%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LCL713^1 : TPTP v9.3.1. Bugfixed v5.0.0.
% 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 : 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 08:14:11 AM UTC 2026
% Result : Theorem 8.72s 3.32s
% Output : Refutation 8.72s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL713^1 : TPTP v9.3.1. Bugfixed v5.0.0.
% 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
% 0.10/0.22 % Computer : n002.cluster.edu
% 0.10/0.22 % Model : x86_64 x86_64
% 0.10/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.22 % Memory : 8046.5625MB
% 0.10/0.22 % 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 09:50:07 UTC 2026
% 0.10/0.22 % CPUTime :
% 0.10/0.22 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
% 0.98/0.80 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.47/1.06 % [INFO] Parsing done (254ms).
% 1.47/1.07 % [INFO] Running in sequential loop mode.
% 2.14/1.46 % [INFO] eprover registered as external prover.
% 2.14/1.47 % [INFO] Scanning for conjecture ...
% 2.57/1.63 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.57/1.67 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.57/1.67 % [INFO] Problem is higher-order (TPTP THF).
% 2.57/1.67 % [INFO] Type checking passed.
% 2.57/1.68 % [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 ...
% 8.72/3.31 % [INFO] Killing All external provers ...
% 8.72/3.31 % Time passed: 2952ms (effective reasoning time: 2232ms)
% 8.72/3.31 % 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)>
% 8.72/3.31 % Axioms used in derivation (0):
% 8.72/3.31 % No. of inferences in proof: 27
% 8.72/3.32 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2952 ms resp. 2232 ms w/o parsing
% 8.72/3.37 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.72/3.37 thf(mu_type, type, mu: $tType).
% 8.72/3.37 thf(mnot_decl, type, mnot: (($i > $o) > ($i > $o))).
% 8.72/3.37 thf(mor_decl, type, mor: (($i > $o) > (($i > $o) > ($i > $o)))).
% 8.72/3.37 thf(mimplies_decl, type, mimplies: (($i > $o) > (($i > $o) > ($i > $o)))).
% 8.72/3.37 thf(mforall_prop_decl, type, mforall_prop: ((($i > $o) > ($i > $o)) > ($i > $o))).
% 8.72/3.37 thf(mbox_decl, type, mbox: (($i > ($i > $o)) > (($i > $o) > ($i > $o)))).
% 8.72/3.37 thf(mdia_decl, type, mdia: (($i > ($i > $o)) > (($i > $o) > ($i > $o)))).
% 8.72/3.37 thf(meuclidean_decl, type, meuclidean: (($i > ($i > $o)) > $o)).
% 8.72/3.37 thf(mvalid_decl, type, mvalid: (($i > $o) > $o)).
% 8.72/3.37 thf(sk1_decl, type, sk1: ($i > ($i > $o))).
% 8.72/3.37 thf(sk2_decl, type, sk2: ($i > (($i > $o) > ($i > $i)))).
% 8.72/3.37 thf(sk3_decl, type, sk3: $i).
% 8.72/3.37 thf(sk4_decl, type, sk4: $i).
% 8.72/3.37 thf(sk5_decl, type, sk5: $i).
% 8.72/3.37 thf(mnot_def, definition, mnot = (^ [A:($i > $o),B:$i]: ~ (A @ B)) ).
% 8.72/3.37 thf(mor_def, definition, mor = (^ [A:($i > $o),B:($i > $o),C:$i]: ((A @ C) | (B @ C))) ).
% 8.72/3.37 thf(mimplies_def, definition, mimplies = (^ [A:($i > $o)]: (mor @ (mnot @ A))) ).
% 8.72/3.37 thf(mforall_prop_def, definition, mforall_prop = (^ [A:(($i > $o) > ($i > $o)),B:$i]: ! [C:($i > $o)]: (A @ C @ B)) ).
% 8.72/3.37 thf(mbox_def, definition, mbox = (^ [A:($i > ($i > $o)),B:($i > $o),C:$i]: ! [D:$i]: (~ (A @ C @ D) | (B @ D))) ).
% 8.72/3.37 thf(mdia_def, definition, mdia = (^ [A:($i > ($i > $o)),B:($i > $o)]: (mnot @ (mbox @ A @ (mnot @ B)))) ).
% 8.72/3.37 thf(meuclidean_def, definition, meuclidean = (^ [A:($i > ($i > $o))]: ! [B:$i,C:$i,D:$i]: (((A @ B @ C) & (A @ B @ D)) => (A @ C @ D))) ).
% 8.72/3.37 thf(mvalid_def, definition, mvalid = ((!) @ $i) ).
% 8.72/3.37 thf(sk1_def, definition, sk1 = (@+ [A:($i > ($i > $o))]: ~ ((! [B:$i,C:($i > $o)]: (! [D:$i]: (~ (A @ B @ D) | ~ (C @ D)) | ! [D:$i]: (~ (A @ B @ D) | ~ (! [E:$i]: (~ (A @ D @ E) | ~ (C @ E)))))) => (! [B:$i,C:$i,D:$i]: (((A @ B @ C) & (A @ B @ D)) => (A @ C @ D))))) ).
% 8.72/3.37 thf(sk2_def, definition, sk2 = (^ [A:$i,B:($i > $o),C:$i]: (@+ [D:$i]: ~ (~ (sk1 @ A @ D) | ~ (B @ D)))) ).
% 8.72/3.37 thf(sk3_def, definition, sk3 = (@+ [A:$i]: ~ (! [B:$i,C:$i]: (((sk1 @ A @ B) & (sk1 @ A @ C)) => (sk1 @ B @ C)))) ).
% 8.72/3.37 thf(sk4_def, definition, sk4 = (@+ [A:$i]: ~ (! [B:$i]: (((sk1 @ sk3 @ A) & (sk1 @ sk3 @ B)) => (sk1 @ A @ B)))) ).
% 8.72/3.37 thf(sk5_def, definition, sk5 = (@+ [A:$i]: ~ (((sk1 @ sk3 @ sk4) & (sk1 @ sk3 @ A)) => (sk1 @ sk4 @ A))) ).
% 8.72/3.37 thf(1,conjecture,((! [A:($i > ($i > $o))]: ((mvalid @ (mforall_prop @ (^ [B:($i > $o)]: (mimplies @ (mdia @ A @ B) @ (mbox @ A @ (mdia @ A @ B)))))) => (meuclidean @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj)).
% 8.72/3.37 thf(2,negated_conjecture,((~ (! [A:($i > ($i > $o))]: ((mvalid @ (mforall_prop @ (^ [B:($i > $o)]: (mimplies @ (mdia @ A @ B) @ (mbox @ A @ (mdia @ A @ B)))))) => (meuclidean @ A))))),inference(neg_conjecture,[status(cth)],[1])).
% 8.72/3.37 thf(3,plain,((~ (! [A:($i > ($i > $o))]: ((! [B:$i,C:($i > $o)]: (! [D:$i]: (~ (A @ B @ D) | ~ (C @ D)) | ! [D:$i]: (~ (A @ B @ D) | ~ (! [E:$i]: (~ (A @ D @ E) | ~ (C @ E)))))) => (! [B:$i,C:$i,D:$i]: (((A @ B @ C) & (A @ B @ D)) => (A @ C @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])).
% 8.72/3.37 thf(4,plain,(! [D:$i,C:$i,B:($i > $o),A:$i] : (((~ (sk1 @ A @ C) | ~ (B @ C) | ~ (sk1 @ A @ D) | (sk1 @ D @ (sk2 @ D @ (B) @ A))) & (~ (sk1 @ A @ C) | ~ (B @ C) | ~ (sk1 @ A @ D) | (B @ (sk2 @ D @ (B) @ A))) & (sk1 @ sk3 @ sk4) & (sk1 @ sk3 @ sk5) & ~ (sk1 @ sk4 @ sk5)))),inference(cnf,[status(esa)],[3])).
% 8.72/3.37 thf(7,plain,((sk1 @ sk3 @ sk5)),inference(cnfConj,[status(thm)],[4])).
% 8.72/3.37 thf(6,plain,(! [D:$i,C:$i,B:($i > $o),A:$i] : ((~ (sk1 @ A @ C)) | (~ (B @ C)) | (~ (sk1 @ A @ D)) | (B @ (sk2 @ D @ (B) @ A)))),inference(cnfConj,[status(thm)],[4])).
% 8.72/3.37 thf(36,plain,(! [D:$i,C:$i,B:($i > $o),A:$i] : (~ (($true)) | (~ (B @ C)) | (~ (sk1 @ A @ D)) | (B @ (sk2 @ D @ (B) @ A)) | ((sk1 @ sk3 @ sk5) != (sk1 @ A @ C)))),inference(paramod_ordered,[status(thm)],[7,6])).
% 8.72/3.37 thf(37,plain,(! [D:$i,C:$i,B:($i > $o),A:$i] : ((~ (B @ C)) | (~ (sk1 @ A @ D)) | (B @ (sk2 @ D @ (B) @ A)) | ((sk1 @ sk3 @ sk5) != (sk1 @ A @ C)))),inference(simp,[status(thm)],[36])).
% 8.72/3.37 thf(38,plain,(! [B:$i,A:($i > $o)] : ((~ (A @ sk5)) | (~ (sk1 @ sk3 @ B)) | (A @ (sk2 @ B @ (A) @ sk3)))),inference(pattern_uni,[status(thm)],[37:[bind(A, $thf(sk3)),bind(B, $thf(B)),bind(C, $thf(sk5))]])).
% 8.72/3.37 thf(56,plain,(! [A:$i] : ((~ (sk5 = sk5)) | (~ (sk1 @ sk3 @ A)) | (sk5 = (sk2 @ A @ ((=) @ $i @ sk5) @ sk3)))),inference(replace_leibeq,[status(thm)],[38:[bind(A, $thf((=) @ $i @ sk5))]])).
% 8.72/3.37 thf(61,plain,(! [A:$i] : ((sk5 != sk5) | ((sk2 @ A @ ((=) @ $i @ sk5) @ sk3) = sk5) | (~ (sk1 @ sk3 @ A)))),inference(lifteq,[status(thm)],[56])).
% 8.72/3.37 thf(71,plain,(! [A:$i] : ((~ (sk1 @ sk3 @ A)) | ((sk2 @ A @ ((=) @ $i @ sk5) @ sk3) = sk5))),inference(pattern_uni,[status(thm)],[61:[]])).
% 8.72/3.37 thf(96,plain,(! [A:$i] : ((~ (sk1 @ sk3 @ A)) | ((sk2 @ A @ ((=) @ $i @ sk5) @ sk3) = sk5))),inference(simp,[status(thm)],[71])).
% 8.72/3.37 thf(8,plain,(! [D:$i,C:$i,B:($i > $o),A:$i] : ((~ (sk1 @ A @ C)) | (~ (B @ C)) | (~ (sk1 @ A @ D)) | (sk1 @ D @ (sk2 @ D @ (B) @ A)))),inference(cnfConj,[status(thm)],[4])).
% 8.72/3.37 thf(5,plain,((~ (sk1 @ sk4 @ sk5))),inference(cnfConj,[status(thm)],[4])).
% 8.72/3.37 thf(163,plain,(! [D:$i,C:$i,B:($i > $o),A:$i] : ((~ (sk1 @ A @ C)) | (~ (B @ C)) | (~ (sk1 @ A @ D)) | ~ (($true)) | ((sk1 @ D @ (sk2 @ D @ (B) @ A)) != (sk1 @ sk4 @ sk5)))),inference(paramod_ordered,[status(thm)],[8,5])).
% 8.72/3.37 thf(164,plain,(! [D:$i,C:$i,B:($i > $o),A:$i] : ((~ (sk1 @ A @ C)) | (~ (B @ C)) | (~ (sk1 @ A @ D)) | ((sk1 @ D @ (sk2 @ D @ (B) @ A)) != (sk1 @ sk4 @ sk5)))),inference(simp,[status(thm)],[163])).
% 8.72/3.37 thf(231,plain,(! [D:$i,C:$i,B:($i > $o),A:$i] : ((~ (sk1 @ A @ C)) | (~ (B @ C)) | (~ (sk1 @ A @ D)) | (D != sk4) | ((sk2 @ D @ (B) @ A) != sk5))),inference(simp,[status(thm)],[164])).
% 8.72/3.37 thf(272,plain,(! [C:$i,B:($i > $o),A:$i] : ((~ (sk1 @ A @ C)) | (~ (B @ C)) | (~ (sk1 @ A @ sk4)) | ((sk2 @ sk4 @ (B) @ A) != sk5))),inference(simp,[status(thm)],[231])).
% 8.72/3.37 thf(417,plain,(! [D:$i,C:($i > $o),B:$i,A:$i] : ((~ (sk1 @ sk3 @ A)) | (~ (sk1 @ B @ D)) | (~ (C @ D)) | (~ (sk1 @ B @ sk4)) | (sk5 != sk5) | ((sk2 @ A @ ((=) @ $i @ sk5) @ sk3) != (sk2 @ sk4 @ (C) @ B)))),inference(paramod_ordered,[status(thm)],[96,272])).
% 8.72/3.37 thf(418,plain,(! [D:$i,C:($i > $o),B:$i,A:$i] : ((~ (sk1 @ sk3 @ A)) | (~ (sk1 @ B @ D)) | (~ (C @ D)) | (~ (sk1 @ B @ sk4)) | ((sk2 @ A @ ((=) @ $i @ sk5) @ sk3) != (sk2 @ sk4 @ (C) @ B)))),inference(simp,[status(thm)],[417])).
% 8.72/3.37 thf(419,plain,(! [A:$i] : ((~ (sk1 @ sk3 @ sk4)) | (~ (sk1 @ sk3 @ A)) | (~ (sk5 = A)) | (~ (sk1 @ sk3 @ sk4)))),inference(pattern_uni,[status(thm)],[418:[bind(A, $thf(sk4)),bind(B, $thf(sk3)),bind(C, $thf((=) @ $i @ sk5)),bind(D, $thf(D))]])).
% 8.72/3.37 thf(442,plain,(! [A:$i] : ((sk5 != A) | (~ (sk1 @ sk3 @ sk4)) | (~ (sk1 @ sk3 @ A)) | (~ (sk1 @ sk3 @ sk4)))),inference(lifteq,[status(thm)],[419])).
% 8.72/3.37 thf(494,plain,((~ (sk1 @ sk3 @ sk4)) | (~ (sk1 @ sk3 @ sk5))),inference(simp,[status(thm)],[442])).
% 8.72/3.37 thf(9,plain,((sk1 @ sk3 @ sk4)),inference(cnfConj,[status(thm)],[4])).
% 8.72/3.37 thf(705,plain,(~ (($true)) | ~ (($true))),inference(rewrite,[status(thm)],[494,7,9])).
% 8.72/3.37 thf(706,plain,(($false)),inference(simp,[status(thm)],[705])).
% 8.72/3.37 % SZS output end Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.72/3.37 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------