%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LCL595^1 : TPTP v9.3.1. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:14:06 AM UTC 2026
% Result : Theorem 21.67s 5.73s
% Output : Refutation 20.16s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL595^1 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.06 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.10/0.17 % Computer : n003.cluster.edu
% 0.10/0.17 % Model : x86_64 x86_64
% 0.10/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.17 % Memory : 8046.5625MB
% 0.10/0.17 % OS : Linux 6.8.0-71-generic
% 0.10/0.17 % CPULimit : 300
% 0.10/0.17 % WCLimit : 300
% 0.10/0.17 % DateTime : Tue Sep 29 09:13:13 UTC 2026
% 0.10/0.17 % CPUTime :
% 0.10/0.17 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.92/0.79 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.72/1.05 % [INFO] Parsing done (257ms).
% 1.72/1.07 % [INFO] Running in sequential loop mode.
% 2.34/1.46 % [INFO] eprover registered as external prover.
% 2.34/1.46 % [INFO] Scanning for conjecture ...
% 2.81/1.63 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.81/1.66 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.81/1.66 % [INFO] Problem is higher-order (TPTP THF).
% 2.81/1.67 % [INFO] Type checking passed.
% 2.81/1.67 % [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 ...
% 21.67/5.72 % External prover 'e' found a proof!
% 21.67/5.73 % [INFO] Killing All external provers ...
% 21.67/5.73 % Time passed: 5375ms (effective reasoning time: 4654ms)
% 21.67/5.73 % 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)>
% 21.67/5.73 % Axioms used in derivation (0):
% 21.67/5.73 % No. of inferences in proof: 134
% 21.67/5.73 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 5375 ms resp. 4654 ms w/o parsing
% 20.16/5.82 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% 20.16/5.82 thf(individuals_type, type, individuals: $tType).
% 20.16/5.82 thf(prop_a_decl, type, prop_a: ($i > $o)).
% 20.16/5.82 thf(prop_b_decl, type, prop_b: ($i > $o)).
% 20.16/5.82 thf(prop_c_decl, type, prop_c: ($i > $o)).
% 20.16/5.82 thf(mnot_decl, type, mnot: (($i > $o) > ($i > $o))).
% 20.16/5.82 thf(mor_decl, type, mor: (($i > $o) > (($i > $o) > ($i > $o)))).
% 20.16/5.82 thf(mimpl_decl, type, mimpl: (($i > $o) > (($i > $o) > ($i > $o)))).
% 20.16/5.82 thf(mbox_decl, type, mbox: (($i > ($i > $o)) > (($i > $o) > ($i > $o)))).
% 20.16/5.82 thf(mvalid_decl, type, mvalid: (($i > $o) > $o)).
% 20.16/5.82 thf(reflexive_decl, type, reflexive: (($i > ($i > $o)) > $o)).
% 20.16/5.82 thf(r_decl, type, r: ($i > ($i > $o))).
% 20.16/5.82 thf(sk1_decl, type, sk1: ($i > $o)).
% 20.16/5.82 thf(sk2_decl, type, sk2: $i).
% 20.16/5.82 thf(sk3_decl, type, sk3: ($i > $i)).
% 20.16/5.82 thf(sk4_decl, type, sk4: ($i > (($i > $o) > $i))).
% 20.16/5.82 thf(mnot_def, definition, mnot = (^ [A:($i > $o),B:$i]: ~ (A @ B)) ).
% 20.16/5.82 thf(mor_def, definition, mor = (^ [A:($i > $o),B:($i > $o),C:$i]: ((A @ C) | (B @ C))) ).
% 20.16/5.82 thf(mimpl_def, definition, mimpl = (^ [A:($i > $o)]: (mor @ (mnot @ A))) ).
% 20.16/5.83 thf(mbox_def, definition, mbox = (^ [A:($i > ($i > $o)),B:($i > $o),C:$i]: ! [D:$i]: ((A @ C @ D) => (B @ D))) ).
% 20.16/5.83 thf(mvalid_def, definition, mvalid = ((!) @ $i) ).
% 20.16/5.83 thf(reflexive_def, definition, reflexive = (^ [A:($i > ($i > $o))]: ! [B:$i]: (A @ B @ B)) ).
% 20.16/5.83 thf(sk1_def, definition, sk1 = (@+ [A:($i > $o)]: ~ (! [B:$i]: (~ (! [C:$i]: ((r @ B @ C) => (A @ C))) | (A @ B)))) ).
% 20.16/5.83 thf(sk2_def, definition, sk2 = (@+ [A:$i]: ~ (~ (! [B:$i]: ((r @ A @ B) => (sk1 @ B))) | (sk1 @ A))) ).
% 20.16/5.83 thf(sk3_def, definition, sk3 = (^ [A:$i]: (@+ [B:$i]: ~ (r @ B @ B))) ).
% 20.16/5.83 thf(sk4_def, definition, sk4 = (^ [A:$i,B:($i > $o)]: (@+ [C:$i]: ~ ((r @ A @ C) => (B @ C)))) ).
% 20.16/5.83 thf(1,conjecture,(((! [A:($i > $o)]: (mvalid @ (mimpl @ (mbox @ r @ A) @ A))) = (reflexive @ r))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm)).
% 20.16/5.83 thf(2,negated_conjecture,((~ ((! [A:($i > $o)]: (mvalid @ (mimpl @ (mbox @ r @ A) @ A))) = (reflexive @ r)))),inference(neg_conjecture,[status(cth)],[1])).
% 20.16/5.83 thf(3,plain,((~ ((! [A:($i > $o),B:$i]: (~ (! [C:$i]: ((r @ B @ C) => (A @ C))) | (A @ B))) = (! [A:$i]: (r @ A @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])).
% 20.16/5.83 thf(4,plain,(((! [A:($i > $o),B:$i]: (~ (! [C:$i]: ((r @ B @ C) => (A @ C))) | (A @ B))) != (! [A:$i]: (r @ A @ A)))),inference(lifteq,[status(thm)],[3])).
% 20.16/5.83 thf(6,plain,((! [A:($i > $o),B:$i]: (~ (! [C:$i]: ((r @ B @ C) => (A @ C))) | (A @ B))) | (! [A:$i]: (r @ A @ A))),inference(bool_ext,[status(thm)],[4])).
% 20.16/5.83 thf(10,plain,(! [C:$i,B:$i,A:($i > $o)] : ((((r @ B @ (sk4 @ B @ (A))) | (A @ B) | (r @ C @ C)) & (~ (A @ (sk4 @ B @ (A))) | (A @ B) | (r @ C @ C))))),inference(cnf,[status(esa)],[6])).
% 20.16/5.83 thf(11,plain,(! [C:$i,B:$i,A:($i > $o)] : ((r @ B @ (sk4 @ B @ (A))) | (A @ B) | (r @ C @ C))),inference(cnfConj,[status(thm)],[10])).
% 20.16/5.83 thf(5,plain,((~ (! [A:($i > $o),B:$i]: (~ (! [C:$i]: ((r @ B @ C) => (A @ C))) | (A @ B)))) | (~ (! [A:$i]: (r @ A @ A)))),inference(bool_ext,[status(thm)],[4])).
% 20.16/5.83 thf(7,plain,(! [A:$i] : (((~ (r @ sk2 @ A) | (sk1 @ A) | ~ (r @ (sk3 @ A) @ (sk3 @ A))) & (~ (sk1 @ sk2) | ~ (r @ (sk3 @ A) @ (sk3 @ A)))))),inference(cnf,[status(esa)],[5])).
% 20.16/5.83 thf(9,plain,(! [A:$i] : ((~ (sk1 @ sk2)) | (~ (r @ (sk3 @ A) @ (sk3 @ A))))),inference(cnfConj,[status(thm)],[7])).
% 20.16/5.83 thf(40,plain,(! [D:$i,C:$i,B:$i,A:($i > $o)] : ((r @ B @ (sk4 @ B @ (A))) | (A @ B) | (~ (sk1 @ sk2)) | ~ (($true)) | ((r @ C @ C) != (r @ (sk3 @ D) @ (sk3 @ D))))),inference(paramod_ordered,[status(thm)],[11,9])).
% 20.16/5.83 thf(41,plain,(! [D:$i,C:$i,B:$i,A:($i > $o)] : ((r @ B @ (sk4 @ B @ (A))) | (A @ B) | (~ (sk1 @ sk2)) | ((r @ C @ C) != (r @ (sk3 @ D) @ (sk3 @ D))))),inference(simp,[status(thm)],[40])).
% 20.16/5.83 thf(42,plain,(! [B:$i,A:($i > $o)] : ((r @ B @ (sk4 @ B @ (A))) | (A @ B) | (~ (sk1 @ sk2)))),inference(pattern_uni,[status(thm)],[41:[bind(A, $thf(A)),bind(B, $thf(B)),bind(C, $thf(sk3 @ E)),bind(D, $thf(E))]])).
% 20.16/5.83 thf(1173,plain,(! [C:$i,B:$i,A:($i > $o)] : ((r @ B @ (sk4 @ B @ (A))) | (~ (sk1 @ sk2)) | (~ (sk1 @ sk2)) | ~ (($true)) | ((A @ B) != (r @ (sk3 @ C) @ (sk3 @ C))))),inference(paramod_ordered,[status(thm)],[42,9])).
% 20.16/5.83 thf(1174,plain,(! [C:$i,B:$i,A:($i > $o)] : ((r @ B @ (sk4 @ B @ (A))) | (~ (sk1 @ sk2)) | ((A @ B) != (r @ (sk3 @ C) @ (sk3 @ C))))),inference(simp,[status(thm)],[1173])).
% 20.16/5.83 thf(1295,plain,(! [A:$i] : ((r @ (sk3 @ A) @ (sk4 @ (sk3 @ A) @ (^ [B:$i]: (r @ B @ B)))) | (~ (sk1 @ sk2)))),inference(pre_uni,[status(thm)],[1174:[bind(A, $thf(^ [D:$i]: (r @ D @ D))),bind(B, $thf(sk3 @ C)),bind(C, $thf(C))]])).
% 20.16/5.83 thf(1354,plain,(! [A:$i] : ((r @ (sk3 @ A) @ (sk4 @ (sk3 @ A) @ (^ [B:$i]: (r @ B @ B)))) | (~ (sk1 @ sk2)))),inference(simp,[status(thm)],[1295])).
% 20.16/5.83 thf(1251,plain,(! [B:$i,A:($i > $o)] : ((r @ B @ (sk4 @ B @ (A))) | (~ (sk1 @ sk2)) | ((A @ B) != (~ (sk1 @ sk2))) | ~ (($true)))),inference(eqfactor_ordered,[status(thm)],[42])).
% 20.16/5.83 thf(1271,plain,((r @ sk2 @ (sk4 @ sk2 @ (^ [A:$i]: ~ (sk1 @ A)))) | (~ (sk1 @ sk2))),inference(pre_uni,[status(thm)],[1251:[bind(A, $thf(^ [C:$i]: ~ (sk1 @ C))),bind(B, $thf(sk2))]])).
% 20.16/5.83 thf(1431,plain,(! [C:$i,B:$i,A:($i > $o)] : ((r @ B @ (sk4 @ B @ (A))) | (r @ C @ C) | (r @ sk2 @ (sk4 @ sk2 @ (^ [D:$i]: ~ (sk1 @ D)))) | ~ (($true)) | ((A @ B) != (sk1 @ sk2)))),inference(paramod_ordered,[status(thm)],[11,1271])).
% 20.16/5.83 thf(1432,plain,(! [C:$i,B:$i,A:($i > $o)] : ((r @ B @ (sk4 @ B @ (A))) | (r @ C @ C) | (r @ sk2 @ (sk4 @ sk2 @ (^ [D:$i]: ~ (sk1 @ D)))) | ((A @ B) != (sk1 @ sk2)))),inference(simp,[status(thm)],[1431])).
% 20.16/5.83 thf(1458,plain,(! [A:$i] : ((r @ sk2 @ (sk4 @ sk2 @ (sk1))) | (r @ A @ A) | (r @ sk2 @ (sk4 @ sk2 @ (^ [B:$i]: ~ (sk1 @ B)))))),inference(pre_uni,[status(thm)],[1432:[bind(A, $thf(sk1)),bind(B, $thf(sk2)),bind(C, $thf(C))]])).
% 20.16/5.83 thf(1467,plain,(! [A:$i] : ((r @ sk2 @ (sk4 @ sk2 @ (sk1))) | (r @ A @ A) | (r @ sk2 @ (sk4 @ sk2 @ (^ [B:$i]: ~ (sk1 @ B)))))),inference(simp,[status(thm)],[1458])).
% 20.16/5.83 thf(8,plain,(! [A:$i] : ((~ (r @ sk2 @ A)) | (sk1 @ A) | (~ (r @ (sk3 @ A) @ (sk3 @ A))))),inference(cnfConj,[status(thm)],[7])).
% 20.16/5.83 thf(52,plain,(! [D:$i,C:$i,B:$i,A:($i > $o)] : ((r @ B @ (sk4 @ B @ (A))) | (A @ B) | ~ (($true)) | (sk1 @ D) | (~ (r @ (sk3 @ D) @ (sk3 @ D))) | ((r @ C @ C) != (r @ sk2 @ D)))),inference(paramod_ordered,[status(thm)],[11,8])).
% 20.16/5.83 thf(53,plain,(! [D:$i,C:$i,B:$i,A:($i > $o)] : ((r @ B @ (sk4 @ B @ (A))) | (A @ B) | (sk1 @ D) | (~ (r @ (sk3 @ D) @ (sk3 @ D))) | ((r @ C @ C) != (r @ sk2 @ D)))),inference(simp,[status(thm)],[52])).
% 20.16/5.83 thf(54,plain,(! [B:$i,A:($i > $o)] : ((r @ B @ (sk4 @ B @ (A))) | (A @ B) | (sk1 @ sk2) | (~ (r @ (sk3 @ sk2) @ (sk3 @ sk2))))),inference(pattern_uni,[status(thm)],[53:[bind(A, $thf(A)),bind(B, $thf(B)),bind(C, $thf(sk2)),bind(D, $thf(sk2))]])).
% 20.16/5.83 thf(2013,plain,(! [B:$i,A:($i > $o)] : ((r @ B @ (sk4 @ B @ (A))) | (sk1 @ sk2) | (~ (r @ (sk3 @ sk2) @ (sk3 @ sk2))) | ((A @ B) != (sk1 @ sk2)) | ~ (($true)))),inference(eqfactor_ordered,[status(thm)],[54])).
% 20.16/5.83 thf(2120,plain,((r @ sk2 @ (sk4 @ sk2 @ (sk1))) | (sk1 @ sk2) | (~ (r @ (sk3 @ sk2) @ (sk3 @ sk2)))),inference(pre_uni,[status(thm)],[2013:[bind(A, $thf(sk1)),bind(B, $thf(sk2))]])).
% 20.16/5.83 thf(2338,plain,(! [A:$i] : ((r @ sk2 @ (sk4 @ sk2 @ (sk1))) | (r @ sk2 @ (sk4 @ sk2 @ (^ [B:$i]: ~ (sk1 @ B)))) | (r @ sk2 @ (sk4 @ sk2 @ (sk1))) | (sk1 @ sk2) | ~ (($true)) | ((r @ A @ A) != (r @ (sk3 @ sk2) @ (sk3 @ sk2))))),inference(paramod_ordered,[status(thm)],[1467,2120])).
% 20.16/5.83 thf(2339,plain,(! [A:$i] : ((r @ sk2 @ (sk4 @ sk2 @ (sk1))) | (r @ sk2 @ (sk4 @ sk2 @ (^ [B:$i]: ~ (sk1 @ B)))) | (sk1 @ sk2) | ((r @ A @ A) != (r @ (sk3 @ sk2) @ (sk3 @ sk2))))),inference(simp,[status(thm)],[2338])).
% 20.16/5.83 thf(2340,plain,((r @ sk2 @ (sk4 @ sk2 @ (sk1))) | (r @ sk2 @ (sk4 @ sk2 @ (^ [A:$i]: ~ (sk1 @ A)))) | (sk1 @ sk2)),inference(pattern_uni,[status(thm)],[2339:[bind(A, $thf(sk3 @ sk2))]])).
% 20.16/5.83 thf(2545,plain,((r @ sk2 @ (sk4 @ sk2 @ (sk1))) | (sk1 @ sk2) | ((r @ sk2 @ (sk4 @ sk2 @ (^ [A:$i]: ~ (sk1 @ A)))) != (r @ sk2 @ (sk4 @ sk2 @ (sk1)))) | ~ (($true))),inference(eqfactor_ordered,[status(thm)],[2340])).
% 20.16/5.83 thf(2553,plain,((r @ sk2 @ (sk4 @ sk2 @ (sk1))) | (sk1 @ sk2) | (sk2 != sk2) | ((sk4 @ sk2 @ (^ [A:$i]: ~ (sk1 @ A))) != (sk4 @ sk2 @ (sk1)))),inference(simp,[status(thm)],[2545])).
% 20.16/5.83 thf(2560,plain,((r @ sk2 @ (sk4 @ sk2 @ (sk1))) | (sk1 @ sk2) | ((sk4 @ sk2 @ (^ [A:$i]: ~ (sk1 @ A))) != (sk4 @ sk2 @ (sk1)))),inference(simp,[status(thm)],[2553])).
% 20.16/5.83 thf(1261,plain,(! [A:$i] : ((r @ A @ (sk4 @ A @ (prop_a))) | (prop_a @ A) | (~ (sk1 @ sk2)))),inference(prim_subst,[status(thm)],[42:[bind(A, $thf(prop_a))]])).
% 20.16/5.83 thf(1407,plain,(! [A:$i] : ((r @ A @ (sk4 @ A @ (prop_a))) | (prop_a @ A) | (~ (sk1 @ sk2)))),inference(simp,[status(thm)],[1261])).
% 20.16/5.83 thf(1270,plain,(! [A:$i] : ((r @ A @ (sk4 @ A @ (^ [B:$i]: ~ (sk1 @ sk2)))) | (~ (sk1 @ sk2)))),inference(pre_uni,[status(thm)],[1251:[bind(A, $thf(^ [C:$i]: ~ (sk1 @ sk2))),bind(B, $thf(B))]])).
% 20.16/5.83 thf(1414,plain,(! [A:$i] : ((r @ A @ (sk4 @ A @ (^ [B:$i]: ~ (sk1 @ sk2)))) | (~ (sk1 @ sk2)))),inference(simp,[status(thm)],[1270])).
% 20.16/5.83 thf(77,plain,(! [B:$i,A:$i] : ((r @ A @ (sk4 @ A @ (^ [C:$i]: (($false))))) | ($false) | (r @ B @ B))),inference(prim_subst,[status(thm)],[11:[bind(A, $thf(^ [D:$i]: (($false))))]])).
% 20.16/5.83 thf(127,plain,(! [B:$i,A:$i] : ((r @ A @ (sk4 @ A @ (^ [C:$i]: (($false))))) | (r @ B @ B))),inference(simp,[status(thm)],[77])).
% 20.16/5.83 thf(224,plain,(! [B:$i,A:$i] : ((r @ A @ (sk4 @ A @ (^ [C:$i]: (($false))))) | ((r @ B @ B) != (r @ A @ (sk4 @ A @ (^ [C:$i]: (($false)))))) | ~ (($true)))),inference(eqfactor_ordered,[status(thm)],[127])).
% 20.16/5.83 thf(230,plain,(! [B:$i,A:$i] : ((r @ A @ (sk4 @ A @ (^ [C:$i]: (($false))))) | ((r @ B @ B) != (r @ A @ (sk4 @ A @ (^ [C:$i]: (($false)))))))),inference(simp,[status(thm)],[224])).
% 20.16/5.83 thf(12,plain,(! [C:$i,B:$i,A:($i > $o)] : ((~ (A @ (sk4 @ B @ (A)))) | (A @ B) | (r @ C @ C))),inference(cnfConj,[status(thm)],[10])).
% 20.16/5.83 thf(249,plain,(! [D:$i,C:$i,B:$i,A:($i > $o)] : ((~ (A @ (sk4 @ B @ (A)))) | (A @ B) | (~ (sk1 @ sk2)) | ~ (($true)) | ((r @ C @ C) != (r @ (sk3 @ D) @ (sk3 @ D))))),inference(paramod_ordered,[status(thm)],[12,9])).
% 20.16/5.83 thf(250,plain,(! [D:$i,C:$i,B:$i,A:($i > $o)] : ((~ (A @ (sk4 @ B @ (A)))) | (A @ B) | (~ (sk1 @ sk2)) | ((r @ C @ C) != (r @ (sk3 @ D) @ (sk3 @ D))))),inference(simp,[status(thm)],[249])).
% 20.16/5.83 thf(251,plain,(! [B:$i,A:($i > $o)] : ((~ (A @ (sk4 @ B @ (A)))) | (A @ B) | (~ (sk1 @ sk2)))),inference(pattern_uni,[status(thm)],[250:[bind(A, $thf(A)),bind(B, $thf(B)),bind(C, $thf(sk3 @ E)),bind(D, $thf(E))]])).
% 20.16/5.83 thf(2305,plain,(! [B:$i,A:$i] : ((r @ A @ (sk4 @ A @ (^ [C:$i]: (($false))))) | (r @ sk2 @ (sk4 @ sk2 @ (sk1))) | (sk1 @ sk2) | ~ (($true)) | ((r @ B @ B) != (r @ (sk3 @ sk2) @ (sk3 @ sk2))))),inference(paramod_ordered,[status(thm)],[127,2120])).
% 20.16/5.83 thf(2306,plain,(! [B:$i,A:$i] : ((r @ A @ (sk4 @ A @ (^ [C:$i]: (($false))))) | (r @ sk2 @ (sk4 @ sk2 @ (sk1))) | (sk1 @ sk2) | ((r @ B @ B) != (r @ (sk3 @ sk2) @ (sk3 @ sk2))))),inference(simp,[status(thm)],[2305])).
% 20.16/5.83 thf(2307,plain,(! [A:$i] : ((r @ A @ (sk4 @ A @ (^ [B:$i]: (($false))))) | (r @ sk2 @ (sk4 @ sk2 @ (sk1))) | (sk1 @ sk2))),inference(pattern_uni,[status(thm)],[2306:[bind(A, $thf(A)),bind(B, $thf(sk3 @ sk2))]])).
% 20.16/5.83 thf(3297,plain,(! [A:$i] : ((r @ sk2 @ (sk4 @ sk2 @ (sk1))) | (sk1 @ sk2) | (r @ sk2 @ (sk4 @ sk2 @ (sk1))) | (sk1 @ sk2) | ~ (($true)) | ((r @ A @ (sk4 @ A @ (^ [B:$i]: (($false))))) != (r @ (sk3 @ sk2) @ (sk3 @ sk2))))),inference(paramod_ordered,[status(thm)],[2307,2120])).
% 20.16/5.83 thf(3298,plain,(! [A:$i] : ((r @ sk2 @ (sk4 @ sk2 @ (sk1))) | (sk1 @ sk2) | ((r @ A @ (sk4 @ A @ (^ [B:$i]: (($false))))) != (r @ (sk3 @ sk2) @ (sk3 @ sk2))))),inference(simp,[status(thm)],[3297])).
% 20.16/5.83 thf(3329,plain,(! [A:$i] : ((r @ sk2 @ (sk4 @ sk2 @ (sk1))) | (sk1 @ sk2) | (A != (sk3 @ sk2)) | ((sk4 @ A @ (^ [B:$i]: (($false)))) != (sk3 @ sk2)))),inference(simp,[status(thm)],[3298])).
% 20.16/5.83 thf(3350,plain,((r @ sk2 @ (sk4 @ sk2 @ (sk1))) | (sk1 @ sk2) | ((sk4 @ (sk3 @ sk2) @ (^ [A:$i]: (($false)))) != (sk3 @ sk2))),inference(simp,[status(thm)],[3329])).
% 20.16/5.83 thf(13,plain,(! [A:$i] : ((~ (r @ sk2 @ A)) | (sk1 @ A) | ((r @ (sk3 @ A) @ (sk3 @ A)) != (r @ sk2 @ A)) | ~ (($true)))),inference(eqfactor_ordered,[status(thm)],[8])).
% 20.16/5.83 thf(14,plain,(! [A:$i] : ((sk1 @ A) | (~ (r @ sk2 @ A)) | ((r @ (sk3 @ A) @ (sk3 @ A)) != (r @ sk2 @ A)))),inference(simp,[status(thm)],[13])).
% 20.16/5.83 thf(198,plain,(! [C:$i,B:$i,A:$i] : ((r @ A @ (sk4 @ A @ (^ [D:$i]: (($false))))) | (~ (sk1 @ sk2)) | ~ (($true)) | ((r @ B @ B) != (r @ (sk3 @ C) @ (sk3 @ C))))),inference(paramod_ordered,[status(thm)],[127,9])).
% 20.16/5.83 thf(199,plain,(! [C:$i,B:$i,A:$i] : ((r @ A @ (sk4 @ A @ (^ [D:$i]: (($false))))) | (~ (sk1 @ sk2)) | ((r @ B @ B) != (r @ (sk3 @ C) @ (sk3 @ C))))),inference(simp,[status(thm)],[198])).
% 20.16/5.83 thf(200,plain,(! [A:$i] : ((r @ A @ (sk4 @ A @ (^ [B:$i]: (($false))))) | (~ (sk1 @ sk2)))),inference(pattern_uni,[status(thm)],[199:[bind(A, $thf(A)),bind(B, $thf(sk3 @ D)),bind(C, $thf(D))]])).
% 20.16/5.83 thf(344,plain,(! [B:$i,A:$i] : ((~ (sk1 @ sk2)) | (~ (sk1 @ sk2)) | ~ (($true)) | ((r @ A @ (sk4 @ A @ (^ [C:$i]: (($false))))) != (r @ (sk3 @ B) @ (sk3 @ B))))),inference(paramod_ordered,[status(thm)],[200,9])).
% 20.16/5.83 thf(345,plain,(! [B:$i,A:$i] : ((~ (sk1 @ sk2)) | ((r @ A @ (sk4 @ A @ (^ [C:$i]: (($false))))) != (r @ (sk3 @ B) @ (sk3 @ B))))),inference(simp,[status(thm)],[344])).
% 20.16/5.83 thf(363,plain,(! [B:$i,A:$i] : ((~ (sk1 @ sk2)) | (A != (sk3 @ B)) | ((sk4 @ A @ (^ [C:$i]: (($false)))) != (sk3 @ B)))),inference(simp,[status(thm)],[345])).
% 20.16/5.83 thf(372,plain,(! [A:$i] : ((~ (sk1 @ sk2)) | ((sk4 @ (sk3 @ A) @ (^ [B:$i]: (($false)))) != (sk3 @ A)))),inference(simp,[status(thm)],[363])).
% 20.16/5.83 thf(1423,plain,(! [A:$i] : ((~ (sk1 @ sk2)) | (~ (sk1 @ sk2)) | ~ (($true)) | ((r @ sk2 @ (sk4 @ sk2 @ (^ [B:$i]: ~ (sk1 @ B)))) != (r @ (sk3 @ A) @ (sk3 @ A))))),inference(paramod_ordered,[status(thm)],[1271,9])).
% 20.16/5.83 thf(1424,plain,(! [A:$i] : ((~ (sk1 @ sk2)) | ((r @ sk2 @ (sk4 @ sk2 @ (^ [B:$i]: ~ (sk1 @ B)))) != (r @ (sk3 @ A) @ (sk3 @ A))))),inference(simp,[status(thm)],[1423])).
% 20.16/5.83 thf(1455,plain,(! [A:$i] : ((~ (sk1 @ sk2)) | ((sk3 @ A) != sk2) | ((sk4 @ sk2 @ (^ [B:$i]: ~ (sk1 @ B))) != (sk3 @ A)))),inference(simp,[status(thm)],[1424])).
% 20.16/5.83 thf(1073,plain,(! [A:$i] : ((~ (prop_c @ (sk4 @ A @ (prop_c)))) | (prop_c @ A) | (~ (sk1 @ sk2)))),inference(prim_subst,[status(thm)],[251:[bind(A, $thf(prop_c))]])).
% 20.16/5.83 thf(1132,plain,(! [A:$i] : ((~ (prop_c @ (sk4 @ A @ (prop_c)))) | (prop_c @ A) | (~ (sk1 @ sk2)))),inference(simp,[status(thm)],[1073])).
% 20.16/5.83 thf(1078,plain,(! [A:$i] : ((~ (prop_a @ (sk4 @ A @ (prop_a)))) | (prop_a @ A) | (~ (sk1 @ sk2)))),inference(prim_subst,[status(thm)],[251:[bind(A, $thf(prop_a))]])).
% 20.16/5.83 thf(1136,plain,(! [A:$i] : ((~ (prop_a @ (sk4 @ A @ (prop_a)))) | (prop_a @ A) | (~ (sk1 @ sk2)))),inference(simp,[status(thm)],[1078])).
% 20.16/5.83 thf(231,plain,(! [B:$i,A:$i] : ((r @ A @ (sk4 @ A @ (^ [C:$i]: (($false))))) | (B != A) | (B != (sk4 @ A @ (^ [C:$i]: (($false))))))),inference(simp,[status(thm)],[224])).
% 20.16/5.83 thf(238,plain,(! [A:$i] : ((r @ A @ (sk4 @ A @ (^ [B:$i]: (($false))))) | ((sk4 @ A @ (^ [B:$i]: (($false)))) != A))),inference(simp,[status(thm)],[231])).
% 20.16/5.83 thf(1536,plain,(! [B:$i,A:$i] : ((~ (sk1 @ sk2)) | (~ (sk1 @ sk2)) | ~ (($true)) | ((r @ A @ (sk4 @ A @ (^ [C:$i]: ~ (sk1 @ sk2)))) != (r @ (sk3 @ B) @ (sk3 @ B))))),inference(paramod_ordered,[status(thm)],[1414,9])).
% 20.16/5.83 thf(1537,plain,(! [B:$i,A:$i] : ((~ (sk1 @ sk2)) | ((r @ A @ (sk4 @ A @ (^ [C:$i]: ~ (sk1 @ sk2)))) != (r @ (sk3 @ B) @ (sk3 @ B))))),inference(simp,[status(thm)],[1536])).
% 20.16/5.83 thf(1584,plain,(! [B:$i,A:$i] : ((~ (sk1 @ sk2)) | (A != (sk3 @ B)) | ((sk4 @ A @ (^ [C:$i]: ~ (sk1 @ sk2))) != (sk3 @ B)))),inference(simp,[status(thm)],[1537])).
% 20.16/5.83 thf(1604,plain,(! [A:$i] : ((~ (sk1 @ sk2)) | ((sk4 @ (sk3 @ A) @ (^ [B:$i]: ~ (sk1 @ sk2))) != (sk3 @ A)))),inference(simp,[status(thm)],[1584])).
% 20.16/5.83 thf(1257,plain,(! [A:$i] : ((r @ A @ (sk4 @ A @ (prop_b))) | (prop_b @ A) | (~ (sk1 @ sk2)))),inference(prim_subst,[status(thm)],[42:[bind(A, $thf(prop_b))]])).
% 20.16/5.83 thf(1402,plain,(! [A:$i] : ((r @ A @ (sk4 @ A @ (prop_b))) | (prop_b @ A) | (~ (sk1 @ sk2)))),inference(simp,[status(thm)],[1257])).
% 20.16/5.83 thf(279,plain,(! [B:$i,A:$i] : ((~ (prop_c @ (sk4 @ A @ (prop_c)))) | (prop_c @ A) | (r @ B @ B))),inference(prim_subst,[status(thm)],[12:[bind(A, $thf(prop_c))]])).
% 20.16/5.83 thf(317,plain,(! [B:$i,A:$i] : ((~ (prop_c @ (sk4 @ A @ (prop_c)))) | (prop_c @ A) | (r @ B @ B))),inference(simp,[status(thm)],[279])).
% 20.16/5.83 thf(15,plain,(! [A:$i] : ((sk1 @ A) | (~ (r @ sk2 @ A)) | ((sk3 @ A) != sk2) | ((sk3 @ A) != A))),inference(simp,[status(thm)],[13])).
% 20.16/5.83 thf(358,plain,(! [B:$i,A:$i] : ((~ (sk1 @ sk2)) | (sk1 @ B) | ~ (($true)) | ((sk3 @ B) != sk2) | ((sk3 @ B) != B) | ((r @ A @ (sk4 @ A @ (^ [C:$i]: (($false))))) != (r @ sk2 @ B)))),inference(paramod_ordered,[status(thm)],[200,15])).
% 20.16/5.83 thf(359,plain,(! [B:$i,A:$i] : ((~ (sk1 @ sk2)) | (sk1 @ B) | ((sk3 @ B) != sk2) | ((sk3 @ B) != B) | ((r @ A @ (sk4 @ A @ (^ [C:$i]: (($false))))) != (r @ sk2 @ B)))),inference(simp,[status(thm)],[358])).
% 20.16/5.83 thf(360,plain,((~ (sk1 @ sk2)) | (sk1 @ (sk4 @ sk2 @ (^ [A:$i]: (($false))))) | ((sk3 @ (sk4 @ sk2 @ (^ [A:$i]: (($false))))) != sk2) | ((sk3 @ (sk4 @ sk2 @ (^ [A:$i]: (($false))))) != (sk4 @ sk2 @ (^ [A:$i]: (($false)))))),inference(pattern_uni,[status(thm)],[359:[bind(A, $thf(sk2)),bind(B, $thf(sk4 @ sk2 @ (^ [C:$i]: (($false)))))]])).
% 20.16/5.83 thf(17,plain,(! [A:$i] : ((sk1 @ A) | (~ (r @ sk2 @ A)) | ((sk3 @ A) != sk2) | ((sk3 @ A) != (sk3 @ A)) | (A != sk2))),inference(eqfactor_ordered,[status(thm)],[15])).
% 20.16/5.83 thf(18,plain,((sk1 @ sk2) | (~ (r @ sk2 @ sk2)) | ((sk3 @ sk2) != sk2)),inference(pattern_uni,[status(thm)],[17:[bind(A, $thf(sk2))]])).
% 20.16/5.83 thf(203,plain,(! [B:$i,A:$i] : ((r @ A @ (sk4 @ A @ (^ [C:$i]: (($false))))) | (sk1 @ sk2) | ~ (($true)) | ((sk3 @ sk2) != sk2) | ((r @ B @ B) != (r @ sk2 @ sk2)))),inference(paramod_ordered,[status(thm)],[127,18])).
% 20.16/5.83 thf(204,plain,(! [B:$i,A:$i] : ((r @ A @ (sk4 @ A @ (^ [C:$i]: (($false))))) | (sk1 @ sk2) | ((sk3 @ sk2) != sk2) | ((r @ B @ B) != (r @ sk2 @ sk2)))),inference(simp,[status(thm)],[203])).
% 20.16/5.83 thf(205,plain,(! [A:$i] : ((r @ A @ (sk4 @ A @ (^ [B:$i]: (($false))))) | (sk1 @ sk2) | ((sk3 @ sk2) != sk2))),inference(pattern_uni,[status(thm)],[204:[bind(A, $thf(A)),bind(B, $thf(sk2))]])).
% 20.16/5.83 thf(28,plain,(! [D:$i,C:$i,B:$i,A:($i > $o)] : ((r @ B @ (sk4 @ B @ (A))) | (A @ B) | (sk1 @ D) | ~ (($true)) | ((r @ (sk3 @ D) @ (sk3 @ D)) != (r @ sk2 @ D)) | ((r @ C @ C) != (r @ sk2 @ D)))),inference(paramod_ordered,[status(thm)],[11,14])).
% 20.16/5.83 thf(29,plain,(! [D:$i,C:$i,B:$i,A:($i > $o)] : ((r @ B @ (sk4 @ B @ (A))) | (A @ B) | (sk1 @ D) | ((r @ (sk3 @ D) @ (sk3 @ D)) != (r @ sk2 @ D)) | ((r @ C @ C) != (r @ sk2 @ D)))),inference(simp,[status(thm)],[28])).
% 20.16/5.83 thf(30,plain,(! [B:$i,A:($i > $o)] : ((r @ B @ (sk4 @ B @ (A))) | (A @ B) | (sk1 @ sk2) | ((r @ (sk3 @ sk2) @ (sk3 @ sk2)) != (r @ sk2 @ sk2)))),inference(pattern_uni,[status(thm)],[29:[bind(A, $thf(A)),bind(B, $thf(B)),bind(C, $thf(sk2)),bind(D, $thf(sk2))]])).
% 20.16/5.83 thf(696,plain,(! [B:$i,A:($i > $o)] : ((r @ B @ (sk4 @ B @ (A))) | (sk1 @ sk2) | ((r @ (sk3 @ sk2) @ (sk3 @ sk2)) != (r @ sk2 @ sk2)) | ((A @ B) != (sk1 @ sk2)) | ~ (($true)))),inference(eqfactor_ordered,[status(thm)],[30])).
% 20.16/5.83 thf(775,plain,((r @ sk2 @ (sk4 @ sk2 @ (sk1))) | (sk1 @ sk2) | ((r @ (sk3 @ sk2) @ (sk3 @ sk2)) != (r @ sk2 @ sk2))),inference(pre_uni,[status(thm)],[696:[bind(A, $thf(sk1)),bind(B, $thf(sk2))]])).
% 20.16/5.83 thf(881,plain,((sk1 @ sk2) | ((r @ (sk3 @ sk2) @ (sk3 @ sk2)) != (r @ sk2 @ sk2)) | (sk1 @ sk2) | ~ (($true)) | ((sk3 @ sk2) != sk2) | ((r @ sk2 @ (sk4 @ sk2 @ (sk1))) != (r @ sk2 @ sk2))),inference(paramod_ordered,[status(thm)],[775,18])).
% 20.16/5.83 thf(882,plain,((sk1 @ sk2) | ((r @ (sk3 @ sk2) @ (sk3 @ sk2)) != (r @ sk2 @ sk2)) | ((sk3 @ sk2) != sk2) | ((r @ sk2 @ (sk4 @ sk2 @ (sk1))) != (r @ sk2 @ sk2))),inference(simp,[status(thm)],[881])).
% 20.16/5.83 thf(932,plain,((sk1 @ sk2) | ((sk3 @ sk2) != sk2) | ((sk3 @ sk2) != sk2) | ((sk3 @ sk2) != sk2) | ((r @ sk2 @ (sk4 @ sk2 @ (sk1))) != (r @ sk2 @ sk2))),inference(simp,[status(thm)],[882])).
% 20.16/5.83 thf(965,plain,((sk1 @ sk2) | ((sk3 @ sk2) != sk2) | ((r @ sk2 @ (sk4 @ sk2 @ (sk1))) != (r @ sk2 @ sk2))),inference(simp,[status(thm)],[932])).
% 20.16/5.83 thf(351,plain,(! [D:$i,C:$i,B:$i,A:($i > $o)] : ((r @ B @ (sk4 @ B @ (A))) | (r @ C @ C) | (r @ D @ (sk4 @ D @ (^ [E:$i]: (($false))))) | ~ (($true)) | ((A @ B) != (sk1 @ sk2)))),inference(paramod_ordered,[status(thm)],[11,200])).
% 20.16/5.83 thf(352,plain,(! [D:$i,C:$i,B:$i,A:($i > $o)] : ((r @ B @ (sk4 @ B @ (A))) | (r @ C @ C) | (r @ D @ (sk4 @ D @ (^ [E:$i]: (($false))))) | ((A @ B) != (sk1 @ sk2)))),inference(simp,[status(thm)],[351])).
% 20.16/5.83 thf(367,plain,(! [B:$i,A:$i] : ((r @ sk2 @ (sk4 @ sk2 @ (sk1))) | (r @ A @ A) | (r @ B @ (sk4 @ B @ (^ [C:$i]: (($false))))))),inference(pre_uni,[status(thm)],[352:[bind(A, $thf(sk1)),bind(B, $thf(sk2)),bind(C, $thf(C)),bind(D, $thf(D))]])).
% 20.16/5.83 thf(375,plain,(! [B:$i,A:$i] : ((r @ sk2 @ (sk4 @ sk2 @ (sk1))) | (r @ A @ A) | (r @ B @ (sk4 @ B @ (^ [C:$i]: (($false))))))),inference(simp,[status(thm)],[367])).
% 20.16/5.83 thf(862,plain,((r @ sk2 @ (sk4 @ sk2 @ (sk1))) | (sk1 @ sk2) | ((sk3 @ sk2) != sk2) | ((sk3 @ sk2) != sk2)),inference(simp,[status(thm)],[775])).
% 20.16/5.83 thf(959,plain,((r @ sk2 @ (sk4 @ sk2 @ (sk1))) | (sk1 @ sk2) | ((sk3 @ sk2) != sk2)),inference(simp,[status(thm)],[862])).
% 20.16/5.83 thf(1750,plain,(! [A:$i] : ((r @ sk2 @ (sk4 @ sk2 @ (sk1))) | (r @ sk2 @ (sk4 @ sk2 @ (^ [B:$i]: ~ (sk1 @ B)))) | ((r @ A @ A) != (r @ sk2 @ (sk4 @ sk2 @ (sk1)))) | ~ (($true)))),inference(eqfactor_ordered,[status(thm)],[1467])).
% 20.16/5.83 thf(1754,plain,(! [A:$i] : ((r @ sk2 @ (sk4 @ sk2 @ (sk1))) | (r @ sk2 @ (sk4 @ sk2 @ (^ [B:$i]: ~ (sk1 @ B)))) | (A != sk2) | (A != (sk4 @ sk2 @ (sk1))))),inference(simp,[status(thm)],[1750])).
% 20.16/5.83 thf(1775,plain,((r @ sk2 @ (sk4 @ sk2 @ (sk1))) | (r @ sk2 @ (sk4 @ sk2 @ (^ [A:$i]: ~ (sk1 @ A)))) | ((sk4 @ sk2 @ (sk1)) != sk2)),inference(simp,[status(thm)],[1754])).
% 20.16/5.83 thf(1472,plain,(! [B:$i,A:$i] : ((~ (sk1 @ sk2)) | (~ (sk1 @ sk2)) | ~ (($true)) | ((r @ (sk3 @ A) @ (sk4 @ (sk3 @ A) @ (^ [C:$i]: (r @ C @ C)))) != (r @ (sk3 @ B) @ (sk3 @ B))))),inference(paramod_ordered,[status(thm)],[1354,9])).
% 20.16/5.83 thf(1473,plain,(! [B:$i,A:$i] : ((~ (sk1 @ sk2)) | ((r @ (sk3 @ A) @ (sk4 @ (sk3 @ A) @ (^ [C:$i]: (r @ C @ C)))) != (r @ (sk3 @ B) @ (sk3 @ B))))),inference(simp,[status(thm)],[1472])).
% 20.16/5.83 thf(1513,plain,(! [B:$i,A:$i] : ((~ (sk1 @ sk2)) | ((sk3 @ A) != (sk3 @ B)) | ((sk4 @ (sk3 @ A) @ (^ [C:$i]: (r @ C @ C))) != (sk3 @ B)))),inference(simp,[status(thm)],[1473])).
% 20.16/5.83 thf(1675,plain,(! [B:$i,A:$i] : ((~ (sk1 @ sk2)) | (A != B) | ((sk4 @ (sk3 @ A) @ (^ [C:$i]: (r @ C @ C))) != (sk3 @ B)))),inference(simp,[status(thm)],[1513])).
% 20.16/5.83 thf(1694,plain,(! [A:$i] : ((~ (sk1 @ sk2)) | ((sk4 @ (sk3 @ A) @ (^ [B:$i]: (r @ B @ B))) != (sk3 @ A)))),inference(simp,[status(thm)],[1675])).
% 20.16/5.83 thf(1076,plain,(! [A:$i] : ((~ (prop_b @ (sk4 @ A @ (prop_b)))) | (prop_b @ A) | (~ (sk1 @ sk2)))),inference(prim_subst,[status(thm)],[251:[bind(A, $thf(prop_b))]])).
% 20.16/5.83 thf(1134,plain,(! [A:$i] : ((~ (prop_b @ (sk4 @ A @ (prop_b)))) | (prop_b @ A) | (~ (sk1 @ sk2)))),inference(simp,[status(thm)],[1076])).
% 20.16/5.83 thf(1752,plain,(! [A:$i] : ((r @ sk2 @ (sk4 @ sk2 @ (sk1))) | (r @ A @ A) | ((r @ sk2 @ (sk4 @ sk2 @ (^ [B:$i]: ~ (sk1 @ B)))) != (r @ A @ A)) | ~ (($true)))),inference(eqfactor_ordered,[status(thm)],[1467])).
% 20.16/5.83 thf(1762,plain,(! [A:$i] : ((r @ sk2 @ (sk4 @ sk2 @ (sk1))) | (r @ A @ A) | (sk2 != A) | ((sk4 @ sk2 @ (^ [B:$i]: ~ (sk1 @ B))) != A))),inference(simp,[status(thm)],[1752])).
% 20.16/5.83 thf(1780,plain,((r @ sk2 @ (sk4 @ sk2 @ (sk1))) | (r @ sk2 @ sk2) | ((sk4 @ sk2 @ (^ [A:$i]: ~ (sk1 @ A))) != sk2)),inference(simp,[status(thm)],[1762])).
% 20.16/5.83 thf(68,plain,(! [C:$i,B:$i,A:($i > $o)] : ((r @ B @ (sk4 @ B @ (A))) | (r @ C @ C) | ((A @ B) != (r @ B @ (sk4 @ B @ (A)))) | ~ (($true)))),inference(eqfactor_ordered,[status(thm)],[11])).
% 20.16/5.83 thf(119,plain,(! [C:$i,B:$i,A:($i > $o)] : ((r @ B @ (sk4 @ B @ (A))) | (r @ C @ C) | ((A @ B) != (r @ B @ (sk4 @ B @ (A)))))),inference(simp,[status(thm)],[68])).
% 20.16/5.83 thf(69,plain,(! [C:$i,B:$i,A:($i > $o)] : ((r @ B @ (sk4 @ B @ (A))) | (A @ B) | ((r @ C @ C) != (r @ B @ (sk4 @ B @ (A)))) | ~ (($true)))),inference(eqfactor_ordered,[status(thm)],[11])).
% 20.16/5.83 thf(82,plain,(! [C:$i,B:$i,A:($i > $o)] : ((r @ B @ (sk4 @ B @ (A))) | (A @ B) | ((r @ C @ C) != (r @ B @ (sk4 @ B @ (A)))))),inference(simp,[status(thm)],[69])).
% 20.16/5.83 thf(934,plain,((sk1 @ sk2) | ((sk3 @ sk2) != sk2) | ((sk3 @ sk2) != sk2) | ((sk3 @ sk2) != sk2) | (sk2 != sk2) | ((sk4 @ sk2 @ (sk1)) != sk2)),inference(simp,[status(thm)],[882])).
% 20.16/5.83 thf(967,plain,((sk1 @ sk2) | ((sk3 @ sk2) != sk2) | ((sk4 @ sk2 @ (sk1)) != sk2)),inference(simp,[status(thm)],[934])).
% 20.16/5.83 thf(3323,plain,(! [A:$i] : ((r @ A @ (sk4 @ A @ (^ [B:$i]: (($false))))) | (sk1 @ sk2) | ((r @ sk2 @ (sk4 @ sk2 @ (sk1))) != (r @ A @ (sk4 @ A @ (^ [B:$i]: (($false)))))) | ~ (($true)))),inference(eqfactor_ordered,[status(thm)],[2307])).
% 20.16/5.83 thf(3348,plain,(! [A:$i] : ((r @ A @ (sk4 @ A @ (^ [B:$i]: (($false))))) | (sk1 @ sk2) | (sk2 != A) | ((sk4 @ sk2 @ (sk1)) != (sk4 @ A @ (^ [B:$i]: (($false))))))),inference(simp,[status(thm)],[3323])).
% 20.16/5.83 thf(3362,plain,((r @ sk2 @ (sk4 @ sk2 @ (^ [A:$i]: (($false))))) | (sk1 @ sk2) | ((sk4 @ sk2 @ (sk1)) != (sk4 @ sk2 @ (^ [A:$i]: (($false)))))),inference(simp,[status(thm)],[3348])).
% 20.16/5.83 thf(1255,plain,(! [A:$i] : ((r @ A @ (sk4 @ A @ (prop_c))) | (prop_c @ A) | (~ (sk1 @ sk2)))),inference(prim_subst,[status(thm)],[42:[bind(A, $thf(prop_c))]])).
% 20.16/5.83 thf(1399,plain,(! [A:$i] : ((r @ A @ (sk4 @ A @ (prop_c))) | (prop_c @ A) | (~ (sk1 @ sk2)))),inference(simp,[status(thm)],[1255])).
% 20.16/5.83 thf(389,plain,(! [A:$i] : (((sk4 @ A @ (^ [B:$i]: (($false)))) != A) | (sk1 @ sk2) | ~ (($true)) | ((sk3 @ sk2) != sk2) | ((r @ A @ (sk4 @ A @ (^ [B:$i]: (($false))))) != (r @ sk2 @ sk2)))),inference(paramod_ordered,[status(thm)],[238,18])).
% 20.16/5.83 thf(390,plain,(! [A:$i] : (((sk4 @ A @ (^ [B:$i]: (($false)))) != A) | (sk1 @ sk2) | ((sk3 @ sk2) != sk2) | ((r @ A @ (sk4 @ A @ (^ [B:$i]: (($false))))) != (r @ sk2 @ sk2)))),inference(simp,[status(thm)],[389])).
% 20.16/5.83 thf(412,plain,(! [A:$i] : ((sk1 @ sk2) | ((sk4 @ A @ (^ [B:$i]: (($false)))) != A) | ((sk3 @ sk2) != sk2) | (A != sk2) | ((sk4 @ A @ (^ [B:$i]: (($false)))) != sk2))),inference(simp,[status(thm)],[390])).
% 20.16/5.83 thf(419,plain,((sk1 @ sk2) | ((sk4 @ sk2 @ (^ [A:$i]: (($false)))) != sk2) | ((sk3 @ sk2) != sk2) | ((sk4 @ sk2 @ (^ [A:$i]: (($false)))) != sk2)),inference(simp,[status(thm)],[412])).
% 20.16/5.83 thf(469,plain,((sk1 @ sk2) | ((sk4 @ sk2 @ (^ [A:$i]: (($false)))) != sk2) | ((sk3 @ sk2) != sk2)),inference(simp,[status(thm)],[419])).
% 20.16/5.83 thf(3913,plain,(($false)),inference(e,[status(thm)],[1354,2560,1407,1414,230,251,127,11,3350,42,14,372,1455,1132,1136,238,1604,2307,1402,317,9,360,205,965,375,12,54,1271,959,1775,3,1694,1467,1134,18,1780,8,119,1513,2120,82,967,30,4,2340,3362,15,200,1399,469,775])).
% 20.16/5.83 % SZS output end Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% 20.16/5.83 % [INFO] Killing All external provers ...
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