%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWV441^1 : TPTP v9.3.1. Released v3.7.0.
% 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 : n020.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 08:39:53 AM UTC 2026
% Result : Theorem 29.88s 6.92s
% Output : Refutation 29.88s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWV441^1 : TPTP v9.3.1. Released v3.7.0.
% 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
% 0.10/0.19 % Computer : n020.cluster.edu
% 0.10/0.19 % Model : x86_64 x86_64
% 0.10/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.19 % Memory : 8046.5625MB
% 0.10/0.19 % OS : Linux 6.8.0-71-generic
% 0.10/0.19 % CPULimit : 300
% 0.10/0.19 % WCLimit : 300
% 0.10/0.19 % DateTime : Tue Sep 29 16:05:04 UTC 2026
% 0.10/0.20 % CPUTime :
% 0.10/0.20 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
% 1.06/0.81 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.55/1.08 % [INFO] Parsing done (272ms).
% 1.55/1.10 % [INFO] Running in sequential loop mode.
% 2.44/1.51 % [INFO] eprover registered as external prover.
% 2.44/1.52 % [INFO] Scanning for conjecture ...
% 2.64/1.67 % [INFO] Found a conjecture (or negated_conjecture) and 6 axioms. Running axiom selection ...
% 2.86/1.71 % [INFO] Axiom selection finished. Selected 6 axioms (removed 0 axioms).
% 2.86/1.72 % [INFO] Problem is higher-order (TPTP THF).
% 2.86/1.73 % [INFO] Type checking passed.
% 2.86/1.73 % [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 ...
% 29.88/6.91 % External prover 'e' found a proof!
% 29.88/6.91 % [INFO] Killing All external provers ...
% 29.88/6.92 % Time passed: 6575ms (effective reasoning time: 5813ms)
% 29.88/6.92 % 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)>
% 29.88/6.92 % Axioms used in derivation (6): trans_axiom_i, trans_axiom_r, loca_strength, refl_axiom_r, ax_i_r_commute, refl_axiom_i
% 29.88/6.92 % No. of inferences in proof: 107
% 29.88/6.92 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 6575 ms resp. 5813 ms w/o parsing
% 29.88/7.04 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 29.88/7.04 thf(individuals_type, type, individuals: $tType).
% 29.88/7.04 thf(prop_a_decl, type, prop_a: ($i > $o)).
% 29.88/7.04 thf(prop_b_decl, type, prop_b: ($i > $o)).
% 29.88/7.04 thf(prop_c_decl, type, prop_c: ($i > $o)).
% 29.88/7.04 thf(mnot_decl, type, mnot: (($i > $o) > ($i > $o))).
% 29.88/7.04 thf(mor_decl, type, mor: (($i > $o) > (($i > $o) > ($i > $o)))).
% 29.88/7.04 thf(mimpl_decl, type, mimpl: (($i > $o) > (($i > $o) > ($i > $o)))).
% 29.88/7.04 thf(mbox_decl, type, mbox: (($i > ($i > $o)) > (($i > $o) > ($i > $o)))).
% 29.88/7.04 thf(mall_decl, type, mall: ((individuals > ($i > $o)) > ($i > $o))).
% 29.88/7.04 thf(mvalid_decl, type, mvalid: (($i > $o) > $o)).
% 29.88/7.04 thf(reli_decl, type, reli: ($i > ($i > $o))).
% 29.88/7.04 thf(relr_decl, type, relr: ($i > ($i > $o))).
% 29.88/7.04 thf(cs4_atom_decl, type, cs4_atom: (($i > $o) > ($i > $o))).
% 29.88/7.04 thf(cs4_impl_decl, type, cs4_impl: (($i > $o) > (($i > $o) > ($i > $o)))).
% 29.88/7.04 thf(cs4_all_decl, type, cs4_all: ((individuals > ($i > $o)) > ($i > $o))).
% 29.88/7.04 thf(cs4_box_decl, type, cs4_box: (($i > $o) > ($i > $o))).
% 29.88/7.04 thf(cs4_valid_decl, type, cs4_valid: (($i > $o) > $o)).
% 29.88/7.04 thf(princ_inj_decl, type, princ_inj: (individuals > ($i > $o))).
% 29.88/7.04 thf(bl_princ_decl, type, bl_princ: (($i > $o) > ($i > $o))).
% 29.88/7.04 thf(bl_impl_decl, type, bl_impl: (($i > $o) > (($i > $o) > ($i > $o)))).
% 29.88/7.04 thf(bl_says_decl, type, bl_says: (individuals > (($i > $o) > ($i > $o)))).
% 29.88/7.04 thf(bl_valid_decl, type, bl_valid: (($i > $o) > $o)).
% 29.88/7.04 thf(loca_decl, type, loca: individuals).
% 29.88/7.04 thf(sk1_decl, type, sk1: individuals).
% 29.88/7.04 thf(sk2_decl, type, sk2: ($i > $o)).
% 29.88/7.04 thf(sk3_decl, type, sk3: ($i > $o)).
% 29.88/7.04 thf(sk4_decl, type, sk4: $i).
% 29.88/7.04 thf(sk5_decl, type, sk5: $i).
% 29.88/7.04 thf(sk6_decl, type, sk6: ($i > ($i > ($i > $i)))).
% 29.88/7.04 thf(sk7_decl, type, sk7: $i).
% 29.88/7.04 thf(sk8_decl, type, sk8: ($i > ($i > ($i > $i)))).
% 29.88/7.04 thf(sk9_decl, type, sk9: $i).
% 29.88/7.04 thf(sk10_decl, type, sk10: $i).
% 29.88/7.04 thf(sk11_decl, type, sk11: $i).
% 29.88/7.04 thf(sk12_decl, type, sk12: ($i > (($i > $o) > $i))).
% 29.88/7.04 thf(mnot_def, definition, mnot = (^ [A:($i > $o),B:$i]: ~ (A @ B)) ).
% 29.88/7.04 thf(mor_def, definition, mor = (^ [A:($i > $o),B:($i > $o),C:$i]: ((A @ C) | (B @ C))) ).
% 29.88/7.04 thf(mimpl_def, definition, mimpl = (^ [A:($i > $o)]: (mor @ (mnot @ A))) ).
% 29.88/7.04 thf(mbox_def, definition, mbox = (^ [A:($i > ($i > $o)),B:($i > $o),C:$i]: ! [D:$i]: ((A @ C @ D) => (B @ D))) ).
% 29.88/7.04 thf(mall_def, definition, mall = (^ [A:(individuals > ($i > $o)),B:$i]: ! [C:individuals]: (A @ C @ B)) ).
% 29.88/7.04 thf(mvalid_def, definition, mvalid = ((!) @ $i) ).
% 29.88/7.04 thf(cs4_atom_def, definition, cs4_atom = (mbox @ reli) ).
% 29.88/7.04 thf(cs4_impl_def, definition, cs4_impl = (^ [A:($i > $o),B:($i > $o)]: (mbox @ reli @ (mimpl @ A @ B))) ).
% 29.88/7.04 thf(cs4_all_def, definition, cs4_all = (^ [A:(individuals > ($i > $o))]: (mbox @ reli @ (mall @ A))) ).
% 29.88/7.04 thf(cs4_box_def, definition, cs4_box = (^ [A:($i > $o)]: (mbox @ reli @ (mbox @ relr @ A))) ).
% 29.88/7.04 thf(cs4_valid_def, definition, cs4_valid = (mvalid) ).
% 29.88/7.04 thf(bl_princ_def, definition, bl_princ = (cs4_atom) ).
% 29.88/7.04 thf(bl_impl_def, definition, bl_impl = (cs4_impl) ).
% 29.88/7.04 thf(bl_says_def, definition, bl_says = (^ [A:individuals,B:($i > $o)]: (cs4_box @ (cs4_impl @ (bl_princ @ (princ_inj @ A)) @ B))) ).
% 29.88/7.04 thf(bl_valid_def, definition, bl_valid = (mvalid) ).
% 29.88/7.04 thf(sk1_def, definition, sk1 = (@+ [A:individuals]: ~ (! [B:($i > $o),C:($i > $o),D:$i,E:$i]: ((reli @ D @ E) => (~ (! [F:$i]: ((reli @ E @ F) => (! [G:$i]: ((relr @ F @ G) => (! [H:$i]: ((reli @ G @ H) => (~ (! [I:$i]: ((reli @ H @ I) => (princ_inj @ A @ I))) | ! [I:$i]: ((reli @ H @ I) => (~ (B @ I) | (C @ I)))))))))) | ! [F:$i]: ((reli @ E @ F) => (~ (! [G:$i]: ((reli @ F @ G) => (! [H:$i]: ((relr @ G @ H) => (! [I:$i]: ((reli @ H @ I) => (~ (! [J:$i]: ((reli @ I @ J) => (princ_inj @ A @ J))) | (B @ I)))))))) | ! [G:$i]: ((reli @ F @ G) => (! [H:$i]: ((relr @ G @ H) => (! [I:$i]: ((reli @ H @ I) => (~ (! [J:$i]: ((reli @ I @ J) => (princ_inj @ A @ J))) | (C @ I))))))))))))) ).
% 29.88/7.04 thf(sk2_def, definition, sk2 = (@+ [A:($i > $o)]: ~ (! [B:($i > $o),C:$i,D:$i]: ((reli @ C @ D) => (~ (! [E:$i]: ((reli @ D @ E) => (! [F:$i]: ((relr @ E @ F) => (! [G:$i]: ((reli @ F @ G) => (~ (! [H:$i]: ((reli @ G @ H) => (princ_inj @ sk1 @ H))) | ! [H:$i]: ((reli @ G @ H) => (~ (A @ H) | (B @ H)))))))))) | ! [E:$i]: ((reli @ D @ E) => (~ (! [F:$i]: ((reli @ E @ F) => (! [G:$i]: ((relr @ F @ G) => (! [H:$i]: ((reli @ G @ H) => (~ (! [I:$i]: ((reli @ H @ I) => (princ_inj @ sk1 @ I))) | (A @ H)))))))) | ! [F:$i]: ((reli @ E @ F) => (! [G:$i]: ((relr @ F @ G) => (! [H:$i]: ((reli @ G @ H) => (~ (! [I:$i]: ((reli @ H @ I) => (princ_inj @ sk1 @ I))) | (B @ H))))))))))))) ).
% 29.88/7.04 thf(sk3_def, definition, sk3 = (@+ [A:($i > $o)]: ~ (! [B:$i,C:$i]: ((reli @ B @ C) => (~ (! [D:$i]: ((reli @ C @ D) => (! [E:$i]: ((relr @ D @ E) => (! [F:$i]: ((reli @ E @ F) => (~ (! [G:$i]: ((reli @ F @ G) => (princ_inj @ sk1 @ G))) | ! [G:$i]: ((reli @ F @ G) => (~ (sk2 @ G) | (A @ G)))))))))) | ! [D:$i]: ((reli @ C @ D) => (~ (! [E:$i]: ((reli @ D @ E) => (! [F:$i]: ((relr @ E @ F) => (! [G:$i]: ((reli @ F @ G) => (~ (! [H:$i]: ((reli @ G @ H) => (princ_inj @ sk1 @ H))) | (sk2 @ G)))))))) | ! [E:$i]: ((reli @ D @ E) => (! [F:$i]: ((relr @ E @ F) => (! [G:$i]: ((reli @ F @ G) => (~ (! [H:$i]: ((reli @ G @ H) => (princ_inj @ sk1 @ H))) | (A @ G))))))))))))) ).
% 29.88/7.04 thf(sk4_def, definition, sk4 = (@+ [A:$i]: ~ (! [B:$i]: ((reli @ A @ B) => (~ (! [C:$i]: ((reli @ B @ C) => (! [D:$i]: ((relr @ C @ D) => (! [E:$i]: ((reli @ D @ E) => (~ (! [F:$i]: ((reli @ E @ F) => (princ_inj @ sk1 @ F))) | ! [F:$i]: ((reli @ E @ F) => (~ (sk2 @ F) | (sk3 @ F)))))))))) | ! [C:$i]: ((reli @ B @ C) => (~ (! [D:$i]: ((reli @ C @ D) => (! [E:$i]: ((relr @ D @ E) => (! [F:$i]: ((reli @ E @ F) => (~ (! [G:$i]: ((reli @ F @ G) => (princ_inj @ sk1 @ G))) | (sk2 @ F)))))))) | ! [D:$i]: ((reli @ C @ D) => (! [E:$i]: ((relr @ D @ E) => (! [F:$i]: ((reli @ E @ F) => (~ (! [G:$i]: ((reli @ F @ G) => (princ_inj @ sk1 @ G))) | (sk3 @ F))))))))))))) ).
% 29.88/7.04 thf(sk5_def, definition, sk5 = (@+ [A:$i]: ~ ((reli @ sk4 @ A) => (~ (! [B:$i]: ((reli @ A @ B) => (! [C:$i]: ((relr @ B @ C) => (! [D:$i]: ((reli @ C @ D) => (~ (! [E:$i]: ((reli @ D @ E) => (princ_inj @ sk1 @ E))) | ! [E:$i]: ((reli @ D @ E) => (~ (sk2 @ E) | (sk3 @ E)))))))))) | ! [B:$i]: ((reli @ A @ B) => (~ (! [C:$i]: ((reli @ B @ C) => (! [D:$i]: ((relr @ C @ D) => (! [E:$i]: ((reli @ D @ E) => (~ (! [F:$i]: ((reli @ E @ F) => (princ_inj @ sk1 @ F))) | (sk2 @ E)))))))) | ! [C:$i]: ((reli @ B @ C) => (! [D:$i]: ((relr @ C @ D) => (! [E:$i]: ((reli @ D @ E) => (~ (! [F:$i]: ((reli @ E @ F) => (princ_inj @ sk1 @ F))) | (sk3 @ E)))))))))))) ).
% 29.88/7.04 thf(sk6_def, definition, sk6 = (^ [A:$i,B:$i,C:$i]: (@+ [D:$i]: ~ ((reli @ A @ D) => (princ_inj @ sk1 @ D)))) ).
% 29.88/7.04 thf(sk7_def, definition, sk7 = (@+ [A:$i]: ~ ((reli @ sk5 @ A) => (~ (! [B:$i]: ((reli @ A @ B) => (! [C:$i]: ((relr @ B @ C) => (! [D:$i]: ((reli @ C @ D) => (~ (! [E:$i]: ((reli @ D @ E) => (princ_inj @ sk1 @ E))) | (sk2 @ D)))))))) | ! [B:$i]: ((reli @ A @ B) => (! [C:$i]: ((relr @ B @ C) => (! [D:$i]: ((reli @ C @ D) => (~ (! [E:$i]: ((reli @ D @ E) => (princ_inj @ sk1 @ E))) | (sk3 @ D)))))))))) ).
% 29.88/7.04 thf(sk8_def, definition, sk8 = (^ [A:$i,B:$i,C:$i]: (@+ [D:$i]: ~ ((reli @ A @ D) => (princ_inj @ sk1 @ D)))) ).
% 29.88/7.04 thf(sk9_def, definition, sk9 = (@+ [A:$i]: ~ ((reli @ sk7 @ A) => (! [B:$i]: ((relr @ A @ B) => (! [C:$i]: ((reli @ B @ C) => (~ (! [D:$i]: ((reli @ C @ D) => (princ_inj @ sk1 @ D))) | (sk3 @ C)))))))) ).
% 29.88/7.04 thf(sk10_def, definition, sk10 = (@+ [A:$i]: ~ ((relr @ sk9 @ A) => (! [B:$i]: ((reli @ A @ B) => (~ (! [C:$i]: ((reli @ B @ C) => (princ_inj @ sk1 @ C))) | (sk3 @ B)))))) ).
% 29.88/7.04 thf(sk11_def, definition, sk11 = (@+ [A:$i]: ~ ((reli @ sk10 @ A) => (~ (! [B:$i]: ((reli @ A @ B) => (princ_inj @ sk1 @ B))) | (sk3 @ A)))) ).
% 29.88/7.04 thf(sk12_def, definition, sk12 = (^ [A:$i,B:($i > $o)]: (@+ [C:$i]: ~ ((reli @ A @ C) => (B @ C)))) ).
% 29.88/7.04 thf(1,conjecture,((! [A:individuals,B:($i > $o),C:($i > $o)]: (bl_valid @ (bl_impl @ (bl_says @ A @ (bl_impl @ B @ C)) @ (bl_impl @ (bl_says @ A @ B) @ (bl_says @ A @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',bl_k)).
% 29.88/7.04 thf(2,negated_conjecture,((~ (! [A:individuals,B:($i > $o),C:($i > $o)]: (bl_valid @ (bl_impl @ (bl_says @ A @ (bl_impl @ B @ C)) @ (bl_impl @ (bl_says @ A @ B) @ (bl_says @ A @ C))))))),inference(neg_conjecture,[status(cth)],[1])).
% 29.88/7.04 thf(9,plain,((~ (! [A:individuals,B:($i > $o),C:($i > $o),D:$i,E:$i]: ((reli @ D @ E) => (~ (! [F:$i]: ((reli @ E @ F) => (! [G:$i]: ((relr @ F @ G) => (! [H:$i]: ((reli @ G @ H) => (~ (! [I:$i]: ((reli @ H @ I) => (princ_inj @ A @ I))) | ! [I:$i]: ((reli @ H @ I) => (~ (B @ I) | (C @ I)))))))))) | ! [F:$i]: ((reli @ E @ F) => (~ (! [G:$i]: ((reli @ F @ G) => (! [H:$i]: ((relr @ G @ H) => (! [I:$i]: ((reli @ H @ I) => (~ (! [J:$i]: ((reli @ I @ J) => (princ_inj @ A @ J))) | (B @ I)))))))) | ! [G:$i]: ((reli @ F @ G) => (! [H:$i]: ((relr @ G @ H) => (! [I:$i]: ((reli @ H @ I) => (~ (! [J:$i]: ((reli @ I @ J) => (princ_inj @ A @ J))) | (C @ I)))))))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])).
% 29.88/7.04 thf(10,plain,(! [H:$i,G:$i,F:$i,E:$i,D:$i,C:$i,B:$i,A:$i] : (((reli @ sk4 @ sk5) & (~ (reli @ sk5 @ A) | ~ (relr @ A @ B) | ~ (reli @ B @ C) | (reli @ C @ (sk6 @ C @ B @ A)) | ~ (reli @ C @ D) | ~ (sk2 @ D) | (sk3 @ D)) & (~ (reli @ sk5 @ A) | ~ (relr @ A @ B) | ~ (reli @ B @ C) | ~ (princ_inj @ sk1 @ (sk6 @ C @ B @ A)) | ~ (reli @ C @ D) | ~ (sk2 @ D) | (sk3 @ D)) & (reli @ sk5 @ sk7) & (~ (reli @ sk7 @ E) | ~ (relr @ E @ F) | ~ (reli @ F @ G) | (reli @ G @ (sk8 @ G @ F @ E)) | (sk2 @ G)) & (~ (reli @ sk7 @ E) | ~ (relr @ E @ F) | ~ (reli @ F @ G) | ~ (princ_inj @ sk1 @ (sk8 @ G @ F @ E)) | (sk2 @ G)) & (reli @ sk7 @ sk9) & (relr @ sk9 @ sk10) & (reli @ sk10 @ sk11) & (~ (reli @ sk11 @ H) | (princ_inj @ sk1 @ H)) & ~ (sk3 @ sk11)))),inference(cnf,[status(esa)],[9])).
% 29.88/7.04 thf(14,plain,((relr @ sk9 @ sk10)),inference(cnfConj,[status(thm)],[10])).
% 29.88/7.04 thf(12,plain,((reli @ sk4 @ sk5)),inference(cnfConj,[status(thm)],[10])).
% 29.88/7.04 thf(11,plain,(! [A:$i] : ((~ (reli @ sk11 @ A)) | (princ_inj @ sk1 @ A))),inference(cnfConj,[status(thm)],[10])).
% 29.88/7.04 thf(23,plain,(! [A:$i] : ((~ (reli @ sk11 @ A)) | (princ_inj @ sk1 @ A))),inference(simp,[status(thm)],[11])).
% 29.88/7.04 thf(151,plain,(! [A:$i] : (~ (($true)) | (princ_inj @ sk1 @ A) | ((reli @ sk11 @ A) != (reli @ sk4 @ sk5)))),inference(paramod_ordered,[status(thm)],[12,23])).
% 29.88/7.04 thf(152,plain,(! [A:$i] : ((princ_inj @ sk1 @ A) | ((reli @ sk11 @ A) != (reli @ sk4 @ sk5)))),inference(simp,[status(thm)],[151])).
% 29.88/7.04 thf(161,plain,(! [A:$i] : ((princ_inj @ sk1 @ A) | (sk11 != sk4) | (A != sk5))),inference(simp,[status(thm)],[152])).
% 29.88/7.04 thf(166,plain,((princ_inj @ sk1 @ sk5) | (sk11 != sk4)),inference(simp,[status(thm)],[161])).
% 29.88/7.04 thf(15,plain,(! [D:$i,C:$i,B:$i,A:$i] : ((~ (reli @ sk5 @ A)) | (~ (relr @ A @ B)) | (~ (reli @ B @ C)) | (~ (princ_inj @ sk1 @ (sk6 @ C @ B @ A))) | (~ (reli @ C @ D)) | (~ (sk2 @ D)) | (sk3 @ D))),inference(cnfConj,[status(thm)],[10])).
% 29.88/7.04 thf(69,plain,(! [D:$i,C:$i,B:$i,A:$i] : (~ (($true)) | (~ (relr @ A @ B)) | (~ (reli @ B @ C)) | (~ (princ_inj @ sk1 @ (sk6 @ C @ B @ A))) | (~ (reli @ C @ D)) | (~ (sk2 @ D)) | (sk3 @ D) | ((reli @ sk5 @ A) != (reli @ sk4 @ sk5)))),inference(paramod_ordered,[status(thm)],[12,15])).
% 29.88/7.04 thf(70,plain,(! [D:$i,C:$i,B:$i,A:$i] : ((~ (relr @ A @ B)) | (~ (reli @ B @ C)) | (~ (princ_inj @ sk1 @ (sk6 @ C @ B @ A))) | (~ (reli @ C @ D)) | (~ (sk2 @ D)) | (sk3 @ D) | ((reli @ sk5 @ A) != (reli @ sk4 @ sk5)))),inference(simp,[status(thm)],[69])).
% 29.88/7.04 thf(80,plain,(! [D:$i,C:$i,B:$i,A:$i] : ((sk3 @ D) | (~ (relr @ A @ B)) | (~ (reli @ B @ C)) | (~ (princ_inj @ sk1 @ (sk6 @ C @ B @ A))) | (~ (reli @ C @ D)) | (~ (sk2 @ D)) | (sk5 != sk4) | (A != sk5))),inference(simp,[status(thm)],[70])).
% 29.88/7.04 thf(83,plain,(! [C:$i,B:$i,A:$i] : ((sk3 @ C) | (~ (relr @ sk5 @ A)) | (~ (reli @ A @ B)) | (~ (princ_inj @ sk1 @ (sk6 @ B @ A @ sk5))) | (~ (reli @ B @ C)) | (~ (sk2 @ C)) | (sk5 != sk4))),inference(simp,[status(thm)],[80])).
% 29.88/7.04 thf(266,plain,(! [C:$i,B:$i,A:$i] : ((sk11 != sk4) | (sk3 @ C) | (~ (relr @ sk5 @ A)) | (~ (reli @ A @ B)) | ~ (($true)) | (~ (reli @ B @ C)) | (~ (sk2 @ C)) | (sk5 != sk4) | ((princ_inj @ sk1 @ (sk6 @ B @ A @ sk5)) != (princ_inj @ sk1 @ sk5)))),inference(paramod_ordered,[status(thm)],[166,83])).
% 29.88/7.04 thf(267,plain,(! [C:$i,B:$i,A:$i] : ((sk11 != sk4) | (sk3 @ C) | (~ (relr @ sk5 @ A)) | (~ (reli @ A @ B)) | (~ (reli @ B @ C)) | (~ (sk2 @ C)) | (sk5 != sk4) | ((princ_inj @ sk1 @ (sk6 @ B @ A @ sk5)) != (princ_inj @ sk1 @ sk5)))),inference(simp,[status(thm)],[266])).
% 29.88/7.04 thf(269,plain,(! [C:$i,B:$i,A:$i] : ((sk3 @ C) | (sk11 != sk4) | (~ (relr @ sk5 @ A)) | (~ (reli @ A @ B)) | (~ (reli @ B @ C)) | (~ (sk2 @ C)) | (sk5 != sk4) | (sk1 != sk1) | ((sk6 @ B @ A @ sk5) != sk5))),inference(simp,[status(thm)],[267])).
% 29.88/7.04 thf(271,plain,(! [C:$i,B:$i,A:$i] : ((sk3 @ C) | (sk11 != sk4) | (~ (relr @ sk5 @ A)) | (~ (reli @ A @ B)) | (~ (reli @ B @ C)) | (~ (sk2 @ C)) | (sk5 != sk4) | ((sk6 @ B @ A @ sk5) != sk5))),inference(simp,[status(thm)],[269])).
% 29.88/7.04 thf(296,plain,(! [C:$i,B:$i,A:$i] : ((sk3 @ C) | (sk11 != sk4) | ~ (($true)) | (~ (reli @ A @ B)) | (~ (reli @ B @ C)) | (~ (sk2 @ C)) | (sk5 != sk4) | ((sk6 @ B @ A @ sk5) != sk5) | ((relr @ sk9 @ sk10) != (relr @ sk5 @ A)))),inference(paramod_ordered,[status(thm)],[14,271])).
% 29.88/7.04 thf(297,plain,(! [C:$i,B:$i,A:$i] : ((sk3 @ C) | (sk11 != sk4) | (~ (reli @ A @ B)) | (~ (reli @ B @ C)) | (~ (sk2 @ C)) | (sk5 != sk4) | ((sk6 @ B @ A @ sk5) != sk5) | ((relr @ sk9 @ sk10) != (relr @ sk5 @ A)))),inference(simp,[status(thm)],[296])).
% 29.88/7.04 thf(329,plain,(! [C:$i,B:$i,A:$i] : ((sk3 @ C) | (sk11 != sk4) | (~ (reli @ A @ B)) | (~ (reli @ B @ C)) | (~ (sk2 @ C)) | (sk5 != sk4) | ((sk6 @ B @ A @ sk5) != sk5) | (sk9 != sk5) | (sk10 != A))),inference(simp,[status(thm)],[297])).
% 29.88/7.04 thf(333,plain,(! [B:$i,A:$i] : ((sk3 @ B) | (sk11 != sk4) | (~ (reli @ sk10 @ A)) | (~ (reli @ A @ B)) | (~ (sk2 @ B)) | (sk5 != sk4) | ((sk6 @ A @ sk10 @ sk5) != sk5) | (sk9 != sk5))),inference(simp,[status(thm)],[329])).
% 29.88/7.04 thf(8,axiom,((cs4_valid @ (cs4_all @ (^ [A:individuals]: (cs4_impl @ (princ_inj @ A) @ (princ_inj @ loca)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',loca_strength)).
% 29.88/7.04 thf(56,plain,((! [A:$i,B:$i]: ((reli @ A @ B) => (! [C:individuals,D:$i]: ((reli @ B @ D) => (~ (princ_inj @ C @ D) | (princ_inj @ loca @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8])).
% 29.88/7.04 thf(20,plain,((reli @ sk10 @ sk11)),inference(cnfConj,[status(thm)],[10])).
% 29.88/7.04 thf(3,axiom,((! [A:($i > $o)]: (mvalid @ (mimpl @ (mbox @ reli @ A) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',refl_axiom_i)).
% 29.88/7.04 thf(25,plain,((! [A:($i > $o),B:$i]: (~ (! [C:$i]: ((reli @ B @ C) => (A @ C))) | (A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3])).
% 29.88/7.04 thf(26,plain,(! [B:$i,A:($i > $o)] : ((((reli @ B @ (sk12 @ B @ (A))) | (A @ B)) & (~ (A @ (sk12 @ B @ (A))) | (A @ B))))),inference(cnf,[status(esa)],[25])).
% 29.88/7.04 thf(27,plain,(! [B:$i,A:($i > $o)] : ((reli @ B @ (sk12 @ B @ (A))) | (A @ B))),inference(cnfConj,[status(thm)],[26])).
% 29.88/7.04 thf(16,plain,((~ (sk3 @ sk11))),inference(cnfConj,[status(thm)],[10])).
% 29.88/7.04 thf(403,plain,(! [B:$i,A:($i > $o)] : ((reli @ B @ (sk12 @ B @ (A))) | ~ (($true)) | ((A @ B) != (sk3 @ sk11)))),inference(paramod_ordered,[status(thm)],[27,16])).
% 29.88/7.04 thf(404,plain,(! [B:$i,A:($i > $o)] : ((reli @ B @ (sk12 @ B @ (A))) | ((A @ B) != (sk3 @ sk11)))),inference(simp,[status(thm)],[403])).
% 29.88/7.04 thf(492,plain,((reli @ sk11 @ (sk12 @ sk11 @ (sk3)))),inference(pre_uni,[status(thm)],[404:[bind(A, $thf(sk3)),bind(B, $thf(sk11))]])).
% 29.88/7.04 thf(471,plain,(! [A:$i] : ((reli @ A @ (sk12 @ A @ (^ [B:$i]: (($false))))) | ($false))),inference(prim_subst,[status(thm)],[27:[bind(A, $thf(^ [C:$i]: (($false))))]])).
% 29.88/7.04 thf(534,plain,(! [A:$i] : ((reli @ A @ (sk12 @ A @ (^ [B:$i]: (($false))))))),inference(simp,[status(thm)],[471])).
% 29.88/7.04 thf(588,plain,(! [A:$i] : (~ (($true)) | (princ_inj @ sk1 @ A) | ((reli @ sk11 @ (sk12 @ sk11 @ (sk3))) != (reli @ sk11 @ A)))),inference(paramod_ordered,[status(thm)],[492,23])).
% 29.88/7.04 thf(589,plain,(! [A:$i] : ((princ_inj @ sk1 @ A) | ((reli @ sk11 @ (sk12 @ sk11 @ (sk3))) != (reli @ sk11 @ A)))),inference(simp,[status(thm)],[588])).
% 29.88/7.04 thf(590,plain,((princ_inj @ sk1 @ (sk12 @ sk11 @ (sk3)))),inference(pattern_uni,[status(thm)],[589:[bind(A, $thf(sk12 @ sk11 @ (sk3)))]])).
% 29.88/7.04 thf(405,plain,(! [C:$i,B:$i,A:($i > $o)] : ((A @ B) | ~ (($true)) | (princ_inj @ sk1 @ C) | ((reli @ B @ (sk12 @ B @ (A))) != (reli @ sk11 @ C)))),inference(paramod_ordered,[status(thm)],[27,23])).
% 29.88/7.04 thf(406,plain,(! [C:$i,B:$i,A:($i > $o)] : ((A @ B) | (princ_inj @ sk1 @ C) | ((reli @ B @ (sk12 @ B @ (A))) != (reli @ sk11 @ C)))),inference(simp,[status(thm)],[405])).
% 29.88/7.05 thf(407,plain,(! [A:($i > $o)] : ((A @ sk11) | (princ_inj @ sk1 @ (sk12 @ sk11 @ (A))))),inference(pattern_uni,[status(thm)],[406:[bind(A, $thf(E)),bind(B, $thf(sk11)),bind(C, $thf(sk12 @ sk11 @ (E)))]])).
% 29.88/7.05 thf(522,plain,(! [A:($i > $o)] : ((A @ sk11) | (princ_inj @ sk1 @ (sk12 @ sk11 @ (A))))),inference(simp,[status(thm)],[407])).
% 29.88/7.05 thf(882,plain,(! [A:($i > $o)] : ((~ (A @ sk11)) | (princ_inj @ sk1 @ (sk12 @ sk11 @ (^ [B:$i]: ~ (A @ B)))))),inference(prim_subst,[status(thm)],[522:[bind(A, $thf(^ [C:$i]: ~ (B @ C)))]])).
% 29.88/7.05 thf(958,plain,(! [A:($i > $o)] : ((~ (A @ sk11)) | (princ_inj @ sk1 @ (sk12 @ sk11 @ (^ [B:$i]: ~ (A @ B)))))),inference(cnf,[status(esa)],[882])).
% 29.88/7.05 thf(959,plain,(! [A:($i > $o)] : ((~ (A @ sk11)) | (princ_inj @ sk1 @ (sk12 @ sk11 @ (^ [B:$i]: ~ (A @ B)))))),inference(simp,[status(thm)],[958])).
% 29.88/7.05 thf(1229,plain,(! [A:($i > $o)] : (~ (($true)) | (princ_inj @ sk1 @ (sk12 @ sk11 @ (^ [B:$i]: ~ (A @ B)))) | ((reli @ sk10 @ sk11) != (A @ sk11)))),inference(paramod_ordered,[status(thm)],[20,959])).
% 29.88/7.05 thf(1230,plain,(! [A:($i > $o)] : ((princ_inj @ sk1 @ (sk12 @ sk11 @ (^ [B:$i]: ~ (A @ B)))) | ((reli @ sk10 @ sk11) != (A @ sk11)))),inference(simp,[status(thm)],[1229])).
% 29.88/7.05 thf(1325,plain,((princ_inj @ sk1 @ (sk12 @ sk11 @ (^ [A:$i]: ~ (reli @ sk10 @ A))))),inference(pre_uni,[status(thm)],[1230:[bind(A, $thf(reli @ sk10))]])).
% 29.88/7.05 thf(18,plain,((reli @ sk5 @ sk7)),inference(cnfConj,[status(thm)],[10])).
% 29.88/7.05 thf(886,plain,((prop_a @ sk11) | (princ_inj @ sk1 @ (sk12 @ sk11 @ (prop_a)))),inference(prim_subst,[status(thm)],[522:[bind(A, $thf(prop_a))]])).
% 29.88/7.05 thf(19,plain,(! [C:$i,B:$i,A:$i] : ((~ (reli @ sk7 @ A)) | (~ (relr @ A @ B)) | (~ (reli @ B @ C)) | (reli @ C @ (sk8 @ C @ B @ A)) | (sk2 @ C))),inference(cnfConj,[status(thm)],[10])).
% 29.88/7.05 thf(24,plain,(! [C:$i,B:$i,A:$i] : ((~ (reli @ sk7 @ A)) | (~ (relr @ A @ B)) | (~ (reli @ B @ C)) | (reli @ C @ (sk8 @ C @ B @ A)) | (sk2 @ C))),inference(simp,[status(thm)],[19])).
% 29.88/7.05 thf(885,plain,((prop_c @ sk11) | (princ_inj @ sk1 @ (sk12 @ sk11 @ (prop_c)))),inference(prim_subst,[status(thm)],[522:[bind(A, $thf(prop_c))]])).
% 29.88/7.05 thf(5,axiom,((! [A:($i > $o)]: (mvalid @ (mimpl @ (mbox @ reli @ A) @ (mbox @ reli @ (mbox @ reli @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',trans_axiom_i)).
% 29.88/7.05 thf(37,plain,((! [A:($i > $o),B:$i]: (~ (! [C:$i]: ((reli @ B @ C) => (A @ C))) | ! [C:$i]: ((reli @ B @ C) => (! [D:$i]: ((reli @ C @ D) => (A @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5])).
% 29.88/7.05 thf(879,plain,((prop_b @ sk11) | (princ_inj @ sk1 @ (sk12 @ sk11 @ (prop_b)))),inference(prim_subst,[status(thm)],[522:[bind(A, $thf(prop_b))]])).
% 29.88/7.05 thf(153,plain,(! [A:$i] : (~ (($true)) | (princ_inj @ sk1 @ A) | ((reli @ sk11 @ A) != (reli @ sk5 @ sk7)))),inference(paramod_ordered,[status(thm)],[18,23])).
% 29.88/7.05 thf(154,plain,(! [A:$i] : ((princ_inj @ sk1 @ A) | ((reli @ sk11 @ A) != (reli @ sk5 @ sk7)))),inference(simp,[status(thm)],[153])).
% 29.88/7.05 thf(164,plain,(! [A:$i] : ((princ_inj @ sk1 @ A) | (sk11 != sk5) | (A != sk7))),inference(simp,[status(thm)],[154])).
% 29.88/7.05 thf(169,plain,((princ_inj @ sk1 @ sk7) | (sk11 != sk5)),inference(simp,[status(thm)],[164])).
% 29.88/7.05 thf(13,plain,((reli @ sk7 @ sk9)),inference(cnfConj,[status(thm)],[10])).
% 29.88/7.05 thf(355,plain,(! [B:$i,A:$i] : ((sk3 @ B) | (sk11 != sk4) | ~ (($true)) | (~ (reli @ A @ B)) | (~ (sk2 @ B)) | (sk5 != sk4) | ((sk6 @ A @ sk10 @ sk5) != sk5) | (sk9 != sk5) | ((reli @ sk10 @ A) != (reli @ sk5 @ sk7)))),inference(paramod_ordered,[status(thm)],[18,333])).
% 29.88/7.05 thf(356,plain,(! [B:$i,A:$i] : ((sk3 @ B) | (sk11 != sk4) | (~ (reli @ A @ B)) | (~ (sk2 @ B)) | (sk5 != sk4) | ((sk6 @ A @ sk10 @ sk5) != sk5) | (sk9 != sk5) | ((reli @ sk10 @ A) != (reli @ sk5 @ sk7)))),inference(simp,[status(thm)],[355])).
% 29.88/7.05 thf(368,plain,(! [B:$i,A:$i] : ((sk3 @ B) | (sk11 != sk4) | (~ (reli @ A @ B)) | (~ (sk2 @ B)) | (sk5 != sk4) | ((sk6 @ A @ sk10 @ sk5) != sk5) | (sk9 != sk5) | (sk10 != sk5) | (A != sk7))),inference(simp,[status(thm)],[356])).
% 29.88/7.05 thf(371,plain,(! [A:$i] : ((sk3 @ A) | (sk11 != sk4) | (~ (reli @ sk7 @ A)) | (~ (sk2 @ A)) | (sk5 != sk4) | ((sk6 @ sk7 @ sk10 @ sk5) != sk5) | (sk9 != sk5) | (sk10 != sk5))),inference(simp,[status(thm)],[368])).
% 29.88/7.05 thf(17,plain,(! [D:$i,C:$i,B:$i,A:$i] : ((~ (reli @ sk5 @ A)) | (~ (relr @ A @ B)) | (~ (reli @ B @ C)) | (reli @ C @ (sk6 @ C @ B @ A)) | (~ (reli @ C @ D)) | (~ (sk2 @ D)) | (sk3 @ D))),inference(cnfConj,[status(thm)],[10])).
% 29.88/7.05 thf(980,plain,(! [A:$i] : ((sk3 @ A) | (sk11 != sk4) | ~ (($true)) | (~ (sk2 @ A)) | (sk5 != sk4) | ((sk6 @ sk7 @ sk10 @ sk5) != sk5) | (sk9 != sk5) | (sk10 != sk5) | ((reli @ sk7 @ A) != (reli @ sk4 @ sk5)))),inference(paramod_ordered,[status(thm)],[12,371])).
% 29.88/7.05 thf(981,plain,(! [A:$i] : ((sk3 @ A) | (sk11 != sk4) | (~ (sk2 @ A)) | (sk5 != sk4) | ((sk6 @ sk7 @ sk10 @ sk5) != sk5) | (sk9 != sk5) | (sk10 != sk5) | ((reli @ sk7 @ A) != (reli @ sk4 @ sk5)))),inference(simp,[status(thm)],[980])).
% 29.88/7.05 thf(997,plain,(! [A:$i] : ((sk3 @ A) | (sk11 != sk4) | (~ (sk2 @ A)) | (sk5 != sk4) | ((sk6 @ sk7 @ sk10 @ sk5) != sk5) | (sk9 != sk5) | (sk10 != sk5) | (sk7 != sk4) | (A != sk5))),inference(simp,[status(thm)],[981])).
% 29.88/7.05 thf(1007,plain,((sk3 @ sk5) | (sk11 != sk4) | (~ (sk2 @ sk5)) | (sk5 != sk4) | ((sk6 @ sk7 @ sk10 @ sk5) != sk5) | (sk9 != sk5) | (sk10 != sk5) | (sk7 != sk4)),inference(simp,[status(thm)],[997])).
% 29.88/7.05 thf(21,plain,(! [C:$i,B:$i,A:$i] : ((~ (reli @ sk7 @ A)) | (~ (relr @ A @ B)) | (~ (reli @ B @ C)) | (~ (princ_inj @ sk1 @ (sk8 @ C @ B @ A))) | (sk2 @ C))),inference(cnfConj,[status(thm)],[10])).
% 29.88/7.05 thf(22,plain,(! [C:$i,B:$i,A:$i] : ((~ (reli @ sk7 @ A)) | (~ (relr @ A @ B)) | (~ (reli @ B @ C)) | (~ (princ_inj @ sk1 @ (sk8 @ C @ B @ A))) | (sk2 @ C))),inference(simp,[status(thm)],[21])).
% 29.88/7.05 thf(7,axiom,((! [A:($i > $o)]: (mvalid @ (mimpl @ (mbox @ reli @ (mbox @ relr @ A)) @ (mbox @ relr @ (mbox @ reli @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_i_r_commute)).
% 29.88/7.05 thf(49,plain,((! [A:($i > $o),B:$i]: (~ (! [C:$i]: ((reli @ B @ C) => (! [D:$i]: ((relr @ C @ D) => (A @ D))))) | ! [C:$i]: ((relr @ B @ C) => (! [D:$i]: ((reli @ C @ D) => (A @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7])).
% 29.88/7.05 thf(982,plain,(! [A:$i] : ((sk3 @ A) | (sk11 != sk4) | ~ (($true)) | (~ (sk2 @ A)) | (sk5 != sk4) | ((sk6 @ sk7 @ sk10 @ sk5) != sk5) | (sk9 != sk5) | (sk10 != sk5) | ((reli @ sk7 @ A) != (reli @ sk5 @ sk7)))),inference(paramod_ordered,[status(thm)],[18,371])).
% 29.88/7.05 thf(983,plain,(! [A:$i] : ((sk3 @ A) | (sk11 != sk4) | (~ (sk2 @ A)) | (sk5 != sk4) | ((sk6 @ sk7 @ sk10 @ sk5) != sk5) | (sk9 != sk5) | (sk10 != sk5) | ((reli @ sk7 @ A) != (reli @ sk5 @ sk7)))),inference(simp,[status(thm)],[982])).
% 29.88/7.05 thf(1005,plain,(! [A:$i] : ((sk3 @ A) | (sk11 != sk4) | (~ (sk2 @ A)) | (sk5 != sk4) | ((sk6 @ sk7 @ sk10 @ sk5) != sk5) | (sk9 != sk5) | (sk10 != sk5) | (sk7 != sk5) | (A != sk7))),inference(simp,[status(thm)],[983])).
% 29.88/7.05 thf(1015,plain,((sk3 @ sk7) | (sk11 != sk4) | (~ (sk2 @ sk7)) | (sk5 != sk4) | ((sk6 @ sk7 @ sk10 @ sk5) != sk5) | (sk9 != sk5) | (sk10 != sk5) | (sk7 != sk5)),inference(simp,[status(thm)],[1005])).
% 29.88/7.05 thf(147,plain,(! [A:$i] : (~ (($true)) | (princ_inj @ sk1 @ A) | ((reli @ sk11 @ A) != (reli @ sk10 @ sk11)))),inference(paramod_ordered,[status(thm)],[20,23])).
% 29.88/7.05 thf(148,plain,(! [A:$i] : ((princ_inj @ sk1 @ A) | ((reli @ sk11 @ A) != (reli @ sk10 @ sk11)))),inference(simp,[status(thm)],[147])).
% 29.88/7.05 thf(162,plain,(! [A:$i] : ((princ_inj @ sk1 @ A) | (sk11 != sk10) | (A != sk11))),inference(simp,[status(thm)],[148])).
% 29.88/7.05 thf(167,plain,((princ_inj @ sk1 @ sk11) | (sk11 != sk10)),inference(simp,[status(thm)],[162])).
% 29.88/7.05 thf(4,axiom,((! [A:($i > $o)]: (mvalid @ (mimpl @ (mbox @ relr @ A) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',refl_axiom_r)).
% 29.88/7.05 thf(31,plain,((! [A:($i > $o),B:$i]: (~ (! [C:$i]: ((relr @ B @ C) => (A @ C))) | (A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4])).
% 29.88/7.05 thf(742,plain,(! [B:$i,A:$i] : (~ (($true)) | (princ_inj @ sk1 @ B) | ((reli @ A @ (sk12 @ A @ (^ [C:$i]: (($false))))) != (reli @ sk11 @ B)))),inference(paramod_ordered,[status(thm)],[534,23])).
% 29.88/7.05 thf(743,plain,(! [B:$i,A:$i] : ((princ_inj @ sk1 @ B) | ((reli @ A @ (sk12 @ A @ (^ [C:$i]: (($false))))) != (reli @ sk11 @ B)))),inference(simp,[status(thm)],[742])).
% 29.88/7.05 thf(744,plain,((princ_inj @ sk1 @ (sk12 @ sk11 @ (^ [A:$i]: (($false)))))),inference(pattern_uni,[status(thm)],[743:[bind(A, $thf(sk11)),bind(B, $thf(sk12 @ sk11 @ (^ [C:$i]: (($false)))))]])).
% 29.88/7.05 thf(1284,plain,((~ (prop_c @ sk11)) | (princ_inj @ sk1 @ (sk12 @ sk11 @ (^ [A:$i]: ~ (prop_c @ A))))),inference(prim_subst,[status(thm)],[959:[bind(A, $thf(prop_c))]])).
% 29.88/7.05 thf(6,axiom,((! [A:($i > $o)]: (mvalid @ (mimpl @ (mbox @ relr @ A) @ (mbox @ relr @ (mbox @ relr @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',trans_axiom_r)).
% 29.88/7.05 thf(43,plain,((! [A:($i > $o),B:$i]: (~ (! [C:$i]: ((relr @ B @ C) => (A @ C))) | ! [C:$i]: ((relr @ B @ C) => (! [D:$i]: ((relr @ C @ D) => (A @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6])).
% 29.88/7.05 thf(149,plain,(! [A:$i] : (~ (($true)) | (princ_inj @ sk1 @ A) | ((reli @ sk11 @ A) != (reli @ sk7 @ sk9)))),inference(paramod_ordered,[status(thm)],[13,23])).
% 29.88/7.05 thf(150,plain,(! [A:$i] : ((princ_inj @ sk1 @ A) | ((reli @ sk11 @ A) != (reli @ sk7 @ sk9)))),inference(simp,[status(thm)],[149])).
% 29.88/7.05 thf(163,plain,(! [A:$i] : ((princ_inj @ sk1 @ A) | (sk11 != sk7) | (A != sk9))),inference(simp,[status(thm)],[150])).
% 29.88/7.05 thf(168,plain,((princ_inj @ sk1 @ sk9) | (sk11 != sk7)),inference(simp,[status(thm)],[163])).
% 29.88/7.05 thf(969,plain,(! [A:$i] : ((sk3 @ A) | (sk11 != sk4) | ~ (($true)) | (~ (sk2 @ A)) | (sk5 != sk4) | ((sk6 @ sk7 @ sk10 @ sk5) != sk5) | (sk9 != sk5) | (sk10 != sk5) | ((reli @ sk10 @ sk11) != (reli @ sk7 @ A)))),inference(paramod_ordered,[status(thm)],[20,371])).
% 29.88/7.05 thf(970,plain,(! [A:$i] : ((sk3 @ A) | (sk11 != sk4) | (~ (sk2 @ A)) | (sk5 != sk4) | ((sk6 @ sk7 @ sk10 @ sk5) != sk5) | (sk9 != sk5) | (sk10 != sk5) | ((reli @ sk10 @ sk11) != (reli @ sk7 @ A)))),inference(simp,[status(thm)],[969])).
% 29.88/7.05 thf(998,plain,(! [A:$i] : ((sk3 @ A) | (sk11 != sk4) | (~ (sk2 @ A)) | (sk5 != sk4) | ((sk6 @ sk7 @ sk10 @ sk5) != sk5) | (sk9 != sk5) | (sk10 != sk5) | (sk10 != sk7) | (sk11 != A))),inference(simp,[status(thm)],[970])).
% 29.88/7.05 thf(1008,plain,((sk3 @ sk11) | (sk11 != sk4) | (~ (sk2 @ sk11)) | (sk5 != sk4) | ((sk6 @ sk7 @ sk10 @ sk5) != sk5) | (sk9 != sk5) | (sk10 != sk5) | (sk10 != sk7)),inference(simp,[status(thm)],[998])).
% 29.88/7.05 thf(1379,plain,(($false) | (sk11 != sk4) | (~ (sk2 @ sk11)) | (sk5 != sk4) | ((sk6 @ sk7 @ sk10 @ sk5) != sk5) | (sk9 != sk5) | (sk10 != sk5) | (sk10 != sk7)),inference(rewrite,[status(thm)],[1008,16])).
% 29.88/7.05 thf(1380,plain,((sk11 != sk4) | (~ (sk2 @ sk11)) | (sk5 != sk4) | ((sk6 @ sk7 @ sk10 @ sk5) != sk5) | (sk9 != sk5) | (sk10 != sk5) | (sk10 != sk7)),inference(simp,[status(thm)],[1379])).
% 29.88/7.05 thf(1231,plain,(! [A:($i > $o)] : (~ (($true)) | (princ_inj @ sk1 @ (sk12 @ sk11 @ (^ [B:$i]: ~ (A @ B)))) | ((reli @ sk11 @ (sk12 @ sk11 @ (sk3))) != (A @ sk11)))),inference(paramod_ordered,[status(thm)],[492,959])).
% 29.88/7.05 thf(1232,plain,(! [A:($i > $o)] : ((princ_inj @ sk1 @ (sk12 @ sk11 @ (^ [B:$i]: ~ (A @ B)))) | ((reli @ sk11 @ (sk12 @ sk11 @ (sk3))) != (A @ sk11)))),inference(simp,[status(thm)],[1231])).
% 29.88/7.05 thf(1299,plain,((princ_inj @ sk1 @ (sk12 @ sk11 @ (^ [A:$i]: ~ (reli @ A @ (sk12 @ A @ sk3)))))),inference(pre_uni,[status(thm)],[1232:[bind(A, $thf(^ [B:$i]: (reli @ B @ (sk12 @ B @ sk3))))]])).
% 29.88/7.05 thf(3740,plain,(($false)),inference(e,[status(thm)],[333,56,14,20,492,534,590,271,1325,18,23,886,83,24,885,37,25,879,522,9,169,13,371,166,17,1007,22,27,12,49,959,1015,167,16,31,744,1284,43,168,1380,15,1299])).
% 29.88/7.05 % SZS output end Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 29.88/7.05 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------