%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LCL714^1 : 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 : n007.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 4.36s 1.76s
% Output : Refutation 4.66s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL714^1 : TPTP v9.3.1. Bugfixed v5.0.0.
% 0.00/0.09 % 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
% 0.09/0.24 % Computer : n007.cluster.edu
% 0.09/0.24 % Model : x86_64 x86_64
% 0.09/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.24 % Memory : 8046.5625MB
% 0.09/0.24 % OS : Linux 6.8.0-71-generic
% 0.09/0.24 % CPULimit : 300
% 0.09/0.24 % WCLimit : 300
% 0.09/0.24 % DateTime : Tue Sep 29 09:46:40 UTC 2026
% 0.09/0.25 % CPUTime :
% 0.09/0.25 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
% 0.95/0.64 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.16/0.80 % [INFO] Parsing done (157ms).
% 1.53/0.80 % [INFO] Running in sequential loop mode.
% 1.78/1.03 % [INFO] eprover registered as external prover.
% 1.78/1.04 % [INFO] Scanning for conjecture ...
% 2.15/1.14 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.48/1.16 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.48/1.16 % [INFO] Problem is higher-order (TPTP THF).
% 2.48/1.16 % [INFO] Type checking passed.
% 2.48/1.17 % [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 ...
% 4.36/1.76 % External prover 'e' found a proof!
% 4.36/1.76 % [INFO] Killing All external provers ...
% 4.36/1.76 % Time passed: 1377ms (effective reasoning time: 951ms)
% 4.36/1.76 % 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)>
% 4.36/1.76 % Axioms used in derivation (0):
% 4.36/1.76 % No. of inferences in proof: 13
% 4.36/1.76 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1377 ms resp. 951 ms w/o parsing
% 4.66/1.86 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.66/1.86 thf(mu_type, type, mu: $tType).
% 4.66/1.86 thf(mnot_decl, type, mnot: (($i > $o) > ($i > $o))).
% 4.66/1.86 thf(mor_decl, type, mor: (($i > $o) > (($i > $o) > ($i > $o)))).
% 4.66/1.86 thf(mimplies_decl, type, mimplies: (($i > $o) > (($i > $o) > ($i > $o)))).
% 4.66/1.86 thf(mforall_prop_decl, type, mforall_prop: ((($i > $o) > ($i > $o)) > ($i > $o))).
% 4.66/1.86 thf(mbox_decl, type, mbox: (($i > ($i > $o)) > (($i > $o) > ($i > $o)))).
% 4.66/1.86 thf(mdia_decl, type, mdia: (($i > ($i > $o)) > (($i > $o) > ($i > $o)))).
% 4.66/1.86 thf(mpartially_functional_decl, type, mpartially_functional: (($i > ($i > $o)) > $o)).
% 4.66/1.86 thf(mvalid_decl, type, mvalid: (($i > $o) > $o)).
% 4.66/1.86 thf(sk1_decl, type, sk1: ($i > ($i > $o))).
% 4.66/1.86 thf(sk2_decl, type, sk2: $i).
% 4.66/1.86 thf(sk3_decl, type, sk3: $i).
% 4.66/1.86 thf(sk4_decl, type, sk4: $i).
% 4.66/1.86 thf(mnot_def, definition, mnot = (^ [A:($i > $o),B:$i]: ~ (A @ B)) ).
% 4.66/1.86 thf(mor_def, definition, mor = (^ [A:($i > $o),B:($i > $o),C:$i]: ((A @ C) | (B @ C))) ).
% 4.66/1.86 thf(mimplies_def, definition, mimplies = (^ [A:($i > $o)]: (mor @ (mnot @ A))) ).
% 4.66/1.86 thf(mforall_prop_def, definition, mforall_prop = (^ [A:(($i > $o) > ($i > $o)),B:$i]: ! [C:($i > $o)]: (A @ C @ B)) ).
% 4.66/1.86 thf(mbox_def, definition, mbox = (^ [A:($i > ($i > $o)),B:($i > $o),C:$i]: ! [D:$i]: (~ (A @ C @ D) | (B @ D))) ).
% 4.66/1.86 thf(mdia_def, definition, mdia = (^ [A:($i > ($i > $o)),B:($i > $o)]: (mnot @ (mbox @ A @ (mnot @ B)))) ).
% 4.66/1.86 thf(mpartially_functional_def, definition, mpartially_functional = (^ [A:($i > ($i > $o))]: ! [B:$i,C:$i,D:$i]: (((A @ B @ C) & (A @ B @ D)) => (C = D))) ).
% 4.66/1.86 thf(mvalid_def, definition, mvalid = ((!) @ $i) ).
% 4.66/1.86 thf(sk1_def, definition, sk1 = (@+ [A:($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:$i,D:$i]: (((A @ B @ C) & (A @ B @ D)) => (C = D))))) ).
% 4.66/1.86 thf(sk2_def, definition, sk2 = (@+ [A:$i]: ~ (! [B:$i,C:$i]: (((sk1 @ A @ B) & (sk1 @ A @ C)) => (B = C)))) ).
% 4.66/1.86 thf(sk3_def, definition, sk3 = (@+ [A:$i]: ~ (! [B:$i]: (((sk1 @ sk2 @ A) & (sk1 @ sk2 @ B)) => (A = B)))) ).
% 4.66/1.86 thf(sk4_def, definition, sk4 = (@+ [A:$i]: ~ (((sk1 @ sk2 @ sk3) & (sk1 @ sk2 @ A)) => (sk3 = A))) ).
% 4.66/1.86 thf(1,conjecture,((! [A:($i > ($i > $o))]: ((mvalid @ (mforall_prop @ (^ [B:($i > $o)]: (mimplies @ (mdia @ A @ B) @ (mbox @ A @ B))))) => (mpartially_functional @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj)).
% 4.66/1.86 thf(2,negated_conjecture,((~ (! [A:($i > ($i > $o))]: ((mvalid @ (mforall_prop @ (^ [B:($i > $o)]: (mimplies @ (mdia @ A @ B) @ (mbox @ A @ B))))) => (mpartially_functional @ A))))),inference(neg_conjecture,[status(cth)],[1])).
% 4.66/1.86 thf(3,plain,((~ (! [A:($i > ($i > $o))]: ((! [B:$i,C:($i > $o)]: (! [D:$i]: (~ (A @ B @ D) | ~ (C @ D)) | ! [D:$i]: (~ (A @ B @ D) | (C @ D)))) => (! [B:$i,C:$i,D:$i]: (((A @ B @ C) & (A @ B @ D)) => (C = D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])).
% 4.66/1.86 thf(4,plain,(! [D:$i,C:$i,B:($i > $o),A:$i] : (((~ (sk1 @ A @ C) | ~ (B @ C) | ~ (sk1 @ A @ D) | (B @ D)) & (sk1 @ sk2 @ sk3) & (sk1 @ sk2 @ sk4) & ~ (sk3 = sk4)))),inference(cnf,[status(esa)],[3])).
% 4.66/1.86 thf(6,plain,((sk1 @ sk2 @ sk3)),inference(cnfConj,[status(thm)],[4])).
% 4.66/1.86 thf(8,plain,((~ (sk3 = sk4))),inference(cnfConj,[status(thm)],[4])).
% 4.66/1.86 thf(12,plain,((sk4 != sk3)),inference(lifteq,[status(thm)],[8])).
% 4.66/1.86 thf(7,plain,((sk1 @ sk2 @ sk4)),inference(cnfConj,[status(thm)],[4])).
% 4.66/1.86 thf(5,plain,(! [D:$i,C:$i,B:($i > $o),A:$i] : ((~ (sk1 @ A @ C)) | (~ (B @ C)) | (~ (sk1 @ A @ D)) | (B @ D))),inference(cnfConj,[status(thm)],[4])).
% 4.66/1.86 thf(9,plain,(! [C:$i,B:$i,A:$i] : ((~ (sk1 @ A @ B)) | (~ (B = B)) | (~ (sk1 @ A @ C)) | (B = C))),inference(replace_leibeq,[status(thm)],[5:[bind(A, $thf(A)),bind(B, $thf((=) @ $i @ C))]])).
% 4.66/1.86 thf(10,plain,(! [C:$i,B:$i,A:$i] : ((B != B) | (B = C) | (~ (sk1 @ A @ B)) | (~ (sk1 @ A @ C)))),inference(lifteq,[status(thm)],[9])).
% 4.66/1.86 thf(11,plain,(! [C:$i,B:$i,A:$i] : ((B = C) | (~ (sk1 @ A @ B)) | (~ (sk1 @ A @ C)))),inference(simp,[status(thm)],[10])).
% 4.66/1.86 thf(88,plain,(($false)),inference(e,[status(thm)],[6,12,7,3,11])).
% 4.66/1.86 % SZS output end Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.66/1.86 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------