%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYO050^2 : TPTP v9.3.1. Released v4.0.0.
% 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 : n009.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 08:45:06 AM UTC 2026
% Result : Theorem 5.08s 2.66s
% Output : Refutation 5.42s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO050^2 : TPTP v9.3.1. Released v4.0.0.
% 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
% 0.08/0.22 % Computer : n009.cluster.edu
% 0.08/0.22 % Model : x86_64 x86_64
% 0.08/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.22 % Memory : 8046.5625MB
% 0.08/0.22 % OS : Linux 6.8.0-71-generic
% 0.08/0.22 % CPULimit : 300
% 0.08/0.22 % WCLimit : 300
% 0.08/0.22 % DateTime : Tue Sep 29 16:24:45 UTC 2026
% 0.08/0.22 % CPUTime :
% 0.08/0.22 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
% 1.04/0.81 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.49/1.09 % [INFO] Parsing done (276ms).
% 1.49/1.10 % [INFO] Running in sequential loop mode.
% 2.42/1.51 % [INFO] eprover registered as external prover.
% 2.42/1.51 % [INFO] Scanning for conjecture ...
% 2.62/1.69 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.86/1.72 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.86/1.73 % [INFO] Problem is higher-order (TPTP THF).
% 2.86/1.73 % [INFO] Type checking passed.
% 2.86/1.74 % [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 ...
% 5.08/2.66 % [INFO] Killing All external provers ...
% 5.08/2.66 % Time passed: 2291ms (effective reasoning time: 1548ms)
% 5.08/2.66 % 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)>
% 5.08/2.66 % Axioms used in derivation (0):
% 5.08/2.66 % No. of inferences in proof: 10
% 5.08/2.66 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2291 ms resp. 1548 ms w/o parsing
% 5.42/2.72 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.42/2.72 thf(mu_type, type, mu: $tType).
% 5.42/2.72 thf(mnot_decl, type, mnot: (($i > $o) > ($i > $o))).
% 5.42/2.72 thf(mor_decl, type, mor: (($i > $o) > (($i > $o) > ($i > $o)))).
% 5.42/2.72 thf(mimplies_decl, type, mimplies: (($i > $o) > (($i > $o) > ($i > $o)))).
% 5.42/2.72 thf(mforall_prop_decl, type, mforall_prop: ((($i > $o) > ($i > $o)) > ($i > $o))).
% 5.42/2.72 thf(mbox_decl, type, mbox: (($i > ($i > $o)) > (($i > $o) > ($i > $o)))).
% 5.42/2.72 thf(mvalid_decl, type, mvalid: (($i > $o) > $o)).
% 5.42/2.72 thf(sk1_decl, type, sk1: (($i > $o) > ($i > (($i > ($i > $o)) > $i)))).
% 5.42/2.72 thf(mnot_def, definition, mnot = (^ [A:($i > $o),B:$i]: ~ (A @ B)) ).
% 5.42/2.72 thf(mor_def, definition, mor = (^ [A:($i > $o),B:($i > $o),C:$i]: ((A @ C) | (B @ C))) ).
% 5.42/2.72 thf(mimplies_def, definition, mimplies = (^ [A:($i > $o)]: (mor @ (mnot @ A))) ).
% 5.42/2.72 thf(mforall_prop_def, definition, mforall_prop = (^ [A:(($i > $o) > ($i > $o)),B:$i]: ! [C:($i > $o)]: (A @ C @ B)) ).
% 5.42/2.72 thf(mbox_def, definition, mbox = (^ [A:($i > ($i > $o)),B:($i > $o),C:$i]: ! [D:$i]: (~ (A @ C @ D) | (B @ D))) ).
% 5.42/2.72 thf(mvalid_def, definition, mvalid = ((!) @ $i) ).
% 5.42/2.72 thf(sk1_def, definition, sk1 = (^ [A:($i > $o),B:$i,C:($i > ($i > $o))]: (@+ [D:$i]: ~ (~ (C @ B @ D) | (A @ D)))) ).
% 5.42/2.72 thf(1,conjecture,((? [A:($i > ($i > $o))]: ~ (mvalid @ (mforall_prop @ (^ [B:($i > $o)]: (mimplies @ (mbox @ A @ B) @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj)).
% 5.42/2.72 thf(2,negated_conjecture,((~ (? [A:($i > ($i > $o))]: ~ (mvalid @ (mforall_prop @ (^ [B:($i > $o)]: (mimplies @ (mbox @ A @ B) @ B))))))),inference(neg_conjecture,[status(cth)],[1])).
% 5.42/2.72 thf(3,plain,((~ (? [A:($i > ($i > $o))]: ~ (! [B:$i,C:($i > $o)]: (~ (! [D:$i]: (~ (A @ B @ D) | (C @ D))) | (C @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])).
% 5.42/2.72 thf(4,plain,((~ (~ (! [A:($i > ($i > $o)),B:$i,C:($i > $o)]: (~ (! [D:$i]: (~ (A @ B @ D) | (C @ D))) | (C @ B)))))),inference(miniscope,[status(thm)],[3])).
% 5.42/2.72 thf(5,plain,(! [C:($i > $o),B:$i,A:($i > ($i > $o))] : ((((A @ B @ (sk1 @ (C) @ B @ (A))) | (C @ B)) & (~ (C @ (sk1 @ (C) @ B @ (A))) | (C @ B))))),inference(cnf,[status(esa)],[4])).
% 5.42/2.72 thf(6,plain,(! [C:($i > $o),B:$i,A:($i > ($i > $o))] : ((A @ B @ (sk1 @ (C) @ B @ (A))) | (C @ B))),inference(cnfConj,[status(thm)],[5])).
% 5.42/2.72 thf(54,plain,(! [B:($i > $o),A:$i] : (($false) | (B @ A))),inference(prim_subst,[status(thm)],[6:[bind(A, $thf(^ [D:$i,E:$i]: (($false))))]])).
% 5.42/2.72 thf(72,plain,(! [B:($i > $o),A:$i] : ((B @ A))),inference(simp,[status(thm)],[54])).
% 5.42/2.72 thf(83,plain,(($false)),inference(prim_subst,[status(thm)],[72:[bind(A, $thf(A)),bind(B, $thf(^ [C:$i]: (($false))))]])).
% 5.42/2.72 thf(88,plain,(($false)),inference(simp,[status(thm)],[83])).
% 5.42/2.72 % SZS output end Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.42/2.72 % [INFO] Killing All external provers ...
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