%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : PHI045^7 : TPTP v9.3.1. Released v9.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n002.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 08:20:15 AM UTC 2026
% Result : Theorem 8.69s 3.38s
% Output : Refutation 8.15s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PHI045^7 : TPTP v9.3.1. Released v9.1.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.11/0.21 % Computer : n002.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 13:22:52 UTC 2026
% 0.11/0.21 % CPUTime :
% 0.11/0.21 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.91/0.78 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.24/0.97 % [INFO] Parsing done (186ms).
% 1.24/1.00 % [INFO] Input problem is non-classical (logic $modal). Running HOL transformation from semantics specification contained in the problem file ...
% 1.49/1.12 % [INFO] Running in sequential loop mode.
% 2.45/1.50 % [INFO] eprover registered as external prover.
% 2.45/1.51 % [INFO] Scanning for conjecture ...
% 2.61/1.62 % [INFO] Found a conjecture (or negated_conjecture) and 4 axioms. Running axiom selection ...
% 2.61/1.65 % [INFO] Axiom selection finished. Selected 4 axioms (removed 0 axioms).
% 2.61/1.68 % [INFO] Problem is higher-order (TPTP THF).
% 2.61/1.68 % [INFO] Type checking passed.
% 2.61/1.69 % [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 ...
% 8.69/3.37 % [INFO] Killing All external provers ...
% 8.69/3.38 % Time passed: 3019ms (effective reasoning time: 2244ms)
% 8.69/3.38 % 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)>
% 8.69/3.38 % Axioms used in derivation (2): axiomC4, axiomC2
% 8.69/3.38 % No. of inferences in proof: 31
% 8.69/3.38 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3019 ms resp. 2244 ms w/o parsing
% 8.15/3.43 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.15/3.43 thf(individual_type, type, individual: $tType).
% 8.15/3.43 thf(mworld_type, type, mworld: $tType).
% 8.15/3.43 thf(mrel_decl, type, mrel: (mworld > (mworld > $o))).
% 8.15/3.43 thf(mbox_decl, type, mbox: ((mworld > $o) > (mworld > $o))).
% 8.15/3.43 thf(mactual_decl, type, mactual: mworld).
% 8.15/3.43 thf(mlocal_decl, type, mlocal: ((mworld > $o) > $o)).
% 8.15/3.43 thf(mglobal_decl, type, mglobal: ((mworld > $o) > $o)).
% 8.15/3.43 thf(positive_decl, type, positive: (mworld > ((individual > $o) > $o))).
% 8.15/3.43 thf(godlike_decl, type, godlike: (mworld > (individual > $o))).
% 8.15/3.43 thf(sk1_decl, type, sk1: (individual > (individual > $o))).
% 8.15/3.43 thf(sk2_decl, type, sk2: (individual > mworld)).
% 8.15/3.43 thf(sk6_decl, type, sk6: (mworld > individual)).
% 8.15/3.43 thf(mbox_def, definition, mbox = (^ [A:(mworld > $o),B:mworld]: ! [C:mworld]: ((mrel @ B @ C) => (A @ C))) ).
% 8.15/3.43 thf(mlocal_def, definition, mlocal = (^ [A:(mworld > $o)]: (A @ mactual)) ).
% 8.15/3.43 thf(mglobal_def, definition, mglobal = ((!) @ mworld) ).
% 8.15/3.43 thf(godlike_def, definition, godlike = (^ [A:mworld,B:individual]: ! [C:(individual > $o)]: ((positive @ A @ C) => (mbox @ (^ [D:mworld]: (C @ B)) @ A))) ).
% 8.15/3.43 thf(sk1_def, definition, sk1 = (^ [A:individual]: (@+ [B:(individual > $o)]: ~ ((positive @ mactual @ B) => ((? [C:mworld]: (mrel @ mactual @ C)) => (B @ A))))) ).
% 8.15/3.43 thf(sk2_def, definition, sk2 = (^ [A:individual]: (@+ [B:mworld]: (mrel @ mactual @ B))) ).
% 8.15/3.43 thf(1,conjecture,((mlocal @ (^ [A:mworld]: ? [B:individual]: (godlike @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',theoremC6)).
% 8.15/3.43 thf(2,negated_conjecture,((~ (mlocal @ (^ [A:mworld]: ? [B:individual]: (godlike @ A @ B))))),inference(neg_conjecture,[status(cth)],[1])).
% 8.15/3.43 thf(7,plain,((~ (? [A:individual]: ! [B:(individual > $o)]: ((positive @ mactual @ (B)) => (! [C:mworld]: ((mrel @ mactual @ C) => (B @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])).
% 8.15/3.43 thf(8,plain,((~ (? [A:individual]: ! [B:(individual > $o)]: ((positive @ mactual @ (B)) => ((? [C:mworld]: (mrel @ mactual @ C)) => (B @ A)))))),inference(miniscope,[status(thm)],[7])).
% 8.15/3.43 thf(9,plain,(! [A:individual] : (((positive @ mactual @ (sk1 @ A)) & (mrel @ mactual @ (sk2 @ A)) & ~ (sk1 @ A @ A)))),inference(cnf,[status(esa)],[8])).
% 8.15/3.43 thf(10,plain,(! [A:individual] : ((positive @ mactual @ (sk1 @ A)))),inference(cnfConj,[status(thm)],[9])).
% 8.15/3.43 thf(11,plain,(! [A:individual] : ((mrel @ mactual @ (sk2 @ A)))),inference(cnfConj,[status(thm)],[9])).
% 8.15/3.43 thf(6,axiom,((mglobal @ (^ [A:mworld]: (positive @ A @ (godlike @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiomC4)).
% 8.15/3.43 thf(25,plain,((! [A:mworld]: (positive @ A @ (^ [B:individual]: ! [C:(individual > $o)]: ((positive @ A @ C) => (! [D:mworld]: ((mrel @ A @ D) => (C @ B)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6])).
% 8.15/3.43 thf(26,plain,(! [A:mworld] : ((positive @ A @ (^ [B:individual]: ! [C:(individual > $o)]: ((positive @ A @ C) => (! [D:mworld]: ((mrel @ A @ D) => (C @ B)))))))),inference(cnf,[status(esa)],[25])).
% 8.15/3.43 thf(5,axiom,((mglobal @ (^ [A:mworld]: ! [B:(individual > $o)]: ~ (positive @ A @ (^ [C:individual]: ((B @ C) & ~ (B @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiomC2)).
% 8.15/3.43 thf(22,plain,((! [A:mworld]: ~ (positive @ A @ (^ [B:individual]: (($false)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5])).
% 8.15/3.43 thf(23,plain,((~ (? [A:mworld]: (positive @ A @ (^ [B:individual]: (($false))))))),inference(miniscope,[status(thm)],[22])).
% 8.15/3.43 thf(24,plain,(! [A:mworld] : ((~ (positive @ A @ (^ [B:individual]: (($false))))))),inference(cnf,[status(esa)],[23])).
% 8.15/3.43 thf(70,plain,(! [B:mworld,A:mworld] : (~ (($true)) | ((positive @ A @ (^ [C:individual]: ! [D:(individual > $o)]: ((positive @ A @ D) => (! [E:mworld]: ((mrel @ A @ E) => (D @ C)))))) != (positive @ B @ (^ [C:individual]: (($false))))))),inference(paramod_ordered,[status(thm)],[26,24])).
% 8.15/3.43 thf(71,plain,(! [B:mworld,A:mworld] : (((positive @ A @ (^ [C:individual]: ! [D:(individual > $o)]: ((positive @ A @ D) => (! [E:mworld]: ((mrel @ A @ E) => (D @ C)))))) != (positive @ B @ (^ [C:individual]: (($false))))))),inference(simp,[status(thm)],[70])).
% 8.15/3.43 thf(80,plain,(! [B:mworld,A:mworld] : ((A != B) | ((^ [C:individual]: ! [D:(individual > $o)]: ((positive @ A @ D) => (! [E:mworld]: ((mrel @ A @ E) => (D @ C))))) != (^ [C:individual]: (($false)))))),inference(simp,[status(thm)],[71])).
% 8.15/3.43 thf(81,plain,(! [A:mworld] : (((^ [B:individual]: ! [C:(individual > $o)]: ((positive @ A @ C) => (! [D:mworld]: ((mrel @ A @ D) => (C @ B))))) != (^ [B:individual]: (($false)))))),inference(simp,[status(thm)],[80])).
% 8.15/3.43 thf(85,plain,(! [A:mworld] : ((! [B:(individual > $o)]: ((positive @ A @ (B)) => (! [C:mworld]: ((mrel @ A @ C) => (B @ (sk6 @ A)))))))),inference(func_ext,[status(esa)],[81])).
% 8.15/3.43 thf(86,plain,(! [C:mworld,B:(individual > $o),A:mworld] : ((~ (positive @ A @ (B))) | (~ (mrel @ A @ C)) | (B @ (sk6 @ A)))),inference(cnf,[status(esa)],[85])).
% 8.15/3.43 thf(130,plain,(! [D:mworld,C:(individual > $o),B:mworld,A:individual] : ((~ (positive @ B @ (C))) | ~ (($true)) | (C @ (sk6 @ B)) | ((mrel @ mactual @ (sk2 @ A)) != (mrel @ B @ D)))),inference(paramod_ordered,[status(thm)],[11,86])).
% 8.15/3.43 thf(131,plain,(! [D:mworld,C:(individual > $o),B:mworld,A:individual] : ((~ (positive @ B @ (C))) | (C @ (sk6 @ B)) | ((mrel @ mactual @ (sk2 @ A)) != (mrel @ B @ D)))),inference(simp,[status(thm)],[130])).
% 8.15/3.43 thf(132,plain,(! [A:(individual > $o)] : ((~ (positive @ mactual @ (A))) | (A @ (sk6 @ mactual)))),inference(pattern_uni,[status(thm)],[131:[bind(A, $thf(E)),bind(B, $thf(mactual)),bind(C, $thf(C)),bind(D, $thf(sk2 @ E))]])).
% 8.15/3.43 thf(181,plain,(! [A:(individual > $o)] : ((~ (positive @ mactual @ (A))) | (A @ (sk6 @ mactual)))),inference(simp,[status(thm)],[132])).
% 8.15/3.43 thf(222,plain,(! [B:(individual > $o),A:individual] : (~ (($true)) | (B @ (sk6 @ mactual)) | ((positive @ mactual @ (sk1 @ A)) != (positive @ mactual @ (B))))),inference(paramod_ordered,[status(thm)],[10,181])).
% 8.15/3.43 thf(223,plain,(! [B:(individual > $o),A:individual] : ((B @ (sk6 @ mactual)) | ((positive @ mactual @ (sk1 @ A)) != (positive @ mactual @ (B))))),inference(simp,[status(thm)],[222])).
% 8.15/3.43 thf(224,plain,(! [A:individual] : ((sk1 @ A @ (sk6 @ mactual)))),inference(pattern_uni,[status(thm)],[223:[bind(A, $thf(A)),bind(B, $thf(sk1 @ A))]])).
% 8.15/3.43 thf(12,plain,(! [A:individual] : ((~ (sk1 @ A @ A)))),inference(cnfConj,[status(thm)],[9])).
% 8.15/3.43 thf(309,plain,(! [B:individual,A:individual] : (~ (($true)) | ((sk1 @ A @ (sk6 @ mactual)) != (sk1 @ B @ B)))),inference(paramod_ordered,[status(thm)],[224,12])).
% 8.15/3.43 thf(310,plain,(! [B:individual,A:individual] : (((sk1 @ A @ (sk6 @ mactual)) != (sk1 @ B @ B)))),inference(simp,[status(thm)],[309])).
% 8.15/3.43 thf(311,plain,(($false)),inference(pattern_uni,[status(thm)],[310:[bind(A, $thf(sk6 @ mactual)),bind(B, $thf(sk6 @ mactual))]])).
% 8.15/3.43 % SZS output end Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.15/3.43 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------