ C) | ! [D:$i]: (~ (r3 @ C @ D) | (B @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[47])).
% 33.98/8.05 thf(5,axiom,((mvalid @ (mforall_prop @ (^ [A:($i > $o)]: (mimplies @ (mbox @ r2 @ A) @ (mnot @ (mbox @ r2 @ (mnot @ A)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_D_for_r2)).
% 33.98/8.05 thf(82,plain,((! [A:$i,B:($i > $o)]: (~ (! [C:$i]: (~ (r2 @ A @ C) | (B @ C))) | ~ (! [C:$i]: (~ (r2 @ A @ C) | ~ (B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5])).
% 33.98/8.05 thf(83,plain,(! [B:($i > $o),A:$i] : ((((r2 @ A @ (sk4 @ (B) @ A)) | (r2 @ A @ (sk5 @ (B) @ A))) & ((r2 @ A @ (sk4 @ (B) @ A)) | (B @ (sk5 @ (B) @ A))) & (~ (B @ (sk4 @ (B) @ A)) | (r2 @ A @ (sk5 @ (B) @ A))) & (~ (B @ (sk4 @ (B) @ A)) | (B @ (sk5 @ (B) @ A)))))),inference(cnf,[status(esa)],[82])).
% 33.98/8.05 thf(85,plain,(! [B:($i > $o),A:$i] : ((r2 @ A @ (sk4 @ (B) @ A)) | (B @ (sk5 @ (B) @ A)))),inference(cnfConj,[status(thm)],[83])).
% 33.98/8.05 thf(584,plain,(! [A:$i] : ((r2 @ A @ (sk4 @ (^ [B:$i]: (($false))) @ A)) | ($false))),inference(prim_subst,[status(thm)],[85:[bind(A, $thf(A)),bind(B, $thf(^ [C:$i]: (($false))))]])).
% 33.98/8.05 thf(619,plain,(! [A:$i] : ((r2 @ A @ (sk4 @ (^ [B:$i]: (($false))) @ A)))),inference(simp,[status(thm)],[584])).
% 33.98/8.05 thf(52,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)).
% 33.98/8.05 thf(344,plain,((! [A:$i,B:mu,C:$i]: (~ (r3 @ A @ C) | ~ (maths_student @ B @ C) | ~ (! [D:$i]: (~ (r2 @ C @ D) | ~ (good_in_maths @ B @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[52])).
% 33.98/8.05 thf(25,axiom,((mvalid @ (mforall_prop @ (^ [A:($i > $o)]: (mimplies @ (mbox @ r1 @ A) @ (mnot @ (mbox @ r1 @ (mnot @ A)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_D_for_r1)).
% 33.98/8.05 thf(196,plain,((! [A:$i,B:($i > $o)]: (~ (! [C:$i]: (~ (r1 @ A @ C) | (B @ C))) | ~ (! [C:$i]: (~ (r1 @ A @ C) | ~ (B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[25])).
% 33.98/8.05 thf(23,axiom,((mvalid @ (mbox @ r2 @ (mathematician @ tom)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_a7)).
% 33.98/8.05 thf(188,plain,((! [A:$i,B:$i]: (~ (r2 @ A @ B) | (mathematician @ tom @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[23])).
% 33.98/8.05 thf(189,plain,(! [B:$i,A:$i] : ((~ (r2 @ A @ B)) | (mathematician @ tom @ B))),inference(cnf,[status(esa)],[188])).
% 33.98/8.05 thf(67,axiom,((mvalid @ (mforall_prop @ (^ [A:($i > $o)]: (mimplies @ (mbox @ r3 @ A) @ (mbox @ r1 @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_I_for_r3_r1)).
% 33.98/8.05 thf(416,plain,((! [A:$i,B:($i > $o)]: (~ (! [C:$i]: (~ (r3 @ A @ C) | (B @ C))) | ! [C:$i]: (~ (r1 @ A @ C) | (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[67])).
% 33.98/8.05 thf(17,axiom,((mvalid @ (mforall_prop @ (^ [A:($i > $o)]: (mimplies @ (mbox @ r4 @ A) @ (mbox @ r5 @ (mbox @ r4 @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4s_for_r4_r5)).
% 33.98/8.05 thf(152,plain,((! [A:$i,B:($i > $o)]: (~ (! [C:$i]: (~ (r4 @ A @ C) | (B @ C))) | ! [C:$i]: (~ (r5 @ A @ C) | ! [D:$i]: (~ (r4 @ C @ D) | (B @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[17])).
% 33.98/8.05 thf(28,axiom,((mvalid @ (mforall_prop @ (^ [A:($i > $o)]: (mimplies @ (mbox @ r3 @ A) @ (mbox @ r5 @ (mbox @ r3 @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4s_for_r3_r5)).
% 33.98/8.05 thf(216,plain,((! [A:$i,B:($i > $o)]: (~ (! [C:$i]: (~ (r3 @ A @ C) | (B @ C))) | ! [C:$i]: (~ (r5 @ A @ C) | ! [D:$i]: (~ (r3 @ C @ D) | (B @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[28])).
% 33.98/8.05 thf(32,axiom,((mvalid @ (mforall_prop @ (^ [A:($i > $o)]: (mimplies @ (mnot @ (mbox @ r5 @ A)) @ (mbox @ r5 @ (mnot @ (mbox @ r5 @ A)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_5_for_r5)).
% 33.98/8.05 thf(238,plain,((! [A:$i,B:($i > $o)]: (! [C:$i]: (~ (r5 @ A @ C) | (B @ C)) | ! [C:$i]: (~ (r5 @ A @ C) | ~ (! [D:$i]: (~ (r5 @ C @ D) | (B @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[32])).
% 33.98/8.05 thf(53,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)).
% 33.98/8.05 thf(348,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)],[53])).
% 33.98/8.05 thf(3063,plain,(! [C:mu,B:$i,A:$i] : ((~ (r3 @ sk1 @ A)) | (~ (r1 @ A @ B)) | ($false) | (~ (good_in_maths @ C @ (sk3 @ (^ [D:$i]: (($false))) @ sk1))))),inference(prim_subst,[status(thm)],[2072:[bind(A, $thf(A)),bind(B, $thf(B)),bind(C, $thf(C)),bind(D, $thf(^ [E:$i]: (($false))))]])).
% 33.98/8.05 thf(3361,plain,(! [C:mu,B:$i,A:$i] : ((~ (r3 @ sk1 @ A)) | (~ (r1 @ A @ B)) | (~ (good_in_maths @ C @ (sk3 @ (^ [D:$i]: (($false))) @ sk1))))),inference(simp,[status(thm)],[3063])).
% 33.98/8.05 thf(65,axiom,((mvalid @ (mbox @ r5 @ (maths_student @ peter)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_a8)).
% 33.98/8.05 thf(410,plain,((! [A:$i,B:$i]: (~ (r5 @ A @ B) | (maths_student @ peter @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[65])).
% 33.98/8.05 thf(411,plain,(! [B:$i,A:$i] : ((~ (r5 @ A @ B)) | (maths_student @ peter @ B))),inference(cnf,[status(esa)],[410])).
% 33.98/8.05 thf(3,axiom,((mvalid @ (mforall_ind @ (^ [A:mu]: (mbox @ r2 @ (mimplies @ (good_in_physics @ A) @ (mdia @ r2 @ (good_in_maths @ A)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_r5)).
% 33.98/8.05 thf(72,plain,((! [A:$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)],[3])).
% 33.98/8.05 thf(73,plain,(! [C:$i,B:mu,A:$i] : (((~ (r2 @ A @ C) | ~ (good_in_physics @ B @ C) | (r2 @ C @ (sk2 @ C @ B @ A))) & (~ (r2 @ A @ C) | ~ (good_in_physics @ B @ C) | (good_in_maths @ B @ (sk2 @ C @ B @ A)))))),inference(cnf,[status(esa)],[72])).
% 33.98/8.05 thf(74,plain,(! [C:$i,B:mu,A:$i] : ((~ (r2 @ A @ C)) | (~ (good_in_physics @ B @ C)) | (r2 @ C @ (sk2 @ C @ B @ A)))),inference(cnfConj,[status(thm)],[73])).
% 33.98/8.05 thf(42,axiom,((mvalid @ (mforall_prop @ (^ [A:($i > $o)]: (mimplies @ (mbox @ r4 @ A) @ (mbox @ r3 @ (mbox @ r4 @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4s_for_r4_r3)).
% 33.98/8.05 thf(292,plain,((! [A:$i,B:($i > $o)]: (~ (! [C:$i]: (~ (r4 @ A @ C) | (B @ C))) | ! [C:$i]: (~ (r3 @ A @ C) | ! [D:$i]: (~ (r4 @ C @ D) | (B @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[42])).
% 33.98/8.05 thf(59,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)).
% 33.98/8.05 thf(380,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)],[59])).
% 33.98/8.05 thf(8,axiom,((mvalid @ (mforall_prop @ (^ [A:($i > $o)]: (mimplies @ (mnot @ (mbox @ r2 @ A)) @ (mbox @ r2 @ (mnot @ (mbox @ r2 @ A)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_5_for_r2)).
% 33.98/8.05 thf(102,plain,((! [A:$i,B:($i > $o)]: (! [C:$i]: (~ (r2 @ A @ C) | (B @ C)) | ! [C:$i]: (~ (r2 @ A @ C) | ~ (! [D:$i]: (~ (r2 @ C @ D) | (B @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8])).
% 33.98/8.05 thf(197,plain,(! [B:($i > $o),A:$i] : ((((r1 @ A @ (sk25 @ (B) @ A)) | (r1 @ A @ (sk26 @ (B) @ A))) & ((r1 @ A @ (sk25 @ (B) @ A)) | (B @ (sk26 @ (B) @ A))) & (~ (B @ (sk25 @ (B) @ A)) | (r1 @ A @ (sk26 @ (B) @ A))) & (~ (B @ (sk25 @ (B) @ A)) | (B @ (sk26 @ (B) @ A)))))),inference(cnf,[status(esa)],[196])).
% 33.98/8.05 thf(201,plain,(! [B:($i > $o),A:$i] : ((~ (B @ (sk25 @ (B) @ A))) | (B @ (sk26 @ (B) @ A)))),inference(cnfConj,[status(thm)],[197])).
% 33.98/8.05 thf(50,axiom,((mvalid @ (mforall_prop @ (^ [A:($i > $o)]: (mimplies @ (mbox @ r5 @ A) @ (mbox @ r3 @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_I_for_r5_r3)).
% 33.98/8.05 thf(334,plain,((! [A:$i,B:($i > $o)]: (~ (! [C:$i]: (~ (r5 @ A @ C) | (B @ C))) | ! [C:$i]: (~ (r3 @ A @ C) | (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[50])).
% 33.98/8.05 thf(75,plain,(! [C:$i,B:mu,A:$i] : ((~ (r2 @ A @ C)) | (~ (good_in_physics @ B @ C)) | (good_in_maths @ B @ (sk2 @ C @ B @ A)))),inference(cnfConj,[status(thm)],[73])).
% 33.98/8.05 thf(912,plain,(! [E:$i,D:mu,C:$i,B:mu,A:$i] : ((~ (r2 @ A @ C)) | (~ (good_in_physics @ B @ C)) | (~ (r1 @ sk1 @ E)) | ~ (($true)) | ((good_in_maths @ B @ (sk2 @ C @ B @ A)) != (good_in_maths @ D @ E)))),inference(paramod_ordered,[status(thm)],[75,71])).
% 33.98/8.05 thf(913,plain,(! [E:$i,D:mu,C:$i,B:mu,A:$i] : ((~ (r2 @ A @ C)) | (~ (good_in_physics @ B @ C)) | (~ (r1 @ sk1 @ E)) | ((good_in_maths @ B @ (sk2 @ C @ B @ A)) != (good_in_maths @ D @ E)))),inference(simp,[status(thm)],[912])).
% 33.98/8.05 thf(914,plain,(! [C:$i,B:mu,A:$i] : ((~ (r2 @ C @ A)) | (~ (good_in_physics @ B @ A)) | (~ (r1 @ sk1 @ (sk2 @ A @ B @ C))))),inference(pattern_uni,[status(thm)],[913:[bind(A, $thf(H)),bind(B, $thf(G)),bind(C, $thf(F)),bind(D, $thf(G)),bind(E, $thf(sk2 @ F @ G @ H))]])).
% 33.98/8.05 thf(957,plain,(! [C:$i,B:mu,A:$i] : ((~ (r2 @ C @ A)) | (~ (good_in_physics @ B @ A)) | (~ (r1 @ sk1 @ (sk2 @ A @ B @ C))))),inference(simp,[status(thm)],[914])).
% 33.98/8.05 thf(44,axiom,((mvalid @ (mforall_prop @ (^ [A:($i > $o)]: (mimplies @ (mbox @ r2 @ A) @ (mbox @ r5 @ (mbox @ r2 @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4s_for_r2_r5)).
% 33.98/8.05 thf(302,plain,((! [A:$i,B:($i > $o)]: (~ (! [C:$i]: (~ (r2 @ A @ C) | (B @ C))) | ! [C:$i]: (~ (r5 @ A @ C) | ! [D:$i]: (~ (r2 @ C @ D) | (B @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[44])).
% 33.98/8.05 thf(36,axiom,((mvalid @ (mforall_prop @ (^ [A:($i > $o)]: (mimplies @ (mbox @ r5 @ A) @ (mbox @ r5 @ (mbox @ r5 @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4s_for_r5_r5)).
% 33.98/8.05 thf(260,plain,((! [A:$i,B:($i > $o)]: (~ (! [C:$i]: (~ (r5 @ A @ C) | (B @ C))) | ! [C:$i]: (~ (r5 @ A @ C) | ! [D:$i]: (~ (r5 @ C @ D) | (B @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[36])).
% 33.98/8.05 thf(563,plain,(! [D:$i,C:mu,B:($i > $o),A:$i] : ((r2 @ A @ (sk4 @ (B) @ A)) | ~ (($true)) | (~ (good_in_maths @ C @ D)) | ((B @ (sk5 @ (B) @ A)) != (r1 @ sk1 @ D)))),inference(paramod_ordered,[status(thm)],[85,71])).
% 33.98/8.05 thf(564,plain,(! [D:$i,C:mu,B:($i > $o),A:$i] : ((r2 @ A @ (sk4 @ (B) @ A)) | (~ (good_in_maths @ C @ D)) | ((B @ (sk5 @ (B) @ A)) != (r1 @ sk1 @ D)))),inference(simp,[status(thm)],[563])).
% 33.98/8.05 thf(600,plain,(! [C:($i > $i),B:mu,A:$i] : ((r2 @ A @ (sk4 @ (^ [D:$i]: (r1 @ sk1 @ (C @ D))) @ A)) | (~ (good_in_maths @ B @ (C @ (sk5 @ (^ [D:$i]: (r1 @ sk1 @ (C @ D))) @ A)))))),inference(pre_uni,[status(thm)],[564:[bind(A, $thf(A)),bind(B, $thf(^ [F:$i]: (r1 @ sk1 @ (F @ F)))),bind(C, $thf(C)),bind(D, $thf(F @ (sk5 @ (^ [F:$i]: (r1 @ sk1 @ (F @ F))) @ A)))]])).
% 33.98/8.05 thf(630,plain,(! [C:($i > $i),B:mu,A:$i] : ((r2 @ A @ (sk4 @ (^ [D:$i]: (r1 @ sk1 @ (C @ D))) @ A)) | (~ (good_in_maths @ B @ (C @ (sk5 @ (^ [D:$i]: (r1 @ sk1 @ (C @ D))) @ A)))))),inference(simp,[status(thm)],[600])).
% 33.98/8.05 thf(61,axiom,((mvalid @ (mforall_prop @ (^ [A:($i > $o)]: (mimplies @ (mnot @ (mbox @ r3 @ A)) @ (mbox @ r3 @ (mnot @ (mbox @ r3 @ A)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_5_for_r3)).
% 33.98/8.05 thf(388,plain,((! [A:$i,B:($i > $o)]: (! [C:$i]: (~ (r3 @ A @ C) | (B @ C)) | ! [C:$i]: (~ (r3 @ A @ C) | ~ (! [D:$i]: (~ (r3 @ C @ D) | (B @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[61])).
% 33.98/8.05 thf(55,axiom,((mvalid @ (mforall_prop @ (^ [A:($i > $o)]: (mimplies @ (mbox @ r3 @ A) @ (mbox @ r4 @ (mbox @ r3 @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4s_for_r3_r4)).
% 33.98/8.05 thf(356,plain,((! [A:$i,B:($i > $o)]: (~ (! [C:$i]: (~ (r3 @ A @ C) | (B @ C))) | ! [C:$i]: (~ (r4 @ A @ C) | ! [D:$i]: (~ (r3 @ C @ D) | (B @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[55])).
% 33.98/8.05 thf(35,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)).
% 33.98/8.05 thf(256,plain,((! [A:$i,B:mu,C:$i]: (~ (r3 @ A @ C) | ~ (maths_student @ B @ C) | ~ (! [D:$i]: (~ (r1 @ C @ D) | ~ (good_in_maths @ B @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[35])).
% 33.98/8.05 thf(7,axiom,((mvalid @ (mforall_prop @ (^ [A:($i > $o)]: (mimplies @ (mbox @ r2 @ A) @ (mbox @ r2 @ (mbox @ r2 @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4s_for_r2_r2)).
% 33.98/8.05 thf(96,plain,((! [A:$i,B:($i > $o)]: (~ (! [C:$i]: (~ (r2 @ A @ C) | (B @ C))) | ! [C:$i]: (~ (r2 @ A @ C) | ! [D:$i]: (~ (r2 @ C @ D) | (B @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7])).
% 33.98/8.05 thf(3053,plain,(! [D:($i > $o),C:mu,B:$i,A:$i] : ((~ (r3 @ sk1 @ A)) | (~ (r1 @ A @ B)) | (~ (good_in_maths @ C @ (sk3 @ (D) @ sk1))) | ((D @ B) != (~ (r3 @ sk1 @ A))) | ~ (($true)))),inference(eqfactor_ordered,[status(thm)],[2072])).
% 33.98/8.05 thf(3082,plain,(! [B:($i > $i),A:mu] : ((~ (r3 @ sk1 @ (B @ sk1))) | (~ (r1 @ (B @ sk1) @ sk1)) | (~ (good_in_maths @ A @ (sk3 @ (^ [C:$i]: ~ (r3 @ C @ (B @ C))) @ sk1))))),inference(pre_uni,[status(thm)],[3053:[bind(A, $thf(G @ sk1)),bind(B, $thf(sk1)),bind(C, $thf(C)),bind(D, $thf(^ [F:$i]: ~ (r3 @ F @ (G @ F))))]])).
% 33.98/8.05 thf(3242,plain,(! [B:($i > $i),A:mu] : ((~ (r3 @ sk1 @ (B @ sk1))) | (~ (r1 @ (B @ sk1) @ sk1)) | (~ (good_in_maths @ A @ (sk3 @ (^ [C:$i]: ~ (r3 @ C @ (B @ C))) @ sk1))))),inference(simp,[status(thm)],[3082])).
% 33.98/8.05 thf(636,plain,(! [E:$i,D:$i,C:($i > $i),B:mu,A:$i] : ((~ (good_in_maths @ B @ (C @ (sk5 @ (^ [F:$i]: (r1 @ sk1 @ (C @ F))) @ A)))) | ~ (($true)) | (mathematician @ tom @ E) | ((r2 @ A @ (sk4 @ (^ [F:$i]: (r1 @ sk1 @ (C @ F))) @ A)) != (r2 @ D @ E)))),inference(paramod_ordered,[status(thm)],[630,189])).
% 33.98/8.05 thf(637,plain,(! [E:$i,D:$i,C:($i > $i),B:mu,A:$i] : ((~ (good_in_maths @ B @ (C @ (sk5 @ (^ [F:$i]: (r1 @ sk1 @ (C @ F))) @ A)))) | (mathematician @ tom @ E) | ((r2 @ A @ (sk4 @ (^ [F:$i]: (r1 @ sk1 @ (C @ F))) @ A)) != (r2 @ D @ E)))),inference(simp,[status(thm)],[636])).
% 33.98/8.05 thf(638,plain,(! [C:($i > $i),B:$i,A:mu] : ((~ (good_in_maths @ A @ (C @ (sk5 @ (^ [D:$i]: (r1 @ sk1 @ (C @ D))) @ B)))) | (mathematician @ tom @ (sk4 @ (^ [D:$i]: (r1 @ sk1 @ (C @ D))) @ B)))),inference(pattern_uni,[status(thm)],[637:[bind(A, $thf(G)),bind(B, $thf(B)),bind(C, $thf(I)),bind(D, $thf(G)),bind(E, $thf(sk4 @ (^ [H:$i]: (r1 @ sk1 @ (I @ H))) @ G))]])).
% 33.98/8.05 thf(654,plain,(! [C:($i > $i),B:$i,A:mu] : ((~ (good_in_maths @ A @ (C @ (sk5 @ (^ [D:$i]: (r1 @ sk1 @ (C @ D))) @ B)))) | (mathematician @ tom @ (sk4 @ (^ [D:$i]: (r1 @ sk1 @ (C @ D))) @ B)))),inference(simp,[status(thm)],[638])).
% 33.98/8.05 thf(14,axiom,((mvalid @ (mforall_prop @ (^ [A:($i > $o)]: (mimplies @ (mbox @ r5 @ A) @ (mbox @ r4 @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_I_for_r5_r4)).
% 33.98/8.05 thf(134,plain,((! [A:$i,B:($i > $o)]: (~ (! [C:$i]: (~ (r5 @ A @ C) | (B @ C))) | ! [C:$i]: (~ (r4 @ A @ C) | (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[14])).
% 33.98/8.05 thf(33,axiom,((mvalid @ (mforall_prop @ (^ [A:($i > $o)]: (mimplies @ (mbox @ r2 @ A) @ (mbox @ r1 @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_I_for_r2_r1)).
% 33.98/8.05 thf(244,plain,((! [A:$i,B:($i > $o)]: (~ (! [C:$i]: (~ (r2 @ A @ C) | (B @ C))) | ! [C:$i]: (~ (r1 @ A @ C) | (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[33])).
% 33.98/8.05 thf(37,axiom,((mvalid @ (mforall_prop @ (^ [A:($i > $o)]: (mimplies @ (mbox @ r5 @ A) @ (mbox @ r1 @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_I_for_r45r1)).
% 33.98/8.05 thf(266,plain,((! [A:$i,B:($i > $o)]: (~ (! [C:$i]: (~ (r5 @ A @ C) | (B @ C))) | ! [C:$i]: (~ (r1 @ A @ C) | (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[37])).
% 33.98/8.05 thf(702,plain,(! [C:$i,B:$i,A:$i] : (~ (($true)) | (mathematician @ tom @ C) | ((r2 @ A @ (sk4 @ (^ [D:$i]: (($false))) @ A)) != (r2 @ B @ C)))),inference(paramod_ordered,[status(thm)],[619,189])).
% 33.98/8.05 thf(703,plain,(! [C:$i,B:$i,A:$i] : ((mathematician @ tom @ C) | ((r2 @ A @ (sk4 @ (^ [D:$i]: (($false))) @ A)) != (r2 @ B @ C)))),inference(simp,[status(thm)],[702])).
% 33.98/8.05 thf(704,plain,(! [A:$i] : ((mathematician @ tom @ (sk4 @ (^ [B:$i]: (($false))) @ A)))),inference(pattern_uni,[status(thm)],[703:[bind(A, $thf(E)),bind(B, $thf(E)),bind(C, $thf(sk4 @ (^ [E:$i]: (($false))) @ E))]])).
% 33.98/8.05 thf(718,plain,(! [A:$i] : ((mathematician @ tom @ (sk4 @ (^ [B:$i]: (($false))) @ A)))),inference(simp,[status(thm)],[704])).
% 33.98/8.05 thf(565,plain,(! [D:$i,C:mu,B:($i > $o),A:$i] : ((r2 @ A @ (sk4 @ (B) @ A)) | (~ (r1 @ sk1 @ D)) | ~ (($true)) | ((B @ (sk5 @ (B) @ A)) != (good_in_maths @ C @ D)))),inference(paramod_ordered,[status(thm)],[85,71])).
% 33.98/8.05 thf(566,plain,(! [D:$i,C:mu,B:($i > $o),A:$i] : ((r2 @ A @ (sk4 @ (B) @ A)) | (~ (r1 @ sk1 @ D)) | ((B @ (sk5 @ (B) @ A)) != (good_in_maths @ C @ D)))),inference(simp,[status(thm)],[565])).
% 33.98/8.05 thf(605,plain,(! [C:($i > $i),B:($i > mu),A:$i] : ((r2 @ A @ (sk4 @ (^ [D:$i]: (good_in_maths @ (B @ D) @ (C @ D))) @ A)) | (~ (r1 @ sk1 @ (C @ (sk5 @ (^ [D:$i]: (good_in_maths @ (B @ D) @ (C @ D))) @ A)))))),inference(pre_uni,[status(thm)],[566:[bind(A, $thf(A)),bind(B, $thf(^ [G:$i]: (good_in_maths @ (E @ G) @ (F @ G)))),bind(C, $thf(E @ (sk5 @ (^ [G:$i]: (good_in_maths @ (E @ G) @ (F @ G))) @ A))),bind(D, $thf(F @ (sk5 @ (^ [G:$i]: (good_in_maths @ (E @ G) @ (F @ G))) @ A)))]])).
% 33.98/8.05 thf(632,plain,(! [C:($i > $i),B:($i > mu),A:$i] : ((r2 @ A @ (sk4 @ (^ [D:$i]: (good_in_maths @ (B @ D) @ (C @ D))) @ A)) | (~ (r1 @ sk1 @ (C @ (sk5 @ (^ [D:$i]: (good_in_maths @ (B @ D) @ (C @ D))) @ A)))))),inference(simp,[status(thm)],[605])).
% 33.98/8.05 thf(866,plain,(! [E:$i,D:$i,C:($i > $i),B:($i > mu),A:$i] : ((~ (r1 @ sk1 @ (C @ (sk5 @ (^ [F:$i]: (good_in_maths @ (B @ F) @ (C @ F))) @ A)))) | ~ (($true)) | (mathematician @ tom @ E) | ((r2 @ A @ (sk4 @ (^ [F:$i]: (good_in_maths @ (B @ F) @ (C @ F))) @ A)) != (r2 @ D @ E)))),inference(paramod_ordered,[status(thm)],[632,189])).
% 33.98/8.05 thf(867,plain,(! [E:$i,D:$i,C:($i > $i),B:($i > mu),A:$i] : ((~ (r1 @ sk1 @ (C @ (sk5 @ (^ [F:$i]: (good_in_maths @ (B @ F) @ (C @ F))) @ A)))) | (mathematician @ tom @ E) | ((r2 @ A @ (sk4 @ (^ [F:$i]: (good_in_maths @ (B @ F) @ (C @ F))) @ A)) != (r2 @ D @ E)))),inference(simp,[status(thm)],[866])).
% 33.98/8.05 thf(868,plain,(! [C:($i > $i),B:($i > mu),A:$i] : ((~ (r1 @ sk1 @ (C @ (sk5 @ (^ [D:$i]: (good_in_maths @ (B @ D) @ (C @ D))) @ A)))) | (mathematician @ tom @ (sk4 @ (^ [D:$i]: (good_in_maths @ (B @ D) @ (C @ D))) @ A)))),inference(pattern_uni,[status(thm)],[867:[bind(A, $thf(G)),bind(B, $thf(H)),bind(C, $thf(I)),bind(D, $thf(G)),bind(E, $thf(sk4 @ (^ [I:$i]: (good_in_maths @ (H @ I) @ (I @ I))) @ G))]])).
% 33.98/8.05 thf(888,plain,(! [C:($i > $i),B:($i > mu),A:$i] : ((~ (r1 @ sk1 @ (C @ (sk5 @ (^ [D:$i]: (good_in_maths @ (B @ D) @ (C @ D))) @ A)))) | (mathematician @ tom @ (sk4 @ (^ [D:$i]: (good_in_maths @ (B @ D) @ (C @ D))) @ A)))),inference(simp,[status(thm)],[868])).
% 33.98/8.05 thf(43,axiom,((mvalid @ (mforall_ind @ (^ [A:mu]: (mbox @ r3 @ (mimplies @ (physics_student @ A) @ (mdia @ r2 @ (good_in_physics @ A)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_r4_2)).
% 33.98/8.05 thf(298,plain,((! [A:$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)],[43])).
% 33.98/8.05 thf(66,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)).
% 33.98/8.05 thf(412,plain,((! [A:$i,B:mu,C:$i]: (~ (r3 @ A @ C) | ~ (maths_student @ B @ C) | ~ (! [D:$i]: (~ (r4 @ C @ D) | ~ (good_in_maths @ B @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[66])).
% 33.98/8.05 thf(482,plain,(! [D:($i > $i),C:mu,B:$i,A:$i] : ((~ (r1 @ (sk3 @ (^ [E:$i]: (r1 @ E @ (D @ E))) @ A) @ (D @ (sk3 @ (^ [E:$i]: (r1 @ E @ (D @ E))) @ A)))) | (~ (r3 @ A @ B)) | (~ (r1 @ B @ sk1)) | (~ (good_in_maths @ C @ (D @ sk1))))),inference(pre_uni,[status(thm)],[433:[bind(A, $thf(A)),bind(B, $thf(^ [H:$i]: (r1 @ H @ (H @ H)))),bind(C, $thf(C)),bind(D, $thf(sk1)),bind(E, $thf(E)),bind(F, $thf(H @ sk1))]])).
% 33.98/8.05 thf(520,plain,(! [D:($i > $i),C:mu,B:$i,A:$i] : ((~ (r1 @ (sk3 @ (^ [E:$i]: (r1 @ E @ (D @ E))) @ A) @ (D @ (sk3 @ (^ [E:$i]: (r1 @ E @ (D @ E))) @ A)))) | (~ (r3 @ A @ B)) | (~ (r1 @ B @ sk1)) | (~ (good_in_maths @ C @ (D @ sk1))))),inference(simp,[status(thm)],[482])).
% 33.98/8.05 thf(797,plain,(! [D:($i > $i),C:mu,B:$i,A:$i] : ((~ (r3 @ A @ B)) | (~ (r1 @ B @ sk1)) | (~ (good_in_maths @ C @ (D @ sk1))) | ((r1 @ (sk3 @ (^ [E:$i]: (r1 @ E @ (D @ E))) @ A) @ (D @ (sk3 @ (^ [E:$i]: (r1 @ E @ (D @ E))) @ A))) != (r1 @ B @ sk1)) | ~ (($true)))),inference(eqfactor_ordered,[status(thm)],[520])).
% 33.98/8.05 thf(798,plain,(! [B:mu,A:$i] : ((~ (r3 @ A @ (sk3 @ (^ [C:$i]: (r1 @ C @ sk1)) @ A))) | (~ (r1 @ (sk3 @ (^ [C:$i]: (r1 @ C @ sk1)) @ A) @ sk1)) | (~ (good_in_maths @ B @ sk1)))),inference(pre_uni,[status(thm)],[797:[bind(A, $thf(A)),bind(B, $thf(sk3 @ (^ [E:$i]: (r1 @ E @ sk1)) @ A)),bind(C, $thf(C)),bind(D, $thf(^ [E:$i]: (sk1)))]])).
% 33.98/8.05 thf(824,plain,(! [B:mu,A:$i] : ((~ (r3 @ A @ (sk3 @ (^ [C:$i]: (r1 @ C @ sk1)) @ A))) | (~ (r1 @ (sk3 @ (^ [C:$i]: (r1 @ C @ sk1)) @ A) @ sk1)) | (~ (good_in_maths @ B @ sk1)))),inference(simp,[status(thm)],[798])).
% 33.98/8.05 thf(19,axiom,((mvalid @ (mforall_prop @ (^ [A:($i > $o)]: (mimplies @ (mbox @ r2 @ A) @ (mbox @ r4 @ (mbox @ r2 @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4s_for_r2_r4)).
% 33.98/8.05 thf(166,plain,((! [A:$i,B:($i > $o)]: (~ (! [C:$i]: (~ (r2 @ A @ C) | (B @ C))) | ! [C:$i]: (~ (r4 @ A @ C) | ! [D:$i]: (~ (r2 @ C @ D) | (B @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[19])).
% 33.98/8.05 thf(18,axiom,((mvalid @ (mforall_prop @ (^ [A:($i > $o)]: (mimplies @ (mbox @ r4 @ A) @ (mnot @ (mbox @ r4 @ (mnot @ A)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_D_for_r4)).
% 33.98/8.05 thf(158,plain,((! [A:$i,B:($i > $o)]: (~ (! [C:$i]: (~ (r4 @ A @ C) | (B @ C))) | ~ (! [C:$i]: (~ (r4 @ A @ C) | ~ (B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[18])).
% 33.98/8.05 thf(159,plain,(! [B:($i > $o),A:$i] : ((((r4 @ A @ (sk18 @ (B) @ A)) | (r4 @ A @ (sk19 @ (B) @ A))) & ((r4 @ A @ (sk18 @ (B) @ A)) | (B @ (sk19 @ (B) @ A))) & (~ (B @ (sk18 @ (B) @ A)) | (r4 @ A @ (sk19 @ (B) @ A))) & (~ (B @ (sk18 @ (B) @ A)) | (B @ (sk19 @ (B) @ A)))))),inference(cnf,[status(esa)],[158])).
% 33.98/8.05 thf(161,plain,(! [B:($i > $o),A:$i] : ((r4 @ A @ (sk18 @ (B) @ A)) | (B @ (sk19 @ (B) @ A)))),inference(cnfConj,[status(thm)],[159])).
% 33.98/8.05 thf(60,axiom,((mvalid @ (mforall_prop @ (^ [A:($i > $o)]: (mimplies @ (mbox @ r3 @ A) @ (mbox @ r2 @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_I_for_r3_r2)).
% 33.98/8.05 thf(382,plain,((! [A:$i,B:($i > $o)]: (~ (! [C:$i]: (~ (r3 @ A @ C) | (B @ C))) | ! [C:$i]: (~ (r2 @ A @ C) | (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[60])).
% 33.98/8.05 thf(64,axiom,((mvalid @ (mforall_ind @ (^ [A:mu]: (mbox @ r3 @ (mimplies @ (physics_student @ A) @ (mdia @ r3 @ (good_in_physics @ A)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_r4_3)).
% 33.98/8.05 thf(406,plain,((! [A:$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)],[64])).
% 33.98/8.05 thf(20,axiom,((mvalid @ (mforall_prop @ (^ [A:($i > $o)]: (mimplies @ (mbox @ r4 @ A) @ (mbox @ r2 @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_I_for_r4_r2)).
% 33.98/8.05 thf(172,plain,((! [A:$i,B:($i > $o)]: (~ (! [C:$i]: (~ (r4 @ A @ C) | (B @ C))) | ! [C:$i]: (~ (r2 @ A @ C) | (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[20])).
% 33.98/8.05 thf(39,axiom,((mvalid @ (mforall_prop @ (^ [A:($i > $o)]: (mimplies @ (mbox @ r5 @ A) @ (mnot @ (mbox @ r5 @ (mnot @ A)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_D_for_r5)).
% 33.98/8.05 thf(274,plain,((! [A:$i,B:($i > $o)]: (~ (! [C:$i]: (~ (r5 @ A @ C) | (B @ C))) | ~ (! [C:$i]: (~ (r5 @ A @ C) | ~ (B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[39])).
% 33.98/8.05 thf(80,plain,(! [D:$i,C:$i,B:($i > $o),A:$i] : ((~ ((sk3 @ (B) @ A) = (sk3 @ ((=) @ $i @ (sk3 @ B @ A)) @ A))) | (~ (r3 @ A @ C)) | (~ (r1 @ C @ D)) | ((sk3 @ (B) @ A) = D))),inference(replace_leibeq,[status(thm)],[79:[bind(A, $thf(A)),bind(B, $thf((=) @ $i @ (sk3 @ B @ A)))]])).
% 33.98/8.05 thf(81,plain,(! [D:$i,C:$i,B:($i > $o),A:$i] : (((sk3 @ (B) @ A) != (sk3 @ ((=) @ $i @ (sk3 @ B @ A)) @ A)) | ((sk3 @ (B) @ A) = D) | (~ (r3 @ A @ C)) | (~ (r1 @ C @ D)))),inference(lifteq,[status(thm)],[80])).
% 33.98/8.05 thf(1441,plain,(! [D:$i,C:mu,B:$i,A:$i] : (~ (($true)) | (~ (good_in_physics @ C @ B)) | (~ (r1 @ sk1 @ (sk2 @ B @ C @ D))) | ((r2 @ A @ (sk4 @ (^ [E:$i]: (($false))) @ A)) != (r2 @ D @ B)))),inference(paramod_ordered,[status(thm)],[619,957])).
% 33.98/8.05 thf(1442,plain,(! [D:$i,C:mu,B:$i,A:$i] : ((~ (good_in_physics @ C @ B)) | (~ (r1 @ sk1 @ (sk2 @ B @ C @ D))) | ((r2 @ A @ (sk4 @ (^ [E:$i]: (($false))) @ A)) != (r2 @ D @ B)))),inference(simp,[status(thm)],[1441])).
% 33.98/8.05 thf(1443,plain,(! [B:$i,A:mu] : ((~ (good_in_physics @ A @ (sk4 @ (^ [C:$i]: (($false))) @ B))) | (~ (r1 @ sk1 @ (sk2 @ (sk4 @ (^ [C:$i]: (($false))) @ B) @ A @ B))))),inference(pattern_uni,[status(thm)],[1442:[bind(A, $thf(F)),bind(B, $thf(sk4 @ (^ [F:$i]: (($false))) @ F)),bind(C, $thf(C)),bind(D, $thf(F))]])).
% 33.98/8.05 thf(1492,plain,(! [B:$i,A:mu] : ((~ (good_in_physics @ A @ (sk4 @ (^ [C:$i]: (($false))) @ B))) | (~ (r1 @ sk1 @ (sk2 @ (sk4 @ (^ [C:$i]: (($false))) @ B) @ A @ B))))),inference(simp,[status(thm)],[1443])).
% 33.98/8.05 thf(31,axiom,((mvalid @ (mforall_prop @ (^ [A:($i > $o)]: (mimplies @ (mbox @ r3 @ A) @ (mnot @ (mbox @ r3 @ (mnot @ A)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_D_for_r3)).
% 33.98/8.05 thf(230,plain,((! [A:$i,B:($i > $o)]: (~ (! [C:$i]: (~ (r3 @ A @ C) | (B @ C))) | ~ (! [C:$i]: (~ (r3 @ A @ C) | ~ (B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[31])).
% 33.98/8.05 thf(56,axiom,((mvalid @ (mforall_prop @ (^ [A:($i > $o)]: (mimplies @ (mnot @ (mbox @ r4 @ A)) @ (mbox @ r4 @ (mnot @ (mbox @ r4 @ A)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_5_for_r4)).
% 33.98/8.05 thf(362,plain,((! [A:$i,B:($i > $o)]: (! [C:$i]: (~ (r4 @ A @ C) | (B @ C)) | ! [C:$i]: (~ (r4 @ A @ C) | ~ (! [D:$i]: (~ (r4 @ C @ D) | (B @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[56])).
% 33.98/8.05 thf(15,axiom,((mvalid @ (mforall_prop @ (^ [A:($i > $o)]: (mimplies @ (mbox @ r3 @ A) @ (mbox @ r3 @ (mbox @ r3 @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4s_for_r3_r3)).
% 33.98/8.05 thf(140,plain,((! [A:$i,B:($i > $o)]: (~ (! [C:$i]: (~ (r3 @ A @ C) | (B @ C))) | ! [C:$i]: (~ (r3 @ A @ C) | ! [D:$i]: (~ (r3 @ C @ D) | (B @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[15])).
% 33.98/8.05 thf(9,axiom,((mvalid @ (mforall_prop @ (^ [A:($i > $o)]: (mimplies @ (mbox @ r1 @ A) @ (mbox @ r4 @ (mbox @ r1 @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4s_for_r1_r4)).
% 33.98/8.05 thf(108,plain,((! [A:$i,B:($i > $o)]: (~ (! [C:$i]: (~ (r1 @ A @ C) | (B @ C))) | ! [C:$i]: (~ (r4 @ A @ C) | ! [D:$i]: (~ (r1 @ C @ D) | (B @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[9])).
% 33.98/8.05 thf(49,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)).
% 33.98/8.05 thf(330,plain,((! [A:$i,B:mu,C:$i]: (~ (r3 @ A @ C) | ~ (physics_student @ B @ C) | ~ (! [D:$i]: (~ (r4 @ C @ D) | ~ (good_in_physics @ B @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[49])).
% 33.98/8.05 thf(13,axiom,((mvalid @ (mforall_ind @ (^ [A:mu]: (mbox @ r3 @ (mimplies @ (maths_student @ A) @ (mdia @ r3 @ (good_in_maths @ A)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_r3_3)).
% 33.98/8.05 thf(130,plain,((! [A:$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)],[13])).
% 33.98/8.05 thf(87,plain,(! [B:($i > $o),A:$i] : ((~ (B @ (sk4 @ (B) @ A))) | (B @ (sk5 @ (B) @ A)))),inference(cnfConj,[status(thm)],[83])).
% 33.98/8.05 thf(1001,plain,(! [D:$i,C:mu,B:($i > $o),A:$i] : ((~ (B @ (sk4 @ (B) @ A))) | ~ (($true)) | (~ (good_in_maths @ C @ D)) | ((B @ (sk5 @ (B) @ A)) != (r1 @ sk1 @ D)))),inference(paramod_ordered,[status(thm)],[87,71])).
% 33.98/8.05 thf(1002,plain,(! [D:$i,C:mu,B:($i > $o),A:$i] : ((~ (B @ (sk4 @ (B) @ A))) | (~ (good_in_maths @ C @ D)) | ((B @ (sk5 @ (B) @ A)) != (r1 @ sk1 @ D)))),inference(simp,[status(thm)],[1001])).
% 33.98/8.05 thf(1110,plain,(! [C:($i > $i),B:mu,A:$i] : ((~ (r1 @ sk1 @ (C @ (sk4 @ (^ [D:$i]: (r1 @ sk1 @ (C @ D))) @ A)))) | (~ (good_in_maths @ B @ (C @ (sk5 @ (^ [D:$i]: (r1 @ sk1 @ (C @ D))) @ A)))))),inference(pre_uni,[status(thm)],[1002:[bind(A, $thf(A)),bind(B, $thf(^ [F:$i]: (r1 @ sk1 @ (F @ F)))),bind(C, $thf(C)),bind(D, $thf(F @ (sk5 @ (^ [F:$i]: (r1 @ sk1 @ (F @ F))) @ A)))]])).
% 33.98/8.05 thf(1176,plain,(! [C:($i > $i),B:mu,A:$i] : ((~ (r1 @ sk1 @ (C @ (sk4 @ (^ [D:$i]: (r1 @ sk1 @ (C @ D))) @ A)))) | (~ (good_in_maths @ B @ (C @ (sk5 @ (^ [D:$i]: (r1 @ sk1 @ (C @ D))) @ A)))))),inference(simp,[status(thm)],[1110])).
% 33.98/8.05 thf(62,axiom,((mvalid @ (mforall_prop @ (^ [A:($i > $o)]: (mimplies @ (mbox @ r5 @ A) @ (mbox @ r2 @ (mbox @ r5 @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4s_for_r5_r2)).
% 33.98/8.05 thf(394,plain,((! [A:$i,B:($i > $o)]: (~ (! [C:$i]: (~ (r5 @ A @ C) | (B @ C))) | ! [C:$i]: (~ (r2 @ A @ C) | ! [D:$i]: (~ (r5 @ C @ D) | (B @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[62])).
% 33.98/8.05 thf(2923,plain,(! [F:$i,E:mu,D:($i > $o),C:mu,B:$i,A:$i] : ((~ (r3 @ sk1 @ A)) | (~ (r1 @ A @ B)) | (~ (good_in_maths @ C @ (sk3 @ (D) @ sk1))) | ~ (($true)) | (~ (good_in_maths @ E @ F)) | ((D @ B) != (r1 @ sk1 @ F)))),inference(paramod_ordered,[status(thm)],[2072,71])).
% 33.98/8.05 thf(2924,plain,(! [F:$i,E:mu,D:($i > $o),C:mu,B:$i,A:$i] : ((~ (r3 @ sk1 @ A)) | (~ (r1 @ A @ B)) | (~ (good_in_maths @ C @ (sk3 @ (D) @ sk1))) | (~ (good_in_maths @ E @ F)) | ((D @ B) != (r1 @ sk1 @ F)))),inference(simp,[status(thm)],[2923])).
% 33.98/8.05 thf(3200,plain,(! [D:($i > $i),C:mu,B:mu,A:$i] : ((~ (r3 @ sk1 @ A)) | (~ (r1 @ A @ sk1)) | (~ (good_in_maths @ B @ (sk3 @ (^ [E:$i]: (r1 @ E @ (D @ E))) @ sk1))) | (~ (good_in_maths @ C @ (D @ sk1))))),inference(pre_uni,[status(thm)],[2924:[bind(A, $thf(A)),bind(B, $thf(sk1)),bind(C, $thf(C)),bind(D, $thf(^ [H:$i]: (r1 @ H @ (H @ H)))),bind(E, $thf(E)),bind(F, $thf(H @ sk1))]])).
% 33.98/8.05 thf(3325,plain,(! [D:($i > $i),C:mu,B:mu,A:$i] : ((~ (r3 @ sk1 @ A)) | (~ (r1 @ A @ sk1)) | (~ (good_in_maths @ B @ (sk3 @ (^ [E:$i]: (r1 @ E @ (D @ E))) @ sk1))) | (~ (good_in_maths @ C @ (D @ sk1))))),inference(simp,[status(thm)],[3200])).
% 33.98/8.05 thf(40,axiom,((mvalid @ (mforall_prop @ (^ [A:($i > $o)]: (mimplies @ (mbox @ r5 @ A) @ (mbox @ r4 @ (mbox @ r5 @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4s_for_r5_r4)).
% 33.98/8.05 thf(282,plain,((! [A:$i,B:($i > $o)]: (~ (! [C:$i]: (~ (r5 @ A @ C) | (B @ C))) | ! [C:$i]: (~ (r4 @ A @ C) | ! [D:$i]: (~ (r5 @ C @ D) | (B @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[40])).
% 33.98/8.05 thf(2743,plain,(! [A:$i] : ((r4 @ A @ (sk18 @ (^ [B:$i]: (($false))) @ A)) | ($false))),inference(prim_subst,[status(thm)],[161:[bind(A, $thf(A)),bind(B, $thf(^ [C:$i]: (($false))))]])).
% 33.98/8.05 thf(2850,plain,(! [A:$i] : ((r4 @ A @ (sk18 @ (^ [B:$i]: (($false))) @ A)))),inference(simp,[status(thm)],[2743])).
% 33.98/8.05 thf(46,axiom,((mvalid @ (mforall_prop @ (^ [A:($i > $o)]: (mimplies @ (mbox @ r4 @ A) @ (mbox @ r1 @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_I_for_r4_r1)).
% 33.98/8.05 thf(314,plain,((! [A:$i,B:($i > $o)]: (~ (! [C:$i]: (~ (r4 @ A @ C) | (B @ C))) | ! [C:$i]: (~ (r1 @ A @ C) | (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[46])).
% 33.98/8.05 thf(34,axiom,((mvalid @ (mforall_prop @ (^ [A:($i > $o)]: (mimplies @ (mbox @ r4 @ A) @ (mbox @ r3 @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_I_for_r4_r3)).
% 33.98/8.05 thf(250,plain,((! [A:$i,B:($i > $o)]: (~ (! [C:$i]: (~ (r4 @ A @ C) | (B @ C))) | ! [C:$i]: (~ (r3 @ A @ C) | (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[34])).
% 33.98/8.05 thf(163,plain,(! [B:($i > $o),A:$i] : ((~ (B @ (sk18 @ (B) @ A))) | (B @ (sk19 @ (B) @ A)))),inference(cnfConj,[status(thm)],[159])).
% 33.98/8.05 thf(1237,plain,(! [D:mu,C:$i,B:($i > $o),A:$i] : ((~ (B @ (sk18 @ (B) @ A))) | (~ (r3 @ C @ (sk3 @ (^ [E:$i]: (r1 @ E @ sk1)) @ C))) | (~ (r1 @ (sk3 @ (^ [E:$i]: (r1 @ E @ sk1)) @ C) @ sk1)) | ~ (($true)) | ((B @ (sk19 @ (B) @ A)) != (good_in_maths @ D @ sk1)))),inference(paramod_ordered,[status(thm)],[163,824])).
% 33.98/8.05 thf(1238,plain,(! [D:mu,C:$i,B:($i > $o),A:$i] : ((~ (B @ (sk18 @ (B) @ A))) | (~ (r3 @ C @ (sk3 @ (^ [E:$i]: (r1 @ E @ sk1)) @ C))) | (~ (r1 @ (sk3 @ (^ [E:$i]: (r1 @ E @ sk1)) @ C) @ sk1)) | ((B @ (sk19 @ (B) @ A)) != (good_in_maths @ D @ sk1)))),inference(simp,[status(thm)],[1237])).
% 33.98/8.05 thf(1335,plain,(! [C:($i > mu),B:$i,A:$i] : ((~ (good_in_maths @ (C @ (sk18 @ (^ [D:$i]: (good_in_maths @ (C @ D) @ sk1)) @ A)) @ sk1)) | (~ (r3 @ B @ (sk3 @ (^ [D:$i]: (r1 @ D @ sk1)) @ B))) | (~ (r1 @ (sk3 @ (^ [D:$i]: (r1 @ D @ sk1)) @ B) @ sk1)))),inference(pre_uni,[status(thm)],[1238:[bind(A, $thf(A)),bind(B, $thf(^ [F:$i]: (good_in_maths @ (E @ F) @ sk1))),bind(C, $thf(C)),bind(D, $thf(E @ (sk19 @ (^ [F:$i]: (good_in_maths @ (E @ F) @ sk1)) @ A)))]])).
% 33.98/8.05 thf(1412,plain,(! [C:($i > mu),B:$i,A:$i] : ((~ (good_in_maths @ (C @ (sk18 @ (^ [D:$i]: (good_in_maths @ (C @ D) @ sk1)) @ A)) @ sk1)) | (~ (r3 @ B @ (sk3 @ (^ [D:$i]: (r1 @ D @ sk1)) @ B))) | (~ (r1 @ (sk3 @ (^ [D:$i]: (r1 @ D @ sk1)) @ B) @ sk1)))),inference(simp,[status(thm)],[1335])).
% 33.98/8.05 thf(57,axiom,((mvalid @ (mforall_prop @ (^ [A:($i > $o)]: (mimplies @ (mbox @ r5 @ A) @ (mbox @ r1 @ (mbox @ r5 @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4s_for_r5_r1)).
% 33.98/8.05 thf(368,plain,((! [A:$i,B:($i > $o)]: (~ (! [C:$i]: (~ (r5 @ A @ C) | (B @ C))) | ! [C:$i]: (~ (r1 @ A @ C) | ! [D:$i]: (~ (r5 @ C @ D) | (B @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[57])).
% 33.98/8.05 thf(10,axiom,((mvalid @ (mforall_prop @ (^ [A:($i > $o)]: (mimplies @ (mbox @ r4 @ A) @ (mbox @ r1 @ (mbox @ r4 @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4s_for_r4_r1)).
% 33.98/8.05 thf(114,plain,((! [A:$i,B:($i > $o)]: (~ (! [C:$i]: (~ (r4 @ A @ C) | (B @ C))) | ! [C:$i]: (~ (r1 @ A @ C) | ! [D:$i]: (~ (r4 @ C @ D) | (B @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[10])).
% 33.98/8.05 thf(38,axiom,((mvalid @ (mbox @ r5 @ (physics_student @ mike)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_a9)).
% 33.98/8.05 thf(272,plain,((! [A:$i,B:$i]: (~ (r5 @ A @ B) | (physics_student @ mike @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[38])).
% 33.98/8.05 thf(16,axiom,((mvalid @ (mforall_prop @ (^ [A:($i > $o)]: (mimplies @ (mbox @ r3 @ A) @ (mbox @ r1 @ (mbox @ r3 @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4s_for_r3_r1)).
% 33.98/8.05 thf(146,plain,((! [A:$i,B:($i > $o)]: (~ (! [C:$i]: (~ (r3 @ A @ C) | (B @ C))) | ! [C:$i]: (~ (r1 @ A @ C) | ! [D:$i]: (~ (r3 @ C @ D) | (B @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[16])).
% 33.98/8.05 thf(24,axiom,((mvalid @ (mforall_prop @ (^ [A:($i > $o)]: (mimplies @ (mbox @ r4 @ A) @ (mbox @ r4 @ (mbox @ r4 @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4s_for_r4_r4)).
% 33.98/8.05 thf(190,plain,((! [A:$i,B:($i > $o)]: (~ (! [C:$i]: (~ (r4 @ A @ C) | (B @ C))) | ! [C:$i]: (~ (r4 @ A @ C) | ! [D:$i]: (~ (r4 @ C @ D) | (B @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[24])).
% 33.98/8.05 thf(68,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)).
% 33.98/8.05 thf(422,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)],[68])).
% 33.98/8.05 thf(273,plain,(! [B:$i,A:$i] : ((~ (r5 @ A @ B)) | (physics_student @ mike @ B))),inference(cnf,[status(esa)],[272])).
% 33.98/8.05 thf(27,axiom,((mvalid @ (mforall_prop @ (^ [A:($i > $o)]: (mimplies @ (mbox @ r2 @ A) @ (mbox @ r3 @ (mbox @ r2 @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4s_for_r2_r3)).
% 33.98/8.05 thf(210,plain,((! [A:$i,B:($i > $o)]: (~ (! [C:$i]: (~ (r2 @ A @ C) | (B @ C))) | ! [C:$i]: (~ (r3 @ A @ C) | ! [D:$i]: (~ (r2 @ C @ D) | (B @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[27])).
% 33.98/8.05 thf(48,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)).
% 33.98/8.05 thf(326,plain,((! [A:$i,B:mu,C:$i]: (~ (r3 @ A @ C) | ~ (maths_student @ B @ C) | ~ (! [D:$i]: (~ (r5 @ C @ D) | ~ (good_in_maths @ B @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[48])).
% 33.98/8.05 thf(12,axiom,((mvalid @ (mforall_ind @ (^ [A:mu]: (mbox @ r3 @ (mimplies @ (physics_student @ A) @ (mdia @ r1 @ (good_in_physics @ A)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_r4_1)).
% 33.98/8.05 thf(126,plain,((! [A:$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)],[12])).
% 33.98/8.05 thf(63,axiom,((mvalid @ (mforall_prop @ (^ [A:($i > $o)]: (mimplies @ (mbox @ r1 @ A) @ (mbox @ r2 @ (mbox @ r1 @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4s_for_r1_r2)).
% 33.98/8.05 thf(400,plain,((! [A:$i,B:($i > $o)]: (~ (! [C:$i]: (~ (r1 @ A @ C) | (B @ C))) | ! [C:$i]: (~ (r2 @ A @ C) | ! [D:$i]: (~ (r1 @ C @ D) | (B @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[63])).
% 33.98/8.05 thf(21,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)).
% 33.98/8.05 thf(178,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)],[21])).
% 33.98/8.05 thf(6,axiom,((mvalid @ (mforall_prop @ (^ [A:($i > $o)]: (mimplies @ (mbox @ r4 @ A) @ (mbox @ r2 @ (mbox @ r4 @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4s_for_r4_r2)).
% 33.98/8.05 thf(90,plain,((! [A:$i,B:($i > $o)]: (~ (! [C:$i]: (~ (r4 @ A @ C) | (B @ C))) | ! [C:$i]: (~ (r2 @ A @ C) | ! [D:$i]: (~ (r4 @ C @ D) | (B @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6])).
% 33.98/8.05 thf(999,plain,(! [D:mu,C:$i,B:($i > $o),A:$i] : ((~ (B @ (sk4 @ (B) @ A))) | (~ (r3 @ C @ (sk3 @ (^ [E:$i]: (r1 @ E @ sk1)) @ C))) | (~ (r1 @ (sk3 @ (^ [E:$i]: (r1 @ E @ sk1)) @ C) @ sk1)) | ~ (($true)) | ((B @ (sk5 @ (B) @ A)) != (good_in_maths @ D @ sk1)))),inference(paramod_ordered,[status(thm)],[87,824])).
% 33.98/8.05 thf(1000,plain,(! [D:mu,C:$i,B:($i > $o),A:$i] : ((~ (B @ (sk4 @ (B) @ A))) | (~ (r3 @ C @ (sk3 @ (^ [E:$i]: (r1 @ E @ sk1)) @ C))) | (~ (r1 @ (sk3 @ (^ [E:$i]: (r1 @ E @ sk1)) @ C) @ sk1)) | ((B @ (sk5 @ (B) @ A)) != (good_in_maths @ D @ sk1)))),inference(simp,[status(thm)],[999])).
% 33.98/8.05 thf(1120,plain,(! [C:($i > mu),B:$i,A:$i] : ((~ (good_in_maths @ (C @ (sk4 @ (^ [D:$i]: (good_in_maths @ (C @ D) @ sk1)) @ A)) @ sk1)) | (~ (r3 @ B @ (sk3 @ (^ [D:$i]: (r1 @ D @ sk1)) @ B))) | (~ (r1 @ (sk3 @ (^ [D:$i]: (r1 @ D @ sk1)) @ B) @ sk1)))),inference(pre_uni,[status(thm)],[1000:[bind(A, $thf(A)),bind(B, $thf(^ [F:$i]: (good_in_maths @ (E @ F) @ sk1))),bind(C, $thf(C)),bind(D, $thf(E @ (sk5 @ (^ [F:$i]: (good_in_maths @ (E @ F) @ sk1)) @ A)))]])).
% 33.98/8.05 thf(1184,plain,(! [C:($i > mu),B:$i,A:$i] : ((~ (good_in_maths @ (C @ (sk4 @ (^ [D:$i]: (good_in_maths @ (C @ D) @ sk1)) @ A)) @ sk1)) | (~ (r3 @ B @ (sk3 @ (^ [D:$i]: (r1 @ D @ sk1)) @ B))) | (~ (r1 @ (sk3 @ (^ [D:$i]: (r1 @ D @ sk1)) @ B) @ sk1)))),inference(simp,[status(thm)],[1120])).
% 33.98/8.05 thf(29,axiom,((mvalid @ (mforall_prop @ (^ [A:($i > $o)]: (mimplies @ (mbox @ r1 @ A) @ (mbox @ r1 @ (mbox @ r1 @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4s_for_r1_r1)).
% 33.98/8.05 thf(222,plain,((! [A:$i,B:($i > $o)]: (~ (! [C:$i]: (~ (r1 @ A @ C) | (B @ C))) | ! [C:$i]: (~ (r1 @ A @ C) | ! [D:$i]: (~ (r1 @ C @ D) | (B @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[29])).
% 33.98/8.05 thf(5494,plain,(($false)),inference(e,[status(thm)],[229,204,374,182,69,2072,352,308,120,550,340,288,320,619,344,196,189,416,152,228,78,216,238,348,3361,411,74,292,380,102,85,201,334,957,302,260,630,519,188,388,356,256,96,3242,654,134,244,266,718,888,298,412,824,166,161,71,382,406,172,274,81,1492,230,362,76,140,520,108,330,130,1176,394,3325,282,2850,72,314,250,87,1412,368,158,114,632,75,272,82,410,146,190,422,273,210,326,126,79,400,163,178,90,1184,222])).
% 33.98/8.05 % SZS output end Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 33.98/8.05 % [INFO] Killing All external provers ...
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