TSTP Solution File: SEU938^5 by Leo-III---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : SEU938^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n005.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 : Tue May 21 03:40:30 EDT 2024

% Result   : Theorem 34.94s 7.84s
% Output   : Refutation 34.94s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.13  % Problem  : SEU938^5 : TPTP v8.2.0. Released v4.0.0.
% 0.06/0.16  % Command  : run_Leo-III %s %d
% 0.13/0.36  % Computer : n005.cluster.edu
% 0.13/0.36  % Model    : x86_64 x86_64
% 0.13/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.36  % Memory   : 8042.1875MB
% 0.13/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.36  % CPULimit : 300
% 0.13/0.36  % WCLimit  : 300
% 0.13/0.36  % DateTime : Sun May 19 15:35:24 EDT 2024
% 0.13/0.37  % CPUTime  : 
% 0.81/0.86  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 0.95/0.97  % [INFO] 	 Parsing done (106ms). 
% 1.23/0.98  % [INFO] 	 Running in sequential loop mode. 
% 1.58/1.20  % [INFO] 	 eprover registered as external prover. 
% 1.58/1.20  % [INFO] 	 cvc4 registered as external prover. 
% 1.58/1.20  % [INFO] 	 Scanning for conjecture ... 
% 1.58/1.26  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 1.58/1.28  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 1.58/1.29  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 1.58/1.29  % [INFO] 	 Type checking passed. 
% 1.58/1.29  % [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 ... 
% 34.94/7.83  % External prover 'e' found a proof!
% 34.94/7.83  % [INFO] 	 Killing All external provers ... 
% 34.94/7.84  % Time passed: 7316ms (effective reasoning time: 6853ms)
% 34.94/7.84  % 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)>
% 34.94/7.84  % Axioms used in derivation (0): 
% 34.94/7.84  % No. of inferences in proof: 95
% 34.94/7.84  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 7316 ms resp. 6853 ms w/o parsing
% 34.94/7.92  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 34.94/7.92  thf(a_type, type, a: $i).
% 34.94/7.92  thf(b_type, type, b: $i).
% 34.94/7.92  thf(h_type, type, h: ($i > $i)).
% 34.94/7.92  thf(sk1_type, type, sk1: (($i > $i) > (($i > $i) > $i))).
% 34.94/7.92  thf(sk2_type, type, sk2: (($i > $i) > (($i > $i) > $o))).
% 34.94/7.92  thf(sk3_type, type, sk3: (($i > $i) > (($i > $i) > (($i > $i) > $o)))).
% 34.94/7.92  thf(sk4_type, type, sk4: ((($i > $i) > $o) > (($i > $i) > (($i > $i) > ($i > $i))))).
% 34.94/7.92  thf(sk8_type, type, sk8: $i).
% 34.94/7.92  thf(1,conjecture,(((((h @ a) = a) & ((h @ b) != a) & ! [A:($i > $i),B:($i > $i)]: ((! [C:$i]: ((A @ C) = (B @ C))) => (A = B))) => (~ (! [A:($i > $i),B:($i > $i)]: ((! [C:(($i > $i) > $o)]: (((C @ A) & ! [D:($i > $i)]: ((C @ D) => (C @ (^ [E:$i]: (A @ (D @ E)))))) => (C @ (^ [D:$i]: (B @ (A @ D)))))) => (! [C:(($i > $i) > $o)]: (((C @ A) & ! [D:($i > $i)]: ((C @ D) => (C @ (^ [E:$i]: (A @ (D @ E)))))) => (C @ B)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM196_pme)).
% 34.94/7.92  thf(2,negated_conjecture,((~ ((((h @ a) = a) & ((h @ b) != a) & ! [A:($i > $i),B:($i > $i)]: ((! [C:$i]: ((A @ C) = (B @ C))) => (A = B))) => (~ (! [A:($i > $i),B:($i > $i)]: ((! [C:(($i > $i) > $o)]: (((C @ A) & ! [D:($i > $i)]: ((C @ D) => (C @ (^ [E:$i]: (A @ (D @ E)))))) => (C @ (^ [D:$i]: (B @ (A @ D)))))) => (! [C:(($i > $i) > $o)]: (((C @ A) & ! [D:($i > $i)]: ((C @ D) => (C @ (^ [E:$i]: (A @ (D @ E)))))) => (C @ B))))))))),inference(neg_conjecture,[status(cth)],[1])).
% 34.94/7.92  thf(3,plain,((~ ((((h @ a) = a) & ~ ((h @ b) = a) & ! [A:($i > $i),B:($i > $i)]: ((! [C:$i]: ((A @ C) = (B @ C))) => ((A) = (B)))) => (~ (! [A:($i > $i),B:($i > $i)]: ((! [C:(($i > $i) > $o)]: (((C @ (A)) & ! [D:($i > $i)]: ((C @ (D)) => (C @ (^ [E:$i]: (A @ (D @ E)))))) => (C @ (^ [D:$i]: (B @ (A @ D)))))) => (! [C:(($i > $i) > $o)]: (((C @ (A)) & ! [D:($i > $i)]: ((C @ (D)) => (C @ (^ [E:$i]: (A @ (D @ E)))))) => (C @ (B)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])).
% 34.94/7.92  thf(7,plain,(! [C:(($i > $i) > $o),B:($i > $i),A:($i > $i)] : ((~ (sk2 @ A @ B)) | (~ (C @ (A))) | (C @ (sk4 @ (C) @ B @ A)) | (C @ (B)))),inference(cnf,[status(esa)],[3])).
% 34.94/7.92  thf(12,plain,(! [B:($i > $i),A:($i > $i)] : ((~ (sk2 @ A @ B)) | (~ ((A) = (A))) | ((A) = (sk4 @ ((=) @ ($i > $i) @ A) @ B @ A)) | ((A) = (B)))),inference(replace_leibeq,[status(thm)],[7:[bind(A, $thf(@)),bind(B, $thf(A)),bind(C, $thf((=) @ ($i > $i) @ @))]])).
% 34.94/7.92  thf(20,plain,(! [B:($i > $i),A:($i > $i)] : (((A) != (A)) | ((A) = (sk4 @ ((=) @ ($i > $i) @ A) @ B @ A)) | ((A) = (B)) | (~ (sk2 @ A @ B)))),inference(lifteq,[status(thm)],[12])).
% 34.94/7.92  thf(21,plain,(! [B:($i > $i),A:($i > $i)] : (((A) = (sk4 @ ((=) @ ($i > $i) @ A) @ B @ A)) | ((A) = (B)) | (~ (sk2 @ A @ B)))),inference(simp,[status(thm)],[20])).
% 34.94/7.92  thf(11,plain,(! [C:(($i > $i) > $o),B:($i > $i),A:($i > $i)] : ((~ (sk2 @ A @ B)) | (~ (C @ (A))) | (~ (C @ (^ [D:$i]: (A @ (sk4 @ C @ B @ A @ D))))) | (C @ (B)))),inference(cnf,[status(esa)],[3])).
% 34.94/7.92  thf(23,plain,(! [C:(($i > $i) > $o),B:($i > $i),A:($i > $i)] : ((~ (sk2 @ A @ B)) | (~ (C @ (A))) | (~ (C @ (^ [D:$i]: (A @ (sk4 @ C @ B @ A @ D))))) | (C @ (B)))),inference(simp,[status(thm)],[11])).
% 34.94/7.92  thf(162,plain,(! [E:(($i > $i) > $o),D:($i > $i),C:($i > $i),B:($i > $i),A:($i > $i)] : (((A) = (B)) | (~ (sk2 @ (A) @ (B))) | (~ (sk2 @ (C) @ (D))) | (~ (E @ (C))) | (~ (E @ (A))) | (E @ (D)) | ((sk4 @ ((=) @ ($i > $i) @ A) @ B @ A) != (^ [F:$i]: (C @ (sk4 @ E @ D @ C @ F)))))),inference(paramod_ordered,[status(thm)],[21,23])).
% 34.94/7.92  thf(194,plain,(! [B:($i > $i),A:($i > $i)] : (((^ [C:$i]: (C)) = (A)) | (~ (sk2 @ (^ [C:$i]: (C)) @ (A))) | (~ (sk2 @ (^ [C:$i]: (C)) @ (B))) | (~ ((^ [C:$i]: (C)) = (^ [C:$i]: (C)))) | (~ ((^ [C:$i]: (C)) = (^ [C:$i]: (C)))) | ((^ [C:$i]: (C)) = (B)) | ((^ [C:$i]: (A)) != (^ [C:$i]: (B))))),inference(pre_uni,[status(thm)],[162:[bind(A, $thf(^ [F:$i]: (F))),bind(B, $thf(B)),bind(C, $thf(^ [F:$i]: (F))),bind(D, $thf(D)),bind(E, $thf((=) @ ($i > $i) @ (^ [F:$i]: (F))))]])).
% 34.94/7.92  thf(195,plain,(! [A:($i > $i)] : (((^ [B:$i]: (B)) = (A)) | (~ ((^ [B:$i]: (B)) = (^ [B:$i]: (B)))) | (~ ((^ [B:$i]: (B)) = (^ [B:$i]: (B)))) | (~ (sk2 @ (^ [B:$i]: (B)) @ (A))) | (~ (sk2 @ (^ [B:$i]: (B)) @ (A))) | ((^ [B:$i]: (B)) = (A)))),inference(pattern_uni,[status(thm)],[194:[bind(A, $thf(@)),bind(B, $thf(@))]])).
% 34.94/7.92  thf(207,plain,(! [A:($i > $i)] : (((^ [B:$i]: (B)) = (A)) | ((^ [B:$i]: (B)) != (^ [B:$i]: (B))) | ((^ [B:$i]: (B)) != (^ [B:$i]: (B))) | (~ (sk2 @ (^ [B:$i]: (B)) @ (A))) | (~ (sk2 @ (^ [B:$i]: (B)) @ (A))) | ((^ [B:$i]: (B)) = (A)))),inference(lifteq,[status(thm)],[195])).
% 34.94/7.92  thf(208,plain,(! [A:($i > $i)] : (((^ [B:$i]: (B)) = (A)) | (~ (sk2 @ (^ [B:$i]: (B)) @ (A))))),inference(simp,[status(thm)],[207])).
% 34.94/7.92  thf(230,plain,(! [B:$i,A:($i > $i)] : (((A @ B) = B) | (~ (sk2 @ (^ [C:$i]: (C)) @ (A))))),inference(func_ext,[status(esa)],[208])).
% 34.94/7.92  thf(9,plain,(! [B:($i > $i),A:($i > $i)] : ((~ ((A @ (sk1 @ (B) @ (A))) = (B @ (sk1 @ (B) @ (A))))) | ((A) = (B)))),inference(cnf,[status(esa)],[3])).
% 34.94/7.92  thf(17,plain,(! [B:($i > $i),A:($i > $i)] : (((A @ (sk1 @ (B) @ (A))) != (B @ (sk1 @ (B) @ (A)))) | ((A) = (B)))),inference(lifteq,[status(thm)],[9])).
% 34.94/7.92  thf(4,plain,(! [B:($i > $i),A:($i > $i)] : ((sk3 @ (B) @ (A) @ (A)) | (sk2 @ A @ B))),inference(cnf,[status(esa)],[3])).
% 34.94/7.92  thf(25,plain,(! [B:($i > $i),A:($i > $i)] : ((sk3 @ (B) @ (A) @ (A)) | (sk2 @ A @ B))),inference(simp,[status(thm)],[4])).
% 34.94/7.92  thf(231,plain,(! [C:($i > $i),B:($i > $i),A:($i > $i)] : ((sk3 @ (B) @ (A) @ (A)) | ((^ [D:$i]: (D)) = (C)) | ((sk2 @ (A) @ (B)) != (sk2 @ (^ [D:$i]: (D)) @ (C))))),inference(paramod_ordered,[status(thm)],[25,208])).
% 34.94/7.92  thf(232,plain,(! [A:($i > $i)] : ((sk3 @ (A) @ (^ [B:$i]: (B)) @ (^ [B:$i]: (B))) | ((^ [B:$i]: (B)) = (A)))),inference(pattern_uni,[status(thm)],[231:[bind(A, $thf(^ [D:$i]: (D))),bind(B, $thf(B)),bind(C, $thf(B))]])).
% 34.94/7.92  thf(322,plain,(! [A:($i > $i)] : ((sk3 @ (A) @ (^ [B:$i]: (B)) @ (^ [B:$i]: (B))) | ((^ [B:$i]: (B)) = (A)))),inference(simp,[status(thm)],[232])).
% 34.94/7.92  thf(6,plain,(((h @ a) = a)),inference(cnf,[status(esa)],[3])).
% 34.94/7.92  thf(16,plain,(((h @ a) = a)),inference(lifteq,[status(thm)],[6])).
% 34.94/7.92  thf(5,plain,((~ ((h @ b) = a))),inference(cnf,[status(esa)],[3])).
% 34.94/7.92  thf(14,plain,(((h @ b) != a)),inference(lifteq,[status(thm)],[5])).
% 34.94/7.92  thf(26,plain,(((h @ b) != (h @ a))),inference(paramod_ordered,[status(thm)],[16,14])).
% 34.94/7.92  thf(27,plain,((b != a)),inference(simp,[status(thm)],[26])).
% 34.94/7.92  thf(529,plain,(! [B:$i,A:($i > $i)] : ((~ (sk2 @ (^ [C:$i]: (C)) @ (A))) | (B != a) | ((A @ B) != b))),inference(paramod_ordered,[status(thm)],[230,27])).
% 34.94/7.92  thf(543,plain,(! [A:$i] : ((~ (sk2 @ (^ [B:$i]: (B)) @ (^ [B:$i]: (b)))) | (A != a))),inference(pre_uni,[status(thm)],[529:[bind(A, $thf(^ [C:$i]: (b)))]])).
% 34.94/7.92  thf(545,plain,((~ (sk2 @ (^ [A:$i]: (A)) @ (^ [A:$i]: (b))))),inference(pattern_uni,[status(thm)],[543:[bind(A, $thf(a))]])).
% 34.94/7.92  thf(591,plain,(! [A:($i > $i)] : ((sk3 @ (A) @ (^ [B:$i]: (B)) @ (^ [B:$i]: (B))) | (~ (sk2 @ (^ [B:$i]: (B)) @ (^ [B:$i]: (B)))) | ((A) != (^ [B:$i]: (b))))),inference(paramod_ordered,[status(thm)],[322,545])).
% 34.94/7.92  thf(592,plain,((sk3 @ (^ [A:$i]: (b)) @ (^ [A:$i]: (A)) @ (^ [A:$i]: (A))) | (~ (sk2 @ (^ [A:$i]: (A)) @ (^ [A:$i]: (A))))),inference(pattern_uni,[status(thm)],[591:[bind(A, $thf(^ [B:$i]: (b)))]])).
% 34.94/7.92  thf(674,plain,(! [A:($i > $i)] : ((~ (sk2 @ (^ [B:$i]: (B)) @ (A))) | (sk3 @ (^ [B:$i]: (b)) @ (^ [B:$i]: (B)) @ (^ [B:$i]: (B))) | ((^ [B:$i]: (B)) != (^ [B:$i]: (B))))),inference(paramod_ordered,[status(thm)],[208,592])).
% 34.94/7.92  thf(675,plain,(! [A:($i > $i)] : ((~ (sk2 @ (^ [B:$i]: (B)) @ (A))) | (sk3 @ (^ [B:$i]: (b)) @ (^ [B:$i]: (B)) @ (^ [B:$i]: (B))))),inference(pattern_uni,[status(thm)],[674:[]])).
% 34.94/7.92  thf(1280,plain,(! [C:($i > $i),B:($i > $i),A:($i > $i)] : ((sk3 @ (B) @ (A) @ (A)) | (sk3 @ (^ [D:$i]: (b)) @ (^ [D:$i]: (D)) @ (^ [D:$i]: (D))) | ((sk2 @ (A) @ (B)) != (sk2 @ (^ [D:$i]: (D)) @ (C))))),inference(paramod_ordered,[status(thm)],[25,675])).
% 34.94/7.92  thf(1281,plain,(! [A:($i > $i)] : ((sk3 @ (A) @ (^ [B:$i]: (B)) @ (^ [B:$i]: (B))) | (sk3 @ (^ [B:$i]: (b)) @ (^ [B:$i]: (B)) @ (^ [B:$i]: (B))))),inference(pattern_uni,[status(thm)],[1280:[bind(A, $thf(^ [D:$i]: (D))),bind(B, $thf(B)),bind(C, $thf(B))]])).
% 34.94/7.92  thf(1368,plain,(! [A:($i > $i)] : ((sk3 @ (A) @ (^ [B:$i]: (B)) @ (^ [B:$i]: (B))) | (sk3 @ (^ [B:$i]: (b)) @ (^ [B:$i]: (B)) @ (^ [B:$i]: (B))))),inference(simp,[status(thm)],[1281])).
% 34.94/7.92  thf(1476,plain,(! [A:($i > $i)] : ((sk3 @ (A) @ (^ [B:$i]: (B)) @ (^ [B:$i]: (B))) | ((sk3 @ (^ [B:$i]: (b)) @ (^ [B:$i]: (B)) @ (^ [B:$i]: (B))) != (sk3 @ (A) @ (^ [B:$i]: (B)) @ (^ [B:$i]: (B)))) | ~ (($true)))),inference(eqfactor_ordered,[status(thm)],[1368])).
% 34.94/7.92  thf(1487,plain,((sk3 @ (^ [A:$i]: (b)) @ (^ [A:$i]: (A)) @ (^ [A:$i]: (A)))),inference(pattern_uni,[status(thm)],[1476:[bind(A, $thf(^ [B:$i]: (b)))]])).
% 34.94/7.92  thf(8,plain,(! [B:($i > $i),A:($i > $i)] : ((~ (sk3 @ (B) @ (A) @ (^ [C:$i]: (B @ (A @ C))))) | (sk2 @ A @ B))),inference(cnf,[status(esa)],[3])).
% 34.94/7.92  thf(24,plain,(! [B:($i > $i),A:($i > $i)] : ((~ (sk3 @ (B) @ (A) @ (^ [C:$i]: (B @ (A @ C))))) | (sk2 @ A @ B))),inference(simp,[status(thm)],[8])).
% 34.94/7.92  thf(1638,plain,(! [B:($i > $i),A:($i > $i)] : ((sk2 @ (A) @ (B)) | ((sk3 @ (^ [C:$i]: (b)) @ (^ [C:$i]: (C)) @ (^ [C:$i]: (C))) != (sk3 @ (B) @ (A) @ (^ [C:$i]: (B @ (A @ C))))))),inference(paramod_ordered,[status(thm)],[1487,24])).
% 34.94/7.92  thf(1680,plain,(! [B:($i > $i),A:($i > $i)] : ((sk2 @ (A) @ (B)) | ((^ [C:$i]: (b)) != (B)) | ((^ [C:$i]: (C)) != (A)) | ((^ [C:$i]: (B @ (A @ C))) != (^ [C:$i]: (C))))),inference(simp,[status(thm)],[1638])).
% 34.94/7.92  thf(1698,plain,((sk2 @ (^ [A:$i]: (A)) @ (^ [A:$i]: (b))) | ((^ [A:$i]: (b)) != (^ [A:$i]: (A)))),inference(simp,[status(thm)],[1680])).
% 34.94/7.92  thf(1719,plain,(($false) | ((^ [A:$i]: (b)) != (^ [A:$i]: (A)))),inference(rewrite,[status(thm)],[1698,545])).
% 34.94/7.92  thf(1720,plain,(((^ [A:$i]: (b)) != (^ [A:$i]: (A)))),inference(simp,[status(thm)],[1719])).
% 34.94/7.92  thf(1724,plain,(! [B:($i > $i),A:($i > $i)] : (((A @ (sk1 @ (B) @ (A))) != (B @ (sk1 @ (B) @ (A)))) | ((B) != (^ [C:$i]: (b))) | ((A) != (^ [C:$i]: (C))))),inference(paramod_ordered,[status(thm)],[17,1720])).
% 34.94/7.92  thf(1725,plain,(! [A:($i > $i)] : (((A @ (sk1 @ (A) @ (^ [B:$i]: (B)))) != (sk1 @ (A) @ (^ [B:$i]: (B)))) | ((A) != (^ [B:$i]: (b))))),inference(pattern_uni,[status(thm)],[1724:[bind(A, $thf(^ [C:$i]: (C)))]])).
% 34.94/7.92  thf(1755,plain,(((sk1 @ (^ [A:$i]: (b)) @ (^ [A:$i]: (A))) != b)),inference(simp,[status(thm)],[1725])).
% 34.94/7.92  thf(2268,plain,(! [B:$i,A:($i > $i)] : ((~ (sk2 @ (^ [C:$i]: (C)) @ (A))) | (B != b) | ((A @ B) != (sk1 @ (^ [C:$i]: (b)) @ (^ [C:$i]: (C)))))),inference(paramod_ordered,[status(thm)],[230,1755])).
% 34.94/7.92  thf(2280,plain,((~ (sk2 @ (^ [A:$i]: (A)) @ (^ [A:$i]: (sk1 @ (^ [B:$i]: (A)) @ (^ [B:$i]: (B)))))) | (b != b)),inference(pre_uni,[status(thm)],[2268:[bind(A, $thf(^ [C:$i]: (sk1 @ (^ [D:$i]: (C)) @ (^ [D:$i]: (D))))),bind(B, $thf(b))]])).
% 34.94/7.92  thf(2282,plain,((~ (sk2 @ (^ [A:$i]: (A)) @ (^ [A:$i]: (sk1 @ (^ [B:$i]: (A)) @ (^ [B:$i]: (B))))))),inference(pattern_uni,[status(thm)],[2280:[]])).
% 34.94/7.92  thf(1734,plain,(! [A:($i > $i)] : ((sk3 @ (A) @ (^ [B:$i]: (B)) @ (^ [B:$i]: (B))) | ((^ [B:$i]: (B)) != (^ [B:$i]: (b))) | ((A) != (^ [B:$i]: (B))))),inference(paramod_ordered,[status(thm)],[322,1720])).
% 34.94/7.92  thf(1735,plain,((sk3 @ (^ [A:$i]: (A)) @ (^ [A:$i]: (A)) @ (^ [A:$i]: (A))) | ((^ [A:$i]: (A)) != (^ [A:$i]: (b)))),inference(pattern_uni,[status(thm)],[1734:[bind(A, $thf(^ [B:$i]: (B)))]])).
% 34.94/7.92  thf(35,plain,(! [C:(($i > $i) > $o),B:($i > $i),A:($i > $i)] : ((~ (sk2 @ A @ B)) | (~ (C @ (A))) | (C @ (B)) | ((C @ (^ [D:$i]: (A @ (sk4 @ C @ B @ A @ D)))) != (sk2 @ A @ B)) | ~ (($true)))),inference(eqfactor_ordered,[status(thm)],[23])).
% 34.94/7.92  thf(63,plain,(! [D:(($i > $i) > ($i > $i)),C:(($i > $i) > ($i > $i)),B:($i > $i),A:($i > $i)] : ((~ (sk2 @ A @ B)) | (~ (sk2 @ (C @ A) @ (D @ A))) | (sk2 @ (C @ B) @ (D @ B)) | ((D @ (^ [E:$i]: (A @ (sk4 @ (^ [F:($i > $i)]: (sk2 @ (C @ F) @ (D @ F))) @ B @ A @ E)))) != (B)) | ((C @ (^ [E:$i]: (A @ (sk4 @ (^ [F:($i > $i)]: (sk2 @ (C @ F) @ (D @ F))) @ B @ A @ E)))) != (A)))),inference(pre_uni,[status(thm)],[35:[bind(A, $thf(A)),bind(B, $thf(B)),bind(C, $thf(^ [F:($i > $i)]: (sk2 @ (D @ F) @ (E @ F))))]])).
% 34.94/7.92  thf(64,plain,(! [D:(($i > $i) > ($i > $i)),C:(($i > $i) > ($i > $i)),B:($i > $i),A:($i > $i)] : ((sk2 @ (C @ B) @ (D @ B)) | (~ (sk2 @ (C @ A) @ (D @ A))) | (~ (sk2 @ A @ B)) | ((D @ (^ [E:$i]: (A @ (sk4 @ (^ [F:($i > $i)]: (sk2 @ (C @ F) @ (D @ F))) @ B @ A @ E)))) != (B)) | ((C @ (^ [E:$i]: (A @ (sk4 @ (^ [F:($i > $i)]: (sk2 @ (C @ F) @ (D @ F))) @ B @ A @ E)))) != (A)))),inference(pre_uni,[status(thm)],[63:[]])).
% 34.94/7.92  thf(78,plain,(! [D:(($i > $i) > ($i > $i)),C:(($i > $i) > ($i > $i)),B:($i > $i),A:($i > $i)] : ((sk2 @ (C @ B) @ (D @ B)) | (~ (sk2 @ (C @ A) @ (D @ A))) | (~ (sk2 @ A @ B)) | ((D @ (^ [E:$i]: (A @ (sk4 @ (^ [F:($i > $i)]: (sk2 @ (C @ F) @ (D @ F))) @ B @ A @ E)))) != (B)) | ((C @ (^ [E:$i]: (A @ (sk4 @ (^ [F:($i > $i)]: (sk2 @ (C @ F) @ (D @ F))) @ B @ A @ E)))) != (A)))),inference(simp,[status(thm)],[64])).
% 34.94/7.92  thf(1728,plain,(! [B:($i > $i),A:($i > $i)] : (((A @ (sk1 @ (B) @ (A))) != (B @ (sk1 @ (B) @ (A)))) | ((A) != (^ [C:$i]: (b))) | ((B) != (^ [C:$i]: (C))))),inference(paramod_ordered,[status(thm)],[17,1720])).
% 34.94/7.92  thf(1729,plain,(! [A:($i > $i)] : (((A @ (sk1 @ (^ [B:$i]: (B)) @ (A))) != (sk1 @ (^ [B:$i]: (B)) @ (A))) | ((A) != (^ [B:$i]: (b))))),inference(pattern_uni,[status(thm)],[1728:[bind(A, $thf(A)),bind(B, $thf(^ [C:$i]: (C)))]])).
% 34.94/7.92  thf(1749,plain,(((sk1 @ (^ [A:$i]: (A)) @ (^ [A:$i]: (b))) != b)),inference(simp,[status(thm)],[1729])).
% 34.94/7.92  thf(1847,plain,(! [B:$i,A:($i > $i)] : ((~ (sk2 @ (^ [C:$i]: (C)) @ (A))) | (B != b) | ((A @ B) != (sk1 @ (^ [C:$i]: (C)) @ (^ [C:$i]: (b)))))),inference(paramod_ordered,[status(thm)],[230,1749])).
% 34.94/7.92  thf(1856,plain,(! [A:$i] : ((~ (sk2 @ (^ [B:$i]: (B)) @ (^ [B:$i]: (sk1 @ (^ [C:$i]: (C)) @ (^ [C:$i]: (b)))))) | (A != b))),inference(pre_uni,[status(thm)],[1847:[bind(A, $thf(^ [C:$i]: (sk1 @ (^ [D:$i]: (D)) @ (^ [D:$i]: (b))))),bind(B, $thf(B))]])).
% 34.94/7.92  thf(1858,plain,((~ (sk2 @ (^ [A:$i]: (A)) @ (^ [A:$i]: (sk1 @ (^ [B:$i]: (B)) @ (^ [B:$i]: (b))))))),inference(pattern_uni,[status(thm)],[1856:[bind(A, $thf(b))]])).
% 34.94/7.92  thf(30,plain,(! [E:(($i > $i) > $o),D:($i > $i),C:($i > $i),B:($i > $i),A:($i > $i)] : ((sk3 @ (B) @ (A) @ (A)) | (~ (E @ (C))) | (~ (E @ (^ [F:$i]: (C @ (sk4 @ E @ D @ C @ F))))) | (E @ (D)) | ((sk2 @ (A) @ (B)) != (sk2 @ (C) @ (D))))),inference(paramod_ordered,[status(thm)],[25,23])).
% 34.94/7.92  thf(31,plain,(! [C:(($i > $i) > $o),B:($i > $i),A:($i > $i)] : ((sk3 @ (B) @ (A) @ (A)) | (~ (C @ (A))) | (~ (C @ (^ [D:$i]: (A @ (sk4 @ C @ B @ A @ D))))) | (C @ (B)))),inference(pattern_uni,[status(thm)],[30:[bind(A, $thf(A)),bind(B, $thf(B)),bind(C, $thf(A)),bind(D, $thf(B))]])).
% 34.94/7.92  thf(47,plain,(! [B:($i > $i),A:($i > $i)] : ((sk3 @ (B) @ (A) @ (A)) | (~ ((A) = (A))) | (~ ((A) = (^ [C:$i]: (A @ (sk4 @ ((=) @ ($i > $i) @ A) @ B @ A @ C))))) | ((A) = (B)))),inference(replace_leibeq,[status(thm)],[31:[bind(A, $thf(?)),bind(B, $thf(@)),bind(C, $thf((=) @ ($i > $i) @ ?))]])).
% 34.94/7.92  thf(56,plain,(! [B:($i > $i),A:($i > $i)] : (((A) != (A)) | ((^ [C:$i]: (A @ (sk4 @ ((=) @ ($i > $i) @ A) @ B @ A @ C))) != (A)) | ((A) = (B)) | (sk3 @ (B) @ (A) @ (A)))),inference(lifteq,[status(thm)],[47])).
% 34.94/7.92  thf(61,plain,(! [B:($i > $i),A:($i > $i)] : ((sk3 @ (B) @ (A) @ (A)) | ((A) = (B)) | ((^ [C:$i]: (A @ (sk4 @ ((=) @ ($i > $i) @ A) @ B @ A @ C))) != (A)))),inference(pre_uni,[status(thm)],[56:[]])).
% 34.94/7.92  thf(524,plain,(! [B:$i,A:($i > $i)] : ((~ (sk2 @ (^ [C:$i]: (C)) @ (A))) | (B != a) | ((A @ B) != (h @ b)))),inference(paramod_ordered,[status(thm)],[230,14])).
% 34.94/7.92  thf(562,plain,(! [A:$i] : ((~ (sk2 @ (^ [B:$i]: (B)) @ (^ [B:$i]: (h @ b)))) | (A != a))),inference(pre_uni,[status(thm)],[524:[bind(A, $thf(^ [C:$i]: (h @ b))),bind(B, $thf(B))]])).
% 34.94/7.92  thf(564,plain,((~ (sk2 @ (^ [A:$i]: (A)) @ (^ [A:$i]: (h @ b))))),inference(pattern_uni,[status(thm)],[562:[bind(A, $thf(a))]])).
% 34.94/7.92  thf(620,plain,(! [A:($i > $i)] : ((sk3 @ (A) @ (^ [B:$i]: (B)) @ (^ [B:$i]: (B))) | (~ (sk2 @ (^ [B:$i]: (B)) @ (^ [B:$i]: (B)))) | ((A) != (^ [B:$i]: (h @ b))))),inference(paramod_ordered,[status(thm)],[322,564])).
% 34.94/7.92  thf(621,plain,((sk3 @ (^ [A:$i]: (h @ b)) @ (^ [A:$i]: (A)) @ (^ [A:$i]: (A))) | (~ (sk2 @ (^ [A:$i]: (A)) @ (^ [A:$i]: (A))))),inference(pattern_uni,[status(thm)],[620:[bind(A, $thf(^ [B:$i]: (h @ b)))]])).
% 34.94/7.92  thf(2050,plain,(! [B:($i > $i),A:($i > $i)] : (((^ [C:$i]: (C)) != (^ [C:$i]: (b))) | (sk2 @ (A) @ (B)) | ((sk3 @ (^ [C:$i]: (C)) @ (^ [C:$i]: (C)) @ (^ [C:$i]: (C))) != (sk3 @ (B) @ (A) @ (^ [C:$i]: (B @ (A @ C))))))),inference(paramod_ordered,[status(thm)],[1735,24])).
% 34.94/7.92  thf(2088,plain,(((^ [A:$i]: (A)) != (^ [A:$i]: (b))) | (sk2 @ (^ [A:$i]: (A)) @ (^ [A:$i]: (A)))),inference(pre_uni,[status(thm)],[2050:[bind(A, $thf(^ [C:$i]: (C))),bind(B, $thf(^ [C:$i]: (C)))]])).
% 34.94/7.92  thf(10,plain,(! [C:($i > $i),B:($i > $i),A:($i > $i)] : ((~ (sk3 @ (B) @ (A) @ (C))) | (sk3 @ (B) @ (A) @ (^ [D:$i]: (A @ (C @ D)))) | (sk2 @ A @ B))),inference(cnf,[status(esa)],[3])).
% 34.94/7.92  thf(15,plain,(! [C:($i > $i),B:($i > $i),A:($i > $i)] : ((~ (sk3 @ (B) @ (A) @ (C))) | (sk3 @ (B) @ (A) @ (^ [D:$i]: (A @ (C @ D)))) | (sk2 @ A @ B))),inference(simp,[status(thm)],[10])).
% 34.94/7.92  thf(1721,plain,((sk8 != b)),inference(func_ext,[status(esa)],[1720])).
% 34.94/7.92  thf(1757,plain,(! [B:$i,A:($i > $i)] : ((~ (sk2 @ (^ [C:$i]: (C)) @ (A))) | (B != b) | ((A @ B) != sk8))),inference(paramod_ordered,[status(thm)],[230,1721])).
% 34.94/7.92  thf(1758,plain,(! [A:$i] : ((~ (sk2 @ (^ [B:$i]: (B)) @ (^ [B:$i]: (sk8)))) | (A != b))),inference(pre_uni,[status(thm)],[1757:[bind(A, $thf(^ [C:$i]: (sk8)))]])).
% 34.94/7.92  thf(1760,plain,((~ (sk2 @ (^ [A:$i]: (A)) @ (^ [A:$i]: (sk8))))),inference(pattern_uni,[status(thm)],[1758:[bind(A, $thf(b))]])).
% 34.94/7.92  thf(22,plain,(! [C:(($i > $i) > $o),B:($i > $i),A:($i > $i)] : ((~ (sk2 @ A @ B)) | (~ (C @ (A))) | (C @ (sk4 @ (C) @ B @ A)) | (C @ (B)))),inference(simp,[status(thm)],[7])).
% 34.94/7.92  thf(1744,plain,(! [A:($i > $i)] : ((~ (sk2 @ (^ [B:$i]: (B)) @ (A))) | ((^ [B:$i]: (B)) != (^ [B:$i]: (b))) | ((A) != (^ [B:$i]: (B))))),inference(paramod_ordered,[status(thm)],[208,1720])).
% 34.94/7.92  thf(1745,plain,((~ (sk2 @ (^ [A:$i]: (A)) @ (^ [A:$i]: (A)))) | ((^ [A:$i]: (A)) != (^ [A:$i]: (b)))),inference(pattern_uni,[status(thm)],[1744:[bind(A, $thf(^ [B:$i]: (B)))]])).
% 34.94/7.92  thf(2158,plain,(((^ [A:$i]: (A)) != (^ [A:$i]: (b))) | ((sk2 @ (^ [A:$i]: (A)) @ (^ [A:$i]: (A))) != (sk2 @ (^ [A:$i]: (A)) @ (^ [A:$i]: (sk8))))),inference(paramod_ordered,[status(thm)],[2088,1760])).
% 34.94/7.92  thf(2205,plain,(((^ [A:$i]: (A)) != (^ [A:$i]: (b))) | ((^ [A:$i]: (A)) != (^ [A:$i]: (A))) | ((^ [A:$i]: (A)) != (^ [A:$i]: (sk8)))),inference(simp,[status(thm)],[2158])).
% 34.94/7.92  thf(2233,plain,(((^ [A:$i]: (A)) != (^ [A:$i]: (b))) | ((^ [A:$i]: (A)) != (^ [A:$i]: (sk8)))),inference(simp,[status(thm)],[2205])).
% 34.94/7.92  thf(13,plain,(! [B:($i > $i),A:($i > $i)] : ((~ (sk2 @ A @ B)) | (~ ((A) = (A))) | (~ ((A) = (^ [C:$i]: (A @ (sk4 @ ((=) @ ($i > $i) @ A) @ B @ A @ C))))) | ((A) = (B)))),inference(replace_leibeq,[status(thm)],[11:[bind(A, $thf(@)),bind(B, $thf(A)),bind(C, $thf((=) @ ($i > $i) @ @))]])).
% 34.94/7.92  thf(18,plain,(! [B:($i > $i),A:($i > $i)] : (((A) != (A)) | ((^ [C:$i]: (A @ (sk4 @ ((=) @ ($i > $i) @ A) @ B @ A @ C))) != (A)) | ((A) = (B)) | (~ (sk2 @ A @ B)))),inference(lifteq,[status(thm)],[13])).
% 34.94/7.92  thf(19,plain,(! [B:($i > $i),A:($i > $i)] : (((^ [C:$i]: (A @ (sk4 @ ((=) @ ($i > $i) @ A) @ B @ A @ C))) != (A)) | ((A) = (B)) | (~ (sk2 @ A @ B)))),inference(simp,[status(thm)],[18])).
% 34.94/7.92  thf(1857,plain,((~ (sk2 @ (^ [A:$i]: (A)) @ (^ [A:$i]: (sk1 @ (^ [B:$i]: (B)) @ (^ [B:$i]: (A)))))) | (b != b)),inference(pre_uni,[status(thm)],[1847:[bind(A, $thf(^ [C:$i]: (sk1 @ (^ [D:$i]: (D)) @ (^ [D:$i]: (C))))),bind(B, $thf(b))]])).
% 34.94/7.92  thf(1859,plain,((~ (sk2 @ (^ [A:$i]: (A)) @ (^ [A:$i]: (sk1 @ (^ [B:$i]: (B)) @ (^ [B:$i]: (A))))))),inference(pattern_uni,[status(thm)],[1857:[]])).
% 34.94/7.92  thf(2621,plain,(($false)),inference(e,[status(thm)],[2282,1735,78,1858,61,1755,1720,17,621,3,16,1749,2088,15,322,24,25,14,1760,1487,21,22,545,27,230,208,1721,1745,23,2233,19,564,1859])).
% 34.94/7.92  % SZS output end Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 34.94/7.92  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------