%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : PHI002^1 : TPTP v9.3.1. Released v6.1.0.
% 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 : n018.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 08:20:12 AM UTC 2026
% Result : Theorem 8.32s 3.43s
% Output : Refutation 8.60s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PHI002^1 : TPTP v9.3.1. Released v6.1.0.
% 0.00/0.08 % 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
% 0.09/0.21 % Computer : n018.cluster.edu
% 0.09/0.21 % Model : x86_64 x86_64
% 0.09/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.21 % Memory : 8046.5625MB
% 0.09/0.21 % OS : Linux 6.8.0-71-generic
% 0.09/0.22 % CPULimit : 300
% 0.09/0.22 % WCLimit : 300
% 0.09/0.22 % DateTime : Tue Sep 29 13:18:51 UTC 2026
% 0.09/0.22 % CPUTime :
% 0.09/0.22 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
% 1.03/0.80 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.55/1.08 % [INFO] Parsing done (275ms).
% 1.55/1.09 % [INFO] Running in sequential loop mode.
% 2.18/1.49 % [INFO] eprover registered as external prover.
% 2.41/1.50 % [INFO] Scanning for conjecture ...
% 2.62/1.66 % [INFO] Found a conjecture (or negated_conjecture) and 5 axioms. Running axiom selection ...
% 2.83/1.70 % [INFO] Axiom selection finished. Selected 5 axioms (removed 0 axioms).
% 2.83/1.71 % [INFO] Problem is higher-order (TPTP THF).
% 2.83/1.71 % [INFO] Type checking passed.
% 2.83/1.72 % [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 ...
% 8.32/3.43 % External prover 'e' found a proof!
% 8.32/3.43 % [INFO] Killing All external provers ...
% 8.32/3.43 % Time passed: 3073ms (effective reasoning time: 2334ms)
% 8.32/3.43 % 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)>
% 8.32/3.43 % Axioms used in derivation (5): axA3, axA1, axA5, axA2, axA4
% 8.32/3.43 % No. of inferences in proof: 14
% 8.32/3.43 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3073 ms resp. 2334 ms w/o parsing
% 8.60/3.50 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.60/3.50 thf(mu_type, type, mu: $tType).
% 8.60/3.50 thf(mnot_decl, type, mnot: (($i > $o) > ($i > $o))).
% 8.60/3.50 thf(mand_decl, type, mand: (($i > $o) > (($i > $o) > ($i > $o)))).
% 8.60/3.50 thf(mimplies_decl, type, mimplies: (($i > $o) > (($i > $o) > ($i > $o)))).
% 8.60/3.50 thf(mequiv_decl, type, mequiv: (($i > $o) > (($i > $o) > ($i > $o)))).
% 8.60/3.50 thf(mforall_ind_decl, type, mforall_ind: ((mu > ($i > $o)) > ($i > $o))).
% 8.60/3.50 thf(mforall_indset_decl, type, mforall_indset: (((mu > ($i > $o)) > ($i > $o)) > ($i > $o))).
% 8.60/3.50 thf(mexists_ind_decl, type, mexists_ind: ((mu > ($i > $o)) > ($i > $o))).
% 8.60/3.50 thf(mbox_generic_decl, type, mbox_generic: (($i > ($i > $o)) > (($i > $o) > ($i > $o)))).
% 8.60/3.50 thf(mdia_generic_decl, type, mdia_generic: (($i > ($i > $o)) > (($i > $o) > ($i > $o)))).
% 8.60/3.50 thf(rel_decl, type, rel: ($i > ($i > $o))).
% 8.60/3.50 thf(mbox_decl, type, mbox: (($i > $o) > ($i > $o))).
% 8.60/3.50 thf(mdia_decl, type, mdia: (($i > $o) > ($i > $o))).
% 8.60/3.50 thf(mvalid_decl, type, mvalid: (($i > $o) > $o)).
% 8.60/3.50 thf(positive_decl, type, positive: ((mu > ($i > $o)) > ($i > $o))).
% 8.60/3.50 thf(god_decl, type, god: (mu > ($i > $o))).
% 8.60/3.50 thf(essence_decl, type, essence: ((mu > ($i > $o)) > (mu > ($i > $o)))).
% 8.60/3.50 thf(necessary_existence_decl, type, necessary_existence: (mu > ($i > $o))).
% 8.60/3.50 thf(mnot_def, definition, mnot = (^ [A:($i > $o),B:$i]: ~ (A @ B)) ).
% 8.60/3.50 thf(mand_def, definition, mand = (^ [A:($i > $o),B:($i > $o),C:$i]: ((A @ C) & (B @ C))) ).
% 8.60/3.50 thf(mimplies_def, definition, mimplies = (^ [A:($i > $o),B:($i > $o),C:$i]: ((A @ C) => (B @ C))) ).
% 8.60/3.50 thf(mequiv_def, definition, mequiv = (^ [A:($i > $o),B:($i > $o),C:$i]: ((A @ C) = (B @ C))) ).
% 8.60/3.50 thf(mforall_ind_def, definition, mforall_ind = (^ [A:(mu > ($i > $o)),B:$i]: ! [C:mu]: (A @ C @ B)) ).
% 8.60/3.50 thf(mforall_indset_def, definition, mforall_indset = (^ [A:((mu > ($i > $o)) > ($i > $o)),B:$i]: ! [C:(mu > ($i > $o))]: (A @ C @ B)) ).
% 8.60/3.50 thf(mexists_ind_def, definition, mexists_ind = (^ [A:(mu > ($i > $o)),B:$i]: ? [C:mu]: (A @ C @ B)) ).
% 8.60/3.50 thf(mbox_generic_def, definition, mbox_generic = (^ [A:($i > ($i > $o)),B:($i > $o),C:$i]: ! [D:$i]: (~ (A @ C @ D) | (B @ D))) ).
% 8.60/3.50 thf(mdia_generic_def, definition, mdia_generic = (^ [A:($i > ($i > $o)),B:($i > $o),C:$i]: ? [D:$i]: ((A @ C @ D) & (B @ D))) ).
% 8.60/3.50 thf(mbox_def, definition, mbox = (mbox_generic @ rel) ).
% 8.60/3.50 thf(mdia_def, definition, mdia = (mdia_generic @ rel) ).
% 8.60/3.50 thf(mvalid_def, definition, mvalid = ((!) @ $i) ).
% 8.60/3.50 thf(god_def, definition, god = (^ [A:mu]: (mforall_indset @ (^ [B:(mu > ($i > $o))]: (mimplies @ (positive @ B) @ (B @ A))))) ).
% 8.60/3.50 thf(essence_def, definition, essence = (^ [A:(mu > ($i > $o)),B:mu]: (mand @ (A @ B) @ (mforall_indset @ (^ [C:(mu > ($i > $o))]: (mimplies @ (C @ B) @ (mbox @ (mforall_ind @ (^ [D:mu]: (mimplies @ (A @ D) @ (C @ D)))))))))) ).
% 8.60/3.50 thf(necessary_existence_def, definition, necessary_existence = (^ [A:mu]: (mforall_indset @ (^ [B:(mu > ($i > $o))]: (mimplies @ (essence @ B @ A) @ (mbox @ (mexists_ind @ B)))))) ).
% 8.60/3.50 thf(7,axiom,((mvalid @ (positive @ necessary_existence))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axA5)).
% 8.60/3.50 thf(24,plain,((! [A:$i]: (positive @ (^ [B:mu,C:$i]: ! [D:(mu > ($i > $o))]: (((D @ B @ C) & ! [E:(mu > ($i > $o))]: ((E @ B @ C) => (! [F:$i]: (~ (rel @ C @ F) | ! [G:mu]: ((D @ G @ F) => (E @ G @ F)))))) => (! [E:$i]: (~ (rel @ C @ E) | ? [F:mu]: (D @ F @ E))))) @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7])).
% 8.60/3.50 thf(5,axiom,((mvalid @ (positive @ god))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axA3)).
% 8.60/3.50 thf(20,plain,((! [A:$i]: (positive @ (^ [B:mu,C:$i]: ! [D:(mu > ($i > $o))]: ((positive @ D @ C) => (D @ B @ C))) @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5])).
% 8.60/3.50 thf(6,axiom,((mvalid @ (mforall_indset @ (^ [A:(mu > ($i > $o))]: (mimplies @ (positive @ A) @ (mbox @ (positive @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axA4)).
% 8.60/3.50 thf(22,plain,((! [A:$i,B:(mu > ($i > $o))]: ((positive @ (B) @ A) => (! [C:$i]: (~ (rel @ A @ C) | (positive @ (B) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6])).
% 8.60/3.50 thf(3,axiom,((mvalid @ (mforall_indset @ (^ [A:(mu > ($i > $o))]: (mequiv @ (positive @ (^ [B:mu]: (mnot @ (A @ B)))) @ (mnot @ (positive @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axA1)).
% 8.60/3.50 thf(12,plain,((! [A:$i,B:(mu > ($i > $o))]: ((positive @ (^ [C:mu,D:$i]: ~ (B @ C @ D)) @ A) = (~ (positive @ (B) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3])).
% 8.60/3.50 thf(1,conjecture,((mvalid @ (mforall_indset @ (^ [A:(mu > ($i > $o))]: (mimplies @ (positive @ A) @ (mdia @ (mexists_ind @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thmT1)).
% 8.60/3.50 thf(2,negated_conjecture,((~ (mvalid @ (mforall_indset @ (^ [A:(mu > ($i > $o))]: (mimplies @ (positive @ A) @ (mdia @ (mexists_ind @ A)))))))),inference(neg_conjecture,[status(cth)],[1])).
% 8.60/3.50 thf(8,plain,((~ (! [A:$i,B:(mu > ($i > $o))]: ((positive @ (B) @ A) => (? [C:$i]: ((rel @ A @ C) & ? [D:mu]: (B @ D @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])).
% 8.60/3.50 thf(4,axiom,((mvalid @ (mforall_indset @ (^ [A:(mu > ($i > $o))]: (mforall_indset @ (^ [B:(mu > ($i > $o))]: (mimplies @ (mand @ (positive @ A) @ (mbox @ (mforall_ind @ (^ [C:mu]: (mimplies @ (A @ C) @ (B @ C)))))) @ (positive @ B)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axA2)).
% 8.60/3.50 thf(15,plain,((! [A:$i,B:(mu > ($i > $o)),C:(mu > ($i > $o))]: (((positive @ (B) @ A) & ! [D:$i]: (~ (rel @ A @ D) | ! [E:mu]: ((B @ E @ D) => (C @ E @ D)))) => (positive @ (C) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4])).
% 8.60/3.50 thf(46,plain,(($false)),inference(e,[status(thm)],[24,20,22,12,8,15])).
% 8.60/3.50 % SZS output end Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.60/3.50 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------