%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEV384^5 : TPTP v9.3.1. Released v4.0.0.
% 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 : n004.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 08:37:12 AM UTC 2026
% Result : Theorem 19.10s 6.00s
% Output : Refutation 19.92s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEV384^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.10 % 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
% 0.09/0.28 % Computer : n004.cluster.edu
% 0.09/0.28 % Model : x86_64 x86_64
% 0.09/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.28 % Memory : 8046.5625MB
% 0.09/0.28 % OS : Linux 6.8.0-71-generic
% 0.09/0.28 % CPULimit : 300
% 0.09/0.28 % WCLimit : 300
% 0.09/0.28 % DateTime : Tue Sep 29 15:43:07 UTC 2026
% 0.09/0.29 % CPUTime :
% 0.09/0.29 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
% 1.32/1.09 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.79/1.35 % [INFO] Parsing done (258ms).
% 1.79/1.37 % [INFO] Running in sequential loop mode.
% 2.56/1.85 % [INFO] eprover registered as external prover.
% 2.56/1.86 % [INFO] Scanning for conjecture ...
% 2.73/2.00 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.96/2.04 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.96/2.05 % [INFO] Problem is higher-order (TPTP THF).
% 2.96/2.05 % [INFO] Type checking passed.
% 2.96/2.06 % [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 ...
% 19.10/5.99 % [INFO] Killing All external provers ...
% 19.10/6.00 % Time passed: 5519ms (effective reasoning time: 4614ms)
% 19.10/6.00 % 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)>
% 19.10/6.00 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 5519 ms resp. 4614 ms w/o parsing
% 19.92/6.07 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% 19.92/6.07 thf(cP_decl, type, cP: ($i > $o)).
% 19.92/6.07 thf(s_decl, type, s: ($i > $o)).
% 19.92/6.07 thf(cR_decl, type, cR: ($i > ($i > $o))).
% 19.92/6.07 thf(sk1_decl, type, sk1: (($i > $o) > $i)).
% 19.92/6.07 thf(sk2_decl, type, sk2: ($i > $i)).
% 19.92/6.07 thf(sk3_decl, type, sk3: $i).
% 19.92/6.07 thf(sk1_def, definition, sk1 = (^ [A:($i > $o)]: (@+ [B:$i]: ((A @ B) & ! [C:$i]: ((cR @ B @ C) => (~ (A @ C)))))) ).
% 19.92/6.07 thf(sk2_def, definition, sk2 = (^ [A:$i]: (@+ [B:$i]: ~ (((s @ B) & (cR @ A @ B)) => (cP @ B)))) ).
% 19.92/6.07 thf(sk3_def, definition, sk3 = (@+ [A:$i]: ~ ((s @ A) => (cP @ A))) ).
% 19.92/6.07 thf(1,conjecture,(((! [A:($i > $o),B:$i]: ((A @ B) => (? [C:$i]: ((A @ C) & ! [D:$i]: ((cR @ C @ D) => (~ (A @ D)))))) & ! [A:$i]: ((! [B:$i]: (((s @ B) & (cR @ A @ B)) => (cP @ B))) => (cP @ A))) => (! [A:$i]: ((s @ A) => (cP @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM117B)).
% 19.92/6.07 thf(2,negated_conjecture,((~ ((! [A:($i > $o),B:$i]: ((A @ B) => (? [C:$i]: ((A @ C) & ! [D:$i]: ((cR @ C @ D) => (~ (A @ D)))))) & ! [A:$i]: ((! [B:$i]: (((s @ B) & (cR @ A @ B)) => (cP @ B))) => (cP @ A))) => (! [A:$i]: ((s @ A) => (cP @ A)))))),inference(neg_conjecture,[status(cth)],[1])).
% 19.92/6.07 thf(3,plain,((~ ((! [A:($i > $o),B:$i]: ((A @ B) => (? [C:$i]: ((A @ C) & ! [D:$i]: ((cR @ C @ D) => (~ (A @ D)))))) & ! [A:$i]: ((! [B:$i]: (((s @ B) & (cR @ A @ B)) => (cP @ B))) => (cP @ A))) => (! [A:$i]: ((s @ A) => (cP @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])).
% 19.92/6.07 thf(4,plain,((~ ((! [A:($i > $o)]: ((? [B:$i]: (A @ B)) => (? [B:$i]: ((A @ B) & ! [C:$i]: ((cR @ B @ C) => (~ (A @ C)))))) & ! [A:$i]: ((! [B:$i]: (((s @ B) & (cR @ A @ B)) => (cP @ B))) => (cP @ A))) => (! [A:$i]: ((s @ A) => (cP @ A)))))),inference(miniscope,[status(thm)],[3])).
% 19.92/6.07 thf(5,plain,(! [D:$i,C:$i,B:$i,A:($i > $o)] : (((~ (A @ B) | (A @ (sk1 @ (A)))) & (~ (A @ B) | ~ (cR @ (sk1 @ (A)) @ C) | ~ (A @ C)) & ((s @ (sk2 @ D)) | (cP @ D)) & ((cR @ D @ (sk2 @ D)) | (cP @ D)) & (~ (cP @ (sk2 @ D)) | (cP @ D)) & (s @ sk3) & ~ (cP @ sk3)))),inference(cnf,[status(esa)],[4])).
% 19.92/6.07 thf(6,plain,((~ (cP @ sk3))),inference(cnfConj,[status(thm)],[5])).
% 19.92/6.07 thf(37,axiom,((? [A:(($i > $o) > $i)]: ! [B:($i > $o)]: ((? [C:$i]: (B @ C)) => (B @ (A @ B))))),introduced(axiom_of_choice)).
% 19.92/6.07 thf(972,plain,(! [A:$i] : ((~ (~ (cP @ A))) | (~ (cP @ (sk1 @ (^ [B:$i]: ~ (cP @ B))))))),inference(choice,[status(esa)],[37])).
% 19.92/6.07 thf(995,plain,(! [A:$i] : ((cP @ A) | (~ (cP @ (sk1 @ (^ [B:$i]: ~ (cP @ B))))))),inference(cnf,[status(esa)],[972])).
% 19.92/6.07 thf(11,plain,(! [A:$i] : ((cR @ A @ (sk2 @ A)) | (cP @ A))),inference(cnfConj,[status(thm)],[5])).
% 19.92/6.07 thf(14,plain,(! [A:$i] : ((cR @ A @ (sk2 @ A)) | (cP @ A))),inference(simp,[status(thm)],[11])).
% 19.92/6.07 thf(12,plain,(! [C:$i,B:$i,A:($i > $o)] : ((~ (A @ B)) | (~ (cR @ (sk1 @ (A)) @ C)) | (~ (A @ C)))),inference(cnfConj,[status(thm)],[5])).
% 19.92/6.07 thf(35,plain,(! [C:($i > $o),B:$i,A:$i] : ((~ (~ (C @ A))) | (~ (cR @ (sk1 @ (^ [D:$i]: ~ (C @ D))) @ B)) | (~ (~ (C @ B))))),inference(prim_subst,[status(thm)],[12:[bind(A, $thf(^ [E:$i]: ~ (D @ E)))]])).
% 19.92/6.07 thf(63,plain,(! [C:($i > $o),B:$i,A:$i] : ((C @ A) | (~ (cR @ (sk1 @ (^ [D:$i]: ~ (C @ D))) @ B)) | (C @ B))),inference(cnf,[status(esa)],[35])).
% 19.92/6.07 thf(64,plain,(! [C:($i > $o),B:$i,A:$i] : ((C @ A) | (~ (cR @ (sk1 @ (^ [D:$i]: ~ (C @ D))) @ B)) | (C @ B))),inference(simp,[status(thm)],[63])).
% 19.92/6.07 thf(177,plain,(! [D:($i > $o),C:$i,B:$i,A:$i] : ((cP @ A) | (D @ B) | ~ (($true)) | (D @ C) | ((cR @ A @ (sk2 @ A)) != (cR @ (sk1 @ (^ [E:$i]: ~ (D @ E))) @ C)))),inference(paramod_ordered,[status(thm)],[14,64])).
% 19.92/6.07 thf(178,plain,(! [D:($i > $o),C:$i,B:$i,A:$i] : ((cP @ A) | (D @ B) | (D @ C) | ((cR @ A @ (sk2 @ A)) != (cR @ (sk1 @ (^ [E:$i]: ~ (D @ E))) @ C)))),inference(simp,[status(thm)],[177])).
% 19.92/6.07 thf(179,plain,(! [B:($i > $o),A:$i] : ((cP @ (sk1 @ (^ [C:$i]: ~ (B @ C)))) | (B @ A) | (B @ (sk2 @ (sk1 @ (^ [C:$i]: ~ (B @ C))))))),inference(pattern_uni,[status(thm)],[178:[bind(A, $thf(sk1 @ (^ [F:$i]: ~ (I @ F)))),bind(B, $thf(B)),bind(C, $thf(sk2 @ (sk1 @ (^ [F:$i]: ~ (I @ F))))),bind(D, $thf(I))]])).
% 19.92/6.07 thf(259,plain,(! [B:($i > $o),A:$i] : ((cP @ (sk1 @ (^ [C:$i]: ~ (B @ C)))) | (B @ A) | (B @ (sk2 @ (sk1 @ (^ [C:$i]: ~ (B @ C))))))),inference(simp,[status(thm)],[179])).
% 19.92/6.07 thf(8,plain,(! [A:$i] : ((~ (cP @ (sk2 @ A))) | (cP @ A))),inference(cnfConj,[status(thm)],[5])).
% 19.92/6.07 thf(15,plain,(! [A:$i] : ((~ (cP @ (sk2 @ A))) | (cP @ A))),inference(simp,[status(thm)],[8])).
% 19.92/6.07 thf(510,plain,(! [C:$i,B:($i > $o),A:$i] : ((cP @ (sk1 @ (^ [D:$i]: ~ (B @ D)))) | (B @ A) | ~ (($true)) | (cP @ C) | ((B @ (sk2 @ (sk1 @ (^ [D:$i]: ~ (B @ D))))) != (cP @ (sk2 @ C))))),inference(paramod_ordered,[status(thm)],[259,15])).
% 19.92/6.07 thf(511,plain,(! [C:$i,B:($i > $o),A:$i] : ((cP @ (sk1 @ (^ [D:$i]: ~ (B @ D)))) | (B @ A) | (cP @ C) | ((B @ (sk2 @ (sk1 @ (^ [D:$i]: ~ (B @ D))))) != (cP @ (sk2 @ C))))),inference(simp,[status(thm)],[510])).
% 19.92/6.07 thf(591,plain,(! [A:$i] : ((cP @ (sk1 @ (^ [B:$i]: ~ (cP @ B)))) | (cP @ A) | (cP @ (sk1 @ (^ [B:$i]: ~ (cP @ B)))))),inference(pre_uni,[status(thm)],[511:[bind(A, $thf(A)),bind(B, $thf(cP)),bind(C, $thf(sk1 @ (^ [D:$i]: ~ (cP @ D))))]])).
% 19.92/6.07 thf(664,plain,(! [A:$i] : ((cP @ (sk1 @ (^ [B:$i]: ~ (cP @ B)))) | (cP @ A))),inference(simp,[status(thm)],[591])).
% 19.92/6.07 thf(971,plain,(! [A:$i] : ((cP @ (sk1 @ (^ [B:$i]: ~ (cP @ B)))) | ((cP @ A) != (cP @ (sk1 @ (^ [B:$i]: ~ (cP @ B))))) | ~ (($true)))),inference(eqfactor_ordered,[status(thm)],[664])).
% 19.92/6.07 thf(993,plain,((cP @ (sk1 @ (^ [A:$i]: ~ (cP @ A))))),inference(pattern_uni,[status(thm)],[971:[bind(A, $thf(sk1 @ (^ [B:$i]: ~ (cP @ B))))]])).
% 19.92/6.07 thf(2100,plain,(! [A:$i] : ((cP @ A) | ~ (($true)))),inference(rewrite,[status(thm)],[995,993])).
% 19.92/6.07 thf(2101,plain,(! [A:$i] : ((cP @ A))),inference(simp,[status(thm)],[2100])).
% 19.92/6.07 thf(2113,plain,(~ (($true))),inference(rewrite,[status(thm)],[6,2101])).
% 19.92/6.07 thf(2114,plain,(($false)),inference(simp,[status(thm)],[2113])).
% 19.92/6.07 % SZS output end Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% 19.92/6.07 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------