%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : PHI005^8 : TPTP v9.3.1. Released v9.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:20:14 AM UTC 2026
% Result : Theorem 10.94s 3.97s
% Output : Refutation 11.61s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : PHI005^8 : TPTP v9.3.1. Released v9.0.0.
% 0.00/0.07 % 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
% 0.08/0.23 % Computer : n001.cluster.edu
% 0.08/0.23 % Model : x86_64 x86_64
% 0.08/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.23 % Memory : 8046.5625MB
% 0.08/0.23 % OS : Linux 6.8.0-71-generic
% 0.08/0.23 % CPULimit : 300
% 0.08/0.23 % WCLimit : 300
% 0.08/0.23 % DateTime : Tue Sep 29 13:25:49 UTC 2026
% 0.08/0.23 % CPUTime :
% 0.08/0.23 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.96/0.82 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.12/1.02 % [INFO] Parsing done (201ms).
% 1.37/1.04 % [INFO] Input problem is non-classical (logic $alethic_modal). Running HOL transformation from semantics specification contained in the problem file ...
% 1.56/1.18 % [INFO] Running in sequential loop mode.
% 2.22/1.55 % [INFO] eprover registered as external prover.
% 2.22/1.56 % [INFO] Scanning for conjecture ...
% 2.38/1.68 % [INFO] Found a conjecture (or negated_conjecture) and 6 axioms. Running axiom selection ...
% 2.59/1.72 % [INFO] Axiom selection finished. Selected 6 axioms (removed 0 axioms).
% 2.59/1.74 % [INFO] Problem is higher-order (TPTP THF).
% 2.59/1.75 % [INFO] Type checking passed.
% 2.59/1.75 % [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 ...
% 10.94/3.96 % [INFO] Killing All external provers ...
% 10.94/3.96 % Time passed: 3592ms (effective reasoning time: 2770ms)
% 10.94/3.96 % 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)>
% 10.94/3.96 % Axioms used in derivation (5): a4, mrel_universal, a3, a1, a2
% 10.94/3.96 % No. of inferences in proof: 51
% 10.94/3.97 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3592 ms resp. 2770 ms w/o parsing
% 11.61/4.04 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 11.61/4.04 thf(mworld_type, type, mworld: $tType).
% 11.61/4.04 thf(mrel_decl, type, mrel: (mworld > (mworld > $o))).
% 11.61/4.04 thf(mbox_decl, type, mbox: ((mworld > $o) > (mworld > $o))).
% 11.61/4.04 thf(mactual_decl, type, mactual: mworld).
% 11.61/4.04 thf(mlocal_decl, type, mlocal: ((mworld > $o) > $o)).
% 11.61/4.04 thf(mglobal_decl, type, mglobal: ((mworld > $o) > $o)).
% 11.61/4.04 thf(positive_decl, type, positive: (mworld > (($i > $o) > $o))).
% 11.61/4.04 thf(godlike_decl, type, godlike: (mworld > ($i > $o))).
% 11.61/4.04 thf(sk1_decl, type, sk1: mworld).
% 11.61/4.04 thf(sk2_decl, type, sk2: ($i > ($i > $o))).
% 11.61/4.04 thf(sk3_decl, type, sk3: (($i > $o) > (($i > $o) > (mworld > mworld)))).
% 11.61/4.04 thf(sk4_decl, type, sk4: (($i > $o) > (($i > $o) > (mworld > $i)))).
% 11.61/4.04 thf(sk7_decl, type, sk7: $i).
% 11.61/4.04 thf(mbox_def, definition, mbox = (^ [A:(mworld > $o),B:mworld]: ! [C:mworld]: ((mrel @ B @ C) => (A @ C))) ).
% 11.61/4.04 thf(mlocal_def, definition, mlocal = (^ [A:(mworld > $o)]: (A @ mactual)) ).
% 11.61/4.04 thf(mglobal_def, definition, mglobal = ((!) @ mworld) ).
% 11.61/4.04 thf(godlike_def, definition, godlike = (^ [A:mworld,B:$i]: ! [C:($i > $o)]: ((positive @ A @ C) => (C @ B))) ).
% 11.61/4.04 thf(sk1_def, definition, sk1 = (@+ [A:mworld]: ~ ((mrel @ mactual @ A) => (? [B:$i]: ! [C:($i > $o)]: ((positive @ A @ (C)) => (C @ B))))) ).
% 11.61/4.04 thf(sk2_def, definition, sk2 = (^ [A:$i]: (@+ [B:($i > $o)]: ~ ((positive @ sk1 @ B) => (B @ A)))) ).
% 11.61/4.04 thf(sk3_def, definition, sk3 = (^ [A:($i > $o),B:($i > $o),C:mworld]: (@+ [D:mworld]: (mrel @ C @ D))) ).
% 11.61/4.04 thf(sk4_def, definition, sk4 = (^ [A:($i > $o),B:($i > $o),C:mworld]: (@+ [D:$i]: ~ ((B @ D) => (A @ D)))) ).
% 11.61/4.04 thf(1,conjecture,((mlocal @ (mbox @ (^ [A:mworld]: ? [B:$i]: (godlike @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3)).
% 11.61/4.04 thf(2,negated_conjecture,((~ (mlocal @ (mbox @ (^ [A:mworld]: ? [B:$i]: (godlike @ A @ B)))))),inference(neg_conjecture,[status(cth)],[1])).
% 11.61/4.04 thf(9,plain,((~ (! [A:mworld]: ((mrel @ mactual @ A) => (? [B:$i]: ! [C:($i > $o)]: ((positive @ A @ (C)) => (C @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])).
% 11.61/4.04 thf(10,plain,(! [A:$i] : (((mrel @ mactual @ sk1) & (positive @ sk1 @ (sk2 @ A)) & ~ (sk2 @ A @ A)))),inference(cnf,[status(esa)],[9])).
% 11.61/4.04 thf(12,plain,(! [A:$i] : ((positive @ sk1 @ (sk2 @ A)))),inference(cnfConj,[status(thm)],[10])).
% 11.61/4.04 thf(7,axiom,((mglobal @ (^ [A:mworld]: ! [B:($i > $o)]: ((positive @ A @ B) => (mbox @ (^ [C:mworld]: (positive @ C @ B)) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a4)).
% 11.61/4.04 thf(27,plain,((! [A:mworld,B:($i > $o)]: ((positive @ A @ (B)) => (! [C:mworld]: ((mrel @ A @ C) => (positive @ C @ (B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7])).
% 11.61/4.04 thf(28,plain,(! [C:mworld,B:($i > $o),A:mworld] : ((~ (positive @ A @ (B))) | (~ (mrel @ A @ C)) | (positive @ C @ (B)))),inference(cnf,[status(esa)],[27])).
% 11.61/4.04 thf(3,axiom,((! [A:mworld,B:mworld]: (mrel @ A @ B))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mrel_universal)).
% 11.61/4.04 thf(14,plain,((! [A:mworld,B:mworld]: (mrel @ A @ B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3])).
% 11.61/4.04 thf(15,plain,(! [B:mworld,A:mworld] : ((mrel @ A @ B))),inference(cnf,[status(esa)],[14])).
% 11.61/4.04 thf(32,plain,(! [C:mworld,B:($i > $o),A:mworld] : ((~ (positive @ A @ (B))) | ~ (($true)) | (positive @ C @ (B)))),inference(rewrite,[status(thm)],[28,15])).
% 11.61/4.04 thf(33,plain,(! [C:mworld,B:($i > $o),A:mworld] : ((~ (positive @ A @ (B))) | (positive @ C @ (B)))),inference(simp,[status(thm)],[32])).
% 11.61/4.04 thf(37,plain,(! [D:mworld,C:($i > $o),B:mworld,A:$i] : (~ (($true)) | (positive @ D @ (C)) | ((positive @ sk1 @ (sk2 @ A)) != (positive @ B @ (C))))),inference(paramod_ordered,[status(thm)],[12,33])).
% 11.61/4.04 thf(38,plain,(! [D:mworld,C:($i > $o),B:mworld,A:$i] : ((positive @ D @ (C)) | ((positive @ sk1 @ (sk2 @ A)) != (positive @ B @ (C))))),inference(simp,[status(thm)],[37])).
% 11.61/4.04 thf(39,plain,(! [B:mworld,A:$i] : ((positive @ B @ (sk2 @ A)))),inference(pattern_uni,[status(thm)],[38:[bind(A, $thf(A)),bind(B, $thf(sk1)),bind(C, $thf(sk2 @ A)),bind(D, $thf(D))]])).
% 11.61/4.04 thf(41,plain,(! [B:mworld,A:$i] : ((positive @ B @ (sk2 @ A)))),inference(simp,[status(thm)],[39])).
% 11.61/4.04 thf(6,axiom,((mglobal @ (^ [A:mworld]: (positive @ A @ (godlike @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a3)).
% 11.61/4.04 thf(25,plain,((! [A:mworld]: (positive @ A @ (^ [B:$i]: ! [C:($i > $o)]: ((positive @ A @ C) => (C @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6])).
% 11.61/4.04 thf(26,plain,(! [A:mworld] : ((positive @ A @ (^ [B:$i]: ! [C:($i > $o)]: ((positive @ A @ C) => (C @ B)))))),inference(cnf,[status(esa)],[25])).
% 11.61/4.04 thf(4,axiom,((mglobal @ (^ [A:mworld]: ! [B:($i > $o)]: ((positive @ A @ (^ [C:$i]: ~ (B @ C))) = (~ (positive @ A @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a1)).
% 11.61/4.04 thf(16,plain,((! [A:mworld,B:($i > $o)]: ((positive @ A @ (^ [C:$i]: ~ (B @ C))) = (~ (positive @ A @ (B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4])).
% 11.61/4.04 thf(17,plain,(! [B:($i > $o),A:mworld] : (((positive @ A @ (^ [C:$i]: ~ (B @ C))) = (~ (positive @ A @ (B)))))),inference(cnf,[status(esa)],[16])).
% 11.61/4.04 thf(18,plain,(! [B:($i > $o),A:mworld] : (((positive @ A @ (^ [C:$i]: ~ (B @ C))) = (~ (positive @ A @ (B)))))),inference(lifteq,[status(thm)],[17])).
% 11.61/4.04 thf(5,axiom,((mglobal @ (^ [A:mworld]: ! [B:($i > $o),C:($i > $o)]: (((positive @ A @ B) & (mbox @ (^ [D:mworld]: ! [E:$i]: ((B @ E) => (C @ E))) @ A)) => (positive @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a2)).
% 11.61/4.04 thf(19,plain,((! [A:mworld,B:($i > $o),C:($i > $o)]: (((positive @ A @ (B)) & ! [D:mworld]: ((mrel @ A @ D) => (! [E:$i]: ((B @ E) => (C @ E))))) => (positive @ A @ (C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5])).
% 11.61/4.04 thf(20,plain,((! [A:mworld,B:($i > $o),C:($i > $o)]: (((positive @ A @ (B)) & ((? [D:mworld]: (mrel @ A @ D)) => (! [D:$i]: ((B @ D) => (C @ D))))) => (positive @ A @ (C))))),inference(miniscope,[status(thm)],[19])).
% 11.61/4.04 thf(21,plain,(! [C:($i > $o),B:($i > $o),A:mworld] : (((~ (positive @ A @ (B)) | (mrel @ A @ (sk3 @ (C) @ (B) @ A)) | (positive @ A @ (C))) & (~ (positive @ A @ (B)) | (B @ (sk4 @ (C) @ (B) @ A)) | (positive @ A @ (C))) & (~ (positive @ A @ (B)) | ~ (C @ (sk4 @ (C) @ (B) @ A)) | (positive @ A @ (C)))))),inference(cnf,[status(esa)],[20])).
% 11.61/4.04 thf(24,plain,(! [C:($i > $o),B:($i > $o),A:mworld] : ((~ (positive @ A @ (B))) | (~ (C @ (sk4 @ (C) @ (B) @ A))) | (positive @ A @ (C)))),inference(cnfConj,[status(thm)],[21])).
% 11.61/4.04 thf(47,plain,(! [D:($i > $o),C:($i > $o),B:mworld,A:$i] : (~ (($true)) | (~ (D @ (sk4 @ (D) @ (C) @ B))) | (positive @ B @ (D)) | ((positive @ sk1 @ (sk2 @ A)) != (positive @ B @ (C))))),inference(paramod_ordered,[status(thm)],[12,24])).
% 11.61/4.04 thf(48,plain,(! [D:($i > $o),C:($i > $o),B:mworld,A:$i] : ((~ (D @ (sk4 @ (D) @ (C) @ B))) | (positive @ B @ (D)) | ((positive @ sk1 @ (sk2 @ A)) != (positive @ B @ (C))))),inference(simp,[status(thm)],[47])).
% 11.61/4.04 thf(49,plain,(! [B:($i > $o),A:$i] : ((~ (B @ (sk4 @ (B) @ (sk2 @ A) @ sk1))) | (positive @ sk1 @ (B)))),inference(pattern_uni,[status(thm)],[48:[bind(A, $thf(A)),bind(B, $thf(sk1)),bind(C, $thf(sk2 @ A)),bind(D, $thf(D))]])).
% 11.61/4.04 thf(73,plain,(! [B:($i > $o),A:$i] : ((~ (B @ (sk4 @ (B) @ (sk2 @ A) @ sk1))) | (positive @ sk1 @ (B)))),inference(simp,[status(thm)],[49])).
% 11.61/4.04 thf(107,plain,(~ (($true)) | (positive @ sk1 @ (^ [A:$i]: (($true))))),inference(prim_subst,[status(thm)],[73:[bind(A, $thf(A)),bind(B, $thf(^ [C:$i]: (($true))))]])).
% 11.61/4.04 thf(125,plain,((positive @ sk1 @ (^ [A:$i]: (($true))))),inference(simp,[status(thm)],[107])).
% 11.61/4.04 thf(151,plain,(! [B:($i > $o),A:mworld] : ((~ (positive @ A @ (B))) | ((positive @ A @ (^ [C:$i]: ~ (B @ C))) != (positive @ sk1 @ (^ [C:$i]: (($true))))))),inference(paramod_ordered,[status(thm)],[18,125])).
% 11.61/4.04 thf(152,plain,(! [B:($i > $o),A:mworld] : ((~ (positive @ A @ (B))) | ((positive @ A @ (^ [C:$i]: ~ (B @ C))) != (positive @ sk1 @ (^ [C:$i]: (($true))))))),inference(simp,[status(thm)],[151])).
% 11.61/4.04 thf(170,plain,(! [B:($i > $o),A:mworld] : ((~ (positive @ A @ (B))) | (A != sk1) | ((^ [C:$i]: ~ (B @ C)) != (^ [C:$i]: (($true)))))),inference(simp,[status(thm)],[152])).
% 11.61/4.04 thf(178,plain,(! [A:($i > $o)] : ((~ (positive @ sk1 @ (A))) | ((^ [B:$i]: ~ (A @ B)) != (^ [B:$i]: (($true)))))),inference(simp,[status(thm)],[170])).
% 11.61/4.04 thf(288,plain,(! [B:($i > $o),A:mworld] : (~ (($true)) | ((^ [C:$i]: ~ (B @ C)) != (^ [C:$i]: (($true)))) | ((positive @ A @ (^ [C:$i]: ! [D:($i > $o)]: ((positive @ A @ D) => (D @ C)))) != (positive @ sk1 @ (B))))),inference(paramod_ordered,[status(thm)],[26,178])).
% 11.61/4.04 thf(289,plain,(! [B:($i > $o),A:mworld] : (((^ [C:$i]: ~ (B @ C)) != (^ [C:$i]: (($true)))) | ((positive @ A @ (^ [C:$i]: ! [D:($i > $o)]: ((positive @ A @ D) => (D @ C)))) != (positive @ sk1 @ (B))))),inference(simp,[status(thm)],[288])).
% 11.61/4.04 thf(290,plain,(((^ [A:$i]: ~ (! [B:($i > $o)]: ((positive @ sk1 @ B) => (B @ A)))) != (^ [A:$i]: (($true))))),inference(pattern_uni,[status(thm)],[289:[bind(A, $thf(sk1)),bind(B, $thf(^ [C:$i]: ! [D:($i > $o)]: ((positive @ sk1 @ D) => (D @ C))))]])).
% 11.61/4.04 thf(297,plain,((~ (~ (! [A:($i > $o)]: ((positive @ sk1 @ (A)) => (A @ sk7)))))),inference(func_ext,[status(esa)],[290])).
% 11.61/4.04 thf(298,plain,(! [A:($i > $o)] : ((~ (positive @ sk1 @ (A))) | (A @ sk7))),inference(cnf,[status(esa)],[297])).
% 11.61/4.04 thf(356,plain,(! [C:($i > $o),B:mworld,A:$i] : (~ (($true)) | (C @ sk7) | ((positive @ B @ (sk2 @ A)) != (positive @ sk1 @ (C))))),inference(paramod_ordered,[status(thm)],[41,298])).
% 11.61/4.04 thf(357,plain,(! [C:($i > $o),B:mworld,A:$i] : ((C @ sk7) | ((positive @ B @ (sk2 @ A)) != (positive @ sk1 @ (C))))),inference(simp,[status(thm)],[356])).
% 11.61/4.04 thf(358,plain,(! [A:$i] : ((sk2 @ A @ sk7))),inference(pattern_uni,[status(thm)],[357:[bind(A, $thf(A)),bind(B, $thf(sk1)),bind(C, $thf(sk2 @ A))]])).
% 11.61/4.04 thf(13,plain,(! [A:$i] : ((~ (sk2 @ A @ A)))),inference(cnfConj,[status(thm)],[10])).
% 11.61/4.04 thf(539,plain,(! [B:$i,A:$i] : (~ (($true)) | ((sk2 @ A @ sk7) != (sk2 @ B @ B)))),inference(paramod_ordered,[status(thm)],[358,13])).
% 11.61/4.04 thf(540,plain,(! [B:$i,A:$i] : (((sk2 @ A @ sk7) != (sk2 @ B @ B)))),inference(simp,[status(thm)],[539])).
% 11.61/4.04 thf(541,plain,(($false)),inference(pattern_uni,[status(thm)],[540:[bind(A, $thf(sk7)),bind(B, $thf(sk7))]])).
% 11.61/4.04 % SZS output end Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 11.61/4.04 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------