%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWV426^4 : 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 : n017.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 19.01s 5.25s
% Output : Refutation 16.60s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWV426^4 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.07 % 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
% 0.09/0.21 % Computer : n017.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 15:57:18 UTC 2026
% 0.09/0.22 % CPUTime :
% 0.09/0.22 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
% 1.02/0.81 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.49/1.09 % [INFO] Parsing done (274ms).
% 1.49/1.10 % [INFO] Running in sequential loop mode.
% 2.40/1.50 % [INFO] eprover registered as external prover.
% 2.40/1.51 % [INFO] Scanning for conjecture ...
% 2.60/1.66 % [INFO] Found a conjecture (or negated_conjecture) and 2 axioms. Running axiom selection ...
% 2.60/1.69 % [INFO] Axiom selection finished. Selected 2 axioms (removed 0 axioms).
% 2.60/1.69 % [INFO] Problem is higher-order (TPTP THF).
% 2.80/1.70 % [INFO] Type checking passed.
% 2.80/1.70 % [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 ...
% 19.01/5.24 % External prover 'e' found a proof!
% 19.01/5.24 % [INFO] Killing All external provers ...
% 19.01/5.25 % Time passed: 4885ms (effective reasoning time: 4139ms)
% 19.01/5.25 % 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)>
% 19.01/5.25 % Axioms used in derivation (2): trans_axiom, refl_axiom
% 19.01/5.25 % No. of inferences in proof: 92
% 19.01/5.25 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 4885 ms resp. 4139 ms w/o parsing
% 16.60/5.34 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 16.60/5.34 thf(individuals_type, type, individuals: $tType).
% 16.60/5.34 thf(prop_b_decl, type, prop_b: ($i > $o)).
% 16.60/5.34 thf(prop_c_decl, type, prop_c: ($i > $o)).
% 16.60/5.34 thf(mnot_decl, type, mnot: (($i > $o) > ($i > $o))).
% 16.60/5.34 thf(mor_decl, type, mor: (($i > $o) > (($i > $o) > ($i > $o)))).
% 16.60/5.34 thf(mimpl_decl, type, mimpl: (($i > $o) > (($i > $o) > ($i > $o)))).
% 16.60/5.34 thf(mbox_decl, type, mbox: (($i > ($i > $o)) > (($i > $o) > ($i > $o)))).
% 16.60/5.34 thf(mvalid_decl, type, mvalid: (($i > $o) > $o)).
% 16.60/5.34 thf(rel_decl, type, rel: ($i > ($i > $o))).
% 16.60/5.34 thf(icl_atom_decl, type, icl_atom: (($i > $o) > ($i > $o))).
% 16.60/5.34 thf(icl_princ_decl, type, icl_princ: (($i > $o) > ($i > $o))).
% 16.60/5.34 thf(icl_impl_decl, type, icl_impl: (($i > $o) > (($i > $o) > ($i > $o)))).
% 16.60/5.34 thf(icl_says_decl, type, icl_says: (($i > $o) > (($i > $o) > ($i > $o)))).
% 16.60/5.34 thf(iclval_decl, type, iclval: (($i > $o) > $o)).
% 16.60/5.34 thf(s_decl, type, s: ($i > $o)).
% 16.60/5.34 thf(a_decl, type, a: ($i > $o)).
% 16.60/5.34 thf(b_decl, type, b: ($i > $o)).
% 16.60/5.34 thf(sk1_decl, type, sk1: $i).
% 16.60/5.34 thf(sk2_decl, type, sk2: $i).
% 16.60/5.34 thf(sk3_decl, type, sk3: $i).
% 16.60/5.34 thf(sk4_decl, type, sk4: $i).
% 16.60/5.34 thf(sk5_decl, type, sk5: $i).
% 16.60/5.34 thf(sk6_decl, type, sk6: ($i > (($i > $o) > $i))).
% 16.60/5.34 thf(sk7_decl, type, sk7: ($i > (($i > $o) > $i))).
% 16.60/5.34 thf(mnot_def, definition, mnot = (^ [A:($i > $o),B:$i]: ~ (A @ B)) ).
% 16.60/5.34 thf(mor_def, definition, mor = (^ [A:($i > $o),B:($i > $o),C:$i]: ((A @ C) | (B @ C))) ).
% 16.60/5.34 thf(mimpl_def, definition, mimpl = (^ [A:($i > $o)]: (mor @ (mnot @ A))) ).
% 16.60/5.34 thf(mbox_def, definition, mbox = (^ [A:($i > ($i > $o)),B:($i > $o),C:$i]: ! [D:$i]: ((A @ C @ D) => (B @ D))) ).
% 16.60/5.34 thf(mvalid_def, definition, mvalid = ((!) @ $i) ).
% 16.60/5.34 thf(icl_atom_def, definition, icl_atom = (mbox @ rel) ).
% 16.60/5.34 thf(icl_princ_def, definition, icl_princ = (^ [A:($i > $o)]: (A)) ).
% 16.60/5.34 thf(icl_impl_def, definition, icl_impl = (^ [A:($i > $o),B:($i > $o)]: (mbox @ rel @ (mimpl @ A @ B))) ).
% 16.60/5.34 thf(icl_says_def, definition, icl_says = (^ [A:($i > $o),B:($i > $o)]: (mbox @ rel @ (mor @ A @ B))) ).
% 16.60/5.34 thf(iclval_def, definition, iclval = (mvalid) ).
% 16.60/5.34 thf(sk1_def, definition, sk1 = (@+ [A:$i]: ~ (! [B:$i]: ((rel @ A @ B) => (~ (! [C:$i]: ((rel @ B @ C) => (! [D:$i]: ((rel @ C @ D) => (~ (a @ D) | (b @ D))) | ! [D:$i]: ((rel @ C @ D) => (s @ D))))) | ! [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:$i]: ((rel @ D @ E) => (s @ E)))))))))) ).
% 16.60/5.34 thf(sk2_def, definition, sk2 = (@+ [A:$i]: ~ ((rel @ sk1 @ A) => (~ (! [B:$i]: ((rel @ A @ B) => (! [C:$i]: ((rel @ B @ C) => (~ (a @ C) | (b @ C))) | ! [C:$i]: ((rel @ B @ C) => (s @ C))))) | ! [B:$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))))))))) ).
% 16.60/5.34 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:$i]: ((rel @ B @ C) => (s @ C))))))) ).
% 16.60/5.34 thf(sk4_def, definition, sk4 = (@+ [A:$i]: ~ ((rel @ sk3 @ A) => ((b @ A) | ! [B:$i]: ((rel @ A @ B) => (s @ B))))) ).
% 16.60/5.34 thf(sk5_def, definition, sk5 = (@+ [A:$i]: ~ ((rel @ sk4 @ A) => (s @ A))) ).
% 16.60/5.34 thf(sk6_def, definition, sk6 = (^ [A:$i,B:($i > $o)]: (@+ [C:$i]: ~ ((rel @ A @ C) => (B @ C)))) ).
% 16.60/5.34 thf(sk7_def, definition, sk7 = (^ [A:$i,B:($i > $o)]: (@+ [C:$i]: ~ ((rel @ A @ C) => (B @ C)))) ).
% 16.60/5.34 thf(1,conjecture,((iclval @ (icl_impl @ (icl_says @ (icl_impl @ (icl_princ @ a) @ (icl_princ @ b)) @ (icl_atom @ s)) @ (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',cuc)).
% 16.60/5.34 thf(2,negated_conjecture,((~ (iclval @ (icl_impl @ (icl_says @ (icl_impl @ (icl_princ @ a) @ (icl_princ @ b)) @ (icl_atom @ s)) @ (icl_impl @ (icl_says @ (icl_princ @ a) @ (icl_atom @ s)) @ (icl_says @ (icl_princ @ b) @ (icl_atom @ s))))))),inference(neg_conjecture,[status(cth)],[1])).
% 16.60/5.34 thf(5,plain,((~ (! [A:$i,B:$i]: ((rel @ A @ B) => (~ (! [C:$i]: ((rel @ B @ C) => (! [D:$i]: ((rel @ C @ D) => (~ (a @ D) | (b @ D))) | ! [D:$i]: ((rel @ C @ D) => (s @ D))))) | ! [C:$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])).
% 16.60/5.34 thf(6,plain,(! [E:$i,D:$i,C:$i,B:$i,A:$i] : (((rel @ sk1 @ sk2) & (~ (rel @ sk2 @ A) | ~ (rel @ A @ B) | ~ (a @ B) | (b @ B) | ~ (rel @ A @ C) | (s @ C)) & (rel @ sk2 @ sk3) & (~ (rel @ sk3 @ D) | (a @ D) | ~ (rel @ D @ E) | (s @ E)) & (rel @ sk3 @ sk4) & ~ (b @ sk4) & (rel @ sk4 @ sk5) & ~ (s @ sk5)))),inference(cnf,[status(esa)],[5])).
% 16.60/5.34 thf(11,plain,((rel @ sk3 @ sk4)),inference(cnfConj,[status(thm)],[6])).
% 16.60/5.34 thf(13,plain,((rel @ sk1 @ sk2)),inference(cnfConj,[status(thm)],[6])).
% 16.60/5.34 thf(4,axiom,((! [A:($i > $o)]: (mvalid @ (mimpl @ (mbox @ rel @ A) @ (mbox @ rel @ (mbox @ rel @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',trans_axiom)).
% 16.60/5.34 thf(22,plain,((! [A:($i > $o),B:$i]: (~ (! [C:$i]: ((rel @ B @ C) => (A @ C))) | ! [C:$i]: ((rel @ B @ C) => (! [D:$i]: ((rel @ C @ D) => (A @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4])).
% 16.60/5.34 thf(23,plain,(! [D:$i,C:$i,B:$i,A:($i > $o)] : ((((rel @ B @ (sk7 @ B @ (A))) | ~ (rel @ B @ C) | ~ (rel @ C @ D) | (A @ D)) & (~ (A @ (sk7 @ B @ (A))) | ~ (rel @ B @ C) | ~ (rel @ C @ D) | (A @ D))))),inference(cnf,[status(esa)],[22])).
% 16.60/5.34 thf(25,plain,(! [D:$i,C:$i,B:$i,A:($i > $o)] : ((~ (A @ (sk7 @ B @ (A)))) | (~ (rel @ B @ C)) | (~ (rel @ C @ D)) | (A @ D))),inference(cnfConj,[status(thm)],[23])).
% 16.60/5.34 thf(8,plain,((~ (b @ sk4))),inference(cnfConj,[status(thm)],[6])).
% 16.60/5.34 thf(52,plain,(! [D:$i,C:$i,B:$i,A:($i > $o)] : ((~ (A @ (sk7 @ B @ (A)))) | (~ (rel @ B @ C)) | (~ (rel @ C @ D)) | ~ (($true)) | ((A @ D) != (b @ sk4)))),inference(paramod_ordered,[status(thm)],[25,8])).
% 16.60/5.34 thf(53,plain,(! [D:$i,C:$i,B:$i,A:($i > $o)] : ((~ (A @ (sk7 @ B @ (A)))) | (~ (rel @ B @ C)) | (~ (rel @ C @ D)) | ((A @ D) != (b @ sk4)))),inference(simp,[status(thm)],[52])).
% 16.60/5.34 thf(98,plain,(! [B:$i,A:$i] : ((~ (b @ (sk7 @ A @ (b)))) | (~ (rel @ A @ B)) | (~ (rel @ B @ sk4)))),inference(pre_uni,[status(thm)],[53:[bind(A, $thf(b)),bind(B, $thf(B)),bind(C, $thf(C)),bind(D, $thf(sk4))]])).
% 16.60/5.34 thf(132,plain,(! [B:$i,A:$i] : ((~ (b @ (sk7 @ A @ (b)))) | (~ (rel @ A @ B)) | (~ (rel @ B @ sk4)))),inference(simp,[status(thm)],[98])).
% 16.60/5.34 thf(348,plain,(! [B:$i,A:$i] : ((~ (b @ (sk7 @ A @ (b)))) | ~ (($true)) | (~ (rel @ B @ sk4)) | ((rel @ sk1 @ sk2) != (rel @ A @ B)))),inference(paramod_ordered,[status(thm)],[13,132])).
% 16.60/5.34 thf(349,plain,(! [B:$i,A:$i] : ((~ (b @ (sk7 @ A @ (b)))) | (~ (rel @ B @ sk4)) | ((rel @ sk1 @ sk2) != (rel @ A @ B)))),inference(simp,[status(thm)],[348])).
% 16.60/5.34 thf(350,plain,((~ (b @ (sk7 @ sk1 @ (b)))) | (~ (rel @ sk2 @ sk4))),inference(pattern_uni,[status(thm)],[349:[bind(A, $thf(sk1)),bind(B, $thf(sk2))]])).
% 16.60/5.34 thf(863,plain,((~ (b @ (sk7 @ sk1 @ (b)))) | ~ (($true)) | ((rel @ sk3 @ sk4) != (rel @ sk2 @ sk4))),inference(paramod_ordered,[status(thm)],[11,350])).
% 16.60/5.34 thf(864,plain,((~ (b @ (sk7 @ sk1 @ (b)))) | ((rel @ sk3 @ sk4) != (rel @ sk2 @ sk4))),inference(simp,[status(thm)],[863])).
% 16.60/5.34 thf(876,plain,((~ (b @ (sk7 @ sk1 @ (b)))) | (sk3 != sk2) | (sk4 != sk4)),inference(simp,[status(thm)],[864])).
% 16.60/5.34 thf(893,plain,((~ (b @ (sk7 @ sk1 @ (b)))) | (sk3 != sk2)),inference(simp,[status(thm)],[876])).
% 16.60/5.34 thf(10,plain,((~ (s @ sk5))),inference(cnfConj,[status(thm)],[6])).
% 16.60/5.34 thf(14,plain,(! [C:$i,B:$i,A:$i] : ((~ (rel @ sk2 @ A)) | (~ (rel @ A @ B)) | (~ (a @ B)) | (b @ B) | (~ (rel @ A @ C)) | (s @ C))),inference(cnfConj,[status(thm)],[6])).
% 16.60/5.34 thf(3,axiom,((! [A:($i > $o)]: (mvalid @ (mimpl @ (mbox @ rel @ A) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',refl_axiom)).
% 16.60/5.34 thf(16,plain,((! [A:($i > $o),B:$i]: (~ (! [C:$i]: ((rel @ B @ C) => (A @ C))) | (A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3])).
% 16.60/5.34 thf(17,plain,(! [B:$i,A:($i > $o)] : ((((rel @ B @ (sk6 @ B @ (A))) | (A @ B)) & (~ (A @ (sk6 @ B @ (A))) | (A @ B))))),inference(cnf,[status(esa)],[16])).
% 16.60/5.34 thf(19,plain,(! [B:$i,A:($i > $o)] : ((~ (A @ (sk6 @ B @ (A)))) | (A @ B))),inference(cnfConj,[status(thm)],[17])).
% 16.60/5.34 thf(275,plain,(! [A:$i] : ((~ (prop_b @ (sk6 @ A @ (prop_b)))) | (prop_b @ A))),inference(prim_subst,[status(thm)],[19:[bind(A, $thf(prop_b))]])).
% 16.60/5.34 thf(307,plain,(! [A:$i] : ((~ (prop_b @ (sk6 @ A @ (prop_b)))) | (prop_b @ A))),inference(simp,[status(thm)],[275])).
% 16.60/5.34 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((=) @ $i @ (sk6 @ B @ A)))]])).
% 16.60/5.34 thf(21,plain,(! [B:$i,A:($i > $o)] : (((sk6 @ B @ (A)) != (sk6 @ B @ ((=) @ $i @ (sk6 @ B @ A)))) | ((sk6 @ B @ (A)) = B))),inference(lifteq,[status(thm)],[20])).
% 16.60/5.34 thf(18,plain,(! [B:$i,A:($i > $o)] : ((rel @ B @ (sk6 @ B @ (A))) | (A @ B))),inference(cnfConj,[status(thm)],[17])).
% 16.60/5.34 thf(412,plain,(! [B:$i,A:($i > $o)] : ((rel @ B @ (sk6 @ B @ (A))) | ~ (($true)) | ((A @ B) != (s @ sk5)))),inference(paramod_ordered,[status(thm)],[18,10])).
% 16.60/5.34 thf(413,plain,(! [B:$i,A:($i > $o)] : ((rel @ B @ (sk6 @ B @ (A))) | ((A @ B) != (s @ sk5)))),inference(simp,[status(thm)],[412])).
% 16.60/5.34 thf(522,plain,((rel @ sk5 @ (sk6 @ sk5 @ (s)))),inference(pre_uni,[status(thm)],[413:[bind(A, $thf(s)),bind(B, $thf(sk5))]])).
% 16.60/5.34 thf(9,plain,((rel @ sk4 @ sk5)),inference(cnfConj,[status(thm)],[6])).
% 16.60/5.34 thf(358,plain,(! [B:$i,A:$i] : ((~ (b @ (sk7 @ A @ (b)))) | ~ (($true)) | (~ (rel @ B @ sk4)) | ((rel @ sk3 @ sk4) != (rel @ A @ B)))),inference(paramod_ordered,[status(thm)],[11,132])).
% 16.60/5.34 thf(359,plain,(! [B:$i,A:$i] : ((~ (b @ (sk7 @ A @ (b)))) | (~ (rel @ B @ sk4)) | ((rel @ sk3 @ sk4) != (rel @ A @ B)))),inference(simp,[status(thm)],[358])).
% 16.60/5.34 thf(360,plain,((~ (b @ (sk7 @ sk3 @ (b)))) | (~ (rel @ sk4 @ sk4))),inference(pattern_uni,[status(thm)],[359:[bind(A, $thf(sk3)),bind(B, $thf(sk4))]])).
% 16.60/5.34 thf(1107,plain,((~ (b @ (sk7 @ sk3 @ (b)))) | ~ (($true)) | ((rel @ sk4 @ sk5) != (rel @ sk4 @ sk4))),inference(paramod_ordered,[status(thm)],[9,360])).
% 16.60/5.34 thf(1108,plain,((~ (b @ (sk7 @ sk3 @ (b)))) | ((rel @ sk4 @ sk5) != (rel @ sk4 @ sk4))),inference(simp,[status(thm)],[1107])).
% 16.60/5.34 thf(1157,plain,((~ (b @ (sk7 @ sk3 @ (b)))) | (sk4 != sk4) | (sk5 != sk4)),inference(simp,[status(thm)],[1108])).
% 16.60/5.34 thf(1160,plain,((~ (b @ (sk7 @ sk3 @ (b)))) | (sk5 != sk4)),inference(simp,[status(thm)],[1157])).
% 16.60/5.34 thf(343,plain,(! [B:$i,A:$i] : ((~ (b @ (sk7 @ A @ (b)))) | ~ (($true)) | (~ (rel @ B @ sk4)) | ((rel @ sk4 @ sk5) != (rel @ A @ B)))),inference(paramod_ordered,[status(thm)],[9,132])).
% 16.60/5.34 thf(344,plain,(! [B:$i,A:$i] : ((~ (b @ (sk7 @ A @ (b)))) | (~ (rel @ B @ sk4)) | ((rel @ sk4 @ sk5) != (rel @ A @ B)))),inference(simp,[status(thm)],[343])).
% 16.60/5.34 thf(345,plain,((~ (b @ (sk7 @ sk4 @ (b)))) | (~ (rel @ sk5 @ sk4))),inference(pattern_uni,[status(thm)],[344:[bind(A, $thf(sk4)),bind(B, $thf(sk5))]])).
% 16.60/5.34 thf(7,plain,((rel @ sk2 @ sk3)),inference(cnfConj,[status(thm)],[6])).
% 16.60/5.34 thf(851,plain,((~ (b @ (sk7 @ sk1 @ (b)))) | ~ (($true)) | ((rel @ sk2 @ sk4) != (rel @ sk2 @ sk3))),inference(paramod_ordered,[status(thm)],[7,350])).
% 16.60/5.34 thf(852,plain,((~ (b @ (sk7 @ sk1 @ (b)))) | ((rel @ sk2 @ sk4) != (rel @ sk2 @ sk3))),inference(simp,[status(thm)],[851])).
% 16.60/5.34 thf(872,plain,((~ (b @ (sk7 @ sk1 @ (b)))) | (sk2 != sk2) | (sk4 != sk3)),inference(simp,[status(thm)],[852])).
% 16.60/5.34 thf(891,plain,((~ (b @ (sk7 @ sk1 @ (b)))) | (sk4 != sk3)),inference(simp,[status(thm)],[872])).
% 16.60/5.34 thf(353,plain,(! [B:$i,A:$i] : ((~ (b @ (sk7 @ A @ (b)))) | ~ (($true)) | (~ (rel @ B @ sk4)) | ((rel @ sk2 @ sk3) != (rel @ A @ B)))),inference(paramod_ordered,[status(thm)],[7,132])).
% 16.60/5.34 thf(354,plain,(! [B:$i,A:$i] : ((~ (b @ (sk7 @ A @ (b)))) | (~ (rel @ B @ sk4)) | ((rel @ sk2 @ sk3) != (rel @ A @ B)))),inference(simp,[status(thm)],[353])).
% 16.60/5.34 thf(355,plain,((~ (b @ (sk7 @ sk2 @ (b)))) | (~ (rel @ sk3 @ sk4))),inference(pattern_uni,[status(thm)],[354:[bind(A, $thf(sk2)),bind(B, $thf(sk3))]])).
% 16.60/5.34 thf(989,plain,((~ (b @ (sk7 @ sk2 @ (b)))) | ~ (($true))),inference(rewrite,[status(thm)],[355,11])).
% 16.60/5.34 thf(990,plain,((~ (b @ (sk7 @ sk2 @ (b))))),inference(simp,[status(thm)],[989])).
% 16.60/5.34 thf(991,plain,(! [B:$i,A:($i > $o)] : ((rel @ B @ (sk6 @ B @ (A))) | ~ (($true)) | ((A @ B) != (b @ (sk7 @ sk2 @ (b)))))),inference(paramod_ordered,[status(thm)],[18,990])).
% 16.60/5.34 thf(992,plain,(! [B:$i,A:($i > $o)] : ((rel @ B @ (sk6 @ B @ (A))) | ((A @ B) != (b @ (sk7 @ sk2 @ (b)))))),inference(simp,[status(thm)],[991])).
% 16.60/5.34 thf(995,plain,((rel @ (sk7 @ sk2 @ (b)) @ (sk6 @ (sk7 @ sk2 @ (b)) @ (b)))),inference(pre_uni,[status(thm)],[992:[bind(A, $thf(b)),bind(B, $thf(sk7 @ sk2 @ (b)))]])).
% 16.60/5.34 thf(290,plain,(! [A:$i] : ((~ (a @ (sk6 @ A @ (a)))) | (a @ A))),inference(prim_subst,[status(thm)],[19:[bind(A, $thf(a))]])).
% 16.60/5.34 thf(305,plain,(! [A:$i] : ((~ (a @ (sk6 @ A @ (a)))) | (a @ A))),inference(simp,[status(thm)],[290])).
% 16.60/5.34 thf(466,plain,(! [B:$i,A:($i > $o)] : ((rel @ B @ (sk6 @ B @ (A))) | ~ (($true)) | ((A @ B) != (b @ sk4)))),inference(paramod_ordered,[status(thm)],[18,8])).
% 16.60/5.34 thf(467,plain,(! [B:$i,A:($i > $o)] : ((rel @ B @ (sk6 @ B @ (A))) | ((A @ B) != (b @ sk4)))),inference(simp,[status(thm)],[466])).
% 16.60/5.34 thf(511,plain,((rel @ sk4 @ (sk6 @ sk4 @ (b)))),inference(pre_uni,[status(thm)],[467:[bind(A, $thf(b)),bind(B, $thf(sk4))]])).
% 16.60/5.34 thf(386,plain,((~ (b @ (sk7 @ sk4 @ (b)))) | ~ (($true)) | ((rel @ sk5 @ sk4) != (rel @ sk4 @ sk5))),inference(paramod_ordered,[status(thm)],[9,345])).
% 16.60/5.34 thf(387,plain,((~ (b @ (sk7 @ sk4 @ (b)))) | ((rel @ sk5 @ sk4) != (rel @ sk4 @ sk5))),inference(simp,[status(thm)],[386])).
% 16.60/5.34 thf(400,plain,((~ (b @ (sk7 @ sk4 @ (b)))) | (sk5 != sk4) | (sk5 != sk4)),inference(simp,[status(thm)],[387])).
% 16.60/5.34 thf(404,plain,((~ (b @ (sk7 @ sk4 @ (b)))) | (sk5 != sk4)),inference(simp,[status(thm)],[400])).
% 16.60/5.34 thf(24,plain,(! [D:$i,C:$i,B:$i,A:($i > $o)] : ((rel @ B @ (sk7 @ B @ (A))) | (~ (rel @ B @ C)) | (~ (rel @ C @ D)) | (A @ D))),inference(cnfConj,[status(thm)],[23])).
% 16.60/5.34 thf(475,plain,(! [A:$i] : ((rel @ A @ (sk6 @ A @ (a))) | (a @ A))),inference(prim_subst,[status(thm)],[18:[bind(A, $thf(a))]])).
% 16.60/5.34 thf(565,plain,(! [A:$i] : ((rel @ A @ (sk6 @ A @ (a))) | (a @ A))),inference(simp,[status(thm)],[475])).
% 16.60/5.34 thf(392,plain,((~ (b @ (sk7 @ sk4 @ (b)))) | ~ (($true)) | ((rel @ sk5 @ sk4) != (rel @ sk3 @ sk4))),inference(paramod_ordered,[status(thm)],[11,345])).
% 16.60/5.34 thf(393,plain,((~ (b @ (sk7 @ sk4 @ (b)))) | ((rel @ sk5 @ sk4) != (rel @ sk3 @ sk4))),inference(simp,[status(thm)],[392])).
% 16.60/5.34 thf(398,plain,((~ (b @ (sk7 @ sk4 @ (b)))) | (sk5 != sk3) | (sk4 != sk4)),inference(simp,[status(thm)],[393])).
% 16.60/5.34 thf(411,plain,((~ (b @ (sk7 @ sk4 @ (b)))) | (sk5 != sk3)),inference(simp,[status(thm)],[398])).
% 16.60/5.34 thf(997,plain,((rel @ sk2 @ (sk6 @ sk2 @ (^ [A:$i]: (b @ (sk7 @ A @ b)))))),inference(pre_uni,[status(thm)],[992:[bind(A, $thf(^ [C:$i]: (b @ (sk7 @ C @ b)))),bind(B, $thf(sk2))]])).
% 16.60/5.34 thf(477,plain,(! [A:$i] : ((rel @ A @ (sk6 @ A @ (prop_c))) | (prop_c @ A))),inference(prim_subst,[status(thm)],[18:[bind(A, $thf(prop_c))]])).
% 16.60/5.34 thf(567,plain,(! [A:$i] : ((rel @ A @ (sk6 @ A @ (prop_c))) | (prop_c @ A))),inference(simp,[status(thm)],[477])).
% 16.60/5.34 thf(1129,plain,((~ (b @ (sk7 @ sk3 @ (b)))) | ~ (($true)) | ((rel @ sk4 @ sk4) != (rel @ sk3 @ sk4))),inference(paramod_ordered,[status(thm)],[11,360])).
% 16.60/5.34 thf(1130,plain,((~ (b @ (sk7 @ sk3 @ (b)))) | ((rel @ sk4 @ sk4) != (rel @ sk3 @ sk4))),inference(simp,[status(thm)],[1129])).
% 16.60/5.34 thf(1149,plain,((~ (b @ (sk7 @ sk3 @ (b)))) | (sk4 != sk3) | (sk4 != sk4)),inference(simp,[status(thm)],[1130])).
% 16.60/5.34 thf(1171,plain,((~ (b @ (sk7 @ sk3 @ (b)))) | (sk4 != sk3)),inference(simp,[status(thm)],[1149])).
% 16.60/5.34 thf(291,plain,(! [A:$i] : ((~ (s @ (sk6 @ A @ (s)))) | (s @ A))),inference(prim_subst,[status(thm)],[19:[bind(A, $thf(s))]])).
% 16.60/5.34 thf(306,plain,(! [A:$i] : ((~ (s @ (sk6 @ A @ (s)))) | (s @ A))),inference(simp,[status(thm)],[291])).
% 16.60/5.34 thf(480,plain,(! [A:$i] : ((rel @ A @ (sk6 @ A @ (^ [B:$i]: (($false))))) | ($false))),inference(prim_subst,[status(thm)],[18:[bind(A, $thf(^ [C:$i]: (($false))))]])).
% 16.60/5.34 thf(571,plain,(! [A:$i] : ((rel @ A @ (sk6 @ A @ (^ [B:$i]: (($false))))))),inference(simp,[status(thm)],[480])).
% 16.60/5.34 thf(12,plain,(! [B:$i,A:$i] : ((~ (rel @ sk3 @ A)) | (a @ A) | (~ (rel @ A @ B)) | (s @ B))),inference(cnfConj,[status(thm)],[6])).
% 16.60/5.34 thf(15,plain,(! [B:$i,A:$i] : ((~ (rel @ sk3 @ A)) | (a @ A) | (~ (rel @ A @ B)) | (s @ B))),inference(simp,[status(thm)],[12])).
% 16.60/5.34 thf(364,plain,(! [B:$i,A:$i] : ((~ (b @ (sk7 @ A @ (b)))) | (~ (rel @ A @ B)) | ((rel @ B @ sk4) != (rel @ A @ B)) | ~ (($true)))),inference(eqfactor_ordered,[status(thm)],[132])).
% 16.60/5.34 thf(369,plain,((~ (b @ (sk7 @ sk4 @ (b)))) | (~ (rel @ sk4 @ sk4))),inference(pattern_uni,[status(thm)],[364:[bind(A, $thf(sk4)),bind(B, $thf(sk4))]])).
% 16.60/5.34 thf(2507,plain,(($false)),inference(e,[status(thm)],[893,10,14,307,21,522,9,1160,360,22,350,345,18,16,891,995,8,19,305,5,511,404,24,565,25,132,411,997,13,990,567,7,1171,306,11,571,15,369])).
% 16.60/5.34 % SZS output end Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 16.60/5.34 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------