%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : GEG006^1 : 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 : n026.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 9.96s 3.64s
% Output : Refutation 10.40s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEG006^1 : TPTP v9.3.1. Released v4.1.0.
% 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
% 0.11/0.21 % Computer : n026.cluster.edu
% 0.11/0.21 % Model : x86_64 x86_64
% 0.11/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.21 % Memory : 8046.5625MB
% 0.11/0.21 % OS : Linux 6.8.0-71-generic
% 0.11/0.21 % CPULimit : 300
% 0.11/0.21 % WCLimit : 300
% 0.11/0.21 % DateTime : Tue Sep 29 18:36:42 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
% 0.85/0.79 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.55/1.04 % [INFO] Parsing done (255ms).
% 1.55/1.06 % [INFO] Running in sequential loop mode.
% 2.18/1.45 % [INFO] eprover registered as external prover.
% 2.18/1.46 % [INFO] Scanning for conjecture ...
% 2.65/1.64 % [INFO] Found a conjecture (or negated_conjecture) and 8 axioms. Running axiom selection ...
% 2.65/1.68 % [INFO] Axiom selection finished. Selected 8 axioms (removed 0 axioms).
% 2.65/1.69 % [INFO] Problem is higher-order (TPTP THF).
% 2.65/1.69 % [INFO] Type checking passed.
% 2.87/1.70 % [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 ...
% 9.96/3.64 % External prover 'e' found a proof!
% 9.96/3.64 % [INFO] Killing All external provers ...
% 9.96/3.64 % Time passed: 3280ms (effective reasoning time: 2576ms)
% 9.96/3.64 % 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)>
% 9.96/3.64 % 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
% 9.96/3.64 % No. of inferences in proof: 20
% 9.96/3.64 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 3280 ms resp. 2576 ms w/o parsing
% 10.40/3.70 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% 10.40/3.70 thf(mu_type, type, mu: $tType).
% 10.40/3.70 thf(reg_type, type, reg: $tType).
% 10.40/3.70 thf(mnot_decl, type, mnot: (($i > $o) > ($i > $o))).
% 10.40/3.70 thf(mor_decl, type, mor: (($i > $o) > (($i > $o) > ($i > $o)))).
% 10.40/3.70 thf(mimplies_decl, type, mimplies: (($i > $o) > (($i > $o) > ($i > $o)))).
% 10.40/3.70 thf(mforall_prop_decl, type, mforall_prop: ((($i > $o) > ($i > $o)) > ($i > $o))).
% 10.40/3.70 thf(mbox_decl, type, mbox: (($i > ($i > $o)) > (($i > $o) > ($i > $o)))).
% 10.40/3.70 thf(mvalid_decl, type, mvalid: (($i > $o) > $o)).
% 10.40/3.70 thf(c_decl, type, c: (reg > (reg > $o))).
% 10.40/3.70 thf(p_decl, type, p: (reg > (reg > $o))).
% 10.40/3.70 thf(o_decl, type, o: (reg > (reg > $o))).
% 10.40/3.70 thf(ec_decl, type, ec: (reg > (reg > $o))).
% 10.40/3.70 thf(pp_decl, type, pp: (reg > (reg > $o))).
% 10.40/3.70 thf(tpp_decl, type, tpp: (reg > (reg > $o))).
% 10.40/3.70 thf(ntpp_decl, type, ntpp: (reg > (reg > $o))).
% 10.40/3.70 thf(catalunya_decl, type, catalunya: reg).
% 10.40/3.70 thf(france_decl, type, france: reg).
% 10.40/3.70 thf(spain_decl, type, spain: reg).
% 10.40/3.70 thf(paris_decl, type, paris: reg).
% 10.40/3.70 thf(a_decl, type, a: ($i > ($i > $o))).
% 10.40/3.70 thf(fool_decl, type, fool: ($i > ($i > $o))).
% 10.40/3.70 thf(mnot_def, definition, mnot = (^ [A:($i > $o),B:$i]: ~ (A @ B)) ).
% 10.40/3.70 thf(mor_def, definition, mor = (^ [A:($i > $o),B:($i > $o),C:$i]: ((A @ C) | (B @ C))) ).
% 10.40/3.70 thf(mimplies_def, definition, mimplies = (^ [A:($i > $o)]: (mor @ (mnot @ A))) ).
% 10.40/3.70 thf(mforall_prop_def, definition, mforall_prop = (^ [A:(($i > $o) > ($i > $o)),B:$i]: ! [C:($i > $o)]: (A @ C @ B)) ).
% 10.40/3.70 thf(mbox_def, definition, mbox = (^ [A:($i > ($i > $o)),B:($i > $o),C:$i]: ! [D:$i]: (~ (A @ C @ D) | (B @ D))) ).
% 10.40/3.70 thf(mvalid_def, definition, mvalid = ((!) @ $i) ).
% 10.40/3.70 thf(p_def, definition, p = (^ [A:reg,B:reg]: ! [C:reg]: ((c @ C @ A) => (c @ C @ B))) ).
% 10.40/3.70 thf(o_def, definition, o = (^ [A:reg,B:reg]: ? [C:reg]: ((p @ C @ A) & (p @ C @ B))) ).
% 10.40/3.70 thf(ec_def, definition, ec = (^ [A:reg,B:reg]: ((c @ A @ B) & ~ (o @ A @ B))) ).
% 10.40/3.70 thf(pp_def, definition, pp = (^ [A:reg,B:reg]: ((p @ A @ B) & ~ (p @ B @ A))) ).
% 10.40/3.70 thf(tpp_def, definition, tpp = (^ [A:reg,B:reg]: ((pp @ A @ B) & ? [C:reg]: ((ec @ C @ A) & (ec @ C @ B)))) ).
% 10.40/3.70 thf(ntpp_def, definition, ntpp = (^ [A:reg,B:reg]: ((pp @ A @ B) & ~ (? [C:reg]: ((ec @ C @ A) & (ec @ C @ B))))) ).
% 10.40/3.70 thf(6,axiom,((mvalid @ (mforall_prop @ (^ [A:($i > $o)]: (mimplies @ (mbox @ fool @ A) @ (mbox @ fool @ (mbox @ fool @ A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',k_axiom_for_fool)).
% 10.40/3.70 thf(37,plain,((! [A:$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])).
% 10.40/3.70 thf(4,axiom,((! [A:reg,B:reg]: ((c @ A @ B) => (c @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_symmetric)).
% 10.40/3.70 thf(29,plain,((! [A:reg,B:reg]: ((c @ A @ B) => (c @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4])).
% 10.40/3.70 thf(9,axiom,((mvalid @ (mbox @ fool @ (^ [A:$i]: (ec @ spain @ france))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax2)).
% 10.40/3.70 thf(73,plain,((! [A:$i,B:$i]: (~ (fool @ A @ B) | ((c @ spain @ france) & ~ (? [C:reg]: (! [D:reg]: ((c @ D @ C) => (c @ D @ spain)) & ! [D:reg]: ((c @ D @ C) => (c @ D @ france)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[9])).
% 10.40/3.70 thf(3,axiom,((! [A:reg]: (c @ A @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_reflexive)).
% 10.40/3.70 thf(27,plain,((! [A:reg]: (c @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3])).
% 10.40/3.70 thf(8,axiom,((mvalid @ (mbox @ a @ (^ [A:$i]: (tpp @ catalunya @ spain))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax1)).
% 10.40/3.70 thf(49,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])).
% 10.40/3.70 thf(10,axiom,((mvalid @ (mbox @ a @ (^ [A:$i]: (ntpp @ paris @ france))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax3)).
% 10.40/3.70 thf(81,plain,((! [A:$i,B:$i]: (~ (a @ A @ B) | (! [C:reg]: ((c @ C @ paris) => (c @ C @ france)) & ~ (! [C:reg]: ((c @ C @ france) => (c @ C @ paris))) & ~ (? [C:reg]: ((c @ C @ paris) & ~ (? [D:reg]: (! [E:reg]: ((c @ E @ D) => (c @ E @ C)) & ! [E:reg]: ((c @ E @ D) => (c @ E @ paris)))) & (c @ C @ france) & ~ (? [D:reg]: (! [E:reg]: ((c @ E @ D) => (c @ E @ C)) & ! [E:reg]: ((c @ E @ D) => (c @ E @ france)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[10])).
% 10.40/3.70 thf(5,axiom,((mvalid @ (mforall_prop @ (^ [A:($i > $o)]: (mimplies @ (mbox @ fool @ A) @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',t_axiom_for_fool)).
% 10.40/3.70 thf(31,plain,((! [A:$i,B:($i > $o)]: (~ (! [C:$i]: (~ (fool @ A @ C) | (B @ C))) | (B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5])).
% 10.40/3.70 thf(1,conjecture,((mvalid @ (mbox @ a @ (^ [A:$i]: ((o @ catalunya @ spain) & (o @ france @ paris)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',con)).
% 10.40/3.70 thf(2,negated_conjecture,((~ (mvalid @ (mbox @ a @ (^ [A:$i]: ((o @ catalunya @ spain) & (o @ france @ paris))))))),inference(neg_conjecture,[status(cth)],[1])).
% 10.40/3.70 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 @ spain))) & ? [C:reg]: (! [D:reg]: ((c @ D @ C) => (c @ D @ france)) & ! [D:reg]: ((c @ D @ C) => (c @ D @ paris)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])).
% 10.40/3.70 thf(7,axiom,((mvalid @ (mforall_prop @ (^ [A:($i > $o)]: (mimplies @ (mbox @ fool @ A) @ (mbox @ a @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',i_axiom_for_fool_a)).
% 10.40/3.70 thf(43,plain,((! [A:$i,B:($i > $o)]: (~ (! [C:$i]: (~ (fool @ A @ C) | (B @ C))) | ! [C:$i]: (~ (a @ A @ C) | (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7])).
% 10.40/3.70 thf(597,plain,(($false)),inference(e,[status(thm)],[37,29,73,27,49,81,31,11,43])).
% 10.40/3.70 % SZS output end Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% 10.40/3.70 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------