%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYO458^2 : TPTP v9.3.1. Released v4.0.0.
% 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 : n012.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 08:45:52 AM UTC 2026
% Result : Theorem 2.04s 1.13s
% Output : Refutation 2.04s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SYO458^2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % 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
% 0.00/0.11 % Computer : n012.cluster.edu
% 0.00/0.11 % Model : x86_64 x86_64
% 0.00/0.11 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.11 % Memory : 8046.5625MB
% 0.00/0.11 % OS : Linux 6.8.0-71-generic
% 0.00/0.11 % CPULimit : 300
% 0.00/0.11 % WCLimit : 300
% 0.00/0.11 % DateTime : Tue Sep 29 16:57:18 UTC 2026
% 0.00/0.11 % CPUTime :
% 0.00/0.11 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
% 0.41/0.40 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.85/0.55 % [INFO] Parsing done (144ms).
% 0.85/0.55 % [INFO] Running in sequential loop mode.
% 1.08/0.74 % [INFO] eprover registered as external prover.
% 1.08/0.75 % [INFO] Scanning for conjecture ...
% 1.30/0.84 % [INFO] Found a conjecture (or negated_conjecture) and 1 axioms. Running axiom selection ...
% 1.30/0.85 % [INFO] Axiom selection finished. Selected 1 axioms (removed 0 axioms).
% 1.30/0.85 % [INFO] Problem is higher-order (TPTP THF).
% 1.30/0.86 % [INFO] Type checking passed.
% 1.30/0.86 % [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 ...
% 2.04/1.13 % External prover 'e' found a proof!
% 2.04/1.13 % [INFO] Killing All external provers ...
% 2.04/1.13 % Time passed: 951ms (effective reasoning time: 578ms)
% 2.04/1.13 % 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)>
% 2.04/1.13 % Axioms used in derivation (1): a1
% 2.04/1.13 % No. of inferences in proof: 6
% 2.04/1.13 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 951 ms resp. 578 ms w/o parsing
% 2.04/1.16 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.04/1.16 thf(mu_type, type, mu: $tType).
% 2.04/1.16 thf(mnot_decl, type, mnot: (($i > $o) > ($i > $o))).
% 2.04/1.16 thf(mor_decl, type, mor: (($i > $o) > (($i > $o) > ($i > $o)))).
% 2.04/1.16 thf(mand_decl, type, mand: (($i > $o) > (($i > $o) > ($i > $o)))).
% 2.04/1.16 thf(mimplies_decl, type, mimplies: (($i > $o) > (($i > $o) > ($i > $o)))).
% 2.04/1.16 thf(mequiv_decl, type, mequiv: (($i > $o) > (($i > $o) > ($i > $o)))).
% 2.04/1.16 thf(mserial_decl, type, mserial: (($i > ($i > $o)) > $o)).
% 2.04/1.16 thf(mvalid_decl, type, mvalid: (($i > $o) > $o)).
% 2.04/1.16 thf(rel_d_decl, type, rel_d: ($i > ($i > $o))).
% 2.04/1.16 thf(mbox_d_decl, type, mbox_d: (($i > $o) > ($i > $o))).
% 2.04/1.16 thf(p_decl, type, p: ($i > $o)).
% 2.04/1.16 thf(q_decl, type, q: ($i > $o)).
% 2.04/1.16 thf(mnot_def, definition, mnot = (^ [A:($i > $o),B:$i]: ~ (A @ B)) ).
% 2.04/1.16 thf(mor_def, definition, mor = (^ [A:($i > $o),B:($i > $o),C:$i]: ((A @ C) | (B @ C))) ).
% 2.04/1.16 thf(mand_def, definition, mand = (^ [A:($i > $o),B:($i > $o)]: (mnot @ (mor @ (mnot @ A) @ (mnot @ B)))) ).
% 2.04/1.16 thf(mimplies_def, definition, mimplies = (^ [A:($i > $o)]: (mor @ (mnot @ A))) ).
% 2.04/1.16 thf(mequiv_def, definition, mequiv = (^ [A:($i > $o),B:($i > $o)]: (mand @ (mimplies @ A @ B) @ (mimplies @ B @ A))) ).
% 2.04/1.16 thf(mserial_def, definition, mserial = (^ [A:($i > ($i > $o))]: ! [B:$i]: ? [C:$i]: (A @ B @ C)) ).
% 2.04/1.16 thf(mvalid_def, definition, mvalid = ((!) @ $i) ).
% 2.04/1.16 thf(mbox_d_def, definition, mbox_d = (^ [A:($i > $o),B:$i]: ! [C:$i]: (~ (rel_d @ B @ C) | (A @ C))) ).
% 2.04/1.16 thf(1,conjecture,((mvalid @ (mimplies @ (mand @ (mbox_d @ p) @ (mbox_d @ q)) @ (mbox_d @ (mequiv @ p @ q))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove)).
% 2.04/1.16 thf(2,negated_conjecture,((~ (mvalid @ (mimplies @ (mand @ (mbox_d @ p) @ (mbox_d @ q)) @ (mbox_d @ (mequiv @ p @ q)))))),inference(neg_conjecture,[status(cth)],[1])).
% 2.04/1.16 thf(4,plain,((~ (! [A:$i]: (~ (! [B:$i]: (~ (rel_d @ A @ B) | (p @ B))) | ~ (! [B:$i]: (~ (rel_d @ A @ B) | (q @ B))) | ! [B:$i]: (~ (rel_d @ A @ B) | ~ (~ (~ (p @ B) | (q @ B)) | ~ (~ (q @ B) | (p @ B)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])).
% 2.04/1.16 thf(3,axiom,((mserial @ rel_d)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a1)).
% 2.04/1.16 thf(14,plain,((! [A:$i]: ? [B:$i]: (rel_d @ A @ B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3])).
% 2.04/1.16 thf(16,plain,(($false)),inference(e,[status(thm)],[4,14])).
% 2.04/1.16 % SZS output end Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.04/1.16 % [INFO] Killing All external provers ...
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