%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYO445^1 : 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 : n015.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 08:45:48 AM UTC 2026
% Result : Theorem 3.89s 2.35s
% Output : Refutation 4.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO445^1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % 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
% 0.10/0.21 % Computer : n015.cluster.edu
% 0.10/0.21 % Model : x86_64 x86_64
% 0.10/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.21 % Memory : 8046.5625MB
% 0.10/0.21 % OS : Linux 6.8.0-71-generic
% 0.10/0.21 % CPULimit : 300
% 0.10/0.21 % WCLimit : 300
% 0.10/0.21 % DateTime : Tue Sep 29 16:55:18 UTC 2026
% 0.10/0.21 % CPUTime :
% 0.10/0.21 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
% 0.88/0.79 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.51/1.12 % [INFO] Parsing done (323ms).
% 1.51/1.14 % [INFO] Running in sequential loop mode.
% 2.32/1.52 % [INFO] eprover registered as external prover.
% 2.32/1.53 % [INFO] Scanning for conjecture ...
% 2.71/1.70 % [INFO] Found a conjecture (or negated_conjecture) and 3 axioms. Running axiom selection ...
% 2.71/1.73 % [INFO] Axiom selection finished. Selected 3 axioms (removed 0 axioms).
% 2.71/1.73 % [INFO] Problem is higher-order (TPTP THF).
% 2.71/1.73 % [INFO] Type checking passed.
% 2.71/1.74 % [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 ...
% 3.89/2.35 % External prover 'e' found a proof!
% 3.89/2.35 % [INFO] Killing All external provers ...
% 3.89/2.35 % Time passed: 1990ms (effective reasoning time: 1205ms)
% 3.89/2.35 % 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)>
% 3.89/2.35 % Axioms used in derivation (3): a1, a2, a3
% 3.89/2.35 % No. of inferences in proof: 10
% 3.89/2.35 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1990 ms resp. 1205 ms w/o parsing
% 4.18/2.41 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.18/2.41 thf(mu_type, type, mu: $tType).
% 4.18/2.41 thf(mnot_decl, type, mnot: (($i > $o) > ($i > $o))).
% 4.18/2.41 thf(mor_decl, type, mor: (($i > $o) > (($i > $o) > ($i > $o)))).
% 4.18/2.41 thf(mand_decl, type, mand: (($i > $o) > (($i > $o) > ($i > $o)))).
% 4.18/2.41 thf(mimplies_decl, type, mimplies: (($i > $o) > (($i > $o) > ($i > $o)))).
% 4.18/2.41 thf(mequiv_decl, type, mequiv: (($i > $o) > (($i > $o) > ($i > $o)))).
% 4.18/2.41 thf(mreflexive_decl, type, mreflexive: (($i > ($i > $o)) > $o)).
% 4.18/2.41 thf(msymmetric_decl, type, msymmetric: (($i > ($i > $o)) > $o)).
% 4.18/2.41 thf(mtransitive_decl, type, mtransitive: (($i > ($i > $o)) > $o)).
% 4.18/2.41 thf(mvalid_decl, type, mvalid: (($i > $o) > $o)).
% 4.18/2.41 thf(rel_s5_decl, type, rel_s5: ($i > ($i > $o))).
% 4.18/2.41 thf(mbox_s5_decl, type, mbox_s5: (($i > $o) > ($i > $o))).
% 4.18/2.41 thf(mdia_s5_decl, type, mdia_s5: (($i > $o) > ($i > $o))).
% 4.18/2.41 thf(p_decl, type, p: ($i > $o)).
% 4.18/2.41 thf(q_decl, type, q: ($i > $o)).
% 4.18/2.41 thf(mnot_def, definition, mnot = (^ [A:($i > $o),B:$i]: ~ (A @ B)) ).
% 4.18/2.41 thf(mor_def, definition, mor = (^ [A:($i > $o),B:($i > $o),C:$i]: ((A @ C) | (B @ C))) ).
% 4.18/2.41 thf(mand_def, definition, mand = (^ [A:($i > $o),B:($i > $o)]: (mnot @ (mor @ (mnot @ A) @ (mnot @ B)))) ).
% 4.18/2.41 thf(mimplies_def, definition, mimplies = (^ [A:($i > $o)]: (mor @ (mnot @ A))) ).
% 4.18/2.41 thf(mequiv_def, definition, mequiv = (^ [A:($i > $o),B:($i > $o)]: (mand @ (mimplies @ A @ B) @ (mimplies @ B @ A))) ).
% 4.18/2.41 thf(mreflexive_def, definition, mreflexive = (^ [A:($i > ($i > $o))]: ! [B:$i]: (A @ B @ B)) ).
% 4.18/2.41 thf(msymmetric_def, definition, msymmetric = (^ [A:($i > ($i > $o))]: ! [B:$i,C:$i]: ((A @ B @ C) => (A @ C @ B))) ).
% 4.18/2.41 thf(mtransitive_def, definition, mtransitive = (^ [A:($i > ($i > $o))]: ! [B:$i,C:$i,D:$i]: (((A @ B @ C) & (A @ C @ D)) => (A @ B @ D))) ).
% 4.18/2.41 thf(mvalid_def, definition, mvalid = ((!) @ $i) ).
% 4.18/2.41 thf(mbox_s5_def, definition, mbox_s5 = (^ [A:($i > $o),B:$i]: ! [C:$i]: (~ (rel_s5 @ B @ C) | (A @ C))) ).
% 4.18/2.41 thf(mdia_s5_def, definition, mdia_s5 = (^ [A:($i > $o)]: (mnot @ (mbox_s5 @ (mnot @ A)))) ).
% 4.18/2.41 thf(1,conjecture,((mvalid @ (mequiv @ (mor @ (mbox_s5 @ p) @ (mdia_s5 @ q)) @ (mbox_s5 @ (mor @ p @ (mdia_s5 @ q)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove)).
% 4.18/2.41 thf(2,negated_conjecture,((~ (mvalid @ (mequiv @ (mor @ (mbox_s5 @ p) @ (mdia_s5 @ q)) @ (mbox_s5 @ (mor @ p @ (mdia_s5 @ q))))))),inference(neg_conjecture,[status(cth)],[1])).
% 4.18/2.41 thf(6,plain,((~ (! [A:$i]: ~ (~ (~ (! [B:$i]: (~ (rel_s5 @ A @ B) | (p @ B)) | ~ (! [B:$i]: (~ (rel_s5 @ A @ B) | ~ (q @ B)))) | ! [B:$i]: (~ (rel_s5 @ A @ B) | (p @ B) | ~ (! [C:$i]: (~ (rel_s5 @ B @ C) | ~ (q @ C))))) | ~ (~ (! [B:$i]: (~ (rel_s5 @ A @ B) | (p @ B) | ~ (! [C:$i]: (~ (rel_s5 @ B @ C) | ~ (q @ C))))) | ! [B:$i]: (~ (rel_s5 @ A @ B) | (p @ B)) | ~ (! [B:$i]: (~ (rel_s5 @ A @ B) | ~ (q @ B)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])).
% 4.18/2.41 thf(3,axiom,((mreflexive @ rel_s5)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a1)).
% 4.18/2.41 thf(23,plain,((! [A:$i]: (rel_s5 @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3])).
% 4.18/2.41 thf(4,axiom,((mtransitive @ rel_s5)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a2)).
% 4.18/2.41 thf(25,plain,((! [A:$i,B:$i,C:$i]: (((rel_s5 @ A @ B) & (rel_s5 @ B @ C)) => (rel_s5 @ A @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4])).
% 4.18/2.41 thf(5,axiom,((msymmetric @ rel_s5)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a3)).
% 4.18/2.41 thf(27,plain,((! [A:$i,B:$i]: ((rel_s5 @ A @ B) => (rel_s5 @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5])).
% 4.18/2.41 thf(29,plain,(($false)),inference(e,[status(thm)],[6,23,25,27])).
% 4.18/2.41 % SZS output end Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.18/2.41 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------