%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWV431^2 : TPTP v9.3.1. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n016.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 08:39:52 AM UTC 2026
% Result : Theorem 87.54s 18.57s
% Output : Refutation 75.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV431^2 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.11/0.24 % Computer : n016.cluster.edu
% 0.11/0.24 % Model : x86_64 x86_64
% 0.11/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.24 % Memory : 8046.5625MB
% 0.11/0.24 % OS : Linux 6.8.0-71-generic
% 0.11/0.24 % CPULimit : 300
% 0.11/0.24 % WCLimit : 300
% 0.11/0.24 % DateTime : Tue Sep 29 16:08:19 UTC 2026
% 0.11/0.24 % CPUTime :
% 0.11/0.24 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 1.17/1.05 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 2.27/1.45 % [INFO] Parsing done (392ms).
% 2.27/1.47 % [INFO] Running in sequential loop mode.
% 3.13/2.00 % [INFO] eprover registered as external prover.
% 3.13/2.02 % [INFO] Scanning for conjecture ...
% 3.75/2.21 % [INFO] Found a conjecture (or negated_conjecture) and 2 axioms. Running axiom selection ...
% 3.75/2.26 % [INFO] Axiom selection finished. Selected 2 axioms (removed 0 axioms).
% 3.75/2.27 % [INFO] Problem is higher-order (TPTP THF).
% 3.75/2.27 % [INFO] Type checking passed.
% 3.75/2.28 % [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 ...
% 87.54/18.56 % External prover 'e' found a proof!
% 87.54/18.56 % [INFO] Killing All external provers ...
% 87.54/18.57 % Time passed: 18102ms (effective reasoning time: 17087ms)
% 87.54/18.57 % 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)>
% 87.54/18.57 % Axioms used in derivation (2): refl_axiom, trans_axiom
% 87.54/18.57 % No. of inferences in proof: 276
% 87.54/18.57 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 18102 ms resp. 17087 ms w/o parsing
% 75.21/18.72 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 75.21/18.72 thf(individuals_type, type, individuals: $tType).
% 75.21/18.72 thf(prop_c_decl, type, prop_c: ($i > $o)).
% 75.21/18.72 thf(mnot_decl, type, mnot: (($i > $o) > ($i > $o))).
% 75.21/18.72 thf(mor_decl, type, mor: (($i > $o) > (($i > $o) > ($i > $o)))).
% 75.21/18.72 thf(mimpl_decl, type, mimpl: (($i > $o) > (($i > $o) > ($i > $o)))).
% 75.21/18.72 thf(mbox_decl, type, mbox: (($i > ($i > $o)) > (($i > $o) > ($i > $o)))).
% 75.21/18.72 thf(mvalid_decl, type, mvalid: (($i > $o) > $o)).
% 75.21/18.72 thf(rel_decl, type, rel: ($i > ($i > $o))).
% 75.21/18.72 thf(icl_atom_decl, type, icl_atom: (($i > $o) > ($i > $o))).
% 75.21/18.72 thf(icl_princ_decl, type, icl_princ: (($i > $o) > ($i > $o))).
% 75.21/18.72 thf(icl_impl_decl, type, icl_impl: (($i > $o) > (($i > $o) > ($i > $o)))).
% 75.21/18.72 thf(icl_says_decl, type, icl_says: (($i > $o) > (($i > $o) > ($i > $o)))).
% 75.21/18.72 thf(iclval_decl, type, iclval: (($i > $o) > $o)).
% 75.21/18.72 thf(icl_impl_princ_decl, type, icl_impl_princ: (($i > $o) > (($i > $o) > ($i > $o)))).
% 75.21/18.72 thf(a_decl, type, a: ($i > $o)).
% 75.21/18.72 thf(b_decl, type, b: ($i > $o)).
% 75.21/18.72 thf(s_decl, type, s: ($i > $o)).
% 75.21/18.72 thf(sk1_decl, type, sk1: $i).
% 75.21/18.72 thf(sk2_decl, type, sk2: $i).
% 75.21/18.72 thf(sk3_decl, type, sk3: $i).
% 75.21/18.72 thf(sk4_decl, type, sk4: $i).
% 75.21/18.72 thf(sk5_decl, type, sk5: $i).
% 75.21/18.72 thf(sk6_decl, type, sk6: ($i > (($i > $o) > $i))).
% 75.21/18.72 thf(sk7_decl, type, sk7: ($i > (($i > $o) > $i))).
% 75.21/18.72 thf(mnot_def, definition, mnot = (^ [A:($i > $o),B:$i]: ~ (A @ B)) ).
% 75.21/18.72 thf(mor_def, definition, mor = (^ [A:($i > $o),B:($i > $o),C:$i]: ((A @ C) | (B @ C))) ).
% 75.21/18.72 thf(mimpl_def, definition, mimpl = (^ [A:($i > $o)]: (mor @ (mnot @ A))) ).
% 75.21/18.72 thf(mbox_def, definition, mbox = (^ [A:($i > ($i > $o)),B:($i > $o),C:$i]: ! [D:$i]: ((A @ C @ D) => (B @ D))) ).
% 75.21/18.72 thf(mvalid_def, definition, mvalid = ((!) @ $i) ).
% 75.21/18.72 thf(icl_atom_def, definition, icl_atom = (mbox @ rel) ).
% 75.21/18.72 thf(icl_princ_def, definition, icl_princ = (^ [A:($i > $o)]: (A)) ).
% 75.21/18.72 thf(icl_impl_def, definition, icl_impl = (^ [A:($i > $o),B:($i > $o)]: (mbox @ rel @ (mimpl @ A @ B))) ).
% 75.21/18.72 thf(icl_says_def, definition, icl_says = (^ [A:($i > $o),B:($i > $o)]: (mbox @ rel @ (mor @ A @ B))) ).
% 75.21/18.72 thf(iclval_def, definition, iclval = (mvalid) ).
% 75.21/18.72 thf(icl_impl_princ_def, definition, icl_impl_princ = (^ [A:($i > $o),B:($i > $o)]: (mbox @ rel @ (mimpl @ A @ B))) ).
% 75.21/18.72 thf(sk1_def, definition, sk1 = (@+ [A:$i]: ~ (! [B:$i]: ((rel @ A @ B) => (~ (! [C:$i]: ((rel @ B @ C) => (~ (a @ C) | (b @ C)))) | ! [C:$i]: ((rel @ B @ C) => (~ (! [D:$i]: ((rel @ C @ D) => ((a @ D) | ! [E:$i]: ((rel @ D @ E) => (s @ E))))) | ! [D:$i]: ((rel @ C @ D) => ((b @ D) | ! [E:$i]: ((rel @ D @ E) => (s @ E)))))))))) ).
% 75.21/18.72 thf(sk2_def, definition, sk2 = (@+ [A:$i]: ~ ((rel @ sk1 @ A) => (~ (! [B:$i]: ((rel @ A @ B) => (~ (a @ B) | (b @ B)))) | ! [B:$i]: ((rel @ A @ B) => (~ (! [C:$i]: ((rel @ B @ C) => ((a @ C) | ! [D:$i]: ((rel @ C @ D) => (s @ D))))) | ! [C:$i]: ((rel @ B @ C) => ((b @ C) | ! [D:$i]: ((rel @ C @ D) => (s @ D))))))))) ).
% 75.21/18.72 thf(sk3_def, definition, sk3 = (@+ [A:$i]: ~ ((rel @ sk2 @ A) => (~ (! [B:$i]: ((rel @ A @ B) => ((a @ B) | ! [C:$i]: ((rel @ B @ C) => (s @ C))))) | ! [B:$i]: ((rel @ A @ B) => ((b @ B) | ! [C:$i]: ((rel @ B @ C) => (s @ C))))))) ).
% 75.21/18.72 thf(sk4_def, definition, sk4 = (@+ [A:$i]: ~ ((rel @ sk3 @ A) => ((b @ A) | ! [B:$i]: ((rel @ A @ B) => (s @ B))))) ).
% 75.21/18.72 thf(sk5_def, definition, sk5 = (@+ [A:$i]: ~ ((rel @ sk4 @ A) => (s @ A))) ).
% 75.21/18.72 thf(sk6_def, definition, sk6 = (^ [A:$i,B:($i > $o)]: (@+ [C:$i]: ~ ((rel @ A @ C) => (B @ C)))) ).
% 75.21/18.72 thf(sk7_def, definition, sk7 = (^ [A:$i,B:($i > $o)]: (@+ [C:$i]: ~ ((rel @ A @ C) => (B @ C)))) ).
% 75.21/18.72 thf(3,axiom,((! [A:($i > $o)]: (mvalid @ (mimpl @ (mbox @ rel @ A) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',refl_axiom)).
% 75.21/18.72 thf(16,plain,((! [A:($i > $o),B:$i]: (~ (! [C:$i]: ((rel @ B @ C) => (A @ C))) | (A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3])).
% 75.21/18.72 thf(17,plain,(! [B:$i,A:($i > $o)] : ((((rel @ B @ (sk6 @ B @ (A))) | (A @ B)) & (~ (A @ (sk6 @ B @ (A))) | (A @ B))))),inference(cnf,[status(esa)],[16])).
% 75.21/18.72 thf(18,plain,(! [B:$i,A:($i > $o)] : ((rel @ B @ (sk6 @ B @ (A))) | (A @ B))),inference(cnfConj,[status(thm)],[17])).
% 75.21/18.72 thf(452,plain,(! [A:$i] : ((rel @ A @ (sk6 @ A @ (^ [B:$i]: (($false))))) | ($false))),inference(prim_subst,[status(thm)],[18:[bind(A, $thf(^ [C:$i]: (($false))))]])).
% 75.21/18.72 thf(519,plain,(! [A:$i] : ((rel @ A @ (sk6 @ A @ (^ [B:$i]: (($false))))))),inference(simp,[status(thm)],[452])).
% 75.21/18.72 thf(1,conjecture,((iclval @ (icl_impl @ (icl_impl_princ @ (icl_princ @ a) @ (icl_princ @ b)) @ (icl_impl @ (icl_says @ (icl_princ @ a) @ (icl_atom @ s)) @ (icl_says @ (icl_princ @ b) @ (icl_atom @ s)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',speaking_for)).
% 75.21/18.72 thf(2,negated_conjecture,((~ (iclval @ (icl_impl @ (icl_impl_princ @ (icl_princ @ a) @ (icl_princ @ b)) @ (icl_impl @ (icl_says @ (icl_princ @ a) @ (icl_atom @ s)) @ (icl_says @ (icl_princ @ b) @ (icl_atom @ s))))))),inference(neg_conjecture,[status(cth)],[1])).
% 75.21/18.72 thf(5,plain,((~ (! [A:$i,B:$i]: ((rel @ A @ B) => (~ (! [C:$i]: ((rel @ B @ C) => (~ (a @ C) | (b @ C)))) | ! [C:$i]: ((rel @ B @ C) => (~ (! [D:$i]: ((rel @ C @ D) => ((a @ D) | ! [E:$i]: ((rel @ D @ E) => (s @ E))))) | ! [D:$i]: ((rel @ C @ D) => ((b @ D) | ! [E:$i]: ((rel @ D @ E) => (s @ E))))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])).
% 75.21/18.72 thf(6,plain,(! [C:$i,B:$i,A:$i] : (((rel @ sk1 @ sk2) & (~ (rel @ sk2 @ A) | ~ (a @ A) | (b @ A)) & (rel @ sk2 @ sk3) & (~ (rel @ sk3 @ B) | (a @ B) | ~ (rel @ B @ C) | (s @ C)) & (rel @ sk3 @ sk4) & ~ (b @ sk4) & (rel @ sk4 @ sk5) & ~ (s @ sk5)))),inference(cnf,[status(esa)],[5])).
% 75.21/18.72 thf(11,plain,((rel @ sk2 @ sk3)),inference(cnfConj,[status(thm)],[6])).
% 75.21/18.72 thf(4,axiom,((! [A:($i > $o)]: (mvalid @ (mimpl @ (mbox @ rel @ A) @ (mbox @ rel @ (mbox @ rel @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',trans_axiom)).
% 75.21/18.72 thf(22,plain,((! [A:($i > $o),B:$i]: (~ (! [C:$i]: ((rel @ B @ C) => (A @ C))) | ! [C:$i]: ((rel @ B @ C) => (! [D:$i]: ((rel @ C @ D) => (A @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4])).
% 75.21/18.72 thf(23,plain,(! [D:$i,C:$i,B:$i,A:($i > $o)] : ((((rel @ B @ (sk7 @ B @ (A))) | ~ (rel @ B @ C) | ~ (rel @ C @ D) | (A @ D)) & (~ (A @ (sk7 @ B @ (A))) | ~ (rel @ B @ C) | ~ (rel @ C @ D) | (A @ D))))),inference(cnf,[status(esa)],[22])).
% 75.21/18.72 thf(25,plain,(! [D:$i,C:$i,B:$i,A:($i > $o)] : ((~ (A @ (sk7 @ B @ (A)))) | (~ (rel @ B @ C)) | (~ (rel @ C @ D)) | (A @ D))),inference(cnfConj,[status(thm)],[23])).
% 75.21/18.72 thf(9,plain,((~ (s @ sk5))),inference(cnfConj,[status(thm)],[6])).
% 75.21/18.72 thf(36,plain,(! [D:$i,C:$i,B:$i,A:($i > $o)] : ((~ (A @ (sk7 @ B @ (A)))) | (~ (rel @ B @ C)) | (~ (rel @ C @ D)) | ~ (($true)) | ((A @ D) != (s @ sk5)))),inference(paramod_ordered,[status(thm)],[25,9])).
% 75.21/18.72 thf(37,plain,(! [D:$i,C:$i,B:$i,A:($i > $o)] : ((~ (A @ (sk7 @ B @ (A)))) | (~ (rel @ B @ C)) | (~ (rel @ C @ D)) | ((A @ D) != (s @ sk5)))),inference(simp,[status(thm)],[36])).
% 75.21/18.72 thf(101,plain,(! [B:$i,A:$i] : ((~ (s @ (sk7 @ A @ (s)))) | (~ (rel @ A @ B)) | (~ (rel @ B @ sk5)))),inference(pre_uni,[status(thm)],[37:[bind(A, $thf(s)),bind(B, $thf(B)),bind(C, $thf(C)),bind(D, $thf(sk5))]])).
% 75.21/18.72 thf(141,plain,(! [B:$i,A:$i] : ((~ (s @ (sk7 @ A @ (s)))) | (~ (rel @ A @ B)) | (~ (rel @ B @ sk5)))),inference(simp,[status(thm)],[101])).
% 75.21/18.72 thf(359,plain,(! [B:$i,A:$i] : ((~ (s @ (sk7 @ A @ (s)))) | ~ (($true)) | (~ (rel @ B @ sk5)) | ((rel @ sk2 @ sk3) != (rel @ A @ B)))),inference(paramod_ordered,[status(thm)],[11,141])).
% 75.21/18.72 thf(360,plain,(! [B:$i,A:$i] : ((~ (s @ (sk7 @ A @ (s)))) | (~ (rel @ B @ sk5)) | ((rel @ sk2 @ sk3) != (rel @ A @ B)))),inference(simp,[status(thm)],[359])).
% 75.21/18.72 thf(361,plain,((~ (s @ (sk7 @ sk2 @ (s)))) | (~ (rel @ sk3 @ sk5))),inference(pattern_uni,[status(thm)],[360:[bind(A, $thf(sk2)),bind(B, $thf(sk3))]])).
% 75.21/18.72 thf(1822,plain,(! [A:$i] : ((~ (s @ (sk7 @ sk2 @ (s)))) | ~ (($true)) | ((rel @ A @ (sk6 @ A @ (^ [B:$i]: (($false))))) != (rel @ sk3 @ sk5)))),inference(paramod_ordered,[status(thm)],[519,361])).
% 75.21/18.72 thf(1823,plain,(! [A:$i] : ((~ (s @ (sk7 @ sk2 @ (s)))) | ((rel @ A @ (sk6 @ A @ (^ [B:$i]: (($false))))) != (rel @ sk3 @ sk5)))),inference(simp,[status(thm)],[1822])).
% 75.21/18.72 thf(1857,plain,(! [A:$i] : ((~ (s @ (sk7 @ sk2 @ (s)))) | (A != sk3) | ((sk6 @ A @ (^ [B:$i]: (($false)))) != sk5))),inference(simp,[status(thm)],[1823])).
% 75.21/18.73 thf(1875,plain,((~ (s @ (sk7 @ sk2 @ (s)))) | ((sk6 @ sk3 @ (^ [A:$i]: (($false)))) != sk5)),inference(simp,[status(thm)],[1857])).
% 75.21/18.73 thf(14,plain,((rel @ sk3 @ sk4)),inference(cnfConj,[status(thm)],[6])).
% 75.21/18.73 thf(343,plain,(! [B:$i,A:$i] : ((~ (s @ (sk7 @ A @ (s)))) | ~ (($true)) | (~ (rel @ B @ sk5)) | ((rel @ sk3 @ sk4) != (rel @ A @ B)))),inference(paramod_ordered,[status(thm)],[14,141])).
% 75.21/18.73 thf(344,plain,(! [B:$i,A:$i] : ((~ (s @ (sk7 @ A @ (s)))) | (~ (rel @ B @ sk5)) | ((rel @ sk3 @ sk4) != (rel @ A @ B)))),inference(simp,[status(thm)],[343])).
% 75.21/18.73 thf(345,plain,((~ (s @ (sk7 @ sk3 @ (s)))) | (~ (rel @ sk4 @ sk5))),inference(pattern_uni,[status(thm)],[344:[bind(A, $thf(sk3)),bind(B, $thf(sk4))]])).
% 75.21/18.73 thf(12,plain,((rel @ sk4 @ sk5)),inference(cnfConj,[status(thm)],[6])).
% 75.21/18.73 thf(677,plain,((~ (s @ (sk7 @ sk3 @ (s)))) | ~ (($true))),inference(rewrite,[status(thm)],[345,12])).
% 75.21/18.73 thf(678,plain,((~ (s @ (sk7 @ sk3 @ (s))))),inference(simp,[status(thm)],[677])).
% 75.21/18.73 thf(681,plain,(! [B:$i,A:($i > $o)] : ((rel @ B @ (sk6 @ B @ (A))) | ~ (($true)) | ((A @ B) != (s @ (sk7 @ sk3 @ (s)))))),inference(paramod_ordered,[status(thm)],[18,678])).
% 75.21/18.73 thf(682,plain,(! [B:$i,A:($i > $o)] : ((rel @ B @ (sk6 @ B @ (A))) | ((A @ B) != (s @ (sk7 @ sk3 @ (s)))))),inference(simp,[status(thm)],[681])).
% 75.21/18.73 thf(688,plain,((rel @ sk3 @ (sk6 @ sk3 @ (^ [A:$i]: (s @ (sk7 @ A @ s)))))),inference(pre_uni,[status(thm)],[682:[bind(A, $thf(^ [C:$i]: (s @ (sk7 @ C @ s)))),bind(B, $thf(sk3))]])).
% 75.21/18.73 thf(1798,plain,((~ (s @ (sk7 @ sk2 @ (s)))) | ~ (($true)) | ((rel @ sk3 @ sk5) != (rel @ sk3 @ sk4))),inference(paramod_ordered,[status(thm)],[14,361])).
% 75.21/18.73 thf(1799,plain,((~ (s @ (sk7 @ sk2 @ (s)))) | ((rel @ sk3 @ sk5) != (rel @ sk3 @ sk4))),inference(simp,[status(thm)],[1798])).
% 75.21/18.73 thf(1864,plain,((~ (s @ (sk7 @ sk2 @ (s)))) | (sk3 != sk3) | (sk5 != sk4)),inference(simp,[status(thm)],[1799])).
% 75.21/18.73 thf(1879,plain,((~ (s @ (sk7 @ sk2 @ (s)))) | (sk5 != sk4)),inference(simp,[status(thm)],[1864])).
% 75.21/18.73 thf(8,plain,(! [B:$i,A:$i] : ((~ (rel @ sk3 @ A)) | (a @ A) | (~ (rel @ A @ B)) | (s @ B))),inference(cnfConj,[status(thm)],[6])).
% 75.21/18.73 thf(15,plain,(! [B:$i,A:$i] : ((~ (rel @ sk3 @ A)) | (a @ A) | (~ (rel @ A @ B)) | (s @ B))),inference(simp,[status(thm)],[8])).
% 75.21/18.73 thf(225,plain,(! [B:$i,A:$i] : ((~ (rel @ sk3 @ A)) | (a @ A) | ~ (($true)) | (s @ B) | ((rel @ sk4 @ sk5) != (rel @ A @ B)))),inference(paramod_ordered,[status(thm)],[12,15])).
% 75.21/18.73 thf(226,plain,(! [B:$i,A:$i] : ((~ (rel @ sk3 @ A)) | (a @ A) | (s @ B) | ((rel @ sk4 @ sk5) != (rel @ A @ B)))),inference(simp,[status(thm)],[225])).
% 75.21/18.73 thf(227,plain,((~ (rel @ sk3 @ sk4)) | (a @ sk4) | (s @ sk5)),inference(pattern_uni,[status(thm)],[226:[bind(A, $thf(sk4)),bind(B, $thf(sk5))]])).
% 75.21/18.73 thf(5970,plain,(~ (($true)) | (a @ sk4) | ($false)),inference(rewrite,[status(thm)],[227,9,14])).
% 75.21/18.73 thf(5971,plain,((a @ sk4)),inference(simp,[status(thm)],[5970])).
% 75.21/18.73 thf(13,plain,(! [A:$i] : ((~ (rel @ sk2 @ A)) | (~ (a @ A)) | (b @ A))),inference(cnfConj,[status(thm)],[6])).
% 75.21/18.73 thf(5987,plain,(! [A:$i] : ((~ (rel @ sk2 @ A)) | ~ (($true)) | (b @ A) | ((a @ sk4) != (a @ A)))),inference(paramod_ordered,[status(thm)],[5971,13])).
% 75.21/18.73 thf(5988,plain,(! [A:$i] : ((~ (rel @ sk2 @ A)) | (b @ A) | ((a @ sk4) != (a @ A)))),inference(simp,[status(thm)],[5987])).
% 75.21/18.73 thf(5989,plain,((~ (rel @ sk2 @ sk4)) | (b @ sk4)),inference(pattern_uni,[status(thm)],[5988:[bind(A, $thf(sk4))]])).
% 75.21/18.73 thf(10,plain,((~ (b @ sk4))),inference(cnfConj,[status(thm)],[6])).
% 75.21/18.73 thf(7389,plain,((~ (rel @ sk2 @ sk4)) | ($false)),inference(rewrite,[status(thm)],[5989,10])).
% 75.21/18.73 thf(7390,plain,((~ (rel @ sk2 @ sk4))),inference(simp,[status(thm)],[7389])).
% 75.21/18.73 thf(7421,plain,(! [B:$i,A:($i > $o)] : ((rel @ B @ (sk6 @ B @ (A))) | ~ (($true)) | ((A @ B) != (rel @ sk2 @ sk4)))),inference(paramod_ordered,[status(thm)],[18,7390])).
% 75.21/18.73 thf(7422,plain,(! [B:$i,A:($i > $o)] : ((rel @ B @ (sk6 @ B @ (A))) | ((A @ B) != (rel @ sk2 @ sk4)))),inference(simp,[status(thm)],[7421])).
% 75.21/18.73 thf(7453,plain,((rel @ sk2 @ (sk6 @ sk2 @ (^ [A:$i]: (rel @ A @ sk4))))),inference(pre_uni,[status(thm)],[7422:[bind(A, $thf(^ [C:$i]: (rel @ C @ sk4))),bind(B, $thf(sk2))]])).
% 75.21/18.73 thf(8141,plain,(~ (($true)) | ((rel @ sk2 @ (sk6 @ sk2 @ (^ [A:$i]: (rel @ A @ sk4)))) != (rel @ sk2 @ sk4))),inference(paramod_ordered,[status(thm)],[7453,7390])).
% 75.21/18.73 thf(8142,plain,(((rel @ sk2 @ (sk6 @ sk2 @ (^ [A:$i]: (rel @ A @ sk4)))) != (rel @ sk2 @ sk4))),inference(simp,[status(thm)],[8141])).
% 75.21/18.73 thf(8247,plain,((sk2 != sk2) | ((sk6 @ sk2 @ (^ [A:$i]: (rel @ A @ sk4))) != sk4)),inference(simp,[status(thm)],[8142])).
% 75.21/18.73 thf(8283,plain,(((sk6 @ sk2 @ (^ [A:$i]: (rel @ A @ sk4))) != sk4)),inference(simp,[status(thm)],[8247])).
% 75.21/18.73 thf(34,plain,(! [H:$i,G:$i,F:$i,E:($i > $o),D:$i,C:$i,B:$i,A:($i > $o)] : ((~ (A @ (sk7 @ B @ (A)))) | (~ (rel @ B @ C)) | (~ (rel @ C @ D)) | (~ (E @ (sk7 @ F @ (E)))) | (~ (rel @ F @ G)) | ~ (($true)) | (E @ H) | ((A @ D) != (rel @ G @ H)))),inference(paramod_ordered,[status(thm)],[25,25])).
% 75.21/18.73 thf(35,plain,(! [H:$i,G:$i,F:$i,E:($i > $o),D:$i,C:$i,B:$i,A:($i > $o)] : ((~ (A @ (sk7 @ B @ (A)))) | (~ (rel @ B @ C)) | (~ (rel @ C @ D)) | (~ (E @ (sk7 @ F @ (E)))) | (~ (rel @ F @ G)) | (E @ H) | ((A @ D) != (rel @ G @ H)))),inference(simp,[status(thm)],[34])).
% 75.21/18.73 thf(79,plain,(! [H:$i,G:$i,F:$i,E:($i > $o),D:$i,C:$i,B:$i,A:($i > $o)] : ((~ (A @ (sk7 @ B @ (A)))) | (~ (rel @ B @ C)) | (~ (rel @ C @ D)) | (~ ((sk7 @ F @ (E)) = (sk7 @ F @ ((=) @ $i @ (sk7 @ F @ E))))) | (~ (rel @ F @ G)) | ((sk7 @ F @ (E)) = H) | ((A @ D) != (rel @ G @ H)))),inference(replace_leibeq,[status(thm)],[35:[bind(A, $thf(A)),bind(B, $thf(B)),bind(C, $thf(C)),bind(D, $thf(D)),bind(E, $thf((=) @ $i @ (sk7 @ F @ E)))]])).
% 75.21/18.73 thf(88,plain,(! [H:$i,G:$i,F:$i,E:($i > $o),D:$i,C:$i,B:$i,A:($i > $o)] : (((sk7 @ F @ (E)) != (sk7 @ F @ ((=) @ $i @ (sk7 @ F @ E)))) | ((sk7 @ F @ (E)) = H) | (~ (A @ (sk7 @ B @ (A)))) | (~ (rel @ B @ C)) | (~ (rel @ C @ D)) | (~ (rel @ F @ G)) | ((A @ D) != (rel @ G @ H)))),inference(lifteq,[status(thm)],[79])).
% 75.21/18.73 thf(7454,plain,((rel @ sk4 @ (sk6 @ sk4 @ (rel @ sk2)))),inference(pre_uni,[status(thm)],[7422:[bind(A, $thf(rel @ sk2)),bind(B, $thf(sk4))]])).
% 75.21/18.73 thf(8340,plain,(~ (($true)) | ((rel @ sk4 @ (sk6 @ sk4 @ (rel @ sk2))) != (rel @ sk2 @ sk4))),inference(paramod_ordered,[status(thm)],[7454,7390])).
% 75.21/18.73 thf(8341,plain,(((rel @ sk4 @ (sk6 @ sk4 @ (rel @ sk2))) != (rel @ sk2 @ sk4))),inference(simp,[status(thm)],[8340])).
% 75.21/18.73 thf(8450,plain,((sk4 != sk2) | ((sk6 @ sk4 @ (rel @ sk2)) != sk4)),inference(simp,[status(thm)],[8341])).
% 75.21/18.73 thf(444,plain,(! [A:$i] : ((rel @ A @ (sk6 @ A @ (prop_c))) | (prop_c @ A))),inference(prim_subst,[status(thm)],[18:[bind(A, $thf(prop_c))]])).
% 75.21/18.73 thf(511,plain,(! [A:$i] : ((rel @ A @ (sk6 @ A @ (prop_c))) | (prop_c @ A))),inference(simp,[status(thm)],[444])).
% 75.21/18.73 thf(7,plain,((rel @ sk1 @ sk2)),inference(cnfConj,[status(thm)],[6])).
% 75.21/18.73 thf(354,plain,(! [B:$i,A:$i] : ((~ (s @ (sk7 @ A @ (s)))) | ~ (($true)) | (~ (rel @ B @ sk5)) | ((rel @ sk1 @ sk2) != (rel @ A @ B)))),inference(paramod_ordered,[status(thm)],[7,141])).
% 75.21/18.73 thf(355,plain,(! [B:$i,A:$i] : ((~ (s @ (sk7 @ A @ (s)))) | (~ (rel @ B @ sk5)) | ((rel @ sk1 @ sk2) != (rel @ A @ B)))),inference(simp,[status(thm)],[354])).
% 75.21/18.73 thf(356,plain,((~ (s @ (sk7 @ sk1 @ (s)))) | (~ (rel @ sk2 @ sk5))),inference(pattern_uni,[status(thm)],[355:[bind(A, $thf(sk1)),bind(B, $thf(sk2))]])).
% 75.21/18.73 thf(1265,plain,((~ (s @ (sk7 @ sk1 @ (s)))) | ~ (($true)) | ((rel @ sk2 @ sk5) != (rel @ sk1 @ sk2))),inference(paramod_ordered,[status(thm)],[7,356])).
% 75.21/18.73 thf(1266,plain,((~ (s @ (sk7 @ sk1 @ (s)))) | ((rel @ sk2 @ sk5) != (rel @ sk1 @ sk2))),inference(simp,[status(thm)],[1265])).
% 75.21/18.73 thf(1305,plain,((~ (s @ (sk7 @ sk1 @ (s)))) | (sk2 != sk1) | (sk5 != sk2)),inference(simp,[status(thm)],[1266])).
% 75.21/18.73 thf(1289,plain,((~ (s @ (sk7 @ sk1 @ (s)))) | ~ (($true)) | ((rel @ sk2 @ sk5) != (rel @ sk2 @ sk3))),inference(paramod_ordered,[status(thm)],[11,356])).
% 75.21/18.73 thf(1290,plain,((~ (s @ (sk7 @ sk1 @ (s)))) | ((rel @ sk2 @ sk5) != (rel @ sk2 @ sk3))),inference(simp,[status(thm)],[1289])).
% 75.21/18.73 thf(1297,plain,((~ (s @ (sk7 @ sk1 @ (s)))) | (sk2 != sk2) | (sk5 != sk3)),inference(simp,[status(thm)],[1290])).
% 75.21/18.73 thf(1327,plain,((~ (s @ (sk7 @ sk1 @ (s)))) | (sk5 != sk3)),inference(simp,[status(thm)],[1297])).
% 75.21/18.73 thf(364,plain,(! [B:$i,A:$i] : ((~ (s @ (sk7 @ A @ (s)))) | (~ (rel @ A @ B)) | ((rel @ B @ sk5) != (rel @ A @ B)) | ~ (($true)))),inference(eqfactor_ordered,[status(thm)],[141])).
% 75.21/18.73 thf(373,plain,((~ (s @ (sk7 @ sk5 @ (s)))) | (~ (rel @ sk5 @ sk5))),inference(pattern_uni,[status(thm)],[364:[bind(A, $thf(sk5)),bind(B, $thf(sk5))]])).
% 75.21/18.73 thf(1979,plain,(! [A:$i] : ((~ (s @ (sk7 @ sk5 @ (s)))) | ~ (($true)) | ((rel @ A @ (sk6 @ A @ (^ [B:$i]: (($false))))) != (rel @ sk5 @ sk5)))),inference(paramod_ordered,[status(thm)],[519,373])).
% 75.21/18.73 thf(1980,plain,(! [A:$i] : ((~ (s @ (sk7 @ sk5 @ (s)))) | ((rel @ A @ (sk6 @ A @ (^ [B:$i]: (($false))))) != (rel @ sk5 @ sk5)))),inference(simp,[status(thm)],[1979])).
% 75.21/18.73 thf(2013,plain,(! [A:$i] : ((~ (s @ (sk7 @ sk5 @ (s)))) | (A != sk5) | ((sk6 @ A @ (^ [B:$i]: (($false)))) != sk5))),inference(simp,[status(thm)],[1980])).
% 75.21/18.73 thf(2042,plain,((~ (s @ (sk7 @ sk5 @ (s)))) | ((sk6 @ sk5 @ (^ [A:$i]: (($false)))) != sk5)),inference(simp,[status(thm)],[2013])).
% 75.21/18.73 thf(220,plain,(! [B:$i,A:$i] : ((~ (rel @ sk3 @ A)) | (a @ A) | ~ (($true)) | (s @ B) | ((rel @ sk3 @ sk4) != (rel @ A @ B)))),inference(paramod_ordered,[status(thm)],[14,15])).
% 75.21/18.73 thf(221,plain,(! [B:$i,A:$i] : ((~ (rel @ sk3 @ A)) | (a @ A) | (s @ B) | ((rel @ sk3 @ sk4) != (rel @ A @ B)))),inference(simp,[status(thm)],[220])).
% 75.21/18.73 thf(222,plain,((~ (rel @ sk3 @ sk3)) | (a @ sk3) | (s @ sk4)),inference(pattern_uni,[status(thm)],[221:[bind(A, $thf(sk3)),bind(B, $thf(sk4))]])).
% 75.21/18.73 thf(2192,plain,(! [B:$i,A:($i > $o)] : ((rel @ B @ (sk6 @ B @ (A))) | ~ (($true)) | (a @ sk3) | (s @ sk4) | ((A @ B) != (rel @ sk3 @ sk3)))),inference(paramod_ordered,[status(thm)],[18,222])).
% 75.21/18.73 thf(2193,plain,(! [B:$i,A:($i > $o)] : ((rel @ B @ (sk6 @ B @ (A))) | (a @ sk3) | (s @ sk4) | ((A @ B) != (rel @ sk3 @ sk3)))),inference(simp,[status(thm)],[2192])).
% 75.21/18.73 thf(2228,plain,((rel @ sk3 @ (sk6 @ sk3 @ (rel @ sk3))) | (a @ sk3) | (s @ sk4)),inference(pre_uni,[status(thm)],[2193:[bind(A, $thf(rel @ sk3)),bind(B, $thf(sk3))]])).
% 75.21/18.73 thf(19,plain,(! [B:$i,A:($i > $o)] : ((~ (A @ (sk6 @ B @ (A)))) | (A @ B))),inference(cnfConj,[status(thm)],[17])).
% 75.21/18.73 thf(4939,plain,(! [B:$i,A:($i > $o)] : ((a @ sk3) | (s @ sk4) | ~ (($true)) | (A @ B) | ((rel @ sk3 @ (sk6 @ sk3 @ (rel @ sk3))) != (A @ (sk6 @ B @ (A)))))),inference(paramod_ordered,[status(thm)],[2228,19])).
% 75.21/18.73 thf(4940,plain,(! [B:$i,A:($i > $o)] : ((a @ sk3) | (s @ sk4) | (A @ B) | ((rel @ sk3 @ (sk6 @ sk3 @ (rel @ sk3))) != (A @ (sk6 @ B @ (A)))))),inference(simp,[status(thm)],[4939])).
% 75.21/18.73 thf(4976,plain,((a @ sk3) | (s @ sk4) | (rel @ sk3 @ sk3)),inference(pre_uni,[status(thm)],[4940:[bind(A, $thf(rel @ sk3)),bind(B, $thf(sk3))]])).
% 75.21/18.73 thf(5357,plain,((a @ sk3) | (s @ sk4) | ~ (($true)) | (a @ sk3) | (s @ sk4) | ((rel @ sk3 @ sk3) != (rel @ sk3 @ sk3))),inference(paramod_ordered,[status(thm)],[4976,222])).
% 75.21/18.73 thf(5358,plain,((a @ sk3) | (s @ sk4) | ((rel @ sk3 @ sk3) != (rel @ sk3 @ sk3))),inference(simp,[status(thm)],[5357])).
% 75.21/18.73 thf(5359,plain,((a @ sk3) | (s @ sk4)),inference(pattern_uni,[status(thm)],[5358:[]])).
% 75.21/18.73 thf(5435,plain,((a @ sk3) | ~ (($true)) | ((s @ (sk7 @ sk3 @ (s))) != (s @ sk4))),inference(paramod_ordered,[status(thm)],[5359,678])).
% 75.21/18.73 thf(5436,plain,((a @ sk3) | ((s @ (sk7 @ sk3 @ (s))) != (s @ sk4))),inference(simp,[status(thm)],[5435])).
% 75.21/18.73 thf(5486,plain,((a @ sk3) | ((sk7 @ sk3 @ (s)) != sk4)),inference(simp,[status(thm)],[5436])).
% 75.21/18.73 thf(24,plain,(! [D:$i,C:$i,B:$i,A:($i > $o)] : ((rel @ B @ (sk7 @ B @ (A))) | (~ (rel @ B @ C)) | (~ (rel @ C @ D)) | (A @ D))),inference(cnfConj,[status(thm)],[23])).
% 75.21/18.73 thf(30,plain,(! [H:$i,G:$i,F:$i,E:($i > $o),D:$i,C:$i,B:$i,A:($i > $o)] : ((~ (A @ (sk7 @ B @ (A)))) | (~ (rel @ B @ C)) | (~ (rel @ C @ D)) | ~ (($true)) | (~ (rel @ F @ G)) | (~ (rel @ G @ H)) | (E @ H) | ((A @ D) != (E @ (sk7 @ F @ (E)))))),inference(paramod_ordered,[status(thm)],[25,25])).
% 75.21/18.73 thf(31,plain,(! [H:$i,G:$i,F:$i,E:($i > $o),D:$i,C:$i,B:$i,A:($i > $o)] : ((~ (A @ (sk7 @ B @ (A)))) | (~ (rel @ B @ C)) | (~ (rel @ C @ D)) | (~ (rel @ F @ G)) | (~ (rel @ G @ H)) | (E @ H) | ((A @ D) != (E @ (sk7 @ F @ (E)))))),inference(simp,[status(thm)],[30])).
% 75.21/18.73 thf(109,plain,(! [H:$i,G:$i,F:$i,E:($i > $o),D:$i,C:$i,B:$i,A:($i > $o)] : ((~ (A @ (sk7 @ B @ (A)))) | (~ (rel @ B @ C)) | (~ (rel @ C @ D)) | (~ (rel @ F @ G)) | (~ (rel @ G @ H)) | (E @ H) | ((A @ D) != (E @ (sk7 @ F @ (E)))))),inference(pre_uni,[status(thm)],[31:[]])).
% 75.21/18.73 thf(110,plain,(! [H:$i,G:$i,F:$i,E:($i > $o),D:$i,C:$i,B:$i,A:($i > $o)] : ((E @ H) | (~ (rel @ G @ H)) | (~ (rel @ F @ G)) | (~ (rel @ C @ D)) | (~ (rel @ B @ C)) | (~ (A @ (sk7 @ B @ (A)))) | ((A @ D) != (E @ (sk7 @ F @ (E)))))),inference(pre_uni,[status(thm)],[109:[]])).
% 75.21/18.73 thf(43,plain,(! [D:$i,C:$i,B:$i,A:($i > $o)] : ((~ (A @ (sk7 @ B @ (A)))) | (~ (rel @ B @ C)) | ~ (($true)) | (A @ D) | ((rel @ sk1 @ sk2) != (rel @ C @ D)))),inference(paramod_ordered,[status(thm)],[7,25])).
% 75.21/18.73 thf(44,plain,(! [D:$i,C:$i,B:$i,A:($i > $o)] : ((~ (A @ (sk7 @ B @ (A)))) | (~ (rel @ B @ C)) | (A @ D) | ((rel @ sk1 @ sk2) != (rel @ C @ D)))),inference(simp,[status(thm)],[43])).
% 75.21/18.73 thf(45,plain,(! [B:$i,A:($i > $o)] : ((~ (A @ (sk7 @ B @ (A)))) | (~ (rel @ B @ sk1)) | (A @ sk2))),inference(pattern_uni,[status(thm)],[44:[bind(A, $thf(A)),bind(B, $thf(B)),bind(C, $thf(sk1)),bind(D, $thf(sk2))]])).
% 75.21/18.73 thf(83,plain,(! [B:$i,A:($i > $o)] : ((~ ((sk7 @ B @ (A)) = (sk7 @ B @ ((=) @ $i @ (sk7 @ B @ A))))) | (~ (rel @ B @ sk1)) | ((sk7 @ B @ (A)) = sk2))),inference(replace_leibeq,[status(thm)],[45:[bind(A, $thf((=) @ $i @ (sk7 @ B @ A)))]])).
% 75.21/18.73 thf(89,plain,(! [B:$i,A:($i > $o)] : (((sk7 @ B @ (A)) != (sk7 @ B @ ((=) @ $i @ (sk7 @ B @ A)))) | ((sk7 @ B @ (A)) = sk2) | (~ (rel @ B @ sk1)))),inference(lifteq,[status(thm)],[83])).
% 75.21/18.73 thf(439,plain,(! [A:$i] : ((rel @ A @ (sk6 @ A @ (b))) | (b @ A))),inference(prim_subst,[status(thm)],[18:[bind(A, $thf(b))]])).
% 75.21/18.73 thf(505,plain,(! [A:$i] : ((rel @ A @ (sk6 @ A @ (b))) | (b @ A))),inference(simp,[status(thm)],[439])).
% 75.21/18.73 thf(7417,plain,(! [A:$i] : ((b @ A) | ~ (($true)) | ((rel @ A @ (sk6 @ A @ (b))) != (rel @ sk2 @ sk4)))),inference(paramod_ordered,[status(thm)],[505,7390])).
% 75.21/18.73 thf(7418,plain,(! [A:$i] : ((b @ A) | ((rel @ A @ (sk6 @ A @ (b))) != (rel @ sk2 @ sk4)))),inference(simp,[status(thm)],[7417])).
% 75.21/18.73 thf(7435,plain,(! [A:$i] : ((b @ A) | (A != sk2) | ((sk6 @ A @ (b)) != sk4))),inference(simp,[status(thm)],[7418])).
% 75.21/18.73 thf(7460,plain,((b @ sk2) | ((sk6 @ sk2 @ (b)) != sk4)),inference(simp,[status(thm)],[7435])).
% 75.21/18.73 thf(1992,plain,((~ (s @ (sk7 @ sk5 @ (s)))) | ~ (($true)) | ((rel @ sk5 @ sk5) != (rel @ sk2 @ sk3))),inference(paramod_ordered,[status(thm)],[11,373])).
% 75.21/18.73 thf(1993,plain,((~ (s @ (sk7 @ sk5 @ (s)))) | ((rel @ sk5 @ sk5) != (rel @ sk2 @ sk3))),inference(simp,[status(thm)],[1992])).
% 75.21/18.73 thf(2011,plain,((~ (s @ (sk7 @ sk5 @ (s)))) | (sk5 != sk2) | (sk5 != sk3)),inference(simp,[status(thm)],[1993])).
% 75.21/18.73 thf(198,plain,(! [A:$i] : (~ (($true)) | (~ (a @ A)) | (b @ A) | ((rel @ sk2 @ sk3) != (rel @ sk2 @ A)))),inference(paramod_ordered,[status(thm)],[11,13])).
% 75.21/18.73 thf(199,plain,(! [A:$i] : ((~ (a @ A)) | (b @ A) | ((rel @ sk2 @ sk3) != (rel @ sk2 @ A)))),inference(simp,[status(thm)],[198])).
% 75.21/18.73 thf(200,plain,((~ (a @ sk3)) | (b @ sk3)),inference(pattern_uni,[status(thm)],[199:[bind(A, $thf(sk3))]])).
% 75.21/18.73 thf(436,plain,(! [B:$i,A:($i > $o)] : ((rel @ B @ (sk6 @ B @ (A))) | ~ (($true)) | (b @ sk3) | ((A @ B) != (a @ sk3)))),inference(paramod_ordered,[status(thm)],[18,200])).
% 75.21/18.73 thf(437,plain,(! [B:$i,A:($i > $o)] : ((rel @ B @ (sk6 @ B @ (A))) | (b @ sk3) | ((A @ B) != (a @ sk3)))),inference(simp,[status(thm)],[436])).
% 75.21/18.73 thf(496,plain,(! [A:$i] : ((rel @ A @ (sk6 @ A @ (^ [B:$i]: (a @ sk3)))) | (b @ sk3))),inference(pre_uni,[status(thm)],[437:[bind(A, $thf(^ [C:$i]: (a @ sk3))),bind(B, $thf(B))]])).
% 75.21/18.73 thf(546,plain,(! [A:$i] : ((rel @ A @ (sk6 @ A @ (^ [B:$i]: (a @ sk3)))) | (b @ sk3))),inference(simp,[status(thm)],[496])).
% 75.21/18.73 thf(57,plain,(! [D:$i,C:$i,B:$i,A:($i > $o)] : ((~ (A @ (sk7 @ B @ (A)))) | (~ (rel @ B @ C)) | (~ (rel @ C @ D)) | ((A @ D) != (~ (A @ (sk7 @ B @ (A))))) | ~ (($true)))),inference(eqfactor_ordered,[status(thm)],[25])).
% 75.21/18.73 thf(102,plain,(! [D:$i,C:$i,B:$i,A:($i > $o)] : ((~ (A @ (sk7 @ B @ (A)))) | (~ (rel @ B @ C)) | (~ (rel @ C @ D)) | ((A @ D) != (~ (A @ (sk7 @ B @ (A))))))),inference(simp,[status(thm)],[57])).
% 75.21/18.73 thf(413,plain,(! [B:$i,A:($i > $o)] : ((rel @ B @ (sk6 @ B @ (A))) | ~ (($true)) | ((A @ B) != (s @ sk5)))),inference(paramod_ordered,[status(thm)],[18,9])).
% 75.21/18.73 thf(414,plain,(! [B:$i,A:($i > $o)] : ((rel @ B @ (sk6 @ B @ (A))) | ((A @ B) != (s @ sk5)))),inference(simp,[status(thm)],[413])).
% 75.21/18.73 thf(469,plain,((rel @ sk5 @ (sk6 @ sk5 @ (s)))),inference(pre_uni,[status(thm)],[414:[bind(A, $thf(s)),bind(B, $thf(sk5))]])).
% 75.21/18.73 thf(7431,plain,(~ (($true)) | ((rel @ sk5 @ (sk6 @ sk5 @ (s))) != (rel @ sk2 @ sk4))),inference(paramod_ordered,[status(thm)],[469,7390])).
% 75.21/18.73 thf(7432,plain,(((rel @ sk5 @ (sk6 @ sk5 @ (s))) != (rel @ sk2 @ sk4))),inference(simp,[status(thm)],[7431])).
% 75.21/18.73 thf(7439,plain,((sk5 != sk2) | ((sk6 @ sk5 @ (s)) != sk4)),inference(simp,[status(thm)],[7432])).
% 75.21/18.73 thf(20,plain,(! [B:$i,A:($i > $o)] : ((~ ((sk6 @ B @ (A)) = (sk6 @ B @ ((=) @ $i @ (sk6 @ B @ A))))) | ((sk6 @ B @ (A)) = B))),inference(replace_leibeq,[status(thm)],[19:[bind(A, $thf((=) @ $i @ (sk6 @ B @ A)))]])).
% 75.21/18.73 thf(21,plain,(! [B:$i,A:($i > $o)] : (((sk6 @ B @ (A)) != (sk6 @ B @ ((=) @ $i @ (sk6 @ B @ A)))) | ((sk6 @ B @ (A)) = B))),inference(lifteq,[status(thm)],[20])).
% 75.21/18.73 thf(51,plain,(! [D:$i,C:$i,B:$i,A:($i > $o)] : ((~ (A @ (sk7 @ B @ (A)))) | (~ (rel @ B @ C)) | ~ (($true)) | (A @ D) | ((rel @ sk2 @ sk3) != (rel @ C @ D)))),inference(paramod_ordered,[status(thm)],[11,25])).
% 75.21/18.73 thf(52,plain,(! [D:$i,C:$i,B:$i,A:($i > $o)] : ((~ (A @ (sk7 @ B @ (A)))) | (~ (rel @ B @ C)) | (A @ D) | ((rel @ sk2 @ sk3) != (rel @ C @ D)))),inference(simp,[status(thm)],[51])).
% 75.21/18.73 thf(53,plain,(! [B:$i,A:($i > $o)] : ((~ (A @ (sk7 @ B @ (A)))) | (~ (rel @ B @ sk2)) | (A @ sk3))),inference(pattern_uni,[status(thm)],[52:[bind(A, $thf(A)),bind(B, $thf(B)),bind(C, $thf(sk2)),bind(D, $thf(sk3))]])).
% 75.21/18.73 thf(348,plain,(! [B:$i,A:$i] : ((~ (s @ (sk7 @ A @ (s)))) | ~ (($true)) | (~ (rel @ B @ sk5)) | ((rel @ sk4 @ sk5) != (rel @ A @ B)))),inference(paramod_ordered,[status(thm)],[12,141])).
% 75.21/18.73 thf(349,plain,(! [B:$i,A:$i] : ((~ (s @ (sk7 @ A @ (s)))) | (~ (rel @ B @ sk5)) | ((rel @ sk4 @ sk5) != (rel @ A @ B)))),inference(simp,[status(thm)],[348])).
% 75.21/18.73 thf(350,plain,((~ (s @ (sk7 @ sk4 @ (s)))) | (~ (rel @ sk5 @ sk5))),inference(pattern_uni,[status(thm)],[349:[bind(A, $thf(sk4)),bind(B, $thf(sk5))]])).
% 75.21/18.73 thf(713,plain,((~ (s @ (sk7 @ sk4 @ (s)))) | ~ (($true)) | ((rel @ sk5 @ (sk6 @ sk5 @ (s))) != (rel @ sk5 @ sk5))),inference(paramod_ordered,[status(thm)],[469,350])).
% 75.21/18.73 thf(714,plain,((~ (s @ (sk7 @ sk4 @ (s)))) | ((rel @ sk5 @ (sk6 @ sk5 @ (s))) != (rel @ sk5 @ sk5))),inference(simp,[status(thm)],[713])).
% 75.21/18.73 thf(719,plain,((~ (s @ (sk7 @ sk4 @ (s)))) | (sk5 != sk5) | ((sk6 @ sk5 @ (s)) != sk5)),inference(simp,[status(thm)],[714])).
% 75.21/18.73 thf(742,plain,((~ (s @ (sk7 @ sk4 @ (s)))) | ((sk6 @ sk5 @ (s)) != sk5)),inference(simp,[status(thm)],[719])).
% 75.21/18.73 thf(1285,plain,(! [A:$i] : ((~ (s @ (sk7 @ sk1 @ (s)))) | ~ (($true)) | ((rel @ A @ (sk6 @ A @ (^ [B:$i]: (($false))))) != (rel @ sk2 @ sk5)))),inference(paramod_ordered,[status(thm)],[519,356])).
% 75.21/18.73 thf(1286,plain,(! [A:$i] : ((~ (s @ (sk7 @ sk1 @ (s)))) | ((rel @ A @ (sk6 @ A @ (^ [B:$i]: (($false))))) != (rel @ sk2 @ sk5)))),inference(simp,[status(thm)],[1285])).
% 75.21/18.73 thf(1306,plain,(! [A:$i] : ((~ (s @ (sk7 @ sk1 @ (s)))) | (A != sk2) | ((sk6 @ A @ (^ [B:$i]: (($false)))) != sk5))),inference(simp,[status(thm)],[1286])).
% 75.21/18.73 thf(1329,plain,((~ (s @ (sk7 @ sk1 @ (s)))) | ((sk6 @ sk2 @ (^ [A:$i]: (($false)))) != sk5)),inference(simp,[status(thm)],[1306])).
% 75.21/18.73 thf(686,plain,((rel @ (sk7 @ sk3 @ (s)) @ (sk6 @ (sk7 @ sk3 @ (s)) @ (s)))),inference(pre_uni,[status(thm)],[682:[bind(A, $thf(s)),bind(B, $thf(sk7 @ sk3 @ (s)))]])).
% 75.21/18.73 thf(194,plain,(! [A:$i] : (~ (($true)) | (~ (a @ A)) | (b @ A) | ((rel @ sk4 @ sk5) != (rel @ sk2 @ A)))),inference(paramod_ordered,[status(thm)],[12,13])).
% 75.21/18.73 thf(195,plain,(! [A:$i] : ((~ (a @ A)) | (b @ A) | ((rel @ sk4 @ sk5) != (rel @ sk2 @ A)))),inference(simp,[status(thm)],[194])).
% 75.21/18.73 thf(206,plain,(! [A:$i] : ((b @ A) | (~ (a @ A)) | (sk4 != sk2) | (sk5 != A))),inference(simp,[status(thm)],[195])).
% 75.21/18.73 thf(212,plain,((b @ sk5) | (~ (a @ sk5)) | (sk4 != sk2)),inference(simp,[status(thm)],[206])).
% 75.21/18.73 thf(707,plain,((~ (s @ (sk7 @ sk4 @ (s)))) | ~ (($true)) | ((rel @ sk5 @ sk5) != (rel @ sk2 @ sk3))),inference(paramod_ordered,[status(thm)],[11,350])).
% 75.21/18.73 thf(708,plain,((~ (s @ (sk7 @ sk4 @ (s)))) | ((rel @ sk5 @ sk5) != (rel @ sk2 @ sk3))),inference(simp,[status(thm)],[707])).
% 75.21/18.73 thf(738,plain,((~ (s @ (sk7 @ sk4 @ (s)))) | (sk5 != sk2) | (sk5 != sk3)),inference(simp,[status(thm)],[708])).
% 75.21/18.73 thf(192,plain,(! [A:$i] : (~ (($true)) | (~ (a @ A)) | (b @ A) | ((rel @ sk3 @ sk4) != (rel @ sk2 @ A)))),inference(paramod_ordered,[status(thm)],[14,13])).
% 75.21/18.73 thf(193,plain,(! [A:$i] : ((~ (a @ A)) | (b @ A) | ((rel @ sk3 @ sk4) != (rel @ sk2 @ A)))),inference(simp,[status(thm)],[192])).
% 75.21/18.73 thf(204,plain,(! [A:$i] : ((b @ A) | (~ (a @ A)) | (sk3 != sk2) | (sk4 != A))),inference(simp,[status(thm)],[193])).
% 75.21/18.73 thf(210,plain,((b @ sk4) | (~ (a @ sk4)) | (sk3 != sk2)),inference(simp,[status(thm)],[204])).
% 75.21/18.73 thf(827,plain,(($false) | (~ (a @ sk4)) | (sk3 != sk2)),inference(rewrite,[status(thm)],[210,10])).
% 75.21/18.73 thf(828,plain,((~ (a @ sk4)) | (sk3 != sk2)),inference(simp,[status(thm)],[827])).
% 75.21/18.73 thf(5972,plain,(~ (($true)) | (sk3 != sk2)),inference(rewrite,[status(thm)],[828,5971])).
% 75.21/18.73 thf(5973,plain,((sk3 != sk2)),inference(simp,[status(thm)],[5972])).
% 75.21/18.73 thf(633,plain,(! [B:$i,A:$i] : (~ (($true)) | (~ (a @ B)) | (b @ B) | ((rel @ A @ (sk6 @ A @ (^ [C:$i]: (($false))))) != (rel @ sk2 @ B)))),inference(paramod_ordered,[status(thm)],[519,13])).
% 75.21/18.73 thf(634,plain,(! [B:$i,A:$i] : ((~ (a @ B)) | (b @ B) | ((rel @ A @ (sk6 @ A @ (^ [C:$i]: (($false))))) != (rel @ sk2 @ B)))),inference(simp,[status(thm)],[633])).
% 75.21/18.73 thf(635,plain,((~ (a @ (sk6 @ sk2 @ (^ [A:$i]: (($false)))))) | (b @ (sk6 @ sk2 @ (^ [A:$i]: (($false)))))),inference(pattern_uni,[status(thm)],[634:[bind(A, $thf(sk2)),bind(B, $thf(sk6 @ sk2 @ (^ [C:$i]: (($false)))))]])).
% 75.21/18.73 thf(2727,plain,(! [B:$i,A:($i > $o)] : ((rel @ B @ (sk6 @ B @ (A))) | ~ (($true)) | (b @ (sk6 @ sk2 @ (^ [C:$i]: (($false))))) | ((A @ B) != (a @ (sk6 @ sk2 @ (^ [C:$i]: (($false)))))))),inference(paramod_ordered,[status(thm)],[18,635])).
% 75.21/18.73 thf(2728,plain,(! [B:$i,A:($i > $o)] : ((rel @ B @ (sk6 @ B @ (A))) | (b @ (sk6 @ sk2 @ (^ [C:$i]: (($false))))) | ((A @ B) != (a @ (sk6 @ sk2 @ (^ [C:$i]: (($false)))))))),inference(simp,[status(thm)],[2727])).
% 75.21/18.73 thf(2766,plain,((rel @ sk2 @ (sk6 @ sk2 @ (^ [A:$i]: (a @ (sk6 @ A @ (^ [B:$i]: (($false)))))))) | (b @ (sk6 @ sk2 @ (^ [A:$i]: (($false)))))),inference(pre_uni,[status(thm)],[2728:[bind(A, $thf(^ [C:$i]: (a @ (sk6 @ C @ (^ [D:$i]: (($false))))))),bind(B, $thf(sk2))]])).
% 75.21/18.73 thf(442,plain,(! [A:$i] : ((rel @ A @ (sk6 @ A @ (s))) | (s @ A))),inference(prim_subst,[status(thm)],[18:[bind(A, $thf(s))]])).
% 75.21/18.73 thf(508,plain,(! [A:$i] : ((rel @ A @ (sk6 @ A @ (s))) | (s @ A))),inference(simp,[status(thm)],[442])).
% 75.21/18.73 thf(290,plain,(! [A:$i] : ((~ (prop_c @ (sk6 @ A @ (prop_c)))) | (prop_c @ A))),inference(prim_subst,[status(thm)],[19:[bind(A, $thf(prop_c))]])).
% 75.21/18.73 thf(311,plain,(! [A:$i] : ((~ (prop_c @ (sk6 @ A @ (prop_c)))) | (prop_c @ A))),inference(simp,[status(thm)],[290])).
% 75.21/18.73 thf(709,plain,(! [A:$i] : ((~ (s @ (sk7 @ sk4 @ (s)))) | ~ (($true)) | ((rel @ A @ (sk6 @ A @ (^ [B:$i]: (($false))))) != (rel @ sk5 @ sk5)))),inference(paramod_ordered,[status(thm)],[519,350])).
% 75.21/18.73 thf(710,plain,(! [A:$i] : ((~ (s @ (sk7 @ sk4 @ (s)))) | ((rel @ A @ (sk6 @ A @ (^ [B:$i]: (($false))))) != (rel @ sk5 @ sk5)))),inference(simp,[status(thm)],[709])).
% 75.21/18.73 thf(720,plain,(! [A:$i] : ((~ (s @ (sk7 @ sk4 @ (s)))) | (A != sk5) | ((sk6 @ A @ (^ [B:$i]: (($false)))) != sk5))),inference(simp,[status(thm)],[710])).
% 75.21/18.73 thf(743,plain,((~ (s @ (sk7 @ sk4 @ (s)))) | ((sk6 @ sk5 @ (^ [A:$i]: (($false)))) != sk5)),inference(simp,[status(thm)],[720])).
% 75.21/18.73 thf(8546,plain,(! [A:$i] : ((s @ A) | ~ (($true)) | ((rel @ A @ (sk6 @ A @ (s))) != (rel @ sk2 @ sk4)))),inference(paramod_ordered,[status(thm)],[508,7390])).
% 75.21/18.73 thf(8547,plain,(! [A:$i] : ((s @ A) | ((rel @ A @ (sk6 @ A @ (s))) != (rel @ sk2 @ sk4)))),inference(simp,[status(thm)],[8546])).
% 75.21/18.73 thf(8656,plain,(! [A:$i] : ((s @ A) | (A != sk2) | ((sk6 @ A @ (s)) != sk4))),inference(simp,[status(thm)],[8547])).
% 75.21/18.73 thf(8697,plain,((s @ sk2) | ((sk6 @ sk2 @ (s)) != sk4)),inference(simp,[status(thm)],[8656])).
% 75.21/18.73 thf(26,plain,(! [D:$i,C:$i,B:$i,A:($i > $o)] : ((~ ((sk7 @ B @ (A)) = (sk7 @ B @ ((=) @ $i @ (sk7 @ B @ A))))) | (~ (rel @ B @ C)) | (~ (rel @ C @ D)) | ((sk7 @ B @ (A)) = D))),inference(replace_leibeq,[status(thm)],[25:[bind(A, $thf((=) @ $i @ (sk7 @ B @ A)))]])).
% 75.21/18.73 thf(27,plain,(! [D:$i,C:$i,B:$i,A:($i > $o)] : (((sk7 @ B @ (A)) != (sk7 @ B @ ((=) @ $i @ (sk7 @ B @ A)))) | ((sk7 @ B @ (A)) = D) | (~ (rel @ B @ C)) | (~ (rel @ C @ D)))),inference(lifteq,[status(thm)],[26])).
% 75.21/18.73 thf(2731,plain,((~ (a @ (sk6 @ sk2 @ (^ [A:$i]: (($false)))))) | ~ (($true)) | ((b @ (sk6 @ sk2 @ (^ [A:$i]: (($false))))) != (b @ sk4))),inference(paramod_ordered,[status(thm)],[635,10])).
% 75.21/18.73 thf(2732,plain,((~ (a @ (sk6 @ sk2 @ (^ [A:$i]: (($false)))))) | ((b @ (sk6 @ sk2 @ (^ [A:$i]: (($false))))) != (b @ sk4))),inference(simp,[status(thm)],[2731])).
% 75.21/18.73 thf(2763,plain,((~ (a @ (sk6 @ sk2 @ (^ [A:$i]: (($false)))))) | ((sk6 @ sk2 @ (^ [A:$i]: (($false)))) != sk4)),inference(simp,[status(thm)],[2732])).
% 75.21/18.73 thf(5980,plain,(~ (($true)) | ((sk6 @ sk2 @ (^ [A:$i]: (($false)))) != sk4) | ((a @ (sk6 @ sk2 @ (^ [A:$i]: (($false))))) != (a @ sk4))),inference(paramod_ordered,[status(thm)],[5971,2763])).
% 75.21/18.73 thf(5981,plain,(((sk6 @ sk2 @ (^ [A:$i]: (($false)))) != sk4) | ((a @ (sk6 @ sk2 @ (^ [A:$i]: (($false))))) != (a @ sk4))),inference(simp,[status(thm)],[5980])).
% 75.21/18.73 thf(6017,plain,(((sk6 @ sk2 @ (^ [A:$i]: (($false)))) != sk4) | ((sk6 @ sk2 @ (^ [A:$i]: (($false)))) != sk4)),inference(simp,[status(thm)],[5981])).
% 75.21/18.73 thf(6024,plain,(((sk6 @ sk2 @ (^ [A:$i]: (($false)))) != sk4)),inference(simp,[status(thm)],[6017])).
% 75.21/18.73 thf(65,plain,(! [D:($i > $i),C:$i,B:$i,A:$i] : ((~ (s @ (D @ (sk7 @ A @ (^ [E:$i]: (s @ (D @ E))))))) | (~ (rel @ A @ B)) | (~ (rel @ B @ C)) | (s @ (D @ C)))),inference(prim_subst,[status(thm)],[25:[bind(A, $thf(^ [F:$i]: (s @ (E @ F))))]])).
% 75.21/18.73 thf(113,plain,(! [D:($i > $i),C:$i,B:$i,A:$i] : ((~ (s @ (D @ (sk7 @ A @ (^ [E:$i]: (s @ (D @ E))))))) | (~ (rel @ A @ B)) | (~ (rel @ B @ C)) | (s @ (D @ C)))),inference(simp,[status(thm)],[65])).
% 75.21/18.73 thf(253,plain,((~ (a @ sk3)) | ~ (($true)) | ((b @ sk4) != (b @ sk3))),inference(paramod_ordered,[status(thm)],[200,10])).
% 75.21/18.73 thf(254,plain,((~ (a @ sk3)) | ((b @ sk4) != (b @ sk3))),inference(simp,[status(thm)],[253])).
% 75.21/18.73 thf(259,plain,((~ (a @ sk3)) | (sk4 != sk3)),inference(simp,[status(thm)],[254])).
% 75.21/18.73 thf(5992,plain,(~ (($true)) | (sk4 != sk3) | ((a @ sk4) != (a @ sk3))),inference(paramod_ordered,[status(thm)],[5971,259])).
% 75.21/18.73 thf(5993,plain,((sk4 != sk3) | ((a @ sk4) != (a @ sk3))),inference(simp,[status(thm)],[5992])).
% 75.21/18.73 thf(6010,plain,((sk4 != sk3) | (sk4 != sk3)),inference(simp,[status(thm)],[5993])).
% 75.21/18.73 thf(6027,plain,((sk4 != sk3)),inference(simp,[status(thm)],[6010])).
% 75.21/18.73 thf(196,plain,(! [A:$i] : (~ (($true)) | (~ (a @ A)) | (b @ A) | ((rel @ sk2 @ A) != (rel @ sk1 @ sk2)))),inference(paramod_ordered,[status(thm)],[7,13])).
% 75.21/18.73 thf(197,plain,(! [A:$i] : ((~ (a @ A)) | (b @ A) | ((rel @ sk2 @ A) != (rel @ sk1 @ sk2)))),inference(simp,[status(thm)],[196])).
% 75.21/18.73 thf(203,plain,(! [A:$i] : ((b @ A) | (~ (a @ A)) | (sk2 != sk1) | (A != sk2))),inference(simp,[status(thm)],[197])).
% 75.21/18.73 thf(209,plain,((b @ sk2) | (~ (a @ sk2)) | (sk2 != sk1)),inference(simp,[status(thm)],[203])).
% 75.21/18.73 thf(806,plain,((~ (a @ sk2)) | (sk2 != sk1) | ~ (($true)) | ((b @ sk4) != (b @ sk2))),inference(paramod_ordered,[status(thm)],[209,10])).
% 75.21/18.73 thf(807,plain,((~ (a @ sk2)) | (sk2 != sk1) | ((b @ sk4) != (b @ sk2))),inference(simp,[status(thm)],[806])).
% 75.21/18.73 thf(822,plain,((~ (a @ sk2)) | (sk2 != sk1) | (sk4 != sk2)),inference(simp,[status(thm)],[807])).
% 75.21/18.73 thf(6003,plain,(~ (($true)) | (sk2 != sk1) | (sk4 != sk2) | ((a @ sk4) != (a @ sk2))),inference(paramod_ordered,[status(thm)],[5971,822])).
% 75.21/18.73 thf(6004,plain,((sk2 != sk1) | (sk4 != sk2) | ((a @ sk4) != (a @ sk2))),inference(simp,[status(thm)],[6003])).
% 75.21/18.73 thf(6012,plain,((sk2 != sk1) | (sk4 != sk2) | (sk4 != sk2)),inference(simp,[status(thm)],[6004])).
% 75.21/18.73 thf(6029,plain,((sk2 != sk1) | (sk4 != sk2)),inference(simp,[status(thm)],[6012])).
% 75.21/18.73 thf(711,plain,((~ (s @ (sk7 @ sk4 @ (s)))) | ~ (($true)) | ((rel @ sk5 @ sk5) != (rel @ sk4 @ sk5))),inference(paramod_ordered,[status(thm)],[12,350])).
% 75.21/18.73 thf(712,plain,((~ (s @ (sk7 @ sk4 @ (s)))) | ((rel @ sk5 @ sk5) != (rel @ sk4 @ sk5))),inference(simp,[status(thm)],[711])).
% 75.21/18.73 thf(732,plain,((~ (s @ (sk7 @ sk4 @ (s)))) | (sk5 != sk4) | (sk5 != sk5)),inference(simp,[status(thm)],[712])).
% 75.21/18.73 thf(749,plain,((~ (s @ (sk7 @ sk4 @ (s)))) | (sk5 != sk4)),inference(simp,[status(thm)],[732])).
% 75.21/18.73 thf(1287,plain,((~ (s @ (sk7 @ sk1 @ (s)))) | ~ (($true)) | ((rel @ sk4 @ sk5) != (rel @ sk2 @ sk5))),inference(paramod_ordered,[status(thm)],[12,356])).
% 75.21/18.73 thf(1288,plain,((~ (s @ (sk7 @ sk1 @ (s)))) | ((rel @ sk4 @ sk5) != (rel @ sk2 @ sk5))),inference(simp,[status(thm)],[1287])).
% 75.21/18.73 thf(1319,plain,((~ (s @ (sk7 @ sk1 @ (s)))) | (sk4 != sk2) | (sk5 != sk5)),inference(simp,[status(thm)],[1288])).
% 75.21/18.73 thf(1340,plain,((~ (s @ (sk7 @ sk1 @ (s)))) | (sk4 != sk2)),inference(simp,[status(thm)],[1319])).
% 75.21/18.73 thf(5439,plain,((a @ sk3) | ~ (($true)) | ((s @ sk5) != (s @ sk4))),inference(paramod_ordered,[status(thm)],[5359,9])).
% 75.21/18.73 thf(5440,plain,((a @ sk3) | ((s @ sk5) != (s @ sk4))),inference(simp,[status(thm)],[5439])).
% 75.21/18.73 thf(5484,plain,((a @ sk3) | (sk5 != sk4)),inference(simp,[status(thm)],[5440])).
% 75.21/18.73 thf(7403,plain,(! [A:$i] : ((b @ sk3) | ~ (($true)) | ((rel @ A @ (sk6 @ A @ (^ [B:$i]: (a @ sk3)))) != (rel @ sk2 @ sk4)))),inference(paramod_ordered,[status(thm)],[546,7390])).
% 75.21/18.73 thf(7404,plain,(! [A:$i] : ((b @ sk3) | ((rel @ A @ (sk6 @ A @ (^ [B:$i]: (a @ sk3)))) != (rel @ sk2 @ sk4)))),inference(simp,[status(thm)],[7403])).
% 75.21/18.73 thf(7440,plain,(! [A:$i] : ((b @ sk3) | (A != sk2) | ((sk6 @ A @ (^ [B:$i]: (a @ sk3))) != sk4))),inference(simp,[status(thm)],[7404])).
% 75.21/18.73 thf(7462,plain,((b @ sk3) | ((sk6 @ sk2 @ (^ [A:$i]: (a @ sk3))) != sk4)),inference(simp,[status(thm)],[7440])).
% 75.21/18.73 thf(382,plain,(! [B:$i,A:($i > $o)] : ((rel @ B @ (sk6 @ B @ (A))) | ~ (($true)) | ((A @ B) != (b @ sk4)))),inference(paramod_ordered,[status(thm)],[18,10])).
% 75.21/18.73 thf(383,plain,(! [B:$i,A:($i > $o)] : ((rel @ B @ (sk6 @ B @ (A))) | ((A @ B) != (b @ sk4)))),inference(simp,[status(thm)],[382])).
% 75.21/18.73 thf(491,plain,((rel @ sk4 @ (sk6 @ sk4 @ (b)))),inference(pre_uni,[status(thm)],[383:[bind(A, $thf(b)),bind(B, $thf(sk4))]])).
% 75.21/18.73 thf(7433,plain,(~ (($true)) | ((rel @ sk4 @ (sk6 @ sk4 @ (b))) != (rel @ sk2 @ sk4))),inference(paramod_ordered,[status(thm)],[491,7390])).
% 75.21/18.73 thf(7434,plain,(((rel @ sk4 @ (sk6 @ sk4 @ (b))) != (rel @ sk2 @ sk4))),inference(simp,[status(thm)],[7433])).
% 75.21/18.73 thf(7443,plain,((sk4 != sk2) | ((sk6 @ sk4 @ (b)) != sk4)),inference(simp,[status(thm)],[7434])).
% 75.21/18.73 thf(1800,plain,((~ (s @ (sk7 @ sk2 @ (s)))) | ~ (($true)) | ((rel @ sk3 @ sk5) != (rel @ sk1 @ sk2))),inference(paramod_ordered,[status(thm)],[7,361])).
% 75.21/18.73 thf(1801,plain,((~ (s @ (sk7 @ sk2 @ (s)))) | ((rel @ sk3 @ sk5) != (rel @ sk1 @ sk2))),inference(simp,[status(thm)],[1800])).
% 75.21/18.73 thf(1849,plain,((~ (s @ (sk7 @ sk2 @ (s)))) | (sk3 != sk1) | (sk5 != sk2)),inference(simp,[status(thm)],[1801])).
% 75.21/18.73 thf(497,plain,((rel @ sk3 @ (sk6 @ sk3 @ (a))) | (b @ sk3)),inference(pre_uni,[status(thm)],[437:[bind(A, $thf(a)),bind(B, $thf(sk3))]])).
% 75.21/18.73 thf(1463,plain,((~ (a @ sk5)) | (sk4 != sk2) | ~ (($true)) | ((b @ sk5) != (b @ sk4))),inference(paramod_ordered,[status(thm)],[212,10])).
% 75.21/18.73 thf(1464,plain,((~ (a @ sk5)) | (sk4 != sk2) | ((b @ sk5) != (b @ sk4))),inference(simp,[status(thm)],[1463])).
% 75.21/18.73 thf(1476,plain,((~ (a @ sk5)) | (sk4 != sk2) | (sk5 != sk4)),inference(simp,[status(thm)],[1464])).
% 75.21/18.73 thf(5997,plain,(~ (($true)) | (sk4 != sk2) | (sk5 != sk4) | ((a @ sk5) != (a @ sk4))),inference(paramod_ordered,[status(thm)],[5971,1476])).
% 75.21/18.73 thf(5998,plain,((sk4 != sk2) | (sk5 != sk4) | ((a @ sk5) != (a @ sk4))),inference(simp,[status(thm)],[5997])).
% 75.21/18.73 thf(6016,plain,((sk4 != sk2) | (sk5 != sk4) | (sk5 != sk4)),inference(simp,[status(thm)],[5998])).
% 75.21/18.73 thf(6023,plain,((sk4 != sk2) | (sk5 != sk4)),inference(simp,[status(thm)],[6016])).
% 75.21/18.73 thf(2764,plain,((rel @ (sk6 @ sk2 @ (^ [A:$i]: (($false)))) @ (sk6 @ (sk6 @ sk2 @ (^ [A:$i]: (($false)))) @ (a))) | (b @ (sk6 @ sk2 @ (^ [A:$i]: (($false)))))),inference(pre_uni,[status(thm)],[2728:[bind(A, $thf(a)),bind(B, $thf(sk6 @ sk2 @ (^ [C:$i]: (($false)))))]])).
% 75.21/18.73 thf(699,plain,((~ (s @ (sk7 @ sk4 @ (s)))) | ~ (($true)) | ((rel @ sk5 @ sk5) != (rel @ sk1 @ sk2))),inference(paramod_ordered,[status(thm)],[7,350])).
% 75.21/18.73 thf(700,plain,((~ (s @ (sk7 @ sk4 @ (s)))) | ((rel @ sk5 @ sk5) != (rel @ sk1 @ sk2))),inference(simp,[status(thm)],[699])).
% 75.21/18.73 thf(731,plain,((~ (s @ (sk7 @ sk4 @ (s)))) | (sk5 != sk1) | (sk5 != sk2)),inference(simp,[status(thm)],[700])).
% 75.21/18.73 thf(1996,plain,((~ (s @ (sk7 @ sk5 @ (s)))) | ~ (($true)) | ((rel @ sk5 @ (sk6 @ sk5 @ (s))) != (rel @ sk5 @ sk5))),inference(paramod_ordered,[status(thm)],[469,373])).
% 75.21/18.73 thf(1997,plain,((~ (s @ (sk7 @ sk5 @ (s)))) | ((rel @ sk5 @ (sk6 @ sk5 @ (s))) != (rel @ sk5 @ sk5))),inference(simp,[status(thm)],[1996])).
% 75.21/18.73 thf(2010,plain,((~ (s @ (sk7 @ sk5 @ (s)))) | (sk5 != sk5) | ((sk6 @ sk5 @ (s)) != sk5)),inference(simp,[status(thm)],[1997])).
% 75.21/18.73 thf(2041,plain,((~ (s @ (sk7 @ sk5 @ (s)))) | ((sk6 @ sk5 @ (s)) != sk5)),inference(simp,[status(thm)],[2010])).
% 75.21/18.73 thf(5547,plain,((sk5 != sk4) | ~ (($true)) | (b @ sk3) | ((a @ sk3) != (a @ sk3))),inference(paramod_ordered,[status(thm)],[5484,200])).
% 75.21/18.73 thf(5548,plain,((sk5 != sk4) | (b @ sk3) | ((a @ sk3) != (a @ sk3))),inference(simp,[status(thm)],[5547])).
% 75.21/18.73 thf(5549,plain,((sk5 != sk4) | (b @ sk3)),inference(pattern_uni,[status(thm)],[5548:[]])).
% 75.21/18.73 thf(10269,plain,(! [A:$i] : ((prop_c @ A) | ~ (($true)) | ((rel @ A @ (sk6 @ A @ (prop_c))) != (rel @ sk2 @ sk4)))),inference(paramod_ordered,[status(thm)],[511,7390])).
% 75.21/18.73 thf(10270,plain,(! [A:$i] : ((prop_c @ A) | ((rel @ A @ (sk6 @ A @ (prop_c))) != (rel @ sk2 @ sk4)))),inference(simp,[status(thm)],[10269])).
% 75.21/18.73 thf(10384,plain,(! [A:$i] : ((prop_c @ A) | (A != sk2) | ((sk6 @ A @ (prop_c)) != sk4))),inference(simp,[status(thm)],[10270])).
% 75.21/18.73 thf(10418,plain,((prop_c @ sk2) | ((sk6 @ sk2 @ (prop_c)) != sk4)),inference(simp,[status(thm)],[10384])).
% 75.21/18.73 thf(1990,plain,((~ (s @ (sk7 @ sk5 @ (s)))) | ~ (($true)) | ((rel @ sk5 @ sk5) != (rel @ sk4 @ sk5))),inference(paramod_ordered,[status(thm)],[12,373])).
% 75.21/18.73 thf(1991,plain,((~ (s @ (sk7 @ sk5 @ (s)))) | ((rel @ sk5 @ sk5) != (rel @ sk4 @ sk5))),inference(simp,[status(thm)],[1990])).
% 75.21/18.73 thf(2009,plain,((~ (s @ (sk7 @ sk5 @ (s)))) | (sk5 != sk4) | (sk5 != sk5)),inference(simp,[status(thm)],[1991])).
% 75.21/18.73 thf(2040,plain,((~ (s @ (sk7 @ sk5 @ (s)))) | (sk5 != sk4)),inference(simp,[status(thm)],[2009])).
% 75.21/18.73 thf(32,plain,(! [H:$i,G:$i,F:$i,E:($i > $o),D:$i,C:$i,B:$i,A:($i > $o)] : ((~ (A @ (sk7 @ B @ (A)))) | (~ (rel @ B @ C)) | (~ (rel @ C @ D)) | (~ (E @ (sk7 @ F @ (E)))) | ~ (($true)) | (~ (rel @ G @ H)) | (E @ H) | ((A @ D) != (rel @ F @ G)))),inference(paramod_ordered,[status(thm)],[25,25])).
% 75.21/18.73 thf(33,plain,(! [H:$i,G:$i,F:$i,E:($i > $o),D:$i,C:$i,B:$i,A:($i > $o)] : ((~ (A @ (sk7 @ B @ (A)))) | (~ (rel @ B @ C)) | (~ (rel @ C @ D)) | (~ (E @ (sk7 @ F @ (E)))) | (~ (rel @ G @ H)) | (E @ H) | ((A @ D) != (rel @ F @ G)))),inference(simp,[status(thm)],[32])).
% 75.21/18.73 thf(82,plain,(! [H:$i,G:$i,F:$i,E:($i > $o),D:$i,C:$i,B:$i,A:($i > $o)] : ((~ (A @ (sk7 @ B @ (A)))) | (~ (rel @ B @ C)) | (~ (rel @ C @ D)) | (~ ((sk7 @ F @ (E)) = (sk7 @ F @ ((=) @ $i @ (sk7 @ F @ E))))) | (~ (rel @ G @ H)) | ((sk7 @ F @ (E)) = H) | ((A @ D) != (rel @ F @ G)))),inference(replace_leibeq,[status(thm)],[33:[bind(A, $thf(A)),bind(B, $thf(B)),bind(C, $thf(C)),bind(D, $thf(D)),bind(E, $thf((=) @ $i @ (sk7 @ F @ E)))]])).
% 75.21/18.73 thf(94,plain,(! [H:$i,G:$i,F:$i,E:($i > $o),D:$i,C:$i,B:$i,A:($i > $o)] : (((sk7 @ F @ (E)) != (sk7 @ F @ ((=) @ $i @ (sk7 @ F @ E)))) | ((sk7 @ F @ (E)) = H) | (~ (A @ (sk7 @ B @ (A)))) | (~ (rel @ B @ C)) | (~ (rel @ C @ D)) | (~ (rel @ G @ H)) | ((A @ D) != (rel @ F @ G)))),inference(lifteq,[status(thm)],[82])).
% 75.21/18.73 thf(78,plain,(! [B:$i,A:($i > $o)] : ((~ ((sk7 @ B @ (A)) = (sk7 @ B @ ((=) @ $i @ (sk7 @ B @ A))))) | (~ (rel @ B @ sk2)) | ((sk7 @ B @ (A)) = sk3))),inference(replace_leibeq,[status(thm)],[53:[bind(A, $thf((=) @ $i @ (sk7 @ B @ A)))]])).
% 75.21/18.73 thf(90,plain,(! [B:$i,A:($i > $o)] : (((sk7 @ B @ (A)) != (sk7 @ B @ ((=) @ $i @ (sk7 @ B @ A)))) | ((sk7 @ B @ (A)) = sk3) | (~ (rel @ B @ sk2)))),inference(lifteq,[status(thm)],[78])).
% 75.21/18.73 thf(16059,plain,(($false)),inference(e,[status(thm)],[1875,361,688,1879,8283,88,8450,5,511,1305,10,1327,2042,5486,24,25,7390,14,110,89,7460,2011,678,546,102,7439,21,9,53,356,141,519,742,1329,7453,686,212,738,5973,13,2766,508,311,5359,45,22,743,8697,27,12,350,6024,113,7,6027,505,6029,209,749,1340,7454,18,5484,7462,16,7443,1849,11,497,6023,2764,731,2041,5549,5971,10418,19,373,635,2040,94,15,200,90,469,491])).
% 75.21/18.73 % SZS output end Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 75.21/18.73 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------