%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : AGT029^1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n007.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 32.96s 7.92s
% Output : Refutation 33.71s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : AGT029^1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.11/0.22 % Computer : n007.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 17:27:34 UTC 2026
% 0.11/0.22 % CPUTime :
% 0.11/0.22 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 1.04/0.82 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.61/1.13 % [INFO] Parsing done (307ms).
% 2.08/1.15 % [INFO] Running in sequential loop mode.
% 2.68/1.55 % [INFO] eprover registered as external prover.
% 2.68/1.55 % [INFO] Scanning for conjecture ...
% 3.20/1.76 % [INFO] Found a conjecture (or negated_conjecture) and 66 axioms. Running axiom selection ...
% 3.41/1.86 % [INFO] Axiom selection finished. Selected 66 axioms (removed 0 axioms).
% 3.75/1.92 % [INFO] Problem is higher-order (TPTP THF).
% 3.75/1.93 % [INFO] Type checking passed.
% 3.75/1.94 % [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 ...
% 32.96/7.91 % External prover 'e' found a proof!
% 32.96/7.91 % [INFO] Killing All external provers ...
% 32.96/7.92 % Time passed: 7544ms (effective reasoning time: 6763ms)
% 32.96/7.92 % 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)>
% 32.96/7.92 % 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
% 32.96/7.92 % No. of inferences in proof: 222
% 32.96/7.92 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 7544 ms resp. 6763 ms w/o parsing
% 33.71/8.08 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% 33.71/8.08 thf(mu_type, type, mu: $tType).
% 33.71/8.08 thf(mnot_decl, type, mnot: (($i > $o) > ($i > $o))).
% 33.71/8.08 thf(mor_decl, type, mor: (($i > $o) > (($i > $o) > ($i > $o)))).
% 33.71/8.08 thf(mimplies_decl, type, mimplies: (($i > $o) > (($i > $o) > ($i > $o)))).
% 33.71/8.08 thf(mforall_ind_decl, type, mforall_ind: ((mu > ($i > $o)) > ($i > $o))).
% 33.71/8.08 thf(mforall_prop_decl, type, mforall_prop: ((($i > $o) > ($i > $o)) > ($i > $o))).
% 33.71/8.08 thf(mexists_ind_decl, type, mexists_ind: ((mu > ($i > $o)) > ($i > $o))).
% 33.71/8.08 thf(mbox_decl, type, mbox: (($i > ($i > $o)) > (($i > $o) > ($i > $o)))).
% 33.71/8.08 thf(mdia_decl, type, mdia: (($i > ($i > $o)) > (($i > $o) > ($i > $o)))).
% 33.71/8.08 thf(mvalid_decl, type, mvalid: (($i > $o) > $o)).
% 33.71/8.08 thf(r1_decl, type, r1: ($i > ($i > $o))).
% 33.71/8.08 thf(r2_decl, type, r2: ($i > ($i > $o))).
% 33.71/8.08 thf(r3_decl, type, r3: ($i > ($i > $o))).
% 33.71/8.08 thf(r4_decl, type, r4: ($i > ($i > $o))).
% 33.71/8.08 thf(r5_decl, type, r5: ($i > ($i > $o))).
% 33.71/8.08 thf(john_decl, type, john: mu).
% 33.71/8.08 thf(tom_decl, type, tom: mu).
% 33.71/8.08 thf(peter_decl, type, peter: mu).
% 33.71/8.08 thf(mike_decl, type, mike: mu).
% 33.71/8.08 thf(good_in_maths_decl, type, good_in_maths: (mu > ($i > $o))).
% 33.71/8.08 thf(maths_teacher_decl, type, maths_teacher: (mu > ($i > $o))).
% 33.71/8.08 thf(mathematician_decl, type, mathematician: (mu > ($i > $o))).
% 33.71/8.08 thf(maths_student_decl, type, maths_student: (mu > ($i > $o))).
% 33.71/8.08 thf(good_in_physics_decl, type, good_in_physics: (mu > ($i > $o))).
% 33.71/8.08 thf(physics_student_decl, type, physics_student: (mu > ($i > $o))).
% 33.71/8.08 thf(sk1_decl, type, sk1: $i).
% 33.71/8.08 thf(sk2_decl, type, sk2: (mu > $i)).
% 33.71/8.08 thf(sk3_decl, type, sk3: ($i > (mu > ($i > $i)))).
% 33.71/8.08 thf(sk4_decl, type, sk4: (($i > $o) > ($i > $i))).
% 33.71/8.08 thf(sk5_decl, type, sk5: (($i > $o) > ($i > $i))).
% 33.71/8.08 thf(sk6_decl, type, sk6: (($i > $o) > ($i > $i))).
% 33.71/8.08 thf(sk19_decl, type, sk19: (($i > $o) > ($i > $i))).
% 33.71/8.08 thf(sk20_decl, type, sk20: (($i > $o) > ($i > $i))).
% 33.71/8.08 thf(sk26_decl, type, sk26: (($i > $o) > ($i > $i))).
% 33.71/8.08 thf(sk27_decl, type, sk27: (($i > $o) > ($i > $i))).
% 33.71/8.08 thf(mnot_def, definition, mnot = (^ [A:($i > $o),B:$i]: ~ (A @ B)) ).
% 33.71/8.08 thf(mor_def, definition, mor = (^ [A:($i > $o),B:($i > $o),C:$i]: ((A @ C) | (B @ C))) ).
% 33.71/8.08 thf(mimplies_def, definition, mimplies = (^ [A:($i > $o)]: (mor @ (mnot @ A))) ).
% 33.71/8.08 thf(mforall_ind_def, definition, mforall_ind = (^ [A:(mu > ($i > $o)),B:$i]: ! [C:mu]: (A @ C @ B)) ).
% 33.71/8.08 thf(mforall_prop_def, definition, mforall_prop = (^ [A:(($i > $o) > ($i > $o)),B:$i]: ! [C:($i > $o)]: (A @ C @ B)) ).
% 33.71/8.08 thf(mexists_ind_def, definition, mexists_ind = (^ [A:(mu > ($i > $o))]: (mnot @ (mforall_ind @ (^ [B:mu]: (mnot @ (A @ B)))))) ).
% 33.71/8.08 thf(mbox_def, definition, mbox = (^ [A:($i > ($i > $o)),B:($i > $o),C:$i]: ! [D:$i]: (~ (A @ C @ D) | (B @ D))) ).
% 33.71/8.08 thf(mdia_def, definition, mdia = (^ [A:($i > ($i > $o)),B:($i > $o)]: (mnot @ (mbox @ A @ (mnot @ B)))) ).
% 33.71/8.08 thf(mvalid_def, definition, mvalid = ((!) @ $i) ).
% 33.71/8.08 thf(sk1_def, definition, sk1 = (@+ [A:$i]: ~ (? [B:mu]: ! [C:$i]: (~ (r2 @ A @ C) | (good_in_maths @ B @ C)))) ).
% 33.71/8.08 thf(sk2_def, definition, sk2 = (^ [A:mu]: (@+ [B:$i]: ~ (~ (r2 @ sk1 @ B) | (good_in_maths @ A @ B)))) ).
% 33.71/8.08 thf(sk3_def, definition, sk3 = (^ [A:$i,B:mu,C:$i]: (@+ [D:$i]: ~ (~ (r2 @ A @ D) | ~ (good_in_maths @ B @ D)))) ).
% 33.71/8.08 thf(sk4_def, definition, sk4 = (^ [A:($i > $o),B:$i]: (@+ [C:$i]: ~ (~ (r1 @ B @ C) | (A @ C)))) ).
% 33.71/8.08 thf(sk5_def, definition, sk5 = (^ [A:($i > $o),B:$i]: (@+ [C:$i]: ~ (~ (r2 @ B @ C) | (A @ C)))) ).
% 33.71/8.08 thf(sk6_def, definition, sk6 = (^ [A:($i > $o),B:$i]: (@+ [C:$i]: ~ (~ (r2 @ B @ C) | ~ (A @ C)))) ).
% 33.71/8.08 thf(sk19_def, definition, sk19 = (^ [A:($i > $o),B:$i]: (@+ [C:$i]: ~ (~ (r4 @ B @ C) | (A @ C)))) ).
% 33.71/8.08 thf(sk20_def, definition, sk20 = (^ [A:($i > $o),B:$i]: (@+ [C:$i]: ~ (~ (r4 @ B @ C) | ~ (A @ C)))) ).
% 33.71/8.08 thf(sk26_def, definition, sk26 = (^ [A:($i > $o),B:$i]: (@+ [C:$i]: ~ (~ (r1 @ B @ C) | (A @ C)))) ).
% 33.71/8.08 thf(sk27_def, definition, sk27 = (^ [A:($i > $o),B:$i]: (@+ [C:$i]: ~ (~ (r1 @ B @ C) | ~ (A @ C)))) ).
% 33.71/8.08 thf(20,axiom,((mvalid @ (mforall_prop @ (^ [A:($i > $o)]: (mimplies @ (mbox @ r4 @ A) @ (mbox @ r2 @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_I_for_r4_r2)).
% 33.71/8.08 thf(174,plain,((! [A:$i,B:($i > $o)]: (~ (! [C:$i]: (~ (r4 @ A @ C) | (B @ C))) | ! [C:$i]: (~ (r2 @ A @ C) | (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[20])).
% 33.71/8.08 thf(51,axiom,((mvalid @ (mforall_ind @ (^ [A:mu]: (mbox @ r5 @ (mimplies @ (mbox @ r1 @ (mathematician @ A)) @ (mbox @ r1 @ (good_in_maths @ A)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_r2_1)).
% 33.71/8.08 thf(342,plain,((! [A:$i,B:mu,C:$i]: (~ (r5 @ A @ C) | ~ (! [D:$i]: (~ (r1 @ C @ D) | (mathematician @ B @ D))) | ! [D:$i]: (~ (r1 @ C @ D) | (good_in_maths @ B @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[51])).
% 33.71/8.08 thf(57,axiom,((mvalid @ (mforall_prop @ (^ [A:($i > $o)]: (mimplies @ (mbox @ r5 @ A) @ (mbox @ r1 @ (mbox @ r5 @ A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_4s_for_r5_r1)).
% 33.71/8.08 thf(370,plain,((! [A:$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])).
% 33.71/8.08 thf(49,axiom,((mvalid @ (mforall_ind @ (^ [A:mu]: (mbox @ r3 @ (mimplies @ (physics_student @ A) @ (mdia @ r4 @ (good_in_physics @ A)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_r4_4)).
% 33.71/8.08 thf(332,plain,((! [A:$i,B:mu,C:$i]: (~ (r3 @ A @ C) | ~ (physics_student @ B @ C) | ~ (! [D:$i]: (~ (r4 @ C @ D) | ~ (good_in_physics @ B @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[49])).
% 33.71/8.08 thf(1,conjecture,((mvalid @ (mexists_ind @ (^ [A:mu]: (mbox @ r2 @ (good_in_maths @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj)).
% 33.71/8.08 thf(2,negated_conjecture,((~ (mvalid @ (mexists_ind @ (^ [A:mu]: (mbox @ r2 @ (good_in_maths @ A))))))),inference(neg_conjecture,[status(cth)],[1])).
% 33.71/8.08 thf(69,plain,((~ (! [A:$i]: ~ (! [B:mu]: ~ (! [C:$i]: (~ (r2 @ A @ C) | (good_in_maths @ B @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])).
% 33.71/8.08 thf(5,axiom,((mvalid @ (mforall_prop @ (^ [A:($i > $o)]: (mimplies @ (mbox @ r2 @ A) @ (mnot @ (mbox @ r2 @ (mnot @ A)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_D_for_r2)).
% 33.71/8.08 thf(84,plain,((! [A:$i,B:($i > $o)]: (~ (! [C:$i]: (~ (r2 @ A @ C) | (B @ C))) | ~ (! [C:$i]: (~ (r2 @ A @ C) | ~ (B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5])).
% 33.71/8.08 thf(85,plain,(! [B:($i > $o),A:$i] : ((((r2 @ A @ (sk5 @ (B) @ A)) | (r2 @ A @ (sk6 @ (B) @ A))) & ((r2 @ A @ (sk5 @ (B) @ A)) | (B @ (sk6 @ (B) @ A))) & (~ (B @ (sk5 @ (B) @ A)) | (r2 @ A @ (sk6 @ (B) @ A))) & (~ (B @ (sk5 @ (B) @ A)) | (B @ (sk6 @ (B) @ A)))))),inference(cnf,[status(esa)],[84])).
% 33.71/8.08 thf(87,plain,(! [B:($i > $o),A:$i] : ((r2 @ A @ (sk5 @ (B) @ A)) | (B @ (sk6 @ (B) @ A)))),inference(cnfConj,[status(thm)],[85])).
% 33.71/8.08 thf(2126,plain,(! [A:$i] : ((r2 @ A @ (sk5 @ (^ [B:$i]: (($false))) @ A)) | ($false))),inference(prim_subst,[status(thm)],[87:[bind(A, $thf(A)),bind(B, $thf(^ [C:$i]: (($false))))]])).
% 33.71/8.08 thf(2191,plain,(! [A:$i] : ((r2 @ A @ (sk5 @ (^ [B:$i]: (($false))) @ A)))),inference(simp,[status(thm)],[2126])).
% 33.71/8.08 thf(3,axiom,((mvalid @ (mforall_ind @ (^ [A:mu]: (mbox @ r2 @ (mimplies @ (good_in_physics @ A) @ (mdia @ r2 @ (good_in_maths @ A)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_r5)).
% 33.71/8.08 thf(74,plain,((! [A:$i,B:mu,C:$i]: (~ (r2 @ A @ C) | ~ (good_in_physics @ B @ C) | ~ (! [D:$i]: (~ (r2 @ C @ D) | ~ (good_in_maths @ B @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3])).
% 33.71/8.08 thf(75,plain,(! [C:$i,B:mu,A:$i] : (((~ (r2 @ A @ C) | ~ (good_in_physics @ B @ C) | (r2 @ C @ (sk3 @ C @ B @ A))) & (~ (r2 @ A @ C) | ~ (good_in_physics @ B @ C) | (good_in_maths @ B @ (sk3 @ C @ B @ A)))))),inference(cnf,[status(esa)],[74])).
% 33.71/8.08 thf(77,plain,(! [C:$i,B:mu,A:$i] : ((~ (r2 @ A @ C)) | (~ (good_in_physics @ B @ C)) | (good_in_maths @ B @ (sk3 @ C @ B @ A)))),inference(cnfConj,[status(thm)],[75])).
% 33.71/8.08 thf(70,plain,((~ (~ (~ (! [A:$i]: ? [B:mu]: ! [C:$i]: (~ (r2 @ A @ C) | (good_in_maths @ B @ C))))))),inference(miniscope,[status(thm)],[69])).
% 33.71/8.08 thf(71,plain,(! [A:mu] : (((r2 @ sk1 @ (sk2 @ A)) & ~ (good_in_maths @ A @ (sk2 @ A))))),inference(cnf,[status(esa)],[70])).
% 33.71/8.08 thf(73,plain,(! [A:mu] : ((~ (good_in_maths @ A @ (sk2 @ A))))),inference(cnfConj,[status(thm)],[71])).
% 33.71/8.08 thf(1072,plain,(! [D:mu,C:$i,B:mu,A:$i] : ((~ (r2 @ A @ C)) | (~ (good_in_physics @ B @ C)) | ~ (($true)) | ((good_in_maths @ B @ (sk3 @ C @ B @ A)) != (good_in_maths @ D @ (sk2 @ D))))),inference(paramod_ordered,[status(thm)],[77,73])).
% 33.71/8.08 thf(1073,plain,(! [D:mu,C:$i,B:mu,A:$i] : ((~ (r2 @ A @ C)) | (~ (good_in_physics @ B @ C)) | ((good_in_maths @ B @ (sk3 @ C @ B @ A)) != (good_in_maths @ D @ (sk2 @ D))))),inference(simp,[status(thm)],[1072])).
% 33.71/8.08 thf(1099,plain,(! [D:mu,C:$i,B:mu,A:$i] : ((~ (r2 @ A @ C)) | (~ (good_in_physics @ B @ C)) | (B != D) | ((sk3 @ C @ B @ A) != (sk2 @ D)))),inference(simp,[status(thm)],[1073])).
% 33.71/8.08 thf(1113,plain,(! [C:mu,B:$i,A:$i] : ((~ (r2 @ A @ B)) | (~ (good_in_physics @ C @ B)) | ((sk3 @ B @ C @ A) != (sk2 @ C)))),inference(simp,[status(thm)],[1099])).
% 33.71/8.08 thf(2581,plain,(! [D:mu,C:$i,B:$i,A:$i] : (~ (($true)) | (~ (good_in_physics @ D @ C)) | ((sk3 @ C @ D @ B) != (sk2 @ D)) | ((r2 @ A @ (sk5 @ (^ [E:$i]: (($false))) @ A)) != (r2 @ B @ C)))),inference(paramod_ordered,[status(thm)],[2191,1113])).
% 33.71/8.08 thf(2582,plain,(! [D:mu,C:$i,B:$i,A:$i] : ((~ (good_in_physics @ D @ C)) | ((sk3 @ C @ D @ B) != (sk2 @ D)) | ((r2 @ A @ (sk5 @ (^ [E:$i]: (($false))) @ A)) != (r2 @ B @ C)))),inference(simp,[status(thm)],[2581])).
% 33.71/8.08 thf(2583,plain,(! [B:$i,A:mu] : ((~ (good_in_physics @ A @ (sk5 @ (^ [C:$i]: (($false))) @ B))) | ((sk3 @ (sk5 @ (^ [C:$i]: (($false))) @ B) @ A @ B) != (sk2 @ A)))),inference(pattern_uni,[status(thm)],[2582:[bind(A, $thf(F)),bind(B, $thf(F)),bind(C, $thf(sk5 @ (^ [F:$i]: (($false))) @ F)),bind(D, $thf(D))]])).
% 33.71/8.08 thf(2630,plain,(! [B:$i,A:mu] : ((~ (good_in_physics @ A @ (sk5 @ (^ [C:$i]: (($false))) @ B))) | ((sk3 @ (sk5 @ (^ [C:$i]: (($false))) @ B) @ A @ B) != (sk2 @ A)))),inference(simp,[status(thm)],[2583])).
% 33.71/8.08 thf(88,plain,(! [B:($i > $o),A:$i] : ((~ (B @ (sk5 @ (B) @ A))) | (r2 @ A @ (sk6 @ (B) @ A)))),inference(cnfConj,[status(thm)],[85])).
% 33.71/8.08 thf(64,axiom,((mvalid @ (mforall_ind @ (^ [A:mu]: (mbox @ r3 @ (mimplies @ (physics_student @ A) @ (mdia @ r3 @ (good_in_physics @ A)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_r4_3)).
% 33.71/8.08 thf(408,plain,((! [A:$i,B:mu,C:$i]: (~ (r3 @ A @ C) | ~ (physics_student @ B @ C) | ~ (! [D:$i]: (~ (r3 @ C @ D) | ~ (good_in_physics @ B @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[64])).
% 33.71/8.08 thf(39,axiom,((mvalid @ (mforall_prop @ (^ [A:($i > $o)]: (mimplies @ (mbox @ r5 @ A) @ (mnot @ (mbox @ r5 @ (mnot @ A)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_D_for_r5)).
% 33.71/8.08 thf(276,plain,((! [A:$i,B:($i > $o)]: (~ (! [C:$i]: (~ (r5 @ A @ C) | (B @ C))) | ~ (! [C:$i]: (~ (r5 @ A @ C) | ~ (B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[39])).
% 33.71/8.08 thf(60,axiom,((mvalid @ (mforall_prop @ (^ [A:($i > $o)]: (mimplies @ (mbox @ r3 @ A) @ (mbox @ r2 @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_I_for_r3_r2)).
% 33.71/8.08 thf(384,plain,((! [A:$i,B:($i > $o)]: (~ (! [C:$i]: (~ (r3 @ A @ C) | (B @ C))) | ! [C:$i]: (~ (r2 @ A @ C) | (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[60])).
% 33.71/8.08 thf(15,axiom,((mvalid @ (mforall_prop @ (^ [A:($i > $o)]: (mimplies @ (mbox @ r3 @ A) @ (mbox @ r3 @ (mbox @ r3 @ A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_4s_for_r3_r3)).
% 33.71/8.08 thf(142,plain,((! [A:$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])).
% 33.71/8.08 thf(22,axiom,((mvalid @ (mforall_prop @ (^ [A:($i > $o)]: (mimplies @ (mbox @ r1 @ A) @ (mbox @ r5 @ (mbox @ r1 @ A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_4s_for_r1_r5)).
% 33.71/8.08 thf(184,plain,((! [A:$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])).
% 33.71/8.08 thf(9,axiom,((mvalid @ (mforall_prop @ (^ [A:($i > $o)]: (mimplies @ (mbox @ r1 @ A) @ (mbox @ r4 @ (mbox @ r1 @ A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_4s_for_r1_r4)).
% 33.71/8.08 thf(110,plain,((! [A:$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])).
% 33.71/8.08 thf(40,axiom,((mvalid @ (mforall_prop @ (^ [A:($i > $o)]: (mimplies @ (mbox @ r5 @ A) @ (mbox @ r4 @ (mbox @ r5 @ A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_4s_for_r5_r4)).
% 33.71/8.08 thf(284,plain,((! [A:$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])).
% 33.71/8.08 thf(46,axiom,((mvalid @ (mforall_prop @ (^ [A:($i > $o)]: (mimplies @ (mbox @ r4 @ A) @ (mbox @ r1 @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_I_for_r4_r1)).
% 33.71/8.08 thf(316,plain,((! [A:$i,B:($i > $o)]: (~ (! [C:$i]: (~ (r4 @ A @ C) | (B @ C))) | ! [C:$i]: (~ (r1 @ A @ C) | (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[46])).
% 33.71/8.08 thf(4,axiom,((mvalid @ (mforall_prop @ (^ [A:($i > $o)]: (mimplies @ (mbox @ r1 @ A) @ (mbox @ r3 @ (mbox @ r1 @ A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_4s_for_r1_r3)).
% 33.71/8.08 thf(78,plain,((! [A:$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])).
% 33.71/8.08 thf(58,axiom,((mvalid @ (mforall_prop @ (^ [A:($i > $o)]: (mimplies @ (mbox @ r5 @ A) @ (mbox @ r2 @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_I_for_r5_r2)).
% 33.71/8.08 thf(376,plain,((! [A:$i,B:($i > $o)]: (~ (! [C:$i]: (~ (r5 @ A @ C) | (B @ C))) | ! [C:$i]: (~ (r2 @ A @ C) | (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[58])).
% 33.71/8.08 thf(72,plain,(! [A:mu] : ((r2 @ sk1 @ (sk2 @ A)))),inference(cnfConj,[status(thm)],[71])).
% 33.71/8.08 thf(1074,plain,(! [D:$i,C:mu,B:$i,A:mu] : (~ (($true)) | (~ (good_in_physics @ C @ D)) | (good_in_maths @ C @ (sk3 @ D @ C @ B)) | ((r2 @ sk1 @ (sk2 @ A)) != (r2 @ B @ D)))),inference(paramod_ordered,[status(thm)],[72,77])).
% 33.71/8.08 thf(1075,plain,(! [D:$i,C:mu,B:$i,A:mu] : ((~ (good_in_physics @ C @ D)) | (good_in_maths @ C @ (sk3 @ D @ C @ B)) | ((r2 @ sk1 @ (sk2 @ A)) != (r2 @ B @ D)))),inference(simp,[status(thm)],[1074])).
% 33.71/8.08 thf(1076,plain,(! [B:mu,A:mu] : ((~ (good_in_physics @ A @ (sk2 @ B))) | (good_in_maths @ A @ (sk3 @ (sk2 @ B) @ A @ sk1)))),inference(pattern_uni,[status(thm)],[1075:[bind(A, $thf(E)),bind(B, $thf(sk1)),bind(C, $thf(C)),bind(D, $thf(sk2 @ E))]])).
% 33.71/8.08 thf(1119,plain,(! [B:mu,A:mu] : ((~ (good_in_physics @ A @ (sk2 @ B))) | (good_in_maths @ A @ (sk3 @ (sk2 @ B) @ A @ sk1)))),inference(simp,[status(thm)],[1076])).
% 33.71/8.08 thf(2219,plain,(! [C:mu,B:mu,A:mu] : ((~ (good_in_physics @ A @ (sk2 @ B))) | ~ (($true)) | ((good_in_maths @ A @ (sk3 @ (sk2 @ B) @ A @ sk1)) != (good_in_maths @ C @ (sk2 @ C))))),inference(paramod_ordered,[status(thm)],[1119,73])).
% 33.71/8.08 thf(2220,plain,(! [C:mu,B:mu,A:mu] : ((~ (good_in_physics @ A @ (sk2 @ B))) | ((good_in_maths @ A @ (sk3 @ (sk2 @ B) @ A @ sk1)) != (good_in_maths @ C @ (sk2 @ C))))),inference(simp,[status(thm)],[2219])).
% 33.71/8.08 thf(2265,plain,(! [C:mu,B:mu,A:mu] : ((~ (good_in_physics @ A @ (sk2 @ B))) | (A != C) | ((sk3 @ (sk2 @ B) @ A @ sk1) != (sk2 @ C)))),inference(simp,[status(thm)],[2220])).
% 33.71/8.08 thf(2291,plain,(! [B:mu,A:mu] : ((~ (good_in_physics @ B @ (sk2 @ A))) | ((sk3 @ (sk2 @ A) @ B @ sk1) != (sk2 @ B)))),inference(simp,[status(thm)],[2265])).
% 33.71/8.08 thf(76,plain,(! [C:$i,B:mu,A:$i] : ((~ (r2 @ A @ C)) | (~ (good_in_physics @ B @ C)) | (r2 @ C @ (sk3 @ C @ B @ A)))),inference(cnfConj,[status(thm)],[75])).
% 33.71/8.08 thf(676,plain,(! [D:$i,C:mu,B:$i,A:mu] : (~ (($true)) | (~ (good_in_physics @ C @ D)) | (r2 @ D @ (sk3 @ D @ C @ B)) | ((r2 @ sk1 @ (sk2 @ A)) != (r2 @ B @ D)))),inference(paramod_ordered,[status(thm)],[72,76])).
% 33.71/8.08 thf(677,plain,(! [D:$i,C:mu,B:$i,A:mu] : ((~ (good_in_physics @ C @ D)) | (r2 @ D @ (sk3 @ D @ C @ B)) | ((r2 @ sk1 @ (sk2 @ A)) != (r2 @ B @ D)))),inference(simp,[status(thm)],[676])).
% 33.71/8.08 thf(678,plain,(! [B:mu,A:mu] : ((~ (good_in_physics @ A @ (sk2 @ B))) | (r2 @ (sk2 @ B) @ (sk3 @ (sk2 @ B) @ A @ sk1)))),inference(pattern_uni,[status(thm)],[677:[bind(A, $thf(E)),bind(B, $thf(sk1)),bind(C, $thf(C)),bind(D, $thf(sk2 @ E))]])).
% 33.71/8.08 thf(701,plain,(! [B:mu,A:mu] : ((~ (good_in_physics @ A @ (sk2 @ B))) | (r2 @ (sk2 @ B) @ (sk3 @ (sk2 @ B) @ A @ sk1)))),inference(simp,[status(thm)],[678])).
% 33.71/8.08 thf(23,axiom,((mvalid @ (mbox @ r2 @ (mathematician @ tom)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_a7)).
% 33.71/8.08 thf(190,plain,((! [A:$i,B:$i]: (~ (r2 @ A @ B) | (mathematician @ tom @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[23])).
% 33.71/8.08 thf(191,plain,(! [B:$i,A:$i] : ((~ (r2 @ A @ B)) | (mathematician @ tom @ B))),inference(cnf,[status(esa)],[190])).
% 33.71/8.08 thf(1023,plain,(! [D:$i,C:$i,B:mu,A:mu] : ((~ (good_in_physics @ A @ (sk2 @ B))) | ~ (($true)) | (mathematician @ tom @ D) | ((r2 @ (sk2 @ B) @ (sk3 @ (sk2 @ B) @ A @ sk1)) != (r2 @ C @ D)))),inference(paramod_ordered,[status(thm)],[701,191])).
% 33.71/8.08 thf(1024,plain,(! [D:$i,C:$i,B:mu,A:mu] : ((~ (good_in_physics @ A @ (sk2 @ B))) | (mathematician @ tom @ D) | ((r2 @ (sk2 @ B) @ (sk3 @ (sk2 @ B) @ A @ sk1)) != (r2 @ C @ D)))),inference(simp,[status(thm)],[1023])).
% 33.71/8.08 thf(1025,plain,(! [B:mu,A:mu] : ((~ (good_in_physics @ A @ (sk2 @ B))) | (mathematician @ tom @ (sk3 @ (sk2 @ B) @ A @ sk1)))),inference(pattern_uni,[status(thm)],[1024:[bind(A, $thf(G)),bind(B, $thf(I)),bind(C, $thf(sk2 @ I)),bind(D, $thf(sk3 @ (sk2 @ I) @ G @ sk1))]])).
% 33.71/8.08 thf(1051,plain,(! [B:mu,A:mu] : ((~ (good_in_physics @ A @ (sk2 @ B))) | (mathematician @ tom @ (sk3 @ (sk2 @ B) @ A @ sk1)))),inference(simp,[status(thm)],[1025])).
% 33.71/8.08 thf(62,axiom,((mvalid @ (mforall_prop @ (^ [A:($i > $o)]: (mimplies @ (mbox @ r5 @ A) @ (mbox @ r2 @ (mbox @ r5 @ A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_4s_for_r5_r2)).
% 33.71/8.08 thf(396,plain,((! [A:$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])).
% 33.71/8.08 thf(89,plain,(! [B:($i > $o),A:$i] : ((~ (B @ (sk5 @ (B) @ A))) | (B @ (sk6 @ (B) @ A)))),inference(cnfConj,[status(thm)],[85])).
% 33.71/8.08 thf(10,axiom,((mvalid @ (mforall_prop @ (^ [A:($i > $o)]: (mimplies @ (mbox @ r4 @ A) @ (mbox @ r1 @ (mbox @ r4 @ A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_4s_for_r4_r1)).
% 33.71/8.08 thf(116,plain,((! [A:$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])).
% 33.71/8.08 thf(26,axiom,((mvalid @ (mforall_prop @ (^ [A:($i > $o)]: (mimplies @ (mbox @ r2 @ A) @ (mbox @ r1 @ (mbox @ r2 @ A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_4s_for_r2_r1)).
% 33.71/8.08 thf(206,plain,((! [A:$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])).
% 33.71/8.08 thf(13,axiom,((mvalid @ (mforall_ind @ (^ [A:mu]: (mbox @ r3 @ (mimplies @ (maths_student @ A) @ (mdia @ r3 @ (good_in_maths @ A)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_r3_3)).
% 33.71/8.08 thf(132,plain,((! [A:$i,B:mu,C:$i]: (~ (r3 @ A @ C) | ~ (maths_student @ B @ C) | ~ (! [D:$i]: (~ (r3 @ C @ D) | ~ (good_in_maths @ B @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[13])).
% 33.71/8.08 thf(3371,plain,(! [A:$i] : (~ (($true)) | (r2 @ A @ (sk6 @ (^ [B:$i]: (($true))) @ A)))),inference(prim_subst,[status(thm)],[88:[bind(A, $thf(A)),bind(B, $thf(^ [C:$i]: (($true))))]])).
% 33.71/8.08 thf(3456,plain,(! [A:$i] : ((r2 @ A @ (sk6 @ (^ [B:$i]: (($true))) @ A)))),inference(simp,[status(thm)],[3371])).
% 33.71/8.08 thf(3530,plain,(! [D:mu,C:$i,B:$i,A:$i] : (~ (($true)) | (~ (good_in_physics @ D @ C)) | ((sk3 @ C @ D @ B) != (sk2 @ D)) | ((r2 @ A @ (sk6 @ (^ [E:$i]: (($true))) @ A)) != (r2 @ B @ C)))),inference(paramod_ordered,[status(thm)],[3456,1113])).
% 33.71/8.08 thf(3531,plain,(! [D:mu,C:$i,B:$i,A:$i] : ((~ (good_in_physics @ D @ C)) | ((sk3 @ C @ D @ B) != (sk2 @ D)) | ((r2 @ A @ (sk6 @ (^ [E:$i]: (($true))) @ A)) != (r2 @ B @ C)))),inference(simp,[status(thm)],[3530])).
% 33.71/8.08 thf(3532,plain,(! [B:$i,A:mu] : ((~ (good_in_physics @ A @ (sk6 @ (^ [C:$i]: (($true))) @ B))) | ((sk3 @ (sk6 @ (^ [C:$i]: (($true))) @ B) @ A @ B) != (sk2 @ A)))),inference(pattern_uni,[status(thm)],[3531:[bind(A, $thf(F)),bind(B, $thf(F)),bind(C, $thf(sk6 @ (^ [F:$i]: (($true))) @ F)),bind(D, $thf(D))]])).
% 33.71/8.08 thf(3582,plain,(! [B:$i,A:mu] : ((~ (good_in_physics @ A @ (sk6 @ (^ [C:$i]: (($true))) @ B))) | ((sk3 @ (sk6 @ (^ [C:$i]: (($true))) @ B) @ A @ B) != (sk2 @ A)))),inference(simp,[status(thm)],[3532])).
% 33.71/8.08 thf(3517,plain,(! [C:$i,B:$i,A:$i] : (~ (($true)) | (mathematician @ tom @ C) | ((r2 @ A @ (sk6 @ (^ [D:$i]: (($true))) @ A)) != (r2 @ B @ C)))),inference(paramod_ordered,[status(thm)],[3456,191])).
% 33.71/8.08 thf(3518,plain,(! [C:$i,B:$i,A:$i] : ((mathematician @ tom @ C) | ((r2 @ A @ (sk6 @ (^ [D:$i]: (($true))) @ A)) != (r2 @ B @ C)))),inference(simp,[status(thm)],[3517])).
% 33.71/8.08 thf(3519,plain,(! [A:$i] : ((mathematician @ tom @ (sk6 @ (^ [B:$i]: (($true))) @ A)))),inference(pattern_uni,[status(thm)],[3518:[bind(A, $thf(E)),bind(B, $thf(E)),bind(C, $thf(sk6 @ (^ [E:$i]: (($true))) @ E))]])).
% 33.71/8.08 thf(3591,plain,(! [A:$i] : ((mathematician @ tom @ (sk6 @ (^ [B:$i]: (($true))) @ A)))),inference(simp,[status(thm)],[3519])).
% 33.71/8.08 thf(1357,plain,(! [D:mu,C:$i,B:$i,A:mu] : (~ (($true)) | (~ (good_in_physics @ D @ C)) | ((sk3 @ C @ D @ B) != (sk2 @ D)) | ((r2 @ sk1 @ (sk2 @ A)) != (r2 @ B @ C)))),inference(paramod_ordered,[status(thm)],[72,1113])).
% 33.71/8.08 thf(1358,plain,(! [D:mu,C:$i,B:$i,A:mu] : ((~ (good_in_physics @ D @ C)) | ((sk3 @ C @ D @ B) != (sk2 @ D)) | ((r2 @ sk1 @ (sk2 @ A)) != (r2 @ B @ C)))),inference(simp,[status(thm)],[1357])).
% 33.71/8.08 thf(1359,plain,(! [B:mu,A:mu] : ((~ (good_in_physics @ A @ (sk2 @ B))) | ((sk3 @ (sk2 @ B) @ A @ sk1) != (sk2 @ A)))),inference(pattern_uni,[status(thm)],[1358:[bind(A, $thf(E)),bind(B, $thf(sk1)),bind(C, $thf(sk2 @ E))]])).
% 33.71/8.08 thf(1387,plain,(! [B:mu,A:mu] : ((~ (good_in_physics @ A @ (sk2 @ B))) | ((sk3 @ (sk2 @ B) @ A @ sk1) != (sk2 @ A)))),inference(simp,[status(thm)],[1359])).
% 33.71/8.08 thf(18,axiom,((mvalid @ (mforall_prop @ (^ [A:($i > $o)]: (mimplies @ (mbox @ r4 @ A) @ (mnot @ (mbox @ r4 @ (mnot @ A)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_D_for_r4)).
% 33.71/8.08 thf(160,plain,((! [A:$i,B:($i > $o)]: (~ (! [C:$i]: (~ (r4 @ A @ C) | (B @ C))) | ~ (! [C:$i]: (~ (r4 @ A @ C) | ~ (B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[18])).
% 33.71/8.08 thf(68,axiom,((mvalid @ (mforall_ind @ (^ [A:mu]: (mbox @ r5 @ (mimplies @ (mbox @ r4 @ (mathematician @ A)) @ (mbox @ r4 @ (good_in_maths @ A)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_r2_4)).
% 33.71/8.08 thf(424,plain,((! [A:$i,B:mu,C:$i]: (~ (r5 @ A @ C) | ~ (! [D:$i]: (~ (r4 @ C @ D) | (mathematician @ B @ D))) | ! [D:$i]: (~ (r4 @ C @ D) | (good_in_maths @ B @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[68])).
% 33.71/8.08 thf(24,axiom,((mvalid @ (mforall_prop @ (^ [A:($i > $o)]: (mimplies @ (mbox @ r4 @ A) @ (mbox @ r4 @ (mbox @ r4 @ A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_4s_for_r4_r4)).
% 33.71/8.08 thf(192,plain,((! [A:$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])).
% 33.71/8.08 thf(38,axiom,((mvalid @ (mbox @ r5 @ (physics_student @ mike)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_a9)).
% 33.71/8.08 thf(274,plain,((! [A:$i,B:$i]: (~ (r5 @ A @ B) | (physics_student @ mike @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[38])).
% 33.71/8.08 thf(275,plain,(! [B:$i,A:$i] : ((~ (r5 @ A @ B)) | (physics_student @ mike @ B))),inference(cnf,[status(esa)],[274])).
% 33.71/8.08 thf(161,plain,(! [B:($i > $o),A:$i] : ((((r4 @ A @ (sk19 @ (B) @ A)) | (r4 @ A @ (sk20 @ (B) @ A))) & ((r4 @ A @ (sk19 @ (B) @ A)) | (B @ (sk20 @ (B) @ A))) & (~ (B @ (sk19 @ (B) @ A)) | (r4 @ A @ (sk20 @ (B) @ A))) & (~ (B @ (sk19 @ (B) @ A)) | (B @ (sk20 @ (B) @ A)))))),inference(cnf,[status(esa)],[160])).
% 33.71/8.08 thf(165,plain,(! [B:($i > $o),A:$i] : ((~ (B @ (sk19 @ (B) @ A))) | (B @ (sk20 @ (B) @ A)))),inference(cnfConj,[status(thm)],[161])).
% 33.71/8.08 thf(6,axiom,((mvalid @ (mforall_prop @ (^ [A:($i > $o)]: (mimplies @ (mbox @ r4 @ A) @ (mbox @ r2 @ (mbox @ r4 @ A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_4s_for_r4_r2)).
% 33.71/8.08 thf(92,plain,((! [A:$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])).
% 33.71/8.08 thf(34,axiom,((mvalid @ (mforall_prop @ (^ [A:($i > $o)]: (mimplies @ (mbox @ r4 @ A) @ (mbox @ r3 @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_I_for_r4_r3)).
% 33.71/8.08 thf(252,plain,((! [A:$i,B:($i > $o)]: (~ (! [C:$i]: (~ (r4 @ A @ C) | (B @ C))) | ! [C:$i]: (~ (r3 @ A @ C) | (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[34])).
% 33.71/8.08 thf(2568,plain,(! [C:$i,B:$i,A:$i] : (~ (($true)) | (mathematician @ tom @ C) | ((r2 @ A @ (sk5 @ (^ [D:$i]: (($false))) @ A)) != (r2 @ B @ C)))),inference(paramod_ordered,[status(thm)],[2191,191])).
% 33.71/8.08 thf(2569,plain,(! [C:$i,B:$i,A:$i] : ((mathematician @ tom @ C) | ((r2 @ A @ (sk5 @ (^ [D:$i]: (($false))) @ A)) != (r2 @ B @ C)))),inference(simp,[status(thm)],[2568])).
% 33.71/8.08 thf(2570,plain,(! [A:$i] : ((mathematician @ tom @ (sk5 @ (^ [B:$i]: (($false))) @ A)))),inference(pattern_uni,[status(thm)],[2569:[bind(A, $thf(E)),bind(B, $thf(E)),bind(C, $thf(sk5 @ (^ [E:$i]: (($false))) @ E))]])).
% 33.71/8.08 thf(2628,plain,(! [A:$i] : ((mathematician @ tom @ (sk5 @ (^ [B:$i]: (($false))) @ A)))),inference(simp,[status(thm)],[2570])).
% 33.71/8.08 thf(79,plain,(! [D:$i,C:$i,B:($i > $o),A:$i] : ((((r1 @ A @ (sk4 @ (B) @ A)) | ~ (r3 @ A @ C) | ~ (r1 @ C @ D) | (B @ D)) & (~ (B @ (sk4 @ (B) @ A)) | ~ (r3 @ A @ C) | ~ (r1 @ C @ D) | (B @ D))))),inference(cnf,[status(esa)],[78])).
% 33.71/8.08 thf(81,plain,(! [D:$i,C:$i,B:($i > $o),A:$i] : ((~ (B @ (sk4 @ (B) @ A))) | (~ (r3 @ A @ C)) | (~ (r1 @ C @ D)) | (B @ D))),inference(cnfConj,[status(thm)],[79])).
% 33.71/8.08 thf(450,plain,(! [D:$i,C:$i,B:($i > $o),A:$i] : ((~ (B @ (sk4 @ (B) @ A))) | (~ (r3 @ A @ C)) | (~ (r1 @ C @ D)) | ((B @ D) != (~ (B @ (sk4 @ (B) @ A)))) | ~ (($true)))),inference(eqfactor_ordered,[status(thm)],[81])).
% 33.71/8.08 thf(493,plain,(! [D:$i,C:$i,B:($i > $o),A:$i] : ((~ (B @ (sk4 @ (B) @ A))) | (~ (r3 @ A @ C)) | (~ (r1 @ C @ D)) | ((B @ D) != (~ (B @ (sk4 @ (B) @ A)))))),inference(simp,[status(thm)],[450])).
% 33.71/8.08 thf(29,axiom,((mvalid @ (mforall_prop @ (^ [A:($i > $o)]: (mimplies @ (mbox @ r1 @ A) @ (mbox @ r1 @ (mbox @ r1 @ A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_4s_for_r1_r1)).
% 33.71/8.08 thf(224,plain,((! [A:$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])).
% 33.71/8.08 thf(48,axiom,((mvalid @ (mforall_ind @ (^ [A:mu]: (mbox @ r3 @ (mimplies @ (maths_student @ A) @ (mdia @ r5 @ (good_in_maths @ A)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_r3_5)).
% 33.71/8.08 thf(328,plain,((! [A:$i,B:mu,C:$i]: (~ (r3 @ A @ C) | ~ (maths_student @ B @ C) | ~ (! [D:$i]: (~ (r5 @ C @ D) | ~ (good_in_maths @ B @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[48])).
% 33.71/8.08 thf(25,axiom,((mvalid @ (mforall_prop @ (^ [A:($i > $o)]: (mimplies @ (mbox @ r1 @ A) @ (mnot @ (mbox @ r1 @ (mnot @ A)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_D_for_r1)).
% 33.71/8.08 thf(198,plain,((! [A:$i,B:($i > $o)]: (~ (! [C:$i]: (~ (r1 @ A @ C) | (B @ C))) | ~ (! [C:$i]: (~ (r1 @ A @ C) | ~ (B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[25])).
% 33.71/8.08 thf(199,plain,(! [B:($i > $o),A:$i] : ((((r1 @ A @ (sk26 @ (B) @ A)) | (r1 @ A @ (sk27 @ (B) @ A))) & ((r1 @ A @ (sk26 @ (B) @ A)) | (B @ (sk27 @ (B) @ A))) & (~ (B @ (sk26 @ (B) @ A)) | (r1 @ A @ (sk27 @ (B) @ A))) & (~ (B @ (sk26 @ (B) @ A)) | (B @ (sk27 @ (B) @ A)))))),inference(cnf,[status(esa)],[198])).
% 33.71/8.08 thf(203,plain,(! [B:($i > $o),A:$i] : ((~ (B @ (sk26 @ (B) @ A))) | (B @ (sk27 @ (B) @ A)))),inference(cnfConj,[status(thm)],[199])).
% 33.71/8.08 thf(1746,plain,(! [B:($i > $o),A:$i] : ((~ (B @ (sk26 @ (B) @ A))) | ((B @ (sk27 @ (B) @ A)) != (~ (B @ (sk26 @ (B) @ A)))) | ~ (($true)))),inference(eqfactor_ordered,[status(thm)],[203])).
% 33.71/8.08 thf(1791,plain,(! [B:($i > $o),A:$i] : ((~ (B @ (sk26 @ (B) @ A))) | ((B @ (sk27 @ (B) @ A)) != (~ (B @ (sk26 @ (B) @ A)))))),inference(simp,[status(thm)],[1746])).
% 33.71/8.08 thf(80,plain,(! [D:$i,C:$i,B:($i > $o),A:$i] : ((r1 @ A @ (sk4 @ (B) @ A)) | (~ (r3 @ A @ C)) | (~ (r1 @ C @ D)) | (B @ D))),inference(cnfConj,[status(thm)],[79])).
% 33.71/8.08 thf(1440,plain,(! [E:mu,D:$i,C:$i,B:($i > $o),A:$i] : ((r1 @ A @ (sk4 @ (B) @ A)) | (~ (r3 @ A @ C)) | (~ (r1 @ C @ D)) | ~ (($true)) | ((B @ D) != (good_in_maths @ E @ (sk2 @ E))))),inference(paramod_ordered,[status(thm)],[80,73])).
% 33.71/8.08 thf(1441,plain,(! [E:mu,D:$i,C:$i,B:($i > $o),A:$i] : ((r1 @ A @ (sk4 @ (B) @ A)) | (~ (r3 @ A @ C)) | (~ (r1 @ C @ D)) | ((B @ D) != (good_in_maths @ E @ (sk2 @ E))))),inference(simp,[status(thm)],[1440])).
% 33.71/8.08 thf(1556,plain,(! [D:mu,C:($i > mu),B:$i,A:$i] : ((r1 @ A @ (sk4 @ (^ [E:$i]: (good_in_maths @ (C @ E) @ E)) @ A)) | (~ (r3 @ A @ B)) | (~ (r1 @ B @ (sk2 @ D))) | (D != (C @ (sk2 @ D))))),inference(pre_uni,[status(thm)],[1441:[bind(A, $thf(A)),bind(B, $thf(^ [G:$i]: (good_in_maths @ (F @ G) @ G))),bind(C, $thf(C)),bind(D, $thf(sk2 @ I)),bind(E, $thf(F @ (sk2 @ I)))]])).
% 33.71/8.08 thf(1558,plain,(! [D:mu,C:($i > mu),B:$i,A:$i] : ((~ (r1 @ B @ (sk2 @ D))) | (~ (r3 @ A @ B)) | (r1 @ A @ (sk4 @ (^ [E:$i]: (good_in_maths @ (C @ E) @ E)) @ A)) | (D != (C @ (sk2 @ D))))),inference(pre_uni,[status(thm)],[1556:[]])).
% 33.71/8.08 thf(1612,plain,(! [D:mu,C:($i > mu),B:$i,A:$i] : ((~ (r1 @ B @ (sk2 @ D))) | (~ (r3 @ A @ B)) | (r1 @ A @ (sk4 @ (^ [E:$i]: (good_in_maths @ (C @ E) @ E)) @ A)) | (D != (C @ (sk2 @ D))))),inference(simp,[status(thm)],[1558])).
% 33.71/8.08 thf(27,axiom,((mvalid @ (mforall_prop @ (^ [A:($i > $o)]: (mimplies @ (mbox @ r2 @ A) @ (mbox @ r3 @ (mbox @ r2 @ A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_4s_for_r2_r3)).
% 33.71/8.08 thf(212,plain,((! [A:$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])).
% 33.71/8.08 thf(798,plain,(! [B:($i > $o),A:$i] : ((~ (B @ (sk5 @ (B) @ A))) | ((B @ (sk6 @ (B) @ A)) != (~ (B @ (sk5 @ (B) @ A)))) | ~ (($true)))),inference(eqfactor_ordered,[status(thm)],[89])).
% 33.71/8.08 thf(837,plain,(! [B:($i > $o),A:$i] : ((~ (B @ (sk5 @ (B) @ A))) | ((B @ (sk6 @ (B) @ A)) != (~ (B @ (sk5 @ (B) @ A)))))),inference(simp,[status(thm)],[798])).
% 33.71/8.08 thf(12,axiom,((mvalid @ (mforall_ind @ (^ [A:mu]: (mbox @ r3 @ (mimplies @ (physics_student @ A) @ (mdia @ r1 @ (good_in_physics @ A)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_r4_1)).
% 33.71/8.08 thf(128,plain,((! [A:$i,B:mu,C:$i]: (~ (r3 @ A @ C) | ~ (physics_student @ B @ C) | ~ (! [D:$i]: (~ (r1 @ C @ D) | ~ (good_in_physics @ B @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[12])).
% 33.71/8.08 thf(65,axiom,((mvalid @ (mbox @ r5 @ (maths_student @ peter)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_a8)).
% 33.71/8.08 thf(412,plain,((! [A:$i,B:$i]: (~ (r5 @ A @ B) | (maths_student @ peter @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[65])).
% 33.71/8.08 thf(16,axiom,((mvalid @ (mforall_prop @ (^ [A:($i > $o)]: (mimplies @ (mbox @ r3 @ A) @ (mbox @ r1 @ (mbox @ r3 @ A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_4s_for_r3_r1)).
% 33.71/8.08 thf(148,plain,((! [A:$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])).
% 33.71/8.08 thf(21,axiom,((mvalid @ (mforall_ind @ (^ [A:mu]: (mbox @ r5 @ (mimplies @ (mbox @ r2 @ (mathematician @ A)) @ (mbox @ r2 @ (good_in_maths @ A)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_r2_2)).
% 33.71/8.08 thf(180,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])).
% 33.71/8.08 thf(413,plain,(! [B:$i,A:$i] : ((~ (r5 @ A @ B)) | (maths_student @ peter @ B))),inference(cnf,[status(esa)],[412])).
% 33.71/8.08 thf(63,axiom,((mvalid @ (mforall_prop @ (^ [A:($i > $o)]: (mimplies @ (mbox @ r1 @ A) @ (mbox @ r2 @ (mbox @ r1 @ A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_4s_for_r1_r2)).
% 33.71/8.08 thf(402,plain,((! [A:$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])).
% 33.71/8.08 thf(59,axiom,((mvalid @ (mforall_ind @ (^ [A:mu]: (mimplies @ (maths_teacher @ A) @ (mbox @ r4 @ (good_in_maths @ A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_r1)).
% 33.71/8.08 thf(382,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])).
% 33.71/8.08 thf(53,axiom,((mvalid @ (mforall_ind @ (^ [A:mu]: (mbox @ r5 @ (mimplies @ (mbox @ r3 @ (mathematician @ A)) @ (mbox @ r3 @ (good_in_maths @ A)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_r2_3)).
% 33.71/8.08 thf(350,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])).
% 33.71/8.08 thf(86,plain,(! [B:($i > $o),A:$i] : ((r2 @ A @ (sk5 @ (B) @ A)) | (r2 @ A @ (sk6 @ (B) @ A)))),inference(cnfConj,[status(thm)],[85])).
% 33.71/8.08 thf(1238,plain,(! [B:($i > $o),A:$i] : ((~ (B @ (sk19 @ (B) @ A))) | ((B @ (sk20 @ (B) @ A)) != (~ (B @ (sk19 @ (B) @ A)))) | ~ (($true)))),inference(eqfactor_ordered,[status(thm)],[165])).
% 33.71/8.08 thf(1282,plain,(! [B:($i > $o),A:$i] : ((~ (B @ (sk19 @ (B) @ A))) | ((B @ (sk20 @ (B) @ A)) != (~ (B @ (sk19 @ (B) @ A)))))),inference(simp,[status(thm)],[1238])).
% 33.71/8.08 thf(30,axiom,((mvalid @ (maths_teacher @ john))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_a6)).
% 33.71/8.08 thf(230,plain,((! [A:$i]: (maths_teacher @ john @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[30])).
% 33.71/8.08 thf(7,axiom,((mvalid @ (mforall_prop @ (^ [A:($i > $o)]: (mimplies @ (mbox @ r2 @ A) @ (mbox @ r2 @ (mbox @ r2 @ A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_4s_for_r2_r2)).
% 33.71/8.08 thf(98,plain,((! [A:$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])).
% 33.71/8.08 thf(32,axiom,((mvalid @ (mforall_prop @ (^ [A:($i > $o)]: (mimplies @ (mnot @ (mbox @ r5 @ A)) @ (mbox @ r5 @ (mnot @ (mbox @ r5 @ A)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_5_for_r5)).
% 33.71/8.08 thf(240,plain,((! [A:$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])).
% 33.71/8.08 thf(428,plain,(! [C:$i,B:$i,A:mu] : (~ (($true)) | (mathematician @ tom @ C) | ((r2 @ sk1 @ (sk2 @ A)) != (r2 @ B @ C)))),inference(paramod_ordered,[status(thm)],[72,191])).
% 33.71/8.08 thf(429,plain,(! [C:$i,B:$i,A:mu] : ((mathematician @ tom @ C) | ((r2 @ sk1 @ (sk2 @ A)) != (r2 @ B @ C)))),inference(simp,[status(thm)],[428])).
% 33.71/8.08 thf(430,plain,(! [A:mu] : ((mathematician @ tom @ (sk2 @ A)))),inference(pattern_uni,[status(thm)],[429:[bind(A, $thf(D)),bind(B, $thf(sk1)),bind(C, $thf(sk2 @ D))]])).
% 33.71/8.08 thf(431,plain,(! [A:mu] : ((mathematician @ tom @ (sk2 @ A)))),inference(simp,[status(thm)],[430])).
% 33.71/8.08 thf(66,axiom,((mvalid @ (mforall_ind @ (^ [A:mu]: (mbox @ r3 @ (mimplies @ (maths_student @ A) @ (mdia @ r4 @ (good_in_maths @ A)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_r3_4)).
% 33.71/8.08 thf(414,plain,((! [A:$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])).
% 33.71/8.08 thf(45,axiom,((mvalid @ (mforall_prop @ (^ [A:($i > $o)]: (mimplies @ (mnot @ (mbox @ r1 @ A)) @ (mbox @ r1 @ (mnot @ (mbox @ r1 @ A)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_5_for_r1)).
% 33.71/8.08 thf(310,plain,((! [A:$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])).
% 33.71/8.08 thf(50,axiom,((mvalid @ (mforall_prop @ (^ [A:($i > $o)]: (mimplies @ (mbox @ r5 @ A) @ (mbox @ r3 @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_I_for_r5_r3)).
% 33.71/8.08 thf(336,plain,((! [A:$i,B:($i > $o)]: (~ (! [C:$i]: (~ (r5 @ A @ C) | (B @ C))) | ! [C:$i]: (~ (r3 @ A @ C) | (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[50])).
% 33.71/8.08 thf(17,axiom,((mvalid @ (mforall_prop @ (^ [A:($i > $o)]: (mimplies @ (mbox @ r4 @ A) @ (mbox @ r5 @ (mbox @ r4 @ A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_4s_for_r4_r5)).
% 33.71/8.08 thf(154,plain,((! [A:$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])).
% 33.71/8.08 thf(231,plain,(! [A:$i] : ((maths_teacher @ john @ A))),inference(cnf,[status(esa)],[230])).
% 33.71/8.08 thf(28,axiom,((mvalid @ (mforall_prop @ (^ [A:($i > $o)]: (mimplies @ (mbox @ r3 @ A) @ (mbox @ r5 @ (mbox @ r3 @ A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_4s_for_r3_r5)).
% 33.71/8.08 thf(218,plain,((! [A:$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])).
% 33.71/8.08 thf(8,axiom,((mvalid @ (mforall_prop @ (^ [A:($i > $o)]: (mimplies @ (mnot @ (mbox @ r2 @ A)) @ (mbox @ r2 @ (mnot @ (mbox @ r2 @ A)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_5_for_r2)).
% 33.71/8.08 thf(104,plain,((! [A:$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])).
% 33.71/8.08 thf(44,axiom,((mvalid @ (mforall_prop @ (^ [A:($i > $o)]: (mimplies @ (mbox @ r2 @ A) @ (mbox @ r5 @ (mbox @ r2 @ A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_4s_for_r2_r5)).
% 33.71/8.08 thf(304,plain,((! [A:$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])).
% 33.71/8.08 thf(35,axiom,((mvalid @ (mforall_ind @ (^ [A:mu]: (mbox @ r3 @ (mimplies @ (maths_student @ A) @ (mdia @ r1 @ (good_in_maths @ A)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_r3_1)).
% 33.71/8.08 thf(258,plain,((! [A:$i,B:mu,C:$i]: (~ (r3 @ A @ C) | ~ (maths_student @ B @ C) | ~ (! [D:$i]: (~ (r1 @ C @ D) | ~ (good_in_maths @ B @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[35])).
% 33.71/8.08 thf(61,axiom,((mvalid @ (mforall_prop @ (^ [A:($i > $o)]: (mimplies @ (mnot @ (mbox @ r3 @ A)) @ (mbox @ r3 @ (mnot @ (mbox @ r3 @ A)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_5_for_r3)).
% 33.71/8.08 thf(390,plain,((! [A:$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])).
% 33.71/8.08 thf(67,axiom,((mvalid @ (mforall_prop @ (^ [A:($i > $o)]: (mimplies @ (mbox @ r3 @ A) @ (mbox @ r1 @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_I_for_r3_r1)).
% 33.71/8.08 thf(418,plain,((! [A:$i,B:($i > $o)]: (~ (! [C:$i]: (~ (r3 @ A @ C) | (B @ C))) | ! [C:$i]: (~ (r1 @ A @ C) | (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[67])).
% 33.71/8.08 thf(41,axiom,((mvalid @ (mforall_ind @ (^ [A:mu]: (mbox @ r3 @ (mimplies @ (physics_student @ A) @ (mdia @ r5 @ (good_in_physics @ A)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_r4_5)).
% 33.71/8.08 thf(290,plain,((! [A:$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])).
% 33.71/8.08 thf(33,axiom,((mvalid @ (mforall_prop @ (^ [A:($i > $o)]: (mimplies @ (mbox @ r2 @ A) @ (mbox @ r1 @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_I_for_r2_r1)).
% 33.71/8.08 thf(246,plain,((! [A:$i,B:($i > $o)]: (~ (! [C:$i]: (~ (r2 @ A @ C) | (B @ C))) | ! [C:$i]: (~ (r1 @ A @ C) | (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[33])).
% 33.71/8.08 thf(52,axiom,((mvalid @ (mforall_ind @ (^ [A:mu]: (mbox @ r3 @ (mimplies @ (maths_student @ A) @ (mdia @ r2 @ (good_in_maths @ A)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_r3_2)).
% 33.71/8.08 thf(346,plain,((! [A:$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])).
% 33.71/8.08 thf(43,axiom,((mvalid @ (mforall_ind @ (^ [A:mu]: (mbox @ r3 @ (mimplies @ (physics_student @ A) @ (mdia @ r2 @ (good_in_physics @ A)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_r4_2)).
% 33.71/8.08 thf(300,plain,((! [A:$i,B:mu,C:$i]: (~ (r3 @ A @ C) | ~ (physics_student @ B @ C) | ~ (! [D:$i]: (~ (r2 @ C @ D) | ~ (good_in_physics @ B @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[43])).
% 33.71/8.08 thf(19,axiom,((mvalid @ (mforall_prop @ (^ [A:($i > $o)]: (mimplies @ (mbox @ r2 @ A) @ (mbox @ r4 @ (mbox @ r2 @ A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_4s_for_r2_r4)).
% 33.71/8.08 thf(168,plain,((! [A:$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])).
% 33.71/8.08 thf(36,axiom,((mvalid @ (mforall_prop @ (^ [A:($i > $o)]: (mimplies @ (mbox @ r5 @ A) @ (mbox @ r5 @ (mbox @ r5 @ A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_4s_for_r5_r5)).
% 33.71/8.08 thf(262,plain,((! [A:$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])).
% 33.71/8.08 thf(37,axiom,((mvalid @ (mforall_prop @ (^ [A:($i > $o)]: (mimplies @ (mbox @ r5 @ A) @ (mbox @ r1 @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_I_for_r45r1)).
% 33.71/8.08 thf(268,plain,((! [A:$i,B:($i > $o)]: (~ (! [C:$i]: (~ (r5 @ A @ C) | (B @ C))) | ! [C:$i]: (~ (r1 @ A @ C) | (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[37])).
% 33.71/8.08 thf(55,axiom,((mvalid @ (mforall_prop @ (^ [A:($i > $o)]: (mimplies @ (mbox @ r3 @ A) @ (mbox @ r4 @ (mbox @ r3 @ A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_4s_for_r3_r4)).
% 33.71/8.08 thf(358,plain,((! [A:$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])).
% 33.71/8.08 thf(42,axiom,((mvalid @ (mforall_prop @ (^ [A:($i > $o)]: (mimplies @ (mbox @ r4 @ A) @ (mbox @ r3 @ (mbox @ r4 @ A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_4s_for_r4_r3)).
% 33.71/8.08 thf(294,plain,((! [A:$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])).
% 33.71/8.08 thf(14,axiom,((mvalid @ (mforall_prop @ (^ [A:($i > $o)]: (mimplies @ (mbox @ r5 @ A) @ (mbox @ r4 @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_I_for_r5_r4)).
% 33.71/8.08 thf(136,plain,((! [A:$i,B:($i > $o)]: (~ (! [C:$i]: (~ (r5 @ A @ C) | (B @ C))) | ! [C:$i]: (~ (r4 @ A @ C) | (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[14])).
% 33.71/8.08 thf(47,axiom,((mvalid @ (mforall_prop @ (^ [A:($i > $o)]: (mimplies @ (mbox @ r3 @ A) @ (mbox @ r2 @ (mbox @ r3 @ A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_4s_for_r3_r2)).
% 33.71/8.08 thf(322,plain,((! [A:$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])).
% 33.71/8.08 thf(11,axiom,((mvalid @ (mforall_prop @ (^ [A:($i > $o)]: (mimplies @ (mbox @ r5 @ A) @ (mbox @ r3 @ (mbox @ r5 @ A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_4s_for_r5_r3)).
% 33.71/8.08 thf(122,plain,((! [A:$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])).
% 33.71/8.08 thf(56,axiom,((mvalid @ (mforall_prop @ (^ [A:($i > $o)]: (mimplies @ (mnot @ (mbox @ r4 @ A)) @ (mbox @ r4 @ (mnot @ (mbox @ r4 @ A)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_5_for_r4)).
% 33.71/8.08 thf(364,plain,((! [A:$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])).
% 33.71/8.08 thf(31,axiom,((mvalid @ (mforall_prop @ (^ [A:($i > $o)]: (mimplies @ (mbox @ r3 @ A) @ (mnot @ (mbox @ r3 @ (mnot @ A)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_D_for_r3)).
% 33.71/8.08 thf(232,plain,((! [A:$i,B:($i > $o)]: (~ (! [C:$i]: (~ (r3 @ A @ C) | (B @ C))) | ~ (! [C:$i]: (~ (r3 @ A @ C) | ~ (B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[31])).
% 33.71/8.08 thf(54,axiom,((mvalid @ (mforall_ind @ (^ [A:mu]: (mbox @ r5 @ (mimplies @ (mbox @ r5 @ (mathematician @ A)) @ (mbox @ r5 @ (good_in_maths @ A)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_r2_5)).
% 33.71/8.08 thf(354,plain,((! [A:$i,B:mu,C:$i]: (~ (r5 @ A @ C) | ~ (! [D:$i]: (~ (r5 @ C @ D) | (mathematician @ B @ D))) | ! [D:$i]: (~ (r5 @ C @ D) | (good_in_maths @ B @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[54])).
% 33.71/8.08 thf(82,plain,(! [D:$i,C:$i,B:($i > $o),A:$i] : ((~ ((sk4 @ (B) @ A) = (sk4 @ ((=) @ $i @ (sk4 @ B @ A)) @ A))) | (~ (r3 @ A @ C)) | (~ (r1 @ C @ D)) | ((sk4 @ (B) @ A) = D))),inference(replace_leibeq,[status(thm)],[81:[bind(A, $thf(A)),bind(B, $thf((=) @ $i @ (sk4 @ B @ A)))]])).
% 33.71/8.08 thf(83,plain,(! [D:$i,C:$i,B:($i > $o),A:$i] : (((sk4 @ (B) @ A) != (sk4 @ ((=) @ $i @ (sk4 @ B @ A)) @ A)) | ((sk4 @ (B) @ A) = D) | (~ (r3 @ A @ C)) | (~ (r1 @ C @ D)))),inference(lifteq,[status(thm)],[82])).
% 33.71/8.08 thf(3836,plain,(($false)),inference(e,[status(thm)],[174,342,370,332,69,2630,88,408,276,384,142,184,110,284,316,78,376,2291,84,1051,396,89,116,74,206,1119,132,3582,3591,1387,160,424,192,275,165,92,252,2628,493,224,328,77,1791,1612,212,837,701,73,128,412,148,180,413,191,402,382,350,86,1282,274,81,230,76,98,3456,240,198,1113,431,80,414,310,336,154,72,231,87,203,218,104,304,258,390,418,290,246,346,300,190,168,262,268,358,294,136,322,122,2191,364,232,354,83])).
% 33.71/8.08 % SZS output end Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% 33.71/8.08 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------