%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYN045^7 : 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 : 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 08:41:29 AM UTC 2026
% Result : Theorem 12.69s 4.57s
% Output : Refutation 11.94s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN045^7 : 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
% 0.10/0.20 % Computer : n018.cluster.edu
% 0.10/0.20 % Model : x86_64 x86_64
% 0.10/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.20 % Memory : 8046.5625MB
% 0.10/0.20 % OS : Linux 6.8.0-71-generic
% 0.10/0.20 % CPULimit : 300
% 0.10/0.20 % WCLimit : 300
% 0.10/0.20 % DateTime : Tue Sep 29 16:16:41 UTC 2026
% 0.10/0.20 % CPUTime :
% 0.10/0.20 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
% 1.05/0.89 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.91/1.24 % [INFO] Parsing done (339ms).
% 1.91/1.26 % [INFO] Running in sequential loop mode.
% 2.92/1.84 % [INFO] eprover registered as external prover.
% 2.92/1.85 % [INFO] Scanning for conjecture ...
% 3.46/2.11 % [INFO] Found a conjecture (or negated_conjecture) and 4 axioms. Running axiom selection ...
% 3.67/2.16 % [INFO] Axiom selection finished. Selected 4 axioms (removed 0 axioms).
% 3.67/2.17 % [INFO] Problem is higher-order (TPTP THF).
% 3.67/2.17 % [INFO] Type checking passed.
% 3.67/2.18 % [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 ...
% 12.69/4.57 % External prover 'e' found a proof!
% 12.69/4.57 % [INFO] Killing All external provers ...
% 12.69/4.57 % Time passed: 4223ms (effective reasoning time: 3304ms)
% 12.69/4.57 % 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)>
% 12.69/4.57 % Axioms used in derivation (4): a1, a2, nonempty_ax, cumulative_ax
% 12.69/4.57 % No. of inferences in proof: 74
% 12.69/4.57 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 4223 ms resp. 3304 ms w/o parsing
% 11.94/4.69 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% 11.94/4.69 thf(mu_type, type, mu: $tType).
% 11.94/4.69 thf(mnot_decl, type, mnot: (($i > $o) > ($i > $o))).
% 11.94/4.69 thf(mor_decl, type, mor: (($i > $o) > (($i > $o) > ($i > $o)))).
% 11.94/4.69 thf(mand_decl, type, mand: (($i > $o) > (($i > $o) > ($i > $o)))).
% 11.94/4.69 thf(mimplies_decl, type, mimplies: (($i > $o) > (($i > $o) > ($i > $o)))).
% 11.94/4.69 thf(exists_in_world_decl, type, exists_in_world: (mu > ($i > $o))).
% 11.94/4.69 thf(mreflexive_decl, type, mreflexive: (($i > ($i > $o)) > $o)).
% 11.94/4.69 thf(mtransitive_decl, type, mtransitive: (($i > ($i > $o)) > $o)).
% 11.94/4.69 thf(mvalid_decl, type, mvalid: (($i > $o) > $o)).
% 11.94/4.69 thf(rel_s4_decl, type, rel_s4: ($i > ($i > $o))).
% 11.94/4.69 thf(mbox_s4_decl, type, mbox_s4: (($i > $o) > ($i > $o))).
% 11.94/4.69 thf(r_decl, type, r: ($i > $o)).
% 11.94/4.69 thf(q_decl, type, q: ($i > $o)).
% 11.94/4.69 thf(p_decl, type, p: ($i > $o)).
% 11.94/4.69 thf(sk1_decl, type, sk1: $o).
% 11.94/4.69 thf(sk2_decl, type, sk2: $i).
% 11.94/4.69 thf(sk3_decl, type, sk3: $i).
% 11.94/4.69 thf(sk4_decl, type, sk4: $o).
% 11.94/4.69 thf(sk5_decl, type, sk5: $i).
% 11.94/4.69 thf(sk6_decl, type, sk6: $i).
% 11.94/4.69 thf(sk7_decl, type, sk7: $i).
% 11.94/4.69 thf(sk8_decl, type, sk8: $i).
% 11.94/4.69 thf(sk9_decl, type, sk9: $i).
% 11.94/4.69 thf(sk10_decl, type, sk10: $i).
% 11.94/4.69 thf(sk11_decl, type, sk11: $i).
% 11.94/4.69 thf(sk12_decl, type, sk12: $i).
% 11.94/4.69 thf(sk13_decl, type, sk13: $i).
% 11.94/4.69 thf(sk14_decl, type, sk14: ($i > mu)).
% 11.94/4.69 thf(mnot_def, definition, mnot = (^ [A:($i > $o),B:$i]: ~ (A @ B)) ).
% 11.94/4.69 thf(mor_def, definition, mor = (^ [A:($i > $o),B:($i > $o),C:$i]: ((A @ C) | (B @ C))) ).
% 11.94/4.69 thf(mand_def, definition, mand = (^ [A:($i > $o),B:($i > $o)]: (mnot @ (mor @ (mnot @ A) @ (mnot @ B)))) ).
% 11.94/4.69 thf(mimplies_def, definition, mimplies = (^ [A:($i > $o)]: (mor @ (mnot @ A))) ).
% 11.94/4.69 thf(mreflexive_def, definition, mreflexive = (^ [A:($i > ($i > $o))]: ! [B:$i]: (A @ B @ B)) ).
% 11.94/4.69 thf(mtransitive_def, definition, mtransitive = (^ [A:($i > ($i > $o))]: ! [B:$i,C:$i,D:$i]: (((A @ B @ C) & (A @ C @ D)) => (A @ B @ D))) ).
% 11.94/4.69 thf(mvalid_def, definition, mvalid = ((!) @ $i) ).
% 11.94/4.69 thf(mbox_s4_def, definition, mbox_s4 = (^ [A:($i > $o),B:$i]: ! [C:$i]: (~ (rel_s4 @ B @ C) | (A @ C))) ).
% 11.94/4.69 thf(sk2_def, definition, sk2 = (@+ [A:$i]: ~ (! [B:$i]: (~ (rel_s4 @ A @ B) | ~ (! [C:$i]: (~ (rel_s4 @ B @ C) | (p @ C)) | ~ (~ (! [C:$i]: (~ (rel_s4 @ B @ C) | (q @ C))) | ~ (! [C:$i]: (~ (rel_s4 @ B @ C) | (r @ C))))) | ~ (~ (! [C:$i]: (~ (rel_s4 @ B @ C) | (p @ C)) | ! [C:$i]: (~ (rel_s4 @ B @ C) | (q @ C))) | ~ (! [C:$i]: (~ (rel_s4 @ B @ C) | (p @ C)) | ! [C:$i]: (~ (rel_s4 @ B @ C) | (r @ C))))))) ).
% 11.94/4.69 thf(sk3_def, definition, sk3 = (@+ [A:$i]: ~ (~ (rel_s4 @ sk2 @ A) | ~ (! [B:$i]: (~ (rel_s4 @ A @ B) | (p @ B)) | ~ (~ (! [B:$i]: (~ (rel_s4 @ A @ B) | (q @ B))) | ~ (! [B:$i]: (~ (rel_s4 @ A @ B) | (r @ B))))) | ~ (~ (! [B:$i]: (~ (rel_s4 @ A @ B) | (p @ B)) | ! [B:$i]: (~ (rel_s4 @ A @ B) | (q @ B))) | ~ (! [B:$i]: (~ (rel_s4 @ A @ B) | (p @ B)) | ! [B:$i]: (~ (rel_s4 @ A @ B) | (r @ B)))))) ).
% 11.94/4.69 thf(sk5_def, definition, sk5 = (@+ [A:$i]: ~ (~ (rel_s4 @ sk3 @ A) | (p @ A))) ).
% 11.94/4.69 thf(sk6_def, definition, sk6 = (@+ [A:$i]: ~ (~ (rel_s4 @ sk3 @ A) | (q @ A))) ).
% 11.94/4.69 thf(sk7_def, definition, sk7 = (@+ [A:$i]: ~ (~ (rel_s4 @ sk3 @ A) | (p @ A))) ).
% 11.94/4.69 thf(sk8_def, definition, sk8 = (@+ [A:$i]: ~ (~ (rel_s4 @ sk3 @ A) | (r @ A))) ).
% 11.94/4.69 thf(sk9_def, definition, sk9 = (@+ [A:$i]: ~ (! [B:$i]: (~ (rel_s4 @ A @ B) | ~ (! [C:$i]: (~ (rel_s4 @ B @ C) | (p @ C)) | ! [C:$i]: (~ (rel_s4 @ B @ C) | (q @ C))) | ~ (! [C:$i]: (~ (rel_s4 @ B @ C) | (p @ C)) | ! [C:$i]: (~ (rel_s4 @ B @ C) | (r @ C))) | ! [C:$i]: (~ (rel_s4 @ B @ C) | (p @ C)) | ~ (~ (! [C:$i]: (~ (rel_s4 @ B @ C) | (q @ C))) | ~ (! [C:$i]: (~ (rel_s4 @ B @ C) | (r @ C))))))) ).
% 11.94/4.69 thf(sk10_def, definition, sk10 = (@+ [A:$i]: ~ (~ (rel_s4 @ sk9 @ A) | ~ (! [B:$i]: (~ (rel_s4 @ A @ B) | (p @ B)) | ! [B:$i]: (~ (rel_s4 @ A @ B) | (q @ B))) | ~ (! [B:$i]: (~ (rel_s4 @ A @ B) | (p @ B)) | ! [B:$i]: (~ (rel_s4 @ A @ B) | (r @ B))) | ! [B:$i]: (~ (rel_s4 @ A @ B) | (p @ B)) | ~ (~ (! [B:$i]: (~ (rel_s4 @ A @ B) | (q @ B))) | ~ (! [B:$i]: (~ (rel_s4 @ A @ B) | (r @ B)))))) ).
% 11.94/4.69 thf(sk11_def, definition, sk11 = (@+ [A:$i]: ~ (~ (rel_s4 @ sk10 @ A) | (p @ A))) ).
% 11.94/4.69 thf(sk12_def, definition, sk12 = (@+ [A:$i]: ~ (~ (rel_s4 @ sk10 @ A) | (q @ A))) ).
% 11.94/4.69 thf(sk13_def, definition, sk13 = (@+ [A:$i]: ~ (~ (rel_s4 @ sk10 @ A) | (r @ A))) ).
% 11.94/4.69 thf(sk14_def, definition, sk14 = (^ [A:$i]: (@+ [B:mu]: (exists_in_world @ B @ A))) ).
% 11.94/4.69 thf(1,conjecture,((mvalid @ (mand @ (mbox_s4 @ (mimplies @ (mor @ (mbox_s4 @ p) @ (mand @ (mbox_s4 @ q) @ (mbox_s4 @ r))) @ (mand @ (mor @ (mbox_s4 @ p) @ (mbox_s4 @ q)) @ (mor @ (mbox_s4 @ p) @ (mbox_s4 @ r))))) @ (mbox_s4 @ (mimplies @ (mand @ (mor @ (mbox_s4 @ p) @ (mbox_s4 @ q)) @ (mor @ (mbox_s4 @ p) @ (mbox_s4 @ r))) @ (mor @ (mbox_s4 @ p) @ (mand @ (mbox_s4 @ q) @ (mbox_s4 @ r)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel13)).
% 11.94/4.69 thf(2,negated_conjecture,((~ (mvalid @ (mand @ (mbox_s4 @ (mimplies @ (mor @ (mbox_s4 @ p) @ (mand @ (mbox_s4 @ q) @ (mbox_s4 @ r))) @ (mand @ (mor @ (mbox_s4 @ p) @ (mbox_s4 @ q)) @ (mor @ (mbox_s4 @ p) @ (mbox_s4 @ r))))) @ (mbox_s4 @ (mimplies @ (mand @ (mor @ (mbox_s4 @ p) @ (mbox_s4 @ q)) @ (mor @ (mbox_s4 @ p) @ (mbox_s4 @ r))) @ (mor @ (mbox_s4 @ p) @ (mand @ (mbox_s4 @ q) @ (mbox_s4 @ r))))))))),inference(neg_conjecture,[status(cth)],[1])).
% 11.94/4.69 thf(7,plain,((~ (! [A:$i]: ~ (~ (! [B:$i]: (~ (rel_s4 @ A @ B) | ~ (! [C:$i]: (~ (rel_s4 @ B @ C) | (p @ C)) | ~ (~ (! [C:$i]: (~ (rel_s4 @ B @ C) | (q @ C))) | ~ (! [C:$i]: (~ (rel_s4 @ B @ C) | (r @ C))))) | ~ (~ (! [C:$i]: (~ (rel_s4 @ B @ C) | (p @ C)) | ! [C:$i]: (~ (rel_s4 @ B @ C) | (q @ C))) | ~ (! [C:$i]: (~ (rel_s4 @ B @ C) | (p @ C)) | ! [C:$i]: (~ (rel_s4 @ B @ C) | (r @ C)))))) | ~ (! [B:$i]: (~ (rel_s4 @ A @ B) | ~ (! [C:$i]: (~ (rel_s4 @ B @ C) | (p @ C)) | ! [C:$i]: (~ (rel_s4 @ B @ C) | (q @ C))) | ~ (! [C:$i]: (~ (rel_s4 @ B @ C) | (p @ C)) | ! [C:$i]: (~ (rel_s4 @ B @ C) | (r @ C))) | ! [C:$i]: (~ (rel_s4 @ B @ C) | (p @ C)) | ~ (~ (! [C:$i]: (~ (rel_s4 @ B @ C) | (q @ C))) | ~ (! [C:$i]: (~ (rel_s4 @ B @ C) | (r @ C)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])).
% 11.94/4.69 thf(8,plain,((~ (~ (~ (! [A:$i,B:$i]: (~ (rel_s4 @ A @ B) | ~ (! [C:$i]: (~ (rel_s4 @ B @ C) | (p @ C)) | ~ (~ (! [C:$i]: (~ (rel_s4 @ B @ C) | (q @ C))) | ~ (! [C:$i]: (~ (rel_s4 @ B @ C) | (r @ C))))) | ~ (~ (! [C:$i]: (~ (rel_s4 @ B @ C) | (p @ C)) | ! [C:$i]: (~ (rel_s4 @ B @ C) | (q @ C))) | ~ (! [C:$i]: (~ (rel_s4 @ B @ C) | (p @ C)) | ! [C:$i]: (~ (rel_s4 @ B @ C) | (r @ C)))))) | ~ (! [A:$i,B:$i]: (~ (rel_s4 @ A @ B) | ~ (! [C:$i]: (~ (rel_s4 @ B @ C) | (p @ C)) | ! [C:$i]: (~ (rel_s4 @ B @ C) | (q @ C))) | ~ (! [C:$i]: (~ (rel_s4 @ B @ C) | (p @ C)) | ! [C:$i]: (~ (rel_s4 @ B @ C) | (r @ C))) | ! [C:$i]: (~ (rel_s4 @ B @ C) | (p @ C)) | ~ (~ (! [C:$i]: (~ (rel_s4 @ B @ C) | (q @ C))) | ~ (! [C:$i]: (~ (rel_s4 @ B @ C) | (r @ C)))))))))),inference(miniscope,[status(thm)],[7])).
% 11.94/4.69 thf(9,plain,(! [G:$i,F:$i,E:$i,D:$i,C:$i,B:$i,A:$i] : ((((rel_s4 @ sk2 @ sk3) | (sk1)) & (~ (rel_s4 @ sk3 @ A) | (p @ A) | ~ (rel_s4 @ sk3 @ B) | (q @ B) | (sk1)) & (~ (rel_s4 @ sk3 @ A) | (p @ A) | ~ (rel_s4 @ sk3 @ C) | (r @ C) | (sk1)) & ((rel_s4 @ sk3 @ sk5) | (sk4) | (sk1)) & (~ (p @ sk5) | (sk4) | (sk1)) & ((rel_s4 @ sk3 @ sk6) | (sk4) | (sk1)) & (~ (q @ sk6) | (sk4) | (sk1)) & (~ (sk4) | (rel_s4 @ sk3 @ sk7) | (sk1)) & (~ (sk4) | ~ (p @ sk7) | (sk1)) & (~ (sk4) | (rel_s4 @ sk3 @ sk8) | (sk1)) & (~ (sk4) | ~ (r @ sk8) | (sk1)) & (~ (sk1) | (rel_s4 @ sk9 @ sk10)) & (~ (sk1) | ~ (rel_s4 @ sk10 @ D) | (p @ D) | ~ (rel_s4 @ sk10 @ E) | (q @ E)) & (~ (sk1) | ~ (rel_s4 @ sk10 @ F) | (p @ F) | ~ (rel_s4 @ sk10 @ G) | (r @ G)) & (~ (sk1) | (rel_s4 @ sk10 @ sk11)) & (~ (sk1) | ~ (p @ sk11)) & (~ (sk1) | (rel_s4 @ sk10 @ sk12) | (rel_s4 @ sk10 @ sk13)) & (~ (sk1) | (rel_s4 @ sk10 @ sk12) | ~ (r @ sk13)) & (~ (sk1) | ~ (q @ sk12) | (rel_s4 @ sk10 @ sk13)) & (~ (sk1) | ~ (q @ sk12) | ~ (r @ sk13))))),inference(cnf,[status(esa)],[8])).
% 11.94/4.69 thf(10,plain,(~ (sk4) | (rel_s4 @ sk3 @ sk7) | sk1),inference(cnfConj,[status(thm)],[9])).
% 11.94/4.69 thf(14,plain,(~ (sk1) | (~ (q @ sk12)) | (~ (r @ sk13))),inference(cnfConj,[status(thm)],[9])).
% 11.94/4.69 thf(13,plain,(~ (sk1) | (rel_s4 @ sk10 @ sk12) | (~ (r @ sk13))),inference(cnfConj,[status(thm)],[9])).
% 11.94/4.69 thf(12,plain,(~ (sk4) | (~ (p @ sk7)) | sk1),inference(cnfConj,[status(thm)],[9])).
% 11.94/4.69 thf(4,axiom,((mreflexive @ rel_s4)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',a1)).
% 11.94/4.69 thf(35,plain,((! [A:$i]: (rel_s4 @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4])).
% 11.94/4.69 thf(11,plain,((rel_s4 @ sk3 @ sk6) | sk4 | sk1),inference(cnfConj,[status(thm)],[9])).
% 11.94/4.69 thf(24,plain,((rel_s4 @ sk2 @ sk3) | sk1),inference(cnfConj,[status(thm)],[9])).
% 11.94/4.69 thf(5,axiom,((mtransitive @ rel_s4)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',a2)).
% 11.94/4.69 thf(37,plain,((! [A:$i,B:$i,C:$i]: (((rel_s4 @ A @ B) & (rel_s4 @ B @ C)) => (rel_s4 @ A @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5])).
% 11.94/4.69 thf(38,plain,(! [C:$i,B:$i,A:$i] : ((~ (rel_s4 @ A @ B)) | (~ (rel_s4 @ B @ C)) | (rel_s4 @ A @ C))),inference(cnf,[status(esa)],[37])).
% 11.94/4.69 thf(176,plain,(! [C:$i,B:$i,A:$i] : (sk1 | (~ (rel_s4 @ A @ B)) | ~ (($true)) | (rel_s4 @ A @ C) | ((rel_s4 @ sk2 @ sk3) != (rel_s4 @ B @ C)))),inference(paramod_ordered,[status(thm)],[24,38])).
% 11.94/4.69 thf(177,plain,(! [C:$i,B:$i,A:$i] : (sk1 | (~ (rel_s4 @ A @ B)) | (rel_s4 @ A @ C) | ((rel_s4 @ sk2 @ sk3) != (rel_s4 @ B @ C)))),inference(simp,[status(thm)],[176])).
% 11.94/4.69 thf(178,plain,(! [A:$i] : (sk1 | (~ (rel_s4 @ A @ sk2)) | (rel_s4 @ A @ sk3))),inference(pattern_uni,[status(thm)],[177:[bind(A, $thf(A)),bind(B, $thf(sk2)),bind(C, $thf(sk3))]])).
% 11.94/4.69 thf(23,plain,(~ (sk1) | (rel_s4 @ sk10 @ sk12) | (rel_s4 @ sk10 @ sk13)),inference(cnfConj,[status(thm)],[9])).
% 11.94/4.69 thf(41,plain,(~ (sk1) | (rel_s4 @ sk10 @ sk12) | ((rel_s4 @ sk10 @ sk13) != (rel_s4 @ sk10 @ sk12)) | ~ (($true))),inference(eqfactor_ordered,[status(thm)],[23])).
% 11.94/4.69 thf(42,plain,((rel_s4 @ sk10 @ sk12) | ~ (sk1) | ((rel_s4 @ sk10 @ sk13) != (rel_s4 @ sk10 @ sk12))),inference(simp,[status(thm)],[41])).
% 11.94/4.69 thf(25,plain,(~ (sk1) | (~ (p @ sk11))),inference(cnfConj,[status(thm)],[9])).
% 11.94/4.69 thf(20,plain,((~ (q @ sk6)) | sk4 | sk1),inference(cnfConj,[status(thm)],[9])).
% 11.94/4.69 thf(150,plain,(! [C:$i,B:$i,A:$i] : (~ (sk1) | (~ (r @ sk13)) | (~ (rel_s4 @ A @ B)) | ~ (($true)) | (rel_s4 @ A @ C) | ((rel_s4 @ sk10 @ sk12) != (rel_s4 @ B @ C)))),inference(paramod_ordered,[status(thm)],[13,38])).
% 11.94/4.69 thf(151,plain,(! [C:$i,B:$i,A:$i] : (~ (sk1) | (~ (r @ sk13)) | (~ (rel_s4 @ A @ B)) | (rel_s4 @ A @ C) | ((rel_s4 @ sk10 @ sk12) != (rel_s4 @ B @ C)))),inference(simp,[status(thm)],[150])).
% 11.94/4.69 thf(152,plain,(! [A:$i] : (~ (sk1) | (~ (r @ sk13)) | (~ (rel_s4 @ A @ sk10)) | (rel_s4 @ A @ sk12))),inference(pattern_uni,[status(thm)],[151:[bind(A, $thf(A)),bind(B, $thf(sk10)),bind(C, $thf(sk12))]])).
% 11.94/4.69 thf(29,plain,(~ (sk4) | (~ (r @ sk8)) | sk1),inference(cnfConj,[status(thm)],[9])).
% 11.94/4.69 thf(21,plain,((~ (p @ sk5)) | sk4 | sk1),inference(cnfConj,[status(thm)],[9])).
% 11.94/4.69 thf(3,axiom,((! [A:$i]: ? [B:mu]: (exists_in_world @ B @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonempty_ax)).
% 11.94/4.69 thf(33,plain,((! [A:$i]: ? [B:mu]: (exists_in_world @ B @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3])).
% 11.94/4.69 thf(28,plain,(! [B:$i,A:$i] : ((~ (rel_s4 @ sk3 @ A)) | (p @ A) | (~ (rel_s4 @ sk3 @ B)) | (r @ B) | sk1)),inference(cnfConj,[status(thm)],[9])).
% 11.94/4.69 thf(32,plain,(! [B:$i,A:$i] : ((~ (rel_s4 @ sk3 @ A)) | (p @ A) | (~ (rel_s4 @ sk3 @ B)) | (r @ B) | sk1)),inference(simp,[status(thm)],[28])).
% 11.94/4.69 thf(34,plain,(! [A:$i] : ((exists_in_world @ (sk14 @ A) @ A))),inference(cnf,[status(esa)],[33])).
% 11.94/4.69 thf(22,plain,(~ (sk1) | (rel_s4 @ sk9 @ sk10)),inference(cnfConj,[status(thm)],[9])).
% 11.94/4.69 thf(43,plain,((rel_s4 @ sk10 @ sk12) | ~ (sk1) | (sk10 != sk10) | (sk13 != sk12)),inference(simp,[status(thm)],[41])).
% 11.94/4.69 thf(44,plain,((rel_s4 @ sk10 @ sk12) | ~ (sk1) | (sk13 != sk12)),inference(simp,[status(thm)],[43])).
% 11.94/4.69 thf(27,plain,(~ (sk1) | (~ (q @ sk12)) | (rel_s4 @ sk10 @ sk13)),inference(cnfConj,[status(thm)],[9])).
% 11.94/4.69 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)).
% 11.94/4.69 thf(39,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])).
% 11.94/4.69 thf(26,plain,(~ (sk1) | (rel_s4 @ sk10 @ sk11)),inference(cnfConj,[status(thm)],[9])).
% 11.94/4.69 thf(206,plain,(! [C:$i,B:$i,A:$i] : (~ (sk1) | (~ (rel_s4 @ A @ B)) | ~ (($true)) | (rel_s4 @ A @ C) | ((rel_s4 @ sk10 @ sk11) != (rel_s4 @ B @ C)))),inference(paramod_ordered,[status(thm)],[26,38])).
% 11.94/4.69 thf(207,plain,(! [C:$i,B:$i,A:$i] : (~ (sk1) | (~ (rel_s4 @ A @ B)) | (rel_s4 @ A @ C) | ((rel_s4 @ sk10 @ sk11) != (rel_s4 @ B @ C)))),inference(simp,[status(thm)],[206])).
% 11.94/4.69 thf(208,plain,(! [A:$i] : (~ (sk1) | (~ (rel_s4 @ A @ sk10)) | (rel_s4 @ A @ sk11))),inference(pattern_uni,[status(thm)],[207:[bind(A, $thf(A)),bind(B, $thf(sk10)),bind(C, $thf(sk11))]])).
% 11.94/4.69 thf(774,plain,(! [A:$i] : (~ (sk1) | ~ (sk1) | ~ (($true)) | (rel_s4 @ A @ sk11) | ((rel_s4 @ sk9 @ sk10) != (rel_s4 @ A @ sk10)))),inference(paramod_ordered,[status(thm)],[22,208])).
% 11.94/4.69 thf(775,plain,(! [A:$i] : (~ (sk1) | (rel_s4 @ A @ sk11) | ((rel_s4 @ sk9 @ sk10) != (rel_s4 @ A @ sk10)))),inference(simp,[status(thm)],[774])).
% 11.94/4.69 thf(776,plain,(~ (sk1) | (rel_s4 @ sk9 @ sk11)),inference(pattern_uni,[status(thm)],[775:[bind(A, $thf(sk9))]])).
% 11.94/4.69 thf(18,plain,(! [B:$i,A:$i] : ((~ (rel_s4 @ sk3 @ A)) | (p @ A) | (~ (rel_s4 @ sk3 @ B)) | (q @ B) | sk1)),inference(cnfConj,[status(thm)],[9])).
% 11.94/4.69 thf(16,plain,((rel_s4 @ sk3 @ sk5) | sk4 | sk1),inference(cnfConj,[status(thm)],[9])).
% 11.94/4.69 thf(15,plain,(! [B:$i,A:$i] : (~ (sk1) | (~ (rel_s4 @ sk10 @ A)) | (p @ A) | (~ (rel_s4 @ sk10 @ B)) | (q @ B))),inference(cnfConj,[status(thm)],[9])).
% 11.94/4.69 thf(31,plain,(! [B:$i,A:$i] : (~ (sk1) | (~ (rel_s4 @ sk10 @ A)) | (p @ A) | (~ (rel_s4 @ sk10 @ B)) | (q @ B))),inference(simp,[status(thm)],[15])).
% 11.94/4.69 thf(58,plain,(! [B:$i,A:$i] : (sk4 | sk1 | (~ (rel_s4 @ sk3 @ A)) | (p @ A) | ~ (($true)) | (q @ B) | sk1 | ((rel_s4 @ sk3 @ sk5) != (rel_s4 @ sk3 @ B)))),inference(paramod_ordered,[status(thm)],[16,18])).
% 11.94/4.69 thf(59,plain,(! [B:$i,A:$i] : (sk4 | sk1 | (~ (rel_s4 @ sk3 @ A)) | (p @ A) | (q @ B) | ((rel_s4 @ sk3 @ sk5) != (rel_s4 @ sk3 @ B)))),inference(simp,[status(thm)],[58])).
% 11.94/4.69 thf(60,plain,(! [A:$i] : (sk4 | sk1 | (~ (rel_s4 @ sk3 @ A)) | (p @ A) | (q @ sk5))),inference(pattern_uni,[status(thm)],[59:[bind(A, $thf(A)),bind(B, $thf(sk5))]])).
% 11.94/4.69 thf(369,plain,(! [A:$i] : (sk4 | sk1 | sk4 | sk1 | ~ (($true)) | (p @ A) | (q @ sk5) | ((rel_s4 @ sk3 @ sk5) != (rel_s4 @ sk3 @ A)))),inference(paramod_ordered,[status(thm)],[16,60])).
% 11.94/4.69 thf(370,plain,(! [A:$i] : (sk4 | sk1 | (p @ A) | (q @ sk5) | ((rel_s4 @ sk3 @ sk5) != (rel_s4 @ sk3 @ A)))),inference(simp,[status(thm)],[369])).
% 11.94/4.69 thf(371,plain,(sk4 | sk1 | (p @ sk5) | (q @ sk5)),inference(pattern_uni,[status(thm)],[370:[bind(A, $thf(sk5))]])).
% 11.94/4.69 thf(430,plain,(sk4 | sk1 | (q @ sk5) | ~ (($true)) | sk4 | sk1 | ((p @ sk5) != (p @ sk5))),inference(paramod_ordered,[status(thm)],[371,21])).
% 11.94/4.69 thf(431,plain,(sk4 | sk1 | (q @ sk5) | ((p @ sk5) != (p @ sk5))),inference(simp,[status(thm)],[430])).
% 11.94/4.69 thf(432,plain,(sk4 | sk1 | (q @ sk5)),inference(pattern_uni,[status(thm)],[431:[]])).
% 11.94/4.69 thf(36,plain,(! [A:$i] : ((rel_s4 @ A @ A))),inference(cnf,[status(esa)],[35])).
% 11.94/4.69 thf(17,plain,(! [B:$i,A:$i] : (~ (sk1) | (~ (rel_s4 @ sk10 @ A)) | (p @ A) | (~ (rel_s4 @ sk10 @ B)) | (r @ B))),inference(cnfConj,[status(thm)],[9])).
% 11.94/4.69 thf(30,plain,(! [B:$i,A:$i] : (~ (sk1) | (~ (rel_s4 @ sk10 @ A)) | (p @ A) | (~ (rel_s4 @ sk10 @ B)) | (r @ B))),inference(simp,[status(thm)],[17])).
% 11.94/4.69 thf(188,plain,(! [C:$i,B:$i,A:$i] : (~ (sk1) | (~ (rel_s4 @ A @ B)) | ~ (($true)) | (rel_s4 @ A @ C) | ((rel_s4 @ sk9 @ sk10) != (rel_s4 @ B @ C)))),inference(paramod_ordered,[status(thm)],[22,38])).
% 11.94/4.69 thf(189,plain,(! [C:$i,B:$i,A:$i] : (~ (sk1) | (~ (rel_s4 @ A @ B)) | (rel_s4 @ A @ C) | ((rel_s4 @ sk9 @ sk10) != (rel_s4 @ B @ C)))),inference(simp,[status(thm)],[188])).
% 11.94/4.69 thf(190,plain,(! [A:$i] : (~ (sk1) | (~ (rel_s4 @ A @ sk9)) | (rel_s4 @ A @ sk10))),inference(pattern_uni,[status(thm)],[189:[bind(A, $thf(A)),bind(B, $thf(sk9)),bind(C, $thf(sk10))]])).
% 11.94/4.69 thf(19,plain,(~ (sk4) | (rel_s4 @ sk3 @ sk8) | sk1),inference(cnfConj,[status(thm)],[9])).
% 11.94/4.69 thf(335,plain,(! [A:$i] : (~ (sk1) | ~ (sk1) | (~ (r @ sk13)) | ~ (($true)) | (rel_s4 @ A @ sk12) | ((rel_s4 @ sk9 @ sk10) != (rel_s4 @ A @ sk10)))),inference(paramod_ordered,[status(thm)],[22,152])).
% 11.94/4.69 thf(336,plain,(! [A:$i] : (~ (sk1) | (~ (r @ sk13)) | (rel_s4 @ A @ sk12) | ((rel_s4 @ sk9 @ sk10) != (rel_s4 @ A @ sk10)))),inference(simp,[status(thm)],[335])).
% 11.94/4.69 thf(337,plain,(~ (sk1) | (~ (r @ sk13)) | (rel_s4 @ sk9 @ sk12)),inference(pattern_uni,[status(thm)],[336:[bind(A, $thf(sk9))]])).
% 11.94/4.69 thf(539,plain,(sk4 | sk1 | ~ (($true)) | sk4 | sk1 | ((q @ sk6) != (q @ sk5))),inference(paramod_ordered,[status(thm)],[432,20])).
% 11.94/4.69 thf(540,plain,(sk4 | sk1 | ((q @ sk6) != (q @ sk5))),inference(simp,[status(thm)],[539])).
% 11.94/4.69 thf(543,plain,(sk4 | sk1 | (sk6 != sk5)),inference(simp,[status(thm)],[540])).
% 11.94/4.69 thf(1525,plain,(($false)),inference(e,[status(thm)],[10,14,13,12,35,11,178,42,24,37,25,20,152,29,38,21,33,32,34,22,44,27,7,39,208,776,18,16,31,26,23,432,36,30,190,19,337,543])).
% 11.94/4.69 % SZS output end Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% 11.94/4.69 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------