%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : GEG010^1 : TPTP v9.3.1. Released v4.1.0.
% 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 : n019.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 07:49:23 AM UTC 2026
% Result : Theorem 15.93s 4.97s
% Output : Refutation 16.73s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEG010^1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.08 % 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
% 0.10/0.21 % Computer : n019.cluster.edu
% 0.10/0.21 % Model : x86_64 x86_64
% 0.10/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.21 % Memory : 8046.5625MB
% 0.10/0.21 % OS : Linux 6.8.0-71-generic
% 0.10/0.22 % CPULimit : 300
% 0.10/0.22 % WCLimit : 300
% 0.10/0.22 % DateTime : Tue Sep 29 18:34:02 UTC 2026
% 0.10/0.22 % CPUTime :
% 0.10/0.22 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
% 1.04/0.81 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 2.00/1.25 % [INFO] Parsing done (433ms).
% 2.00/1.27 % [INFO] Running in sequential loop mode.
% 2.93/1.78 % [INFO] eprover registered as external prover.
% 2.93/1.79 % [INFO] Scanning for conjecture ...
% 3.36/2.00 % [INFO] Found a conjecture (or negated_conjecture) and 8 axioms. Running axiom selection ...
% 3.62/2.04 % [INFO] Axiom selection finished. Selected 8 axioms (removed 0 axioms).
% 3.62/2.05 % [INFO] Problem is higher-order (TPTP THF).
% 3.62/2.05 % [INFO] Type checking passed.
% 3.62/2.05 % [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 ...
% 15.93/4.96 % External prover 'e' found a proof!
% 15.93/4.96 % [INFO] Killing All external provers ...
% 15.93/4.96 % Time passed: 4610ms (effective reasoning time: 3684ms)
% 15.93/4.96 % 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)>
% 15.93/4.97 % Axioms used in derivation (8): k_axiom_for_fool, ax2, c_symmetric, i_axiom_for_fool_a, ax1, t_axiom_for_fool, ax3, c_reflexive
% 15.93/4.97 % No. of inferences in proof: 115
% 15.93/4.97 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 4610 ms resp. 3684 ms w/o parsing
% 16.73/5.07 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% 16.73/5.07 thf(mu_type, type, mu: $tType).
% 16.73/5.07 thf(reg_type, type, reg: $tType).
% 16.73/5.07 thf(mnot_decl, type, mnot: (($i > $o) > ($i > $o))).
% 16.73/5.07 thf(mor_decl, type, mor: (($i > $o) > (($i > $o) > ($i > $o)))).
% 16.73/5.07 thf(mimplies_decl, type, mimplies: (($i > $o) > (($i > $o) > ($i > $o)))).
% 16.73/5.07 thf(mforall_prop_decl, type, mforall_prop: ((($i > $o) > ($i > $o)) > ($i > $o))).
% 16.73/5.07 thf(mbox_decl, type, mbox: (($i > ($i > $o)) > (($i > $o) > ($i > $o)))).
% 16.73/5.07 thf(mvalid_decl, type, mvalid: (($i > $o) > $o)).
% 16.73/5.07 thf(c_decl, type, c: (reg > (reg > $o))).
% 16.73/5.07 thf(p_decl, type, p: (reg > (reg > $o))).
% 16.73/5.07 thf(o_decl, type, o: (reg > (reg > $o))).
% 16.73/5.07 thf(ec_decl, type, ec: (reg > (reg > $o))).
% 16.73/5.07 thf(pp_decl, type, pp: (reg > (reg > $o))).
% 16.73/5.07 thf(tpp_decl, type, tpp: (reg > (reg > $o))).
% 16.73/5.07 thf(ntpp_decl, type, ntpp: (reg > (reg > $o))).
% 16.73/5.07 thf(catalunya_decl, type, catalunya: reg).
% 16.73/5.07 thf(france_decl, type, france: reg).
% 16.73/5.07 thf(spain_decl, type, spain: reg).
% 16.73/5.07 thf(paris_decl, type, paris: reg).
% 16.73/5.07 thf(a_decl, type, a: ($i > ($i > $o))).
% 16.73/5.07 thf(fool_decl, type, fool: ($i > ($i > $o))).
% 16.73/5.07 thf(sk1_decl, type, sk1: $i).
% 16.73/5.07 thf(sk2_decl, type, sk2: $i).
% 16.73/5.07 thf(sk3_decl, type, sk3: reg).
% 16.73/5.07 thf(sk4_decl, type, sk4: (($i > $o) > ($i > $i))).
% 16.73/5.07 thf(sk5_decl, type, sk5: (($i > $o) > ($i > $i))).
% 16.73/5.07 thf(sk7_decl, type, sk7: reg).
% 16.73/5.07 thf(sk8_decl, type, sk8: reg).
% 16.73/5.07 thf(sk9_decl, type, sk9: (reg > reg)).
% 16.73/5.07 thf(sk10_decl, type, sk10: (reg > reg)).
% 16.73/5.07 thf(sk11_decl, type, sk11: (reg > reg)).
% 16.73/5.07 thf(sk12_decl, type, sk12: (reg > reg)).
% 16.73/5.07 thf(sk15_decl, type, sk15: reg).
% 16.73/5.07 thf(sk16_decl, type, sk16: (reg > reg)).
% 16.73/5.07 thf(sk17_decl, type, sk17: (reg > reg)).
% 16.73/5.07 thf(mnot_def, definition, mnot = (^ [A:($i > $o),B:$i]: ~ (A @ B)) ).
% 16.73/5.07 thf(mor_def, definition, mor = (^ [A:($i > $o),B:($i > $o),C:$i]: ((A @ C) | (B @ C))) ).
% 16.73/5.07 thf(mimplies_def, definition, mimplies = (^ [A:($i > $o)]: (mor @ (mnot @ A))) ).
% 16.73/5.07 thf(mforall_prop_def, definition, mforall_prop = (^ [A:(($i > $o) > ($i > $o)),B:$i]: ! [C:($i > $o)]: (A @ C @ B)) ).
% 16.73/5.07 thf(mbox_def, definition, mbox = (^ [A:($i > ($i > $o)),B:($i > $o),C:$i]: ! [D:$i]: (~ (A @ C @ D) | (B @ D))) ).
% 16.73/5.07 thf(mvalid_def, definition, mvalid = ((!) @ $i) ).
% 16.73/5.07 thf(p_def, definition, p = (^ [A:reg,B:reg]: ! [C:reg]: ((c @ C @ A) => (c @ C @ B))) ).
% 16.73/5.07 thf(o_def, definition, o = (^ [A:reg,B:reg]: ? [C:reg]: ((p @ C @ A) & (p @ C @ B))) ).
% 16.73/5.07 thf(ec_def, definition, ec = (^ [A:reg,B:reg]: ((c @ A @ B) & ~ (o @ A @ B))) ).
% 16.73/5.07 thf(pp_def, definition, pp = (^ [A:reg,B:reg]: ((p @ A @ B) & ~ (p @ B @ A))) ).
% 16.73/5.07 thf(tpp_def, definition, tpp = (^ [A:reg,B:reg]: ((pp @ A @ B) & ? [C:reg]: ((ec @ C @ A) & (ec @ C @ B)))) ).
% 16.73/5.07 thf(ntpp_def, definition, ntpp = (^ [A:reg,B:reg]: ((pp @ A @ B) & ~ (? [C:reg]: ((ec @ C @ A) & (ec @ C @ B))))) ).
% 16.73/5.07 thf(sk1_def, definition, sk1 = (@+ [A:$i]: ? [B:$i]: (a @ A @ B)) ).
% 16.73/5.07 thf(sk2_def, definition, sk2 = (@+ [A:$i]: (a @ sk1 @ A)) ).
% 16.73/5.07 thf(sk3_def, definition, sk3 = (@+ [A:reg]: ~ ((! [B:reg]: ((c @ B @ A) => (c @ B @ catalunya))) => (~ (! [B:reg]: ((c @ B @ A) => (c @ B @ paris)))))) ).
% 16.73/5.07 thf(sk4_def, definition, sk4 = (^ [A:($i > $o),B:$i]: (@+ [C:$i]: ~ (~ (fool @ B @ C) | (A @ C)))) ).
% 16.73/5.07 thf(sk5_def, definition, sk5 = (^ [A:($i > $o),B:$i]: (@+ [C:$i]: ~ (~ (fool @ B @ C) | (A @ C)))) ).
% 16.73/5.07 thf(sk7_def, definition, sk7 = (@+ [A:reg]: ~ ((c @ A @ spain) => (c @ A @ catalunya))) ).
% 16.73/5.07 thf(sk8_def, definition, sk8 = (@+ [A:reg]: ((c @ A @ catalunya) & ~ (? [B:reg]: (! [C:reg]: ((c @ C @ B) => (c @ C @ A)) & ! [C:reg]: ((c @ C @ B) => (c @ C @ catalunya)))) & (c @ A @ spain) & ~ (? [B:reg]: (! [C:reg]: ((c @ C @ B) => (c @ C @ A)) & ! [C:reg]: ((c @ C @ B) => (c @ C @ spain)))))) ).
% 16.73/5.07 thf(sk9_def, definition, sk9 = (^ [A:reg]: (@+ [B:reg]: ~ ((c @ B @ A) => (c @ B @ sk8)))) ).
% 16.73/5.07 thf(sk10_def, definition, sk10 = (^ [A:reg]: (@+ [B:reg]: ~ ((c @ B @ A) => (c @ B @ catalunya)))) ).
% 16.73/5.07 thf(sk11_def, definition, sk11 = (^ [A:reg]: (@+ [B:reg]: ~ ((c @ B @ A) => (c @ B @ sk8)))) ).
% 16.73/5.07 thf(sk12_def, definition, sk12 = (^ [A:reg]: (@+ [B:reg]: ~ ((c @ B @ A) => (c @ B @ spain)))) ).
% 16.73/5.07 thf(sk15_def, definition, sk15 = (@+ [A:reg]: ~ ((c @ A @ france) => (c @ A @ paris))) ).
% 16.73/5.07 thf(sk16_def, definition, sk16 = (^ [A:reg]: (@+ [B:reg]: (! [C:reg]: ((c @ C @ B) => (c @ C @ A)) & ! [C:reg]: ((c @ C @ B) => (c @ C @ paris))))) ).
% 16.73/5.07 thf(sk17_def, definition, sk17 = (^ [A:reg]: (@+ [B:reg]: (! [C:reg]: ((c @ C @ B) => (c @ C @ A)) & ! [C:reg]: ((c @ C @ B) => (c @ C @ france))))) ).
% 16.73/5.07 thf(3,axiom,((! [A:reg]: (c @ A @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_reflexive)).
% 16.73/5.07 thf(18,plain,((! [A:reg]: (c @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3])).
% 16.73/5.07 thf(19,plain,(! [A:reg] : ((c @ A @ A))),inference(cnf,[status(esa)],[18])).
% 16.73/5.07 thf(1,conjecture,((mvalid @ (mbox @ a @ (^ [A:$i]: ! [B:reg]: ((p @ B @ catalunya) => (~ (p @ B @ paris))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',con)).
% 16.73/5.07 thf(2,negated_conjecture,((~ (mvalid @ (mbox @ a @ (^ [A:$i]: ! [B:reg]: ((p @ B @ catalunya) => (~ (p @ B @ paris)))))))),inference(neg_conjecture,[status(cth)],[1])).
% 16.73/5.07 thf(11,plain,((~ (! [A:$i,B:$i]: (~ (a @ A @ B) | ! [C:reg]: ((! [D:reg]: ((c @ D @ C) => (c @ D @ catalunya))) => (~ (! [D:reg]: ((c @ D @ C) => (c @ D @ paris))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])).
% 16.73/5.07 thf(12,plain,((~ (~ (? [A:$i,B:$i]: (a @ A @ B)) | ! [A:reg]: ((! [B:reg]: ((c @ B @ A) => (c @ B @ catalunya))) => (~ (! [B:reg]: ((c @ B @ A) => (c @ B @ paris)))))))),inference(miniscope,[status(thm)],[11])).
% 16.73/5.07 thf(13,plain,(! [B:reg,A:reg] : (((a @ sk1 @ sk2) & (~ (c @ A @ sk3) | (c @ A @ catalunya)) & (~ (c @ B @ sk3) | (c @ B @ paris))))),inference(cnf,[status(esa)],[12])).
% 16.73/5.07 thf(16,plain,(! [A:reg] : ((~ (c @ A @ sk3)) | (c @ A @ paris))),inference(cnfConj,[status(thm)],[13])).
% 16.73/5.07 thf(17,plain,(! [A:reg] : ((~ (c @ A @ sk3)) | (c @ A @ paris))),inference(simp,[status(thm)],[16])).
% 16.73/5.07 thf(140,plain,(! [B:reg,A:reg] : (~ (($true)) | (c @ B @ paris) | ((c @ A @ A) != (c @ B @ sk3)))),inference(paramod_ordered,[status(thm)],[19,17])).
% 16.73/5.07 thf(141,plain,(! [B:reg,A:reg] : ((c @ B @ paris) | ((c @ A @ A) != (c @ B @ sk3)))),inference(simp,[status(thm)],[140])).
% 16.73/5.07 thf(142,plain,((c @ sk3 @ paris)),inference(pattern_uni,[status(thm)],[141:[bind(A, $thf(sk3)),bind(B, $thf(sk3))]])).
% 16.73/5.07 thf(4,axiom,((! [A:reg,B:reg]: ((c @ A @ B) => (c @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_symmetric)).
% 16.73/5.07 thf(20,plain,((! [A:reg,B:reg]: ((c @ A @ B) => (c @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4])).
% 16.73/5.07 thf(21,plain,(! [B:reg,A:reg] : ((~ (c @ A @ B)) | (c @ B @ A))),inference(cnf,[status(esa)],[20])).
% 16.73/5.07 thf(168,plain,(! [B:reg,A:reg] : (~ (($true)) | (c @ B @ A) | ((c @ sk3 @ paris) != (c @ A @ B)))),inference(paramod_ordered,[status(thm)],[142,21])).
% 16.73/5.07 thf(169,plain,(! [B:reg,A:reg] : ((c @ B @ A) | ((c @ sk3 @ paris) != (c @ A @ B)))),inference(simp,[status(thm)],[168])).
% 16.73/5.07 thf(170,plain,((c @ paris @ sk3)),inference(pattern_uni,[status(thm)],[169:[bind(A, $thf(sk3)),bind(B, $thf(paris))]])).
% 16.73/5.07 thf(5,axiom,((mvalid @ (mforall_prop @ (^ [A:($i > $o)]: (mimplies @ (mbox @ fool @ A) @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',t_axiom_for_fool)).
% 16.73/5.07 thf(22,plain,((! [A:$i,B:($i > $o)]: (~ (! [C:$i]: (~ (fool @ A @ C) | (B @ C))) | (B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5])).
% 16.73/5.08 thf(23,plain,(! [B:($i > $o),A:$i] : ((((fool @ A @ (sk4 @ (B) @ A)) | (B @ A)) & (~ (B @ (sk4 @ (B) @ A)) | (B @ A))))),inference(cnf,[status(esa)],[22])).
% 16.73/5.08 thf(24,plain,(! [B:($i > $o),A:$i] : ((fool @ A @ (sk4 @ (B) @ A)) | (B @ A))),inference(cnfConj,[status(thm)],[23])).
% 16.73/5.08 thf(121,plain,(! [A:$i] : ((fool @ A @ (sk4 @ (^ [B:$i]: (($false))) @ A)) | ($false))),inference(prim_subst,[status(thm)],[24:[bind(A, $thf(A)),bind(B, $thf(^ [C:$i]: (($false))))]])).
% 16.73/5.08 thf(133,plain,(! [A:$i] : ((fool @ A @ (sk4 @ (^ [B:$i]: (($false))) @ A)))),inference(simp,[status(thm)],[121])).
% 16.73/5.08 thf(138,plain,(! [C:reg,B:($i > $o),A:$i] : ((fool @ A @ (sk4 @ (B) @ A)) | ~ (($true)) | (c @ C @ paris) | ((B @ A) != (c @ C @ sk3)))),inference(paramod_ordered,[status(thm)],[24,17])).
% 16.73/5.08 thf(139,plain,(! [C:reg,B:($i > $o),A:$i] : ((fool @ A @ (sk4 @ (B) @ A)) | (c @ C @ paris) | ((B @ A) != (c @ C @ sk3)))),inference(simp,[status(thm)],[138])).
% 16.73/5.08 thf(144,plain,(! [B:($i > reg),A:$i] : ((fool @ A @ (sk4 @ (^ [C:$i]: (c @ (B @ C) @ sk3)) @ A)) | (c @ (B @ A) @ paris))),inference(pre_uni,[status(thm)],[139:[bind(A, $thf(A)),bind(B, $thf(^ [E:$i]: (c @ (D @ E) @ sk3))),bind(C, $thf(D @ A))]])).
% 16.73/5.08 thf(145,plain,(! [B:($i > reg),A:$i] : ((fool @ A @ (sk4 @ (^ [C:$i]: (c @ (B @ C) @ sk3)) @ A)) | (c @ (B @ A) @ paris))),inference(simp,[status(thm)],[144])).
% 16.73/5.08 thf(14,plain,((a @ sk1 @ sk2)),inference(cnfConj,[status(thm)],[13])).
% 16.73/5.08 thf(10,axiom,((mvalid @ (mbox @ a @ (^ [A:$i]: (ntpp @ paris @ france))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax3)).
% 16.73/5.08 thf(72,plain,((! [A:$i,B:$i]: (~ (a @ A @ B) | (! [C:reg]: ((c @ C @ paris) => (c @ C @ france)) & ~ (! [C:reg]: ((c @ C @ france) => (c @ C @ paris))) & ~ (? [C:reg]: ((c @ C @ paris) & ~ (? [D:reg]: (! [E:reg]: ((c @ E @ D) => (c @ E @ C)) & ! [E:reg]: ((c @ E @ D) => (c @ E @ paris)))) & (c @ C @ france) & ~ (? [D:reg]: (! [E:reg]: ((c @ E @ D) => (c @ E @ C)) & ! [E:reg]: ((c @ E @ D) => (c @ E @ france)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[10])).
% 16.73/5.08 thf(73,plain,((~ (? [A:$i,B:$i]: (a @ A @ B)) | (! [A:reg]: ((c @ A @ paris) => (c @ A @ france)) & ~ (! [A:reg]: ((c @ A @ france) => (c @ A @ paris))) & ~ (? [A:reg]: ((c @ A @ paris) & ~ (? [B:reg]: (! [C:reg]: ((c @ C @ B) => (c @ C @ A)) & ! [C:reg]: ((c @ C @ B) => (c @ C @ paris)))) & (c @ A @ france) & ~ (? [B:reg]: (! [C:reg]: ((c @ C @ B) => (c @ C @ A)) & ! [C:reg]: ((c @ C @ B) => (c @ C @ france))))))))),inference(miniscope,[status(thm)],[72])).
% 16.73/5.08 thf(74,plain,(! [H:reg,G:reg,F:reg,E:reg,D:reg,C:reg,B:$i,A:$i] : (((~ (a @ A @ B) | ~ (c @ C @ paris) | (c @ C @ france)) & (~ (a @ A @ B) | (c @ sk15 @ france)) & (~ (a @ A @ B) | ~ (c @ sk15 @ paris)) & (~ (a @ A @ B) | ~ (c @ D @ paris) | ~ (c @ E @ (sk16 @ D)) | (c @ E @ D) | ~ (c @ D @ france) | ~ (c @ G @ (sk17 @ D)) | (c @ G @ D)) & (~ (a @ A @ B) | ~ (c @ D @ paris) | ~ (c @ E @ (sk16 @ D)) | (c @ E @ D) | ~ (c @ D @ france) | ~ (c @ H @ (sk17 @ D)) | (c @ H @ france)) & (~ (a @ A @ B) | ~ (c @ D @ paris) | ~ (c @ F @ (sk16 @ D)) | (c @ F @ paris) | ~ (c @ D @ france) | ~ (c @ G @ (sk17 @ D)) | (c @ G @ D)) & (~ (a @ A @ B) | ~ (c @ D @ paris) | ~ (c @ F @ (sk16 @ D)) | (c @ F @ paris) | ~ (c @ D @ france) | ~ (c @ H @ (sk17 @ D)) | (c @ H @ france))))),inference(cnf,[status(esa)],[73])).
% 16.73/5.08 thf(75,plain,(! [B:$i,A:$i] : ((~ (a @ A @ B)) | (~ (c @ sk15 @ paris)))),inference(cnfConj,[status(thm)],[74])).
% 16.73/5.08 thf(423,plain,(! [B:$i,A:$i] : (~ (($true)) | (~ (c @ sk15 @ paris)) | ((a @ sk1 @ sk2) != (a @ A @ B)))),inference(paramod_ordered,[status(thm)],[14,75])).
% 16.73/5.08 thf(424,plain,(! [B:$i,A:$i] : ((~ (c @ sk15 @ paris)) | ((a @ sk1 @ sk2) != (a @ A @ B)))),inference(simp,[status(thm)],[423])).
% 16.73/5.08 thf(425,plain,((~ (c @ sk15 @ paris))),inference(pattern_uni,[status(thm)],[424:[bind(A, $thf(sk1)),bind(B, $thf(sk2))]])).
% 16.73/5.08 thf(939,plain,(! [B:($i > reg),A:$i] : ((fool @ A @ (sk4 @ (^ [C:$i]: (c @ (B @ C) @ sk3)) @ A)) | ~ (($true)) | ((c @ (B @ A) @ paris) != (c @ sk15 @ paris)))),inference(paramod_ordered,[status(thm)],[145,425])).
% 16.73/5.08 thf(940,plain,(! [B:($i > reg),A:$i] : ((fool @ A @ (sk4 @ (^ [C:$i]: (c @ (B @ C) @ sk3)) @ A)) | ((c @ (B @ A) @ paris) != (c @ sk15 @ paris)))),inference(simp,[status(thm)],[939])).
% 16.73/5.08 thf(980,plain,(! [A:$i] : ((fool @ A @ (sk4 @ (^ [B:$i]: (c @ sk15 @ sk3)) @ A)))),inference(pre_uni,[status(thm)],[940:[bind(A, $thf(A)),bind(B, $thf(^ [C:$i]: (sk15)))]])).
% 16.73/5.08 thf(8,axiom,((mvalid @ (mbox @ a @ (^ [A:$i]: (tpp @ catalunya @ spain))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax1)).
% 16.73/5.08 thf(40,plain,((! [A:$i,B:$i]: (~ (a @ A @ B) | (! [C:reg]: ((c @ C @ catalunya) => (c @ C @ spain)) & ~ (! [C:reg]: ((c @ C @ spain) => (c @ C @ catalunya))) & ? [C:reg]: ((c @ C @ catalunya) & ~ (? [D:reg]: (! [E:reg]: ((c @ E @ D) => (c @ E @ C)) & ! [E:reg]: ((c @ E @ D) => (c @ E @ catalunya)))) & (c @ C @ spain) & ~ (? [D:reg]: (! [E:reg]: ((c @ E @ D) => (c @ E @ C)) & ! [E:reg]: ((c @ E @ D) => (c @ E @ spain))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8])).
% 16.73/5.08 thf(15,plain,(! [A:reg] : ((~ (c @ A @ sk3)) | (c @ A @ catalunya))),inference(cnfConj,[status(thm)],[13])).
% 16.73/5.08 thf(114,plain,(! [C:reg,B:($i > $o),A:$i] : ((fool @ A @ (sk4 @ (B) @ A)) | ~ (($true)) | (c @ C @ catalunya) | ((B @ A) != (c @ C @ sk3)))),inference(paramod_ordered,[status(thm)],[24,15])).
% 16.73/5.08 thf(115,plain,(! [C:reg,B:($i > $o),A:$i] : ((fool @ A @ (sk4 @ (B) @ A)) | (c @ C @ catalunya) | ((B @ A) != (c @ C @ sk3)))),inference(simp,[status(thm)],[114])).
% 16.73/5.08 thf(126,plain,(! [B:($i > reg),A:$i] : ((fool @ A @ (sk4 @ (^ [C:$i]: (c @ (B @ C) @ sk3)) @ A)) | (c @ (B @ A) @ catalunya))),inference(pre_uni,[status(thm)],[115:[bind(A, $thf(A)),bind(B, $thf(^ [E:$i]: (c @ (D @ E) @ sk3))),bind(C, $thf(D @ A))]])).
% 16.73/5.08 thf(135,plain,(! [B:($i > reg),A:$i] : ((fool @ A @ (sk4 @ (^ [C:$i]: (c @ (B @ C) @ sk3)) @ A)) | (c @ (B @ A) @ catalunya))),inference(simp,[status(thm)],[126])).
% 16.73/5.08 thf(41,plain,((~ (? [A:$i,B:$i]: (a @ A @ B)) | (! [A:reg]: ((c @ A @ catalunya) => (c @ A @ spain)) & ~ (! [A:reg]: ((c @ A @ spain) => (c @ A @ catalunya))) & ? [A:reg]: ((c @ A @ catalunya) & ~ (? [B:reg]: (! [C:reg]: ((c @ C @ B) => (c @ C @ A)) & ! [C:reg]: ((c @ C @ B) => (c @ C @ catalunya)))) & (c @ A @ spain) & ~ (? [B:reg]: (! [C:reg]: ((c @ C @ B) => (c @ C @ A)) & ! [C:reg]: ((c @ C @ B) => (c @ C @ spain)))))))),inference(miniscope,[status(thm)],[40])).
% 16.73/5.08 thf(42,plain,(! [E:reg,D:reg,C:reg,B:$i,A:$i] : (((~ (a @ A @ B) | ~ (c @ C @ catalunya) | (c @ C @ spain)) & (~ (a @ A @ B) | (c @ sk7 @ spain)) & (~ (a @ A @ B) | ~ (c @ sk7 @ catalunya)) & (~ (a @ A @ B) | (c @ sk8 @ catalunya)) & (~ (a @ A @ B) | (c @ (sk9 @ D) @ D) | (c @ (sk10 @ D) @ D)) & (~ (a @ A @ B) | (c @ (sk9 @ D) @ D) | ~ (c @ (sk10 @ D) @ catalunya)) & (~ (a @ A @ B) | ~ (c @ (sk9 @ D) @ sk8) | (c @ (sk10 @ D) @ D)) & (~ (a @ A @ B) | ~ (c @ (sk9 @ D) @ sk8) | ~ (c @ (sk10 @ D) @ catalunya)) & (~ (a @ A @ B) | (c @ sk8 @ spain)) & (~ (a @ A @ B) | (c @ (sk11 @ E) @ E) | (c @ (sk12 @ E) @ E)) & (~ (a @ A @ B) | (c @ (sk11 @ E) @ E) | ~ (c @ (sk12 @ E) @ spain)) & (~ (a @ A @ B) | ~ (c @ (sk11 @ E) @ sk8) | (c @ (sk12 @ E) @ E)) & (~ (a @ A @ B) | ~ (c @ (sk11 @ E) @ sk8) | ~ (c @ (sk12 @ E) @ spain))))),inference(cnf,[status(esa)],[41])).
% 16.73/5.08 thf(47,plain,(! [B:$i,A:$i] : ((~ (a @ A @ B)) | (~ (c @ sk7 @ catalunya)))),inference(cnfConj,[status(thm)],[42])).
% 16.73/5.08 thf(95,plain,(! [B:$i,A:$i] : (~ (($true)) | (~ (c @ sk7 @ catalunya)) | ((a @ sk1 @ sk2) != (a @ A @ B)))),inference(paramod_ordered,[status(thm)],[14,47])).
% 16.73/5.08 thf(96,plain,(! [B:$i,A:$i] : ((~ (c @ sk7 @ catalunya)) | ((a @ sk1 @ sk2) != (a @ A @ B)))),inference(simp,[status(thm)],[95])).
% 16.73/5.08 thf(97,plain,((~ (c @ sk7 @ catalunya))),inference(pattern_uni,[status(thm)],[96:[bind(A, $thf(sk1)),bind(B, $thf(sk2))]])).
% 16.73/5.08 thf(346,plain,(! [B:($i > reg),A:$i] : ((fool @ A @ (sk4 @ (^ [C:$i]: (c @ (B @ C) @ sk3)) @ A)) | ~ (($true)) | ((c @ (B @ A) @ catalunya) != (c @ sk7 @ catalunya)))),inference(paramod_ordered,[status(thm)],[135,97])).
% 16.73/5.08 thf(347,plain,(! [B:($i > reg),A:$i] : ((fool @ A @ (sk4 @ (^ [C:$i]: (c @ (B @ C) @ sk3)) @ A)) | ((c @ (B @ A) @ catalunya) != (c @ sk7 @ catalunya)))),inference(simp,[status(thm)],[346])).
% 16.73/5.08 thf(358,plain,(! [A:$i] : ((fool @ A @ (sk4 @ (^ [B:$i]: (c @ sk7 @ sk3)) @ A)))),inference(pre_uni,[status(thm)],[347:[bind(A, $thf(A)),bind(B, $thf(^ [C:$i]: (sk7)))]])).
% 16.73/5.08 thf(106,plain,(! [A:reg] : (~ (($true)) | ((c @ A @ A) != (c @ sk7 @ catalunya)))),inference(paramod_ordered,[status(thm)],[19,97])).
% 16.73/5.08 thf(107,plain,(! [A:reg] : (((c @ A @ A) != (c @ sk7 @ catalunya)))),inference(simp,[status(thm)],[106])).
% 16.73/5.08 thf(109,plain,(! [A:reg] : ((A != sk7) | (A != catalunya))),inference(simp,[status(thm)],[107])).
% 16.73/5.08 thf(111,plain,((sk7 != catalunya)),inference(simp,[status(thm)],[109])).
% 16.73/5.08 thf(461,plain,(! [A:reg] : (~ (($true)) | ((c @ A @ A) != (c @ sk15 @ paris)))),inference(paramod_ordered,[status(thm)],[19,425])).
% 16.73/5.08 thf(462,plain,(! [A:reg] : (((c @ A @ A) != (c @ sk15 @ paris)))),inference(simp,[status(thm)],[461])).
% 16.73/5.08 thf(475,plain,(! [A:reg] : ((A != sk15) | (A != paris))),inference(simp,[status(thm)],[462])).
% 16.73/5.08 thf(479,plain,((sk15 != paris)),inference(simp,[status(thm)],[475])).
% 16.73/5.08 thf(86,plain,(! [B:reg,A:reg] : (~ (($true)) | (c @ B @ catalunya) | ((c @ A @ A) != (c @ B @ sk3)))),inference(paramod_ordered,[status(thm)],[19,15])).
% 16.73/5.08 thf(87,plain,(! [B:reg,A:reg] : ((c @ B @ catalunya) | ((c @ A @ A) != (c @ B @ sk3)))),inference(simp,[status(thm)],[86])).
% 16.73/5.08 thf(88,plain,((c @ sk3 @ catalunya)),inference(pattern_uni,[status(thm)],[87:[bind(A, $thf(sk3)),bind(B, $thf(sk3))]])).
% 16.73/5.08 thf(25,plain,(! [B:($i > $o),A:$i] : ((~ (B @ (sk4 @ (B) @ A))) | (B @ A))),inference(cnfConj,[status(thm)],[23])).
% 16.73/5.08 thf(104,plain,(~ (($true)) | ((c @ sk7 @ catalunya) != (c @ sk3 @ catalunya))),inference(paramod_ordered,[status(thm)],[88,97])).
% 16.73/5.08 thf(105,plain,(((c @ sk7 @ catalunya) != (c @ sk3 @ catalunya))),inference(simp,[status(thm)],[104])).
% 16.73/5.08 thf(108,plain,((sk7 != sk3) | (catalunya != catalunya)),inference(simp,[status(thm)],[105])).
% 16.73/5.08 thf(110,plain,((sk7 != sk3)),inference(simp,[status(thm)],[108])).
% 16.73/5.08 thf(165,plain,(! [B:reg,A:reg] : (~ (($true)) | (c @ B @ A) | ((c @ sk3 @ catalunya) != (c @ A @ B)))),inference(paramod_ordered,[status(thm)],[88,21])).
% 16.73/5.08 thf(166,plain,(! [B:reg,A:reg] : ((c @ B @ A) | ((c @ sk3 @ catalunya) != (c @ A @ B)))),inference(simp,[status(thm)],[165])).
% 16.73/5.08 thf(167,plain,((c @ catalunya @ sk3)),inference(pattern_uni,[status(thm)],[166:[bind(A, $thf(sk3)),bind(B, $thf(catalunya))]])).
% 16.73/5.08 thf(197,plain,(! [A:reg] : (~ (($true)) | (c @ A @ paris) | ((c @ catalunya @ sk3) != (c @ A @ sk3)))),inference(paramod_ordered,[status(thm)],[167,17])).
% 16.73/5.08 thf(198,plain,(! [A:reg] : ((c @ A @ paris) | ((c @ catalunya @ sk3) != (c @ A @ sk3)))),inference(simp,[status(thm)],[197])).
% 16.73/5.08 thf(199,plain,((c @ catalunya @ paris)),inference(pattern_uni,[status(thm)],[198:[bind(A, $thf(catalunya))]])).
% 16.73/5.08 thf(176,plain,(! [B:reg,A:reg] : ((~ (c @ A @ B)) | ~ (($true)) | ((c @ B @ A) != (c @ sk7 @ catalunya)))),inference(paramod_ordered,[status(thm)],[21,97])).
% 16.73/5.08 thf(177,plain,(! [B:reg,A:reg] : ((~ (c @ A @ B)) | ((c @ B @ A) != (c @ sk7 @ catalunya)))),inference(simp,[status(thm)],[176])).
% 16.73/5.08 thf(178,plain,((~ (c @ catalunya @ sk7))),inference(pattern_uni,[status(thm)],[177:[bind(A, $thf(catalunya)),bind(B, $thf(sk7))]])).
% 16.73/5.08 thf(247,plain,(~ (($true)) | ((c @ catalunya @ sk7) != (c @ catalunya @ paris))),inference(paramod_ordered,[status(thm)],[199,178])).
% 16.73/5.08 thf(248,plain,(((c @ catalunya @ sk7) != (c @ catalunya @ paris))),inference(simp,[status(thm)],[247])).
% 16.73/5.08 thf(249,plain,((catalunya != catalunya) | (sk7 != paris)),inference(simp,[status(thm)],[248])).
% 16.73/5.08 thf(253,plain,((sk7 != paris)),inference(simp,[status(thm)],[249])).
% 16.73/5.08 thf(457,plain,(~ (($true)) | ((c @ sk15 @ paris) != (c @ catalunya @ paris))),inference(paramod_ordered,[status(thm)],[199,425])).
% 16.73/5.08 thf(458,plain,(((c @ sk15 @ paris) != (c @ catalunya @ paris))),inference(simp,[status(thm)],[457])).
% 16.73/5.08 thf(476,plain,((sk15 != catalunya) | (paris != paris)),inference(simp,[status(thm)],[458])).
% 16.73/5.08 thf(480,plain,((sk15 != catalunya)),inference(simp,[status(thm)],[476])).
% 16.73/5.08 thf(6,axiom,((mvalid @ (mforall_prop @ (^ [A:($i > $o)]: (mimplies @ (mbox @ fool @ A) @ (mbox @ fool @ (mbox @ fool @ A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',k_axiom_for_fool)).
% 16.73/5.08 thf(28,plain,((! [A:$i,B:($i > $o)]: (~ (! [C:$i]: (~ (fool @ A @ C) | (B @ C))) | ! [C:$i]: (~ (fool @ A @ C) | ! [D:$i]: (~ (fool @ C @ D) | (B @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6])).
% 16.73/5.08 thf(29,plain,(! [D:$i,C:$i,B:($i > $o),A:$i] : ((((fool @ A @ (sk5 @ (B) @ A)) | ~ (fool @ A @ C) | ~ (fool @ C @ D) | (B @ D)) & (~ (B @ (sk5 @ (B) @ A)) | ~ (fool @ A @ C) | ~ (fool @ C @ D) | (B @ D))))),inference(cnf,[status(esa)],[28])).
% 16.73/5.08 thf(31,plain,(! [D:$i,C:$i,B:($i > $o),A:$i] : ((~ (B @ (sk5 @ (B) @ A))) | (~ (fool @ A @ C)) | (~ (fool @ C @ D)) | (B @ D))),inference(cnfConj,[status(thm)],[29])).
% 16.73/5.08 thf(32,plain,(! [D:$i,C:$i,B:($i > $o),A:$i] : ((~ ((sk5 @ (B) @ A) = (sk5 @ ((=) @ $i @ (sk5 @ B @ A)) @ A))) | (~ (fool @ A @ C)) | (~ (fool @ C @ D)) | ((sk5 @ (B) @ A) = D))),inference(replace_leibeq,[status(thm)],[31:[bind(A, $thf(A)),bind(B, $thf((=) @ $i @ (sk5 @ B @ A)))]])).
% 16.73/5.08 thf(33,plain,(! [D:$i,C:$i,B:($i > $o),A:$i] : (((sk5 @ (B) @ A) != (sk5 @ ((=) @ $i @ (sk5 @ B @ A)) @ A)) | ((sk5 @ (B) @ A) = D) | (~ (fool @ A @ C)) | (~ (fool @ C @ D)))),inference(lifteq,[status(thm)],[32])).
% 16.73/5.08 thf(454,plain,(! [B:reg,A:reg] : ((~ (c @ A @ B)) | ~ (($true)) | ((c @ B @ A) != (c @ sk15 @ paris)))),inference(paramod_ordered,[status(thm)],[21,425])).
% 16.73/5.08 thf(455,plain,(! [B:reg,A:reg] : ((~ (c @ A @ B)) | ((c @ B @ A) != (c @ sk15 @ paris)))),inference(simp,[status(thm)],[454])).
% 16.73/5.08 thf(456,plain,((~ (c @ paris @ sk15))),inference(pattern_uni,[status(thm)],[455:[bind(A, $thf(paris)),bind(B, $thf(sk15))]])).
% 16.73/5.08 thf(7,axiom,((mvalid @ (mforall_prop @ (^ [A:($i > $o)]: (mimplies @ (mbox @ fool @ A) @ (mbox @ a @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',i_axiom_for_fool_a)).
% 16.73/5.08 thf(34,plain,((! [A:$i,B:($i > $o)]: (~ (! [C:$i]: (~ (fool @ A @ C) | (B @ C))) | ! [C:$i]: (~ (a @ A @ C) | (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7])).
% 16.73/5.08 thf(45,plain,(! [B:$i,A:$i] : ((~ (a @ A @ B)) | (c @ sk7 @ spain))),inference(cnfConj,[status(thm)],[42])).
% 16.73/5.08 thf(9,axiom,((mvalid @ (mbox @ fool @ (^ [A:$i]: (ec @ spain @ france))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax2)).
% 16.73/5.08 thf(64,plain,((! [A:$i,B:$i]: (~ (fool @ A @ B) | ((c @ spain @ france) & ~ (? [C:reg]: (! [D:reg]: ((c @ D @ C) => (c @ D @ spain)) & ! [D:reg]: ((c @ D @ C) => (c @ D @ france)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[9])).
% 16.73/5.08 thf(26,plain,(! [B:($i > $o),A:$i] : ((~ ((sk4 @ (B) @ A) = (sk4 @ ((=) @ $i @ (sk4 @ B @ A)) @ A))) | ((sk4 @ (B) @ A) = A))),inference(replace_leibeq,[status(thm)],[25:[bind(A, $thf(A)),bind(B, $thf((=) @ $i @ (sk4 @ B @ A)))]])).
% 16.73/5.08 thf(27,plain,(! [B:($i > $o),A:$i] : (((sk4 @ (B) @ A) != (sk4 @ ((=) @ $i @ (sk4 @ B @ A)) @ A)) | ((sk4 @ (B) @ A) = A))),inference(lifteq,[status(thm)],[26])).
% 16.73/5.08 thf(452,plain,(~ (($true)) | ((c @ sk15 @ paris) != (c @ sk3 @ paris))),inference(paramod_ordered,[status(thm)],[142,425])).
% 16.73/5.08 thf(453,plain,(((c @ sk15 @ paris) != (c @ sk3 @ paris))),inference(simp,[status(thm)],[452])).
% 16.73/5.08 thf(472,plain,((sk15 != sk3) | (paris != paris)),inference(simp,[status(thm)],[453])).
% 16.73/5.08 thf(478,plain,((sk15 != sk3)),inference(simp,[status(thm)],[472])).
% 16.73/5.08 thf(212,plain,(! [A:reg] : (~ (($true)) | (c @ A @ catalunya) | ((c @ paris @ sk3) != (c @ A @ sk3)))),inference(paramod_ordered,[status(thm)],[170,15])).
% 16.73/5.08 thf(213,plain,(! [A:reg] : ((c @ A @ catalunya) | ((c @ paris @ sk3) != (c @ A @ sk3)))),inference(simp,[status(thm)],[212])).
% 16.73/5.08 thf(214,plain,((c @ paris @ catalunya)),inference(pattern_uni,[status(thm)],[213:[bind(A, $thf(paris))]])).
% 16.73/5.08 thf(30,plain,(! [D:$i,C:$i,B:($i > $o),A:$i] : ((fool @ A @ (sk5 @ (B) @ A)) | (~ (fool @ A @ C)) | (~ (fool @ C @ D)) | (B @ D))),inference(cnfConj,[status(thm)],[29])).
% 16.73/5.08 thf(1304,plain,(($false)),inference(e,[status(thm)],[170,142,20,133,980,145,18,40,358,111,479,88,24,25,14,110,253,480,28,21,33,97,456,425,34,45,64,17,22,27,135,167,199,31,11,72,478,214,30,19,15,178])).
% 16.73/5.08 % SZS output end Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% 16.73/5.08 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------