%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LCL715^1 : TPTP v9.3.1. Bugfixed v5.0.0.
% 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 : n005.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 08:14:11 AM UTC 2026
% Result : Theorem 25.54s 6.77s
% Output : Refutation 21.96s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL715^1 : TPTP v9.3.1. Bugfixed v5.0.0.
% 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
% 0.12/0.26 % Computer : n005.cluster.edu
% 0.12/0.26 % Model : x86_64 x86_64
% 0.12/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.26 % Memory : 8046.5625MB
% 0.12/0.26 % OS : Linux 6.8.0-71-generic
% 0.12/0.26 % CPULimit : 300
% 0.12/0.26 % WCLimit : 300
% 0.12/0.26 % DateTime : Tue Sep 29 09:49:31 UTC 2026
% 0.12/0.27 % CPUTime :
% 0.12/0.27 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
% 1.15/1.02 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.80/1.26 % [INFO] Parsing done (235ms).
% 1.80/1.27 % [INFO] Running in sequential loop mode.
% 2.78/1.67 % [INFO] eprover registered as external prover.
% 2.78/1.68 % [INFO] Scanning for conjecture ...
% 3.26/1.88 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 3.48/1.91 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 3.48/1.91 % [INFO] Problem is higher-order (TPTP THF).
% 3.48/1.92 % [INFO] Type checking passed.
% 3.48/1.92 % [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 ...
% 25.54/6.76 % [INFO] Killing All external provers ...
% 25.54/6.77 % Time passed: 6315ms (effective reasoning time: 5488ms)
% 25.54/6.77 % 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)>
% 25.54/6.77 % Axioms used in derivation (0):
% 25.54/6.77 % No. of inferences in proof: 33
% 25.54/6.77 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 6315 ms resp. 5488 ms w/o parsing
% 21.96/6.89 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% 21.96/6.89 thf(mu_type, type, mu: $tType).
% 21.96/6.89 thf(mnot_decl, type, mnot: (($i > $o) > ($i > $o))).
% 21.96/6.89 thf(mor_decl, type, mor: (($i > $o) > (($i > $o) > ($i > $o)))).
% 21.96/6.89 thf(mand_decl, type, mand: (($i > $o) > (($i > $o) > ($i > $o)))).
% 21.96/6.89 thf(mimplies_decl, type, mimplies: (($i > $o) > (($i > $o) > ($i > $o)))).
% 21.96/6.89 thf(mequiv_decl, type, mequiv: (($i > $o) > (($i > $o) > ($i > $o)))).
% 21.96/6.89 thf(mforall_prop_decl, type, mforall_prop: ((($i > $o) > ($i > $o)) > ($i > $o))).
% 21.96/6.89 thf(mbox_decl, type, mbox: (($i > ($i > $o)) > (($i > $o) > ($i > $o)))).
% 21.96/6.89 thf(mdia_decl, type, mdia: (($i > ($i > $o)) > (($i > $o) > ($i > $o)))).
% 21.96/6.89 thf(mfunctional_decl, type, mfunctional: (($i > ($i > $o)) > $o)).
% 21.96/6.89 thf(mvalid_decl, type, mvalid: (($i > $o) > $o)).
% 21.96/6.89 thf(sk1_decl, type, sk1: ($i > ($i > $o))).
% 21.96/6.89 thf(sk2_decl, type, sk2: (($i > $o) > ($i > $i))).
% 21.96/6.89 thf(sk3_decl, type, sk3: (($i > $o) > ($i > $i))).
% 21.96/6.89 thf(sk4_decl, type, sk4: $i).
% 21.96/6.89 thf(sk5_decl, type, sk5: ($i > $i)).
% 21.96/6.89 thf(mnot_def, definition, mnot = (^ [A:($i > $o),B:$i]: ~ (A @ B)) ).
% 21.96/6.89 thf(mor_def, definition, mor = (^ [A:($i > $o),B:($i > $o),C:$i]: ((A @ C) | (B @ C))) ).
% 21.96/6.89 thf(mand_def, definition, mand = (^ [A:($i > $o),B:($i > $o)]: (mnot @ (mor @ (mnot @ A) @ (mnot @ B)))) ).
% 21.96/6.89 thf(mimplies_def, definition, mimplies = (^ [A:($i > $o)]: (mor @ (mnot @ A))) ).
% 21.96/6.89 thf(mequiv_def, definition, mequiv = (^ [A:($i > $o),B:($i > $o)]: (mand @ (mimplies @ A @ B) @ (mimplies @ B @ A))) ).
% 21.96/6.89 thf(mforall_prop_def, definition, mforall_prop = (^ [A:(($i > $o) > ($i > $o)),B:$i]: ! [C:($i > $o)]: (A @ C @ B)) ).
% 21.96/6.89 thf(mbox_def, definition, mbox = (^ [A:($i > ($i > $o)),B:($i > $o),C:$i]: ! [D:$i]: (~ (A @ C @ D) | (B @ D))) ).
% 21.96/6.89 thf(mdia_def, definition, mdia = (^ [A:($i > ($i > $o)),B:($i > $o)]: (mnot @ (mbox @ A @ (mnot @ B)))) ).
% 21.96/6.89 thf(mfunctional_def, definition, mfunctional = (^ [A:($i > ($i > $o))]: ! [B:$i]: ? [C:$i]: ((A @ B @ C) & ! [D:$i]: ((A @ B @ D) => (C = D)))) ).
% 21.96/6.89 thf(mvalid_def, definition, mvalid = ((!) @ $i) ).
% 21.96/6.89 thf(sk1_def, definition, sk1 = (@+ [A:($i > ($i > $o))]: ~ ((~ (~ (! [B:$i,C:($i > $o)]: (! [D:$i]: (~ (A @ B @ D) | ~ (C @ D)) | ! [D:$i]: (~ (A @ B @ D) | (C @ D)))) | ~ (! [B:$i,C:($i > $o)]: (~ (! [D:$i]: (~ (A @ B @ D) | (C @ D))) | ~ (! [D:$i]: (~ (A @ B @ D) | ~ (C @ D))))))) => (! [B:$i]: ? [C:$i]: ((A @ B @ C) & ! [D:$i]: ((A @ B @ D) => (C = D)))))) ).
% 21.96/6.89 thf(sk2_def, definition, sk2 = (^ [A:($i > $o),B:$i]: (@+ [C:$i]: ~ (~ (sk1 @ B @ C) | (A @ C)))) ).
% 21.96/6.89 thf(sk3_def, definition, sk3 = (^ [A:($i > $o),B:$i]: (@+ [C:$i]: ~ (~ (sk1 @ B @ C) | ~ (A @ C)))) ).
% 21.96/6.89 thf(sk4_def, definition, sk4 = (@+ [A:$i]: ~ (? [B:$i]: ((sk1 @ A @ B) & ! [C:$i]: ((sk1 @ A @ C) => (B = C))))) ).
% 21.96/6.89 thf(sk5_def, definition, sk5 = (^ [A:$i]: (@+ [B:$i]: ~ ((sk1 @ sk4 @ B) => (A = B)))) ).
% 21.96/6.89 thf(1,conjecture,((! [A:($i > ($i > $o))]: ((mvalid @ (mforall_prop @ (^ [B:($i > $o)]: (mequiv @ (mdia @ A @ B) @ (mbox @ A @ B))))) => (mfunctional @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj)).
% 21.96/6.89 thf(2,negated_conjecture,((~ (! [A:($i > ($i > $o))]: ((mvalid @ (mforall_prop @ (^ [B:($i > $o)]: (mequiv @ (mdia @ A @ B) @ (mbox @ A @ B))))) => (mfunctional @ A))))),inference(neg_conjecture,[status(cth)],[1])).
% 21.96/6.89 thf(3,plain,((~ (! [A:($i > ($i > $o))]: ((! [B:$i,C:($i > $o)]: ~ (~ (! [D:$i]: (~ (A @ B @ D) | ~ (C @ D)) | ! [D:$i]: (~ (A @ B @ D) | (C @ D))) | ~ (~ (! [D:$i]: (~ (A @ B @ D) | (C @ D))) | ~ (! [D:$i]: (~ (A @ B @ D) | ~ (C @ D)))))) => (! [B:$i]: ? [C:$i]: ((A @ B @ C) & ! [D:$i]: ((A @ B @ D) => (C = D)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])).
% 21.96/6.89 thf(4,plain,((~ (! [A:($i > ($i > $o))]: ((~ (~ (! [B:$i,C:($i > $o)]: (! [D:$i]: (~ (A @ B @ D) | ~ (C @ D)) | ! [D:$i]: (~ (A @ B @ D) | (C @ D)))) | ~ (! [B:$i,C:($i > $o)]: (~ (! [D:$i]: (~ (A @ B @ D) | (C @ D))) | ~ (! [D:$i]: (~ (A @ B @ D) | ~ (C @ D))))))) => (! [B:$i]: ? [C:$i]: ((A @ B @ C) & ! [D:$i]: ((A @ B @ D) => (C = D)))))))),inference(miniscope,[status(thm)],[3])).
% 21.96/6.89 thf(5,plain,(! [G:$i,F:($i > $o),E:$i,D:$i,C:$i,B:($i > $o),A:$i] : (((~ (sk1 @ A @ C) | ~ (B @ C) | ~ (sk1 @ A @ D) | (B @ D)) & ((sk1 @ E @ (sk2 @ (F) @ E)) | (sk1 @ E @ (sk3 @ (F) @ E))) & ((sk1 @ E @ (sk2 @ (F) @ E)) | (F @ (sk3 @ (F) @ E))) & (~ (F @ (sk2 @ (F) @ E)) | (sk1 @ E @ (sk3 @ (F) @ E))) & (~ (F @ (sk2 @ (F) @ E)) | (F @ (sk3 @ (F) @ E))) & (~ (sk1 @ sk4 @ G) | (sk1 @ sk4 @ (sk5 @ G))) & (~ (sk1 @ sk4 @ G) | ~ (G = (sk5 @ G)))))),inference(cnf,[status(esa)],[4])).
% 21.96/6.89 thf(8,plain,(! [B:($i > $o),A:$i] : ((sk1 @ A @ (sk2 @ (B) @ A)) | (B @ (sk3 @ (B) @ A)))),inference(cnfConj,[status(thm)],[5])).
% 21.96/6.89 thf(25,plain,(! [B:($i > $o),A:$i] : ((sk1 @ A @ (sk2 @ (B) @ A)) | (B @ (sk3 @ (B) @ A)))),inference(simp,[status(thm)],[8])).
% 21.96/6.89 thf(114,plain,(! [A:$i] : ((sk1 @ A @ (sk2 @ (^ [B:$i]: (($false))) @ A)) | ($false))),inference(prim_subst,[status(thm)],[25:[bind(A, $thf(A)),bind(B, $thf(^ [C:$i]: (($false))))]])).
% 21.96/6.89 thf(126,plain,(! [A:$i] : ((sk1 @ A @ (sk2 @ (^ [B:$i]: (($false))) @ A)))),inference(simp,[status(thm)],[114])).
% 21.96/6.89 thf(6,plain,(! [A:$i] : ((~ (sk1 @ sk4 @ A)) | (sk1 @ sk4 @ (sk5 @ A)))),inference(cnfConj,[status(thm)],[5])).
% 21.96/6.89 thf(18,plain,(! [A:$i] : ((~ (sk1 @ sk4 @ A)) | (sk1 @ sk4 @ (sk5 @ A)))),inference(simp,[status(thm)],[6])).
% 21.96/6.89 thf(151,plain,(! [B:$i,A:$i] : (~ (($true)) | (sk1 @ sk4 @ (sk5 @ B)) | ((sk1 @ A @ (sk2 @ (^ [C:$i]: (($false))) @ A)) != (sk1 @ sk4 @ B)))),inference(paramod_ordered,[status(thm)],[126,18])).
% 21.96/6.89 thf(152,plain,(! [B:$i,A:$i] : ((sk1 @ sk4 @ (sk5 @ B)) | ((sk1 @ A @ (sk2 @ (^ [C:$i]: (($false))) @ A)) != (sk1 @ sk4 @ B)))),inference(simp,[status(thm)],[151])).
% 21.96/6.89 thf(153,plain,((sk1 @ sk4 @ (sk5 @ (sk2 @ (^ [A:$i]: (($false))) @ sk4)))),inference(pattern_uni,[status(thm)],[152:[bind(A, $thf(sk4)),bind(B, $thf(sk2 @ (^ [C:$i]: (($false))) @ sk4))]])).
% 21.96/6.89 thf(9,plain,(! [D:$i,C:$i,B:($i > $o),A:$i] : ((~ (sk1 @ A @ C)) | (~ (B @ C)) | (~ (sk1 @ A @ D)) | (B @ D))),inference(cnfConj,[status(thm)],[5])).
% 21.96/6.89 thf(177,plain,(! [D:$i,C:$i,B:($i > $o),A:$i] : (~ (($true)) | (~ (B @ C)) | (~ (sk1 @ A @ D)) | (B @ D) | ((sk1 @ sk4 @ (sk5 @ (sk2 @ (^ [E:$i]: (($false))) @ sk4))) != (sk1 @ A @ C)))),inference(paramod_ordered,[status(thm)],[153,9])).
% 21.96/6.89 thf(178,plain,(! [D:$i,C:$i,B:($i > $o),A:$i] : ((~ (B @ C)) | (~ (sk1 @ A @ D)) | (B @ D) | ((sk1 @ sk4 @ (sk5 @ (sk2 @ (^ [E:$i]: (($false))) @ sk4))) != (sk1 @ A @ C)))),inference(simp,[status(thm)],[177])).
% 21.96/6.89 thf(179,plain,(! [B:$i,A:($i > $o)] : ((~ (A @ (sk5 @ (sk2 @ (^ [C:$i]: (($false))) @ sk4)))) | (~ (sk1 @ sk4 @ B)) | (A @ B))),inference(pattern_uni,[status(thm)],[178:[bind(A, $thf(sk4)),bind(B, $thf(B)),bind(C, $thf(sk5 @ (sk2 @ (^ [E:$i]: (($false))) @ sk4))),bind(D, $thf(D))]])).
% 21.96/6.89 thf(258,plain,(! [A:$i] : ((~ ((sk5 @ (sk2 @ (^ [B:$i]: (($false))) @ sk4)) = (sk5 @ (sk2 @ (^ [B:$i]: (($false))) @ sk4)))) | (~ (sk1 @ sk4 @ A)) | ((sk5 @ (sk2 @ (^ [B:$i]: (($false))) @ sk4)) = A))),inference(replace_leibeq,[status(thm)],[179:[bind(A, $thf((=) @ $i @ (sk5 @ (sk2 @ (^ [C:$i]: (($false))) @ sk4))))]])).
% 21.96/6.89 thf(284,plain,(! [A:$i] : (((sk5 @ (sk2 @ (^ [B:$i]: (($false))) @ sk4)) != (sk5 @ (sk2 @ (^ [B:$i]: (($false))) @ sk4))) | ((sk5 @ (sk2 @ (^ [B:$i]: (($false))) @ sk4)) = A) | (~ (sk1 @ sk4 @ A)))),inference(lifteq,[status(thm)],[258])).
% 21.96/6.89 thf(288,plain,(! [A:$i] : ((~ (sk1 @ sk4 @ A)) | ((sk5 @ (sk2 @ (^ [B:$i]: (($false))) @ sk4)) = A))),inference(pattern_uni,[status(thm)],[284:[]])).
% 21.96/6.89 thf(355,plain,(! [A:$i] : ((~ (sk1 @ sk4 @ A)) | ((sk5 @ (sk2 @ (^ [B:$i]: (($false))) @ sk4)) = A))),inference(simp,[status(thm)],[288])).
% 21.96/6.89 thf(7,plain,(! [A:$i] : ((~ (sk1 @ sk4 @ A)) | (~ (A = (sk5 @ A))))),inference(cnfConj,[status(thm)],[5])).
% 21.96/6.89 thf(22,plain,(! [A:$i] : (((sk5 @ A) != A) | (~ (sk1 @ sk4 @ A)))),inference(lifteq,[status(thm)],[7])).
% 21.96/6.89 thf(23,plain,(! [A:$i] : (((sk5 @ A) != A) | (~ (sk1 @ sk4 @ A)))),inference(simp,[status(thm)],[22])).
% 21.96/6.89 thf(145,plain,(! [B:$i,A:$i] : (((sk5 @ B) != B) | ~ (($true)) | ((sk1 @ A @ (sk2 @ (^ [C:$i]: (($false))) @ A)) != (sk1 @ sk4 @ B)))),inference(paramod_ordered,[status(thm)],[126,23])).
% 21.96/6.89 thf(146,plain,(! [B:$i,A:$i] : (((sk5 @ B) != B) | ((sk1 @ A @ (sk2 @ (^ [C:$i]: (($false))) @ A)) != (sk1 @ sk4 @ B)))),inference(simp,[status(thm)],[145])).
% 21.96/6.89 thf(147,plain,(((sk5 @ (sk2 @ (^ [A:$i]: (($false))) @ sk4)) != (sk2 @ (^ [A:$i]: (($false))) @ sk4))),inference(pattern_uni,[status(thm)],[146:[bind(A, $thf(sk4)),bind(B, $thf(sk2 @ (^ [C:$i]: (($false))) @ sk4))]])).
% 21.96/6.89 thf(1117,plain,(! [A:$i] : ((~ (sk1 @ sk4 @ A)) | (A != (sk2 @ (^ [B:$i]: (($false))) @ sk4)) | ((sk5 @ (sk2 @ (^ [B:$i]: (($false))) @ sk4)) != (sk5 @ (sk2 @ (^ [B:$i]: (($false))) @ sk4))))),inference(paramod_ordered,[status(thm)],[355,147])).
% 21.96/6.89 thf(1118,plain,(! [A:$i] : ((~ (sk1 @ sk4 @ A)) | (A != (sk2 @ (^ [B:$i]: (($false))) @ sk4)))),inference(pattern_uni,[status(thm)],[1117:[]])).
% 21.96/6.89 thf(1411,plain,((~ (sk1 @ sk4 @ (sk2 @ (^ [A:$i]: (($false))) @ sk4)))),inference(simp,[status(thm)],[1118])).
% 21.96/6.89 thf(2093,plain,(~ (($true))),inference(rewrite,[status(thm)],[1411,126])).
% 21.96/6.89 thf(2094,plain,(($false)),inference(simp,[status(thm)],[2093])).
% 21.96/6.89 % SZS output end Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% 21.96/6.89 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------