%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : KRS276^7 : TPTP v9.3.1. Released v5.5.0.
% 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 : n014.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 08:11:54 AM UTC 2026
% Result : Theorem 4.08s 2.22s
% Output : Refutation 4.08s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KRS276^7 : TPTP v9.3.1. Released v5.5.0.
% 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
% 0.12/0.21 % Computer : n014.cluster.edu
% 0.12/0.21 % Model : x86_64 x86_64
% 0.12/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.21 % Memory : 8046.5625MB
% 0.12/0.21 % OS : Linux 6.8.0-71-generic
% 0.12/0.21 % CPULimit : 300
% 0.12/0.21 % WCLimit : 300
% 0.12/0.21 % DateTime : Tue Sep 29 08:41:45 UTC 2026
% 0.12/0.21 % CPUTime :
% 0.12/0.21 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
% 0.84/0.78 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.58/1.05 % [INFO] Parsing done (264ms).
% 1.58/1.06 % [INFO] Running in sequential loop mode.
% 2.22/1.44 % [INFO] eprover registered as external prover.
% 2.22/1.45 % [INFO] Scanning for conjecture ...
% 2.70/1.62 % [INFO] Found a conjecture (or negated_conjecture) and 11 axioms. Running axiom selection ...
% 2.70/1.66 % [INFO] Axiom selection finished. Selected 11 axioms (removed 0 axioms).
% 2.70/1.67 % [INFO] Problem is higher-order (TPTP THF).
% 2.70/1.67 % [INFO] Type checking passed.
% 2.70/1.68 % [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 ...
% 4.08/2.22 % External prover 'e' found a proof!
% 4.08/2.22 % [INFO] Killing All external provers ...
% 4.08/2.22 % Time passed: 1873ms (effective reasoning time: 1148ms)
% 4.08/2.22 % 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)>
% 4.08/2.22 % Axioms used in derivation (11): existence_of_cs_ax, existence_of_mary_ax, db, existence_of_john_ax, cumulative_ax, existence_of_psych_ax, a1, nonempty_ax, a2, existence_of_math_ax, existence_of_sue_ax
% 4.08/2.22 % No. of inferences in proof: 26
% 4.08/2.22 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1873 ms resp. 1148 ms w/o parsing
% 4.08/2.29 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.08/2.29 thf(mu_type, type, mu: $tType).
% 4.08/2.29 thf(mnot_decl, type, mnot: (($i > $o) > ($i > $o))).
% 4.08/2.29 thf(mor_decl, type, mor: (($i > $o) > (($i > $o) > ($i > $o)))).
% 4.08/2.29 thf(mand_decl, type, mand: (($i > $o) > (($i > $o) > ($i > $o)))).
% 4.08/2.29 thf(exists_in_world_decl, type, exists_in_world: (mu > ($i > $o))).
% 4.08/2.29 thf(mforall_ind_decl, type, mforall_ind: ((mu > ($i > $o)) > ($i > $o))).
% 4.08/2.29 thf(mexists_ind_decl, type, mexists_ind: ((mu > ($i > $o)) > ($i > $o))).
% 4.08/2.29 thf(mreflexive_decl, type, mreflexive: (($i > ($i > $o)) > $o)).
% 4.08/2.29 thf(mtransitive_decl, type, mtransitive: (($i > ($i > $o)) > $o)).
% 4.08/2.29 thf(mvalid_decl, type, mvalid: (($i > $o) > $o)).
% 4.08/2.29 thf(rel_s4_decl, type, rel_s4: ($i > ($i > $o))).
% 4.08/2.29 thf(mbox_s4_decl, type, mbox_s4: (($i > $o) > ($i > $o))).
% 4.08/2.29 thf(teach_decl, type, teach: (mu > (mu > ($i > $o)))).
% 4.08/2.29 thf(sue_decl, type, sue: mu).
% 4.08/2.29 thf(psych_decl, type, psych: mu).
% 4.08/2.29 thf(mary_decl, type, mary: mu).
% 4.08/2.29 thf(math_decl, type, math: mu).
% 4.08/2.29 thf(john_decl, type, john: mu).
% 4.08/2.29 thf(cs_decl, type, cs: mu).
% 4.08/2.29 thf(mnot_def, definition, mnot = (^ [A:($i > $o),B:$i]: ~ (A @ B)) ).
% 4.08/2.29 thf(mor_def, definition, mor = (^ [A:($i > $o),B:($i > $o),C:$i]: ((A @ C) | (B @ C))) ).
% 4.08/2.29 thf(mand_def, definition, mand = (^ [A:($i > $o),B:($i > $o)]: (mnot @ (mor @ (mnot @ A) @ (mnot @ B)))) ).
% 4.08/2.29 thf(mforall_ind_def, definition, mforall_ind = (^ [A:(mu > ($i > $o)),B:$i]: ! [C:mu]: ((exists_in_world @ C @ B) => (A @ C @ B))) ).
% 4.08/2.29 thf(mexists_ind_def, definition, mexists_ind = (^ [A:(mu > ($i > $o))]: (mnot @ (mforall_ind @ (^ [B:mu]: (mnot @ (A @ B)))))) ).
% 4.08/2.29 thf(mreflexive_def, definition, mreflexive = (^ [A:($i > ($i > $o))]: ! [B:$i]: (A @ B @ B)) ).
% 4.08/2.29 thf(mtransitive_def, definition, mtransitive = (^ [A:($i > ($i > $o))]: ! [B:$i,C:$i,D:$i]: (((A @ B @ C) & (A @ C @ D)) => (A @ B @ D))) ).
% 4.08/2.29 thf(mvalid_def, definition, mvalid = ((!) @ $i) ).
% 4.08/2.29 thf(mbox_s4_def, definition, mbox_s4 = (^ [A:($i > $o),B:$i]: ! [C:$i]: (~ (rel_s4 @ B @ C) | (A @ C))) ).
% 4.08/2.29 thf(6,axiom,((! [A:mu,B:$i,C:$i]: (((exists_in_world @ A @ B) & (rel_s4 @ B @ C)) => (exists_in_world @ A @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cumulative_ax)).
% 4.08/2.29 thf(24,plain,((! [A:mu,B:$i,C:$i]: (((exists_in_world @ A @ B) & (rel_s4 @ B @ C)) => (exists_in_world @ A @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6])).
% 4.08/2.29 thf(1,conjecture,((mvalid @ (mbox_s4 @ (mexists_ind @ (^ [A:mu]: (teach @ A @ cs)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',query)).
% 4.08/2.29 thf(2,negated_conjecture,((~ (mvalid @ (mbox_s4 @ (mexists_ind @ (^ [A:mu]: (teach @ A @ cs))))))),inference(neg_conjecture,[status(cth)],[1])).
% 4.08/2.29 thf(14,plain,((~ (! [A:$i,B:$i]: (~ (rel_s4 @ A @ B) | ~ (! [C:mu]: ((exists_in_world @ C @ B) => (~ (teach @ C @ cs @ B)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])).
% 4.08/2.29 thf(4,axiom,((mreflexive @ rel_s4)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a1)).
% 4.08/2.29 thf(20,plain,((! [A:$i]: (rel_s4 @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4])).
% 4.08/2.29 thf(5,axiom,((mtransitive @ rel_s4)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a2)).
% 4.08/2.29 thf(22,plain,((! [A:$i,B:$i,C:$i]: (((rel_s4 @ A @ B) & (rel_s4 @ B @ C)) => (rel_s4 @ A @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5])).
% 4.08/2.29 thf(3,axiom,((! [A:$i]: ? [B:mu]: (exists_in_world @ B @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonempty_ax)).
% 4.08/2.29 thf(18,plain,((! [A:$i]: ? [B:mu]: (exists_in_world @ B @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3])).
% 4.08/2.29 thf(7,axiom,((! [A:$i]: (exists_in_world @ sue @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_sue_ax)).
% 4.08/2.29 thf(26,plain,((! [A:$i]: (exists_in_world @ sue @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7])).
% 4.08/2.29 thf(8,axiom,((! [A:$i]: (exists_in_world @ psych @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_psych_ax)).
% 4.08/2.29 thf(28,plain,((! [A:$i]: (exists_in_world @ psych @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8])).
% 4.08/2.29 thf(13,axiom,((mvalid @ (mbox_s4 @ (mand @ (teach @ john @ math) @ (mand @ (mexists_ind @ (^ [A:mu]: (teach @ A @ cs))) @ (mand @ (teach @ mary @ psych) @ (teach @ sue @ psych))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',db)).
% 4.08/2.29 thf(38,plain,((! [A:$i,B:$i]: (~ (rel_s4 @ A @ B) | ~ (~ (teach @ john @ math @ B) | ! [C:mu]: ((exists_in_world @ C @ B) => (~ (teach @ C @ cs @ B))) | ~ (teach @ mary @ psych @ B) | ~ (teach @ sue @ psych @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[13])).
% 4.08/2.29 thf(10,axiom,((! [A:$i]: (exists_in_world @ math @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_math_ax)).
% 4.08/2.29 thf(32,plain,((! [A:$i]: (exists_in_world @ math @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[10])).
% 4.08/2.29 thf(11,axiom,((! [A:$i]: (exists_in_world @ john @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_john_ax)).
% 4.08/2.29 thf(34,plain,((! [A:$i]: (exists_in_world @ john @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[11])).
% 4.08/2.29 thf(12,axiom,((! [A:$i]: (exists_in_world @ cs @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_cs_ax)).
% 4.08/2.29 thf(36,plain,((! [A:$i]: (exists_in_world @ cs @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[12])).
% 4.08/2.29 thf(9,axiom,((! [A:$i]: (exists_in_world @ mary @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_mary_ax)).
% 4.08/2.29 thf(30,plain,((! [A:$i]: (exists_in_world @ mary @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[9])).
% 4.08/2.29 thf(45,plain,(($false)),inference(e,[status(thm)],[24,14,20,22,18,26,28,38,32,34,36,30])).
% 4.08/2.29 % SZS output end Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.08/2.29 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------