TSTP Solution File: GRA028^1 by Leo-III---1.7.15
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.15
% Problem : GRA028^1 : TPTP v8.2.0. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Jun 24 06:36:16 EDT 2024
% Result : Theorem 183.41s 82.13s
% Output : Refutation 183.65s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : GRA028^1 : TPTP v8.2.0. Released v3.6.0.
% 0.10/0.12 % Command : run_Leo-III %s %d THM
% 0.13/0.33 % Computer : n014.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Tue Jun 18 15:18:55 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.85/0.85 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.21/0.96 % [INFO] Parsing done (106ms).
% 1.21/0.97 % [INFO] Running in sequential loop mode.
% 1.51/1.16 % [INFO] eprover registered as external prover.
% 1.51/1.17 % [INFO] Scanning for conjecture ...
% 1.79/1.23 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 1.93/1.26 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 1.93/1.26 % [INFO] Problem is higher-order (TPTP THF).
% 1.93/1.26 % [INFO] Type checking passed.
% 1.93/1.27 % [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 ...
% 183.41/82.13 % External prover 'e' found a proof!
% 183.41/82.13 % [INFO] Killing All external provers ...
% 183.41/82.13 % Time passed: 81608ms (effective reasoning time: 81162ms)
% 183.41/82.13 % 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)>
% 183.41/82.13 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 81608 ms resp. 81162 ms w/o parsing
% 183.65/82.28 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% 183.65/82.28 thf(sk1_type, type, sk1: (($o > $o) > (($o > $o) > $o))).
% 183.65/82.28 thf(1,conjecture,((! [A:(($o > $o) > (($o > $o) > $o))]: ((! [B:($o > $o),C:($o > $o)]: ((A @ B @ C) => (A @ C @ B))) => (? [B:($o > $o),C:($o > $o),D:(($o > $o) > $o)]: ((D @ B) & ~ (D @ C) & (A @ C @ B)) | ? [B:($o > $o),C:($o > $o),D:($o > $o),E:($o > $o),F:(($o > $o) > $o),G:(($o > $o) > $o),H:(($o > $o) > $o)]: ((F @ B) & ~ (F @ C) & ~ (F @ D) & ~ (F @ E) & ~ (G @ B) & (G @ C) & ~ (G @ D) & ~ (G @ E) & ~ (H @ B) & ~ (H @ C) & (H @ D) & ~ (H @ E) & ~ (A @ C @ B) & ~ (A @ D @ B) & ~ (A @ D @ C) & ~ (A @ E @ B) & ~ (A @ E @ C) & ~ (A @ E @ D)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',ramsey_u_2_4_4)).
% 183.65/82.28 thf(2,negated_conjecture,((~ (! [A:(($o > $o) > (($o > $o) > $o))]: ((! [B:($o > $o),C:($o > $o)]: ((A @ B @ C) => (A @ C @ B))) => (? [B:($o > $o),C:($o > $o),D:(($o > $o) > $o)]: ((D @ B) & ~ (D @ C) & (A @ C @ B)) | ? [B:($o > $o),C:($o > $o),D:($o > $o),E:($o > $o),F:(($o > $o) > $o),G:(($o > $o) > $o),H:(($o > $o) > $o)]: ((F @ B) & ~ (F @ C) & ~ (F @ D) & ~ (F @ E) & ~ (G @ B) & (G @ C) & ~ (G @ D) & ~ (G @ E) & ~ (H @ B) & ~ (H @ C) & (H @ D) & ~ (H @ E) & ~ (A @ C @ B) & ~ (A @ D @ B) & ~ (A @ D @ C) & ~ (A @ E @ B) & ~ (A @ E @ C) & ~ (A @ E @ D))))))),inference(neg_conjecture,[status(cth)],[1])).
% 183.65/82.28 thf(3,plain,((~ (! [A:(($o > $o) > (($o > $o) > $o))]: ((! [B:($o > $o),C:($o > $o)]: ((A @ (B) @ (C)) => (A @ (C) @ (B)))) => (? [B:($o > $o),C:($o > $o),D:(($o > $o) > $o)]: ((D @ (B)) & ~ (D @ (C)) & (A @ (C) @ (B))) | ? [B:($o > $o),C:($o > $o),D:($o > $o),E:($o > $o),F:(($o > $o) > $o),G:(($o > $o) > $o),H:(($o > $o) > $o)]: ((F @ (B)) & ~ (F @ (C)) & ~ (F @ (D)) & ~ (F @ (E)) & ~ (G @ (B)) & (G @ (C)) & ~ (G @ (D)) & ~ (G @ (E)) & ~ (H @ (B)) & ~ (H @ (C)) & (H @ (D)) & ~ (H @ (E)) & ~ (A @ (C) @ (B)) & ~ (A @ (D) @ (B)) & ~ (A @ (D) @ (C)) & ~ (A @ (E) @ (B)) & ~ (A @ (E) @ (C)) & ~ (A @ (E) @ (D)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])).
% 183.65/82.28 thf(4,plain,((~ (! [A:(($o > $o) > (($o > $o) > $o))]: ((! [B:($o > $o),C:($o > $o)]: ((A @ (B) @ (C)) => (A @ (C) @ (B)))) => (? [B:($o > $o),C:($o > $o),D:(($o > $o) > $o)]: ((D @ (B)) & ~ (D @ (C)) & (A @ (C) @ (B))) | ? [B:($o > $o),C:($o > $o),D:($o > $o),E:($o > $o),F:(($o > $o) > $o)]: ((F @ (B)) & ~ (F @ (C)) & ~ (F @ (D)) & ~ (F @ (E)) & ? [G:(($o > $o) > $o)]: (~ (G @ (B)) & (G @ (C)) & ~ (G @ (D)) & ~ (G @ (E)) & ? [H:(($o > $o) > $o)]: (~ (H @ (B)) & ~ (H @ (C)) & (H @ (D)) & ~ (H @ (E)) & ~ (A @ (C) @ (B)) & ~ (A @ (D) @ (B)) & ~ (A @ (D) @ (C)) & ~ (A @ (E) @ (B)) & ~ (A @ (E) @ (C)) & ~ (A @ (E) @ (D)))))))))),inference(miniscope,[status(thm)],[3])).
% 183.65/82.28 thf(6,plain,(! [C:(($o > $o) > $o),B:($o > $o),A:($o > $o)] : ((~ (C @ (A))) | (C @ (B)) | (~ (sk1 @ (B) @ (A))))),inference(cnf,[status(esa)],[4])).
% 183.65/82.28 thf(9,plain,(! [B:($o > $o),A:($o > $o)] : ((~ ((A) = (A))) | ((A) = (B)) | (~ (sk1 @ (B) @ (A))))),inference(replace_leibeq,[status(thm)],[6:[bind(A, $thf(A)),bind(B, $thf(B)),bind(C, $thf((=) @ ($o > $o) @ A))]])).
% 183.65/82.28 thf(12,plain,(! [B:($o > $o),A:($o > $o)] : (((A) != (A)) | ((A) = (B)) | (~ (sk1 @ (B) @ (A))))),inference(lifteq,[status(thm)],[9])).
% 183.65/82.28 thf(13,plain,(! [B:($o > $o),A:($o > $o)] : (((A) = (B)) | (~ (sk1 @ (B) @ (A))))),inference(simp,[status(thm)],[12])).
% 183.65/82.28 thf(16,plain,(! [C:$o,B:($o > $o),A:($o > $o)] : (((A @ C) = (B @ C)) | (~ (sk1 @ (B) @ (A))))),inference(func_ext,[status(esa)],[13])).
% 183.65/82.28 thf(7,plain,(! [B:($o > $o),A:($o > $o)] : ((~ (sk1 @ (A) @ (B))) | (sk1 @ (B) @ (A)))),inference(cnf,[status(esa)],[4])).
% 183.65/82.28 thf(35,plain,(! [E:$o,D:($o > $o),C:($o > $o),B:($o > $o),A:($o > $o)] : ((~ (sk1 @ (A) @ (B))) | (C @ E) | (~ (sk1 @ (D) @ (C))) | ((sk1 @ (B) @ (A)) != (D @ E)))),inference(paramod_ordered,[status(thm)],[7,16])).
% 183.65/82.28 thf(47,plain,(! [C:($o > $o),B:($o > $o),A:($o > $o)] : ((~ (sk1 @ (A) @ (B))) | (C @ (sk1 @ (B) @ (A))) | (~ (sk1 @ (^ [D:$o]: (D)) @ (C))))),inference(pre_uni,[status(thm)],[35:[bind(A, $thf(A)),bind(B, $thf(B)),bind(C, $thf(C)),bind(D, $thf(^ [F:$o]: (F))),bind(E, $thf(sk1 @ (B) @ (A)))]])).
% 183.65/82.28 thf(31,plain,(! [E:($o > $o),D:($o > $o),C:$o,B:($o > $o),A:($o > $o)] : ((~ (sk1 @ (B) @ (A))) | (~ (sk1 @ (D) @ (E))) | (B @ C) | ((A @ C) != (sk1 @ (E) @ (D))))),inference(paramod_ordered,[status(thm)],[16,7])).
% 183.65/82.28 thf(49,plain,(! [C:($o > $o),B:($o > $o),A:($o > $o)] : ((~ (sk1 @ (A) @ (^ [D:$o]: (D)))) | (~ (sk1 @ (B) @ (C))) | (A @ (sk1 @ (C) @ (B))))),inference(pre_uni,[status(thm)],[31:[bind(A, $thf(^ [F:$o]: (F))),bind(B, $thf(B)),bind(C, $thf(sk1 @ (E) @ (D)))]])).
% 183.65/82.28 thf(73,plain,(! [C:($o > $o),B:($o > $o),A:($o > $o)] : ((~ (sk1 @ (A) @ (^ [D:$o]: (D)))) | (~ (sk1 @ (B) @ (C))) | (A @ (sk1 @ (C) @ (B))))),inference(simp,[status(thm)],[49])).
% 183.65/82.28 thf(37941,plain,(! [C:($o > $o),B:($o > $o),A:($o > $o)] : ((~ (sk1 @ (A) @ (^ [D:$o]: (D)))) | (~ (sk1 @ (B) @ (C))) | ((A @ (sk1 @ (C) @ (B))) != (~ (sk1 @ (A) @ (^ [D:$o]: (D))))) | ~ (($true)))),inference(eqfactor_ordered,[status(thm)],[73])).
% 183.65/82.28 thf(38251,plain,((~ (sk1 @ ((~)) @ (^ [A:$o]: (A)))) | (~ (sk1 @ (^ [A:$o]: (A)) @ ((~))))),inference(pre_uni,[status(thm)],[37941:[bind(A, $thf((~))),bind(B, $thf(^ [D:$o]: (D))),bind(C, $thf((~)))]])).
% 183.65/82.28 thf(42237,plain,(! [C:($o > $o),B:($o > $o),A:($o > $o)] : ((~ (sk1 @ (A) @ (B))) | (~ (sk1 @ (^ [D:$o]: (D)) @ (C))) | (~ (sk1 @ ((~)) @ (^ [D:$o]: (D)))) | ((C @ (sk1 @ (B) @ (A))) != (sk1 @ (^ [D:$o]: (D)) @ ((~)))))),inference(paramod_ordered,[status(thm)],[47,38251])).
% 183.65/82.28 thf(42521,plain,((~ (sk1 @ ((~)) @ (^ [A:$o]: (A)))) | (~ (sk1 @ (^ [A:$o]: (A)) @ (^ [A:$o]: (A)))) | (~ (sk1 @ ((~)) @ (^ [A:$o]: (A))))),inference(pre_uni,[status(thm)],[42237:[bind(A, $thf((~))),bind(B, $thf(^ [D:$o]: (D))),bind(C, $thf(^ [D:$o]: (D)))]])).
% 183.65/82.28 thf(42620,plain,((~ (sk1 @ ((~)) @ (^ [A:$o]: (A)))) | (~ (sk1 @ (^ [A:$o]: (A)) @ (^ [A:$o]: (A))))),inference(simp,[status(thm)],[42521])).
% 183.65/82.28 thf(43664,plain,((~ (sk1 @ (^ [A:$o]: (A)) @ (^ [A:$o]: (A)))) | ((sk1 @ ((~)) @ (^ [A:$o]: (A))) != (sk1 @ (^ [A:$o]: (A)) @ (^ [A:$o]: (A)))) | ~ (($true))),inference(eqfactor_ordered,[status(thm)],[42620])).
% 183.65/82.28 thf(43811,plain,((~ (sk1 @ (^ [A:$o]: (A)) @ (^ [A:$o]: (A)))) | ((sk1 @ ((~)) @ (^ [A:$o]: (A))) != (sk1 @ (^ [A:$o]: (A)) @ (^ [A:$o]: (A))))),inference(simp,[status(thm)],[43664])).
% 183.65/82.28 thf(49574,plain,(! [C:$o,B:($o > $o),A:($o > $o)] : ((~ (sk1 @ (B) @ (A))) | (~ (sk1 @ (^ [D:$o]: (D)) @ (^ [D:$o]: (D)))) | ((A @ C) != (sk1 @ (^ [D:$o]: (D)) @ (^ [D:$o]: (D)))) | ((B @ C) != (sk1 @ ((~)) @ (^ [D:$o]: (D)))))),inference(paramod_ordered,[status(thm)],[16,43811])).
% 183.65/82.28 thf(49804,plain,(! [A:($o > $o)] : ((~ (sk1 @ (^ [B:$o]: (B)) @ (A))) | (~ (sk1 @ (^ [B:$o]: (B)) @ (^ [B:$o]: (B)))) | ((A @ (sk1 @ ((~)) @ (^ [B:$o]: (B)))) != (sk1 @ (^ [B:$o]: (B)) @ (^ [B:$o]: (B)))))),inference(pre_uni,[status(thm)],[49574:[bind(A, $thf(A)),bind(B, $thf(^ [D:$o]: (D))),bind(C, $thf(sk1 @ ((~)) @ (^ [D:$o]: (D))))]])).
% 183.65/82.28 thf(49806,plain,((~ (sk1 @ (^ [A:$o]: (A)) @ (^ [A:$o]: (A)))) | (~ (sk1 @ (^ [A:$o]: (A)) @ (^ [A:$o]: (sk1 @ (^ [B:$o]: (B)) @ (^ [B:$o]: (B))))))),inference(pre_uni,[status(thm)],[49804:[bind(A, $thf(^ [B:$o]: (sk1 @ (^ [C:$o]: (C)) @ (^ [C:$o]: (C)))))]])).
% 183.65/82.28 thf(122,axiom,((? [A:(($o > $o) > $o)]: ! [B:($o > $o)]: ((? [C:$o]: (B @ C)) => (B @ (A @ B))))),introduced(axiom_of_choice)).
% 183.65/82.28 thf(282,plain,(! [A:$o] : (~ (A) | (@+ [B:$o]: (B)))),inference(choice,[status(esa)],[122])).
% 183.65/82.28 thf(10767,plain,((@+ [A:$o]: (A))),inference(simp,[status(thm)],[282])).
% 183.65/82.28 thf(10986,plain,(! [C:$o,B:($o > $o),A:($o > $o)] : ((A @ C) | (~ (sk1 @ (B) @ (A))) | ((@+ [D:$o]: (D)) != (B @ C)))),inference(paramod_ordered,[status(thm)],[10767,16])).
% 183.65/82.28 thf(11063,plain,(! [A:($o > $o)] : ((A @ (@+ [B:$o]: (B))) | (~ (sk1 @ (^ [B:$o]: (B)) @ (A))))),inference(pre_uni,[status(thm)],[10986:[bind(A, $thf(A)),bind(B, $thf(^ [D:$o]: (D))),bind(C, $thf(@+ [D:$o]: (D)))]])).
% 183.65/82.28 thf(27548,plain,(! [A:($o > $o)] : ((A @ ($true)) | (~ (sk1 @ (^ [B:$o]: (B)) @ (A))))),inference(rewrite,[status(thm)],[11063,10767])).
% 183.65/82.28 thf(43333,plain,(! [A:($o > $o)] : ((~ (sk1 @ (^ [B:$o]: (B)) @ (A))) | (~ (sk1 @ (^ [B:$o]: (B)) @ (^ [B:$o]: (B)))) | ((A @ ($true)) != (sk1 @ ((~)) @ (^ [B:$o]: (B)))))),inference(paramod_ordered,[status(thm)],[27548,42620])).
% 183.65/82.28 thf(43806,plain,((~ (sk1 @ (^ [A:$o]: (A)) @ (^ [A:$o]: (sk1 @ (~) @ (^ [B:$o]: (B)))))) | (~ (sk1 @ (^ [A:$o]: (A)) @ (^ [A:$o]: (A))))),inference(pre_uni,[status(thm)],[43333:[bind(A, $thf(^ [B:$o]: (sk1 @ (~) @ (^ [C:$o]: (C)))))]])).
% 183.65/82.28 thf(11,plain,(! [C:(($o > $o) > $o),B:($o > $o),A:($o > $o)] : ((~ (C @ (A))) | (C @ (B)) | (~ (sk1 @ (B) @ (A))))),inference(simp,[status(thm)],[6])).
% 183.65/82.28 thf(105,plain,(! [C:(($o > $o) > $o),B:($o > $o),A:($o > $o)] : ((~ (C @ (A))) | (~ (sk1 @ (B) @ (A))) | ((C @ (B)) != (~ (C @ (A)))) | ~ (($true)))),inference(eqfactor_ordered,[status(thm)],[11])).
% 183.65/82.28 thf(137,plain,(! [B:(($o > $o) > $o),A:($o > $o)] : ((~ (A @ (~ (B @ (A))))) | (~ (sk1 @ (^ [C:$o]: (C)) @ (A))) | ((B @ (^ [C:$o]: (C))) != (A @ (~ (B @ (A))))))),inference(pre_uni,[status(thm)],[105:[bind(A, $thf(A)),bind(B, $thf(^ [D:$o]: (D))),bind(C, $thf(^ [E:($o > $o)]: (E @ (~ (L @ E)))))]])).
% 183.65/82.28 thf(141,plain,(! [B:(($o > $o) > $o),A:($o > $o)] : ((~ (sk1 @ (^ [C:$o]: (C)) @ (A))) | (~ (A @ (~ (B @ (A))))) | ((B @ (^ [C:$o]: (C))) != (A @ (~ (B @ (A))))))),inference(pre_uni,[status(thm)],[137:[]])).
% 183.65/82.28 thf(197,plain,(! [B:(($o > $o) > $o),A:($o > $o)] : ((~ (sk1 @ (^ [C:$o]: (C)) @ (A))) | (~ (A @ (~ (B @ (A))))) | ((B @ (^ [C:$o]: (C))) != (A @ (~ (B @ (A))))))),inference(simp,[status(thm)],[141])).
% 183.65/82.28 thf(275,plain,(! [B:(($o > $o) > $o),A:($o > $o)] : ((~ (sk1 @ (^ [C:$o]: (C)) @ (A))) | (~ (A @ (~ (B @ (A))))) | ((B @ (^ [C:$o]: (C))) != (A @ (~ (B @ (A))))) | (~ (A @ (~ (B @ (A))))))),inference(eqfactor_ordered,[status(thm)],[197])).
% 183.65/82.28 thf(331,plain,((~ (sk1 @ (^ [A:$o]: (A)) @ (^ [A:$o]: (($true))))) | ~ (($true))),inference(pre_uni,[status(thm)],[275:[bind(A, $thf(^ [C:$o]: (($true)))),bind(B, $thf(^ [C:($o > $o)]: (($true))))]])).
% 183.65/82.28 thf(388,plain,((~ (sk1 @ (^ [A:$o]: (A)) @ (^ [A:$o]: (($true)))))),inference(simp,[status(thm)],[331])).
% 183.65/82.28 thf(5,plain,(! [G:(($o > $o) > $o),F:(($o > $o) > $o),E:(($o > $o) > $o),D:($o > $o),C:($o > $o),B:($o > $o),A:($o > $o)] : ((~ (E @ (A))) | (E @ (B)) | (E @ (C)) | (E @ (D)) | (F @ (A)) | (~ (F @ (B))) | (F @ (C)) | (F @ (D)) | (G @ (A)) | (G @ (B)) | (~ (G @ (C))) | (G @ (D)) | (sk1 @ (B) @ (A)) | (sk1 @ (C) @ (A)) | (sk1 @ (C) @ (B)) | (sk1 @ (D) @ (A)) | (sk1 @ (D) @ (B)) | (sk1 @ (D) @ (C)))),inference(cnf,[status(esa)],[4])).
% 183.65/82.28 thf(8,plain,(! [D:($o > $o),C:($o > $o),B:($o > $o),A:($o > $o)] : ((~ ((A) = (A))) | ((A) = (B)) | ((A) = (C)) | ((A) = (D)) | ((B) = (A)) | (~ ((B) = (B))) | ((B) = (C)) | ((B) = (D)) | ((C) = (A)) | ((C) = (B)) | (~ ((C) = (C))) | ((C) = (D)) | (sk1 @ (B) @ (A)) | (sk1 @ (C) @ (A)) | (sk1 @ (C) @ (B)) | (sk1 @ (D) @ (A)) | (sk1 @ (D) @ (B)) | (sk1 @ (D) @ (C)))),inference(replace_leibeq,[status(thm)],[5:[bind(A, $thf(A)),bind(B, $thf(B)),bind(C, $thf(C)),bind(D, $thf(D)),bind(E, $thf((=) @ ($o > $o) @ A)),bind(F, $thf((=) @ ($o > $o) @ B)),bind(G, $thf((=) @ ($o > $o) @ C))]])).
% 183.65/82.28 thf(14,plain,(! [D:($o > $o),C:($o > $o),B:($o > $o),A:($o > $o)] : (((A) != (A)) | ((A) = (B)) | ((A) = (C)) | ((A) = (D)) | ((B) = (A)) | ((B) != (B)) | ((B) = (C)) | ((B) = (D)) | ((C) = (A)) | ((C) = (B)) | ((C) != (C)) | ((C) = (D)) | (sk1 @ (B) @ (A)) | (sk1 @ (C) @ (A)) | (sk1 @ (C) @ (B)) | (sk1 @ (D) @ (A)) | (sk1 @ (D) @ (B)) | (sk1 @ (D) @ (C)))),inference(lifteq,[status(thm)],[8])).
% 183.65/82.28 thf(15,plain,(! [D:($o > $o),C:($o > $o),B:($o > $o),A:($o > $o)] : (((A) = (B)) | ((A) = (C)) | ((A) = (D)) | ((B) = (C)) | ((B) = (D)) | ((C) = (D)) | (sk1 @ (B) @ (A)) | (sk1 @ (C) @ (A)) | (sk1 @ (C) @ (B)) | (sk1 @ (D) @ (A)) | (sk1 @ (D) @ (B)) | (sk1 @ (D) @ (C)))),inference(simp,[status(thm)],[14])).
% 183.65/82.28 thf(1055,plain,(! [D:($o > $o),C:($o > $o),B:($o > $o),A:($o > $o)] : (((A) = (B)) | ((A) = (C)) | ((A) = (D)) | ((B) = (C)) | ((B) = (D)) | ((C) = (D)) | (sk1 @ (B) @ (A)) | (sk1 @ (C) @ (A)) | (sk1 @ (C) @ (B)) | (sk1 @ (D) @ (A)) | (sk1 @ (D) @ (B)) | ((sk1 @ (D) @ (C)) != (sk1 @ (^ [E:$o]: (E)) @ (^ [E:$o]: (($true))))))),inference(paramod_ordered,[status(thm)],[15,388])).
% 183.65/82.28 thf(1056,plain,(! [B:($o > $o),A:($o > $o)] : (((A) = (B)) | ((A) = (^ [C:$o]: (($true)))) | ((A) = (^ [C:$o]: (C))) | ((B) = (^ [C:$o]: (($true)))) | ((B) = (^ [C:$o]: (C))) | ((^ [C:$o]: (($true))) = (^ [C:$o]: (C))) | (sk1 @ (B) @ (A)) | (sk1 @ (^ [C:$o]: (($true))) @ (A)) | (sk1 @ (^ [C:$o]: (($true))) @ (B)) | (sk1 @ (^ [C:$o]: (C)) @ (A)) | (sk1 @ (^ [C:$o]: (C)) @ (B)))),inference(pattern_uni,[status(thm)],[1055:[bind(A, $thf(A)),bind(B, $thf(B)),bind(C, $thf(^ [E:$o]: (($true)))),bind(D, $thf(^ [E:$o]: (E)))]])).
% 183.65/82.28 thf(7209,plain,(! [E:(($o > $o) > $o),D:($o > $o),C:($o > $o),B:($o > $o),A:($o > $o)] : (((A) = (B)) | ((A) = (^ [F:$o]: (($true)))) | ((A) = (^ [F:$o]: (F))) | ((B) = (^ [F:$o]: (($true)))) | ((B) = (^ [F:$o]: (F))) | ((^ [F:$o]: (($true))) = (^ [F:$o]: (F))) | (sk1 @ (^ [F:$o]: (($true))) @ (A)) | (sk1 @ (^ [F:$o]: (($true))) @ (B)) | (sk1 @ (^ [F:$o]: (F)) @ (A)) | (sk1 @ (^ [F:$o]: (F)) @ (B)) | (~ (E @ (C))) | (E @ (D)) | ((sk1 @ (B) @ (A)) != (sk1 @ (D) @ (C))))),inference(paramod_ordered,[status(thm)],[1056,11])).
% 183.65/82.28 thf(7210,plain,(! [C:(($o > $o) > $o),B:($o > $o),A:($o > $o)] : (((A) = (B)) | ((A) = (^ [D:$o]: (($true)))) | ((A) = (^ [D:$o]: (D))) | ((B) = (^ [D:$o]: (($true)))) | ((B) = (^ [D:$o]: (D))) | ((^ [D:$o]: (($true))) = (^ [D:$o]: (D))) | (sk1 @ (^ [D:$o]: (($true))) @ (A)) | (sk1 @ (^ [D:$o]: (($true))) @ (B)) | (sk1 @ (^ [D:$o]: (D)) @ (A)) | (sk1 @ (^ [D:$o]: (D)) @ (B)) | (~ (C @ (A))) | (C @ (B)))),inference(pattern_uni,[status(thm)],[7209:[bind(A, $thf(A)),bind(B, $thf(B)),bind(C, $thf(A)),bind(D, $thf(B))]])).
% 183.65/82.28 thf(7717,plain,(! [B:($o > $o),A:($o > $o)] : (((A) = (B)) | ((A) = (^ [C:$o]: (($true)))) | ((A) = (^ [C:$o]: (C))) | ((B) = (^ [C:$o]: (($true)))) | ((B) = (^ [C:$o]: (C))) | ((^ [C:$o]: (($true))) = (^ [C:$o]: (C))) | (sk1 @ (^ [C:$o]: (($true))) @ (A)) | (sk1 @ (^ [C:$o]: (($true))) @ (B)) | (sk1 @ (^ [C:$o]: (C)) @ (A)) | (sk1 @ (^ [C:$o]: (C)) @ (B)) | (~ ((A) = (A))) | ((A) = (B)))),inference(replace_leibeq,[status(thm)],[7210:[bind(A, $thf(?)),bind(B, $thf(@)),bind(C, $thf((=) @ ($o > $o) @ ?))]])).
% 183.65/82.28 thf(7749,plain,(! [B:($o > $o),A:($o > $o)] : (((A) != (A)) | ((A) = (B)) | ((A) = (B)) | ((A) = (^ [C:$o]: (($true)))) | ((A) = (^ [C:$o]: (C))) | ((B) = (^ [C:$o]: (($true)))) | ((B) = (^ [C:$o]: (C))) | ((^ [C:$o]: (($true))) = (^ [C:$o]: (C))) | (sk1 @ (^ [C:$o]: (($true))) @ (A)) | (sk1 @ (^ [C:$o]: (($true))) @ (B)) | (sk1 @ (^ [C:$o]: (C)) @ (A)) | (sk1 @ (^ [C:$o]: (C)) @ (B)))),inference(lifteq,[status(thm)],[7717])).
% 183.65/82.28 thf(7992,plain,(! [B:($o > $o),A:($o > $o)] : ((sk1 @ (^ [C:$o]: (C)) @ (B)) | (sk1 @ (^ [C:$o]: (C)) @ (A)) | (sk1 @ (^ [C:$o]: (($true))) @ (B)) | (sk1 @ (^ [C:$o]: (($true))) @ (A)) | ((^ [C:$o]: (($true))) = (^ [C:$o]: (C))) | ((B) = (^ [C:$o]: (C))) | ((B) = (^ [C:$o]: (($true)))) | ((A) = (^ [C:$o]: (C))) | ((A) = (^ [C:$o]: (($true)))) | ((A) = (B)) | ((A) = (B)))),inference(pattern_uni,[status(thm)],[7749:[]])).
% 183.65/82.28 thf(8756,plain,(! [B:($o > $o),A:($o > $o)] : ((sk1 @ (^ [C:$o]: (C)) @ (B)) | (sk1 @ (^ [C:$o]: (C)) @ (A)) | (sk1 @ (^ [C:$o]: (($true))) @ (B)) | (sk1 @ (^ [C:$o]: (($true))) @ (A)) | ((^ [C:$o]: (($true))) = (^ [C:$o]: (C))) | ((B) = (^ [C:$o]: (C))) | ((B) = (^ [C:$o]: (($true)))) | ((A) = (^ [C:$o]: (C))) | ((A) = (^ [C:$o]: (($true)))) | ((A) = (B)))),inference(simp,[status(thm)],[7992])).
% 183.65/82.28 thf(19,plain,(! [D:($o > $o),C:($o > $o),B:($o > $o),A:($o > $o)] : ((~ (sk1 @ (A) @ (B))) | ((C) = (D)) | ((sk1 @ (B) @ (A)) != (sk1 @ (D) @ (C))))),inference(paramod_ordered,[status(thm)],[7,13])).
% 183.65/82.28 thf(20,plain,(! [B:($o > $o),A:($o > $o)] : ((~ (sk1 @ (A) @ (B))) | ((A) = (B)))),inference(pattern_uni,[status(thm)],[19:[bind(A, $thf(A)),bind(B, $thf(B)),bind(C, $thf(A)),bind(D, $thf(B))]])).
% 183.65/82.28 thf(21,plain,(! [C:$o,B:($o > $o),A:($o > $o)] : (((A @ C) = (B @ C)) | (~ (sk1 @ (A) @ (B))))),inference(func_ext,[status(esa)],[20])).
% 183.65/82.28 thf(10976,plain,(! [C:$o,B:($o > $o),A:($o > $o)] : ((A @ C) | (~ (sk1 @ (A) @ (B))) | ((@+ [D:$o]: (D)) != (B @ C)))),inference(paramod_ordered,[status(thm)],[10767,21])).
% 183.65/82.28 thf(11049,plain,(! [A:($o > $o)] : ((A @ (@+ [B:$o]: (B))) | (~ (sk1 @ (A) @ (^ [B:$o]: (B)))))),inference(pre_uni,[status(thm)],[10976:[bind(A, $thf(A)),bind(B, $thf(^ [D:$o]: (D))),bind(C, $thf(@+ [D:$o]: (D)))]])).
% 183.65/82.28 thf(17085,plain,(! [A:($o > $o)] : ((A @ ($true)) | (~ (sk1 @ (A) @ (^ [B:$o]: (B)))))),inference(rewrite,[status(thm)],[11049,10767])).
% 183.65/82.28 thf(17253,plain,(($false) | (~ (sk1 @ (^ [A:$o]: (($false))) @ (^ [A:$o]: (A))))),inference(prim_subst,[status(thm)],[17085:[bind(A, $thf(^ [B:$o]: (($false))))]])).
% 183.65/82.28 thf(17618,plain,((~ (sk1 @ (^ [A:$o]: (($false))) @ (^ [A:$o]: (A))))),inference(simp,[status(thm)],[17253])).
% 183.65/82.28 thf(18606,plain,(! [B:($o > $o),A:($o > $o)] : ((~ (sk1 @ (A) @ (B))) | ((sk1 @ (B) @ (A)) != (sk1 @ (^ [C:$o]: (($false))) @ (^ [C:$o]: (C)))))),inference(paramod_ordered,[status(thm)],[7,17618])).
% 183.65/82.28 thf(18607,plain,((~ (sk1 @ (^ [A:$o]: (A)) @ (^ [A:$o]: (($false)))))),inference(pattern_uni,[status(thm)],[18606:[bind(A, $thf(^ [C:$o]: (C))),bind(B, $thf(^ [C:$o]: (($false))))]])).
% 183.65/82.28 thf(19833,plain,(! [B:($o > $o),A:($o > $o)] : ((sk1 @ (^ [C:$o]: (C)) @ (A)) | (sk1 @ (^ [C:$o]: (($true))) @ (B)) | (sk1 @ (^ [C:$o]: (($true))) @ (A)) | ((^ [C:$o]: (($true))) = (^ [C:$o]: (C))) | ((B) = (^ [C:$o]: (C))) | ((B) = (^ [C:$o]: (($true)))) | ((A) = (^ [C:$o]: (C))) | ((A) = (^ [C:$o]: (($true)))) | ((A) = (B)) | ((sk1 @ (^ [C:$o]: (C)) @ (B)) != (sk1 @ (^ [C:$o]: (C)) @ (^ [C:$o]: (($false))))))),inference(paramod_ordered,[status(thm)],[8756,18607])).
% 183.65/82.28 thf(19834,plain,(! [A:($o > $o)] : ((sk1 @ (^ [B:$o]: (B)) @ (A)) | (sk1 @ (^ [B:$o]: (($true))) @ (^ [B:$o]: (($false)))) | (sk1 @ (^ [B:$o]: (($true))) @ (A)) | ((^ [B:$o]: (($true))) = (^ [B:$o]: (B))) | ((^ [B:$o]: (($false))) = (^ [B:$o]: (B))) | ((^ [B:$o]: (($false))) = (^ [B:$o]: (($true)))) | ((A) = (^ [B:$o]: (B))) | ((A) = (^ [B:$o]: (($true)))) | ((A) = (^ [B:$o]: (($false)))))),inference(pattern_uni,[status(thm)],[19833:[bind(A, $thf(A)),bind(B, $thf(^ [C:$o]: (($false))))]])).
% 183.65/82.28 thf(20248,plain,(! [A:($o > $o)] : ((sk1 @ (^ [B:$o]: (B)) @ (A)) | (sk1 @ (^ [B:$o]: (($true))) @ (^ [B:$o]: (($false)))) | (sk1 @ (^ [B:$o]: (($true))) @ (A)) | ((^ [B:$o]: (($true))) = (^ [B:$o]: (B))) | ((^ [B:$o]: (($false))) = (^ [B:$o]: (B))) | ((A) = (^ [B:$o]: (B))) | ((A) = (^ [B:$o]: (($true)))) | ((A) = (^ [B:$o]: (($false)))))),inference(simp,[status(thm)],[19834])).
% 183.65/82.28 thf(46,plain,(! [D:($o > ($o > $o)),C:($o > ($o > $o)),B:$o,A:($o > $o)] : ((~ (sk1 @ (D @ B) @ (C @ B))) | (A @ B) | (~ (sk1 @ (^ [E:$o]: (sk1 @ (C @ E) @ (D @ E))) @ (A))))),inference(pre_uni,[status(thm)],[35:[bind(A, $thf(G @ E)),bind(B, $thf(F @ E)),bind(C, $thf(C)),bind(D, $thf(^ [H:$o]: (sk1 @ (F @ H) @ (G @ H))))]])).
% 183.65/82.28 thf(71,plain,(! [D:($o > ($o > $o)),C:($o > ($o > $o)),B:$o,A:($o > $o)] : ((~ (sk1 @ (D @ B) @ (C @ B))) | (A @ B) | (~ (sk1 @ (^ [E:$o]: (sk1 @ (C @ E) @ (D @ E))) @ (A))))),inference(simp,[status(thm)],[46])).
% 183.65/82.28 thf(29,plain,(! [E:($o > $o),D:($o > $o),C:$o,B:($o > $o),A:($o > $o)] : ((~ (sk1 @ (B) @ (A))) | (~ (A @ C)) | ((D) = (E)) | ((B @ C) != (sk1 @ (D) @ (E))))),inference(paramod_ordered,[status(thm)],[16,20])).
% 183.65/82.28 thf(41,plain,(! [C:($o > $o),B:($o > $o),A:($o > $o)] : ((~ (sk1 @ (^ [D:$o]: (D)) @ (A))) | (~ (A @ (sk1 @ (B) @ (C)))) | ((B) = (C)))),inference(pre_uni,[status(thm)],[29:[bind(A, $thf(A)),bind(B, $thf(^ [F:$o]: (F))),bind(C, $thf(sk1 @ (D) @ (E)))]])).
% 183.65/82.28 thf(66,plain,(! [C:($o > $o),B:($o > $o),A:($o > $o)] : ((~ (sk1 @ (^ [D:$o]: (D)) @ (A))) | (~ (A @ (sk1 @ (B) @ (C)))) | ((B) = (C)))),inference(simp,[status(thm)],[41])).
% 183.65/82.28 thf(10,plain,(! [G:(($o > $o) > $o),F:(($o > $o) > $o),E:(($o > $o) > $o),D:($o > $o),C:($o > $o),B:($o > $o),A:($o > $o)] : ((~ (E @ (A))) | (E @ (B)) | (E @ (C)) | (E @ (D)) | (F @ (A)) | (~ (F @ (B))) | (F @ (C)) | (F @ (D)) | (G @ (A)) | (G @ (B)) | (~ (G @ (C))) | (G @ (D)) | (sk1 @ (B) @ (A)) | (sk1 @ (C) @ (A)) | (sk1 @ (C) @ (B)) | (sk1 @ (D) @ (A)) | (sk1 @ (D) @ (B)) | (sk1 @ (D) @ (C)))),inference(simp,[status(thm)],[5])).
% 183.65/82.28 thf(276,plain,(! [B:(($o > $o) > $o),A:($o > $o)] : ((~ (sk1 @ (^ [C:$o]: (C)) @ (A))) | (~ (A @ (~ (B @ (A))))) | (~ (B @ (^ [C:$o]: (C)))) | ((A @ (~ (B @ (A)))) != (A @ (~ (B @ (A))))))),inference(eqfactor_ordered,[status(thm)],[197])).
% 183.65/82.28 thf(319,plain,(! [A:($o > $o)] : ((~ (sk1 @ (^ [B:$o]: (B)) @ (A))) | (~ (A @ (~ (($true))))))),inference(pre_uni,[status(thm)],[276:[bind(A, $thf(A)),bind(B, $thf(^ [C:($o > $o)]: (($true))))]])).
% 183.65/82.28 thf(385,plain,(! [A:($o > $o)] : ((~ (sk1 @ (^ [B:$o]: (B)) @ (A))) | (~ (A @ ($false))))),inference(simp,[status(thm)],[319])).
% 183.65/82.28 thf(17090,plain,(! [A:($o > $o)] : ((~ (sk1 @ (A) @ (^ [B:$o]: (B)))) | ((A @ ($true)) != (sk1 @ (^ [B:$o]: (B)) @ (^ [B:$o]: (($true))))))),inference(paramod_ordered,[status(thm)],[17085,388])).
% 183.65/82.28 thf(17362,plain,((~ (sk1 @ (^ [A:$o]: (sk1 @ (^ [B:$o]: (B)) @ (^ [B:$o]: (A)))) @ (^ [A:$o]: (A))))),inference(pre_uni,[status(thm)],[17090:[bind(A, $thf(^ [B:$o]: (sk1 @ (^ [C:$o]: (C)) @ (^ [C:$o]: (B)))))]])).
% 183.65/82.28 thf(24,plain,(! [C:$o,B:($o > $o),A:($o > $o)] : ((~ (sk1 @ (B) @ (A))) | (~ (A @ C)) | (B @ C))),inference(bool_ext,[status(thm)],[16])).
% 183.65/82.28 thf(25,plain,(! [C:$o,B:($o > $o),A:($o > $o)] : ((~ (sk1 @ (B) @ (A))) | (A @ C) | (~ (B @ C)))),inference(bool_ext,[status(thm)],[16])).
% 183.65/82.28 thf(17809,plain,(! [B:($o > $o),A:($o > $o)] : ((~ (sk1 @ (A) @ (B))) | ((sk1 @ (B) @ (A)) != (sk1 @ (^ [C:$o]: (sk1 @ (^ [D:$o]: (D)) @ (^ [D:$o]: (C)))) @ (^ [C:$o]: (C)))))),inference(paramod_ordered,[status(thm)],[7,17362])).
% 183.65/82.28 thf(17810,plain,((~ (sk1 @ (^ [A:$o]: (A)) @ (^ [A:$o]: (sk1 @ (^ [B:$o]: (B)) @ (^ [B:$o]: (A))))))),inference(pattern_uni,[status(thm)],[17809:[bind(A, $thf(^ [C:$o]: (C))),bind(B, $thf(^ [C:$o]: (sk1 @ (^ [D:$o]: (D)) @ (^ [D:$o]: (C)))))]])).
% 183.65/82.28 thf(22477,plain,(! [A:($o > $o)] : ((sk1 @ (^ [B:$o]: (($true))) @ (^ [B:$o]: (($false)))) | (sk1 @ (^ [B:$o]: (($true))) @ (A)) | ((^ [B:$o]: (($true))) = (^ [B:$o]: (B))) | ((^ [B:$o]: (($false))) = (^ [B:$o]: (B))) | ((A) = (^ [B:$o]: (B))) | ((A) = (^ [B:$o]: (($true)))) | ((A) = (^ [B:$o]: (($false)))) | ((sk1 @ (^ [B:$o]: (B)) @ (A)) != (sk1 @ (^ [B:$o]: (B)) @ (^ [B:$o]: (sk1 @ (^ [C:$o]: (C)) @ (^ [C:$o]: (B)))))))),inference(paramod_ordered,[status(thm)],[20248,17810])).
% 183.65/82.28 thf(22478,plain,((sk1 @ (^ [A:$o]: (($true))) @ (^ [A:$o]: (($false)))) | (sk1 @ (^ [A:$o]: (($true))) @ (^ [A:$o]: (sk1 @ (^ [B:$o]: (B)) @ (^ [B:$o]: (A))))) | ((^ [A:$o]: (($true))) = (^ [A:$o]: (A))) | ((^ [A:$o]: (($false))) = (^ [A:$o]: (A))) | ((^ [A:$o]: (sk1 @ (^ [B:$o]: (B)) @ (^ [B:$o]: (A)))) = (^ [A:$o]: (A))) | ((^ [A:$o]: (sk1 @ (^ [B:$o]: (B)) @ (^ [B:$o]: (A)))) = (^ [A:$o]: (($true)))) | ((^ [A:$o]: (sk1 @ (^ [B:$o]: (B)) @ (^ [B:$o]: (A)))) = (^ [A:$o]: (($false))))),inference(pattern_uni,[status(thm)],[22477:[bind(A, $thf(^ [B:$o]: (sk1 @ (^ [C:$o]: (C)) @ (^ [C:$o]: (B)))))]])).
% 183.65/82.28 thf(30892,plain,(! [B:($o > $o),A:($o > $o)] : ((sk1 @ (^ [C:$o]: (($true))) @ (^ [C:$o]: (($false)))) | ((^ [C:$o]: (($true))) = (^ [C:$o]: (C))) | ((^ [C:$o]: (($false))) = (^ [C:$o]: (C))) | ((^ [C:$o]: (sk1 @ (^ [D:$o]: (D)) @ (^ [D:$o]: (C)))) = (^ [C:$o]: (C))) | ((^ [C:$o]: (sk1 @ (^ [D:$o]: (D)) @ (^ [D:$o]: (C)))) = (^ [C:$o]: (($true)))) | ((^ [C:$o]: (sk1 @ (^ [D:$o]: (D)) @ (^ [D:$o]: (C)))) = (^ [C:$o]: (($false)))) | ((A) = (B)) | ((sk1 @ (^ [C:$o]: (($true))) @ (^ [C:$o]: (sk1 @ (^ [D:$o]: (D)) @ (^ [D:$o]: (C))))) != (sk1 @ (B) @ (A))))),inference(paramod_ordered,[status(thm)],[22478,13])).
% 183.65/82.28 thf(30893,plain,((sk1 @ (^ [A:$o]: (($true))) @ (^ [A:$o]: (($false)))) | ((^ [A:$o]: (($true))) = (^ [A:$o]: (A))) | ((^ [A:$o]: (($false))) = (^ [A:$o]: (A))) | ((^ [A:$o]: (sk1 @ (^ [B:$o]: (B)) @ (^ [B:$o]: (A)))) = (^ [A:$o]: (A))) | ((^ [A:$o]: (sk1 @ (^ [B:$o]: (B)) @ (^ [B:$o]: (A)))) = (^ [A:$o]: (($true)))) | ((^ [A:$o]: (sk1 @ (^ [B:$o]: (B)) @ (^ [B:$o]: (A)))) = (^ [A:$o]: (($false)))) | ((^ [A:$o]: (sk1 @ (^ [B:$o]: (B)) @ (^ [B:$o]: (A)))) = (^ [A:$o]: (($true))))),inference(pattern_uni,[status(thm)],[30892:[bind(A, $thf(^ [C:$o]: (sk1 @ (^ [D:$o]: (D)) @ (^ [D:$o]: (C))))),bind(B, $thf(^ [C:$o]: (($true))))]])).
% 183.65/82.28 thf(31652,plain,((sk1 @ (^ [A:$o]: (($true))) @ (^ [A:$o]: (($false)))) | ((^ [A:$o]: (($true))) = (^ [A:$o]: (A))) | ((^ [A:$o]: (($false))) = (^ [A:$o]: (A))) | ((^ [A:$o]: (sk1 @ (^ [B:$o]: (B)) @ (^ [B:$o]: (A)))) = (^ [A:$o]: (A))) | ((^ [A:$o]: (sk1 @ (^ [B:$o]: (B)) @ (^ [B:$o]: (A)))) = (^ [A:$o]: (($true)))) | ((^ [A:$o]: (sk1 @ (^ [B:$o]: (B)) @ (^ [B:$o]: (A)))) = (^ [A:$o]: (($false))))),inference(simp,[status(thm)],[30893])).
% 183.65/82.28 thf(31990,plain,(! [B:($o > $o),A:($o > $o)] : (((^ [C:$o]: (($true))) = (^ [C:$o]: (C))) | ((^ [C:$o]: (($false))) = (^ [C:$o]: (C))) | ((^ [C:$o]: (sk1 @ (^ [D:$o]: (D)) @ (^ [D:$o]: (C)))) = (^ [C:$o]: (C))) | ((^ [C:$o]: (sk1 @ (^ [D:$o]: (D)) @ (^ [D:$o]: (C)))) = (^ [C:$o]: (($true)))) | ((^ [C:$o]: (sk1 @ (^ [D:$o]: (D)) @ (^ [D:$o]: (C)))) = (^ [C:$o]: (($false)))) | ((A) = (B)) | ((sk1 @ (^ [C:$o]: (($true))) @ (^ [C:$o]: (($false)))) != (sk1 @ (B) @ (A))))),inference(paramod_ordered,[status(thm)],[31652,13])).
% 183.65/82.28 thf(31991,plain,(((^ [A:$o]: (($true))) = (^ [A:$o]: (A))) | ((^ [A:$o]: (($false))) = (^ [A:$o]: (A))) | ((^ [A:$o]: (sk1 @ (^ [B:$o]: (B)) @ (^ [B:$o]: (A)))) = (^ [A:$o]: (A))) | ((^ [A:$o]: (sk1 @ (^ [B:$o]: (B)) @ (^ [B:$o]: (A)))) = (^ [A:$o]: (($true)))) | ((^ [A:$o]: (sk1 @ (^ [B:$o]: (B)) @ (^ [B:$o]: (A)))) = (^ [A:$o]: (($false)))) | ((^ [A:$o]: (($false))) = (^ [A:$o]: (($true))))),inference(pattern_uni,[status(thm)],[31990:[bind(A, $thf(^ [C:$o]: (($false)))),bind(B, $thf(^ [C:$o]: (($true))))]])).
% 183.65/82.28 thf(32844,plain,(((^ [A:$o]: (($true))) = (^ [A:$o]: (A))) | ((^ [A:$o]: (($false))) = (^ [A:$o]: (A))) | ((^ [A:$o]: (sk1 @ (^ [B:$o]: (B)) @ (^ [B:$o]: (A)))) = (^ [A:$o]: (A))) | ((^ [A:$o]: (sk1 @ (^ [B:$o]: (B)) @ (^ [B:$o]: (A)))) = (^ [A:$o]: (($true)))) | ((^ [A:$o]: (sk1 @ (^ [B:$o]: (B)) @ (^ [B:$o]: (A)))) = (^ [A:$o]: (($false))))),inference(simp,[status(thm)],[31991])).
% 183.65/82.28 thf(26,plain,(! [F:$o,E:($o > $o),D:($o > $o),C:$o,B:($o > $o),A:($o > $o)] : ((~ (sk1 @ (B) @ (A))) | ((D @ F) = (E @ F)) | (~ (B @ C)) | ((A @ C) != (sk1 @ (E) @ (D))))),inference(paramod_ordered,[status(thm)],[16,16])).
% 183.65/82.28 thf(50,plain,(! [E:($o > ($o > $o)),D:($o > ($o > $o)),C:$o,B:$o,A:($o > $o)] : ((~ (sk1 @ (A) @ (^ [F:$o]: (sk1 @ (D @ F) @ (E @ F))))) | ((E @ B @ C) = (D @ B @ C)) | (~ (A @ B)))),inference(pre_uni,[status(thm)],[26:[bind(A, $thf(^ [I:$o]: (sk1 @ (G @ I) @ (H @ I)))),bind(B, $thf(B)),bind(C, $thf(C)),bind(D, $thf(H @ C)),bind(E, $thf(G @ C))]])).
% 183.65/82.28 thf(74,plain,(! [E:($o > ($o > $o)),D:($o > ($o > $o)),C:$o,B:$o,A:($o > $o)] : ((~ (sk1 @ (A) @ (^ [F:$o]: (sk1 @ (D @ F) @ (E @ F))))) | ((E @ B @ C) = (D @ B @ C)) | (~ (A @ B)))),inference(simp,[status(thm)],[50])).
% 183.65/82.28 thf(39,plain,(! [E:($o > $o),D:($o > $o),C:$o,B:($o > $o),A:($o > $o)] : ((~ (sk1 @ (B) @ (A))) | ((D) = (E)) | (~ (A @ C)) | ((B @ C) != (sk1 @ (E) @ (D))))),inference(paramod_ordered,[status(thm)],[16,13])).
% 183.65/82.28 thf(45,plain,(! [C:($o > $o),B:($o > $o),A:($o > $o)] : ((~ (sk1 @ (^ [D:$o]: (D)) @ (A))) | ((B) = (C)) | (~ (A @ (sk1 @ (C) @ (B)))))),inference(pre_uni,[status(thm)],[39:[bind(A, $thf(A)),bind(B, $thf(^ [F:$o]: (F))),bind(C, $thf(sk1 @ (E) @ (D)))]])).
% 183.65/82.28 thf(70,plain,(! [C:($o > $o),B:($o > $o),A:($o > $o)] : ((~ (sk1 @ (^ [D:$o]: (D)) @ (A))) | ((B) = (C)) | (~ (A @ (sk1 @ (C) @ (B)))))),inference(simp,[status(thm)],[45])).
% 183.65/82.28 thf(40,plain,(! [D:($o > ($o > $o)),C:($o > ($o > $o)),B:$o,A:($o > $o)] : ((~ (sk1 @ (^ [E:$o]: (sk1 @ (C @ E) @ (D @ E))) @ (A))) | (~ (A @ B)) | ((C @ B) = (D @ B)))),inference(pre_uni,[status(thm)],[29:[bind(A, $thf(A)),bind(B, $thf(^ [H:$o]: (sk1 @ (F @ H) @ (G @ H)))),bind(C, $thf(C)),bind(D, $thf(F @ C)),bind(E, $thf(G @ C))]])).
% 183.65/82.28 thf(65,plain,(! [D:($o > ($o > $o)),C:($o > ($o > $o)),B:$o,A:($o > $o)] : ((~ (sk1 @ (^ [E:$o]: (sk1 @ (C @ E) @ (D @ E))) @ (A))) | (~ (A @ B)) | ((C @ B) = (D @ B)))),inference(simp,[status(thm)],[40])).
% 183.65/82.28 thf(47619,plain,((~ (sk1 @ (^ [A:$o]: (A)) @ (^ [A:$o]: (A)))) | ((sk1 @ (^ [A:$o]: (A)) @ (^ [A:$o]: (sk1 @ (~) @ (^ [B:$o]: (B))))) != (sk1 @ (^ [A:$o]: (A)) @ (^ [A:$o]: (A)))) | ~ (($true))),inference(eqfactor_ordered,[status(thm)],[43806])).
% 183.65/82.28 thf(47951,plain,((~ (sk1 @ (^ [A:$o]: (A)) @ (^ [A:$o]: (A)))) | ((^ [A:$o]: (A)) != (^ [A:$o]: (A))) | ((^ [A:$o]: (sk1 @ (~) @ (^ [B:$o]: (B)))) != (^ [A:$o]: (A)))),inference(simp,[status(thm)],[47619])).
% 183.65/82.28 thf(48325,plain,((~ (sk1 @ (^ [A:$o]: (A)) @ (^ [A:$o]: (A)))) | ((^ [A:$o]: (sk1 @ (~) @ (^ [B:$o]: (B)))) != (^ [A:$o]: (A)))),inference(simp,[status(thm)],[47951])).
% 183.65/82.28 thf(991,plain,(! [C:$o,B:($o > $o),A:($o > $o)] : ((~ (sk1 @ (B) @ (A))) | (~ (B @ C)) | ((A @ C) != (sk1 @ (^ [D:$o]: (D)) @ (^ [D:$o]: (($true))))))),inference(paramod_ordered,[status(thm)],[16,388])).
% 183.65/82.28 thf(1070,plain,(! [A:($o > $o)] : ((~ (sk1 @ (A) @ (^ [B:$o]: (B)))) | (~ (A @ (sk1 @ (^ [B:$o]: (B)) @ (^ [B:$o]: (($true)))))))),inference(pre_uni,[status(thm)],[991:[bind(A, $thf(^ [D:$o]: (D))),bind(B, $thf(B)),bind(C, $thf(sk1 @ (^ [D:$o]: (D)) @ (^ [D:$o]: (($true)))))]])).
% 183.65/82.28 thf(1093,plain,(! [A:($o > $o)] : ((~ (sk1 @ (A) @ (^ [B:$o]: (B)))) | (~ (A @ (sk1 @ (^ [B:$o]: (B)) @ (^ [B:$o]: (($true)))))))),inference(simp,[status(thm)],[1070])).
% 183.65/82.28 thf(13075,plain,(! [A:($o > $o)] : ((~ (sk1 @ (A) @ (^ [B:$o]: (B)))) | (~ (A @ ($false))))),inference(rewrite,[status(thm)],[1093,388])).
% 183.65/82.28 thf(989,plain,(! [B:($o > $o),A:($o > $o)] : ((~ (sk1 @ (A) @ (B))) | ((sk1 @ (B) @ (A)) != (sk1 @ (^ [C:$o]: (C)) @ (^ [C:$o]: (($true))))))),inference(paramod_ordered,[status(thm)],[7,388])).
% 183.65/82.28 thf(990,plain,((~ (sk1 @ (^ [A:$o]: (($true))) @ (^ [A:$o]: (A))))),inference(pattern_uni,[status(thm)],[989:[bind(A, $thf(^ [C:$o]: (($true)))),bind(B, $thf(^ [C:$o]: (C)))]])).
% 183.65/82.28 thf(17204,plain,(! [A:($o > $o)] : ((~ (sk1 @ (A) @ (^ [B:$o]: (B)))) | ((A @ ($true)) != (sk1 @ (^ [B:$o]: (($true))) @ (^ [B:$o]: (B)))))),inference(paramod_ordered,[status(thm)],[17085,990])).
% 183.65/82.28 thf(17418,plain,((~ (sk1 @ (^ [A:$o]: (sk1 @ (^ [B:$o]: (A)) @ (^ [B:$o]: (B)))) @ (^ [A:$o]: (A))))),inference(pre_uni,[status(thm)],[17204:[bind(A, $thf(^ [B:$o]: (sk1 @ (^ [C:$o]: (B)) @ (^ [C:$o]: (C)))))]])).
% 183.65/82.28 thf(18212,plain,(! [B:($o > $o),A:($o > $o)] : ((~ (sk1 @ (A) @ (B))) | ((sk1 @ (B) @ (A)) != (sk1 @ (^ [C:$o]: (sk1 @ (^ [D:$o]: (C)) @ (^ [D:$o]: (D)))) @ (^ [C:$o]: (C)))))),inference(paramod_ordered,[status(thm)],[7,17418])).
% 183.65/82.28 thf(18213,plain,((~ (sk1 @ (^ [A:$o]: (A)) @ (^ [A:$o]: (sk1 @ (^ [B:$o]: (A)) @ (^ [B:$o]: (B))))))),inference(pattern_uni,[status(thm)],[18212:[bind(A, $thf(^ [C:$o]: (C))),bind(B, $thf(^ [C:$o]: (sk1 @ (^ [D:$o]: (C)) @ (^ [D:$o]: (D)))))]])).
% 183.65/82.28 thf(30,plain,(! [E:($o > $o),D:($o > $o),C:$o,B:($o > $o),A:($o > $o)] : ((~ (sk1 @ (B) @ (A))) | (~ (B @ C)) | (sk1 @ (E) @ (D)) | ((A @ C) != (sk1 @ (D) @ (E))))),inference(paramod_ordered,[status(thm)],[16,7])).
% 183.65/82.28 thf(52,plain,(! [D:($o > ($o > $o)),C:($o > ($o > $o)),B:$o,A:($o > $o)] : ((~ (sk1 @ (A) @ (^ [E:$o]: (sk1 @ (C @ E) @ (D @ E))))) | (~ (A @ B)) | (sk1 @ (D @ B) @ (C @ B)))),inference(pre_uni,[status(thm)],[30:[bind(A, $thf(^ [H:$o]: (sk1 @ (F @ H) @ (G @ H)))),bind(B, $thf(B)),bind(C, $thf(C)),bind(D, $thf(F @ C)),bind(E, $thf(G @ C))]])).
% 183.65/82.28 thf(76,plain,(! [D:($o > ($o > $o)),C:($o > ($o > $o)),B:$o,A:($o > $o)] : ((~ (sk1 @ (A) @ (^ [E:$o]: (sk1 @ (C @ E) @ (D @ E))))) | (~ (A @ B)) | (sk1 @ (D @ B) @ (C @ B)))),inference(simp,[status(thm)],[52])).
% 183.65/82.28 thf(27,plain,(! [F:$o,E:($o > $o),D:($o > $o),C:$o,B:($o > $o),A:($o > $o)] : ((~ (sk1 @ (B) @ (A))) | ((D @ F) = (E @ F)) | (~ (A @ C)) | ((B @ C) != (sk1 @ (E) @ (D))))),inference(paramod_ordered,[status(thm)],[16,16])).
% 183.65/82.28 thf(42,plain,(! [E:($o > ($o > $o)),D:($o > ($o > $o)),C:$o,B:$o,A:($o > $o)] : ((~ (sk1 @ (^ [F:$o]: (sk1 @ (D @ F) @ (E @ F))) @ (A))) | ((E @ B @ C) = (D @ B @ C)) | (~ (A @ B)))),inference(pre_uni,[status(thm)],[27:[bind(A, $thf(A)),bind(B, $thf(^ [I:$o]: (sk1 @ (G @ I) @ (H @ I)))),bind(C, $thf(C)),bind(D, $thf(H @ C)),bind(E, $thf(G @ C))]])).
% 183.65/82.28 thf(67,plain,(! [E:($o > ($o > $o)),D:($o > ($o > $o)),C:$o,B:$o,A:($o > $o)] : ((~ (sk1 @ (^ [F:$o]: (sk1 @ (D @ F) @ (E @ F))) @ (A))) | ((E @ B @ C) = (D @ B @ C)) | (~ (A @ B)))),inference(simp,[status(thm)],[42])).
% 183.65/82.28 thf(48,plain,(! [D:($o > ($o > $o)),C:($o > ($o > $o)),B:$o,A:($o > $o)] : ((~ (sk1 @ (A) @ (^ [E:$o]: (sk1 @ (C @ E) @ (D @ E))))) | (~ (sk1 @ (D @ B) @ (C @ B))) | (A @ B))),inference(pre_uni,[status(thm)],[31:[bind(A, $thf(^ [H:$o]: (sk1 @ (F @ H) @ (G @ H)))),bind(B, $thf(B)),bind(C, $thf(C)),bind(D, $thf(G @ C)),bind(E, $thf(F @ C))]])).
% 183.65/82.28 thf(72,plain,(! [D:($o > ($o > $o)),C:($o > ($o > $o)),B:$o,A:($o > $o)] : ((~ (sk1 @ (A) @ (^ [E:$o]: (sk1 @ (C @ E) @ (D @ E))))) | (~ (sk1 @ (D @ B) @ (C @ B))) | (A @ B))),inference(simp,[status(thm)],[48])).
% 183.65/82.28 thf(42221,plain,(! [B:($o > $o),A:($o > $o)] : ((~ (sk1 @ (A) @ (B))) | (~ (sk1 @ (^ [C:$o]: (C)) @ ((~)))) | ((sk1 @ (B) @ (A)) != (sk1 @ ((~)) @ (^ [C:$o]: (C)))))),inference(paramod_ordered,[status(thm)],[7,38251])).
% 183.65/82.28 thf(42222,plain,((~ (sk1 @ (^ [A:$o]: (A)) @ ((~)))) | (~ (sk1 @ (^ [A:$o]: (A)) @ ((~))))),inference(pattern_uni,[status(thm)],[42221:[bind(A, $thf(^ [C:$o]: (C))),bind(B, $thf((~)))]])).
% 183.65/82.28 thf(42721,plain,((~ (sk1 @ (^ [A:$o]: (A)) @ ((~))))),inference(simp,[status(thm)],[42222])).
% 183.65/82.28 thf(51,plain,(! [D:$o,C:($o > $o),B:($o > $o),A:($o > $o)] : ((~ (sk1 @ (A) @ (^ [E:$o]: (E)))) | ((B @ D) = (C @ D)) | (~ (A @ (sk1 @ (C) @ (B)))))),inference(pre_uni,[status(thm)],[26:[bind(A, $thf(^ [G:$o]: (G))),bind(B, $thf(B)),bind(C, $thf(sk1 @ (E) @ (D)))]])).
% 183.65/82.28 thf(75,plain,(! [D:$o,C:($o > $o),B:($o > $o),A:($o > $o)] : ((~ (sk1 @ (A) @ (^ [E:$o]: (E)))) | ((B @ D) = (C @ D)) | (~ (A @ (sk1 @ (C) @ (B)))))),inference(simp,[status(thm)],[51])).
% 183.65/82.28 thf(43,plain,(! [D:$o,C:($o > $o),B:($o > $o),A:($o > $o)] : ((~ (sk1 @ (^ [E:$o]: (E)) @ (A))) | ((B @ D) = (C @ D)) | (~ (A @ (sk1 @ (C) @ (B)))))),inference(pre_uni,[status(thm)],[27:[bind(A, $thf(A)),bind(B, $thf(^ [G:$o]: (G))),bind(C, $thf(sk1 @ (E) @ (D)))]])).
% 183.65/82.28 thf(68,plain,(! [D:$o,C:($o > $o),B:($o > $o),A:($o > $o)] : ((~ (sk1 @ (^ [E:$o]: (E)) @ (A))) | ((B @ D) = (C @ D)) | (~ (A @ (sk1 @ (C) @ (B)))))),inference(simp,[status(thm)],[43])).
% 183.65/82.28 thf(53986,plain,(($false)),inference(e,[status(thm)],[49806,43806,388,20248,73,71,66,3,10767,27548,10,385,17362,24,25,20,17085,32844,74,18607,8756,70,21,197,65,42620,48325,13,13075,17618,18213,990,17418,76,7,67,16,11,72,42721,75,43811,17810,47,15,68])).
% 183.65/82.28 % SZS output end Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% 183.65/82.28 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------