%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : PHI043^2 : TPTP v9.3.1. Released v7.5.0.
% 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 : n011.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 08:20:14 AM UTC 2026
% Result : Theorem 4.56s 2.35s
% Output : Refutation 4.81s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : PHI043^2 : TPTP v9.3.1. Released v7.5.0.
% 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
% 0.07/0.19 % Computer : n011.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Tue Sep 29 13:20:16 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 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
% 0.90/0.77 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.24/1.03 % [INFO] Parsing done (261ms).
% 1.65/1.05 % [INFO] Running in sequential loop mode.
% 2.34/1.44 % [INFO] eprover registered as external prover.
% 2.34/1.45 % [INFO] Scanning for conjecture ...
% 2.79/1.60 % [INFO] Found a conjecture (or negated_conjecture) and 3 axioms. Running axiom selection ...
% 2.79/1.64 % [INFO] Axiom selection finished. Selected 3 axioms (removed 0 axioms).
% 2.79/1.64 % [INFO] Problem is higher-order (TPTP THF).
% 2.79/1.65 % [INFO] Type checking passed.
% 2.79/1.65 % [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 ...
% 4.56/2.35 % External prover 'e' found a proof!
% 4.56/2.35 % [INFO] Killing All external provers ...
% 4.56/2.35 % Time passed: 2021ms (effective reasoning time: 1293ms)
% 4.56/2.35 % 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)>
% 4.56/2.35 % Axioms used in derivation (3): nonempty_ind, ax16, axii
% 4.56/2.35 % No. of inferences in proof: 10
% 4.56/2.35 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2021 ms resp. 1293 ms w/o parsing
% 4.81/2.41 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.81/2.41 thf(mu_type, type, mu: $tType).
% 4.81/2.41 thf(mnot_decl, type, mnot: (($i > $o) > ($i > $o))).
% 4.81/2.41 thf(mimplies_decl, type, mimplies: (($i > $o) > (($i > $o) > ($i > $o)))).
% 4.81/2.41 thf(mequiv_decl, type, mequiv: (($i > $o) > (($i > $o) > ($i > $o)))).
% 4.81/2.41 thf(mforall_indset_decl, type, mforall_indset: (((mu > ($i > $o)) > ($i > $o)) > ($i > $o))).
% 4.81/2.41 thf(mbox_generic_decl, type, mbox_generic: (($i > ($i > $o)) > (($i > $o) > ($i > $o)))).
% 4.81/2.41 thf(mdia_generic_decl, type, mdia_generic: (($i > ($i > $o)) > (($i > $o) > ($i > $o)))).
% 4.81/2.41 thf(rel_decl, type, rel: ($i > ($i > $o))).
% 4.81/2.41 thf(mbox_decl, type, mbox: (($i > $o) > ($i > $o))).
% 4.81/2.41 thf(mdia_decl, type, mdia: (($i > $o) > ($i > $o))).
% 4.81/2.41 thf(mvalid_decl, type, mvalid: (($i > $o) > $o)).
% 4.81/2.41 thf(eiw_ind_decl, type, eiw_ind: ($i > (mu > $o))).
% 4.81/2.41 thf(mforall_eiw_ind_decl, type, mforall_eiw_ind: ((mu > ($i > $o)) > ($i > $o))).
% 4.81/2.41 thf(mexists_eiw_ind_decl, type, mexists_eiw_ind: ((mu > ($i > $o)) > ($i > $o))).
% 4.81/2.41 thf(p_decl, type, p: ((mu > ($i > $o)) > ($i > $o))).
% 4.81/2.41 thf(mnot_def, definition, mnot = (^ [A:($i > $o),B:$i]: ~ (A @ B)) ).
% 4.81/2.41 thf(mimplies_def, definition, mimplies = (^ [A:($i > $o),B:($i > $o),C:$i]: ((A @ C) => (B @ C))) ).
% 4.81/2.41 thf(mequiv_def, definition, mequiv = (^ [A:($i > $o),B:($i > $o),C:$i]: ((A @ C) = (B @ C))) ).
% 4.81/2.41 thf(mforall_indset_def, definition, mforall_indset = (^ [A:((mu > ($i > $o)) > ($i > $o)),B:$i]: ! [C:(mu > ($i > $o))]: (A @ C @ B)) ).
% 4.81/2.41 thf(mbox_generic_def, definition, mbox_generic = (^ [A:($i > ($i > $o)),B:($i > $o),C:$i]: ! [D:$i]: (~ (A @ C @ D) | (B @ D))) ).
% 4.81/2.41 thf(mdia_generic_def, definition, mdia_generic = (^ [A:($i > ($i > $o)),B:($i > $o),C:$i]: ? [D:$i]: ((A @ C @ D) & (B @ D))) ).
% 4.81/2.41 thf(mbox_def, definition, mbox = (mbox_generic @ rel) ).
% 4.81/2.41 thf(mdia_def, definition, mdia = (mdia_generic @ rel) ).
% 4.81/2.41 thf(mvalid_def, definition, mvalid = ((!) @ $i) ).
% 4.81/2.41 thf(mforall_eiw_ind_def, definition, mforall_eiw_ind = (^ [A:(mu > ($i > $o)),B:$i]: ! [C:mu]: ((eiw_ind @ B @ C) => (A @ C @ B))) ).
% 4.81/2.41 thf(mexists_eiw_ind_def, definition, mexists_eiw_ind = (^ [A:(mu > ($i > $o))]: (mnot @ (mforall_eiw_ind @ (^ [B:mu]: (mnot @ (A @ B)))))) ).
% 4.81/2.41 thf(1,conjecture,((mvalid @ (mforall_indset @ (^ [A:(mu > ($i > $o))]: (mimplies @ (p @ A) @ (mdia @ (mexists_eiw_ind @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',possible_instantiation_of_the_positive_variable_domain)).
% 4.81/2.41 thf(2,negated_conjecture,((~ (mvalid @ (mforall_indset @ (^ [A:(mu > ($i > $o))]: (mimplies @ (p @ A) @ (mdia @ (mexists_eiw_ind @ A)))))))),inference(neg_conjecture,[status(cth)],[1])).
% 4.81/2.41 thf(6,plain,((~ (! [A:$i,B:(mu > ($i > $o))]: ((p @ (B) @ A) => (? [C:$i]: ((rel @ A @ C) & ~ (! [D:mu]: ((eiw_ind @ C @ D) => (~ (B @ D @ C)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])).
% 4.81/2.41 thf(3,axiom,((! [A:$i]: ? [B:mu]: (eiw_ind @ A @ B))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonempty_ind)).
% 4.81/2.41 thf(10,plain,((! [A:$i]: ? [B:mu]: (eiw_ind @ A @ B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3])).
% 4.81/2.41 thf(4,axiom,((mvalid @ (mnot @ (p @ (^ [A:mu,B:$i]: (A != A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax16)).
% 4.81/2.41 thf(12,plain,((! [A:$i]: ~ (p @ (^ [B:mu,C:$i]: (($false))) @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4])).
% 4.81/2.41 thf(5,axiom,((mvalid @ (mforall_indset @ (^ [A:(mu > ($i > $o))]: (mforall_indset @ (^ [B:(mu > ($i > $o))]: (mimplies @ (mbox @ (mforall_eiw_ind @ (^ [C:mu]: (mequiv @ (A @ C) @ (B @ C))))) @ (mequiv @ (p @ A) @ (p @ B))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axii)).
% 4.81/2.41 thf(15,plain,((! [A:$i,B:(mu > ($i > $o)),C:(mu > ($i > $o))]: ((! [D:$i]: (~ (rel @ A @ D) | ! [E:mu]: ((eiw_ind @ D @ E) => ((B @ E @ D) = (C @ E @ D))))) => ((p @ (B) @ A) = (p @ (C) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5])).
% 4.81/2.41 thf(27,plain,(($false)),inference(e,[status(thm)],[6,10,12,15])).
% 4.81/2.41 % SZS output end Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.81/2.41 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------