%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYN367^7 : 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 : n006.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 08:41:31 AM UTC 2026
% Result : Theorem 42.92s 9.18s
% Output : Refutation 36.50s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN367^7 : 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
% 0.10/0.21 % Computer : n006.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 16:15:09 UTC 2026
% 0.10/0.21 % CPUTime :
% 0.10/0.21 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
% 1.05/0.87 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.46/1.13 % [INFO] Parsing done (253ms).
% 1.85/1.14 % [INFO] Running in sequential loop mode.
% 2.43/1.54 % [INFO] eprover registered as external prover.
% 2.43/1.55 % [INFO] Scanning for conjecture ...
% 2.88/1.73 % [INFO] Found a conjecture (or negated_conjecture) and 4 axioms. Running axiom selection ...
% 2.88/1.77 % [INFO] Axiom selection finished. Selected 4 axioms (removed 0 axioms).
% 2.88/1.77 % [INFO] Problem is higher-order (TPTP THF).
% 2.88/1.78 % [INFO] Type checking passed.
% 2.88/1.78 % [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 ...
% 42.92/9.17 % External prover 'e' found a proof!
% 42.92/9.17 % [INFO] Killing All external provers ...
% 42.92/9.17 % Time passed: 8817ms (effective reasoning time: 8028ms)
% 42.92/9.17 % 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)>
% 42.92/9.18 % Axioms used in derivation (4): a2, a1, nonempty_ax, cumulative_ax
% 42.92/9.18 % No. of inferences in proof: 95
% 42.92/9.18 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 8817 ms resp. 8028 ms w/o parsing
% 36.50/9.28 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 36.50/9.28 thf(mu_type, type, mu: $tType).
% 36.50/9.28 thf(mnot_decl, type, mnot: (($i > $o) > ($i > $o))).
% 36.50/9.28 thf(mor_decl, type, mor: (($i > $o) > (($i > $o) > ($i > $o)))).
% 36.50/9.28 thf(mand_decl, type, mand: (($i > $o) > (($i > $o) > ($i > $o)))).
% 36.50/9.28 thf(mimplies_decl, type, mimplies: (($i > $o) > (($i > $o) > ($i > $o)))).
% 36.50/9.28 thf(exists_in_world_decl, type, exists_in_world: (mu > ($i > $o))).
% 36.50/9.28 thf(mforall_ind_decl, type, mforall_ind: ((mu > ($i > $o)) > ($i > $o))).
% 36.50/9.28 thf(mreflexive_decl, type, mreflexive: (($i > ($i > $o)) > $o)).
% 36.50/9.28 thf(mtransitive_decl, type, mtransitive: (($i > ($i > $o)) > $o)).
% 36.50/9.28 thf(mvalid_decl, type, mvalid: (($i > $o) > $o)).
% 36.50/9.28 thf(rel_s4_decl, type, rel_s4: ($i > ($i > $o))).
% 36.50/9.28 thf(mbox_s4_decl, type, mbox_s4: (($i > $o) > ($i > $o))).
% 36.50/9.28 thf(p_decl, type, p: ($i > $o)).
% 36.50/9.28 thf(big_r_decl, type, big_r: (mu > ($i > $o))).
% 36.50/9.28 thf(big_q_decl, type, big_q: (mu > ($i > $o))).
% 36.50/9.28 thf(sk1_decl, type, sk1: $i).
% 36.50/9.28 thf(sk2_decl, type, sk2: $i).
% 36.50/9.28 thf(sk3_decl, type, sk3: ($i > (mu > $o))).
% 36.50/9.28 thf(sk4_decl, type, sk4: ($i > (mu > ($i > $i)))).
% 36.50/9.28 thf(sk5_decl, type, sk5: $i).
% 36.50/9.28 thf(sk6_decl, type, sk6: mu).
% 36.50/9.28 thf(sk7_decl, type, sk7: $i).
% 36.50/9.28 thf(sk8_decl, type, sk8: $i).
% 36.50/9.28 thf(sk9_decl, type, sk9: mu).
% 36.50/9.28 thf(sk10_decl, type, sk10: $i).
% 36.50/9.28 thf(sk11_decl, type, sk11: ($i > mu)).
% 36.50/9.28 thf(mnot_def, definition, mnot = (^ [A:($i > $o),B:$i]: ~ (A @ B)) ).
% 36.50/9.28 thf(mor_def, definition, mor = (^ [A:($i > $o),B:($i > $o),C:$i]: ((A @ C) | (B @ C))) ).
% 36.50/9.28 thf(mand_def, definition, mand = (^ [A:($i > $o),B:($i > $o)]: (mnot @ (mor @ (mnot @ A) @ (mnot @ B)))) ).
% 36.50/9.28 thf(mimplies_def, definition, mimplies = (^ [A:($i > $o)]: (mor @ (mnot @ A))) ).
% 36.50/9.28 thf(mforall_ind_def, definition, mforall_ind = (^ [A:(mu > ($i > $o)),B:$i]: ! [C:mu]: ((exists_in_world @ C @ B) => (A @ C @ B))) ).
% 36.50/9.28 thf(mreflexive_def, definition, mreflexive = (^ [A:($i > ($i > $o))]: ! [B:$i]: (A @ B @ B)) ).
% 36.50/9.28 thf(mtransitive_def, definition, mtransitive = (^ [A:($i > ($i > $o))]: ! [B:$i,C:$i,D:$i]: (((A @ B @ C) & (A @ C @ D)) => (A @ B @ D))) ).
% 36.50/9.28 thf(mvalid_def, definition, mvalid = ((!) @ $i) ).
% 36.50/9.28 thf(mbox_s4_def, definition, mbox_s4 = (^ [A:($i > $o),B:$i]: ! [C:$i]: (~ (rel_s4 @ B @ C) | (A @ C))) ).
% 36.50/9.28 thf(sk1_def, definition, sk1 = (@+ [A:$i]: ~ (! [B:$i]: (~ (rel_s4 @ A @ B) | ~ (! [C:$i]: (~ (rel_s4 @ B @ C) | ! [D:mu]: ((exists_in_world @ D @ C) => (~ (~ (! [E:$i]: (~ (rel_s4 @ C @ E) | (p @ E))) | ~ (! [E:$i]: (~ (rel_s4 @ C @ E) | (big_q @ D @ E)))) | ~ (~ (! [E:$i]: (~ (rel_s4 @ C @ E) | ~ (! [F:$i]: (~ (rel_s4 @ E @ F) | (p @ F))))) | ~ (! [E:$i]: (~ (rel_s4 @ C @ E) | (big_r @ D @ E)))))))) | ! [C:$i]: (~ (rel_s4 @ B @ C) | ! [D:mu]: ((exists_in_world @ D @ C) => (! [E:$i]: (~ (rel_s4 @ C @ E) | (big_q @ D @ E))))) | ! [C:$i]: (~ (rel_s4 @ B @ C) | ! [D:mu]: ((exists_in_world @ D @ C) => (! [E:$i]: (~ (rel_s4 @ C @ E) | (big_r @ D @ E)))))))) ).
% 36.50/9.28 thf(sk2_def, definition, sk2 = (@+ [A:$i]: ~ (~ (rel_s4 @ sk1 @ A) | ~ (! [B:$i]: (~ (rel_s4 @ A @ B) | ! [C:mu]: ((exists_in_world @ C @ B) => (~ (~ (! [D:$i]: (~ (rel_s4 @ B @ D) | (p @ D))) | ~ (! [D:$i]: (~ (rel_s4 @ B @ D) | (big_q @ C @ D)))) | ~ (~ (! [D:$i]: (~ (rel_s4 @ B @ D) | ~ (! [E:$i]: (~ (rel_s4 @ D @ E) | (p @ E))))) | ~ (! [D:$i]: (~ (rel_s4 @ B @ D) | (big_r @ C @ D)))))))) | ! [B:$i]: (~ (rel_s4 @ A @ B) | ! [C:mu]: ((exists_in_world @ C @ B) => (! [D:$i]: (~ (rel_s4 @ B @ D) | (big_q @ C @ D))))) | ! [B:$i]: (~ (rel_s4 @ A @ B) | ! [C:mu]: ((exists_in_world @ C @ B) => (! [D:$i]: (~ (rel_s4 @ B @ D) | (big_r @ C @ D))))))) ).
% 36.50/9.28 thf(sk4_def, definition, sk4 = (^ [A:$i,B:mu,C:$i]: (@+ [D:$i]: ~ (~ (rel_s4 @ A @ D) | (p @ D)))) ).
% 36.50/9.28 thf(sk5_def, definition, sk5 = (@+ [A:$i]: ~ (~ (rel_s4 @ sk2 @ A) | ! [B:mu]: ((exists_in_world @ B @ A) => (! [C:$i]: (~ (rel_s4 @ A @ C) | (big_q @ B @ C)))))) ).
% 36.50/9.28 thf(sk6_def, definition, sk6 = (@+ [A:mu]: ~ ((exists_in_world @ A @ sk5) => (! [B:$i]: (~ (rel_s4 @ sk5 @ B) | (big_q @ A @ B))))) ).
% 36.50/9.28 thf(sk7_def, definition, sk7 = (@+ [A:$i]: ~ (~ (rel_s4 @ sk5 @ A) | (big_q @ sk6 @ A))) ).
% 36.50/9.28 thf(sk8_def, definition, sk8 = (@+ [A:$i]: ~ (~ (rel_s4 @ sk2 @ A) | ! [B:mu]: ((exists_in_world @ B @ A) => (! [C:$i]: (~ (rel_s4 @ A @ C) | (big_r @ B @ C)))))) ).
% 36.50/9.28 thf(sk9_def, definition, sk9 = (@+ [A:mu]: ~ ((exists_in_world @ A @ sk8) => (! [B:$i]: (~ (rel_s4 @ sk8 @ B) | (big_r @ A @ B))))) ).
% 36.50/9.28 thf(sk10_def, definition, sk10 = (@+ [A:$i]: ~ (~ (rel_s4 @ sk8 @ A) | (big_r @ sk9 @ A))) ).
% 36.50/9.28 thf(sk11_def, definition, sk11 = (^ [A:$i]: (@+ [B:mu]: (exists_in_world @ B @ A))) ).
% 36.50/9.28 thf(1,conjecture,((mvalid @ (mbox_s4 @ (mimplies @ (mbox_s4 @ (mforall_ind @ (^ [A:mu]: (mor @ (mand @ (mbox_s4 @ p) @ (mbox_s4 @ (big_q @ A))) @ (mand @ (mbox_s4 @ (mnot @ (mbox_s4 @ p))) @ (mbox_s4 @ (big_r @ A))))))) @ (mor @ (mbox_s4 @ (mforall_ind @ (^ [A:mu]: (mbox_s4 @ (big_q @ A))))) @ (mbox_s4 @ (mforall_ind @ (^ [A:mu]: (mbox_s4 @ (big_r @ A)))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x2118)).
% 36.50/9.28 thf(2,negated_conjecture,((~ (mvalid @ (mbox_s4 @ (mimplies @ (mbox_s4 @ (mforall_ind @ (^ [A:mu]: (mor @ (mand @ (mbox_s4 @ p) @ (mbox_s4 @ (big_q @ A))) @ (mand @ (mbox_s4 @ (mnot @ (mbox_s4 @ p))) @ (mbox_s4 @ (big_r @ A))))))) @ (mor @ (mbox_s4 @ (mforall_ind @ (^ [A:mu]: (mbox_s4 @ (big_q @ A))))) @ (mbox_s4 @ (mforall_ind @ (^ [A:mu]: (mbox_s4 @ (big_r @ A))))))))))),inference(neg_conjecture,[status(cth)],[1])).
% 36.50/9.28 thf(7,plain,((~ (! [A:$i,B:$i]: (~ (rel_s4 @ A @ B) | ~ (! [C:$i]: (~ (rel_s4 @ B @ C) | ! [D:mu]: ((exists_in_world @ D @ C) => (~ (~ (! [E:$i]: (~ (rel_s4 @ C @ E) | (p @ E))) | ~ (! [E:$i]: (~ (rel_s4 @ C @ E) | (big_q @ D @ E)))) | ~ (~ (! [E:$i]: (~ (rel_s4 @ C @ E) | ~ (! [F:$i]: (~ (rel_s4 @ E @ F) | (p @ F))))) | ~ (! [E:$i]: (~ (rel_s4 @ C @ E) | (big_r @ D @ E)))))))) | ! [C:$i]: (~ (rel_s4 @ B @ C) | ! [D:mu]: ((exists_in_world @ D @ C) => (! [E:$i]: (~ (rel_s4 @ C @ E) | (big_q @ D @ E))))) | ! [C:$i]: (~ (rel_s4 @ B @ C) | ! [D:mu]: ((exists_in_world @ D @ C) => (! [E:$i]: (~ (rel_s4 @ C @ E) | (big_r @ D @ E))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])).
% 36.50/9.28 thf(8,plain,(! [F:$i,E:$i,D:$i,C:$i,B:mu,A:$i] : (((rel_s4 @ sk1 @ sk2) & (~ (rel_s4 @ sk2 @ A) | ~ (exists_in_world @ B @ A) | ~ (rel_s4 @ A @ C) | (p @ C) | (sk3 @ A @ B)) & (~ (rel_s4 @ sk2 @ A) | ~ (exists_in_world @ B @ A) | ~ (rel_s4 @ A @ D) | (big_q @ B @ D) | (sk3 @ A @ B)) & (~ (rel_s4 @ sk2 @ A) | ~ (exists_in_world @ B @ A) | ~ (sk3 @ A @ B) | ~ (rel_s4 @ A @ E) | (rel_s4 @ E @ (sk4 @ E @ B @ A))) & (~ (rel_s4 @ sk2 @ A) | ~ (exists_in_world @ B @ A) | ~ (sk3 @ A @ B) | ~ (rel_s4 @ A @ E) | ~ (p @ (sk4 @ E @ B @ A))) & (~ (rel_s4 @ sk2 @ A) | ~ (exists_in_world @ B @ A) | ~ (sk3 @ A @ B) | ~ (rel_s4 @ A @ F) | (big_r @ B @ F)) & (rel_s4 @ sk2 @ sk5) & (exists_in_world @ sk6 @ sk5) & (rel_s4 @ sk5 @ sk7) & ~ (big_q @ sk6 @ sk7) & (rel_s4 @ sk2 @ sk8) & (exists_in_world @ sk9 @ sk8) & (rel_s4 @ sk8 @ sk10) & ~ (big_r @ sk9 @ sk10)))),inference(cnf,[status(esa)],[7])).
% 36.50/9.28 thf(11,plain,((rel_s4 @ sk2 @ sk5)),inference(cnfConj,[status(thm)],[8])).
% 36.50/9.28 thf(5,axiom,((mtransitive @ rel_s4)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a2)).
% 36.50/9.28 thf(31,plain,((! [A:$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])).
% 36.50/9.28 thf(32,plain,(! [C:$i,B:$i,A:$i] : ((~ (rel_s4 @ A @ B)) | (~ (rel_s4 @ B @ C)) | (rel_s4 @ A @ C))),inference(cnf,[status(esa)],[31])).
% 36.50/9.28 thf(113,plain,(! [C:$i,B:$i,A:$i] : ((~ (rel_s4 @ A @ B)) | ~ (($true)) | (rel_s4 @ A @ C) | ((rel_s4 @ sk2 @ sk5) != (rel_s4 @ B @ C)))),inference(paramod_ordered,[status(thm)],[11,32])).
% 36.50/9.28 thf(114,plain,(! [C:$i,B:$i,A:$i] : ((~ (rel_s4 @ A @ B)) | (rel_s4 @ A @ C) | ((rel_s4 @ sk2 @ sk5) != (rel_s4 @ B @ C)))),inference(simp,[status(thm)],[113])).
% 36.50/9.28 thf(115,plain,(! [A:$i] : ((~ (rel_s4 @ A @ sk2)) | (rel_s4 @ A @ sk5))),inference(pattern_uni,[status(thm)],[114:[bind(A, $thf(A)),bind(B, $thf(sk2)),bind(C, $thf(sk5))]])).
% 36.50/9.28 thf(10,plain,((rel_s4 @ sk5 @ sk7)),inference(cnfConj,[status(thm)],[8])).
% 36.50/9.28 thf(9,plain,((rel_s4 @ sk1 @ sk2)),inference(cnfConj,[status(thm)],[8])).
% 36.50/9.28 thf(107,plain,(! [C:$i,B:$i,A:$i] : ((~ (rel_s4 @ A @ B)) | ~ (($true)) | (rel_s4 @ A @ C) | ((rel_s4 @ sk1 @ sk2) != (rel_s4 @ B @ C)))),inference(paramod_ordered,[status(thm)],[9,32])).
% 36.50/9.28 thf(108,plain,(! [C:$i,B:$i,A:$i] : ((~ (rel_s4 @ A @ B)) | (rel_s4 @ A @ C) | ((rel_s4 @ sk1 @ sk2) != (rel_s4 @ B @ C)))),inference(simp,[status(thm)],[107])).
% 36.50/9.28 thf(109,plain,(! [A:$i] : ((~ (rel_s4 @ A @ sk1)) | (rel_s4 @ A @ sk2))),inference(pattern_uni,[status(thm)],[108:[bind(A, $thf(A)),bind(B, $thf(sk1)),bind(C, $thf(sk2))]])).
% 36.50/9.28 thf(17,plain,((rel_s4 @ sk8 @ sk10)),inference(cnfConj,[status(thm)],[8])).
% 36.50/9.28 thf(613,plain,(! [A:$i] : (~ (($true)) | (rel_s4 @ A @ sk2) | ((rel_s4 @ sk8 @ sk10) != (rel_s4 @ A @ sk1)))),inference(paramod_ordered,[status(thm)],[17,109])).
% 36.50/9.28 thf(614,plain,(! [A:$i] : ((rel_s4 @ A @ sk2) | ((rel_s4 @ sk8 @ sk10) != (rel_s4 @ A @ sk1)))),inference(simp,[status(thm)],[613])).
% 36.50/9.28 thf(637,plain,(! [A:$i] : ((rel_s4 @ A @ sk2) | (sk8 != A) | (sk10 != sk1))),inference(simp,[status(thm)],[614])).
% 36.50/9.28 thf(657,plain,((rel_s4 @ sk8 @ sk2) | (sk10 != sk1)),inference(simp,[status(thm)],[637])).
% 36.50/9.28 thf(12,plain,((exists_in_world @ sk6 @ sk5)),inference(cnfConj,[status(thm)],[8])).
% 36.50/9.28 thf(101,plain,(! [C:$i,B:$i,A:$i] : ((~ (rel_s4 @ A @ B)) | ~ (($true)) | (rel_s4 @ A @ C) | ((rel_s4 @ sk5 @ sk7) != (rel_s4 @ B @ C)))),inference(paramod_ordered,[status(thm)],[10,32])).
% 36.50/9.28 thf(102,plain,(! [C:$i,B:$i,A:$i] : ((~ (rel_s4 @ A @ B)) | (rel_s4 @ A @ C) | ((rel_s4 @ sk5 @ sk7) != (rel_s4 @ B @ C)))),inference(simp,[status(thm)],[101])).
% 36.50/9.28 thf(103,plain,(! [A:$i] : ((~ (rel_s4 @ A @ sk5)) | (rel_s4 @ A @ sk7))),inference(pattern_uni,[status(thm)],[102:[bind(A, $thf(A)),bind(B, $thf(sk5)),bind(C, $thf(sk7))]])).
% 36.50/9.28 thf(929,plain,(! [A:$i] : ((sk10 != sk1) | ~ (($true)) | (rel_s4 @ A @ sk5) | ((rel_s4 @ sk8 @ sk2) != (rel_s4 @ A @ sk2)))),inference(paramod_ordered,[status(thm)],[657,115])).
% 36.50/9.28 thf(930,plain,(! [A:$i] : ((sk10 != sk1) | (rel_s4 @ A @ sk5) | ((rel_s4 @ sk8 @ sk2) != (rel_s4 @ A @ sk2)))),inference(simp,[status(thm)],[929])).
% 36.50/9.28 thf(931,plain,((sk10 != sk1) | (rel_s4 @ sk8 @ sk5)),inference(pattern_uni,[status(thm)],[930:[bind(A, $thf(sk8))]])).
% 36.50/9.28 thf(13,plain,(! [C:$i,B:mu,A:$i] : ((~ (rel_s4 @ sk2 @ A)) | (~ (exists_in_world @ B @ A)) | (~ (sk3 @ A @ B)) | (~ (rel_s4 @ A @ C)) | (~ (p @ (sk4 @ C @ B @ A))))),inference(cnfConj,[status(thm)],[8])).
% 36.50/9.28 thf(24,plain,(! [C:$i,B:mu,A:$i] : ((~ (rel_s4 @ sk2 @ A)) | (~ (exists_in_world @ B @ A)) | (~ (sk3 @ A @ B)) | (~ (rel_s4 @ A @ C)) | (~ (p @ (sk4 @ C @ B @ A))))),inference(simp,[status(thm)],[13])).
% 36.50/9.28 thf(18,plain,(! [C:$i,B:mu,A:$i] : ((~ (rel_s4 @ sk2 @ A)) | (~ (exists_in_world @ B @ A)) | (~ (rel_s4 @ A @ C)) | (big_q @ B @ C) | (sk3 @ A @ B))),inference(cnfConj,[status(thm)],[8])).
% 36.50/9.28 thf(25,plain,(! [C:$i,B:mu,A:$i] : ((~ (rel_s4 @ sk2 @ A)) | (~ (exists_in_world @ B @ A)) | (~ (rel_s4 @ A @ C)) | (big_q @ B @ C) | (sk3 @ A @ B))),inference(simp,[status(thm)],[18])).
% 36.50/9.28 thf(573,plain,(! [A:$i] : (~ (($true)) | (rel_s4 @ A @ sk2) | ((rel_s4 @ sk5 @ sk7) != (rel_s4 @ A @ sk1)))),inference(paramod_ordered,[status(thm)],[10,109])).
% 36.50/9.28 thf(574,plain,(! [A:$i] : ((rel_s4 @ A @ sk2) | ((rel_s4 @ sk5 @ sk7) != (rel_s4 @ A @ sk1)))),inference(simp,[status(thm)],[573])).
% 36.50/9.28 thf(631,plain,(! [A:$i] : ((rel_s4 @ A @ sk2) | (sk5 != A) | (sk7 != sk1))),inference(simp,[status(thm)],[574])).
% 36.50/9.28 thf(651,plain,((rel_s4 @ sk5 @ sk2) | (sk7 != sk1)),inference(simp,[status(thm)],[631])).
% 36.50/9.28 thf(20,plain,((~ (big_q @ sk6 @ sk7))),inference(cnfConj,[status(thm)],[8])).
% 36.50/9.28 thf(978,plain,(! [A:$i] : (~ (($true)) | (rel_s4 @ A @ sk5) | ((rel_s4 @ sk8 @ sk10) != (rel_s4 @ A @ sk2)))),inference(paramod_ordered,[status(thm)],[17,115])).
% 36.50/9.28 thf(979,plain,(! [A:$i] : ((rel_s4 @ A @ sk5) | ((rel_s4 @ sk8 @ sk10) != (rel_s4 @ A @ sk2)))),inference(simp,[status(thm)],[978])).
% 36.50/9.28 thf(999,plain,(! [A:$i] : ((rel_s4 @ A @ sk5) | (sk8 != A) | (sk10 != sk2))),inference(simp,[status(thm)],[979])).
% 36.50/9.28 thf(1013,plain,((rel_s4 @ sk8 @ sk5) | (sk10 != sk2)),inference(simp,[status(thm)],[999])).
% 36.50/9.28 thf(21,plain,((exists_in_world @ sk9 @ sk8)),inference(cnfConj,[status(thm)],[8])).
% 36.50/9.28 thf(235,plain,(! [C:$i,B:mu,A:$i] : ((~ (rel_s4 @ sk2 @ A)) | ~ (($true)) | (~ (sk3 @ A @ B)) | (~ (rel_s4 @ A @ C)) | (~ (p @ (sk4 @ C @ B @ A))) | ((exists_in_world @ sk9 @ sk8) != (exists_in_world @ B @ A)))),inference(paramod_ordered,[status(thm)],[21,24])).
% 36.50/9.29 thf(236,plain,(! [C:$i,B:mu,A:$i] : ((~ (rel_s4 @ sk2 @ A)) | (~ (sk3 @ A @ B)) | (~ (rel_s4 @ A @ C)) | (~ (p @ (sk4 @ C @ B @ A))) | ((exists_in_world @ sk9 @ sk8) != (exists_in_world @ B @ A)))),inference(simp,[status(thm)],[235])).
% 36.50/9.29 thf(237,plain,(! [A:$i] : ((~ (rel_s4 @ sk2 @ sk8)) | (~ (sk3 @ sk8 @ sk9)) | (~ (rel_s4 @ sk8 @ A)) | (~ (p @ (sk4 @ A @ sk9 @ sk8))))),inference(pattern_uni,[status(thm)],[236:[bind(A, $thf(sk8)),bind(B, $thf(sk9))]])).
% 36.50/9.29 thf(273,plain,(! [A:$i] : ((~ (rel_s4 @ sk2 @ sk8)) | (~ (sk3 @ sk8 @ sk9)) | (~ (rel_s4 @ sk8 @ A)) | (~ (p @ (sk4 @ A @ sk9 @ sk8))))),inference(simp,[status(thm)],[237])).
% 36.50/9.29 thf(15,plain,((rel_s4 @ sk2 @ sk8)),inference(cnfConj,[status(thm)],[8])).
% 36.50/9.29 thf(284,plain,(! [A:$i] : (~ (($true)) | (~ (sk3 @ sk8 @ sk9)) | (~ (rel_s4 @ sk8 @ A)) | (~ (p @ (sk4 @ A @ sk9 @ sk8))))),inference(rewrite,[status(thm)],[273,15])).
% 36.50/9.29 thf(285,plain,(! [A:$i] : ((~ (sk3 @ sk8 @ sk9)) | (~ (rel_s4 @ sk8 @ A)) | (~ (p @ (sk4 @ A @ sk9 @ sk8))))),inference(simp,[status(thm)],[284])).
% 36.50/9.29 thf(286,plain,(! [A:$i] : ((~ (sk3 @ sk8 @ sk9)) | ~ (($true)) | (~ (p @ (sk4 @ A @ sk9 @ sk8))) | ((rel_s4 @ sk8 @ A) != (rel_s4 @ sk5 @ sk7)))),inference(paramod_ordered,[status(thm)],[10,285])).
% 36.50/9.29 thf(287,plain,(! [A:$i] : ((~ (sk3 @ sk8 @ sk9)) | (~ (p @ (sk4 @ A @ sk9 @ sk8))) | ((rel_s4 @ sk8 @ A) != (rel_s4 @ sk5 @ sk7)))),inference(simp,[status(thm)],[286])).
% 36.50/9.29 thf(311,plain,(! [A:$i] : ((~ (sk3 @ sk8 @ sk9)) | (~ (p @ (sk4 @ A @ sk9 @ sk8))) | (sk8 != sk5) | (A != sk7))),inference(simp,[status(thm)],[287])).
% 36.50/9.29 thf(316,plain,((~ (sk3 @ sk8 @ sk9)) | (~ (p @ (sk4 @ sk7 @ sk9 @ sk8))) | (sk8 != sk5)),inference(simp,[status(thm)],[311])).
% 36.50/9.29 thf(4,axiom,((mreflexive @ rel_s4)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a1)).
% 36.50/9.29 thf(29,plain,((! [A:$i]: (rel_s4 @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4])).
% 36.50/9.29 thf(300,plain,(! [A:$i] : ((~ (sk3 @ sk8 @ sk9)) | ~ (($true)) | (~ (p @ (sk4 @ A @ sk9 @ sk8))) | ((rel_s4 @ sk8 @ sk10) != (rel_s4 @ sk8 @ A)))),inference(paramod_ordered,[status(thm)],[17,285])).
% 36.50/9.29 thf(301,plain,(! [A:$i] : ((~ (sk3 @ sk8 @ sk9)) | (~ (p @ (sk4 @ A @ sk9 @ sk8))) | ((rel_s4 @ sk8 @ sk10) != (rel_s4 @ sk8 @ A)))),inference(simp,[status(thm)],[300])).
% 36.50/9.29 thf(302,plain,((~ (sk3 @ sk8 @ sk9)) | (~ (p @ (sk4 @ sk10 @ sk9 @ sk8)))),inference(pattern_uni,[status(thm)],[301:[bind(A, $thf(sk10))]])).
% 36.50/9.29 thf(3,axiom,((! [A:$i]: ? [B:mu]: (exists_in_world @ B @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonempty_ax)).
% 36.50/9.29 thf(27,plain,((! [A:$i]: ? [B:mu]: (exists_in_world @ B @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3])).
% 36.50/9.29 thf(28,plain,(! [A:$i] : ((exists_in_world @ (sk11 @ A) @ A))),inference(cnf,[status(esa)],[27])).
% 36.50/9.29 thf(163,plain,(! [A:$i] : (~ (($true)) | (rel_s4 @ A @ sk7) | ((rel_s4 @ sk2 @ sk5) != (rel_s4 @ A @ sk5)))),inference(paramod_ordered,[status(thm)],[11,103])).
% 36.50/9.29 thf(164,plain,(! [A:$i] : ((rel_s4 @ A @ sk7) | ((rel_s4 @ sk2 @ sk5) != (rel_s4 @ A @ sk5)))),inference(simp,[status(thm)],[163])).
% 36.50/9.29 thf(165,plain,((rel_s4 @ sk2 @ sk7)),inference(pattern_uni,[status(thm)],[164:[bind(A, $thf(sk2))]])).
% 36.50/9.29 thf(6,axiom,((! [A:mu,B:$i,C:$i]: (((exists_in_world @ A @ B) & (rel_s4 @ B @ C)) => (exists_in_world @ A @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cumulative_ax)).
% 36.50/9.29 thf(33,plain,((! [A:mu,B:$i,C:$i]: (((exists_in_world @ A @ B) & (rel_s4 @ B @ C)) => (exists_in_world @ A @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6])).
% 36.50/9.29 thf(926,plain,(! [A:$i] : (~ (($true)) | (rel_s4 @ A @ sk5) | ((rel_s4 @ sk1 @ sk2) != (rel_s4 @ A @ sk2)))),inference(paramod_ordered,[status(thm)],[9,115])).
% 36.50/9.29 thf(927,plain,(! [A:$i] : ((rel_s4 @ A @ sk5) | ((rel_s4 @ sk1 @ sk2) != (rel_s4 @ A @ sk2)))),inference(simp,[status(thm)],[926])).
% 36.50/9.29 thf(928,plain,((rel_s4 @ sk1 @ sk5)),inference(pattern_uni,[status(thm)],[927:[bind(A, $thf(sk1))]])).
% 36.50/9.29 thf(1030,plain,(! [A:$i] : (~ (($true)) | (rel_s4 @ A @ sk7) | ((rel_s4 @ sk1 @ sk5) != (rel_s4 @ A @ sk5)))),inference(paramod_ordered,[status(thm)],[928,103])).
% 36.50/9.29 thf(1031,plain,(! [A:$i] : ((rel_s4 @ A @ sk7) | ((rel_s4 @ sk1 @ sk5) != (rel_s4 @ A @ sk5)))),inference(simp,[status(thm)],[1030])).
% 36.50/9.29 thf(1032,plain,((rel_s4 @ sk1 @ sk7)),inference(pattern_uni,[status(thm)],[1031:[bind(A, $thf(sk1))]])).
% 36.50/9.29 thf(293,plain,(! [A:$i] : ((~ (sk3 @ sk8 @ sk9)) | ~ (($true)) | (~ (p @ (sk4 @ A @ sk9 @ sk8))) | ((rel_s4 @ sk8 @ A) != (rel_s4 @ sk2 @ sk5)))),inference(paramod_ordered,[status(thm)],[11,285])).
% 36.50/9.29 thf(294,plain,(! [A:$i] : ((~ (sk3 @ sk8 @ sk9)) | (~ (p @ (sk4 @ A @ sk9 @ sk8))) | ((rel_s4 @ sk8 @ A) != (rel_s4 @ sk2 @ sk5)))),inference(simp,[status(thm)],[293])).
% 36.50/9.29 thf(312,plain,(! [A:$i] : ((~ (sk3 @ sk8 @ sk9)) | (~ (p @ (sk4 @ A @ sk9 @ sk8))) | (sk8 != sk2) | (A != sk5))),inference(simp,[status(thm)],[294])).
% 36.50/9.29 thf(317,plain,((~ (sk3 @ sk8 @ sk9)) | (~ (p @ (sk4 @ sk5 @ sk9 @ sk8))) | (sk8 != sk2)),inference(simp,[status(thm)],[312])).
% 36.50/9.29 thf(22,plain,((~ (big_r @ sk9 @ sk10))),inference(cnfConj,[status(thm)],[8])).
% 36.50/9.29 thf(288,plain,(! [A:$i] : ((~ (sk3 @ sk8 @ sk9)) | ~ (($true)) | (~ (p @ (sk4 @ A @ sk9 @ sk8))) | ((rel_s4 @ sk8 @ A) != (rel_s4 @ sk1 @ sk2)))),inference(paramod_ordered,[status(thm)],[9,285])).
% 36.50/9.29 thf(289,plain,(! [A:$i] : ((~ (sk3 @ sk8 @ sk9)) | (~ (p @ (sk4 @ A @ sk9 @ sk8))) | ((rel_s4 @ sk8 @ A) != (rel_s4 @ sk1 @ sk2)))),inference(simp,[status(thm)],[288])).
% 36.50/9.29 thf(309,plain,(! [A:$i] : ((~ (sk3 @ sk8 @ sk9)) | (~ (p @ (sk4 @ A @ sk9 @ sk8))) | (sk8 != sk1) | (A != sk2))),inference(simp,[status(thm)],[289])).
% 36.50/9.29 thf(314,plain,((~ (sk3 @ sk8 @ sk9)) | (~ (p @ (sk4 @ sk2 @ sk9 @ sk8))) | (sk8 != sk1)),inference(simp,[status(thm)],[309])).
% 36.50/9.29 thf(16,plain,(! [C:$i,B:mu,A:$i] : ((~ (rel_s4 @ sk2 @ A)) | (~ (exists_in_world @ B @ A)) | (~ (sk3 @ A @ B)) | (~ (rel_s4 @ A @ C)) | (big_r @ B @ C))),inference(cnfConj,[status(thm)],[8])).
% 36.50/9.29 thf(26,plain,(! [C:$i,B:mu,A:$i] : ((~ (rel_s4 @ sk2 @ A)) | (~ (exists_in_world @ B @ A)) | (~ (sk3 @ A @ B)) | (~ (rel_s4 @ A @ C)) | (big_r @ B @ C))),inference(simp,[status(thm)],[16])).
% 36.50/9.29 thf(14,plain,(! [C:$i,B:mu,A:$i] : ((~ (rel_s4 @ sk2 @ A)) | (~ (exists_in_world @ B @ A)) | (~ (sk3 @ A @ B)) | (~ (rel_s4 @ A @ C)) | (rel_s4 @ C @ (sk4 @ C @ B @ A)))),inference(cnfConj,[status(thm)],[8])).
% 36.50/9.29 thf(23,plain,(! [C:$i,B:mu,A:$i] : ((~ (rel_s4 @ sk2 @ A)) | (~ (exists_in_world @ B @ A)) | (~ (sk3 @ A @ B)) | (~ (rel_s4 @ A @ C)) | (rel_s4 @ C @ (sk4 @ C @ B @ A)))),inference(simp,[status(thm)],[14])).
% 36.50/9.29 thf(30,plain,(! [A:$i] : ((rel_s4 @ A @ A))),inference(cnf,[status(esa)],[29])).
% 36.50/9.29 thf(19,plain,(! [C:$i,B:mu,A:$i] : ((~ (rel_s4 @ sk2 @ A)) | (~ (exists_in_world @ B @ A)) | (~ (rel_s4 @ A @ C)) | (p @ C) | (sk3 @ A @ B))),inference(cnfConj,[status(thm)],[8])).
% 36.50/9.29 thf(303,plain,(! [B:$i,A:$i] : ((~ (sk3 @ sk8 @ sk9)) | ~ (($true)) | (~ (p @ (sk4 @ B @ sk9 @ sk8))) | ((rel_s4 @ A @ A) != (rel_s4 @ sk8 @ B)))),inference(paramod_ordered,[status(thm)],[30,285])).
% 36.50/9.29 thf(304,plain,(! [B:$i,A:$i] : ((~ (sk3 @ sk8 @ sk9)) | (~ (p @ (sk4 @ B @ sk9 @ sk8))) | ((rel_s4 @ A @ A) != (rel_s4 @ sk8 @ B)))),inference(simp,[status(thm)],[303])).
% 36.50/9.29 thf(305,plain,((~ (sk3 @ sk8 @ sk9)) | (~ (p @ (sk4 @ sk8 @ sk9 @ sk8)))),inference(pattern_uni,[status(thm)],[304:[bind(A, $thf(sk8)),bind(B, $thf(sk8))]])).
% 36.50/9.29 thf(177,plain,(! [A:$i] : (~ (($true)) | (rel_s4 @ A @ sk7) | ((rel_s4 @ sk8 @ sk10) != (rel_s4 @ A @ sk5)))),inference(paramod_ordered,[status(thm)],[17,103])).
% 36.50/9.29 thf(178,plain,(! [A:$i] : ((rel_s4 @ A @ sk7) | ((rel_s4 @ sk8 @ sk10) != (rel_s4 @ A @ sk5)))),inference(simp,[status(thm)],[177])).
% 36.50/9.29 thf(191,plain,(! [A:$i] : ((rel_s4 @ A @ sk7) | (sk8 != A) | (sk10 != sk5))),inference(simp,[status(thm)],[178])).
% 36.50/9.29 thf(200,plain,((rel_s4 @ sk8 @ sk7) | (sk10 != sk5)),inference(simp,[status(thm)],[191])).
% 36.50/9.29 thf(23579,plain,(($false)),inference(e,[status(thm)],[115,10,109,657,12,7,103,31,931,24,25,651,20,1013,316,29,302,28,21,165,33,1032,285,317,9,32,17,22,27,11,314,26,23,30,19,305,928,15,200])).
% 36.50/9.29 % SZS output end Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 36.50/9.29 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------