%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYO482^6 : 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 : n020.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 08:45:59 AM UTC 2026
% Result : Theorem 3.28s 1.93s
% Output : Refutation 3.28s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO482^6 : 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
% 0.10/0.20 % Computer : n020.cluster.edu
% 0.10/0.20 % Model : x86_64 x86_64
% 0.10/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.20 % Memory : 8046.5625MB
% 0.10/0.20 % OS : Linux 6.8.0-71-generic
% 0.10/0.20 % CPULimit : 300
% 0.10/0.20 % WCLimit : 300
% 0.10/0.20 % DateTime : Tue Sep 29 17:09:49 UTC 2026
% 0.10/0.20 % CPUTime :
% 0.10/0.20 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
% 1.05/0.80 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.60/1.05 % [INFO] Parsing done (247ms).
% 1.60/1.06 % [INFO] Running in sequential loop mode.
% 2.22/1.46 % [INFO] eprover registered as external prover.
% 2.22/1.47 % [INFO] Scanning for conjecture ...
% 2.71/1.65 % [INFO] Found a conjecture (or negated_conjecture) and 3 axioms. Running axiom selection ...
% 2.71/1.69 % [INFO] Axiom selection finished. Selected 3 axioms (removed 0 axioms).
% 2.71/1.69 % [INFO] Problem is higher-order (TPTP THF).
% 2.71/1.69 % [INFO] Type checking passed.
% 2.89/1.70 % [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 ...
% 3.28/1.92 % [INFO] Killing All external provers ...
% 3.28/1.93 % Time passed: 1572ms (effective reasoning time: 853ms)
% 3.28/1.93 % 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)>
% 3.28/1.93 % Axioms used in derivation (0):
% 3.28/1.93 % No. of inferences in proof: 8
% 3.28/1.93 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1572 ms resp. 853 ms w/o parsing
% 3.28/2.00 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.28/2.00 thf(mu_type, type, mu: $tType).
% 3.28/2.00 thf(meq_ind_decl, type, meq_ind: (mu > (mu > ($i > $o)))).
% 3.28/2.00 thf(mnot_decl, type, mnot: (($i > $o) > ($i > $o))).
% 3.28/2.00 thf(mforall_ind_decl, type, mforall_ind: ((mu > ($i > $o)) > ($i > $o))).
% 3.28/2.00 thf(mexists_ind_decl, type, mexists_ind: ((mu > ($i > $o)) > ($i > $o))).
% 3.28/2.00 thf(mvalid_decl, type, mvalid: (($i > $o) > $o)).
% 3.28/2.00 thf(rel_s5_decl, type, rel_s5: ($i > ($i > $o))).
% 3.28/2.00 thf(mbox_s5_decl, type, mbox_s5: (($i > $o) > ($i > $o))).
% 3.28/2.00 thf(sk1_decl, type, sk1: $i).
% 3.28/2.00 thf(sk2_decl, type, sk2: $i).
% 3.28/2.00 thf(sk3_decl, type, sk3: mu).
% 3.28/2.00 thf(meq_ind_def, definition, meq_ind = (^ [A:mu,B:mu,C:$i]: (A = B)) ).
% 3.28/2.00 thf(mnot_def, definition, mnot = (^ [A:($i > $o),B:$i]: ~ (A @ B)) ).
% 3.28/2.00 thf(mforall_ind_def, definition, mforall_ind = (^ [A:(mu > ($i > $o)),B:$i]: ! [C:mu]: (A @ C @ B)) ).
% 3.28/2.00 thf(mexists_ind_def, definition, mexists_ind = (^ [A:(mu > ($i > $o))]: (mnot @ (mforall_ind @ (^ [B:mu]: (mnot @ (A @ B)))))) ).
% 3.28/2.00 thf(mvalid_def, definition, mvalid = ((!) @ $i) ).
% 3.28/2.00 thf(mbox_s5_def, definition, mbox_s5 = (^ [A:($i > $o),B:$i]: ! [C:$i]: (~ (rel_s5 @ B @ C) | (A @ C))) ).
% 3.28/2.00 thf(sk1_def, definition, sk1 = (@+ [A:$i]: ? [B:$i]: (rel_s5 @ A @ B)) ).
% 3.28/2.00 thf(sk2_def, definition, sk2 = (@+ [A:$i]: (rel_s5 @ sk1 @ A)) ).
% 3.28/2.00 thf(sk3_def, definition, sk3 = (@+ [A:mu]: ~ (? [B:mu]: (A = B))) ).
% 3.28/2.00 thf(1,conjecture,((mvalid @ (mforall_ind @ (^ [A:mu]: (mbox_s5 @ (mexists_ind @ (meq_ind @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove)).
% 3.28/2.00 thf(2,negated_conjecture,((~ (mvalid @ (mforall_ind @ (^ [A:mu]: (mbox_s5 @ (mexists_ind @ (meq_ind @ A)))))))),inference(neg_conjecture,[status(cth)],[1])).
% 3.28/2.00 thf(6,plain,((~ (! [A:$i,B:mu,C:$i]: (~ (rel_s5 @ A @ C) | ~ (! [D:mu]: ~ (B = D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])).
% 3.28/2.00 thf(7,plain,((~ (~ (? [A:$i,B:$i]: (rel_s5 @ A @ B)) | ~ (~ (! [A:mu]: ? [B:mu]: (A = B)))))),inference(miniscope,[status(thm)],[6])).
% 3.28/2.00 thf(8,plain,(! [A:mu] : (((rel_s5 @ sk1 @ sk2) & ~ (sk3 = A)))),inference(cnf,[status(esa)],[7])).
% 3.28/2.00 thf(10,plain,(! [A:mu] : ((~ (sk3 = A)))),inference(cnfConj,[status(thm)],[8])).
% 3.28/2.00 thf(11,plain,(! [A:mu] : ((sk3 != A))),inference(lifteq,[status(thm)],[10])).
% 3.28/2.00 thf(12,plain,(($false)),inference(simp,[status(thm)],[11])).
% 3.28/2.00 % SZS output end Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.28/2.00 % [INFO] Killing All external provers ...
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