%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWV061^7 : 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 : n003.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 08:39:50 AM UTC 2026
% Result : Theorem 37.91s 10.82s
% Output : Refutation 37.91s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV061^7 : TPTP v9.3.1. Released v5.5.0.
% 0.00/0.07 % 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 : n003.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 16:01:43 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
% 0.90/0.79 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 2.41/1.20 % [INFO] Parsing done (409ms).
% 2.41/1.21 % [INFO] Running in sequential loop mode.
% 3.04/1.43 % [INFO] eprover registered as external prover.
% 3.04/1.43 % [INFO] Scanning for conjecture ...
% 3.41/1.59 % [INFO] Found a conjecture (or negated_conjecture) and 166 axioms. Running axiom selection ...
% 3.84/1.69 % [INFO] Axiom selection finished. Selected 166 axioms (removed 0 axioms).
% 4.77/1.88 % [INFO] Problem is higher-order (TPTP THF).
% 5.12/1.90 % [INFO] Type checking passed.
% 5.12/1.90 % [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 ...
% 37.91/10.81 % [INFO] Killing All external provers ...
% 37.91/10.81 % Time passed: 10465ms (effective reasoning time: 9602ms)
% 37.91/10.81 % 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)>
% 37.91/10.82 % Axioms used in derivation (2): a1, ttrue
% 37.91/10.82 % No. of inferences in proof: 21
% 37.91/10.82 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 10465 ms resp. 9602 ms w/o parsing
% 37.91/10.87 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% 37.91/10.87 thf(mu_type, type, mu: $tType).
% 37.91/10.87 thf(mnot_decl, type, mnot: (($i > $o) > ($i > $o))).
% 37.91/10.87 thf(mor_decl, type, mor: (($i > $o) > (($i > $o) > ($i > $o)))).
% 37.91/10.87 thf(mand_decl, type, mand: (($i > $o) > (($i > $o) > ($i > $o)))).
% 37.91/10.87 thf(mimplies_decl, type, mimplies: (($i > $o) > (($i > $o) > ($i > $o)))).
% 37.91/10.87 thf(mreflexive_decl, type, mreflexive: (($i > ($i > $o)) > $o)).
% 37.91/10.87 thf(mvalid_decl, type, mvalid: (($i > $o) > $o)).
% 37.91/10.87 thf(rel_s4_decl, type, rel_s4: ($i > ($i > $o))).
% 37.91/10.87 thf(mbox_s4_decl, type, mbox_s4: (($i > $o) > ($i > $o))).
% 37.91/10.87 thf(true_decl, type, true: ($i > $o)).
% 37.91/10.87 thf(gt_decl, type, gt: (mu > (mu > ($i > $o)))).
% 37.91/10.87 thf(loopcounter_decl, type, loopcounter: mu).
% 37.91/10.87 thf(n1_decl, type, n1: mu).
% 37.91/10.87 thf(sk1_decl, type, sk1: $i).
% 37.91/10.87 thf(sk2_decl, type, sk2: $i).
% 37.91/10.87 thf(sk3_decl, type, sk3: $o).
% 37.91/10.87 thf(sk4_decl, type, sk4: $i).
% 37.91/10.87 thf(sk5_decl, type, sk5: ($i > $i)).
% 37.91/10.87 thf(sk6_decl, type, sk6: $i).
% 37.91/10.87 thf(sk7_decl, type, sk7: $i).
% 37.91/10.87 thf(sk8_decl, type, sk8: $i).
% 37.91/10.87 thf(mnot_def, definition, mnot = (^ [A:($i > $o),B:$i]: ~ (A @ B)) ).
% 37.91/10.87 thf(mor_def, definition, mor = (^ [A:($i > $o),B:($i > $o),C:$i]: ((A @ C) | (B @ C))) ).
% 37.91/10.87 thf(mand_def, definition, mand = (^ [A:($i > $o),B:($i > $o)]: (mnot @ (mor @ (mnot @ A) @ (mnot @ B)))) ).
% 37.91/10.87 thf(mimplies_def, definition, mimplies = (^ [A:($i > $o)]: (mor @ (mnot @ A))) ).
% 37.91/10.87 thf(mreflexive_def, definition, mreflexive = (^ [A:($i > ($i > $o))]: ! [B:$i]: (A @ B @ B)) ).
% 37.91/10.87 thf(mvalid_def, definition, mvalid = ((!) @ $i) ).
% 37.91/10.87 thf(mbox_s4_def, definition, mbox_s4 = (^ [A:($i > $o),B:$i]: ! [C:$i]: (~ (rel_s4 @ B @ C) | (A @ C))) ).
% 37.91/10.87 thf(sk1_def, definition, sk1 = (@+ [A:$i]: ~ (! [B:$i]: (~ (rel_s4 @ A @ B) | ~ (! [C:$i]: (~ (rel_s4 @ B @ C) | (true @ C))) | ~ (~ (! [C:$i]: (~ (rel_s4 @ B @ C) | ~ (! [D:$i]: (~ (rel_s4 @ C @ D) | ~ (! [E:$i]: (~ (rel_s4 @ D @ E) | (gt @ loopcounter @ n1 @ E))))) | ! [D:$i]: (~ (rel_s4 @ C @ D) | (true @ D)))) | ~ (! [C:$i]: (~ (rel_s4 @ B @ C) | ~ (! [D:$i]: (~ (rel_s4 @ C @ D) | (gt @ loopcounter @ n1 @ D))) | ! [D:$i]: (~ (rel_s4 @ C @ D) | (true @ D)))))))) ).
% 37.91/10.87 thf(sk2_def, definition, sk2 = (@+ [A:$i]: ~ (~ (rel_s4 @ sk1 @ A) | ~ (! [B:$i]: (~ (rel_s4 @ A @ B) | (true @ B))) | ~ (~ (! [B:$i]: (~ (rel_s4 @ A @ B) | ~ (! [C:$i]: (~ (rel_s4 @ B @ C) | ~ (! [D:$i]: (~ (rel_s4 @ C @ D) | (gt @ loopcounter @ n1 @ D))))) | ! [C:$i]: (~ (rel_s4 @ B @ C) | (true @ C)))) | ~ (! [B:$i]: (~ (rel_s4 @ A @ B) | ~ (! [C:$i]: (~ (rel_s4 @ B @ C) | (gt @ loopcounter @ n1 @ C))) | ! [C:$i]: (~ (rel_s4 @ B @ C) | (true @ C))))))) ).
% 37.91/10.87 thf(sk4_def, definition, sk4 = (@+ [A:$i]: ~ (~ (rel_s4 @ sk2 @ A) | ~ (! [B:$i]: (~ (rel_s4 @ A @ B) | ~ (! [C:$i]: (~ (rel_s4 @ B @ C) | (gt @ loopcounter @ n1 @ C))))) | ! [B:$i]: (~ (rel_s4 @ A @ B) | (true @ B)))) ).
% 37.91/10.87 thf(sk5_def, definition, sk5 = (^ [A:$i]: (@+ [B:$i]: ~ (~ (rel_s4 @ A @ B) | (gt @ loopcounter @ n1 @ B)))) ).
% 37.91/10.87 thf(sk6_def, definition, sk6 = (@+ [A:$i]: ~ (~ (rel_s4 @ sk4 @ A) | (true @ A))) ).
% 37.91/10.87 thf(sk7_def, definition, sk7 = (@+ [A:$i]: ~ (~ (rel_s4 @ sk2 @ A) | ~ (! [B:$i]: (~ (rel_s4 @ A @ B) | (gt @ loopcounter @ n1 @ B))) | ! [B:$i]: (~ (rel_s4 @ A @ B) | (true @ B)))) ).
% 37.91/10.87 thf(sk8_def, definition, sk8 = (@+ [A:$i]: ~ (~ (rel_s4 @ sk7 @ A) | (true @ A))) ).
% 37.91/10.87 thf(1,conjecture,((mvalid @ (mbox_s4 @ (mimplies @ (mbox_s4 @ true) @ (mand @ (mbox_s4 @ (mimplies @ (mbox_s4 @ (mnot @ (mbox_s4 @ (gt @ loopcounter @ n1)))) @ (mbox_s4 @ true))) @ (mbox_s4 @ (mimplies @ (mbox_s4 @ (gt @ loopcounter @ n1)) @ (mbox_s4 @ true)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',cl5_nebula_array_0002)).
% 37.91/10.87 thf(2,negated_conjecture,((~ (mvalid @ (mbox_s4 @ (mimplies @ (mbox_s4 @ true) @ (mand @ (mbox_s4 @ (mimplies @ (mbox_s4 @ (mnot @ (mbox_s4 @ (gt @ loopcounter @ n1)))) @ (mbox_s4 @ true))) @ (mbox_s4 @ (mimplies @ (mbox_s4 @ (gt @ loopcounter @ n1)) @ (mbox_s4 @ true))))))))),inference(neg_conjecture,[status(cth)],[1])).
% 37.91/10.87 thf(169,plain,((~ (! [A:$i,B:$i]: (~ (rel_s4 @ A @ B) | ~ (! [C:$i]: (~ (rel_s4 @ B @ C) | (true @ C))) | ~ (~ (! [C:$i]: (~ (rel_s4 @ B @ C) | ~ (! [D:$i]: (~ (rel_s4 @ C @ D) | ~ (! [E:$i]: (~ (rel_s4 @ D @ E) | (gt @ loopcounter @ n1 @ E))))) | ! [D:$i]: (~ (rel_s4 @ C @ D) | (true @ D)))) | ~ (! [C:$i]: (~ (rel_s4 @ B @ C) | ~ (! [D:$i]: (~ (rel_s4 @ C @ D) | (gt @ loopcounter @ n1 @ D))) | ! [D:$i]: (~ (rel_s4 @ C @ D) | (true @ D))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])).
% 37.91/10.87 thf(170,plain,(! [C:$i,B:$i,A:$i] : (((rel_s4 @ sk1 @ sk2) & (~ (rel_s4 @ sk2 @ A) | (true @ A)) & ((rel_s4 @ sk2 @ sk4) | (sk3)) & (~ (rel_s4 @ sk4 @ B) | (rel_s4 @ B @ (sk5 @ B)) | (sk3)) & (~ (rel_s4 @ sk4 @ B) | ~ (gt @ loopcounter @ n1 @ (sk5 @ B)) | (sk3)) & ((rel_s4 @ sk4 @ sk6) | (sk3)) & (~ (true @ sk6) | (sk3)) & (~ (sk3) | (rel_s4 @ sk2 @ sk7)) & (~ (sk3) | ~ (rel_s4 @ sk7 @ C) | (gt @ loopcounter @ n1 @ C)) & (~ (sk3) | (rel_s4 @ sk7 @ sk8)) & (~ (sk3) | ~ (true @ sk8))))),inference(cnf,[status(esa)],[169])).
% 37.91/10.87 thf(178,plain,((~ (true @ sk6)) | sk3),inference(cnfConj,[status(thm)],[170])).
% 37.91/10.87 thf(136,axiom,((mreflexive @ rel_s4)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',a1)).
% 37.91/10.87 thf(933,plain,((! [A:$i]: (rel_s4 @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[136])).
% 37.91/10.87 thf(934,plain,(! [A:$i] : ((rel_s4 @ A @ A))),inference(cnf,[status(esa)],[933])).
% 37.91/10.87 thf(121,axiom,((mvalid @ (mbox_s4 @ true))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',ttrue)).
% 37.91/10.87 thf(883,plain,((! [A:$i,B:$i]: (~ (rel_s4 @ A @ B) | (true @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[121])).
% 37.91/10.87 thf(884,plain,(! [B:$i,A:$i] : ((~ (rel_s4 @ A @ B)) | (true @ B))),inference(cnf,[status(esa)],[883])).
% 37.91/10.87 thf(3211,plain,(! [C:$i,B:$i,A:$i] : (~ (($true)) | (true @ C) | ((rel_s4 @ A @ A) != (rel_s4 @ B @ C)))),inference(paramod_ordered,[status(thm)],[934,884])).
% 37.91/10.87 thf(3212,plain,(! [C:$i,B:$i,A:$i] : ((true @ C) | ((rel_s4 @ A @ A) != (rel_s4 @ B @ C)))),inference(simp,[status(thm)],[3211])).
% 37.91/10.87 thf(3213,plain,(! [A:$i] : ((true @ A))),inference(pattern_uni,[status(thm)],[3212:[bind(A, $thf(A)),bind(B, $thf(A)),bind(C, $thf(A))]])).
% 37.91/10.87 thf(3250,plain,(~ (($true)) | sk3),inference(rewrite,[status(thm)],[178,3213])).
% 37.91/10.87 thf(3251,plain,(sk3),inference(simp,[status(thm)],[3250])).
% 37.91/10.87 thf(171,plain,(~ (sk3) | (~ (true @ sk8))),inference(cnfConj,[status(thm)],[170])).
% 37.91/10.87 thf(3248,plain,(~ (sk3) | ~ (($true))),inference(rewrite,[status(thm)],[171,3213])).
% 37.91/10.87 thf(3249,plain,(~ (sk3)),inference(simp,[status(thm)],[3248])).
% 37.91/10.87 thf(3294,plain,(($false)),inference(rewrite,[status(thm)],[3251,3249])).
% 37.91/10.87 thf(3295,plain,(($false)),inference(simp,[status(thm)],[3294])).
% 37.91/10.87 % SZS output end Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% 37.91/10.87 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------