%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWV425^2 : 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 : n007.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 11.90s 3.79s
% Output : Refutation 10.78s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV425^2 : 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
% 0.11/0.20 % Computer : n007.cluster.edu
% 0.11/0.20 % Model : x86_64 x86_64
% 0.11/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.20 % Memory : 8046.5625MB
% 0.11/0.20 % OS : Linux 6.8.0-71-generic
% 0.11/0.20 % CPULimit : 300
% 0.11/0.20 % WCLimit : 300
% 0.11/0.20 % DateTime : Tue Sep 29 15:59:56 UTC 2026
% 0.11/0.21 % CPUTime :
% 0.11/0.21 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
% 0.93/0.74 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.27/1.00 % [INFO] Parsing done (254ms).
% 1.27/1.01 % [INFO] Running in sequential loop mode.
% 2.31/1.41 % [INFO] eprover registered as external prover.
% 2.31/1.42 % [INFO] Scanning for conjecture ...
% 2.49/1.56 % [INFO] Found a conjecture (or negated_conjecture) and 2 axioms. Running axiom selection ...
% 2.49/1.59 % [INFO] Axiom selection finished. Selected 2 axioms (removed 0 axioms).
% 2.69/1.60 % [INFO] Problem is higher-order (TPTP THF).
% 2.69/1.60 % [INFO] Type checking passed.
% 2.69/1.61 % [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 ...
% 11.90/3.79 % External prover 'e' found a proof!
% 11.90/3.79 % [INFO] Killing All external provers ...
% 11.90/3.79 % Time passed: 3430ms (effective reasoning time: 2772ms)
% 11.90/3.79 % 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)>
% 11.90/3.79 % Axioms used in derivation (2): trans_axiom, refl_axiom
% 11.90/3.79 % No. of inferences in proof: 89
% 11.90/3.79 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 3430 ms resp. 2772 ms w/o parsing
% 10.78/3.88 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% 10.78/3.88 thf(individuals_type, type, individuals: $tType).
% 10.78/3.88 thf(prop_a_decl, type, prop_a: ($i > $o)).
% 10.78/3.88 thf(prop_b_decl, type, prop_b: ($i > $o)).
% 10.78/3.88 thf(prop_c_decl, type, prop_c: ($i > $o)).
% 10.78/3.88 thf(mnot_decl, type, mnot: (($i > $o) > ($i > $o))).
% 10.78/3.88 thf(mor_decl, type, mor: (($i > $o) > (($i > $o) > ($i > $o)))).
% 10.78/3.88 thf(mimpl_decl, type, mimpl: (($i > $o) > (($i > $o) > ($i > $o)))).
% 10.78/3.88 thf(mbox_decl, type, mbox: (($i > ($i > $o)) > (($i > $o) > ($i > $o)))).
% 10.78/3.88 thf(mvalid_decl, type, mvalid: (($i > $o) > $o)).
% 10.78/3.88 thf(rel_decl, type, rel: ($i > ($i > $o))).
% 10.78/3.88 thf(icl_atom_decl, type, icl_atom: (($i > $o) > ($i > $o))).
% 10.78/3.88 thf(icl_princ_decl, type, icl_princ: (($i > $o) > ($i > $o))).
% 10.78/3.88 thf(icl_impl_decl, type, icl_impl: (($i > $o) > (($i > $o) > ($i > $o)))).
% 10.78/3.88 thf(icl_says_decl, type, icl_says: (($i > $o) > (($i > $o) > ($i > $o)))).
% 10.78/3.88 thf(iclval_decl, type, iclval: (($i > $o) > $o)).
% 10.78/3.88 thf(s_decl, type, s: ($i > $o)).
% 10.78/3.88 thf(a_decl, type, a: ($i > $o)).
% 10.78/3.88 thf(sk1_decl, type, sk1: $i).
% 10.78/3.88 thf(sk2_decl, type, sk2: $i).
% 10.78/3.88 thf(sk3_decl, type, sk3: $i).
% 10.78/3.88 thf(sk4_decl, type, sk4: $i).
% 10.78/3.88 thf(sk5_decl, type, sk5: ($i > (($i > $o) > $i))).
% 10.78/3.88 thf(sk6_decl, type, sk6: ($i > (($i > $o) > $i))).
% 10.78/3.88 thf(mnot_def, definition, mnot = (^ [A:($i > $o),B:$i]: ~ (A @ B)) ).
% 10.78/3.88 thf(mor_def, definition, mor = (^ [A:($i > $o),B:($i > $o),C:$i]: ((A @ C) | (B @ C))) ).
% 10.78/3.88 thf(mimpl_def, definition, mimpl = (^ [A:($i > $o)]: (mor @ (mnot @ A))) ).
% 10.78/3.88 thf(mbox_def, definition, mbox = (^ [A:($i > ($i > $o)),B:($i > $o),C:$i]: ! [D:$i]: ((A @ C @ D) => (B @ D))) ).
% 10.78/3.88 thf(mvalid_def, definition, mvalid = ((!) @ $i) ).
% 10.78/3.88 thf(icl_atom_def, definition, icl_atom = (mbox @ rel) ).
% 10.78/3.88 thf(icl_princ_def, definition, icl_princ = (^ [A:($i > $o)]: (A)) ).
% 10.78/3.88 thf(icl_impl_def, definition, icl_impl = (^ [A:($i > $o),B:($i > $o)]: (mbox @ rel @ (mimpl @ A @ B))) ).
% 10.78/3.88 thf(icl_says_def, definition, icl_says = (^ [A:($i > $o),B:($i > $o)]: (mbox @ rel @ (mor @ A @ B))) ).
% 10.78/3.88 thf(iclval_def, definition, iclval = (mvalid) ).
% 10.78/3.88 thf(sk1_def, definition, sk1 = (@+ [A:$i]: ~ (! [B:$i]: ((rel @ A @ B) => (~ (! [C:$i]: ((rel @ B @ C) => (s @ C))) | ! [C:$i]: ((rel @ B @ C) => ((a @ C) | ! [D:$i]: ((rel @ C @ D) => (s @ D)))))))) ).
% 10.78/3.88 thf(sk2_def, definition, sk2 = (@+ [A:$i]: ~ ((rel @ sk1 @ A) => (~ (! [B:$i]: ((rel @ A @ B) => (s @ B))) | ! [B:$i]: ((rel @ A @ B) => ((a @ B) | ! [C:$i]: ((rel @ B @ C) => (s @ C))))))) ).
% 10.78/3.88 thf(sk3_def, definition, sk3 = (@+ [A:$i]: ~ ((rel @ sk2 @ A) => ((a @ A) | ! [B:$i]: ((rel @ A @ B) => (s @ B))))) ).
% 10.78/3.88 thf(sk4_def, definition, sk4 = (@+ [A:$i]: ~ ((rel @ sk3 @ A) => (s @ A))) ).
% 10.78/3.88 thf(sk5_def, definition, sk5 = (^ [A:$i,B:($i > $o)]: (@+ [C:$i]: ~ ((rel @ A @ C) => (B @ C)))) ).
% 10.78/3.88 thf(sk6_def, definition, sk6 = (^ [A:$i,B:($i > $o)]: (@+ [C:$i]: ~ ((rel @ A @ C) => (B @ C)))) ).
% 10.78/3.88 thf(1,conjecture,((iclval @ (icl_impl @ (icl_atom @ s) @ (icl_says @ (icl_princ @ a) @ (icl_atom @ s))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',unit)).
% 10.78/3.88 thf(2,negated_conjecture,((~ (iclval @ (icl_impl @ (icl_atom @ s) @ (icl_says @ (icl_princ @ a) @ (icl_atom @ s)))))),inference(neg_conjecture,[status(cth)],[1])).
% 10.78/3.88 thf(5,plain,((~ (! [A:$i,B:$i]: ((rel @ A @ B) => (~ (! [C:$i]: ((rel @ B @ C) => (s @ C))) | ! [C:$i]: ((rel @ B @ C) => ((a @ C) | ! [D:$i]: ((rel @ C @ D) => (s @ D))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])).
% 10.78/3.88 thf(6,plain,(! [A:$i] : (((rel @ sk1 @ sk2) & (~ (rel @ sk2 @ A) | (s @ A)) & (rel @ sk2 @ sk3) & ~ (a @ sk3) & (rel @ sk3 @ sk4) & ~ (s @ sk4)))),inference(cnf,[status(esa)],[5])).
% 10.78/3.88 thf(10,plain,((~ (s @ sk4))),inference(cnfConj,[status(thm)],[6])).
% 10.78/3.88 thf(11,plain,((rel @ sk2 @ sk3)),inference(cnfConj,[status(thm)],[6])).
% 10.78/3.88 thf(4,axiom,((! [A:($i > $o)]: (mvalid @ (mimpl @ (mbox @ rel @ A) @ (mbox @ rel @ (mbox @ rel @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',trans_axiom)).
% 10.78/3.88 thf(19,plain,((! [A:($i > $o),B:$i]: (~ (! [C:$i]: ((rel @ B @ C) => (A @ C))) | ! [C:$i]: ((rel @ B @ C) => (! [D:$i]: ((rel @ C @ D) => (A @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4])).
% 10.78/3.88 thf(20,plain,(! [D:$i,C:$i,B:$i,A:($i > $o)] : ((((rel @ B @ (sk6 @ B @ (A))) | ~ (rel @ B @ C) | ~ (rel @ C @ D) | (A @ D)) & (~ (A @ (sk6 @ B @ (A))) | ~ (rel @ B @ C) | ~ (rel @ C @ D) | (A @ D))))),inference(cnf,[status(esa)],[19])).
% 10.78/3.88 thf(22,plain,(! [D:$i,C:$i,B:$i,A:($i > $o)] : ((~ (A @ (sk6 @ B @ (A)))) | (~ (rel @ B @ C)) | (~ (rel @ C @ D)) | (A @ D))),inference(cnfConj,[status(thm)],[20])).
% 10.78/3.88 thf(8,plain,((~ (a @ sk3))),inference(cnfConj,[status(thm)],[6])).
% 10.78/3.88 thf(49,plain,(! [D:$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])).
% 10.78/3.88 thf(50,plain,(! [D:$i,C:$i,B:$i,A:($i > $o)] : ((~ (A @ (sk6 @ B @ (A)))) | (~ (rel @ B @ C)) | (~ (rel @ C @ D)) | ((A @ D) != (a @ sk3)))),inference(simp,[status(thm)],[49])).
% 10.78/3.88 thf(101,plain,(! [B:$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, $thf(sk3))]])).
% 10.78/3.88 thf(128,plain,(! [B:$i,A:$i] : ((~ (a @ (sk6 @ A @ (a)))) | (~ (rel @ A @ B)) | (~ (rel @ B @ sk3)))),inference(simp,[status(thm)],[101])).
% 10.78/3.88 thf(374,plain,(! [B:$i,A:$i] : ((~ (a @ (sk6 @ A @ (a)))) | ~ (($true)) | (~ (rel @ B @ sk3)) | ((rel @ sk2 @ sk3) != (rel @ A @ B)))),inference(paramod_ordered,[status(thm)],[11,128])).
% 10.78/3.88 thf(375,plain,(! [B:$i,A:$i] : ((~ (a @ (sk6 @ A @ (a)))) | (~ (rel @ B @ sk3)) | ((rel @ sk2 @ sk3) != (rel @ A @ B)))),inference(simp,[status(thm)],[374])).
% 10.78/3.88 thf(376,plain,((~ (a @ (sk6 @ sk2 @ (a)))) | (~ (rel @ sk3 @ sk3))),inference(pattern_uni,[status(thm)],[375:[bind(A, $thf(sk2)),bind(B, $thf(sk3))]])).
% 10.78/3.88 thf(7,plain,((rel @ sk3 @ sk4)),inference(cnfConj,[status(thm)],[6])).
% 10.78/3.88 thf(364,plain,(! [B:$i,A:$i] : ((~ (a @ (sk6 @ A @ (a)))) | ~ (($true)) | (~ (rel @ B @ sk3)) | ((rel @ sk3 @ sk4) != (rel @ A @ B)))),inference(paramod_ordered,[status(thm)],[7,128])).
% 10.78/3.88 thf(365,plain,(! [B:$i,A:$i] : ((~ (a @ (sk6 @ A @ (a)))) | (~ (rel @ B @ sk3)) | ((rel @ sk3 @ sk4) != (rel @ A @ B)))),inference(simp,[status(thm)],[364])).
% 10.78/3.88 thf(366,plain,((~ (a @ (sk6 @ sk3 @ (a)))) | (~ (rel @ sk4 @ sk3))),inference(pattern_uni,[status(thm)],[365:[bind(A, $thf(sk3)),bind(B, $thf(sk4))]])).
% 10.78/3.88 thf(21,plain,(! [D:$i,C:$i,B:$i,A:($i > $o)] : ((rel @ B @ (sk6 @ B @ (A))) | (~ (rel @ B @ C)) | (~ (rel @ C @ D)) | (A @ D))),inference(cnfConj,[status(thm)],[20])).
% 10.78/3.88 thf(9,plain,(! [A:$i] : ((~ (rel @ sk2 @ A)) | (s @ A))),inference(cnfConj,[status(thm)],[6])).
% 10.78/3.88 thf(12,plain,((rel @ sk1 @ sk2)),inference(cnfConj,[status(thm)],[6])).
% 10.78/3.88 thf(359,plain,(! [B:$i,A:$i] : ((~ (a @ (sk6 @ A @ (a)))) | ~ (($true)) | (~ (rel @ B @ sk3)) | ((rel @ sk1 @ sk2) != (rel @ A @ B)))),inference(paramod_ordered,[status(thm)],[12,128])).
% 10.78/3.88 thf(360,plain,(! [B:$i,A:$i] : ((~ (a @ (sk6 @ A @ (a)))) | (~ (rel @ B @ sk3)) | ((rel @ sk1 @ sk2) != (rel @ A @ B)))),inference(simp,[status(thm)],[359])).
% 10.78/3.88 thf(361,plain,((~ (a @ (sk6 @ sk1 @ (a)))) | (~ (rel @ sk2 @ sk3))),inference(pattern_uni,[status(thm)],[360:[bind(A, $thf(sk1)),bind(B, $thf(sk2))]])).
% 10.78/3.88 thf(546,plain,((~ (a @ (sk6 @ sk1 @ (a)))) | ~ (($true))),inference(rewrite,[status(thm)],[361,11])).
% 10.78/3.88 thf(547,plain,((~ (a @ (sk6 @ sk1 @ (a))))),inference(simp,[status(thm)],[546])).
% 10.78/3.88 thf(3,axiom,((! [A:($i > $o)]: (mvalid @ (mimpl @ (mbox @ rel @ A) @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',refl_axiom)).
% 10.78/3.88 thf(13,plain,((! [A:($i > $o),B:$i]: (~ (! [C:$i]: ((rel @ B @ C) => (A @ C))) | (A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3])).
% 10.78/3.88 thf(14,plain,(! [B:$i,A:($i > $o)] : ((((rel @ B @ (sk5 @ B @ (A))) | (A @ B)) & (~ (A @ (sk5 @ B @ (A))) | (A @ B))))),inference(cnf,[status(esa)],[13])).
% 10.78/3.88 thf(15,plain,(! [B:$i,A:($i > $o)] : ((rel @ B @ (sk5 @ B @ (A))) | (A @ B))),inference(cnfConj,[status(thm)],[14])).
% 10.78/3.88 thf(224,plain,(! [A:$i] : ((rel @ A @ (sk5 @ A @ (^ [B:$i]: (($false))))) | ($false))),inference(prim_subst,[status(thm)],[15:[bind(A, $thf(^ [C:$i]: (($false))))]])).
% 10.78/3.88 thf(264,plain,(! [A:$i] : ((rel @ A @ (sk5 @ A @ (^ [B:$i]: (($false))))))),inference(simp,[status(thm)],[224])).
% 10.78/3.88 thf(189,plain,(! [B:$i,A:($i > $o)] : ((rel @ B @ (sk5 @ B @ (A))) | ~ (($true)) | ((A @ B) != (s @ sk4)))),inference(paramod_ordered,[status(thm)],[15,10])).
% 10.78/3.88 thf(190,plain,(! [B:$i,A:($i > $o)] : ((rel @ B @ (sk5 @ B @ (A))) | ((A @ B) != (s @ sk4)))),inference(simp,[status(thm)],[189])).
% 10.78/3.88 thf(240,plain,((rel @ sk4 @ (sk5 @ sk4 @ (s)))),inference(pre_uni,[status(thm)],[190:[bind(A, $thf(s)),bind(B, $thf(sk4))]])).
% 10.78/3.88 thf(16,plain,(! [B:$i,A:($i > $o)] : ((~ (A @ (sk5 @ B @ (A)))) | (A @ B))),inference(cnfConj,[status(thm)],[14])).
% 10.78/3.88 thf(191,plain,(! [C:$i,B:$i,A:($i > $o)] : ((A @ B) | ~ (($true)) | (s @ C) | ((rel @ B @ (sk5 @ B @ (A))) != (rel @ sk2 @ C)))),inference(paramod_ordered,[status(thm)],[15,9])).
% 10.78/3.88 thf(192,plain,(! [C:$i,B:$i,A:($i > $o)] : ((A @ B) | (s @ C) | ((rel @ B @ (sk5 @ B @ (A))) != (rel @ sk2 @ C)))),inference(simp,[status(thm)],[191])).
% 10.78/3.88 thf(193,plain,(! [A:($i > $o)] : ((A @ sk2) | (s @ (sk5 @ sk2 @ (A))))),inference(pattern_uni,[status(thm)],[192:[bind(A, $thf(E)),bind(B, $thf(sk2)),bind(C, $thf(sk5 @ sk2 @ (E)))]])).
% 10.78/3.88 thf(249,plain,(! [A:($i > $o)] : ((A @ sk2) | (s @ (sk5 @ sk2 @ (A))))),inference(simp,[status(thm)],[193])).
% 10.78/3.88 thf(550,plain,(! [B:$i,A:($i > $o)] : ((rel @ B @ (sk5 @ B @ (A))) | ~ (($true)) | ((A @ B) != (a @ (sk6 @ sk1 @ (a)))))),inference(paramod_ordered,[status(thm)],[15,547])).
% 10.78/3.88 thf(551,plain,(! [B:$i,A:($i > $o)] : ((rel @ B @ (sk5 @ B @ (A))) | ((A @ B) != (a @ (sk6 @ sk1 @ (a)))))),inference(simp,[status(thm)],[550])).
% 10.78/3.88 thf(555,plain,((rel @ (sk6 @ sk1 @ (a)) @ (sk5 @ (sk6 @ sk1 @ (a)) @ (a)))),inference(pre_uni,[status(thm)],[551:[bind(A, $thf(a)),bind(B, $thf(sk6 @ sk1 @ (a)))]])).
% 10.78/3.88 thf(730,plain,((prop_a @ sk2) | (s @ (sk5 @ sk2 @ (prop_a)))),inference(prim_subst,[status(thm)],[249:[bind(A, $thf(prop_a))]])).
% 10.78/3.88 thf(738,plain,((a @ sk2) | (s @ (sk5 @ sk2 @ (a)))),inference(prim_subst,[status(thm)],[249:[bind(A, $thf(a))]])).
% 10.78/3.88 thf(171,plain,(! [A:$i] : (~ (($true)) | (s @ A) | ((rel @ sk2 @ sk3) != (rel @ sk2 @ A)))),inference(paramod_ordered,[status(thm)],[11,9])).
% 10.78/3.88 thf(172,plain,(! [A:$i] : ((s @ A) | ((rel @ sk2 @ sk3) != (rel @ sk2 @ A)))),inference(simp,[status(thm)],[171])).
% 10.78/3.88 thf(173,plain,((s @ sk3)),inference(pattern_uni,[status(thm)],[172:[bind(A, $thf(sk3))]])).
% 10.78/3.88 thf(210,plain,(! [B:$i,A:($i > $o)] : ((rel @ B @ (sk5 @ B @ (A))) | ~ (($true)) | ((A @ B) != (a @ sk3)))),inference(paramod_ordered,[status(thm)],[15,8])).
% 10.78/3.88 thf(211,plain,(! [B:$i,A:($i > $o)] : ((rel @ B @ (sk5 @ B @ (A))) | ((A @ B) != (a @ sk3)))),inference(simp,[status(thm)],[210])).
% 10.78/3.88 thf(244,plain,((rel @ sk3 @ (sk5 @ sk3 @ (a)))),inference(pre_uni,[status(thm)],[211:[bind(A, $thf(a)),bind(B, $thf(sk3))]])).
% 10.78/3.88 thf(169,plain,(! [A:$i] : (~ (($true)) | (s @ A) | ((rel @ sk3 @ sk4) != (rel @ sk2 @ A)))),inference(paramod_ordered,[status(thm)],[7,9])).
% 10.78/3.88 thf(170,plain,(! [A:$i] : ((s @ A) | ((rel @ sk3 @ sk4) != (rel @ sk2 @ A)))),inference(simp,[status(thm)],[169])).
% 10.78/3.88 thf(177,plain,(! [A:$i] : ((s @ A) | (sk3 != sk2) | (sk4 != A))),inference(simp,[status(thm)],[170])).
% 10.78/3.88 thf(179,plain,((s @ sk4) | (sk3 != sk2)),inference(simp,[status(thm)],[177])).
% 10.78/3.88 thf(454,plain,(($false) | (sk3 != sk2)),inference(rewrite,[status(thm)],[179,10])).
% 10.78/3.88 thf(455,plain,((sk3 != sk2)),inference(simp,[status(thm)],[454])).
% 10.78/3.88 thf(277,plain,(! [A:$i] : (~ (($true)) | (s @ A) | ((rel @ sk4 @ (sk5 @ sk4 @ (s))) != (rel @ sk2 @ A)))),inference(paramod_ordered,[status(thm)],[240,9])).
% 10.78/3.88 thf(278,plain,(! [A:$i] : ((s @ A) | ((rel @ sk4 @ (sk5 @ sk4 @ (s))) != (rel @ sk2 @ A)))),inference(simp,[status(thm)],[277])).
% 10.78/3.88 thf(292,plain,(! [A:$i] : ((s @ A) | (sk4 != sk2) | ((sk5 @ sk4 @ (s)) != A))),inference(simp,[status(thm)],[278])).
% 10.78/3.88 thf(295,plain,((s @ (sk5 @ sk4 @ (s))) | (sk4 != sk2)),inference(simp,[status(thm)],[292])).
% 10.78/3.88 thf(650,plain,(! [B:$i,A:($i > $o)] : ((sk4 != sk2) | ~ (($true)) | (A @ B) | ((s @ (sk5 @ sk4 @ (s))) != (A @ (sk5 @ B @ (A)))))),inference(paramod_ordered,[status(thm)],[295,16])).
% 10.78/3.88 thf(651,plain,(! [B:$i,A:($i > $o)] : ((sk4 != sk2) | (A @ B) | ((s @ (sk5 @ sk4 @ (s))) != (A @ (sk5 @ B @ (A)))))),inference(simp,[status(thm)],[650])).
% 10.78/3.88 thf(654,plain,((sk4 != sk2) | (s @ sk4)),inference(pre_uni,[status(thm)],[651:[bind(A, $thf(s)),bind(B, $thf(sk4))]])).
% 10.78/3.88 thf(657,plain,((sk4 != sk2) | ($false)),inference(rewrite,[status(thm)],[654,10])).
% 10.78/3.88 thf(658,plain,((sk4 != sk2)),inference(simp,[status(thm)],[657])).
% 10.78/3.88 thf(557,plain,((rel @ sk1 @ (sk5 @ sk1 @ (^ [A:$i]: (a @ (sk6 @ A @ a)))))),inference(pre_uni,[status(thm)],[551:[bind(A, $thf(^ [C:$i]: (a @ (sk6 @ C @ a)))),bind(B, $thf(sk1))]])).
% 10.78/3.88 thf(17,plain,(! [B:$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((=) @ $i @ (sk5 @ B @ A)))]])).
% 10.78/3.88 thf(18,plain,(! [B:$i,A:($i > $o)] : (((sk5 @ B @ (A)) != (sk5 @ B @ ((=) @ $i @ (sk5 @ B @ A)))) | ((sk5 @ B @ (A)) = B))),inference(lifteq,[status(thm)],[17])).
% 10.78/3.88 thf(317,plain,(! [B:$i,A:$i] : (~ (($true)) | (s @ B) | ((rel @ A @ (sk5 @ A @ (^ [C:$i]: (($false))))) != (rel @ sk2 @ B)))),inference(paramod_ordered,[status(thm)],[264,9])).
% 10.78/3.88 thf(318,plain,(! [B:$i,A:$i] : ((s @ B) | ((rel @ A @ (sk5 @ A @ (^ [C:$i]: (($false))))) != (rel @ sk2 @ B)))),inference(simp,[status(thm)],[317])).
% 10.78/3.88 thf(319,plain,((s @ (sk5 @ sk2 @ (^ [A:$i]: (($false)))))),inference(pattern_uni,[status(thm)],[318:[bind(A, $thf(sk2)),bind(B, $thf(sk5 @ sk2 @ (^ [C:$i]: (($false)))))]])).
% 10.78/3.88 thf(182,plain,(~ (($true)) | ((s @ sk4) != (s @ sk3))),inference(paramod_ordered,[status(thm)],[173,10])).
% 10.78/3.88 thf(183,plain,(((s @ sk4) != (s @ sk3))),inference(simp,[status(thm)],[182])).
% 10.78/3.88 thf(186,plain,((sk4 != sk3)),inference(simp,[status(thm)],[183])).
% 10.78/3.88 thf(715,plain,(! [C:$i,B:($i > $o),A:($i > $o)] : ((A @ sk2) | ~ (($true)) | (B @ C) | ((s @ (sk5 @ sk2 @ (A))) != (B @ (sk5 @ C @ (B)))))),inference(paramod_ordered,[status(thm)],[249,16])).
% 10.78/3.88 thf(716,plain,(! [C:$i,B:($i > $o),A:($i > $o)] : ((A @ sk2) | (B @ C) | ((s @ (sk5 @ sk2 @ (A))) != (B @ (sk5 @ C @ (B)))))),inference(simp,[status(thm)],[715])).
% 10.78/3.88 thf(758,plain,((s @ sk2) | (s @ sk2)),inference(pre_uni,[status(thm)],[716:[bind(A, $thf(s)),bind(B, $thf(s)),bind(C, $thf(sk2))]])).
% 10.78/3.88 thf(786,plain,((s @ sk2)),inference(simp,[status(thm)],[758])).
% 10.78/3.88 thf(735,plain,((prop_b @ sk2) | (s @ (sk5 @ sk2 @ (prop_b)))),inference(prim_subst,[status(thm)],[249:[bind(A, $thf(prop_b))]])).
% 10.78/3.88 thf(740,plain,((prop_c @ sk2) | (s @ (sk5 @ sk2 @ (prop_c)))),inference(prim_subst,[status(thm)],[249:[bind(A, $thf(prop_c))]])).
% 10.78/3.88 thf(432,plain,(~ (($true)) | ((s @ (sk5 @ sk2 @ (^ [A:$i]: (($false))))) != (s @ sk4))),inference(paramod_ordered,[status(thm)],[319,10])).
% 10.78/3.88 thf(433,plain,(((s @ (sk5 @ sk2 @ (^ [A:$i]: (($false))))) != (s @ sk4))),inference(simp,[status(thm)],[432])).
% 10.78/3.88 thf(442,plain,(((sk5 @ sk2 @ (^ [A:$i]: (($false)))) != sk4)),inference(simp,[status(thm)],[433])).
% 10.78/3.88 thf(1491,plain,(($false)),inference(e,[status(thm)],[10,376,366,21,9,547,264,22,12,7,240,16,11,8,249,555,730,5,738,173,13,128,244,455,658,557,18,319,186,786,19,735,740,15,442])).
% 10.78/3.88 % SZS output end Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% 10.78/3.88 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------