%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LCL729^5 : TPTP v9.3.1. Released v4.0.0.
% 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 : n007.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 08:14:13 AM UTC 2026
% Result : Theorem 42.89s 10.77s
% Output : Refutation 35.56s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL729^5 : TPTP v9.3.1. Released v4.0.0.
% 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
% 0.10/0.20 % Computer : n007.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 09:59:02 UTC 2026
% 0.10/0.20 % CPUTime :
% 0.10/0.20 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
% 0.86/0.77 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.26/0.96 % [INFO] Parsing done (189ms).
% 1.26/0.98 % [INFO] Running in sequential loop mode.
% 1.86/1.38 % [INFO] eprover registered as external prover.
% 1.86/1.39 % [INFO] Scanning for conjecture ...
% 2.06/1.47 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.23/1.51 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.23/1.51 % [INFO] Problem is higher-order (TPTP THF).
% 2.23/1.51 % [INFO] Type checking passed.
% 2.23/1.52 % [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 ...
% 42.89/10.77 % External prover 'e' found a proof!
% 42.89/10.77 % [INFO] Killing All external provers ...
% 42.89/10.77 % Time passed: 10434ms (effective reasoning time: 9785ms)
% 42.89/10.77 % 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)>
% 42.89/10.77 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 10434 ms resp. 9785 ms w/o parsing
% 35.56/10.91 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 35.56/10.91 thf(a_type, type, a: $tType).
% 35.56/10.91 thf(sk1_decl, type, sk1: ((a > $o) > (a > $o))).
% 35.56/10.91 thf(sk2_decl, type, sk2: (((a > $o) > a) > (a > $o))).
% 35.56/10.91 thf(sk3_decl, type, sk3: (((a > $o) > a) > a)).
% 35.56/10.91 thf(sk4_decl, type, sk4: (((a > $o) > a) > ((a > $o) > $o))).
% 35.56/10.91 thf(sk5_decl, type, sk5: ((a > $o) > (((a > $o) > a) > a))).
% 35.56/10.91 thf(sk6_decl, type, sk6: (((a > $o) > a) > (((a > $o) > a) > (a > $o)))).
% 35.56/10.91 thf(sk7_decl, type, sk7: (((a > $o) > (a > $o)) > ((a > $o) > a))).
% 35.56/10.91 thf(sk8_decl, type, sk8: (((a > $o) > $o) > (a > ((a > $o) > (((a > $o) > (a > $o)) > (a > $o)))))).
% 35.56/10.91 thf(sk9_decl, type, sk9: (((a > $o) > $o) > (a > ((a > $o) > (((a > $o) > (a > $o)) > ((a > $o) > a)))))).
% 35.56/10.91 thf(sk1_def, definition, sk1 = (@+ [A:((a > $o) > (a > $o))]: ~ (? [B:((a > $o) > a)]: ! [C:(a > $o)]: ((? [D:a]: (A @ (C) @ D)) => (A @ (C) @ (B @ (C)))))) ).
% 35.56/10.91 thf(sk2_def, definition, sk2 = (^ [A:((a > $o) > a)]: (@+ [B:(a > $o)]: ~ ((? [C:a]: (sk1 @ (B) @ C)) => (sk1 @ B @ (A @ B))))) ).
% 35.56/10.91 thf(sk3_def, definition, sk3 = (^ [A:((a > $o) > a)]: (@+ [B:a]: (sk1 @ (sk2 @ (A)) @ B))) ).
% 35.56/10.91 thf(sk4_def, definition, sk4 = (^ [A:((a > $o) > a)]: (@+ [B:((a > $o) > $o)]: ~ ((! [C:(a > $o)]: ((B @ C) => (? [D:a]: (C @ D)))) => (? [C:((a > $o) > a)]: ! [D:(a > $o)]: ((B @ D) => (D @ (C @ D))))))) ).
% 35.56/10.91 thf(sk5_def, definition, sk5 = (^ [A:(a > $o),B:((a > $o) > a)]: (@+ [C:a]: (A @ C))) ).
% 35.56/10.91 thf(sk6_def, definition, sk6 = (^ [A:((a > $o) > a),B:((a > $o) > a)]: (@+ [C:(a > $o)]: ~ ((sk4 @ B @ C) => (C @ (A @ C))))) ).
% 35.56/10.91 thf(sk7_def, definition, sk7 = (^ [A:((a > $o) > (a > $o))]: (@+ [B:((a > $o) > a)]: ! [C:(a > $o)]: ((? [D:a]: (A @ (C) @ D)) => (A @ C @ (B @ C))))) ).
% 35.56/10.91 thf(sk8_def, definition, sk8 = (^ [A:((a > $o) > $o),B:a,C:(a > $o),D:((a > $o) > (a > $o))]: (@+ [E:(a > $o)]: ~ ((A @ E) => (? [F:a]: (E @ F))))) ).
% 35.56/10.91 thf(sk9_def, definition, sk9 = (^ [A:((a > $o) > $o),B:a,C:(a > $o),D:((a > $o) > (a > $o))]: (@+ [E:((a > $o) > a)]: ! [F:(a > $o)]: ((A @ F) => (F @ (E @ F))))) ).
% 35.56/10.91 thf(1,conjecture,(((! [A:((a > $o) > (a > $o))]: ? [B:((a > $o) > a)]: ! [C:(a > $o)]: ((? [D:a]: (A @ C @ D)) => (A @ C @ (B @ C)))) = (! [A:((a > $o) > $o)]: ((! [B:(a > $o)]: ((A @ B) => (? [C:a]: (B @ C)))) => (? [B:((a > $o) > a)]: ! [C:(a > $o)]: ((A @ C) => (C @ (B @ C)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM560)).
% 35.56/10.91 thf(2,negated_conjecture,((~ ((! [A:((a > $o) > (a > $o))]: ? [B:((a > $o) > a)]: ! [C:(a > $o)]: ((? [D:a]: (A @ C @ D)) => (A @ C @ (B @ C)))) = (! [A:((a > $o) > $o)]: ((! [B:(a > $o)]: ((A @ B) => (? [C:a]: (B @ C)))) => (? [B:((a > $o) > a)]: ! [C:(a > $o)]: ((A @ C) => (C @ (B @ C))))))))),inference(neg_conjecture,[status(cth)],[1])).
% 35.56/10.91 thf(3,plain,((~ ((! [A:((a > $o) > (a > $o))]: ? [B:((a > $o) > a)]: ! [C:(a > $o)]: ((? [D:a]: (A @ (C) @ D)) => (A @ (C) @ (B @ (C))))) = (! [A:((a > $o) > $o)]: ((! [B:(a > $o)]: ((A @ (B)) => (? [C:a]: (B @ C)))) => (? [B:((a > $o) > a)]: ! [C:(a > $o)]: ((A @ (C)) => (C @ (B @ (C)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])).
% 35.56/10.91 thf(4,plain,(((! [A:((a > $o) > (a > $o))]: ? [B:((a > $o) > a)]: ! [C:(a > $o)]: ((? [D:a]: (A @ (C) @ D)) => (A @ (C) @ (B @ (C))))) != (! [A:((a > $o) > $o)]: ((! [B:(a > $o)]: ((A @ (B)) => (? [C:a]: (B @ C)))) => (? [B:((a > $o) > a)]: ! [C:(a > $o)]: ((A @ (C)) => (C @ (B @ (C))))))))),inference(lifteq,[status(thm)],[3])).
% 35.56/10.91 thf(5,plain,((~ (! [A:((a > $o) > (a > $o))]: ? [B:((a > $o) > a)]: ! [C:(a > $o)]: ((? [D:a]: (A @ (C) @ D)) => (A @ (C) @ (B @ (C)))))) | (~ (! [A:((a > $o) > $o)]: ((! [B:(a > $o)]: ((A @ (B)) => (? [C:a]: (B @ C)))) => (? [B:((a > $o) > a)]: ! [C:(a > $o)]: ((A @ (C)) => (C @ (B @ (C))))))))),inference(bool_ext,[status(thm)],[4])).
% 35.56/10.91 thf(7,plain,(! [C:((a > $o) > a),B:(a > $o),A:((a > $o) > a)] : ((((sk1 @ (sk2 @ (A)) @ (sk3 @ (A))) | ~ (sk4 @ (A) @ (B)) | (B @ (sk5 @ (B) @ (A)))) & ((sk1 @ (sk2 @ (A)) @ (sk3 @ (A))) | (sk4 @ (A) @ (sk6 @ (C) @ (A)))) & ((sk1 @ (sk2 @ (A)) @ (sk3 @ (A))) | ~ (sk6 @ (C) @ (A) @ (C @ (sk6 @ (C) @ (A))))) & (~ (sk1 @ (sk2 @ (A)) @ (A @ (sk2 @ (A)))) | ~ (sk4 @ (A) @ (B)) | (B @ (sk5 @ (B) @ (A)))) & (~ (sk1 @ (sk2 @ (A)) @ (A @ (sk2 @ (A)))) | (sk4 @ (A) @ (sk6 @ (C) @ (A)))) & (~ (sk1 @ (sk2 @ (A)) @ (A @ (sk2 @ (A)))) | ~ (sk6 @ (C) @ (A) @ (C @ (sk6 @ (C) @ (A)))))))),inference(cnf,[status(esa)],[5])).
% 35.56/10.91 thf(9,plain,(! [B:((a > $o) > a),A:((a > $o) > a)] : ((sk1 @ (sk2 @ (A)) @ (sk3 @ (A))) | (sk4 @ (A) @ (sk6 @ (B) @ (A))))),inference(cnfConj,[status(thm)],[7])).
% 35.56/10.91 thf(14,plain,(! [B:((a > $o) > a),A:((a > $o) > a)] : ((sk1 @ (sk2 @ (A)) @ (sk3 @ (A))) | (sk4 @ (A) @ (sk6 @ (B) @ (A))))),inference(simp,[status(thm)],[9])).
% 35.56/10.91 thf(11,plain,(! [B:(a > $o),A:((a > $o) > a)] : ((sk1 @ (sk2 @ (A)) @ (sk3 @ (A))) | (~ (sk4 @ (A) @ (B))) | (B @ (sk5 @ (B) @ (A))))),inference(cnfConj,[status(thm)],[7])).
% 35.56/10.91 thf(88,plain,(! [D:(a > $o),C:((a > $o) > a),B:((a > $o) > a),A:((a > $o) > a)] : ((sk1 @ (sk2 @ (A)) @ (sk3 @ (A))) | (sk1 @ (sk2 @ (C)) @ (sk3 @ (C))) | ~ (($true)) | (D @ (sk5 @ (D) @ (C))) | ((sk4 @ (A) @ (sk6 @ (B) @ (A))) != (sk4 @ (C) @ (D))))),inference(paramod_ordered,[status(thm)],[14,11])).
% 35.56/10.91 thf(89,plain,(! [D:(a > $o),C:((a > $o) > a),B:((a > $o) > a),A:((a > $o) > a)] : ((sk1 @ (sk2 @ (A)) @ (sk3 @ (A))) | (sk1 @ (sk2 @ (C)) @ (sk3 @ (C))) | (D @ (sk5 @ (D) @ (C))) | ((sk4 @ (A) @ (sk6 @ (B) @ (A))) != (sk4 @ (C) @ (D))))),inference(simp,[status(thm)],[88])).
% 35.56/10.91 thf(90,plain,(! [B:((a > $o) > a),A:((a > $o) > a)] : ((sk1 @ (sk2 @ (A)) @ (sk3 @ (A))) | (sk1 @ (sk2 @ (A)) @ (sk3 @ (A))) | (sk6 @ (B) @ (A) @ (sk5 @ (sk6 @ (B) @ (A)) @ (A))))),inference(pattern_uni,[status(thm)],[89:[bind(A, $thf(A)),bind(B, $thf(B)),bind(C, $thf(A)),bind(D, $thf(sk6 @ (B) @ (A)))]])).
% 35.56/10.91 thf(144,plain,(! [B:((a > $o) > a),A:((a > $o) > a)] : ((sk1 @ (sk2 @ (A)) @ (sk3 @ (A))) | (sk6 @ (B) @ (A) @ (sk5 @ (sk6 @ (B) @ (A)) @ (A))))),inference(simp,[status(thm)],[90])).
% 35.56/10.91 thf(22,axiom,((? [A:((a > $o) > a)]: ! [B:(a > $o)]: ((? [C:a]: (B @ C)) => (B @ (A @ B))))),introduced(axiom_of_choice)).
% 35.56/10.91 thf(27,plain,(! [C:a,B:((a > $o) > a),A:((a > $o) > a)] : ((~ (sk6 @ (B) @ (A) @ C)) | (sk6 @ (B) @ (A) @ (@+ [D:a]: (sk6 @ (B) @ (A) @ D))))),inference(choice,[status(esa)],[22])).
% 35.56/10.91 thf(12,plain,(! [B:((a > $o) > a),A:((a > $o) > a)] : ((sk1 @ (sk2 @ (A)) @ (sk3 @ (A))) | (~ (sk6 @ (B) @ (A) @ (B @ (sk6 @ (B) @ (A))))))),inference(cnfConj,[status(thm)],[7])).
% 35.56/10.91 thf(16,plain,(! [B:((a > $o) > a),A:((a > $o) > a)] : ((sk1 @ (sk2 @ (A)) @ (sk3 @ (A))) | (~ (sk6 @ (B) @ (A) @ (B @ (sk6 @ (B) @ (A))))))),inference(simp,[status(thm)],[12])).
% 35.56/10.91 thf(235,plain,(! [E:((a > $o) > a),D:((a > $o) > a),C:a,B:((a > $o) > a),A:((a > $o) > a)] : ((~ (sk6 @ (B) @ (A) @ C)) | (sk1 @ (sk2 @ (D)) @ (sk3 @ (D))) | ~ (($true)) | ((sk6 @ (B) @ (A) @ (@+ [F:a]: (sk6 @ (B) @ (A) @ F))) != (sk6 @ (E) @ (D) @ (E @ (sk6 @ (E) @ (D))))))),inference(paramod_ordered,[status(thm)],[27,16])).
% 35.56/10.91 thf(236,plain,(! [E:((a > $o) > a),D:((a > $o) > a),C:a,B:((a > $o) > a),A:((a > $o) > a)] : ((~ (sk6 @ (B) @ (A) @ C)) | (sk1 @ (sk2 @ (D)) @ (sk3 @ (D))) | ((sk6 @ (B) @ (A) @ (@+ [F:a]: (sk6 @ (B) @ (A) @ F))) != (sk6 @ (E) @ (D) @ (E @ (sk6 @ (E) @ (D))))))),inference(simp,[status(thm)],[235])).
% 35.56/10.91 thf(241,plain,(! [B:((a > $o) > a),A:a] : ((~ (sk6 @ ((@+) @ a) @ (B) @ A)) | (sk1 @ (sk2 @ (B)) @ (sk3 @ (B))))),inference(pre_uni,[status(thm)],[236:[bind(A, $thf(D)),bind(B, $thf((@+) @ a)),bind(C, $thf(C)),bind(D, $thf(D)),bind(E, $thf((@+) @ a))]])).
% 35.56/10.91 thf(244,plain,(! [B:((a > $o) > a),A:a] : ((~ (sk6 @ ((@+) @ a) @ (B) @ A)) | (sk1 @ (sk2 @ (B)) @ (sk3 @ (B))))),inference(simp,[status(thm)],[241])).
% 35.56/10.91 thf(253,plain,(! [E:((a > $o) > a),D:a,C:a,B:((a > $o) > a),A:((a > $o) > a)] : ((~ (sk6 @ (B) @ (A) @ C)) | ~ (($true)) | (sk1 @ (sk2 @ (E)) @ (sk3 @ (E))) | ((sk6 @ (B) @ (A) @ (@+ [F:a]: (sk6 @ (B) @ (A) @ F))) != (sk6 @ ((@+) @ a) @ (E) @ D)))),inference(paramod_ordered,[status(thm)],[27,244])).
% 35.56/10.91 thf(254,plain,(! [E:((a > $o) > a),D:a,C:a,B:((a > $o) > a),A:((a > $o) > a)] : ((~ (sk6 @ (B) @ (A) @ C)) | (sk1 @ (sk2 @ (E)) @ (sk3 @ (E))) | ((sk6 @ (B) @ (A) @ (@+ [F:a]: (sk6 @ (B) @ (A) @ F))) != (sk6 @ ((@+) @ a) @ (E) @ D)))),inference(simp,[status(thm)],[253])).
% 35.56/10.91 thf(255,plain,(! [B:a,A:((a > $o) > a)] : ((~ (sk6 @ ((@+) @ a) @ (A) @ B)) | (sk1 @ (sk2 @ (A)) @ (sk3 @ (A))))),inference(pattern_uni,[status(thm)],[254:[bind(A, $thf(A)),bind(B, $thf((@+) @ a)),bind(C, $thf(C)),bind(D, $thf(@+ [F:a]: (sk6 @ ((@+) @ a) @ (A) @ F))),bind(E, $thf(A))]])).
% 35.56/10.91 thf(270,plain,(! [B:a,A:((a > $o) > a)] : ((~ (sk6 @ ((@+) @ a) @ (A) @ B)) | (sk1 @ (sk2 @ (A)) @ (sk3 @ (A))))),inference(simp,[status(thm)],[255])).
% 35.56/10.91 thf(447,plain,(! [D:a,C:((a > $o) > a),B:((a > $o) > a),A:((a > $o) > a)] : ((sk1 @ (sk2 @ (A)) @ (sk3 @ (A))) | ~ (($true)) | (sk1 @ (sk2 @ (C)) @ (sk3 @ (C))) | ((sk6 @ (B) @ (A) @ (sk5 @ (sk6 @ (B) @ (A)) @ (A))) != (sk6 @ ((@+) @ a) @ (C) @ D)))),inference(paramod_ordered,[status(thm)],[144,270])).
% 35.56/10.91 thf(448,plain,(! [D:a,C:((a > $o) > a),B:((a > $o) > a),A:((a > $o) > a)] : ((sk1 @ (sk2 @ (A)) @ (sk3 @ (A))) | (sk1 @ (sk2 @ (C)) @ (sk3 @ (C))) | ((sk6 @ (B) @ (A) @ (sk5 @ (sk6 @ (B) @ (A)) @ (A))) != (sk6 @ ((@+) @ a) @ (C) @ D)))),inference(simp,[status(thm)],[447])).
% 35.56/10.91 thf(449,plain,(! [A:((a > $o) > a)] : ((sk1 @ (sk2 @ (A)) @ (sk3 @ (A))) | (sk1 @ (sk2 @ (A)) @ (sk3 @ (A))))),inference(pattern_uni,[status(thm)],[448:[bind(A, $thf(H)),bind(B, $thf((@+) @ a)),bind(C, $thf(H)),bind(D, $thf(sk5 @ (sk6 @ ((@+) @ a) @ (H)) @ (H)))]])).
% 35.56/10.91 thf(455,plain,(! [A:((a > $o) > a)] : ((sk1 @ (sk2 @ (A)) @ (sk3 @ (A))))),inference(simp,[status(thm)],[449])).
% 35.56/10.91 thf(10,plain,(! [B:(a > $o),A:((a > $o) > a)] : ((~ (sk1 @ (sk2 @ (A)) @ (A @ (sk2 @ (A))))) | (~ (sk4 @ (A) @ (B))) | (B @ (sk5 @ (B) @ (A))))),inference(cnfConj,[status(thm)],[7])).
% 35.56/10.91 thf(51,plain,(! [A:((a > $o) > a)] : ((~ (sk1 @ (sk2 @ (A)) @ (A @ (sk2 @ (A))))) | (~ (sk4 @ (A) @ (^ [B:a]: (($false))))) | ($false))),inference(prim_subst,[status(thm)],[10:[bind(A, $thf(A)),bind(B, $thf(^ [C:a]: (($false))))]])).
% 35.56/10.91 thf(72,plain,(! [A:((a > $o) > a)] : ((~ (sk1 @ (sk2 @ (A)) @ (A @ (sk2 @ (A))))) | (~ (sk4 @ (A) @ (^ [B:a]: (($false))))))),inference(simp,[status(thm)],[51])).
% 35.56/10.91 thf(469,plain,(! [B:((a > $o) > a),A:((a > $o) > a)] : (~ (($true)) | (~ (sk4 @ (B) @ (^ [C:a]: (($false))))) | ((sk1 @ (sk2 @ (A)) @ (sk3 @ (A))) != (sk1 @ (sk2 @ (B)) @ (B @ (sk2 @ (B))))))),inference(paramod_ordered,[status(thm)],[455,72])).
% 35.56/10.91 thf(470,plain,(! [B:((a > $o) > a),A:((a > $o) > a)] : ((~ (sk4 @ (B) @ (^ [C:a]: (($false))))) | ((sk1 @ (sk2 @ (A)) @ (sk3 @ (A))) != (sk1 @ (sk2 @ (B)) @ (B @ (sk2 @ (B))))))),inference(simp,[status(thm)],[469])).
% 35.56/10.91 thf(477,plain,(! [B:((a > $o) > a),A:((a > $o) > a)] : ((~ (sk4 @ (B) @ (^ [C:a]: (($false))))) | ((sk2 @ (A)) != (sk2 @ (B))) | ((sk3 @ (A)) != (B @ (sk2 @ (B)))))),inference(simp,[status(thm)],[470])).
% 35.56/10.91 thf(957,plain,(! [B:((a > $o) > a),A:((a > $o) > a)] : ((~ (sk4 @ (B) @ (^ [C:a]: (($false))))) | ((^ [C:a]: (A)) != (^ [C:a]: (B))) | ((^ [C:a]: (C)) != (^ [C:a]: (C))) | ((sk3 @ (A)) != (B @ (sk2 @ (B)))))),inference(simp,[status(thm)],[477])).
% 35.56/10.91 thf(994,plain,(! [B:((a > $o) > a),A:((a > $o) > a)] : ((~ (sk4 @ (B) @ (^ [C:a]: (($false))))) | ((^ [C:a]: (A)) != (^ [C:a]: (B))) | ((sk3 @ (A)) != (B @ (sk2 @ (B)))))),inference(simp,[status(thm)],[957])).
% 35.56/10.91 thf(6,plain,((! [A:((a > $o) > (a > $o))]: ? [B:((a > $o) > a)]: ! [C:(a > $o)]: ((? [D:a]: (A @ (C) @ D)) => (A @ (C) @ (B @ (C))))) | (! [A:((a > $o) > $o)]: ((! [B:(a > $o)]: ((A @ (B)) => (? [C:a]: (B @ C)))) => (? [B:((a > $o) > a)]: ! [C:(a > $o)]: ((A @ (C)) => (C @ (B @ (C)))))))),inference(bool_ext,[status(thm)],[4])).
% 35.56/10.91 thf(18,plain,(! [F:(a > $o),E:a,D:((a > $o) > $o),C:a,B:(a > $o),A:((a > $o) > (a > $o))] : (((~ (A @ (B) @ C) | (A @ (B) @ (sk7 @ (A) @ (B))) | (D @ (sk8 @ (D) @ C @ B @ (A))) | ~ (D @ (F)) | (F @ (sk9 @ (D) @ C @ (B) @ (A) @ (F)))) & (~ (A @ (B) @ C) | (A @ (B) @ (sk7 @ (A) @ (B))) | ~ (sk8 @ (D) @ C @ (B) @ (A) @ E) | ~ (D @ (F)) | (F @ (sk9 @ (D) @ C @ (B) @ (A) @ (F))))))),inference(cnf,[status(esa)],[6])).
% 35.56/10.91 thf(19,plain,(! [E:(a > $o),D:((a > $o) > $o),C:a,B:(a > $o),A:((a > $o) > (a > $o))] : ((~ (A @ (B) @ C)) | (A @ (B) @ (sk7 @ (A) @ (B))) | (D @ (sk8 @ (D) @ C @ B @ (A))) | (~ (D @ (E))) | (E @ (sk9 @ (D) @ C @ (B) @ (A) @ (E))))),inference(cnfConj,[status(thm)],[18])).
% 35.56/10.91 thf(21,plain,(! [E:(a > $o),D:((a > $o) > $o),C:a,B:(a > $o),A:((a > $o) > (a > $o))] : ((~ (A @ (B) @ C)) | (A @ (B) @ (sk7 @ (A) @ (B))) | (D @ (sk8 @ (D) @ C @ B @ (A))) | (~ (D @ (E))) | (E @ (sk9 @ (D) @ C @ (B) @ (A) @ (E))))),inference(simp,[status(thm)],[19])).
% 35.56/10.91 thf(8,plain,(! [B:((a > $o) > a),A:((a > $o) > a)] : ((~ (sk1 @ (sk2 @ (A)) @ (A @ (sk2 @ (A))))) | (~ (sk6 @ (B) @ (A) @ (B @ (sk6 @ (B) @ (A))))))),inference(cnfConj,[status(thm)],[7])).
% 35.56/10.91 thf(17,plain,(! [B:((a > $o) > a),A:((a > $o) > a)] : ((~ (sk1 @ (sk2 @ (A)) @ (A @ (sk2 @ (A))))) | (~ (sk6 @ (B) @ (A) @ (B @ (sk6 @ (B) @ (A))))))),inference(simp,[status(thm)],[8])).
% 35.56/10.91 thf(230,plain,(! [E:((a > $o) > a),D:((a > $o) > a),C:a,B:((a > $o) > a),A:((a > $o) > a)] : ((~ (sk6 @ (B) @ (A) @ C)) | (~ (sk1 @ (sk2 @ (D)) @ (D @ (sk2 @ (D))))) | ~ (($true)) | ((sk6 @ (B) @ (A) @ (@+ [F:a]: (sk6 @ (B) @ (A) @ F))) != (sk6 @ (E) @ (D) @ (E @ (sk6 @ (E) @ (D))))))),inference(paramod_ordered,[status(thm)],[27,17])).
% 35.56/10.91 thf(231,plain,(! [E:((a > $o) > a),D:((a > $o) > a),C:a,B:((a > $o) > a),A:((a > $o) > a)] : ((~ (sk6 @ (B) @ (A) @ C)) | (~ (sk1 @ (sk2 @ (D)) @ (D @ (sk2 @ (D))))) | ((sk6 @ (B) @ (A) @ (@+ [F:a]: (sk6 @ (B) @ (A) @ F))) != (sk6 @ (E) @ (D) @ (E @ (sk6 @ (E) @ (D))))))),inference(simp,[status(thm)],[230])).
% 35.56/10.91 thf(242,plain,(! [B:((a > $o) > a),A:a] : ((~ (sk6 @ ((@+) @ a) @ (B) @ A)) | (~ (sk1 @ (sk2 @ (B)) @ (B @ (sk2 @ (B))))))),inference(pre_uni,[status(thm)],[231:[bind(A, $thf(D)),bind(B, $thf((@+) @ a)),bind(C, $thf(C)),bind(D, $thf(D)),bind(E, $thf((@+) @ a))]])).
% 35.56/10.91 thf(245,plain,(! [B:((a > $o) > a),A:a] : ((~ (sk6 @ ((@+) @ a) @ (B) @ A)) | (~ (sk1 @ (sk2 @ (B)) @ (B @ (sk2 @ (B))))))),inference(simp,[status(thm)],[242])).
% 35.56/10.91 thf(23,plain,(! [B:a,A:((a > $o) > a)] : ((~ (sk2 @ (A) @ B)) | (sk2 @ (A) @ (@+ [C:a]: (sk2 @ (A) @ C))))),inference(choice,[status(esa)],[22])).
% 35.56/10.91 thf(13,plain,(! [B:((a > $o) > a),A:((a > $o) > a)] : ((~ (sk1 @ (sk2 @ (A)) @ (A @ (sk2 @ (A))))) | (sk4 @ (A) @ (sk6 @ (B) @ (A))))),inference(cnfConj,[status(thm)],[7])).
% 35.56/10.91 thf(15,plain,(! [B:((a > $o) > a),A:((a > $o) > a)] : ((~ (sk1 @ (sk2 @ (A)) @ (A @ (sk2 @ (A))))) | (sk4 @ (A) @ (sk6 @ (B) @ (A))))),inference(simp,[status(thm)],[13])).
% 35.56/10.91 thf(20,plain,(! [F:(a > $o),E:a,D:((a > $o) > $o),C:a,B:(a > $o),A:((a > $o) > (a > $o))] : ((~ (A @ (B) @ C)) | (A @ (B) @ (sk7 @ (A) @ (B))) | (~ (sk8 @ (D) @ C @ (B) @ (A) @ E)) | (~ (D @ (F))) | (F @ (sk9 @ (D) @ C @ (B) @ (A) @ (F))))),inference(cnfConj,[status(thm)],[18])).
% 35.56/10.91 thf(113,plain,(! [A:((a > $o) > a)] : ((sk1 @ (sk2 @ (A)) @ (sk3 @ (A))) | (~ (sk4 @ (A) @ (^ [B:a]: (($false))))) | ($false))),inference(prim_subst,[status(thm)],[11:[bind(A, $thf(A)),bind(B, $thf(^ [C:a]: (($false))))]])).
% 35.56/10.91 thf(139,plain,(! [A:((a > $o) > a)] : ((sk1 @ (sk2 @ (A)) @ (sk3 @ (A))) | (~ (sk4 @ (A) @ (^ [B:a]: (($false))))))),inference(simp,[status(thm)],[113])).
% 35.56/10.91 thf(196,plain,(! [B:((a > $o) > a),A:((a > $o) > a)] : ((~ (sk4 @ (A) @ (^ [C:a]: (($false))))) | ~ (($true)) | (~ (sk4 @ (B) @ (^ [C:a]: (($false))))) | ((sk1 @ (sk2 @ (A)) @ (sk3 @ (A))) != (sk1 @ (sk2 @ (B)) @ (B @ (sk2 @ (B))))))),inference(paramod_ordered,[status(thm)],[139,72])).
% 35.56/10.91 thf(197,plain,(! [B:((a > $o) > a),A:((a > $o) > a)] : ((~ (sk4 @ (A) @ (^ [C:a]: (($false))))) | (~ (sk4 @ (B) @ (^ [C:a]: (($false))))) | ((sk1 @ (sk2 @ (A)) @ (sk3 @ (A))) != (sk1 @ (sk2 @ (B)) @ (B @ (sk2 @ (B))))))),inference(simp,[status(thm)],[196])).
% 35.56/10.91 thf(201,plain,(! [B:((a > $o) > a),A:((a > $o) > a)] : ((~ (sk4 @ (A) @ (^ [C:a]: (($false))))) | (~ (sk4 @ (B) @ (^ [C:a]: (($false))))) | ((sk2 @ (A)) != (sk2 @ (B))) | ((sk3 @ (A)) != (B @ (sk2 @ (B)))))),inference(simp,[status(thm)],[197])).
% 35.56/10.91 thf(387,plain,(! [B:((a > $o) > a),A:((a > $o) > a)] : ((~ (sk4 @ (A) @ (^ [C:a]: (($false))))) | ((sk2 @ (A)) != (sk2 @ (B))) | ((sk3 @ (A)) != (B @ (sk2 @ (B)))) | ((sk4 @ (B) @ (^ [C:a]: (($false)))) != (sk4 @ (A) @ (^ [C:a]: (($false))))) | ~ (($true)))),inference(eqfactor_ordered,[status(thm)],[201])).
% 35.56/10.91 thf(395,plain,(! [A:((a > $o) > a)] : ((~ (sk4 @ (A) @ (^ [B:a]: (($false))))) | ((sk2 @ (A)) != (sk2 @ (A))) | ((sk3 @ (A)) != (A @ (sk2 @ (A)))))),inference(pattern_uni,[status(thm)],[387:[bind(A, $thf(B))]])).
% 35.56/10.91 thf(416,plain,(! [A:((a > $o) > a)] : ((~ (sk4 @ (A) @ (^ [B:a]: (($false))))) | ((sk3 @ (A)) != (A @ (sk2 @ (A)))))),inference(simp,[status(thm)],[395])).
% 35.56/10.91 thf(303,plain,(! [E:((a > $o) > a),D:a,C:a,B:((a > $o) > a),A:((a > $o) > a)] : ((~ (sk6 @ (B) @ (A) @ C)) | ~ (($true)) | (~ (sk1 @ (sk2 @ (E)) @ (E @ (sk2 @ (E))))) | ((sk6 @ (B) @ (A) @ (@+ [F:a]: (sk6 @ (B) @ (A) @ F))) != (sk6 @ ((@+) @ a) @ (E) @ D)))),inference(paramod_ordered,[status(thm)],[27,245])).
% 35.56/10.91 thf(304,plain,(! [E:((a > $o) > a),D:a,C:a,B:((a > $o) > a),A:((a > $o) > a)] : ((~ (sk6 @ (B) @ (A) @ C)) | (~ (sk1 @ (sk2 @ (E)) @ (E @ (sk2 @ (E))))) | ((sk6 @ (B) @ (A) @ (@+ [F:a]: (sk6 @ (B) @ (A) @ F))) != (sk6 @ ((@+) @ a) @ (E) @ D)))),inference(simp,[status(thm)],[303])).
% 35.56/10.91 thf(305,plain,(! [B:a,A:((a > $o) > a)] : ((~ (sk6 @ ((@+) @ a) @ (A) @ B)) | (~ (sk1 @ (sk2 @ (A)) @ (A @ (sk2 @ (A))))))),inference(pattern_uni,[status(thm)],[304:[bind(A, $thf(A)),bind(B, $thf((@+) @ a)),bind(C, $thf(C)),bind(D, $thf(@+ [F:a]: (sk6 @ ((@+) @ a) @ (A) @ F))),bind(E, $thf(A))]])).
% 35.56/10.91 thf(325,plain,(! [B:a,A:((a > $o) > a)] : ((~ (sk6 @ ((@+) @ a) @ (A) @ B)) | (~ (sk1 @ (sk2 @ (A)) @ (A @ (sk2 @ (A))))))),inference(simp,[status(thm)],[305])).
% 35.56/10.91 thf(2181,plain,(($false)),inference(e,[status(thm)],[994,10,21,17,27,245,477,72,23,4,15,20,416,325,455,3])).
% 35.56/10.91 % SZS output end Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 35.56/10.91 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------