%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SET575^7 : TPTP v9.3.1. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n007.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 08:22:56 AM UTC 2026
% Result : Theorem 17.45s 3.85s
% Output : Refutation 16.29s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET575^7 : TPTP v9.3.1. Released v5.5.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.10/0.21 % Computer : n007.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 13:35:40 UTC 2026
% 0.10/0.21 % CPUTime :
% 0.10/0.21 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.64/0.53 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.01/0.68 % [INFO] Parsing done (150ms).
% 1.01/0.69 % [INFO] Running in sequential loop mode.
% 1.61/0.89 % [INFO] eprover registered as external prover.
% 1.61/0.89 % [INFO] Scanning for conjecture ...
% 1.84/0.98 % [INFO] Found a conjecture (or negated_conjecture) and 6 axioms. Running axiom selection ...
% 1.84/1.00 % [INFO] Axiom selection finished. Selected 6 axioms (removed 0 axioms).
% 1.84/1.01 % [INFO] Problem is higher-order (TPTP THF).
% 1.84/1.01 % [INFO] Type checking passed.
% 1.84/1.02 % [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 ...
% 17.45/3.84 % External prover 'e' found a proof!
% 17.45/3.84 % [INFO] Killing All external provers ...
% 17.45/3.85 % Time passed: 3533ms (effective reasoning time: 3157ms)
% 17.45/3.85 % 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)>
% 17.45/3.85 % Axioms used in derivation (6): intersect_defn, cumulative_ax, a1, nonempty_ax, symmetry_of_intersect, a2
% 17.45/3.85 % No. of inferences in proof: 16
% 17.45/3.85 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 3533 ms resp. 3157 ms w/o parsing
% 16.29/3.91 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% 16.29/3.91 thf(mu_type, type, mu: $tType).
% 16.29/3.91 thf(mnot_decl, type, mnot: (($i > $o) > ($i > $o))).
% 16.29/3.91 thf(mor_decl, type, mor: (($i > $o) > (($i > $o) > ($i > $o)))).
% 16.29/3.91 thf(mand_decl, type, mand: (($i > $o) > (($i > $o) > ($i > $o)))).
% 16.29/3.91 thf(mimplies_decl, type, mimplies: (($i > $o) > (($i > $o) > ($i > $o)))).
% 16.29/3.91 thf(exists_in_world_decl, type, exists_in_world: (mu > ($i > $o))).
% 16.29/3.91 thf(mforall_ind_decl, type, mforall_ind: ((mu > ($i > $o)) > ($i > $o))).
% 16.29/3.91 thf(mexists_ind_decl, type, mexists_ind: ((mu > ($i > $o)) > ($i > $o))).
% 16.29/3.91 thf(mreflexive_decl, type, mreflexive: (($i > ($i > $o)) > $o)).
% 16.29/3.91 thf(mtransitive_decl, type, mtransitive: (($i > ($i > $o)) > $o)).
% 16.29/3.91 thf(mvalid_decl, type, mvalid: (($i > $o) > $o)).
% 16.29/3.91 thf(rel_s4_decl, type, rel_s4: ($i > ($i > $o))).
% 16.29/3.91 thf(mbox_s4_decl, type, mbox_s4: (($i > $o) > ($i > $o))).
% 16.29/3.91 thf(member_decl, type, member: (mu > (mu > ($i > $o)))).
% 16.29/3.91 thf(intersect_decl, type, intersect: (mu > (mu > ($i > $o)))).
% 16.29/3.91 thf(mnot_def, definition, mnot = (^ [A:($i > $o),B:$i]: ~ (A @ B)) ).
% 16.29/3.91 thf(mor_def, definition, mor = (^ [A:($i > $o),B:($i > $o),C:$i]: ((A @ C) | (B @ C))) ).
% 16.29/3.91 thf(mand_def, definition, mand = (^ [A:($i > $o),B:($i > $o)]: (mnot @ (mor @ (mnot @ A) @ (mnot @ B)))) ).
% 16.29/3.91 thf(mimplies_def, definition, mimplies = (^ [A:($i > $o)]: (mor @ (mnot @ A))) ).
% 16.29/3.91 thf(mforall_ind_def, definition, mforall_ind = (^ [A:(mu > ($i > $o)),B:$i]: ! [C:mu]: ((exists_in_world @ C @ B) => (A @ C @ B))) ).
% 16.29/3.91 thf(mexists_ind_def, definition, mexists_ind = (^ [A:(mu > ($i > $o))]: (mnot @ (mforall_ind @ (^ [B:mu]: (mnot @ (A @ B)))))) ).
% 16.29/3.91 thf(mreflexive_def, definition, mreflexive = (^ [A:($i > ($i > $o))]: ! [B:$i]: (A @ B @ B)) ).
% 16.29/3.91 thf(mtransitive_def, definition, mtransitive = (^ [A:($i > ($i > $o))]: ! [B:$i,C:$i,D:$i]: (((A @ B @ C) & (A @ C @ D)) => (A @ B @ D))) ).
% 16.29/3.91 thf(mvalid_def, definition, mvalid = ((!) @ $i) ).
% 16.29/3.91 thf(mbox_s4_def, definition, mbox_s4 = (^ [A:($i > $o),B:$i]: ! [C:$i]: (~ (rel_s4 @ B @ C) | (A @ C))) ).
% 16.29/3.91 thf(3,axiom,((! [A:$i]: ? [B:mu]: (exists_in_world @ B @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonempty_ax)).
% 16.29/3.91 thf(25,plain,((! [A:$i]: ? [B:mu]: (exists_in_world @ B @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3])).
% 16.29/3.91 thf(5,axiom,((mtransitive @ rel_s4)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',a2)).
% 16.29/3.91 thf(29,plain,((! [A:$i,B:$i,C:$i]: (((rel_s4 @ A @ B) & (rel_s4 @ B @ C)) => (rel_s4 @ A @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5])).
% 16.29/3.91 thf(7,axiom,((mvalid @ (mbox_s4 @ (mforall_ind @ (^ [A:mu]: (mbox_s4 @ (mforall_ind @ (^ [B:mu]: (mand @ (mbox_s4 @ (mimplies @ (mbox_s4 @ (intersect @ A @ B)) @ (mexists_ind @ (^ [C:mu]: (mand @ (mbox_s4 @ (member @ C @ A)) @ (mbox_s4 @ (member @ C @ B))))))) @ (mbox_s4 @ (mimplies @ (mexists_ind @ (^ [C:mu]: (mand @ (mbox_s4 @ (member @ C @ A)) @ (mbox_s4 @ (member @ C @ B))))) @ (mbox_s4 @ (intersect @ A @ B))))))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersect_defn)).
% 16.29/3.91 thf(33,plain,((! [A:$i,B:$i]: (~ (rel_s4 @ A @ B) | ! [C:mu]: ((exists_in_world @ C @ B) => (! [D:$i]: (~ (rel_s4 @ B @ D) | ! [E:mu]: ((exists_in_world @ E @ D) => (~ (~ (! [F:$i]: (~ (rel_s4 @ D @ F) | ~ (! [G:$i]: (~ (rel_s4 @ F @ G) | (intersect @ C @ E @ G))) | ~ (! [G:mu]: ((exists_in_world @ G @ F) => (~ (! [H:$i]: (~ (rel_s4 @ F @ H) | (member @ G @ C @ H))) | ~ (! [H:$i]: (~ (rel_s4 @ F @ H) | (member @ G @ E @ H)))))))) | ~ (! [F:$i]: (~ (rel_s4 @ D @ F) | ! [G:mu]: ((exists_in_world @ G @ F) => (~ (! [H:$i]: (~ (rel_s4 @ F @ H) | (member @ G @ C @ H))) | ~ (! [H:$i]: (~ (rel_s4 @ F @ H) | (member @ G @ E @ H))))) | ! [G:$i]: (~ (rel_s4 @ F @ G) | (intersect @ C @ E @ G))))))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7])).
% 16.29/3.91 thf(1,conjecture,((mvalid @ (mbox_s4 @ (mforall_ind @ (^ [A:mu]: (mbox_s4 @ (mforall_ind @ (^ [B:mu]: (mbox_s4 @ (mimplies @ (mbox_s4 @ (intersect @ A @ B)) @ (mexists_ind @ (^ [C:mu]: (mand @ (mbox_s4 @ (member @ C @ A)) @ (mbox_s4 @ (member @ C @ B))))))))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th15)).
% 16.29/3.91 thf(2,negated_conjecture,((~ (mvalid @ (mbox_s4 @ (mforall_ind @ (^ [A:mu]: (mbox_s4 @ (mforall_ind @ (^ [B:mu]: (mbox_s4 @ (mimplies @ (mbox_s4 @ (intersect @ A @ B)) @ (mexists_ind @ (^ [C:mu]: (mand @ (mbox_s4 @ (member @ C @ A)) @ (mbox_s4 @ (member @ C @ B)))))))))))))))),inference(neg_conjecture,[status(cth)],[1])).
% 16.29/3.91 thf(9,plain,((~ (! [A:$i,B:$i]: (~ (rel_s4 @ A @ B) | ! [C:mu]: ((exists_in_world @ C @ B) => (! [D:$i]: (~ (rel_s4 @ B @ D) | ! [E:mu]: ((exists_in_world @ E @ D) => (! [F:$i]: (~ (rel_s4 @ D @ F) | ~ (! [G:$i]: (~ (rel_s4 @ F @ G) | (intersect @ C @ E @ G))) | ~ (! [G:mu]: ((exists_in_world @ G @ F) => (~ (! [H:$i]: (~ (rel_s4 @ F @ H) | (member @ G @ C @ H))) | ~ (! [H:$i]: (~ (rel_s4 @ F @ H) | (member @ G @ E @ H)))))))))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])).
% 16.29/3.91 thf(4,axiom,((mreflexive @ rel_s4)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',a1)).
% 16.29/3.91 thf(27,plain,((! [A:$i]: (rel_s4 @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4])).
% 16.29/3.91 thf(8,axiom,((mvalid @ (mbox_s4 @ (mforall_ind @ (^ [A:mu]: (mbox_s4 @ (mforall_ind @ (^ [B:mu]: (mbox_s4 @ (mimplies @ (mbox_s4 @ (intersect @ A @ B)) @ (mbox_s4 @ (intersect @ B @ A)))))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_of_intersect)).
% 16.29/3.91 thf(49,plain,((! [A:$i,B:$i]: (~ (rel_s4 @ A @ B) | ! [C:mu]: ((exists_in_world @ C @ B) => (! [D:$i]: (~ (rel_s4 @ B @ D) | ! [E:mu]: ((exists_in_world @ E @ D) => (! [F:$i]: (~ (rel_s4 @ D @ F) | ~ (! [G:$i]: (~ (rel_s4 @ F @ G) | (intersect @ C @ E @ G))) | ! [G:$i]: (~ (rel_s4 @ F @ G) | (intersect @ E @ C @ G))))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8])).
% 16.29/3.91 thf(6,axiom,((! [A:mu,B:$i,C:$i]: (((exists_in_world @ A @ B) & (rel_s4 @ B @ C)) => (exists_in_world @ A @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',cumulative_ax)).
% 16.29/3.91 thf(31,plain,((! [A:mu,B:$i,C:$i]: (((exists_in_world @ A @ B) & (rel_s4 @ B @ C)) => (exists_in_world @ A @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6])).
% 16.29/3.91 thf(2624,plain,(($false)),inference(e,[status(thm)],[25,29,33,9,27,49,31])).
% 16.29/3.91 % SZS output end Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% 16.29/3.91 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------