%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWV427^2 : 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 : n018.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 08:39:51 AM UTC 2026
% Result : Theorem 83.65s 18.45s
% Output : Refutation 71.75s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV427^2 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.08 % 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
% 0.09/0.21 % Computer : n018.cluster.edu
% 0.09/0.21 % Model : x86_64 x86_64
% 0.09/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.21 % Memory : 8046.5625MB
% 0.09/0.21 % OS : Linux 6.8.0-71-generic
% 0.09/0.21 % CPULimit : 300
% 0.09/0.21 % WCLimit : 300
% 0.09/0.21 % DateTime : Tue Sep 29 16:04:07 UTC 2026
% 0.09/0.21 % CPUTime :
% 0.09/0.21 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
% 1.03/0.87 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.49/1.12 % [INFO] Parsing done (253ms).
% 1.91/1.13 % [INFO] Running in sequential loop mode.
% 2.40/1.47 % [INFO] eprover registered as external prover.
% 2.40/1.48 % [INFO] Scanning for conjecture ...
% 2.97/1.60 % [INFO] Found a conjecture (or negated_conjecture) and 2 axioms. Running axiom selection ...
% 2.97/1.63 % [INFO] Axiom selection finished. Selected 2 axioms (removed 0 axioms).
% 2.97/1.64 % [INFO] Problem is higher-order (TPTP THF).
% 2.97/1.64 % [INFO] Type checking passed.
% 2.97/1.65 % [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 ...
% 83.65/18.44 % External prover 'e' found a proof!
% 83.65/18.44 % [INFO] Killing All external provers ...
% 83.65/18.45 % Time passed: 18092ms (effective reasoning time: 17308ms)
% 83.65/18.45 % 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)>
% 83.65/18.45 % Axioms used in derivation (2): trans_axiom, refl_axiom
% 83.65/18.45 % No. of inferences in proof: 248
% 83.65/18.45 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 18092 ms resp. 17308 ms w/o parsing
% 71.32/18.60 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% 71.32/18.60 thf(individuals_type, type, individuals: $tType).
% 71.32/18.60 thf(prop_a_decl, type, prop_a: ($i > $o)).
% 71.32/18.60 thf(prop_b_decl, type, prop_b: ($i > $o)).
% 71.32/18.60 thf(prop_c_decl, type, prop_c: ($i > $o)).
% 71.32/18.60 thf(mnot_decl, type, mnot: (($i > $o) > ($i > $o))).
% 71.32/18.60 thf(mor_decl, type, mor: (($i > $o) > (($i > $o) > ($i > $o)))).
% 71.32/18.60 thf(mimpl_decl, type, mimpl: (($i > $o) > (($i > $o) > ($i > $o)))).
% 71.32/18.60 thf(mbox_decl, type, mbox: (($i > ($i > $o)) > (($i > $o) > ($i > $o)))).
% 71.32/18.60 thf(mvalid_decl, type, mvalid: (($i > $o) > $o)).
% 71.32/18.60 thf(rel_decl, type, rel: ($i > ($i > $o))).
% 71.32/18.60 thf(icl_atom_decl, type, icl_atom: (($i > $o) > ($i > $o))).
% 71.32/18.60 thf(icl_princ_decl, type, icl_princ: (($i > $o) > ($i > $o))).
% 71.32/18.60 thf(icl_impl_decl, type, icl_impl: (($i > $o) > (($i > $o) > ($i > $o)))).
% 71.32/18.60 thf(icl_says_decl, type, icl_says: (($i > $o) > (($i > $o) > ($i > $o)))).
% 71.32/18.60 thf(iclval_decl, type, iclval: (($i > $o) > $o)).
% 71.32/18.60 thf(s_decl, type, s: ($i > $o)).
% 71.32/18.60 thf(a_decl, type, a: ($i > $o)).
% 71.32/18.60 thf(sk1_decl, type, sk1: $i).
% 71.75/18.60 thf(sk2_decl, type, sk2: $i).
% 71.75/18.60 thf(sk3_decl, type, sk3: $i).
% 71.75/18.60 thf(sk4_decl, type, sk4: $i).
% 71.75/18.60 thf(sk5_decl, type, sk5: ($i > (($i > $o) > $i))).
% 71.75/18.60 thf(sk6_decl, type, sk6: ($i > (($i > $o) > $i))).
% 71.75/18.60 thf(mnot_def, definition, mnot = (^ [A:($i > $o),B:$i]: ~ (A @ B)) ).
% 71.75/18.60 thf(mor_def, definition, mor = (^ [A:($i > $o),B:($i > $o),C:$i]: ((A @ C) | (B @ C))) ).
% 71.75/18.60 thf(mimpl_def, definition, mimpl = (^ [A:($i > $o)]: (mor @ (mnot @ A))) ).
% 71.75/18.60 thf(mbox_def, definition, mbox = (^ [A:($i > ($i > $o)),B:($i > $o),C:$i]: ! [D:$i]: ((A @ C @ D) => (B @ D))) ).
% 71.75/18.60 thf(mvalid_def, definition, mvalid = ((!) @ $i) ).
% 71.75/18.60 thf(icl_atom_def, definition, icl_atom = (mbox @ rel) ).
% 71.75/18.60 thf(icl_princ_def, definition, icl_princ = (^ [A:($i > $o)]: (A)) ).
% 71.75/18.60 thf(icl_impl_def, definition, icl_impl = (^ [A:($i > $o),B:($i > $o)]: (mbox @ rel @ (mimpl @ A @ B))) ).
% 71.75/18.60 thf(icl_says_def, definition, icl_says = (^ [A:($i > $o),B:($i > $o)]: (mbox @ rel @ (mor @ A @ B))) ).
% 71.75/18.60 thf(iclval_def, definition, iclval = (mvalid) ).
% 71.75/18.60 thf(sk1_def, definition, sk1 = (@+ [A:$i]: ~ (! [B:$i]: ((rel @ A @ B) => (~ (! [C:$i]: ((rel @ B @ C) => ((a @ C) | ! [D:$i]: ((rel @ C @ D) => ((a @ D) | ! [E:$i]: ((rel @ D @ E) => (s @ E))))))) | ! [C:$i]: ((rel @ B @ C) => ((a @ C) | ! [D:$i]: ((rel @ C @ D) => (s @ D)))))))) ).
% 71.75/18.60 thf(sk2_def, definition, sk2 = (@+ [A:$i]: ~ ((rel @ sk1 @ A) => (~ (! [B:$i]: ((rel @ A @ B) => ((a @ B) | ! [C:$i]: ((rel @ B @ C) => ((a @ C) | ! [D:$i]: ((rel @ C @ D) => (s @ D))))))) | ! [B:$i]: ((rel @ A @ B) => ((a @ B) | ! [C:$i]: ((rel @ B @ C) => (s @ C))))))) ).
% 71.75/18.60 thf(sk3_def, definition, sk3 = (@+ [A:$i]: ~ ((rel @ sk2 @ A) => ((a @ A) | ! [B:$i]: ((rel @ A @ B) => (s @ B))))) ).
% 71.75/18.60 thf(sk4_def, definition, sk4 = (@+ [A:$i]: ~ ((rel @ sk3 @ A) => (s @ A))) ).
% 71.75/18.60 thf(sk5_def, definition, sk5 = (^ [A:$i,B:($i > $o)]: (@+ [C:$i]: ~ ((rel @ A @ C) => (B @ C)))) ).
% 71.75/18.60 thf(sk6_def, definition, sk6 = (^ [A:$i,B:($i > $o)]: (@+ [C:$i]: ~ ((rel @ A @ C) => (B @ C)))) ).
% 71.75/18.60 thf(1,conjecture,((iclval @ (icl_impl @ (icl_says @ (icl_princ @ a) @ (icl_says @ (icl_princ @ a) @ (icl_atom @ s))) @ (icl_says @ (icl_princ @ a) @ (icl_atom @ s))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',idem)).
% 71.75/18.60 thf(2,negated_conjecture,((~ (iclval @ (icl_impl @ (icl_says @ (icl_princ @ a) @ (icl_says @ (icl_princ @ a) @ (icl_atom @ s))) @ (icl_says @ (icl_princ @ a) @ (icl_atom @ s)))))),inference(neg_conjecture,[status(cth)],[1])).
% 71.75/18.60 thf(5,plain,((~ (! [A:$i,B:$i]: ((rel @ A @ B) => (~ (! [C:$i]: ((rel @ B @ C) => ((a @ C) | ! [D:$i]: ((rel @ C @ D) => ((a @ D) | ! [E:$i]: ((rel @ D @ E) => (s @ E))))))) | ! [C:$i]: ((rel @ B @ C) => ((a @ C) | ! [D:$i]: ((rel @ C @ D) => (s @ D))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])).
% 71.75/18.60 thf(6,plain,(! [C:$i,B:$i,A:$i] : (((rel @ sk1 @ sk2) & (~ (rel @ sk2 @ A) | (a @ A) | ~ (rel @ A @ B) | (a @ B) | ~ (rel @ B @ C) | (s @ C)) & (rel @ sk2 @ sk3) & ~ (a @ sk3) & (rel @ sk3 @ sk4) & ~ (s @ sk4)))),inference(cnf,[status(esa)],[5])).
% 71.75/18.60 thf(12,plain,((rel @ sk1 @ sk2)),inference(cnfConj,[status(thm)],[6])).
% 71.75/18.60 thf(11,plain,((rel @ sk2 @ sk3)),inference(cnfConj,[status(thm)],[6])).
% 71.75/18.60 thf(4,axiom,((! [A:($i > $o)]: (mvalid @ (mimpl @ (mbox @ rel @ A) @ (mbox @ rel @ (mbox @ rel @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',trans_axiom)).
% 71.75/18.60 thf(19,plain,((! [A:($i > $o),B:$i]: (~ (! [C:$i]: ((rel @ B @ C) => (A @ C))) | ! [C:$i]: ((rel @ B @ C) => (! [D:$i]: ((rel @ C @ D) => (A @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4])).
% 71.75/18.60 thf(20,plain,(! [D:$i,C:$i,B:$i,A:($i > $o)] : ((((rel @ B @ (sk6 @ B @ (A))) | ~ (rel @ B @ C) | ~ (rel @ C @ D) | (A @ D)) & (~ (A @ (sk6 @ B @ (A))) | ~ (rel @ B @ C) | ~ (rel @ C @ D) | (A @ D))))),inference(cnf,[status(esa)],[19])).
% 71.75/18.60 thf(22,plain,(! [D:$i,C:$i,B:$i,A:($i > $o)] : ((~ (A @ (sk6 @ B @ (A)))) | (~ (rel @ B @ C)) | (~ (rel @ C @ D)) | (A @ D))),inference(cnfConj,[status(thm)],[20])).
% 71.75/18.60 thf(46,plain,(! [D:$i,C:$i,B:$i,A:($i > $o)] : ((~ (A @ (sk6 @ B @ (A)))) | (~ (rel @ B @ C)) | ~ (($true)) | (A @ D) | ((rel @ sk2 @ sk3) != (rel @ C @ D)))),inference(paramod_ordered,[status(thm)],[11,22])).
% 71.75/18.60 thf(47,plain,(! [D:$i,C:$i,B:$i,A:($i > $o)] : ((~ (A @ (sk6 @ B @ (A)))) | (~ (rel @ B @ C)) | (A @ D) | ((rel @ sk2 @ sk3) != (rel @ C @ D)))),inference(simp,[status(thm)],[46])).
% 71.75/18.60 thf(48,plain,(! [B:$i,A:($i > $o)] : ((~ (A @ (sk6 @ B @ (A)))) | (~ (rel @ B @ sk2)) | (A @ sk3))),inference(pattern_uni,[status(thm)],[47:[bind(A, $thf(A)),bind(B, $thf(B)),bind(C, $thf(sk2)),bind(D, $thf(sk3))]])).
% 71.75/18.60 thf(2803,plain,(! [B:$i,A:($i > $o)] : ((~ (A @ (sk6 @ B @ (A)))) | ~ (($true)) | (A @ sk3) | ((rel @ sk1 @ sk2) != (rel @ B @ sk2)))),inference(paramod_ordered,[status(thm)],[12,48])).
% 71.75/18.60 thf(2804,plain,(! [B:$i,A:($i > $o)] : ((~ (A @ (sk6 @ B @ (A)))) | (A @ sk3) | ((rel @ sk1 @ sk2) != (rel @ B @ sk2)))),inference(simp,[status(thm)],[2803])).
% 71.75/18.60 thf(2805,plain,(! [A:($i > $o)] : ((~ (A @ (sk6 @ sk1 @ (A)))) | (A @ sk3))),inference(pattern_uni,[status(thm)],[2804:[bind(A, $thf(A)),bind(B, $thf(sk1))]])).
% 71.75/18.60 thf(8085,plain,((~ (prop_b @ (sk6 @ sk1 @ (prop_b)))) | (prop_b @ sk3)),inference(prim_subst,[status(thm)],[2805:[bind(A, $thf(prop_b))]])).
% 71.75/18.60 thf(3,axiom,((! [A:($i > $o)]: (mvalid @ (mimpl @ (mbox @ rel @ A) @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',refl_axiom)).
% 71.75/18.60 thf(13,plain,((! [A:($i > $o),B:$i]: (~ (! [C:$i]: ((rel @ B @ C) => (A @ C))) | (A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3])).
% 71.75/18.60 thf(14,plain,(! [B:$i,A:($i > $o)] : ((((rel @ B @ (sk5 @ B @ (A))) | (A @ B)) & (~ (A @ (sk5 @ B @ (A))) | (A @ B))))),inference(cnf,[status(esa)],[13])).
% 71.75/18.60 thf(15,plain,(! [B:$i,A:($i > $o)] : ((rel @ B @ (sk5 @ B @ (A))) | (A @ B))),inference(cnfConj,[status(thm)],[14])).
% 71.75/18.60 thf(7,plain,((rel @ sk3 @ sk4)),inference(cnfConj,[status(thm)],[6])).
% 71.75/18.60 thf(38,plain,(! [D:$i,C:$i,B:$i,A:($i > $o)] : ((~ (A @ (sk6 @ B @ (A)))) | (~ (rel @ B @ C)) | ~ (($true)) | (A @ D) | ((rel @ sk3 @ sk4) != (rel @ C @ D)))),inference(paramod_ordered,[status(thm)],[7,22])).
% 71.75/18.60 thf(39,plain,(! [D:$i,C:$i,B:$i,A:($i > $o)] : ((~ (A @ (sk6 @ B @ (A)))) | (~ (rel @ B @ C)) | (A @ D) | ((rel @ sk3 @ sk4) != (rel @ C @ D)))),inference(simp,[status(thm)],[38])).
% 71.75/18.60 thf(40,plain,(! [B:$i,A:($i > $o)] : ((~ (A @ (sk6 @ B @ (A)))) | (~ (rel @ B @ sk3)) | (A @ sk4))),inference(pattern_uni,[status(thm)],[39:[bind(A, $thf(A)),bind(B, $thf(B)),bind(C, $thf(sk3)),bind(D, $thf(sk4))]])).
% 71.75/18.60 thf(2149,plain,(! [B:$i,A:($i > $o)] : ((~ (A @ (sk6 @ B @ (A)))) | ~ (($true)) | (A @ sk4) | ((rel @ sk2 @ sk3) != (rel @ B @ sk3)))),inference(paramod_ordered,[status(thm)],[11,40])).
% 71.75/18.60 thf(2150,plain,(! [B:$i,A:($i > $o)] : ((~ (A @ (sk6 @ B @ (A)))) | (A @ sk4) | ((rel @ sk2 @ sk3) != (rel @ B @ sk3)))),inference(simp,[status(thm)],[2149])).
% 71.75/18.60 thf(2151,plain,(! [A:($i > $o)] : ((~ (A @ (sk6 @ sk2 @ (A)))) | (A @ sk4))),inference(pattern_uni,[status(thm)],[2150:[bind(A, $thf(A)),bind(B, $thf(sk2))]])).
% 71.75/18.60 thf(4452,plain,((~ (prop_b @ (sk6 @ sk2 @ (prop_b)))) | (prop_b @ sk4)),inference(prim_subst,[status(thm)],[2151:[bind(A, $thf(prop_b))]])).
% 71.75/18.60 thf(5796,plain,(! [B:$i,A:($i > $o)] : ((rel @ B @ (sk5 @ B @ (A))) | ~ (($true)) | (prop_b @ sk4) | ((A @ B) != (prop_b @ (sk6 @ sk2 @ (prop_b)))))),inference(paramod_ordered,[status(thm)],[15,4452])).
% 71.75/18.60 thf(5797,plain,(! [B:$i,A:($i > $o)] : ((rel @ B @ (sk5 @ B @ (A))) | (prop_b @ sk4) | ((A @ B) != (prop_b @ (sk6 @ sk2 @ (prop_b)))))),inference(simp,[status(thm)],[5796])).
% 71.75/18.60 thf(5808,plain,((rel @ sk2 @ (sk5 @ sk2 @ (^ [A:$i]: (prop_b @ (sk6 @ A @ prop_b))))) | (prop_b @ sk4)),inference(pre_uni,[status(thm)],[5797:[bind(A, $thf(^ [C:$i]: (prop_b @ (sk6 @ C @ prop_b)))),bind(B, $thf(sk2))]])).
% 71.75/18.60 thf(16,plain,(! [B:$i,A:($i > $o)] : ((~ (A @ (sk5 @ B @ (A)))) | (A @ B))),inference(cnfConj,[status(thm)],[14])).
% 71.75/18.60 thf(8,plain,((~ (a @ sk3))),inference(cnfConj,[status(thm)],[6])).
% 71.75/18.60 thf(49,plain,(! [D:$i,C:$i,B:$i,A:($i > $o)] : ((~ (A @ (sk6 @ B @ (A)))) | (~ (rel @ B @ C)) | (~ (rel @ C @ D)) | ~ (($true)) | ((A @ D) != (a @ sk3)))),inference(paramod_ordered,[status(thm)],[22,8])).
% 71.75/18.60 thf(50,plain,(! [D:$i,C:$i,B:$i,A:($i > $o)] : ((~ (A @ (sk6 @ B @ (A)))) | (~ (rel @ B @ C)) | (~ (rel @ C @ D)) | ((A @ D) != (a @ sk3)))),inference(simp,[status(thm)],[49])).
% 71.75/18.60 thf(101,plain,(! [B:$i,A:$i] : ((~ (a @ (sk6 @ A @ (a)))) | (~ (rel @ A @ B)) | (~ (rel @ B @ sk3)))),inference(pre_uni,[status(thm)],[50:[bind(A, $thf(a)),bind(B, $thf(B)),bind(C, $thf(C)),bind(D, $thf(sk3))]])).
% 71.75/18.60 thf(128,plain,(! [B:$i,A:$i] : ((~ (a @ (sk6 @ A @ (a)))) | (~ (rel @ A @ B)) | (~ (rel @ B @ sk3)))),inference(simp,[status(thm)],[101])).
% 71.75/18.60 thf(300,plain,(! [B:$i,A:$i] : ((~ (a @ (sk6 @ A @ (a)))) | ~ (($true)) | (~ (rel @ B @ sk3)) | ((rel @ sk3 @ sk4) != (rel @ A @ B)))),inference(paramod_ordered,[status(thm)],[7,128])).
% 71.75/18.60 thf(301,plain,(! [B:$i,A:$i] : ((~ (a @ (sk6 @ A @ (a)))) | (~ (rel @ B @ sk3)) | ((rel @ sk3 @ sk4) != (rel @ A @ B)))),inference(simp,[status(thm)],[300])).
% 71.75/18.60 thf(302,plain,((~ (a @ (sk6 @ sk3 @ (a)))) | (~ (rel @ sk4 @ sk3))),inference(pattern_uni,[status(thm)],[301:[bind(A, $thf(sk3)),bind(B, $thf(sk4))]])).
% 71.75/18.60 thf(718,plain,((~ (a @ (sk6 @ sk3 @ (a)))) | ~ (($true)) | ((rel @ sk4 @ sk3) != (rel @ sk2 @ sk3))),inference(paramod_ordered,[status(thm)],[11,302])).
% 71.75/18.60 thf(719,plain,((~ (a @ (sk6 @ sk3 @ (a)))) | ((rel @ sk4 @ sk3) != (rel @ sk2 @ sk3))),inference(simp,[status(thm)],[718])).
% 71.75/18.60 thf(728,plain,((~ (a @ (sk6 @ sk3 @ (a)))) | (sk4 != sk2) | (sk3 != sk3)),inference(simp,[status(thm)],[719])).
% 71.75/18.60 thf(754,plain,((~ (a @ (sk6 @ sk3 @ (a)))) | (sk4 != sk2)),inference(simp,[status(thm)],[728])).
% 71.75/18.60 thf(760,plain,(! [B:$i,A:($i > $o)] : ((rel @ B @ (sk5 @ B @ (A))) | ~ (($true)) | (sk4 != sk2) | ((A @ B) != (a @ (sk6 @ sk3 @ (a)))))),inference(paramod_ordered,[status(thm)],[15,754])).
% 71.75/18.60 thf(761,plain,(! [B:$i,A:($i > $o)] : ((rel @ B @ (sk5 @ B @ (A))) | (sk4 != sk2) | ((A @ B) != (a @ (sk6 @ sk3 @ (a)))))),inference(simp,[status(thm)],[760])).
% 71.75/18.60 thf(767,plain,((rel @ sk3 @ (sk5 @ sk3 @ (^ [A:$i]: (a @ (sk6 @ A @ a))))) | (sk4 != sk2)),inference(pre_uni,[status(thm)],[761:[bind(A, $thf(^ [C:$i]: (a @ (sk6 @ C @ a)))),bind(B, $thf(sk3))]])).
% 71.75/18.60 thf(710,plain,(! [B:$i,A:($i > $o)] : ((rel @ B @ (sk5 @ B @ (A))) | (~ (a @ (sk6 @ sk3 @ (a)))) | ~ (($true)) | ((A @ B) != (rel @ sk4 @ sk3)))),inference(paramod_ordered,[status(thm)],[15,302])).
% 71.75/18.60 thf(711,plain,(! [B:$i,A:($i > $o)] : ((rel @ B @ (sk5 @ B @ (A))) | (~ (a @ (sk6 @ sk3 @ (a)))) | ((A @ B) != (rel @ sk4 @ sk3)))),inference(simp,[status(thm)],[710])).
% 71.75/18.60 thf(730,plain,((rel @ sk4 @ (sk5 @ sk4 @ (^ [A:$i]: (rel @ A @ sk3)))) | (~ (a @ (sk6 @ sk3 @ (a))))),inference(pre_uni,[status(thm)],[711:[bind(A, $thf(^ [C:$i]: (rel @ C @ sk3))),bind(B, $thf(sk4))]])).
% 71.75/18.60 thf(4457,plain,((~ (s @ (sk6 @ sk2 @ (s)))) | (s @ sk4)),inference(prim_subst,[status(thm)],[2151:[bind(A, $thf(s))]])).
% 71.75/18.60 thf(10,plain,((~ (s @ sk4))),inference(cnfConj,[status(thm)],[6])).
% 71.75/18.60 thf(5821,plain,((~ (s @ (sk6 @ sk2 @ (s)))) | ($false)),inference(rewrite,[status(thm)],[4457,10])).
% 71.75/18.60 thf(5822,plain,((~ (s @ (sk6 @ sk2 @ (s))))),inference(simp,[status(thm)],[5821])).
% 71.75/18.60 thf(5832,plain,(! [B:$i,A:($i > $o)] : ((rel @ B @ (sk5 @ B @ (A))) | ~ (($true)) | ((A @ B) != (s @ (sk6 @ sk2 @ (s)))))),inference(paramod_ordered,[status(thm)],[15,5822])).
% 71.75/18.60 thf(5833,plain,(! [B:$i,A:($i > $o)] : ((rel @ B @ (sk5 @ B @ (A))) | ((A @ B) != (s @ (sk6 @ sk2 @ (s)))))),inference(simp,[status(thm)],[5832])).
% 71.75/18.60 thf(5842,plain,((rel @ (sk6 @ sk2 @ (s)) @ (sk5 @ (sk6 @ sk2 @ (s)) @ (s)))),inference(pre_uni,[status(thm)],[5833:[bind(A, $thf(s)),bind(B, $thf(sk6 @ sk2 @ (s)))]])).
% 71.75/18.60 thf(337,plain,(! [B:$i,A:($i > $o)] : ((rel @ B @ (sk5 @ B @ (A))) | ~ (($true)) | ((A @ B) != (s @ sk4)))),inference(paramod_ordered,[status(thm)],[15,10])).
% 71.75/18.60 thf(338,plain,(! [B:$i,A:($i > $o)] : ((rel @ B @ (sk5 @ B @ (A))) | ((A @ B) != (s @ sk4)))),inference(simp,[status(thm)],[337])).
% 71.75/18.60 thf(446,plain,((rel @ sk4 @ (sk5 @ sk4 @ (s)))),inference(pre_uni,[status(thm)],[338:[bind(A, $thf(s)),bind(B, $thf(sk4))]])).
% 71.75/18.60 thf(509,plain,(! [B:$i,A:$i] : ((~ (a @ (sk6 @ A @ (a)))) | ~ (($true)) | (~ (rel @ B @ sk3)) | ((rel @ sk4 @ (sk5 @ sk4 @ (s))) != (rel @ A @ B)))),inference(paramod_ordered,[status(thm)],[446,128])).
% 71.75/18.60 thf(510,plain,(! [B:$i,A:$i] : ((~ (a @ (sk6 @ A @ (a)))) | (~ (rel @ B @ sk3)) | ((rel @ sk4 @ (sk5 @ sk4 @ (s))) != (rel @ A @ B)))),inference(simp,[status(thm)],[509])).
% 71.75/18.60 thf(511,plain,((~ (a @ (sk6 @ sk4 @ (a)))) | (~ (rel @ (sk5 @ sk4 @ (s)) @ sk3))),inference(pattern_uni,[status(thm)],[510:[bind(A, $thf(sk4)),bind(B, $thf(sk5 @ sk4 @ (s)))]])).
% 71.75/18.60 thf(8478,plain,(! [B:$i,A:($i > $o)] : ((rel @ B @ (sk5 @ B @ (A))) | ~ (($true)) | (prop_b @ sk3) | ((A @ B) != (prop_b @ (sk6 @ sk1 @ (prop_b)))))),inference(paramod_ordered,[status(thm)],[15,8085])).
% 71.75/18.60 thf(8479,plain,(! [B:$i,A:($i > $o)] : ((rel @ B @ (sk5 @ B @ (A))) | (prop_b @ sk3) | ((A @ B) != (prop_b @ (sk6 @ sk1 @ (prop_b)))))),inference(simp,[status(thm)],[8478])).
% 71.75/18.60 thf(8490,plain,((rel @ sk1 @ (sk5 @ sk1 @ (^ [A:$i]: (prop_b @ (sk6 @ A @ prop_b))))) | (prop_b @ sk3)),inference(pre_uni,[status(thm)],[8479:[bind(A, $thf(^ [C:$i]: (prop_b @ (sk6 @ C @ prop_b)))),bind(B, $thf(sk1))]])).
% 71.75/18.60 thf(395,plain,(! [A:$i] : ((rel @ A @ (sk5 @ A @ (^ [B:$i]: (($false))))) | ($false))),inference(prim_subst,[status(thm)],[15:[bind(A, $thf(^ [C:$i]: (($false))))]])).
% 71.75/18.60 thf(454,plain,(! [A:$i] : ((rel @ A @ (sk5 @ A @ (^ [B:$i]: (($false))))))),inference(simp,[status(thm)],[395])).
% 71.75/18.60 thf(722,plain,(! [A:$i] : ((~ (a @ (sk6 @ sk3 @ (a)))) | ~ (($true)) | ((rel @ A @ (sk5 @ A @ (^ [B:$i]: (($false))))) != (rel @ sk4 @ sk3)))),inference(paramod_ordered,[status(thm)],[454,302])).
% 71.75/18.60 thf(723,plain,(! [A:$i] : ((~ (a @ (sk6 @ sk3 @ (a)))) | ((rel @ A @ (sk5 @ A @ (^ [B:$i]: (($false))))) != (rel @ sk4 @ sk3)))),inference(simp,[status(thm)],[722])).
% 71.75/18.60 thf(738,plain,(! [A:$i] : ((~ (a @ (sk6 @ sk3 @ (a)))) | (A != sk4) | ((sk5 @ A @ (^ [B:$i]: (($false)))) != sk3))),inference(simp,[status(thm)],[723])).
% 71.75/18.60 thf(747,plain,((~ (a @ (sk6 @ sk3 @ (a)))) | ((sk5 @ sk4 @ (^ [A:$i]: (($false)))) != sk3)),inference(simp,[status(thm)],[738])).
% 71.75/18.60 thf(4446,plain,((~ (prop_a @ (sk6 @ sk2 @ (prop_a)))) | (prop_a @ sk4)),inference(prim_subst,[status(thm)],[2151:[bind(A, $thf(prop_a))]])).
% 71.75/18.60 thf(5728,plain,(! [B:$i,A:($i > $o)] : ((rel @ B @ (sk5 @ B @ (A))) | ~ (($true)) | (prop_a @ sk4) | ((A @ B) != (prop_a @ (sk6 @ sk2 @ (prop_a)))))),inference(paramod_ordered,[status(thm)],[15,4446])).
% 71.75/18.60 thf(5729,plain,(! [B:$i,A:($i > $o)] : ((rel @ B @ (sk5 @ B @ (A))) | (prop_a @ sk4) | ((A @ B) != (prop_a @ (sk6 @ sk2 @ (prop_a)))))),inference(simp,[status(thm)],[5728])).
% 71.75/18.60 thf(5740,plain,((rel @ sk2 @ (sk5 @ sk2 @ (^ [A:$i]: (prop_a @ (sk6 @ A @ prop_a))))) | (prop_a @ sk4)),inference(pre_uni,[status(thm)],[5729:[bind(A, $thf(^ [C:$i]: (prop_a @ (sk6 @ C @ prop_a)))),bind(B, $thf(sk2))]])).
% 71.75/18.60 thf(8086,plain,((~ (s @ (sk6 @ sk1 @ (s)))) | (s @ sk3)),inference(prim_subst,[status(thm)],[2805:[bind(A, $thf(s))]])).
% 71.75/18.60 thf(716,plain,((~ (a @ (sk6 @ sk3 @ (a)))) | ~ (($true)) | ((rel @ sk4 @ sk3) != (rel @ sk3 @ sk4))),inference(paramod_ordered,[status(thm)],[7,302])).
% 71.75/18.60 thf(717,plain,((~ (a @ (sk6 @ sk3 @ (a)))) | ((rel @ sk4 @ sk3) != (rel @ sk3 @ sk4))),inference(simp,[status(thm)],[716])).
% 71.75/18.60 thf(733,plain,((~ (a @ (sk6 @ sk3 @ (a)))) | (sk4 != sk3) | (sk4 != sk3)),inference(simp,[status(thm)],[717])).
% 71.75/18.60 thf(756,plain,((~ (a @ (sk6 @ sk3 @ (a)))) | (sk4 != sk3)),inference(simp,[status(thm)],[733])).
% 71.75/18.60 thf(775,plain,(! [B:$i,A:($i > $o)] : ((rel @ B @ (sk5 @ B @ (A))) | ~ (($true)) | (sk4 != sk3) | ((A @ B) != (a @ (sk6 @ sk3 @ (a)))))),inference(paramod_ordered,[status(thm)],[15,756])).
% 71.75/18.60 thf(776,plain,(! [B:$i,A:($i > $o)] : ((rel @ B @ (sk5 @ B @ (A))) | (sk4 != sk3) | ((A @ B) != (a @ (sk6 @ sk3 @ (a)))))),inference(simp,[status(thm)],[775])).
% 71.75/18.60 thf(782,plain,((rel @ sk3 @ (sk5 @ sk3 @ (^ [A:$i]: (a @ (sk6 @ A @ a))))) | (sk4 != sk3)),inference(pre_uni,[status(thm)],[776:[bind(A, $thf(^ [C:$i]: (a @ (sk6 @ C @ a)))),bind(B, $thf(sk3))]])).
% 71.75/18.60 thf(235,plain,(! [A:$i] : ((~ (a @ (sk5 @ A @ (a)))) | (a @ A))),inference(prim_subst,[status(thm)],[16:[bind(A, $thf(a))]])).
% 71.75/18.60 thf(257,plain,(! [A:$i] : ((~ (a @ (sk5 @ A @ (a)))) | (a @ A))),inference(simp,[status(thm)],[235])).
% 71.75/18.60 thf(295,plain,(! [B:$i,A:$i] : ((~ (a @ (sk6 @ A @ (a)))) | ~ (($true)) | (~ (rel @ B @ sk3)) | ((rel @ sk1 @ sk2) != (rel @ A @ B)))),inference(paramod_ordered,[status(thm)],[12,128])).
% 71.75/18.60 thf(296,plain,(! [B:$i,A:$i] : ((~ (a @ (sk6 @ A @ (a)))) | (~ (rel @ B @ sk3)) | ((rel @ sk1 @ sk2) != (rel @ A @ B)))),inference(simp,[status(thm)],[295])).
% 71.75/18.60 thf(297,plain,((~ (a @ (sk6 @ sk1 @ (a)))) | (~ (rel @ sk2 @ sk3))),inference(pattern_uni,[status(thm)],[296:[bind(A, $thf(sk1)),bind(B, $thf(sk2))]])).
% 71.75/18.60 thf(327,plain,((~ (a @ (sk6 @ sk1 @ (a)))) | ~ (($true))),inference(rewrite,[status(thm)],[297,11])).
% 71.75/18.60 thf(328,plain,((~ (a @ (sk6 @ sk1 @ (a))))),inference(simp,[status(thm)],[327])).
% 71.75/18.60 thf(356,plain,(! [B:$i,A:($i > $o)] : ((rel @ B @ (sk5 @ B @ (A))) | ~ (($true)) | ((A @ B) != (a @ (sk6 @ sk1 @ (a)))))),inference(paramod_ordered,[status(thm)],[15,328])).
% 71.75/18.60 thf(357,plain,(! [B:$i,A:($i > $o)] : ((rel @ B @ (sk5 @ B @ (A))) | ((A @ B) != (a @ (sk6 @ sk1 @ (a)))))),inference(simp,[status(thm)],[356])).
% 71.75/18.60 thf(417,plain,((rel @ (sk6 @ sk1 @ (a)) @ (sk5 @ (sk6 @ sk1 @ (a)) @ (a)))),inference(pre_uni,[status(thm)],[357:[bind(A, $thf(a)),bind(B, $thf(sk6 @ sk1 @ (a)))]])).
% 71.75/18.60 thf(23,plain,(! [D:$i,C:$i,B:$i,A:($i > $o)] : ((~ ((sk6 @ B @ (A)) = (sk6 @ B @ ((=) @ $i @ (sk6 @ B @ A))))) | (~ (rel @ B @ C)) | (~ (rel @ C @ D)) | ((sk6 @ B @ (A)) = D))),inference(replace_leibeq,[status(thm)],[22:[bind(A, $thf((=) @ $i @ (sk6 @ B @ A)))]])).
% 71.75/18.60 thf(24,plain,(! [D:$i,C:$i,B:$i,A:($i > $o)] : (((sk6 @ B @ (A)) != (sk6 @ B @ ((=) @ $i @ (sk6 @ B @ A)))) | ((sk6 @ B @ (A)) = D) | (~ (rel @ B @ C)) | (~ (rel @ C @ D)))),inference(lifteq,[status(thm)],[23])).
% 71.75/18.60 thf(8089,plain,((~ (prop_a @ (sk6 @ sk1 @ (prop_a)))) | (prop_a @ sk3)),inference(prim_subst,[status(thm)],[2805:[bind(A, $thf(prop_a))]])).
% 71.75/18.60 thf(720,plain,((~ (a @ (sk6 @ sk3 @ (a)))) | ~ (($true)) | ((rel @ sk4 @ (sk5 @ sk4 @ (s))) != (rel @ sk4 @ sk3))),inference(paramod_ordered,[status(thm)],[446,302])).
% 71.75/18.60 thf(721,plain,((~ (a @ (sk6 @ sk3 @ (a)))) | ((rel @ sk4 @ (sk5 @ sk4 @ (s))) != (rel @ sk4 @ sk3))),inference(simp,[status(thm)],[720])).
% 71.75/18.60 thf(742,plain,((~ (a @ (sk6 @ sk3 @ (a)))) | (sk4 != sk4) | ((sk5 @ sk4 @ (s)) != sk3)),inference(simp,[status(thm)],[721])).
% 71.75/18.60 thf(751,plain,((~ (a @ (sk6 @ sk3 @ (a)))) | ((sk5 @ sk4 @ (s)) != sk3)),inference(simp,[status(thm)],[742])).
% 71.75/18.60 thf(311,plain,(! [B:$i,A:$i] : ((~ (a @ (sk6 @ A @ (a)))) | (~ (rel @ A @ B)) | ((rel @ B @ sk3) != (rel @ A @ B)) | ~ (($true)))),inference(eqfactor_ordered,[status(thm)],[128])).
% 71.75/18.60 thf(312,plain,((~ (a @ (sk6 @ sk3 @ (a)))) | (~ (rel @ sk3 @ sk3))),inference(pattern_uni,[status(thm)],[311:[bind(A, $thf(sk3)),bind(B, $thf(sk3))]])).
% 71.75/18.60 thf(1263,plain,(! [A:$i] : ((~ (a @ (sk6 @ sk3 @ (a)))) | ~ (($true)) | ((rel @ A @ (sk5 @ A @ (^ [B:$i]: (($false))))) != (rel @ sk3 @ sk3)))),inference(paramod_ordered,[status(thm)],[454,312])).
% 71.75/18.60 thf(1264,plain,(! [A:$i] : ((~ (a @ (sk6 @ sk3 @ (a)))) | ((rel @ A @ (sk5 @ A @ (^ [B:$i]: (($false))))) != (rel @ sk3 @ sk3)))),inference(simp,[status(thm)],[1263])).
% 71.75/18.60 thf(1270,plain,(! [A:$i] : ((~ (a @ (sk6 @ sk3 @ (a)))) | (A != sk3) | ((sk5 @ A @ (^ [B:$i]: (($false)))) != sk3))),inference(simp,[status(thm)],[1264])).
% 71.75/18.60 thf(1313,plain,((~ (a @ (sk6 @ sk3 @ (a)))) | ((sk5 @ sk3 @ (^ [A:$i]: (($false)))) != sk3)),inference(simp,[status(thm)],[1270])).
% 71.75/18.60 thf(2337,plain,((~ (a @ (sk6 @ sk4 @ (a)))) | ~ (($true)) | ((rel @ (sk5 @ sk4 @ (s)) @ sk3) != (rel @ sk1 @ sk2))),inference(paramod_ordered,[status(thm)],[12,511])).
% 71.75/18.60 thf(2338,plain,((~ (a @ (sk6 @ sk4 @ (a)))) | ((rel @ (sk5 @ sk4 @ (s)) @ sk3) != (rel @ sk1 @ sk2))),inference(simp,[status(thm)],[2337])).
% 71.75/18.60 thf(2403,plain,((~ (a @ (sk6 @ sk4 @ (a)))) | ((sk5 @ sk4 @ (s)) != sk1) | (sk3 != sk2)),inference(simp,[status(thm)],[2338])).
% 71.75/18.60 thf(308,plain,(! [B:$i,A:$i] : ((~ (a @ (sk6 @ A @ (a)))) | (~ (rel @ A @ B)) | ~ (($true)) | ((rel @ sk2 @ sk3) != (rel @ B @ sk3)))),inference(paramod_ordered,[status(thm)],[11,128])).
% 71.75/18.60 thf(309,plain,(! [B:$i,A:$i] : ((~ (a @ (sk6 @ A @ (a)))) | (~ (rel @ A @ B)) | ((rel @ sk2 @ sk3) != (rel @ B @ sk3)))),inference(simp,[status(thm)],[308])).
% 71.75/18.60 thf(310,plain,(! [A:$i] : ((~ (a @ (sk6 @ A @ (a)))) | (~ (rel @ A @ sk2)))),inference(pattern_uni,[status(thm)],[309:[bind(A, $thf(A)),bind(B, $thf(sk2))]])).
% 71.75/18.60 thf(2012,plain,(! [A:$i] : ((~ (a @ (sk6 @ A @ (a)))) | ~ (($true)) | ((rel @ sk4 @ (sk5 @ sk4 @ (s))) != (rel @ A @ sk2)))),inference(paramod_ordered,[status(thm)],[446,310])).
% 71.75/18.60 thf(2013,plain,(! [A:$i] : ((~ (a @ (sk6 @ A @ (a)))) | ((rel @ sk4 @ (sk5 @ sk4 @ (s))) != (rel @ A @ sk2)))),inference(simp,[status(thm)],[2012])).
% 71.75/18.60 thf(2024,plain,(! [A:$i] : ((~ (a @ (sk6 @ A @ (a)))) | (sk4 != A) | ((sk5 @ sk4 @ (s)) != sk2))),inference(simp,[status(thm)],[2013])).
% 71.75/18.60 thf(2049,plain,((~ (a @ (sk6 @ sk4 @ (a)))) | ((sk5 @ sk4 @ (s)) != sk2)),inference(simp,[status(thm)],[2024])).
% 71.75/18.60 thf(305,plain,(! [B:$i,A:$i] : ((~ (a @ (sk6 @ A @ (a)))) | ~ (($true)) | (~ (rel @ B @ sk3)) | ((rel @ sk2 @ sk3) != (rel @ A @ B)))),inference(paramod_ordered,[status(thm)],[11,128])).
% 71.75/18.60 thf(306,plain,(! [B:$i,A:$i] : ((~ (a @ (sk6 @ A @ (a)))) | (~ (rel @ B @ sk3)) | ((rel @ sk2 @ sk3) != (rel @ A @ B)))),inference(simp,[status(thm)],[305])).
% 71.75/18.60 thf(307,plain,((~ (a @ (sk6 @ sk2 @ (a)))) | (~ (rel @ sk3 @ sk3))),inference(pattern_uni,[status(thm)],[306:[bind(A, $thf(sk2)),bind(B, $thf(sk3))]])).
% 71.75/18.60 thf(799,plain,(! [B:$i,A:($i > $o)] : ((rel @ B @ (sk5 @ B @ (A))) | (~ (a @ (sk6 @ sk2 @ (a)))) | ~ (($true)) | ((A @ B) != (rel @ sk3 @ sk3)))),inference(paramod_ordered,[status(thm)],[15,307])).
% 71.75/18.60 thf(800,plain,(! [B:$i,A:($i > $o)] : ((rel @ B @ (sk5 @ B @ (A))) | (~ (a @ (sk6 @ sk2 @ (a)))) | ((A @ B) != (rel @ sk3 @ sk3)))),inference(simp,[status(thm)],[799])).
% 71.75/18.60 thf(823,plain,((rel @ sk3 @ (sk5 @ sk3 @ (rel @ sk3))) | (~ (a @ (sk6 @ sk2 @ (a))))),inference(pre_uni,[status(thm)],[800:[bind(A, $thf(rel @ sk3)),bind(B, $thf(sk3))]])).
% 71.75/18.60 thf(14139,plain,(! [B:$i,A:($i > $o)] : ((~ (a @ (sk6 @ sk2 @ (a)))) | ~ (($true)) | (A @ B) | ((rel @ sk3 @ (sk5 @ sk3 @ (rel @ sk3))) != (A @ (sk5 @ B @ (A)))))),inference(paramod_ordered,[status(thm)],[823,16])).
% 71.75/18.60 thf(14140,plain,(! [B:$i,A:($i > $o)] : ((~ (a @ (sk6 @ sk2 @ (a)))) | (A @ B) | ((rel @ sk3 @ (sk5 @ sk3 @ (rel @ sk3))) != (A @ (sk5 @ B @ (A)))))),inference(simp,[status(thm)],[14139])).
% 71.75/18.60 thf(14353,plain,((~ (a @ (sk6 @ sk2 @ (a)))) | (rel @ sk3 @ sk3)),inference(pre_uni,[status(thm)],[14140:[bind(A, $thf(rel @ sk3)),bind(B, $thf(sk3))]])).
% 71.75/18.60 thf(14448,plain,((~ (a @ (sk6 @ sk2 @ (a)))) | (~ (a @ (sk6 @ sk2 @ (a)))) | ~ (($true)) | ((rel @ sk3 @ sk3) != (rel @ sk3 @ sk3))),inference(paramod_ordered,[status(thm)],[14353,307])).
% 71.75/18.60 thf(14449,plain,((~ (a @ (sk6 @ sk2 @ (a)))) | ((rel @ sk3 @ sk3) != (rel @ sk3 @ sk3))),inference(simp,[status(thm)],[14448])).
% 71.75/18.60 thf(14450,plain,((~ (a @ (sk6 @ sk2 @ (a))))),inference(pattern_uni,[status(thm)],[14449:[]])).
% 71.75/18.60 thf(15103,plain,(! [B:$i,A:($i > $o)] : ((rel @ B @ (sk5 @ B @ (A))) | ~ (($true)) | ((A @ B) != (a @ (sk6 @ sk2 @ (a)))))),inference(paramod_ordered,[status(thm)],[15,14450])).
% 71.75/18.60 thf(15104,plain,(! [B:$i,A:($i > $o)] : ((rel @ B @ (sk5 @ B @ (A))) | ((A @ B) != (a @ (sk6 @ sk2 @ (a)))))),inference(simp,[status(thm)],[15103])).
% 71.75/18.60 thf(15110,plain,((rel @ (sk6 @ sk2 @ (a)) @ (sk5 @ (sk6 @ sk2 @ (a)) @ (a)))),inference(pre_uni,[status(thm)],[15104:[bind(A, $thf(a)),bind(B, $thf(sk6 @ sk2 @ (a)))]])).
% 71.75/18.60 thf(1241,plain,(! [B:$i,A:($i > $o)] : ((rel @ B @ (sk5 @ B @ (A))) | (~ (a @ (sk6 @ sk3 @ (a)))) | ~ (($true)) | ((A @ B) != (rel @ sk3 @ sk3)))),inference(paramod_ordered,[status(thm)],[15,312])).
% 71.75/18.60 thf(1242,plain,(! [B:$i,A:($i > $o)] : ((rel @ B @ (sk5 @ B @ (A))) | (~ (a @ (sk6 @ sk3 @ (a)))) | ((A @ B) != (rel @ sk3 @ sk3)))),inference(simp,[status(thm)],[1241])).
% 71.75/18.60 thf(1274,plain,((rel @ sk3 @ (sk5 @ sk3 @ (^ [A:$i]: (rel @ A @ A)))) | (~ (a @ (sk6 @ sk3 @ (a))))),inference(pre_uni,[status(thm)],[1242:[bind(A, $thf(^ [C:$i]: (rel @ C @ C))),bind(B, $thf(sk3))]])).
% 71.75/18.60 thf(3817,plain,(! [B:$i,A:($i > $o)] : ((rel @ B @ (sk5 @ B @ (A))) | (rel @ sk3 @ (sk5 @ sk3 @ (^ [C:$i]: (rel @ C @ C)))) | ~ (($true)) | ((A @ B) != (a @ (sk6 @ sk3 @ (a)))))),inference(paramod_ordered,[status(thm)],[15,1274])).
% 71.75/18.60 thf(3818,plain,(! [B:$i,A:($i > $o)] : ((rel @ B @ (sk5 @ B @ (A))) | (rel @ sk3 @ (sk5 @ sk3 @ (^ [C:$i]: (rel @ C @ C)))) | ((A @ B) != (a @ (sk6 @ sk3 @ (a)))))),inference(simp,[status(thm)],[3817])).
% 71.75/18.60 thf(3851,plain,((rel @ sk3 @ (sk5 @ sk3 @ (^ [A:$i]: (a @ (sk6 @ A @ a))))) | (rel @ sk3 @ (sk5 @ sk3 @ (^ [A:$i]: (rel @ A @ A))))),inference(pre_uni,[status(thm)],[3818:[bind(A, $thf(^ [C:$i]: (a @ (sk6 @ C @ a)))),bind(B, $thf(sk3))]])).
% 71.75/18.60 thf(5738,plain,((rel @ (sk6 @ sk2 @ (prop_a)) @ (sk5 @ (sk6 @ sk2 @ (prop_a)) @ (prop_a))) | (prop_a @ sk4)),inference(pre_uni,[status(thm)],[5729:[bind(A, $thf(prop_a)),bind(B, $thf(sk6 @ sk2 @ (prop_a)))]])).
% 71.75/18.60 thf(394,plain,(! [A:$i] : ((rel @ A @ (sk5 @ A @ (a))) | (a @ A))),inference(prim_subst,[status(thm)],[15:[bind(A, $thf(a))]])).
% 71.75/18.60 thf(453,plain,(! [A:$i] : ((rel @ A @ (sk5 @ A @ (a))) | (a @ A))),inference(simp,[status(thm)],[394])).
% 71.75/18.60 thf(8091,plain,((~ (prop_c @ (sk6 @ sk1 @ (prop_c)))) | (prop_c @ sk3)),inference(prim_subst,[status(thm)],[2805:[bind(A, $thf(prop_c))]])).
% 71.75/18.60 thf(8598,plain,(! [B:$i,A:($i > $o)] : ((rel @ B @ (sk5 @ B @ (A))) | ~ (($true)) | (prop_c @ sk3) | ((A @ B) != (prop_c @ (sk6 @ sk1 @ (prop_c)))))),inference(paramod_ordered,[status(thm)],[15,8091])).
% 71.75/18.60 thf(8599,plain,(! [B:$i,A:($i > $o)] : ((rel @ B @ (sk5 @ B @ (A))) | (prop_c @ sk3) | ((A @ B) != (prop_c @ (sk6 @ sk1 @ (prop_c)))))),inference(simp,[status(thm)],[8598])).
% 71.75/18.60 thf(8613,plain,((rel @ sk1 @ (sk5 @ sk1 @ (^ [A:$i]: (prop_c @ (sk6 @ A @ prop_c))))) | (prop_c @ sk3)),inference(pre_uni,[status(thm)],[8599:[bind(A, $thf(^ [C:$i]: (prop_c @ (sk6 @ C @ prop_c)))),bind(B, $thf(sk1))]])).
% 71.75/18.60 thf(12025,plain,((~ (a @ (sk6 @ sk3 @ (a)))) | (~ (a @ (sk6 @ sk3 @ (a)))) | ~ (($true)) | ((rel @ sk4 @ (sk5 @ sk4 @ (^ [A:$i]: (rel @ A @ sk3)))) != (rel @ sk4 @ sk3))),inference(paramod_ordered,[status(thm)],[730,302])).
% 71.75/18.60 thf(12026,plain,((~ (a @ (sk6 @ sk3 @ (a)))) | ((rel @ sk4 @ (sk5 @ sk4 @ (^ [A:$i]: (rel @ A @ sk3)))) != (rel @ sk4 @ sk3))),inference(simp,[status(thm)],[12025])).
% 71.75/18.60 thf(12160,plain,((~ (a @ (sk6 @ sk3 @ (a)))) | (sk4 != sk4) | ((sk5 @ sk4 @ (^ [A:$i]: (rel @ A @ sk3))) != sk3)),inference(simp,[status(thm)],[12026])).
% 71.75/18.60 thf(12205,plain,((~ (a @ (sk6 @ sk3 @ (a)))) | ((sk5 @ sk4 @ (^ [A:$i]: (rel @ A @ sk3))) != sk3)),inference(simp,[status(thm)],[12160])).
% 71.75/18.60 thf(21,plain,(! [D:$i,C:$i,B:$i,A:($i > $o)] : ((rel @ B @ (sk6 @ B @ (A))) | (~ (rel @ B @ C)) | (~ (rel @ C @ D)) | (A @ D))),inference(cnfConj,[status(thm)],[20])).
% 71.75/18.60 thf(2379,plain,(! [A:$i] : ((~ (a @ (sk6 @ sk4 @ (a)))) | ~ (($true)) | ((rel @ A @ (sk5 @ A @ (^ [B:$i]: (($false))))) != (rel @ (sk5 @ sk4 @ (s)) @ sk3)))),inference(paramod_ordered,[status(thm)],[454,511])).
% 71.75/18.60 thf(2380,plain,(! [A:$i] : ((~ (a @ (sk6 @ sk4 @ (a)))) | ((rel @ A @ (sk5 @ A @ (^ [B:$i]: (($false))))) != (rel @ (sk5 @ sk4 @ (s)) @ sk3)))),inference(simp,[status(thm)],[2379])).
% 71.75/18.60 thf(2381,plain,(! [A:$i] : ((~ (a @ (sk6 @ sk4 @ (a)))) | (A != (sk5 @ sk4 @ (s))) | ((sk5 @ A @ (^ [B:$i]: (($false)))) != sk3))),inference(simp,[status(thm)],[2380])).
% 71.75/18.60 thf(2414,plain,((~ (a @ (sk6 @ sk4 @ (a)))) | ((sk5 @ (sk5 @ sk4 @ (s)) @ (^ [A:$i]: (($false)))) != sk3)),inference(simp,[status(thm)],[2381])).
% 71.75/18.60 thf(3758,plain,(! [B:$i,A:$i] : ((~ (a @ (sk6 @ sk3 @ (a)))) | (~ (a @ (sk6 @ A @ (a)))) | ~ (($true)) | (~ (rel @ B @ sk3)) | ((rel @ sk3 @ (sk5 @ sk3 @ (^ [C:$i]: (rel @ C @ C)))) != (rel @ A @ B)))),inference(paramod_ordered,[status(thm)],[1274,128])).
% 71.75/18.60 thf(3759,plain,(! [B:$i,A:$i] : ((~ (a @ (sk6 @ sk3 @ (a)))) | (~ (a @ (sk6 @ A @ (a)))) | (~ (rel @ B @ sk3)) | ((rel @ sk3 @ (sk5 @ sk3 @ (^ [C:$i]: (rel @ C @ C)))) != (rel @ A @ B)))),inference(simp,[status(thm)],[3758])).
% 71.75/18.60 thf(3760,plain,((~ (a @ (sk6 @ sk3 @ (a)))) | (~ (a @ (sk6 @ sk3 @ (a)))) | (~ (rel @ (sk5 @ sk3 @ (^ [A:$i]: (rel @ A @ A))) @ sk3))),inference(pattern_uni,[status(thm)],[3759:[bind(A, $thf(sk3)),bind(B, $thf(sk5 @ sk3 @ (^ [C:$i]: (rel @ C @ C))))]])).
% 71.75/18.60 thf(3865,plain,((~ (a @ (sk6 @ sk3 @ (a)))) | (~ (rel @ (sk5 @ sk3 @ (^ [A:$i]: (rel @ A @ A))) @ sk3))),inference(simp,[status(thm)],[3760])).
% 71.75/18.60 thf(4052,plain,((~ (a @ (sk6 @ sk3 @ (a)))) | ~ (($true)) | ((rel @ (sk5 @ sk3 @ (^ [A:$i]: (rel @ A @ A))) @ sk3) != (rel @ sk2 @ sk3))),inference(paramod_ordered,[status(thm)],[11,3865])).
% 71.75/18.60 thf(4053,plain,((~ (a @ (sk6 @ sk3 @ (a)))) | ((rel @ (sk5 @ sk3 @ (^ [A:$i]: (rel @ A @ A))) @ sk3) != (rel @ sk2 @ sk3))),inference(simp,[status(thm)],[4052])).
% 71.75/18.60 thf(4107,plain,((~ (a @ (sk6 @ sk3 @ (a)))) | ((sk5 @ sk3 @ (^ [A:$i]: (rel @ A @ A))) != sk2) | (sk3 != sk3)),inference(simp,[status(thm)],[4053])).
% 71.75/18.60 thf(4123,plain,((~ (a @ (sk6 @ sk3 @ (a)))) | ((sk5 @ sk3 @ (^ [A:$i]: (rel @ A @ A))) != sk2)),inference(simp,[status(thm)],[4107])).
% 71.75/18.60 thf(9,plain,(! [C:$i,B:$i,A:$i] : ((~ (rel @ sk2 @ A)) | (a @ A) | (~ (rel @ A @ B)) | (a @ B) | (~ (rel @ B @ C)) | (s @ C))),inference(cnfConj,[status(thm)],[6])).
% 71.75/18.60 thf(27,plain,(! [H:$i,G:$i,F:$i,E:($i > $o),D:$i,C:$i,B:$i,A:($i > $o)] : ((~ (A @ (sk6 @ B @ (A)))) | (~ (rel @ B @ C)) | (~ (rel @ C @ D)) | ~ (($true)) | (~ (rel @ F @ G)) | (~ (rel @ G @ H)) | (E @ H) | ((A @ D) != (E @ (sk6 @ F @ (E)))))),inference(paramod_ordered,[status(thm)],[22,22])).
% 71.75/18.60 thf(28,plain,(! [H:$i,G:$i,F:$i,E:($i > $o),D:$i,C:$i,B:$i,A:($i > $o)] : ((~ (A @ (sk6 @ B @ (A)))) | (~ (rel @ B @ C)) | (~ (rel @ C @ D)) | (~ (rel @ F @ G)) | (~ (rel @ G @ H)) | (E @ H) | ((A @ D) != (E @ (sk6 @ F @ (E)))))),inference(simp,[status(thm)],[27])).
% 71.75/18.60 thf(95,plain,(! [H:$i,G:$i,F:$i,E:($i > $o),D:$i,C:$i,B:$i,A:($i > $o)] : ((~ (A @ (sk6 @ B @ (A)))) | (~ (rel @ B @ C)) | (~ (rel @ C @ D)) | (~ (rel @ F @ G)) | (~ (rel @ G @ H)) | (E @ H) | ((A @ D) != (E @ (sk6 @ F @ (E)))))),inference(pre_uni,[status(thm)],[28:[]])).
% 71.75/18.60 thf(96,plain,(! [H:$i,G:$i,F:$i,E:($i > $o),D:$i,C:$i,B:$i,A:($i > $o)] : ((E @ H) | (~ (rel @ G @ H)) | (~ (rel @ F @ G)) | (~ (rel @ C @ D)) | (~ (rel @ B @ C)) | (~ (A @ (sk6 @ B @ (A)))) | ((A @ D) != (E @ (sk6 @ F @ (E)))))),inference(pre_uni,[status(thm)],[95:[]])).
% 71.75/18.60 thf(389,plain,(! [B:$i,A:($i > $o)] : ((rel @ B @ (sk5 @ B @ (A))) | ~ (($true)) | ((A @ B) != (a @ sk3)))),inference(paramod_ordered,[status(thm)],[15,8])).
% 71.75/18.60 thf(390,plain,(! [B:$i,A:($i > $o)] : ((rel @ B @ (sk5 @ B @ (A))) | ((A @ B) != (a @ sk3)))),inference(simp,[status(thm)],[389])).
% 71.75/18.60 thf(450,plain,((rel @ sk3 @ (sk5 @ sk3 @ (a)))),inference(pre_uni,[status(thm)],[390:[bind(A, $thf(a)),bind(B, $thf(sk3))]])).
% 71.75/18.60 thf(546,plain,(! [B:$i,A:$i] : ((~ (a @ (sk6 @ A @ (a)))) | ~ (($true)) | (~ (rel @ B @ sk3)) | ((rel @ sk3 @ (sk5 @ sk3 @ (a))) != (rel @ A @ B)))),inference(paramod_ordered,[status(thm)],[450,128])).
% 71.75/18.60 thf(547,plain,(! [B:$i,A:$i] : ((~ (a @ (sk6 @ A @ (a)))) | (~ (rel @ B @ sk3)) | ((rel @ sk3 @ (sk5 @ sk3 @ (a))) != (rel @ A @ B)))),inference(simp,[status(thm)],[546])).
% 71.75/18.60 thf(548,plain,((~ (a @ (sk6 @ sk3 @ (a)))) | (~ (rel @ (sk5 @ sk3 @ (a)) @ sk3))),inference(pattern_uni,[status(thm)],[547:[bind(A, $thf(sk3)),bind(B, $thf(sk5 @ sk3 @ (a)))]])).
% 71.75/18.60 thf(2479,plain,(! [A:$i] : ((~ (a @ (sk6 @ sk3 @ (a)))) | ~ (($true)) | ((rel @ A @ (sk5 @ A @ (^ [B:$i]: (($false))))) != (rel @ (sk5 @ sk3 @ (a)) @ sk3)))),inference(paramod_ordered,[status(thm)],[454,548])).
% 71.75/18.60 thf(2480,plain,(! [A:$i] : ((~ (a @ (sk6 @ sk3 @ (a)))) | ((rel @ A @ (sk5 @ A @ (^ [B:$i]: (($false))))) != (rel @ (sk5 @ sk3 @ (a)) @ sk3)))),inference(simp,[status(thm)],[2479])).
% 71.75/18.60 thf(2491,plain,(! [A:$i] : ((~ (a @ (sk6 @ sk3 @ (a)))) | (A != (sk5 @ sk3 @ (a))) | ((sk5 @ A @ (^ [B:$i]: (($false)))) != sk3))),inference(simp,[status(thm)],[2480])).
% 71.75/18.60 thf(2536,plain,((~ (a @ (sk6 @ sk3 @ (a)))) | ((sk5 @ (sk5 @ sk3 @ (a)) @ (^ [A:$i]: (($false)))) != sk3)),inference(simp,[status(thm)],[2491])).
% 71.75/18.60 thf(8518,plain,(! [B:$i,A:($i > $o)] : ((rel @ B @ (sk5 @ B @ (A))) | ~ (($true)) | (s @ sk3) | ((A @ B) != (s @ (sk6 @ sk1 @ (s)))))),inference(paramod_ordered,[status(thm)],[15,8086])).
% 71.75/18.60 thf(8519,plain,(! [B:$i,A:($i > $o)] : ((rel @ B @ (sk5 @ B @ (A))) | (s @ sk3) | ((A @ B) != (s @ (sk6 @ sk1 @ (s)))))),inference(simp,[status(thm)],[8518])).
% 71.75/18.60 thf(8527,plain,((rel @ sk1 @ (sk5 @ sk1 @ (^ [A:$i]: (s @ (sk6 @ A @ s))))) | (s @ sk3)),inference(pre_uni,[status(thm)],[8519:[bind(A, $thf(^ [C:$i]: (s @ (sk6 @ C @ s)))),bind(B, $thf(sk1))]])).
% 71.75/18.60 thf(3781,plain,((~ (a @ (sk6 @ sk3 @ (a)))) | (~ (a @ (sk6 @ sk3 @ (a)))) | ~ (($true)) | ((rel @ sk3 @ (sk5 @ sk3 @ (^ [A:$i]: (rel @ A @ A)))) != (rel @ sk3 @ sk3))),inference(paramod_ordered,[status(thm)],[1274,312])).
% 71.75/18.60 thf(3782,plain,((~ (a @ (sk6 @ sk3 @ (a)))) | ((rel @ sk3 @ (sk5 @ sk3 @ (^ [A:$i]: (rel @ A @ A)))) != (rel @ sk3 @ sk3))),inference(simp,[status(thm)],[3781])).
% 71.75/18.60 thf(3844,plain,((~ (a @ (sk6 @ sk3 @ (a)))) | (sk3 != sk3) | ((sk5 @ sk3 @ (^ [A:$i]: (rel @ A @ A))) != sk3)),inference(simp,[status(thm)],[3782])).
% 71.75/18.60 thf(3856,plain,((~ (a @ (sk6 @ sk3 @ (a)))) | ((sk5 @ sk3 @ (^ [A:$i]: (rel @ A @ A))) != sk3)),inference(simp,[status(thm)],[3844])).
% 71.75/18.60 thf(1979,plain,(! [A:$i] : ((~ (a @ (sk6 @ A @ (a)))) | ~ (($true)) | ((rel @ sk3 @ (sk5 @ sk3 @ (a))) != (rel @ A @ sk2)))),inference(paramod_ordered,[status(thm)],[450,310])).
% 71.75/18.60 thf(1980,plain,(! [A:$i] : ((~ (a @ (sk6 @ A @ (a)))) | ((rel @ sk3 @ (sk5 @ sk3 @ (a))) != (rel @ A @ sk2)))),inference(simp,[status(thm)],[1979])).
% 71.75/18.60 thf(2023,plain,(! [A:$i] : ((~ (a @ (sk6 @ A @ (a)))) | (sk3 != A) | ((sk5 @ sk3 @ (a)) != sk2))),inference(simp,[status(thm)],[1980])).
% 71.75/18.60 thf(2048,plain,((~ (a @ (sk6 @ sk3 @ (a)))) | ((sk5 @ sk3 @ (a)) != sk2)),inference(simp,[status(thm)],[2023])).
% 71.75/18.60 thf(5844,plain,((rel @ sk2 @ (sk5 @ sk2 @ (^ [A:$i]: (s @ (sk6 @ A @ s)))))),inference(pre_uni,[status(thm)],[5833:[bind(A, $thf(^ [C:$i]: (s @ (sk6 @ C @ s)))),bind(B, $thf(sk2))]])).
% 71.75/18.60 thf(2373,plain,((~ (a @ (sk6 @ sk4 @ (a)))) | ~ (($true)) | ((rel @ (sk5 @ sk4 @ (s)) @ sk3) != (rel @ sk3 @ sk4))),inference(paramod_ordered,[status(thm)],[7,511])).
% 71.75/18.60 thf(2374,plain,((~ (a @ (sk6 @ sk4 @ (a)))) | ((rel @ (sk5 @ sk4 @ (s)) @ sk3) != (rel @ sk3 @ sk4))),inference(simp,[status(thm)],[2373])).
% 71.75/18.60 thf(2398,plain,((~ (a @ (sk6 @ sk4 @ (a)))) | ((sk5 @ sk4 @ (s)) != sk3) | (sk4 != sk3)),inference(simp,[status(thm)],[2374])).
% 71.75/18.60 thf(29,plain,(! [H:$i,G:$i,F:$i,E:($i > $o),D:$i,C:$i,B:$i,A:($i > $o)] : ((~ (A @ (sk6 @ B @ (A)))) | (~ (rel @ B @ C)) | (~ (rel @ C @ D)) | (~ (E @ (sk6 @ F @ (E)))) | ~ (($true)) | (~ (rel @ G @ H)) | (E @ H) | ((A @ D) != (rel @ F @ G)))),inference(paramod_ordered,[status(thm)],[22,22])).
% 71.75/18.60 thf(30,plain,(! [H:$i,G:$i,F:$i,E:($i > $o),D:$i,C:$i,B:$i,A:($i > $o)] : ((~ (A @ (sk6 @ B @ (A)))) | (~ (rel @ B @ C)) | (~ (rel @ C @ D)) | (~ (E @ (sk6 @ F @ (E)))) | (~ (rel @ G @ H)) | (E @ H) | ((A @ D) != (rel @ F @ G)))),inference(simp,[status(thm)],[29])).
% 71.75/18.60 thf(79,plain,(! [H:$i,G:$i,F:$i,E:($i > $o),D:$i,C:$i,B:$i,A:($i > $o)] : ((~ (A @ (sk6 @ B @ (A)))) | (~ (rel @ B @ C)) | (~ (rel @ C @ D)) | (~ ((sk6 @ F @ (E)) = (sk6 @ F @ ((=) @ $i @ (sk6 @ F @ E))))) | (~ (rel @ G @ H)) | ((sk6 @ F @ (E)) = H) | ((A @ D) != (rel @ F @ G)))),inference(replace_leibeq,[status(thm)],[30:[bind(A, $thf(A)),bind(B, $thf(B)),bind(C, $thf(C)),bind(D, $thf(D)),bind(E, $thf((=) @ $i @ (sk6 @ F @ E)))]])).
% 71.75/18.60 thf(86,plain,(! [H:$i,G:$i,F:$i,E:($i > $o),D:$i,C:$i,B:$i,A:($i > $o)] : (((sk6 @ F @ (E)) != (sk6 @ F @ ((=) @ $i @ (sk6 @ F @ E)))) | ((sk6 @ F @ (E)) = H) | (~ (A @ (sk6 @ B @ (A)))) | (~ (rel @ B @ C)) | (~ (rel @ C @ D)) | (~ (rel @ G @ H)) | ((A @ D) != (rel @ F @ G)))),inference(lifteq,[status(thm)],[79])).
% 71.75/18.60 thf(419,plain,((rel @ sk1 @ (sk5 @ sk1 @ (^ [A:$i]: (a @ (sk6 @ A @ a)))))),inference(pre_uni,[status(thm)],[357:[bind(A, $thf(^ [C:$i]: (a @ (sk6 @ C @ a)))),bind(B, $thf(sk1))]])).
% 71.75/18.60 thf(77,plain,(! [B:$i,A:($i > $o)] : ((~ ((sk6 @ B @ (A)) = (sk6 @ B @ ((=) @ $i @ (sk6 @ B @ A))))) | (~ (rel @ B @ sk2)) | ((sk6 @ B @ (A)) = sk3))),inference(replace_leibeq,[status(thm)],[48:[bind(A, $thf((=) @ $i @ (sk6 @ B @ A)))]])).
% 71.75/18.60 thf(81,plain,(! [B:$i,A:($i > $o)] : (((sk6 @ B @ (A)) != (sk6 @ B @ ((=) @ $i @ (sk6 @ B @ A)))) | ((sk6 @ B @ (A)) = sk3) | (~ (rel @ B @ sk2)))),inference(lifteq,[status(thm)],[77])).
% 71.75/18.60 thf(1235,plain,((~ (a @ (sk6 @ sk3 @ (a)))) | ~ (($true)) | ((rel @ sk3 @ (sk5 @ sk3 @ (a))) != (rel @ sk3 @ sk3))),inference(paramod_ordered,[status(thm)],[450,312])).
% 71.75/18.60 thf(1236,plain,((~ (a @ (sk6 @ sk3 @ (a)))) | ((rel @ sk3 @ (sk5 @ sk3 @ (a))) != (rel @ sk3 @ sk3))),inference(simp,[status(thm)],[1235])).
% 71.75/18.60 thf(1295,plain,((~ (a @ (sk6 @ sk3 @ (a)))) | (sk3 != sk3) | ((sk5 @ sk3 @ (a)) != sk3)),inference(simp,[status(thm)],[1236])).
% 71.75/18.60 thf(1307,plain,((~ (a @ (sk6 @ sk3 @ (a)))) | ((sk5 @ sk3 @ (a)) != sk3)),inference(simp,[status(thm)],[1295])).
% 71.75/18.60 thf(64,plain,(! [C:$i,B:$i,A:$i] : ((~ (a @ (sk6 @ A @ (a)))) | (~ (rel @ A @ B)) | (~ (rel @ B @ C)) | (a @ C))),inference(prim_subst,[status(thm)],[22:[bind(A, $thf(a))]])).
% 71.75/18.60 thf(108,plain,(! [C:$i,B:$i,A:$i] : ((~ (a @ (sk6 @ A @ (a)))) | (~ (rel @ A @ B)) | (~ (rel @ B @ C)) | (a @ C))),inference(simp,[status(thm)],[64])).
% 71.75/18.60 thf(403,plain,(! [A:$i] : ((rel @ A @ (sk5 @ A @ (prop_b))) | (prop_b @ A))),inference(prim_subst,[status(thm)],[15:[bind(A, $thf(prop_b))]])).
% 71.75/18.60 thf(462,plain,(! [A:$i] : ((rel @ A @ (sk5 @ A @ (prop_b))) | (prop_b @ A))),inference(simp,[status(thm)],[403])).
% 71.75/18.60 thf(15112,plain,((rel @ sk2 @ (sk5 @ sk2 @ (^ [A:$i]: (a @ (sk6 @ A @ a)))))),inference(pre_uni,[status(thm)],[15104:[bind(A, $thf(^ [C:$i]: (a @ (sk6 @ C @ a)))),bind(B, $thf(sk2))]])).
% 71.75/18.60 thf(17,plain,(! [B:$i,A:($i > $o)] : ((~ ((sk5 @ B @ (A)) = (sk5 @ B @ ((=) @ $i @ (sk5 @ B @ A))))) | ((sk5 @ B @ (A)) = B))),inference(replace_leibeq,[status(thm)],[16:[bind(A, $thf((=) @ $i @ (sk5 @ B @ A)))]])).
% 71.75/18.60 thf(18,plain,(! [B:$i,A:($i > $o)] : (((sk5 @ B @ (A)) != (sk5 @ B @ ((=) @ $i @ (sk5 @ B @ A)))) | ((sk5 @ B @ (A)) = B))),inference(lifteq,[status(thm)],[17])).
% 71.75/18.60 thf(708,plain,(! [B:$i,A:($i > $o)] : ((rel @ B @ (sk5 @ B @ (A))) | ~ (($true)) | (~ (rel @ sk4 @ sk3)) | ((A @ B) != (a @ (sk6 @ sk3 @ (a)))))),inference(paramod_ordered,[status(thm)],[15,302])).
% 71.75/18.60 thf(709,plain,(! [B:$i,A:($i > $o)] : ((rel @ B @ (sk5 @ B @ (A))) | (~ (rel @ sk4 @ sk3)) | ((A @ B) != (a @ (sk6 @ sk3 @ (a)))))),inference(simp,[status(thm)],[708])).
% 71.75/18.60 thf(727,plain,((rel @ sk3 @ (sk5 @ sk3 @ (^ [A:$i]: (a @ (sk6 @ A @ a))))) | (~ (rel @ sk4 @ sk3))),inference(pre_uni,[status(thm)],[709:[bind(A, $thf(^ [C:$i]: (a @ (sk6 @ C @ a)))),bind(B, $thf(sk3))]])).
% 71.75/18.60 thf(731,plain,((rel @ sk3 @ (sk5 @ sk3 @ (rel @ sk4))) | (~ (a @ (sk6 @ sk3 @ (a))))),inference(pre_uni,[status(thm)],[711:[bind(A, $thf(rel @ sk4)),bind(B, $thf(sk3))]])).
% 71.75/18.60 thf(13242,plain,((~ (a @ (sk6 @ sk3 @ (a)))) | (~ (a @ (sk6 @ sk3 @ (a)))) | ~ (($true)) | ((rel @ sk3 @ (sk5 @ sk3 @ (rel @ sk4))) != (rel @ sk3 @ sk3))),inference(paramod_ordered,[status(thm)],[731,312])).
% 71.75/18.60 thf(13243,plain,((~ (a @ (sk6 @ sk3 @ (a)))) | ((rel @ sk3 @ (sk5 @ sk3 @ (rel @ sk4))) != (rel @ sk3 @ sk3))),inference(simp,[status(thm)],[13242])).
% 71.75/18.60 thf(13391,plain,((~ (a @ (sk6 @ sk3 @ (a)))) | (sk3 != sk3) | ((sk5 @ sk3 @ (rel @ sk4)) != sk3)),inference(simp,[status(thm)],[13243])).
% 71.75/18.60 thf(13460,plain,((~ (a @ (sk6 @ sk3 @ (a)))) | ((sk5 @ sk3 @ (rel @ sk4)) != sk3)),inference(simp,[status(thm)],[13391])).
% 71.75/18.60 thf(54,plain,(! [D:$i,C:$i,B:$i,A:($i > $o)] : ((~ (A @ (sk6 @ B @ (A)))) | (~ (rel @ B @ C)) | (~ (rel @ C @ D)) | ((A @ D) != (~ (A @ (sk6 @ B @ (A))))) | ~ (($true)))),inference(eqfactor_ordered,[status(thm)],[22])).
% 71.75/18.60 thf(99,plain,(! [D:$i,C:$i,B:$i,A:($i > $o)] : ((~ (A @ (sk6 @ B @ (A)))) | (~ (rel @ B @ C)) | (~ (rel @ C @ D)) | ((A @ D) != (~ (A @ (sk6 @ B @ (A))))))),inference(simp,[status(thm)],[54])).
% 71.75/18.60 thf(78,plain,(! [B:$i,A:($i > $o)] : ((~ ((sk6 @ B @ (A)) = (sk6 @ B @ ((=) @ $i @ (sk6 @ B @ A))))) | (~ (rel @ B @ sk3)) | ((sk6 @ B @ (A)) = sk4))),inference(replace_leibeq,[status(thm)],[40:[bind(A, $thf((=) @ $i @ (sk6 @ B @ A)))]])).
% 71.75/18.60 thf(87,plain,(! [B:$i,A:($i > $o)] : (((sk6 @ B @ (A)) != (sk6 @ B @ ((=) @ $i @ (sk6 @ B @ A)))) | ((sk6 @ B @ (A)) = sk4) | (~ (rel @ B @ sk3)))),inference(lifteq,[status(thm)],[78])).
% 71.75/18.60 thf(1259,plain,((~ (a @ (sk6 @ sk3 @ (a)))) | ~ (($true)) | ((rel @ sk3 @ sk3) != (rel @ sk2 @ sk3))),inference(paramod_ordered,[status(thm)],[11,312])).
% 71.75/18.60 thf(1260,plain,((~ (a @ (sk6 @ sk3 @ (a)))) | ((rel @ sk3 @ sk3) != (rel @ sk2 @ sk3))),inference(simp,[status(thm)],[1259])).
% 71.75/18.60 thf(1265,plain,((~ (a @ (sk6 @ sk3 @ (a)))) | (sk3 != sk2) | (sk3 != sk3)),inference(simp,[status(thm)],[1260])).
% 71.75/18.60 thf(1308,plain,((~ (a @ (sk6 @ sk3 @ (a)))) | (sk3 != sk2)),inference(simp,[status(thm)],[1265])).
% 71.75/18.60 thf(1318,plain,(! [B:$i,A:($i > $o)] : ((rel @ B @ (sk5 @ B @ (A))) | ~ (($true)) | (sk3 != sk2) | ((A @ B) != (a @ (sk6 @ sk3 @ (a)))))),inference(paramod_ordered,[status(thm)],[15,1308])).
% 71.75/18.60 thf(1319,plain,(! [B:$i,A:($i > $o)] : ((rel @ B @ (sk5 @ B @ (A))) | (sk3 != sk2) | ((A @ B) != (a @ (sk6 @ sk3 @ (a)))))),inference(simp,[status(thm)],[1318])).
% 71.75/18.60 thf(1326,plain,((rel @ sk3 @ (sk5 @ sk3 @ (^ [A:$i]: (a @ (sk6 @ A @ a))))) | (sk3 != sk2)),inference(pre_uni,[status(thm)],[1319:[bind(A, $thf(^ [C:$i]: (a @ (sk6 @ C @ a)))),bind(B, $thf(sk3))]])).
% 71.75/18.60 thf(237,plain,(! [A:$i] : ((~ (s @ (sk5 @ A @ (s)))) | (s @ A))),inference(prim_subst,[status(thm)],[16:[bind(A, $thf(s))]])).
% 71.75/18.60 thf(258,plain,(! [A:$i] : ((~ (s @ (sk5 @ A @ (s)))) | (s @ A))),inference(simp,[status(thm)],[237])).
% 71.75/18.60 thf(4451,plain,((~ (prop_c @ (sk6 @ sk2 @ (prop_c)))) | (prop_c @ sk4)),inference(prim_subst,[status(thm)],[2151:[bind(A, $thf(prop_c))]])).
% 71.75/18.60 thf(405,plain,(! [A:$i] : ((rel @ A @ (sk5 @ A @ (s))) | (s @ A))),inference(prim_subst,[status(thm)],[15:[bind(A, $thf(s))]])).
% 71.75/18.60 thf(464,plain,(! [A:$i] : ((rel @ A @ (sk5 @ A @ (s))) | (s @ A))),inference(simp,[status(thm)],[405])).
% 71.75/18.60 thf(8558,plain,(! [B:$i,A:($i > $o)] : ((rel @ B @ (sk5 @ B @ (A))) | ~ (($true)) | (prop_a @ sk3) | ((A @ B) != (prop_a @ (sk6 @ sk1 @ (prop_a)))))),inference(paramod_ordered,[status(thm)],[15,8089])).
% 71.75/18.60 thf(8559,plain,(! [B:$i,A:($i > $o)] : ((rel @ B @ (sk5 @ B @ (A))) | (prop_a @ sk3) | ((A @ B) != (prop_a @ (sk6 @ sk1 @ (prop_a)))))),inference(simp,[status(thm)],[8558])).
% 71.75/18.60 thf(8570,plain,((rel @ sk1 @ (sk5 @ sk1 @ (^ [A:$i]: (prop_a @ (sk6 @ A @ prop_a))))) | (prop_a @ sk3)),inference(pre_uni,[status(thm)],[8559:[bind(A, $thf(^ [C:$i]: (prop_a @ (sk6 @ C @ prop_a)))),bind(B, $thf(sk1))]])).
% 71.75/18.60 thf(5762,plain,(! [B:$i,A:($i > $o)] : ((rel @ B @ (sk5 @ B @ (A))) | ~ (($true)) | (prop_c @ sk4) | ((A @ B) != (prop_c @ (sk6 @ sk2 @ (prop_c)))))),inference(paramod_ordered,[status(thm)],[15,4451])).
% 71.75/18.60 thf(5763,plain,(! [B:$i,A:($i > $o)] : ((rel @ B @ (sk5 @ B @ (A))) | (prop_c @ sk4) | ((A @ B) != (prop_c @ (sk6 @ sk2 @ (prop_c)))))),inference(simp,[status(thm)],[5762])).
% 71.75/18.60 thf(5774,plain,((rel @ sk2 @ (sk5 @ sk2 @ (^ [A:$i]: (prop_c @ (sk6 @ A @ prop_c))))) | (prop_c @ sk4)),inference(pre_uni,[status(thm)],[5763:[bind(A, $thf(^ [C:$i]: (prop_c @ (sk6 @ C @ prop_c)))),bind(B, $thf(sk2))]])).
% 71.75/18.60 thf(233,plain,(! [A:$i] : ((~ (prop_b @ (sk5 @ A @ (prop_b)))) | (prop_b @ A))),inference(prim_subst,[status(thm)],[16:[bind(A, $thf(prop_b))]])).
% 71.75/18.60 thf(254,plain,(! [A:$i] : ((~ (prop_b @ (sk5 @ A @ (prop_b)))) | (prop_b @ A))),inference(simp,[status(thm)],[233])).
% 71.75/18.60 thf(31,plain,(! [H:$i,G:$i,F:$i,E:($i > $o),D:$i,C:$i,B:$i,A:($i > $o)] : ((~ (A @ (sk6 @ B @ (A)))) | (~ (rel @ B @ C)) | (~ (rel @ C @ D)) | (~ (E @ (sk6 @ F @ (E)))) | (~ (rel @ F @ G)) | ~ (($true)) | (E @ H) | ((A @ D) != (rel @ G @ H)))),inference(paramod_ordered,[status(thm)],[22,22])).
% 71.75/18.60 thf(32,plain,(! [H:$i,G:$i,F:$i,E:($i > $o),D:$i,C:$i,B:$i,A:($i > $o)] : ((~ (A @ (sk6 @ B @ (A)))) | (~ (rel @ B @ C)) | (~ (rel @ C @ D)) | (~ (E @ (sk6 @ F @ (E)))) | (~ (rel @ F @ G)) | (E @ H) | ((A @ D) != (rel @ G @ H)))),inference(simp,[status(thm)],[31])).
% 71.75/18.60 thf(76,plain,(! [H:$i,G:$i,F:$i,E:($i > $o),D:$i,C:$i,B:$i,A:($i > $o)] : ((~ (A @ (sk6 @ B @ (A)))) | (~ (rel @ B @ C)) | (~ (rel @ C @ D)) | (~ ((sk6 @ F @ (E)) = (sk6 @ F @ ((=) @ $i @ (sk6 @ F @ E))))) | (~ (rel @ F @ G)) | ((sk6 @ F @ (E)) = H) | ((A @ D) != (rel @ G @ H)))),inference(replace_leibeq,[status(thm)],[32:[bind(A, $thf(A)),bind(B, $thf(B)),bind(C, $thf(C)),bind(D, $thf(D)),bind(E, $thf((=) @ $i @ (sk6 @ F @ E)))]])).
% 71.75/18.60 thf(83,plain,(! [H:$i,G:$i,F:$i,E:($i > $o),D:$i,C:$i,B:$i,A:($i > $o)] : (((sk6 @ F @ (E)) != (sk6 @ F @ ((=) @ $i @ (sk6 @ F @ E)))) | ((sk6 @ F @ (E)) = H) | (~ (A @ (sk6 @ B @ (A)))) | (~ (rel @ B @ C)) | (~ (rel @ C @ D)) | (~ (rel @ F @ G)) | ((A @ D) != (rel @ G @ H)))),inference(lifteq,[status(thm)],[76])).
% 71.75/18.60 thf(18525,plain,(($false)),inference(e,[status(thm)],[8085,5808,16,767,730,5842,5,511,10,8490,747,5740,8086,782,257,417,24,8089,751,1313,2403,2049,15110,756,3851,5738,453,312,8613,12205,1274,2805,8091,302,21,2414,4123,9,328,96,2536,13,128,8527,3856,2048,22,5844,2398,12,86,2151,419,81,7,1307,4452,108,462,548,15112,754,48,5822,18,310,11,727,13460,446,450,99,87,1326,40,258,731,4451,8,1308,4446,3865,19,464,8570,15,5774,254,83,14450,454])).
% 71.75/18.60 % SZS output end Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% 71.75/18.60 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------