0.00/0.04	% Problem  : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.00/0.11	% Command  : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 180 -p  --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
0.23/0.51	% Computer : n022.cluster.edu
0.23/0.51	% Model    : x86_64 x86_64
0.23/0.51	% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.23/0.51	% Memory   : 8046.5625MB
0.23/0.51	% OS       : Linux 6.8.0-71-generic
0.23/0.51	% CPULimit : 1440
0.23/0.51	% WCLimit  : 180
0.23/0.51	% DateTime : Mon Jul 27 10:16:13 UTC 2026
0.23/0.51	% CPUTime  : 
0.23/0.51	Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 180 -p  --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
1.10/1.04	% [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
2.50/1.41	% [INFO] 	 Parsing done (372ms). 
2.50/1.42	% [INFO] 	 Running in sequential loop mode. 
3.76/1.73	% [INFO] 	 eprover registered as external prover. 
3.76/1.74	% [INFO] 	 Scanning for conjecture ... 
4.12/1.88	% [INFO] 	 Found a conjecture (or negated_conjecture) and 269 axioms. Running axiom selection ... 
4.42/2.02	% [INFO] 	 Axiom selection finished. Selected 264 axioms (removed 5 axioms). 
6.01/2.32	% [INFO] 	 Problem is higher-order (TPTP THF). 
6.01/2.35	% [INFO] 	 Type checking passed. 
6.01/2.36	% [CONFIG] 	 Using configuration: timeout(180) 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 ... 
74.59/24.45	% External prover 'e' found a proof!
74.59/24.45	% [INFO] 	 Killing All external provers ... 
74.59/24.45	% Time passed: 23823ms (effective reasoning time: 23025ms)
74.59/24.45	% 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)>
74.59/24.46	% Axioms used in derivation (264): fact_45_order_Onot__eq__order__implies__strict, fact_48_dual__order_Ostrict__iff__order, fact_186_order__less__le__subst2, fact_55_nres__order__simps_I5_J, fact_169_leD, fact_177_order__le__less__subst1, fact_140_dual__order_Oasym, fact_253_GreatestI2__order, fact_191_le__neq__trans, fact_167_less__nres_Oelims_I1_J, fact_104_prod__cases, fact_54_less__eq__nres_Osimps_I2_J, fact_148_less__imp__triv, fact_184_order__less__le__subst1, fact_200_less__le__trans, fact_129_less__asym, fact_159_order_Ostrict__implies__not__eq, fact_110_ord__eq__less__subst, fact_77_eq__refl, fact_224_subsetI, fact_123_order__less__subst2, fact_185_order__less__le__subst1, fact_5_nofail__simps_I2_J, fact_216_dual__order_Ostrict__trans2, fact_181_order__le__less__subst2, fact_12_less__eq__nres_Oinduct, fact_254_Greatest__equality, fact_41_mem__Collect__eq, fact_197_less__imp__le, fact_22_pw__le__iff, fact_155_less__imp__not__less, fact_161_dual__order_Ostrict__implies__not__eq, fact_126_less__imp__neq, fact_157_dual__order_Ostrict__trans, fact_252_GreatestI2__order, fact_20_pw__leI, fact_31_inres__def, fact_24_less__nres_Osimps_I2_J, fact_117_order__less__subst1, fact_27_sup__nres_Ocases, fact_115_ord__less__eq__subst, fact_260_bex2I, fact_70_ord__le__eq__subst, fact_6_nofail__RES__conv, fact_244_subset__psubset__trans, fact_102_order__mono__setup_Omono__if, fact_118_order__less__subst1, fact_215_dual__order_Ostrict__trans1, fact_246_less__nres_Opelims_I1_J, fact_222_psubsetI, fact_261_Refine__Misc_Oif__mono, fact_193_antisym__conv1, fact_34_le__nofailI, fact_182_order__less__le__subst1, fact_188_order__less__le__subst2, fact_74_eq__iff, fact_76_antisym, fact_210_order_Oorder__iff__strict, fact_69_ord__le__eq__subst, fact_127_less__imp__neq, fact_67_ord__eq__le__subst, fact_259_ord__eq__le__eq__trans, fact_89_order__class_Oorder_Oantisym, fact_235_set__eq__subset, fact_241_psubset__imp__subset, fact_231_subset__iff, fact_168_leD, fact_93_dual__order_Orefl, fact_25_less__eq__nres_Ocases, fact_18_inres__simps_I3_J, fact_263_chain__subset__def, fact_183_order__less__le__subst1, fact_227_equalityE, fact_87_ord__le__eq__trans, fact_187_order__less__le__subst2, fact_56_less__nres_Osimps_I3_J, fact_171_le__less, fact_19_nofail__simps_I3_J, fact_46_dual__order_Ostrict__implies__order, fact_79_order_Otrans, fact_92_order__trans, fact_113_ord__less__eq__subst, fact_53_order_Ostrict__implies__order, fact_176_order__le__less__subst1, fact_132_less__trans, fact_8_nres_Oinduct, fact_90_order__class_Oorder_Oantisym, fact_29_nres__order__simps_I20_J, fact_3_the__RES_Osimps, fact_10_sup__nres_Oinduct, fact_121_order__less__subst2, fact_47_dual__order_Ostrict__implies__order, fact_111_ord__eq__less__subst, fact_195_antisym__conv2, fact_223_subset__antisym, fact_64_order__subst2, fact_160_dual__order_Ostrict__implies__not__eq, fact_59_order__subst1, fact_26_less__nres_Ocases, fact_202_le__imp__less__or__eq, fact_21_pw__leI_H, fact_247_less__nres_Opelims_I2_J, fact_257_relprop__triggers_I6_J, fact_107_old_Oprod_Oinducts, fact_190_le__neq__trans, fact_237_psubsetD, fact_145_less__not__sym, fact_75_antisym, fact_146_less__imp__not__eq2, fact_11_less__nres_Oinduct, fact_232_subset__refl, fact_250_less__eq__nres_Opelims_I2_J, fact_4_inres__simps_I2_J, fact_40_order__mono__setup_Orefl, fact_32_less__nres_Osimps_I1_J, fact_217_dual__order_Ostrict__trans2, fact_136_ord__eq__less__trans, fact_114_ord__less__eq__subst, fact_97_dual__order_Oeq__iff, fact_38_prod_Oinject, fact_60_order__subst1, fact_84_order__class_Oorder_Oeq__iff, fact_88_ord__le__eq__trans, fact_163_less__eq__nres_Oelims_I2_J, fact_33_less__eq__nres_Osimps_I1_J, fact_125_order_Oasym, fact_2_nf__inres__RES, fact_94_dual__order_Orefl, fact_37_old_Oprod_Oinject, fact_166_less__nres_Oelims_I2_J, fact_199_le__less__trans, fact_14_pw__eqI, fact_100_dual__order_Oantisym, fact_65_ord__eq__le__subst, fact_98_dual__order_Oeq__iff, fact_225_in__mono, fact_196_less__imp__le, fact_30_nres__order__simps_I21_J, fact_134_less__irrefl, fact_238_psubset__trans, fact_51_dual__order_Oorder__iff__strict, fact_42_Collect__mem__eq, fact_233_Collect__mono, fact_61_order__subst2, fact_221_verit__comp__simplify1_I1_J, fact_101_order__mono__setup_Omono__if, fact_128_less__asym, fact_209_order_Ostrict__trans2, fact_80_order_Otrans, fact_109_ord__eq__less__subst, fact_95_dual__order_Otrans, fact_133_less__trans, fact_135_less__irrefl, fact_242_psubset__subset__trans, fact_52_order_Ostrict__implies__order, fact_180_order__le__less__subst2, fact_71_ord__le__eq__subst, fact_81_antisym__conv, fact_50_dual__order_Oorder__iff__strict, fact_15_pw__eq__iff, fact_207_order_Ostrict__trans1, fact_173_less__le, fact_44_order_Onot__eq__order__implies__strict, fact_205_less__le__not__le, fact_239_psubsetE, fact_86_ord__eq__le__trans, fact_258_ord__eq__le__eq__trans, fact_172_less__le, fact_13_the__RES__inv, fact_1_nres_Oinject, fact_35_pwD1, fact_174_order__le__less__subst1, fact_73_eq__iff, fact_175_order__le__less__subst1, fact_212_order_Ostrict__iff__order, fact_112_ord__less__eq__subst, fact_228_subset__eq, fact_7_nres_Odistinct_I1_J, fact_119_order__less__subst1, fact_116_order__less__subst1, fact_120_order__less__subst2, fact_39_order__mono__setup_Orefl, fact_154_less__imp__not__less, fact_68_ord__eq__le__subst, fact_124_order_Oasym, fact_152_order_Ostrict__trans, fact_122_order__less__subst2, fact_219_relChain__def, fact_141_dual__order_Oasym, fact_236_Collect__mono__iff, fact_208_order_Ostrict__trans2, fact_164_less__eq__nres_Oelims_I1_J, fact_85_ord__eq__le__trans, fact_23_less__eq__nres_Osimps_I3_J, fact_105_Pair__inject, fact_206_order_Ostrict__trans1, fact_57_order__subst1, fact_214_dual__order_Ostrict__trans1, fact_72_ord__le__eq__subst, fact_49_dual__order_Ostrict__iff__order, fact_251_less__eq__nres_Opelims_I1_J, fact_130_less__asym_H, fact_43_Collect__cong, fact_204_less__le__not__le, fact_156_dual__order_Ostrict__trans, fact_178_order__le__less__subst2, fact_245_subset__iff__psubset__eq, fact_150_dual__order_Oirrefl, fact_249_less__eq__nres_Opelims_I3_J, fact_9_nres_Oexhaust, fact_108_ord__eq__less__subst, fact_138_ord__less__eq__trans, fact_106_old_Oprod_Oexhaust, fact_192_antisym__conv1, fact_255_Greatest__equality, fact_194_antisym__conv2, fact_151_dual__order_Oirrefl, fact_198_le__less__trans, fact_28_nres__more__simps_I6_J, fact_99_dual__order_Oantisym, fact_149_less__imp__triv, fact_158_order_Ostrict__implies__not__eq, fact_220_verit__comp__simplify1_I1_J, fact_137_ord__eq__less__trans, fact_17_nf__inres__def, fact_63_order__subst2, fact_82_antisym__conv, fact_165_less__nres_Oelims_I3_J, fact_229_equalityD1, fact_142_less__imp__not__eq, fact_213_order_Ostrict__iff__order, fact_91_order__trans, fact_170_le__less, fact_143_less__imp__not__eq, fact_262_Refine__Misc_Oif__mono, fact_256_subset__Collect__conv, fact_16_not__nofail__inres, fact_103_surj__pair, fact_153_order_Ostrict__trans, fact_162_less__eq__nres_Oelims_I3_J, fact_139_ord__less__eq__trans, fact_0_nres__more__simps_I4_J, fact_144_less__not__sym, fact_83_order__class_Oorder_Oeq__iff, fact_66_ord__eq__le__subst, fact_189_order__less__le__subst2, fact_179_order__le__less__subst2, fact_243_subset__not__subset__eq, fact_240_psubset__eq, fact_96_dual__order_Otrans, fact_203_le__imp__less__or__eq, fact_211_order_Oorder__iff__strict, fact_201_less__le__trans, fact_58_order__subst1, fact_226_subsetD, fact_36_pwD2, fact_62_order__subst2, fact_248_less__nres_Opelims_I3_J, fact_78_eq__refl, fact_230_equalityD2, fact_234_subset__trans, fact_218_relChain__def, fact_147_less__imp__not__eq2, fact_131_less__asym_H
74.59/24.46	% No. of inferences in proof: 610
74.59/24.46	% SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 23823 ms resp. 23025 ms w/o parsing
76.32/24.84	% SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
76.32/24.84	thf(set_Pr384614482nres_a_type, type, set_Pr384614482nres_a: $tType).
76.32/24.84	thf(produc1609974940nres_a_type, type, produc1609974940nres_a: $tType).
76.32/24.84	thf(refine424419629nres_a_type, type, refine424419629nres_a: $tType).
76.32/24.84	thf(set_set_a_type, type, set_set_a: $tType).
76.32/24.84	thf(set_a_type, type, set_a: $tType).
76.32/24.84	thf(a_type, type, a: $tType).
76.32/24.84	thf(bNF_Ca459084161nres_a_decl, type, bNF_Ca459084161nres_a: (set_Pr384614482nres_a > ((refine424419629nres_a > refine424419629nres_a) > $o))).
76.32/24.84	thf(bNF_Ca953716171_set_a_decl, type, bNF_Ca953716171_set_a: (set_Pr384614482nres_a > ((refine424419629nres_a > set_a) > $o))).
76.32/24.84	thf(if_Ref1724547303nres_a_decl, type, if_Ref1724547303nres_a: ($o > (refine424419629nres_a > (refine424419629nres_a > refine424419629nres_a)))).
76.32/24.84	thf(if_set_a_decl, type, if_set_a: ($o > (set_a > (set_a > set_a)))).
76.32/24.84	thf(ord_le1480771457nres_a_decl, type, ord_le1480771457nres_a: (refine424419629nres_a > (refine424419629nres_a > $o))).
76.32/24.84	thf(ord_less_set_a_decl, type, ord_less_set_a: (set_a > (set_a > $o))).
76.32/24.84	thf(ord_le519537037nres_a_decl, type, ord_le519537037nres_a: (refine424419629nres_a > (refine424419629nres_a > $o))).
76.32/24.84	thf(ord_less_eq_set_a_decl, type, ord_less_eq_set_a: (set_a > (set_a > $o))).
76.32/24.84	thf(order_1714329108nres_a_decl, type, order_1714329108nres_a: ((refine424419629nres_a > $o) > refine424419629nres_a)).
76.32/24.84	thf(order_Greatest_set_a_decl, type, order_Greatest_set_a: ((set_a > $o) > set_a)).
76.32/24.84	thf(produc1136923598nres_a_decl, type, produc1136923598nres_a: (refine424419629nres_a > (refine424419629nres_a > produc1609974940nres_a))).
76.32/24.84	thf(refine2063221604TURN_a_decl, type, refine2063221604TURN_a: (a > refine424419629nres_a)).
76.32/24.84	thf(refine1001002027nres_a_decl, type, refine1001002027nres_a: (refine424419629nres_a > (a > $o))).
76.32/24.84	thf(refine1048213316_rel_a_decl, type, refine1048213316_rel_a: (produc1609974940nres_a > (produc1609974940nres_a > $o))).
76.32/24.84	thf(refine260105272_rel_a_decl, type, refine260105272_rel_a: (produc1609974940nres_a > (produc1609974940nres_a > $o))).
76.32/24.84	thf(refine1312857699nres_a_decl, type, refine1312857699nres_a: (refine424419629nres_a > (a > $o))).
76.32/24.84	thf(refine412683989fail_a_decl, type, refine412683989fail_a: (refine424419629nres_a > $o)).
76.32/24.84	thf(refine464223677AILi_a_decl, type, refine464223677AILi_a: refine424419629nres_a).
76.32/24.84	thf(refine1198353288_RES_a_decl, type, refine1198353288_RES_a: (set_a > refine424419629nres_a)).
76.32/24.84	thf(refine1822134885_RES_a_decl, type, refine1822134885_RES_a: (refine424419629nres_a > set_a)).
76.32/24.84	thf(collect_a_decl, type, collect_a: ((a > $o) > set_a)).
76.32/24.84	thf(accp_P624619091nres_a_decl, type, accp_P624619091nres_a: ((produc1609974940nres_a > (produc1609974940nres_a > $o)) > (produc1609974940nres_a > $o))).
76.32/24.84	thf(chain_subset_a_decl, type, chain_subset_a: (set_set_a > $o)).
76.32/24.84	thf(member1468928819nres_a_decl, type, member1468928819nres_a: (produc1609974940nres_a > (set_Pr384614482nres_a > $o))).
76.32/24.84	thf(member_set_a_decl, type, member_set_a: (set_a > (set_set_a > $o))).
76.32/24.84	thf(member_a_decl, type, member_a: (a > (set_a > $o))).
76.32/24.84	thf(phi_decl, type, phi: (a > $o)).
76.32/24.84	thf(x_decl, type, x: a).
76.32/24.84	thf(sk1_decl, type, sk1: ((refine424419629nres_a > (refine424419629nres_a > $o)) > (set_Pr384614482nres_a > (refine424419629nres_a > (refine424419629nres_a > refine424419629nres_a))))).
76.32/24.84	thf(sk2_decl, type, sk2: ((refine424419629nres_a > (refine424419629nres_a > $o)) > (set_Pr384614482nres_a > (refine424419629nres_a > (refine424419629nres_a > refine424419629nres_a))))).
76.32/24.84	thf(sk1_def, definition, sk1 = (^ [A:(refine424419629nres_a > (refine424419629nres_a > $o)),B:set_Pr384614482nres_a,C:refine424419629nres_a,D:refine424419629nres_a]: (@+ [E:refine424419629nres_a]: ? [F:refine424419629nres_a]: ((A @ E @ F) & (member1468928819nres_a @ (produc1136923598nres_a @ E @ F) @ B)))) ).
76.32/24.84	thf(sk2_def, definition, sk2 = (^ [A:(refine424419629nres_a > (refine424419629nres_a > $o)),B:set_Pr384614482nres_a,C:refine424419629nres_a,D:refine424419629nres_a]: (@+ [E:refine424419629nres_a]: ((A @ (sk1 @ A @ B @ C @ D) @ E) & (member1468928819nres_a @ (produc1136923598nres_a @ (sk1 @ A @ B @ C @ D) @ E) @ B)))) ).
76.32/24.84	thf(239,axiom,((! [A:(a > $o),B:(a > $o)]: ((ord_less_eq_set_a @ (collect_a @ A) @ (collect_a @ B)) = (! [C:a]: ((A @ C) => (B @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_236_Collect__mono__iff)).
76.32/24.84	thf(1337,plain,((! [A:(a > $o),B:(a > $o)]: ((ord_less_eq_set_a @ (collect_a @ (A)) @ (collect_a @ (B))) = (! [C:a]: ((A @ C) => (B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[239])).
76.32/24.84	thf(215,axiom,((ord_less_eq_set_a = (^ [A:set_a,B:set_a]: ! [C:a]: ((member_a @ C @ B) <= (member_a @ C @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_231_subset__iff)).
76.32/24.84	thf(1105,plain,(((ord_less_eq_set_a) = (^ [A:set_a,B:set_a]: ! [C:a]: ((member_a @ C @ A) => (member_a @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[215])).
76.32/24.84	thf(146,axiom,((! [A:refine424419629nres_a,B:refine424419629nres_a,C:refine424419629nres_a]: (((ord_le519537037nres_a @ A @ C) <= (ord_le519537037nres_a @ B @ C)) <= (ord_le519537037nres_a @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_order__trans)).
76.32/24.84	thf(846,plain,((! [A:refine424419629nres_a,B:refine424419629nres_a,C:refine424419629nres_a]: ((ord_le519537037nres_a @ A @ B) => ((ord_le519537037nres_a @ B @ C) => (ord_le519537037nres_a @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[146])).
76.32/24.84	thf(177,axiom,((! [A:refine424419629nres_a,B:(set_a > refine424419629nres_a),C:set_a,D:set_a]: (((ord_less_set_a @ C @ D) => ((! [E:set_a,F:set_a]: ((ord_less_set_a @ E @ F) => (ord_le1480771457nres_a @ (B @ E) @ (B @ F)))) => (ord_le1480771457nres_a @ A @ (B @ D)))) <= (ord_le1480771457nres_a @ A @ (B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_117_order__less__subst1)).
76.32/24.84	thf(962,plain,((! [A:refine424419629nres_a,B:(set_a > refine424419629nres_a),C:set_a,D:set_a]: ((ord_le1480771457nres_a @ A @ (B @ C)) => ((ord_less_set_a @ C @ D) => ((! [E:set_a,F:set_a]: ((ord_less_set_a @ E @ F) => (ord_le1480771457nres_a @ (B @ E) @ (B @ F)))) => (ord_le1480771457nres_a @ A @ (B @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[177])).
76.32/24.84	thf(70,axiom,((! [A:set_a,B:set_a,C:set_a]: ((ord_less_set_a @ A @ B) => ((ord_less_eq_set_a @ B @ C) => (ord_less_set_a @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_201_less__le__trans)).
76.32/24.84	thf(555,plain,((! [A:set_a,B:set_a,C:set_a]: ((ord_less_set_a @ A @ B) => ((ord_less_eq_set_a @ B @ C) => (ord_less_set_a @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[70])).
76.32/24.84	thf(217,axiom,((ord_less_eq_set_a = (^ [A:set_a,B:set_a]: ((A = B) | (ord_less_set_a @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_245_subset__iff__psubset__eq)).
76.32/24.84	thf(1110,plain,(((ord_less_eq_set_a) = (^ [A:set_a,B:set_a]: ((A = B) | (ord_less_set_a @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[217])).
76.32/24.84	thf(191,axiom,((! [A:set_a,B:set_a]: ((ord_less_set_a @ A @ B) => (~ (ord_less_set_a @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_145_less__not__sym)).
76.32/24.84	thf(1024,plain,((! [A:set_a,B:set_a]: ((ord_less_set_a @ A @ B) => (~ (ord_less_set_a @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[191])).
76.32/24.84	thf(258,axiom,((refine1312857699nres_a = (^ [A:refine424419629nres_a,B:a]: ((refine412683989fail_a @ A) & (refine1001002027nres_a @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_nf__inres__def)).
76.32/24.84	thf(1468,plain,(((refine1312857699nres_a) = (^ [A:refine424419629nres_a,B:a]: ((refine412683989fail_a @ A) & (refine1001002027nres_a @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[258])).
76.32/24.84	thf(1469,plain,(((refine1312857699nres_a) = (^ [A:refine424419629nres_a,B:a]: ((refine412683989fail_a @ A) & (refine1001002027nres_a @ A @ B))))),inference(lifteq,[status(thm)],[1468])).
76.32/24.84	thf(163,axiom,((! [A:refine424419629nres_a,B:refine424419629nres_a]: (((ord_le519537037nres_a @ A @ B) => (ord_le1480771457nres_a @ A @ B)) <= (A != B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_order_Onot__eq__order__implies__strict)).
76.32/24.84	thf(909,plain,((! [A:refine424419629nres_a,B:refine424419629nres_a]: ((~ (A = B)) => ((ord_le519537037nres_a @ A @ B) => (ord_le1480771457nres_a @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[163])).
76.32/24.84	thf(89,axiom,((chain_subset_a = (^ [A:set_set_a]: ! [B:set_a]: ((member_set_a @ B @ A) => (! [C:set_a]: ((member_set_a @ C @ A) => ((ord_less_eq_set_a @ B @ C) | (ord_less_eq_set_a @ C @ B)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_263_chain__subset__def)).
76.32/24.84	thf(628,plain,(((chain_subset_a) = (^ [A:set_set_a]: ! [B:set_a]: ((member_set_a @ B @ A) => (! [C:set_a]: ((member_set_a @ C @ A) => ((ord_less_eq_set_a @ B @ C) | (ord_less_eq_set_a @ C @ B)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[89])).
76.32/24.84	thf(60,axiom,((ord_less_set_a = (^ [A:set_a,B:set_a]: ((A != B) & (ord_less_eq_set_a @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_240_psubset__eq)).
76.32/24.84	thf(522,plain,(((ord_less_set_a) = (^ [A:set_a,B:set_a]: (~ (A = B) & (ord_less_eq_set_a @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[60])).
76.32/24.84	thf(523,plain,(((ord_less_set_a) = (^ [A:set_a,B:set_a]: (~ (A = B) & (ord_less_eq_set_a @ A @ B))))),inference(lifteq,[status(thm)],[522])).
76.32/24.84	thf(103,axiom,((! [A:set_a,B:set_a]: ((ord_less_eq_set_a @ A @ B) <= (ord_less_set_a @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_dual__order_Ostrict__implies__order)).
76.32/24.84	thf(683,plain,((! [A:set_a,B:set_a]: ((ord_less_set_a @ A @ B) => (ord_less_eq_set_a @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[103])).
76.32/24.84	thf(4,axiom,((! [A:refine424419629nres_a,B:refine424419629nres_a,C:set_Pr384614482nres_a,D:(refine424419629nres_a > (refine424419629nres_a > $o))]: ((member1468928819nres_a @ (produc1136923598nres_a @ A @ B) @ C) => ((? [E:refine424419629nres_a,F:refine424419629nres_a]: ((D @ E @ F) & (member1468928819nres_a @ (produc1136923598nres_a @ E @ F) @ C))) <= ((member1468928819nres_a @ (produc1136923598nres_a @ A @ B) @ C) => (D @ A @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_260_bex2I)).
76.32/24.84	thf(271,plain,((! [A:refine424419629nres_a,B:refine424419629nres_a,C:set_Pr384614482nres_a,D:(refine424419629nres_a > (refine424419629nres_a > $o))]: ((member1468928819nres_a @ (produc1136923598nres_a @ A @ B) @ C) => (((member1468928819nres_a @ (produc1136923598nres_a @ A @ B) @ C) => (D @ A @ B)) => (? [E:refine424419629nres_a,F:refine424419629nres_a]: ((D @ E @ F) & (member1468928819nres_a @ (produc1136923598nres_a @ E @ F) @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4])).
76.32/24.84	thf(272,plain,((! [A:refine424419629nres_a,B:refine424419629nres_a,C:set_Pr384614482nres_a]: ((member1468928819nres_a @ (produc1136923598nres_a @ A @ B) @ C) => (! [D:(refine424419629nres_a > (refine424419629nres_a > $o))]: (((member1468928819nres_a @ (produc1136923598nres_a @ A @ B) @ C) => (D @ A @ B)) => (? [E:refine424419629nres_a,F:refine424419629nres_a]: ((D @ E @ F) & (member1468928819nres_a @ (produc1136923598nres_a @ E @ F) @ C)))))))),inference(miniscope,[status(thm)],[271])).
76.32/24.84	thf(273,plain,(! [D:(refine424419629nres_a > (refine424419629nres_a > $o)),C:set_Pr384614482nres_a,B:refine424419629nres_a,A:refine424419629nres_a] : (((~ (member1468928819nres_a @ (produc1136923598nres_a @ A @ B) @ C) | (member1468928819nres_a @ (produc1136923598nres_a @ A @ B) @ C) | (D @ (sk1 @ (D) @ C @ B @ A) @ (sk2 @ (D) @ C @ B @ A))) & (~ (member1468928819nres_a @ (produc1136923598nres_a @ A @ B) @ C) | (member1468928819nres_a @ (produc1136923598nres_a @ A @ B) @ C) | (member1468928819nres_a @ (produc1136923598nres_a @ (sk1 @ (D) @ C @ B @ A) @ (sk2 @ (D) @ C @ B @ A)) @ C)) & (~ (member1468928819nres_a @ (produc1136923598nres_a @ A @ B) @ C) | ~ (D @ A @ B) | (D @ (sk1 @ (D) @ C @ B @ A) @ (sk2 @ (D) @ C @ B @ A))) & (~ (member1468928819nres_a @ (produc1136923598nres_a @ A @ B) @ C) | ~ (D @ A @ B) | (member1468928819nres_a @ (produc1136923598nres_a @ (sk1 @ (D) @ C @ B @ A) @ (sk2 @ (D) @ C @ B @ A)) @ C))))),inference(cnf,[status(esa)],[272])).
76.32/24.84	thf(276,plain,(! [D:(refine424419629nres_a > (refine424419629nres_a > $o)),C:set_Pr384614482nres_a,B:refine424419629nres_a,A:refine424419629nres_a] : ((~ (member1468928819nres_a @ (produc1136923598nres_a @ A @ B) @ C)) | (~ (D @ A @ B)) | (D @ (sk1 @ (D) @ C @ B @ A) @ (sk2 @ (D) @ C @ B @ A)))),inference(cnfConj,[status(thm)],[273])).
76.32/24.84	thf(264,axiom,((! [A:refine424419629nres_a,B:refine424419629nres_a]: (((~ (! [C:set_a]: ((A = (refine1198353288_RES_a @ C)) => (! [D:set_a]: ((~ (ord_less_set_a @ C @ D)) <= (B = (refine1198353288_RES_a @ D))))))) <= ((? [C:set_a]: (A = (refine1198353288_RES_a @ C))) => (B != refine464223677AILi_a))) <= (ord_le1480771457nres_a @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_166_less__nres_Oelims_I2_J)).
76.32/24.84	thf(1522,plain,((! [A:refine424419629nres_a,B:refine424419629nres_a]: ((ord_le1480771457nres_a @ A @ B) => (((? [C:set_a]: (A = (refine1198353288_RES_a @ C))) => (~ (B = refine464223677AILi_a))) => (~ (! [C:set_a]: ((A = (refine1198353288_RES_a @ C)) => (! [D:set_a]: ((B = (refine1198353288_RES_a @ D)) => (~ (ord_less_set_a @ C @ D))))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[264])).
76.32/24.84	thf(254,axiom,((! [A:(refine424419629nres_a > (refine424419629nres_a > $o)),B:refine424419629nres_a,C:refine424419629nres_a]: ((! [D:refine424419629nres_a]: (A @ D @ refine464223677AILi_a)) => (((A @ B @ C) <= (! [D:set_a,E:set_a]: (A @ (refine1198353288_RES_a @ D) @ (refine1198353288_RES_a @ E)))) <= (! [D:set_a]: (A @ refine464223677AILi_a @ (refine1198353288_RES_a @ D))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_sup__nres_Oinduct)).
76.32/24.84	thf(1443,plain,((! [A:(refine424419629nres_a > (refine424419629nres_a > $o)),B:refine424419629nres_a,C:refine424419629nres_a]: ((! [D:refine424419629nres_a]: (A @ D @ refine464223677AILi_a)) => ((! [D:set_a]: (A @ refine464223677AILi_a @ (refine1198353288_RES_a @ D))) => ((! [D:set_a,E:set_a]: (A @ (refine1198353288_RES_a @ D) @ (refine1198353288_RES_a @ E))) => (A @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[254])).
76.32/24.84	thf(182,axiom,((! [A:set_a,B:set_a,C:set_a]: ((A = B) => ((ord_less_set_a @ A @ C) <= (ord_less_set_a @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_137_ord__eq__less__trans)).
76.32/24.84	thf(994,plain,((! [A:set_a,B:set_a,C:set_a]: ((A = B) => ((ord_less_set_a @ B @ C) => (ord_less_set_a @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[182])).
76.32/24.84	thf(120,axiom,((! [A:set_a,B:set_a,C:(set_a > refine424419629nres_a),D:refine424419629nres_a]: ((((! [E:set_a,F:set_a]: ((ord_le519537037nres_a @ (C @ E) @ (C @ F)) <= (ord_less_eq_set_a @ E @ F))) => (ord_le1480771457nres_a @ (C @ A) @ D)) <= (ord_le1480771457nres_a @ (C @ B) @ D)) <= (ord_less_eq_set_a @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_180_order__le__less__subst2)).
76.32/24.84	thf(741,plain,((! [A:set_a,B:set_a,C:(set_a > refine424419629nres_a),D:refine424419629nres_a]: ((ord_less_eq_set_a @ A @ B) => ((ord_le1480771457nres_a @ (C @ B) @ D) => ((! [E:set_a,F:set_a]: ((ord_less_eq_set_a @ E @ F) => (ord_le519537037nres_a @ (C @ E) @ (C @ F)))) => (ord_le1480771457nres_a @ (C @ A) @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[120])).
76.32/24.84	thf(154,axiom,((! [A:set_a,B:set_a]: ((ord_less_set_a @ A @ B) => (ord_less_eq_set_a @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_241_psubset__imp__subset)).
76.32/24.84	thf(873,plain,((! [A:set_a,B:set_a]: ((ord_less_set_a @ A @ B) => (ord_less_eq_set_a @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[154])).
76.32/24.84	thf(156,axiom,((! [A:set_a,B:set_a,C:set_a]: ((ord_less_eq_set_a @ A @ B) => ((ord_less_set_a @ B @ C) => (ord_less_set_a @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_207_order_Ostrict__trans1)).
76.32/24.84	thf(878,plain,((! [A:set_a,B:set_a,C:set_a]: ((ord_less_eq_set_a @ A @ B) => ((ord_less_set_a @ B @ C) => (ord_less_set_a @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[156])).
76.32/24.84	thf(3,axiom,((! [A:set_a,B:set_a]: ((~ (ord_less_set_a @ B @ A)) <= (ord_less_set_a @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_129_less__asym)).
76.32/24.84	thf(269,plain,((! [A:set_a,B:set_a]: ((ord_less_set_a @ A @ B) => (~ (ord_less_set_a @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3])).
76.32/24.84	thf(80,axiom,((! [A:refine424419629nres_a,B:a]: ((~ (refine412683989fail_a @ A)) => (refine1001002027nres_a @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_not__nofail__inres)).
76.32/24.84	thf(597,plain,((! [A:refine424419629nres_a,B:a]: ((~ (refine412683989fail_a @ A)) => (refine1001002027nres_a @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[80])).
76.32/24.84	thf(224,axiom,((! [A:set_a,B:(set_a > set_a),C:set_a,D:set_a]: ((ord_less_set_a @ A @ (B @ C)) => (((ord_less_set_a @ A @ (B @ D)) <= (! [E:set_a,F:set_a]: ((ord_less_set_a @ E @ F) => (ord_less_set_a @ (B @ E) @ (B @ F))))) <= (ord_less_set_a @ C @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_119_order__less__subst1)).
76.32/24.84	thf(1142,plain,((! [A:set_a,B:(set_a > set_a),C:set_a,D:set_a]: ((ord_less_set_a @ A @ (B @ C)) => ((ord_less_set_a @ C @ D) => ((! [E:set_a,F:set_a]: ((ord_less_set_a @ E @ F) => (ord_less_set_a @ (B @ E) @ (B @ F)))) => (ord_less_set_a @ A @ (B @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[224])).
76.32/24.84	thf(28,axiom,((! [A:set_a,B:set_a,C:set_a]: (((ord_less_eq_set_a @ B @ C) => (ord_less_set_a @ A @ C)) <= (ord_less_set_a @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_242_psubset__subset__trans)).
76.32/24.84	thf(379,plain,((! [A:set_a,B:set_a,C:set_a]: ((ord_less_set_a @ A @ B) => ((ord_less_eq_set_a @ B @ C) => (ord_less_set_a @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[28])).
76.32/24.84	thf(1,conjecture,(((refine1312857699nres_a @ (refine1198353288_RES_a @ (collect_a @ phi)) @ x) = (phi @ x))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0)).
76.32/24.84	thf(2,negated_conjecture,((~ ((refine1312857699nres_a @ (refine1198353288_RES_a @ (collect_a @ phi)) @ x) = (phi @ x)))),inference(neg_conjecture,[status(cth)],[1])).
76.32/24.84	thf(267,plain,((~ ((refine1312857699nres_a @ (refine1198353288_RES_a @ (collect_a @ (phi))) @ x) = (phi @ x)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])).
76.32/24.84	thf(268,plain,(((refine1312857699nres_a @ (refine1198353288_RES_a @ (collect_a @ (phi))) @ x) != (phi @ x))),inference(lifteq,[status(thm)],[267])).
76.32/24.84	thf(1565,plain,((refine1312857699nres_a @ (refine1198353288_RES_a @ (collect_a @ (phi))) @ x) | (phi @ x)),inference(bool_ext,[status(thm)],[268])).
76.32/24.84	thf(1615,plain,(! [D:(refine424419629nres_a > (refine424419629nres_a > $o)),C:set_Pr384614482nres_a,B:refine424419629nres_a,A:refine424419629nres_a] : ((phi @ x) | (~ (member1468928819nres_a @ (produc1136923598nres_a @ A @ B) @ C)) | ~ (($true)) | (D @ (sk1 @ (D) @ C @ B @ A) @ (sk2 @ (D) @ C @ B @ A)) | ((refine1312857699nres_a @ (refine1198353288_RES_a @ (collect_a @ (phi))) @ x) != (D @ A @ B)))),inference(paramod_ordered,[status(thm)],[1565,276])).
76.32/24.84	thf(1616,plain,(! [D:(refine424419629nres_a > (refine424419629nres_a > $o)),C:set_Pr384614482nres_a,B:refine424419629nres_a,A:refine424419629nres_a] : ((phi @ x) | (~ (member1468928819nres_a @ (produc1136923598nres_a @ A @ B) @ C)) | (D @ (sk1 @ (D) @ C @ B @ A) @ (sk2 @ (D) @ C @ B @ A)) | ((refine1312857699nres_a @ (refine1198353288_RES_a @ (collect_a @ (phi))) @ x) != (D @ A @ B)))),inference(simp,[status(thm)],[1615])).
76.32/24.84	thf(1651,plain,(! [B:set_Pr384614482nres_a,A:refine424419629nres_a] : ((phi @ x) | (~ (member1468928819nres_a @ (produc1136923598nres_a @ A @ (refine1198353288_RES_a @ (collect_a @ (phi)))) @ B)) | (refine1312857699nres_a @ (sk2 @ (^ [C:refine424419629nres_a,D:refine424419629nres_a]: (refine1312857699nres_a @ D @ x)) @ B @ (refine1198353288_RES_a @ (collect_a @ (phi))) @ A) @ x))),inference(pre_uni,[status(thm)],[1616:[bind(A, $thf(A)),bind(B, $thf(refine1198353288_RES_a @ (collect_a @ (phi)))),bind(C, $thf(C)),bind(D, $thf(^ [E:refine424419629nres_a,F:refine424419629nres_a]: (refine1312857699nres_a @ F @ x)))]])).
76.32/24.84	thf(1705,plain,(! [B:set_Pr384614482nres_a,A:refine424419629nres_a] : ((phi @ x) | (~ (member1468928819nres_a @ (produc1136923598nres_a @ A @ (refine1198353288_RES_a @ (collect_a @ (phi)))) @ B)) | (refine1312857699nres_a @ (sk2 @ (^ [C:refine424419629nres_a,D:refine424419629nres_a]: (refine1312857699nres_a @ D @ x)) @ B @ (refine1198353288_RES_a @ (collect_a @ (phi))) @ A) @ x))),inference(simp,[status(thm)],[1651])).
76.32/24.84	thf(30,axiom,((! [A:set_a,B:set_a]: (((A = B) <= (ord_less_eq_set_a @ B @ A)) <= (ord_less_eq_set_a @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_order__class_Oorder_Oantisym)).
76.32/24.84	thf(385,plain,((! [A:set_a,B:set_a]: ((ord_less_eq_set_a @ A @ B) => ((ord_less_eq_set_a @ B @ A) => (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[30])).
76.32/24.84	thf(54,axiom,((! [A:refine424419629nres_a,B:refine424419629nres_a]: (((ord_le519537037nres_a @ A @ B) = (A = B)) <= (~ (ord_le1480771457nres_a @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_192_antisym__conv1)).
76.32/24.84	thf(500,plain,((! [A:refine424419629nres_a,B:refine424419629nres_a]: ((~ (ord_le1480771457nres_a @ A @ B)) => ((ord_le519537037nres_a @ A @ B) = (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[54])).
76.32/24.84	thf(133,axiom,((! [A:set_a,B:set_a]: ((ord_less_eq_set_a @ A @ B) => ((ord_less_eq_set_a @ B @ A) => (A = B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_antisym)).
76.32/24.84	thf(797,plain,((! [A:set_a,B:set_a]: ((ord_less_eq_set_a @ A @ B) => ((ord_less_eq_set_a @ B @ A) => (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[133])).
76.32/24.84	thf(241,axiom,((! [A:a,B:(a > $o)]: ((member_a @ A @ (collect_a @ B)) = (B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_mem__Collect__eq)).
76.32/24.84	thf(1342,plain,((! [A:a,B:(a > $o)]: ((member_a @ A @ (collect_a @ (B))) = (B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[241])).
76.32/24.84	thf(99,axiom,((! [A:set_a,B:set_a]: (((ord_less_eq_set_a @ B @ A) = (B = A)) <= (ord_less_eq_set_a @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_antisym__conv)).
76.32/24.84	thf(670,plain,((! [A:set_a,B:set_a]: ((ord_less_eq_set_a @ A @ B) => ((ord_less_eq_set_a @ B @ A) = (B = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[99])).
76.32/24.84	thf(34,axiom,((((=) @ refine424419629nres_a) = (^ [A:refine424419629nres_a,B:refine424419629nres_a]: (! [C:a]: ((refine1001002027nres_a @ A @ C) = (refine1001002027nres_a @ B @ C)) & ((refine412683989fail_a @ A) = (refine412683989fail_a @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_pw__eq__iff)).
76.32/24.84	thf(404,plain,((((=) @ refine424419629nres_a) = (^ [A:refine424419629nres_a,B:refine424419629nres_a]: (! [C:a]: ((refine1001002027nres_a @ A @ C) = (refine1001002027nres_a @ B @ C)) & ((refine412683989fail_a @ A) = (refine412683989fail_a @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[34])).
76.32/24.84	thf(111,axiom,((! [A:refine424419629nres_a,B:refine424419629nres_a,C:refine424419629nres_a]: (((ord_le1480771457nres_a @ B @ C) => (ord_le1480771457nres_a @ A @ C)) <= (ord_le519537037nres_a @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_198_le__less__trans)).
76.32/24.84	thf(709,plain,((! [A:refine424419629nres_a,B:refine424419629nres_a,C:refine424419629nres_a]: ((ord_le519537037nres_a @ A @ B) => ((ord_le1480771457nres_a @ B @ C) => (ord_le1480771457nres_a @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[111])).
76.32/24.84	thf(37,axiom,((! [A:refine424419629nres_a,B:refine424419629nres_a,C:(refine424419629nres_a > set_a),D:set_a]: ((ord_le1480771457nres_a @ A @ B) => ((ord_less_eq_set_a @ (C @ B) @ D) => ((ord_less_set_a @ (C @ A) @ D) <= (! [E:refine424419629nres_a,F:refine424419629nres_a]: ((ord_le1480771457nres_a @ E @ F) => (ord_less_set_a @ (C @ E) @ (C @ F))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_188_order__less__le__subst2)).
76.32/24.84	thf(417,plain,((! [A:refine424419629nres_a,B:refine424419629nres_a,C:(refine424419629nres_a > set_a),D:set_a]: ((ord_le1480771457nres_a @ A @ B) => ((ord_less_eq_set_a @ (C @ B) @ D) => ((! [E:refine424419629nres_a,F:refine424419629nres_a]: ((ord_le1480771457nres_a @ E @ F) => (ord_less_set_a @ (C @ E) @ (C @ F)))) => (ord_less_set_a @ (C @ A) @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[37])).
76.32/24.84	thf(197,axiom,((! [A:refine424419629nres_a,B:refine424419629nres_a]: ((A != B) <= (ord_le1480771457nres_a @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_126_less__imp__neq)).
76.32/24.84	thf(1046,plain,((! [A:refine424419629nres_a,B:refine424419629nres_a]: ((ord_le1480771457nres_a @ A @ B) => (~ (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[197])).
76.32/24.84	thf(8,axiom,((! [A:set_a,B:set_a,C:set_a]: ((ord_less_eq_set_a @ A @ B) => ((ord_less_eq_set_a @ A @ C) <= (B = C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_ord__le__eq__trans)).
76.32/24.84	thf(288,plain,((! [A:set_a,B:set_a,C:set_a]: ((ord_less_eq_set_a @ A @ B) => ((B = C) => (ord_less_eq_set_a @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8])).
76.32/24.84	thf(246,axiom,((! [A:set_a,B:set_a]: ((ord_le519537037nres_a @ (refine1198353288_RES_a @ A) @ (refine1198353288_RES_a @ B)) = (ord_less_eq_set_a @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_less__eq__nres_Osimps_I2_J)).
76.32/24.84	thf(1359,plain,((! [A:set_a,B:set_a]: ((ord_le519537037nres_a @ (refine1198353288_RES_a @ A) @ (refine1198353288_RES_a @ B)) = (ord_less_eq_set_a @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[246])).
76.32/24.84	thf(94,axiom,((! [A:refine424419629nres_a,B:(refine424419629nres_a > refine424419629nres_a),C:refine424419629nres_a,D:refine424419629nres_a]: ((ord_le1480771457nres_a @ A @ (B @ C)) => ((ord_le519537037nres_a @ C @ D) => ((! [E:refine424419629nres_a,F:refine424419629nres_a]: ((ord_le519537037nres_a @ E @ F) => (ord_le519537037nres_a @ (B @ E) @ (B @ F)))) => (ord_le1480771457nres_a @ A @ (B @ D))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_182_order__less__le__subst1)).
76.32/24.84	thf(651,plain,((! [A:refine424419629nres_a,B:(refine424419629nres_a > refine424419629nres_a),C:refine424419629nres_a,D:refine424419629nres_a]: ((ord_le1480771457nres_a @ A @ (B @ C)) => ((ord_le519537037nres_a @ C @ D) => ((! [E:refine424419629nres_a,F:refine424419629nres_a]: ((ord_le519537037nres_a @ E @ F) => (ord_le519537037nres_a @ (B @ E) @ (B @ F)))) => (ord_le1480771457nres_a @ A @ (B @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[94])).
76.32/24.84	thf(31,axiom,((ord_less_set_a = (^ [A:set_a,B:set_a]: ((ord_less_eq_set_a @ A @ B) & ~ (ord_less_eq_set_a @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_205_less__le__not__le)).
76.32/24.84	thf(388,plain,(((ord_less_set_a) = (^ [A:set_a,B:set_a]: ((ord_less_eq_set_a @ A @ B) & ~ (ord_less_eq_set_a @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[31])).
76.32/24.84	thf(389,plain,(((ord_less_set_a) = (^ [A:set_a,B:set_a]: ((ord_less_eq_set_a @ A @ B) & ~ (ord_less_eq_set_a @ B @ A))))),inference(lifteq,[status(thm)],[388])).
76.32/24.84	thf(200,axiom,((((=) @ set_a) = (^ [A:set_a,B:set_a]: ((ord_less_eq_set_a @ A @ B) & (ord_less_eq_set_a @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_order__class_Oorder_Oeq__iff)).
76.32/24.84	thf(1054,plain,((((=) @ set_a) = (^ [A:set_a,B:set_a]: ((ord_less_eq_set_a @ A @ B) & (ord_less_eq_set_a @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[200])).
76.32/24.84	thf(1055,plain,(((^ [A:set_a,B:set_a]: ((ord_less_eq_set_a @ A @ B) & (ord_less_eq_set_a @ B @ A))) = ((=) @ set_a))),inference(lifteq,[status(thm)],[1054])).
76.32/24.84	thf(128,axiom,((! [A:refine424419629nres_a]: (ord_le519537037nres_a @ A @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_order__mono__setup_Orefl)).
76.32/24.84	thf(785,plain,((! [A:refine424419629nres_a]: (ord_le519537037nres_a @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[128])).
76.32/24.84	thf(55,axiom,((ord_le1480771457nres_a = (^ [A:refine424419629nres_a,B:refine424419629nres_a]: ((ord_le519537037nres_a @ A @ B) & (A != B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_212_order_Ostrict__iff__order)).
76.32/24.84	thf(503,plain,(((ord_le1480771457nres_a) = (^ [A:refine424419629nres_a,B:refine424419629nres_a]: ((ord_le519537037nres_a @ A @ B) & ~ (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[55])).
76.32/24.84	thf(504,plain,(((ord_le1480771457nres_a) = (^ [A:refine424419629nres_a,B:refine424419629nres_a]: ((ord_le519537037nres_a @ A @ B) & ~ (A = B))))),inference(lifteq,[status(thm)],[503])).
76.32/24.84	thf(166,axiom,((! [A:refine424419629nres_a,B:(set_a > refine424419629nres_a),C:set_a,D:set_a]: ((ord_le1480771457nres_a @ A @ (B @ C)) => (((! [E:set_a,F:set_a]: ((ord_less_eq_set_a @ E @ F) => (ord_le519537037nres_a @ (B @ E) @ (B @ F)))) => (ord_le1480771457nres_a @ A @ (B @ D))) <= (ord_less_eq_set_a @ C @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_184_order__less__le__subst1)).
76.32/24.84	thf(917,plain,((! [A:refine424419629nres_a,B:(set_a > refine424419629nres_a),C:set_a,D:set_a]: ((ord_le1480771457nres_a @ A @ (B @ C)) => ((ord_less_eq_set_a @ C @ D) => ((! [E:set_a,F:set_a]: ((ord_less_eq_set_a @ E @ F) => (ord_le519537037nres_a @ (B @ E) @ (B @ F)))) => (ord_le1480771457nres_a @ A @ (B @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[166])).
76.32/24.84	thf(23,axiom,((! [A:set_a,B:set_a]: (((A = B) <= (ord_less_eq_set_a @ B @ A)) <= (ord_less_eq_set_a @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_223_subset__antisym)).
76.32/24.84	thf(357,plain,((! [A:set_a,B:set_a]: ((ord_less_eq_set_a @ A @ B) => ((ord_less_eq_set_a @ B @ A) => (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[23])).
76.32/24.84	thf(202,axiom,((! [A:refine424419629nres_a,B:refine424419629nres_a]: ((ord_le519537037nres_a @ A @ B) => ((ord_le519537037nres_a @ B @ A) = (B = A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_antisym__conv)).
76.32/24.84	thf(1059,plain,((! [A:refine424419629nres_a,B:refine424419629nres_a]: ((ord_le519537037nres_a @ A @ B) => ((ord_le519537037nres_a @ B @ A) = (B = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[202])).
76.32/24.84	thf(174,axiom,((! [A:refine424419629nres_a,B:(refine424419629nres_a > refine424419629nres_a),C:refine424419629nres_a,D:refine424419629nres_a]: (((ord_le519537037nres_a @ C @ D) => ((! [E:refine424419629nres_a,F:refine424419629nres_a]: ((ord_le519537037nres_a @ E @ F) => (ord_le519537037nres_a @ (B @ E) @ (B @ F)))) => (ord_le519537037nres_a @ A @ (B @ D)))) <= (ord_le519537037nres_a @ A @ (B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_order__subst1)).
76.32/24.84	thf(949,plain,((! [A:refine424419629nres_a,B:(refine424419629nres_a > refine424419629nres_a),C:refine424419629nres_a,D:refine424419629nres_a]: ((ord_le519537037nres_a @ A @ (B @ C)) => ((ord_le519537037nres_a @ C @ D) => ((! [E:refine424419629nres_a,F:refine424419629nres_a]: ((ord_le519537037nres_a @ E @ F) => (ord_le519537037nres_a @ (B @ E) @ (B @ F)))) => (ord_le519537037nres_a @ A @ (B @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[174])).
76.32/24.84	thf(135,axiom,((ord_le519537037nres_a = (^ [A:refine424419629nres_a,B:refine424419629nres_a]: ((A = B) | (ord_le1480771457nres_a @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_170_le__less)).
76.32/24.84	thf(802,plain,(((ord_le519537037nres_a) = (^ [A:refine424419629nres_a,B:refine424419629nres_a]: ((A = B) | (ord_le1480771457nres_a @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[135])).
76.32/24.84	thf(20,axiom,((! [A:produc1609974940nres_a]: ~ (! [B:refine424419629nres_a,C:refine424419629nres_a]: (A != (produc1136923598nres_a @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_106_old_Oprod_Oexhaust)).
76.32/24.84	thf(344,plain,((! [A:produc1609974940nres_a]: ~ (! [B:refine424419629nres_a,C:refine424419629nres_a]: ~ (A = (produc1136923598nres_a @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[20])).
76.32/24.84	thf(161,axiom,((! [A:set_a,B:set_a]: ((A = B) => (ord_less_eq_set_a @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_eq__refl)).
76.32/24.84	thf(902,plain,((! [A:set_a,B:set_a]: ((A = B) => (ord_less_eq_set_a @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[161])).
76.32/24.84	thf(225,axiom,((! [A:produc1609974940nres_a]: (((! [B:set_a]: (A != (produc1136923598nres_a @ (refine1198353288_RES_a @ B) @ refine464223677AILi_a))) => (~ (! [B:set_a,C:set_a]: (A != (produc1136923598nres_a @ (refine1198353288_RES_a @ B) @ (refine1198353288_RES_a @ C)))))) <= (! [B:refine424419629nres_a]: (A != (produc1136923598nres_a @ refine464223677AILi_a @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_less__nres_Ocases)).
76.32/24.84	thf(1147,plain,((! [A:produc1609974940nres_a]: ((! [B:refine424419629nres_a]: ~ (A = (produc1136923598nres_a @ refine464223677AILi_a @ B))) => ((! [B:set_a]: ~ (A = (produc1136923598nres_a @ (refine1198353288_RES_a @ B) @ refine464223677AILi_a))) => (~ (! [B:set_a,C:set_a]: ~ (A = (produc1136923598nres_a @ (refine1198353288_RES_a @ B) @ (refine1198353288_RES_a @ C))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[225])).
76.32/24.84	thf(1650,plain,(! [B:set_Pr384614482nres_a,A:refine424419629nres_a] : ((phi @ x) | (~ (member1468928819nres_a @ (produc1136923598nres_a @ (refine1198353288_RES_a @ (collect_a @ (phi))) @ A) @ B)) | (refine1312857699nres_a @ (sk1 @ (^ [C:refine424419629nres_a,D:refine424419629nres_a]: (refine1312857699nres_a @ C @ x)) @ B @ A @ (refine1198353288_RES_a @ (collect_a @ (phi)))) @ x))),inference(pre_uni,[status(thm)],[1616:[bind(A, $thf(refine1198353288_RES_a @ (collect_a @ (phi)))),bind(B, $thf(B)),bind(C, $thf(C)),bind(D, $thf(^ [E:refine424419629nres_a,F:refine424419629nres_a]: (refine1312857699nres_a @ E @ x)))]])).
76.32/24.84	thf(1704,plain,(! [B:set_Pr384614482nres_a,A:refine424419629nres_a] : ((phi @ x) | (~ (member1468928819nres_a @ (produc1136923598nres_a @ (refine1198353288_RES_a @ (collect_a @ (phi))) @ A) @ B)) | (refine1312857699nres_a @ (sk1 @ (^ [C:refine424419629nres_a,D:refine424419629nres_a]: (refine1312857699nres_a @ C @ x)) @ B @ A @ (refine1198353288_RES_a @ (collect_a @ (phi)))) @ x))),inference(simp,[status(thm)],[1650])).
76.32/24.84	thf(187,axiom,((! [A:refine424419629nres_a,B:refine424419629nres_a]: ((ord_le1480771457nres_a @ A @ B) => (~ (ord_le1480771457nres_a @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_140_dual__order_Oasym)).
76.32/24.84	thf(1013,plain,((! [A:refine424419629nres_a,B:refine424419629nres_a]: ((ord_le1480771457nres_a @ A @ B) => (~ (ord_le1480771457nres_a @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[187])).
76.32/24.84	thf(157,axiom,((! [A:$o,B:refine424419629nres_a,C:refine424419629nres_a,D:refine424419629nres_a,E:refine424419629nres_a]: ((((ord_le519537037nres_a @ D @ E) <= (~ (A))) => (ord_le519537037nres_a @ (if_Ref1724547303nres_a @ A @ B @ D) @ (if_Ref1724547303nres_a @ A @ C @ E))) <= ((ord_le519537037nres_a @ B @ C) <= (A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_261_Refine__Misc_Oif__mono)).
76.32/24.84	thf(881,plain,((! [A:$o,B:refine424419629nres_a,C:refine424419629nres_a,D:refine424419629nres_a,E:refine424419629nres_a]: (((A) => (ord_le519537037nres_a @ B @ C)) => (((~ (A)) => (ord_le519537037nres_a @ D @ E)) => (ord_le519537037nres_a @ (if_Ref1724547303nres_a @ A @ B @ D) @ (if_Ref1724547303nres_a @ A @ C @ E)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[157])).
76.32/24.84	thf(16,axiom,((ord_less_set_a = (^ [A:set_a,B:set_a]: (~ (ord_less_eq_set_a @ B @ A) & (ord_less_eq_set_a @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_243_subset__not__subset__eq)).
76.32/24.84	thf(316,plain,(((ord_less_set_a) = (^ [A:set_a,B:set_a]: (~ (ord_less_eq_set_a @ B @ A) & (ord_less_eq_set_a @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[16])).
76.32/24.84	thf(247,axiom,((! [A:refine424419629nres_a]: ((refine412683989fail_a @ A) => ((refine1198353288_RES_a @ (refine1822134885_RES_a @ A)) = A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_the__RES__inv)).
76.32/24.84	thf(1362,plain,((! [A:refine424419629nres_a]: ((refine412683989fail_a @ A) => ((refine1198353288_RES_a @ (refine1822134885_RES_a @ A)) = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[247])).
76.32/24.84	thf(256,axiom,((! [A:set_a]: (refine412683989fail_a @ (refine1198353288_RES_a @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_nofail__simps_I2_J)).
76.32/24.84	thf(1450,plain,((! [A:set_a]: (refine412683989fail_a @ (refine1198353288_RES_a @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[256])).
76.32/24.84	thf(27,axiom,((! [A:refine424419629nres_a,B:refine424419629nres_a,C:refine424419629nres_a]: (((ord_le1480771457nres_a @ C @ A) => (ord_le1480771457nres_a @ C @ B)) <= (ord_le519537037nres_a @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_214_dual__order_Ostrict__trans1)).
76.32/24.84	thf(376,plain,((! [A:refine424419629nres_a,B:refine424419629nres_a,C:refine424419629nres_a]: ((ord_le519537037nres_a @ A @ B) => ((ord_le1480771457nres_a @ C @ A) => (ord_le1480771457nres_a @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[27])).
76.32/24.84	thf(238,axiom,((! [A:set_a]: ((refine1001002027nres_a @ (refine1198353288_RES_a @ A)) = (^ [B:a]: (member_a @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_inres__simps_I2_J)).
76.32/24.84	thf(1334,plain,((! [A:set_a]: ((refine1001002027nres_a @ (refine1198353288_RES_a @ A)) = (^ [B:a]: (member_a @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[238])).
76.32/24.84	thf(50,axiom,((! [A:set_a,B:(refine424419629nres_a > set_a),C:refine424419629nres_a,D:refine424419629nres_a]: (((ord_le519537037nres_a @ C @ D) => ((! [E:refine424419629nres_a,F:refine424419629nres_a]: ((ord_le519537037nres_a @ E @ F) => (ord_less_eq_set_a @ (B @ E) @ (B @ F)))) => (ord_less_set_a @ A @ (B @ D)))) <= (ord_less_set_a @ A @ (B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_183_order__less__le__subst1)).
76.32/24.84	thf(485,plain,((! [A:set_a,B:(refine424419629nres_a > set_a),C:refine424419629nres_a,D:refine424419629nres_a]: ((ord_less_set_a @ A @ (B @ C)) => ((ord_le519537037nres_a @ C @ D) => ((! [E:refine424419629nres_a,F:refine424419629nres_a]: ((ord_le519537037nres_a @ E @ F) => (ord_less_eq_set_a @ (B @ E) @ (B @ F)))) => (ord_less_set_a @ A @ (B @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[50])).
76.32/24.84	thf(226,axiom,((! [A:refine424419629nres_a,B:refine424419629nres_a,C:$o]: (((((~ ((! [D:set_a]: (((~ (accp_P624619091nres_a @ refine1048213316_rel_a @ (produc1136923598nres_a @ refine464223677AILi_a @ (refine1198353288_RES_a @ D)))) <= (~ (C))) <= (B = (refine1198353288_RES_a @ D)))) <= (A = refine464223677AILi_a))) <= (! [D:set_a]: ((! [E:set_a]: ((B = (refine1198353288_RES_a @ E)) => ((C = (ord_less_eq_set_a @ D @ E)) => (~ (accp_P624619091nres_a @ refine1048213316_rel_a @ (produc1136923598nres_a @ (refine1198353288_RES_a @ D) @ (refine1198353288_RES_a @ E))))))) <= (A = (refine1198353288_RES_a @ D))))) <= ((B = refine464223677AILi_a) => ((~ (accp_P624619091nres_a @ refine1048213316_rel_a @ (produc1136923598nres_a @ A @ refine464223677AILi_a))) <= (C)))) <= (accp_P624619091nres_a @ refine1048213316_rel_a @ (produc1136923598nres_a @ A @ B))) <= ((ord_le519537037nres_a @ A @ B) = C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_251_less__eq__nres_Opelims_I1_J)).
76.32/24.84	thf(1151,plain,((! [A:refine424419629nres_a,B:refine424419629nres_a,C:$o]: (((ord_le519537037nres_a @ A @ B) = C) => ((accp_P624619091nres_a @ (refine1048213316_rel_a) @ (produc1136923598nres_a @ A @ B)) => (((B = refine464223677AILi_a) => ((C) => (~ (accp_P624619091nres_a @ (refine1048213316_rel_a) @ (produc1136923598nres_a @ A @ refine464223677AILi_a))))) => ((! [D:set_a]: ((A = (refine1198353288_RES_a @ D)) => (! [E:set_a]: ((B = (refine1198353288_RES_a @ E)) => ((C = (ord_less_eq_set_a @ D @ E)) => (~ (accp_P624619091nres_a @ (refine1048213316_rel_a) @ (produc1136923598nres_a @ (refine1198353288_RES_a @ D) @ (refine1198353288_RES_a @ E))))))))) => (~ ((A = refine464223677AILi_a) => (! [D:set_a]: ((B = (refine1198353288_RES_a @ D)) => ((~ (C)) => (~ (accp_P624619091nres_a @ (refine1048213316_rel_a) @ (produc1136923598nres_a @ refine464223677AILi_a @ (refine1198353288_RES_a @ D))))))))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[226])).
76.32/24.84	thf(22,axiom,((! [A:refine424419629nres_a,B:refine424419629nres_a]: ((A != B) <= (ord_le1480771457nres_a @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_142_less__imp__not__eq)).
76.32/24.84	thf(353,plain,((! [A:refine424419629nres_a,B:refine424419629nres_a]: ((ord_le1480771457nres_a @ A @ B) => (~ (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[22])).
76.32/24.84	thf(142,axiom,((! [A:refine424419629nres_a,B:refine424419629nres_a,C:refine424419629nres_a,D:refine424419629nres_a]: (((produc1136923598nres_a @ A @ B) = (produc1136923598nres_a @ C @ D)) = ((A = C) & (B = D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_old_Oprod_Oinject)).
76.32/24.84	thf(821,plain,((! [A:refine424419629nres_a,B:refine424419629nres_a,C:refine424419629nres_a,D:refine424419629nres_a]: (((produc1136923598nres_a @ A @ B) = (produc1136923598nres_a @ C @ D)) = ((A = C) & (B = D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[142])).
76.32/24.84	thf(49,axiom,((! [A:set_a,B:(refine424419629nres_a > set_a),C:refine424419629nres_a,D:refine424419629nres_a]: ((ord_less_set_a @ A @ (B @ C)) => ((ord_le1480771457nres_a @ C @ D) => ((! [E:refine424419629nres_a,F:refine424419629nres_a]: ((ord_le1480771457nres_a @ E @ F) => (ord_less_set_a @ (B @ E) @ (B @ F)))) => (ord_less_set_a @ A @ (B @ D))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_118_order__less__subst1)).
76.32/24.84	thf(480,plain,((! [A:set_a,B:(refine424419629nres_a > set_a),C:refine424419629nres_a,D:refine424419629nres_a]: ((ord_less_set_a @ A @ (B @ C)) => ((ord_le1480771457nres_a @ C @ D) => ((! [E:refine424419629nres_a,F:refine424419629nres_a]: ((ord_le1480771457nres_a @ E @ F) => (ord_less_set_a @ (B @ E) @ (B @ F)))) => (ord_less_set_a @ A @ (B @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[49])).
76.32/24.84	thf(77,axiom,((! [A:set_a,B:(set_a > set_a),C:set_a,D:set_a]: ((((! [E:set_a,F:set_a]: ((ord_less_eq_set_a @ E @ F) => (ord_less_eq_set_a @ (B @ E) @ (B @ F)))) => (ord_less_eq_set_a @ A @ (B @ D))) <= (ord_less_eq_set_a @ C @ D)) <= (ord_less_eq_set_a @ A @ (B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_order__subst1)).
76.32/24.84	thf(574,plain,((! [A:set_a,B:(set_a > set_a),C:set_a,D:set_a]: ((ord_less_eq_set_a @ A @ (B @ C)) => ((ord_less_eq_set_a @ C @ D) => ((! [E:set_a,F:set_a]: ((ord_less_eq_set_a @ E @ F) => (ord_less_eq_set_a @ (B @ E) @ (B @ F)))) => (ord_less_eq_set_a @ A @ (B @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[77])).
76.32/24.84	thf(189,axiom,((! [A:refine424419629nres_a,B:refine424419629nres_a]: ((ord_le1480771457nres_a @ A @ B) => (ord_le519537037nres_a @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_196_less__imp__le)).
76.32/24.84	thf(1020,plain,((! [A:refine424419629nres_a,B:refine424419629nres_a]: ((ord_le1480771457nres_a @ A @ B) => (ord_le519537037nres_a @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[189])).
76.32/24.84	thf(21,axiom,((! [A:refine424419629nres_a,B:refine424419629nres_a,C:refine424419629nres_a,D:refine424419629nres_a]: (((ord_le519537037nres_a @ B @ C) => ((C = D) => (ord_le519537037nres_a @ A @ D))) <= (A = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_258_ord__eq__le__eq__trans)).
76.32/24.84	thf(348,plain,((! [A:refine424419629nres_a,B:refine424419629nres_a,C:refine424419629nres_a,D:refine424419629nres_a]: ((A = B) => ((ord_le519537037nres_a @ B @ C) => ((C = D) => (ord_le519537037nres_a @ A @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[21])).
76.32/24.84	thf(124,axiom,((((=) @ set_a) = (^ [A:set_a,B:set_a]: ((ord_less_eq_set_a @ B @ A) & (ord_less_eq_set_a @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_dual__order_Oeq__iff)).
76.32/24.84	thf(766,plain,((((=) @ set_a) = (^ [A:set_a,B:set_a]: ((ord_less_eq_set_a @ B @ A) & (ord_less_eq_set_a @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[124])).
76.32/24.84	thf(5,axiom,((! [A:refine424419629nres_a,B:refine424419629nres_a]: ((ord_le519537037nres_a @ A @ B) => ((~ (ord_le1480771457nres_a @ A @ B)) = (A = B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_194_antisym__conv2)).
76.32/24.84	thf(278,plain,((! [A:refine424419629nres_a,B:refine424419629nres_a]: ((ord_le519537037nres_a @ A @ B) => ((~ (ord_le1480771457nres_a @ A @ B)) = (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5])).
76.32/24.84	thf(279,plain,(! [B:refine424419629nres_a,A:refine424419629nres_a] : ((~ (ord_le519537037nres_a @ A @ B)) | ((~ (ord_le1480771457nres_a @ A @ B)) = (A = B)))),inference(cnf,[status(esa)],[278])).
76.32/24.84	thf(280,plain,(! [B:refine424419629nres_a,A:refine424419629nres_a] : (((~ (ord_le1480771457nres_a @ A @ B)) = (A = B)) | (~ (ord_le519537037nres_a @ A @ B)))),inference(lifteq,[status(thm)],[279])).
76.32/24.84	thf(9,axiom,((! [A:refine424419629nres_a,B:refine424419629nres_a]: ((A = B) => (ord_le519537037nres_a @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_eq__refl)).
76.32/24.84	thf(293,plain,((! [A:refine424419629nres_a,B:refine424419629nres_a]: ((A = B) => (ord_le519537037nres_a @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[9])).
76.32/24.84	thf(152,axiom,((! [A:refine424419629nres_a,B:refine424419629nres_a,C:refine424419629nres_a]: ((ord_le519537037nres_a @ A @ B) => ((B = C) => (ord_le519537037nres_a @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_ord__le__eq__trans)).
76.32/24.84	thf(866,plain,((! [A:refine424419629nres_a,B:refine424419629nres_a,C:refine424419629nres_a]: ((ord_le519537037nres_a @ A @ B) => ((B = C) => (ord_le519537037nres_a @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[152])).
76.32/24.84	thf(207,axiom,((! [A:refine424419629nres_a,B:refine424419629nres_a]: ((ord_le519537037nres_a @ A @ B) => ((A != B) => (ord_le1480771457nres_a @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_190_le__neq__trans)).
76.32/24.84	thf(1072,plain,((! [A:refine424419629nres_a,B:refine424419629nres_a]: ((ord_le519537037nres_a @ A @ B) => ((~ (A = B)) => (ord_le1480771457nres_a @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[207])).
76.32/24.84	thf(242,axiom,((! [A:set_a]: (refine464223677AILi_a != (refine1198353288_RES_a @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_nres_Odistinct_I1_J)).
76.32/24.84	thf(1345,plain,((! [A:set_a]: ~ (refine464223677AILi_a = (refine1198353288_RES_a @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[242])).
76.32/24.84	thf(147,axiom,((ord_le519537037nres_a = (^ [A:refine424419629nres_a,B:refine424419629nres_a]: ((ord_le1480771457nres_a @ A @ B) | (A = B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_210_order_Oorder__iff__strict)).
76.32/24.84	thf(849,plain,(((ord_le519537037nres_a) = (^ [A:refine424419629nres_a,B:refine424419629nres_a]: ((ord_le1480771457nres_a @ A @ B) | (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[147])).
76.32/24.84	thf(1564,plain,((~ (refine1312857699nres_a @ (refine1198353288_RES_a @ (collect_a @ (phi))) @ x)) | (~ (phi @ x))),inference(bool_ext,[status(thm)],[268])).
76.32/24.84	thf(13,axiom,((! [A:set_a,B:set_a]: ((ord_less_set_a @ A @ B) => (~ (ord_less_set_a @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_155_less__imp__not__less)).
76.32/24.84	thf(307,plain,((! [A:set_a,B:set_a]: ((ord_less_set_a @ A @ B) => (~ (ord_less_set_a @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[13])).
76.32/24.84	thf(43,axiom,((! [A:refine424419629nres_a,B:(set_a > refine424419629nres_a),C:set_a,D:set_a]: ((ord_le519537037nres_a @ A @ (B @ C)) => ((ord_less_eq_set_a @ C @ D) => ((ord_le519537037nres_a @ A @ (B @ D)) <= (! [E:set_a,F:set_a]: ((ord_less_eq_set_a @ E @ F) => (ord_le519537037nres_a @ (B @ E) @ (B @ F))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_order__subst1)).
76.32/24.84	thf(452,plain,((! [A:refine424419629nres_a,B:(set_a > refine424419629nres_a),C:set_a,D:set_a]: ((ord_le519537037nres_a @ A @ (B @ C)) => ((ord_less_eq_set_a @ C @ D) => ((! [E:set_a,F:set_a]: ((ord_less_eq_set_a @ E @ F) => (ord_le519537037nres_a @ (B @ E) @ (B @ F)))) => (ord_le519537037nres_a @ A @ (B @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[43])).
76.32/24.84	thf(58,axiom,((! [A:refine424419629nres_a,B:refine424419629nres_a,C:(refine424419629nres_a > refine424419629nres_a),D:refine424419629nres_a]: ((ord_le519537037nres_a @ A @ B) => (((ord_le1480771457nres_a @ (C @ A) @ D) <= (! [E:refine424419629nres_a,F:refine424419629nres_a]: ((ord_le519537037nres_a @ E @ F) => (ord_le519537037nres_a @ (C @ E) @ (C @ F))))) <= (ord_le1480771457nres_a @ (C @ B) @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_178_order__le__less__subst2)).
76.32/24.84	thf(512,plain,((! [A:refine424419629nres_a,B:refine424419629nres_a,C:(refine424419629nres_a > refine424419629nres_a),D:refine424419629nres_a]: ((ord_le519537037nres_a @ A @ B) => ((ord_le1480771457nres_a @ (C @ B) @ D) => ((! [E:refine424419629nres_a,F:refine424419629nres_a]: ((ord_le519537037nres_a @ E @ F) => (ord_le519537037nres_a @ (C @ E) @ (C @ F)))) => (ord_le1480771457nres_a @ (C @ A) @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[58])).
76.32/24.84	thf(168,axiom,((! [A:refine424419629nres_a,B:refine424419629nres_a,C:refine424419629nres_a,D:refine424419629nres_a]: (((produc1136923598nres_a @ A @ B) = (produc1136923598nres_a @ C @ D)) = ((A = C) & (B = D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_prod_Oinject)).
76.32/24.84	thf(925,plain,((! [A:refine424419629nres_a,B:refine424419629nres_a,C:refine424419629nres_a,D:refine424419629nres_a]: (((produc1136923598nres_a @ A @ B) = (produc1136923598nres_a @ C @ D)) = ((A = C) & (B = D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[168])).
76.32/24.84	thf(259,axiom,((refine412683989fail_a = (^ [A:refine424419629nres_a]: ? [B:set_a]: (A = (refine1198353288_RES_a @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_nofail__RES__conv)).
76.32/24.84	thf(1470,plain,(((refine412683989fail_a) = (^ [A:refine424419629nres_a]: ? [B:set_a]: (A = (refine1198353288_RES_a @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[259])).
76.32/24.84	thf(64,axiom,((ord_less_eq_set_a = (^ [A:set_a,B:set_a]: ((B = A) | (ord_less_set_a @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_dual__order_Oorder__iff__strict)).
76.32/24.84	thf(534,plain,(((ord_less_eq_set_a) = (^ [A:set_a,B:set_a]: ((B = A) | (ord_less_set_a @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[64])).
76.32/24.84	thf(205,axiom,((! [A:set_a,B:set_a,C:a]: (((member_a @ C @ A) => (member_a @ C @ B)) <= (ord_less_eq_set_a @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_226_subsetD)).
76.32/24.84	thf(1067,plain,((! [A:set_a,B:set_a,C:a]: ((ord_less_eq_set_a @ A @ B) => ((member_a @ C @ A) => (member_a @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[205])).
76.32/24.84	thf(113,axiom,((! [A:refine424419629nres_a,B:(set_a > refine424419629nres_a),C:set_a,D:set_a]: (((ord_less_set_a @ C @ D) => ((ord_le1480771457nres_a @ A @ (B @ D)) <= (! [E:set_a,F:set_a]: ((ord_less_set_a @ E @ F) => (ord_le1480771457nres_a @ (B @ E) @ (B @ F)))))) <= (A = (B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_110_ord__eq__less__subst)).
76.32/24.84	thf(714,plain,((! [A:refine424419629nres_a,B:(set_a > refine424419629nres_a),C:set_a,D:set_a]: ((A = (B @ C)) => ((ord_less_set_a @ C @ D) => ((! [E:set_a,F:set_a]: ((ord_less_set_a @ E @ F) => (ord_le1480771457nres_a @ (B @ E) @ (B @ F)))) => (ord_le1480771457nres_a @ A @ (B @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[113])).
76.32/24.84	thf(270,plain,(! [B:set_a,A:set_a] : ((~ (ord_less_set_a @ A @ B)) | (~ (ord_less_set_a @ B @ A)))),inference(cnf,[status(esa)],[269])).
76.32/24.84	thf(62,axiom,((ord_le1480771457nres_a = (^ [A:refine424419629nres_a,B:refine424419629nres_a]: ((ord_le519537037nres_a @ A @ B) & (B != A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_dual__order_Ostrict__iff__order)).
76.32/24.84	thf(529,plain,(((ord_le1480771457nres_a) = (^ [A:refine424419629nres_a,B:refine424419629nres_a]: ((ord_le519537037nres_a @ A @ B) & ~ (B = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[62])).
76.32/24.84	thf(159,axiom,((! [A:refine424419629nres_a,B:(set_a > refine424419629nres_a),C:set_a,D:set_a]: ((ord_le519537037nres_a @ A @ (B @ C)) => (((ord_le1480771457nres_a @ A @ (B @ D)) <= (! [E:set_a,F:set_a]: ((ord_le1480771457nres_a @ (B @ E) @ (B @ F)) <= (ord_less_set_a @ E @ F)))) <= (ord_less_set_a @ C @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_175_order__le__less__subst1)).
76.32/24.84	thf(894,plain,((! [A:refine424419629nres_a,B:(set_a > refine424419629nres_a),C:set_a,D:set_a]: ((ord_le519537037nres_a @ A @ (B @ C)) => ((ord_less_set_a @ C @ D) => ((! [E:set_a,F:set_a]: ((ord_less_set_a @ E @ F) => (ord_le1480771457nres_a @ (B @ E) @ (B @ F)))) => (ord_le1480771457nres_a @ A @ (B @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[159])).
76.32/24.84	thf(121,axiom,((((=) @ refine424419629nres_a) = (^ [A:refine424419629nres_a,B:refine424419629nres_a]: ((ord_le519537037nres_a @ B @ A) & (ord_le519537037nres_a @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_dual__order_Oeq__iff)).
76.32/24.84	thf(746,plain,((((=) @ refine424419629nres_a) = (^ [A:refine424419629nres_a,B:refine424419629nres_a]: ((ord_le519537037nres_a @ B @ A) & (ord_le519537037nres_a @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[121])).
76.32/24.84	thf(263,axiom,((! [A:set_a,B:set_a]: (((refine1198353288_RES_a @ A) = (refine1198353288_RES_a @ B)) = (A = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_nres__more__simps_I4_J)).
76.32/24.84	thf(1519,plain,((! [A:set_a,B:set_a]: (((refine1198353288_RES_a @ A) = (refine1198353288_RES_a @ B)) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[263])).
76.32/24.84	thf(245,axiom,((! [A:refine424419629nres_a]: ((A != refine464223677AILi_a) => (~ (! [B:set_a]: (A != (refine1198353288_RES_a @ B))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_nres_Oexhaust)).
76.32/24.84	thf(1355,plain,((! [A:refine424419629nres_a]: ((~ (A = refine464223677AILi_a)) => (~ (! [B:set_a]: ~ (A = (refine1198353288_RES_a @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[245])).
76.32/24.84	thf(72,axiom,((! [A:set_a,B:set_a]: ((ord_less_eq_set_a @ A @ B) => ((A != B) => (ord_less_set_a @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_191_le__neq__trans)).
76.32/24.84	thf(561,plain,((! [A:set_a,B:set_a]: ((ord_less_eq_set_a @ A @ B) => ((~ (A = B)) => (ord_less_set_a @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[72])).
76.32/24.84	thf(261,axiom,((! [A:refine424419629nres_a,B:refine424419629nres_a]: ((ord_le519537037nres_a @ A @ B) => ((B != refine464223677AILi_a) => (~ (! [C:set_a]: ((! [D:set_a]: ((B = (refine1198353288_RES_a @ D)) => (~ (ord_less_eq_set_a @ C @ D)))) <= (A = (refine1198353288_RES_a @ C))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_163_less__eq__nres_Oelims_I2_J)).
76.32/24.84	thf(1487,plain,((! [A:refine424419629nres_a,B:refine424419629nres_a]: ((ord_le519537037nres_a @ A @ B) => ((~ (B = refine464223677AILi_a)) => (~ (! [C:set_a]: ((A = (refine1198353288_RES_a @ C)) => (! [D:set_a]: ((B = (refine1198353288_RES_a @ D)) => (~ (ord_less_eq_set_a @ C @ D))))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[261])).
76.32/24.84	thf(10,axiom,((! [A:set_a,B:set_a,C:(set_a > refine424419629nres_a),D:refine424419629nres_a]: ((((ord_le519537037nres_a @ (C @ A) @ D) <= (! [E:set_a,F:set_a]: ((ord_le519537037nres_a @ (C @ E) @ (C @ F)) <= (ord_less_eq_set_a @ E @ F)))) <= (ord_le519537037nres_a @ (C @ B) @ D)) <= (ord_less_eq_set_a @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_order__subst2)).
76.32/24.84	thf(297,plain,((! [A:set_a,B:set_a,C:(set_a > refine424419629nres_a),D:refine424419629nres_a]: ((ord_less_eq_set_a @ A @ B) => ((ord_le519537037nres_a @ (C @ B) @ D) => ((! [E:set_a,F:set_a]: ((ord_less_eq_set_a @ E @ F) => (ord_le519537037nres_a @ (C @ E) @ (C @ F)))) => (ord_le519537037nres_a @ (C @ A) @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[10])).
76.32/24.84	thf(231,axiom,((! [A:set_a]: ~ (ord_le519537037nres_a @ refine464223677AILi_a @ (refine1198353288_RES_a @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_less__eq__nres_Osimps_I3_J)).
76.32/24.84	thf(1255,plain,((! [A:set_a]: ~ (ord_le519537037nres_a @ refine464223677AILi_a @ (refine1198353288_RES_a @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[231])).
76.32/24.84	thf(11,axiom,((! [A:refine424419629nres_a]: (ord_le519537037nres_a @ A @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_dual__order_Orefl)).
76.32/24.84	thf(302,plain,((! [A:refine424419629nres_a]: (ord_le519537037nres_a @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[11])).
76.32/24.84	thf(106,axiom,((! [A:refine424419629nres_a,B:refine424419629nres_a]: ((ord_le519537037nres_a @ B @ A) <= ((ord_le519537037nres_a @ B @ A) <= (refine412683989fail_a @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_le__nofailI)).
76.32/24.84	thf(693,plain,((! [A:refine424419629nres_a,B:refine424419629nres_a]: (((refine412683989fail_a @ A) => (ord_le519537037nres_a @ B @ A)) => (ord_le519537037nres_a @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[106])).
76.32/24.84	thf(90,axiom,((! [A:set_a,B:set_a,C:(set_a > set_a),D:set_a]: ((((! [E:set_a,F:set_a]: ((ord_less_eq_set_a @ E @ F) => (ord_less_eq_set_a @ (C @ E) @ (C @ F)))) => (ord_less_eq_set_a @ (C @ A) @ D)) <= ((C @ B) = D)) <= (ord_less_eq_set_a @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_ord__le__eq__subst)).
76.32/24.84	thf(630,plain,((! [A:set_a,B:set_a,C:(set_a > set_a),D:set_a]: ((ord_less_eq_set_a @ A @ B) => (((C @ B) = D) => ((! [E:set_a,F:set_a]: ((ord_less_eq_set_a @ E @ F) => (ord_less_eq_set_a @ (C @ E) @ (C @ F)))) => (ord_less_eq_set_a @ (C @ A) @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[90])).
76.32/24.84	thf(47,axiom,((! [A:refine424419629nres_a]: ~ (ord_le1480771457nres_a @ A @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_220_verit__comp__simplify1_I1_J)).
76.32/24.84	thf(467,plain,((! [A:refine424419629nres_a]: ~ (ord_le1480771457nres_a @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[47])).
76.32/24.84	thf(248,axiom,((! [A:set_a,B:(a > $o)]: ((ord_less_eq_set_a @ A @ (collect_a @ B)) = (! [C:a]: ((B @ C) <= (member_a @ C @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_256_subset__Collect__conv)).
76.32/24.84	thf(1365,plain,((! [A:set_a,B:(a > $o)]: ((ord_less_eq_set_a @ A @ (collect_a @ (B))) = (! [C:a]: ((member_a @ C @ A) => (B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[248])).
76.32/24.84	thf(158,axiom,((! [A:refine424419629nres_a,B:refine424419629nres_a,C:(refine424419629nres_a > set_a),D:set_a]: ((((! [E:refine424419629nres_a,F:refine424419629nres_a]: ((ord_less_eq_set_a @ (C @ E) @ (C @ F)) <= (ord_le519537037nres_a @ E @ F))) => (ord_less_set_a @ (C @ A) @ D)) <= (ord_less_set_a @ (C @ B) @ D)) <= (ord_le519537037nres_a @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_179_order__le__less__subst2)).
76.32/24.84	thf(889,plain,((! [A:refine424419629nres_a,B:refine424419629nres_a,C:(refine424419629nres_a > set_a),D:set_a]: ((ord_le519537037nres_a @ A @ B) => ((ord_less_set_a @ (C @ B) @ D) => ((! [E:refine424419629nres_a,F:refine424419629nres_a]: ((ord_le519537037nres_a @ E @ F) => (ord_less_eq_set_a @ (C @ E) @ (C @ F)))) => (ord_less_set_a @ (C @ A) @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[158])).
76.32/24.84	thf(227,axiom,((! [A:set_a,B:set_a]: ((ord_le1480771457nres_a @ (refine1198353288_RES_a @ A) @ (refine1198353288_RES_a @ B)) = (ord_less_set_a @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_less__nres_Osimps_I3_J)).
76.32/24.84	thf(1210,plain,((! [A:set_a,B:set_a]: ((ord_le1480771457nres_a @ (refine1198353288_RES_a @ A) @ (refine1198353288_RES_a @ B)) = (ord_less_set_a @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[227])).
76.32/24.84	thf(209,axiom,((! [A:set_a,B:set_a,C:(set_a > refine424419629nres_a),D:refine424419629nres_a]: ((ord_less_eq_set_a @ A @ B) => (((C @ B) = D) => ((ord_le519537037nres_a @ (C @ A) @ D) <= (! [E:set_a,F:set_a]: ((ord_less_eq_set_a @ E @ F) => (ord_le519537037nres_a @ (C @ E) @ (C @ F))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_ord__le__eq__subst)).
76.32/24.84	thf(1079,plain,((! [A:set_a,B:set_a,C:(set_a > refine424419629nres_a),D:refine424419629nres_a]: ((ord_less_eq_set_a @ A @ B) => (((C @ B) = D) => ((! [E:set_a,F:set_a]: ((ord_less_eq_set_a @ E @ F) => (ord_le519537037nres_a @ (C @ E) @ (C @ F)))) => (ord_le519537037nres_a @ (C @ A) @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[209])).
76.32/24.84	thf(123,axiom,((! [A:refine424419629nres_a,B:refine424419629nres_a,C:(refine424419629nres_a > set_a),D:set_a]: ((((C @ B) = D) => ((! [E:refine424419629nres_a,F:refine424419629nres_a]: ((ord_less_eq_set_a @ (C @ E) @ (C @ F)) <= (ord_le519537037nres_a @ E @ F))) => (ord_less_eq_set_a @ (C @ A) @ D))) <= (ord_le519537037nres_a @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_ord__le__eq__subst)).
76.32/24.84	thf(757,plain,((! [A:refine424419629nres_a,B:refine424419629nres_a,C:(refine424419629nres_a > set_a),D:set_a]: ((ord_le519537037nres_a @ A @ B) => (((C @ B) = D) => ((! [E:refine424419629nres_a,F:refine424419629nres_a]: ((ord_le519537037nres_a @ E @ F) => (ord_less_eq_set_a @ (C @ E) @ (C @ F)))) => (ord_less_eq_set_a @ (C @ A) @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[123])).
76.32/24.84	thf(68,axiom,((((=) @ refine424419629nres_a) = (^ [A:refine424419629nres_a,B:refine424419629nres_a]: ((ord_le519537037nres_a @ A @ B) & (ord_le519537037nres_a @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_eq__iff)).
76.32/24.84	thf(551,plain,((((=) @ refine424419629nres_a) = (^ [A:refine424419629nres_a,B:refine424419629nres_a]: ((ord_le519537037nres_a @ A @ B) & (ord_le519537037nres_a @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[68])).
76.32/24.84	thf(145,axiom,((! [A:set_a,B:set_a]: ((~ ((ord_less_eq_set_a @ B @ A) <= (ord_less_eq_set_a @ A @ B))) <= (ord_less_set_a @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_239_psubsetE)).
76.32/24.84	thf(842,plain,((! [A:set_a,B:set_a]: ((ord_less_set_a @ A @ B) => (~ ((ord_less_eq_set_a @ A @ B) => (ord_less_eq_set_a @ B @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[145])).
76.32/24.84	thf(107,axiom,((! [A:set_a]: ~ (ord_less_set_a @ A @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_151_dual__order_Oirrefl)).
76.32/24.84	thf(697,plain,((! [A:set_a]: ~ (ord_less_set_a @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[107])).
76.32/24.84	thf(317,plain,(((ord_less_set_a) = (^ [A:set_a,B:set_a]: (~ (ord_less_eq_set_a @ B @ A) & (ord_less_eq_set_a @ A @ B))))),inference(lifteq,[status(thm)],[316])).
76.32/24.84	thf(93,axiom,((! [A:set_a,B:set_a]: ((ord_less_set_a @ A @ B) => (A != B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_127_less__imp__neq)).
76.32/24.84	thf(647,plain,((! [A:set_a,B:set_a]: ((ord_less_set_a @ A @ B) => (~ (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[93])).
76.32/24.84	thf(648,plain,(! [B:set_a,A:set_a] : ((~ (ord_less_set_a @ A @ B)) | (~ (A = B)))),inference(cnf,[status(esa)],[647])).
76.32/24.84	thf(649,plain,(! [B:set_a,A:set_a] : ((A != B) | (~ (ord_less_set_a @ A @ B)))),inference(lifteq,[status(thm)],[648])).
76.32/24.84	thf(650,plain,(! [A:set_a] : ((~ (ord_less_set_a @ A @ A)))),inference(simp,[status(thm)],[649])).
76.32/24.84	thf(86,axiom,((! [A:refine424419629nres_a,B:refine424419629nres_a]: (((refine412683989fail_a @ B) => (refine412683989fail_a @ A)) <= (ord_le519537037nres_a @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_pwD1)).
76.32/24.84	thf(615,plain,((! [A:refine424419629nres_a,B:refine424419629nres_a]: ((ord_le519537037nres_a @ A @ B) => ((refine412683989fail_a @ B) => (refine412683989fail_a @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[86])).
76.32/24.84	thf(236,axiom,((! [A:(refine424419629nres_a > (refine424419629nres_a > $o)),B:refine424419629nres_a,C:refine424419629nres_a]: ((((A @ B @ C) <= (! [D:set_a,E:set_a]: (A @ (refine1198353288_RES_a @ D) @ (refine1198353288_RES_a @ E)))) <= (! [D:set_a]: (A @ (refine1198353288_RES_a @ D) @ refine464223677AILi_a))) <= (! [D:refine424419629nres_a]: (A @ refine464223677AILi_a @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_less__nres_Oinduct)).
76.32/24.84	thf(1328,plain,((! [A:(refine424419629nres_a > (refine424419629nres_a > $o)),B:refine424419629nres_a,C:refine424419629nres_a]: ((! [D:refine424419629nres_a]: (A @ refine464223677AILi_a @ D)) => ((! [D:set_a]: (A @ (refine1198353288_RES_a @ D) @ refine464223677AILi_a)) => ((! [D:set_a,E:set_a]: (A @ (refine1198353288_RES_a @ D) @ (refine1198353288_RES_a @ E))) => (A @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[236])).
76.32/24.84	thf(251,axiom,((! [A:refine424419629nres_a,B:refine424419629nres_a,C:$o]: (((((A = refine464223677AILi_a) => ((~ (accp_P624619091nres_a @ refine260105272_rel_a @ (produc1136923598nres_a @ refine464223677AILi_a @ B))) <= (~ (C)))) => ((! [D:set_a]: ((((~ (accp_P624619091nres_a @ refine260105272_rel_a @ (produc1136923598nres_a @ (refine1198353288_RES_a @ D) @ refine464223677AILi_a))) <= (C)) <= (B = refine464223677AILi_a)) <= (A = (refine1198353288_RES_a @ D)))) => (~ (! [D:set_a]: ((! [E:set_a]: (((C = (ord_less_set_a @ D @ E)) => (~ (accp_P624619091nres_a @ refine260105272_rel_a @ (produc1136923598nres_a @ (refine1198353288_RES_a @ D) @ (refine1198353288_RES_a @ E))))) <= (B = (refine1198353288_RES_a @ E)))) <= (A = (refine1198353288_RES_a @ D))))))) <= (accp_P624619091nres_a @ refine260105272_rel_a @ (produc1136923598nres_a @ A @ B))) <= ((ord_le1480771457nres_a @ A @ B) = C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_246_less__nres_Opelims_I1_J)).
76.32/24.84	thf(1375,plain,((! [A:refine424419629nres_a,B:refine424419629nres_a,C:$o]: (((ord_le1480771457nres_a @ A @ B) = C) => ((accp_P624619091nres_a @ (refine260105272_rel_a) @ (produc1136923598nres_a @ A @ B)) => (((A = refine464223677AILi_a) => ((~ (C)) => (~ (accp_P624619091nres_a @ (refine260105272_rel_a) @ (produc1136923598nres_a @ refine464223677AILi_a @ B))))) => ((! [D:set_a]: ((A = (refine1198353288_RES_a @ D)) => ((B = refine464223677AILi_a) => ((C) => (~ (accp_P624619091nres_a @ (refine260105272_rel_a) @ (produc1136923598nres_a @ (refine1198353288_RES_a @ D) @ refine464223677AILi_a))))))) => (~ (! [D:set_a]: ((A = (refine1198353288_RES_a @ D)) => (! [E:set_a]: ((B = (refine1198353288_RES_a @ E)) => ((C = (ord_less_set_a @ D @ E)) => (~ (accp_P624619091nres_a @ (refine260105272_rel_a) @ (produc1136923598nres_a @ (refine1198353288_RES_a @ D) @ (refine1198353288_RES_a @ E)))))))))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[251])).
76.32/24.84	thf(185,axiom,((! [A:set_a,B:(refine424419629nres_a > set_a),C:refine424419629nres_a,D:refine424419629nres_a]: ((ord_less_eq_set_a @ A @ (B @ C)) => ((ord_le1480771457nres_a @ C @ D) => ((ord_less_set_a @ A @ (B @ D)) <= (! [E:refine424419629nres_a,F:refine424419629nres_a]: ((ord_le1480771457nres_a @ E @ F) => (ord_less_set_a @ (B @ E) @ (B @ F))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_176_order__le__less__subst1)).
76.32/24.84	thf(1006,plain,((! [A:set_a,B:(refine424419629nres_a > set_a),C:refine424419629nres_a,D:refine424419629nres_a]: ((ord_less_eq_set_a @ A @ (B @ C)) => ((ord_le1480771457nres_a @ C @ D) => ((! [E:refine424419629nres_a,F:refine424419629nres_a]: ((ord_le1480771457nres_a @ E @ F) => (ord_less_set_a @ (B @ E) @ (B @ F)))) => (ord_less_set_a @ A @ (B @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[185])).
76.32/24.84	thf(181,axiom,((! [A:refine424419629nres_a,B:refine424419629nres_a,C:(refine424419629nres_a > refine424419629nres_a),D:refine424419629nres_a]: ((((! [E:refine424419629nres_a,F:refine424419629nres_a]: ((ord_le1480771457nres_a @ (C @ E) @ (C @ F)) <= (ord_le1480771457nres_a @ E @ F))) => (ord_le1480771457nres_a @ (C @ A) @ D)) <= (ord_le1480771457nres_a @ (C @ B) @ D)) <= (ord_le1480771457nres_a @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_120_order__less__subst2)).
76.32/24.84	thf(989,plain,((! [A:refine424419629nres_a,B:refine424419629nres_a,C:(refine424419629nres_a > refine424419629nres_a),D:refine424419629nres_a]: ((ord_le1480771457nres_a @ A @ B) => ((ord_le1480771457nres_a @ (C @ B) @ D) => ((! [E:refine424419629nres_a,F:refine424419629nres_a]: ((ord_le1480771457nres_a @ E @ F) => (ord_le1480771457nres_a @ (C @ E) @ (C @ F)))) => (ord_le1480771457nres_a @ (C @ A) @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[181])).
76.32/24.84	thf(223,axiom,((! [A:set_a,B:set_a]: ((ord_less_eq_set_a @ B @ A) <= (A = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_230_equalityD2)).
76.32/24.84	thf(1138,plain,((! [A:set_a,B:set_a]: ((A = B) => (ord_less_eq_set_a @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[223])).
76.32/24.84	thf(354,plain,(! [B:refine424419629nres_a,A:refine424419629nres_a] : ((~ (ord_le1480771457nres_a @ A @ B)) | (~ (A = B)))),inference(cnf,[status(esa)],[353])).
76.32/24.84	thf(355,plain,(! [B:refine424419629nres_a,A:refine424419629nres_a] : ((A != B) | (~ (ord_le1480771457nres_a @ A @ B)))),inference(lifteq,[status(thm)],[354])).
76.32/24.84	thf(356,plain,(! [A:refine424419629nres_a] : ((~ (ord_le1480771457nres_a @ A @ A)))),inference(simp,[status(thm)],[355])).
76.32/24.84	thf(19,axiom,((! [A:set_a,B:(set_a > set_a),C:set_a,D:set_a]: ((ord_less_eq_set_a @ A @ (B @ C)) => ((ord_less_set_a @ C @ D) => ((! [E:set_a,F:set_a]: ((ord_less_set_a @ E @ F) => (ord_less_set_a @ (B @ E) @ (B @ F)))) => (ord_less_set_a @ A @ (B @ D))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_177_order__le__less__subst1)).
76.32/24.84	thf(339,plain,((! [A:set_a,B:(set_a > set_a),C:set_a,D:set_a]: ((ord_less_eq_set_a @ A @ (B @ C)) => ((ord_less_set_a @ C @ D) => ((! [E:set_a,F:set_a]: ((ord_less_set_a @ E @ F) => (ord_less_set_a @ (B @ E) @ (B @ F)))) => (ord_less_set_a @ A @ (B @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[19])).
76.32/24.84	thf(170,axiom,((! [A:refine424419629nres_a,B:refine424419629nres_a,C:(refine424419629nres_a > set_a),D:set_a]: ((ord_le519537037nres_a @ A @ B) => (((ord_less_eq_set_a @ (C @ A) @ D) <= (! [E:refine424419629nres_a,F:refine424419629nres_a]: ((ord_le519537037nres_a @ E @ F) => (ord_less_eq_set_a @ (C @ E) @ (C @ F))))) <= (ord_less_eq_set_a @ (C @ B) @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_order__subst2)).
76.32/24.84	thf(933,plain,((! [A:refine424419629nres_a,B:refine424419629nres_a,C:(refine424419629nres_a > set_a),D:set_a]: ((ord_le519537037nres_a @ A @ B) => ((ord_less_eq_set_a @ (C @ B) @ D) => ((! [E:refine424419629nres_a,F:refine424419629nres_a]: ((ord_le519537037nres_a @ E @ F) => (ord_less_eq_set_a @ (C @ E) @ (C @ F)))) => (ord_less_eq_set_a @ (C @ A) @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[170])).
76.32/24.84	thf(98,axiom,((! [A:refine424419629nres_a]: (ord_le519537037nres_a @ A @ refine464223677AILi_a))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_less__eq__nres_Osimps_I1_J)).
76.32/24.84	thf(668,plain,((! [A:refine424419629nres_a]: (ord_le519537037nres_a @ A @ refine464223677AILi_a))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[98])).
76.32/24.84	thf(669,plain,(! [A:refine424419629nres_a] : ((ord_le519537037nres_a @ A @ refine464223677AILi_a))),inference(cnf,[status(esa)],[668])).
76.32/24.84	thf(208,axiom,((! [A:refine424419629nres_a,B:refine424419629nres_a]: ((ord_le1480771457nres_a @ A @ B) => (B != A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_146_less__imp__not__eq2)).
76.32/24.84	thf(1075,plain,((! [A:refine424419629nres_a,B:refine424419629nres_a]: ((ord_le1480771457nres_a @ A @ B) => (~ (B = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[208])).
76.32/24.84	thf(92,axiom,((! [A:set_a,B:(refine424419629nres_a > set_a),C:refine424419629nres_a,D:refine424419629nres_a]: (((ord_le519537037nres_a @ C @ D) => ((ord_less_eq_set_a @ A @ (B @ D)) <= (! [E:refine424419629nres_a,F:refine424419629nres_a]: ((ord_le519537037nres_a @ E @ F) => (ord_less_eq_set_a @ (B @ E) @ (B @ F)))))) <= (ord_less_eq_set_a @ A @ (B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_order__subst1)).
76.32/24.84	thf(642,plain,((! [A:set_a,B:(refine424419629nres_a > set_a),C:refine424419629nres_a,D:refine424419629nres_a]: ((ord_less_eq_set_a @ A @ (B @ C)) => ((ord_le519537037nres_a @ C @ D) => ((! [E:refine424419629nres_a,F:refine424419629nres_a]: ((ord_le519537037nres_a @ E @ F) => (ord_less_eq_set_a @ (B @ E) @ (B @ F)))) => (ord_less_eq_set_a @ A @ (B @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[92])).
76.32/24.84	thf(255,axiom,((! [A:produc1609974940nres_a]: ((! [B:refine424419629nres_a]: (A != (produc1136923598nres_a @ B @ refine464223677AILi_a))) => ((! [B:set_a,C:set_a]: (A != (produc1136923598nres_a @ (refine1198353288_RES_a @ B) @ (refine1198353288_RES_a @ C)))) => (~ (! [B:set_a]: (A != (produc1136923598nres_a @ refine464223677AILi_a @ (refine1198353288_RES_a @ B))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_less__eq__nres_Ocases)).
76.32/24.84	thf(1446,plain,((! [A:produc1609974940nres_a]: ((! [B:refine424419629nres_a]: ~ (A = (produc1136923598nres_a @ B @ refine464223677AILi_a))) => ((! [B:set_a,C:set_a]: ~ (A = (produc1136923598nres_a @ (refine1198353288_RES_a @ B) @ (refine1198353288_RES_a @ C)))) => (~ (! [B:set_a]: ~ (A = (produc1136923598nres_a @ refine464223677AILi_a @ (refine1198353288_RES_a @ B))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[255])).
76.32/24.84	thf(110,axiom,((! [A:refine424419629nres_a,B:refine424419629nres_a,C:refine424419629nres_a]: (((ord_le1480771457nres_a @ A @ C) <= (ord_le519537037nres_a @ B @ C)) <= (ord_le1480771457nres_a @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_200_less__le__trans)).
76.32/24.84	thf(706,plain,((! [A:refine424419629nres_a,B:refine424419629nres_a,C:refine424419629nres_a]: ((ord_le1480771457nres_a @ A @ B) => ((ord_le519537037nres_a @ B @ C) => (ord_le1480771457nres_a @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[110])).
76.32/24.84	thf(266,axiom,((! [A:refine424419629nres_a,B:refine424419629nres_a]: (((((B = refine464223677AILi_a) => (~ (accp_P624619091nres_a @ refine1048213316_rel_a @ (produc1136923598nres_a @ A @ refine464223677AILi_a)))) => (~ (! [C:set_a]: ((! [D:set_a]: (((accp_P624619091nres_a @ refine1048213316_rel_a @ (produc1136923598nres_a @ (refine1198353288_RES_a @ C) @ (refine1198353288_RES_a @ D))) => (~ (ord_less_eq_set_a @ C @ D))) <= (B = (refine1198353288_RES_a @ D)))) <= (A = (refine1198353288_RES_a @ C)))))) <= (accp_P624619091nres_a @ refine1048213316_rel_a @ (produc1136923598nres_a @ A @ B))) <= (ord_le519537037nres_a @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_250_less__eq__nres_Opelims_I2_J)).
76.32/24.84	thf(1539,plain,((! [A:refine424419629nres_a,B:refine424419629nres_a]: ((ord_le519537037nres_a @ A @ B) => ((accp_P624619091nres_a @ (refine1048213316_rel_a) @ (produc1136923598nres_a @ A @ B)) => (((B = refine464223677AILi_a) => (~ (accp_P624619091nres_a @ (refine1048213316_rel_a) @ (produc1136923598nres_a @ A @ refine464223677AILi_a)))) => (~ (! [C:set_a]: ((A = (refine1198353288_RES_a @ C)) => (! [D:set_a]: ((B = (refine1198353288_RES_a @ D)) => ((accp_P624619091nres_a @ (refine1048213316_rel_a) @ (produc1136923598nres_a @ (refine1198353288_RES_a @ C) @ (refine1198353288_RES_a @ D))) => (~ (ord_less_eq_set_a @ C @ D))))))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[266])).
76.32/24.84	thf(75,axiom,((! [A:refine424419629nres_a,B:refine424419629nres_a,C:refine424419629nres_a]: (((ord_le1480771457nres_a @ A @ C) <= (ord_le1480771457nres_a @ B @ C)) <= (ord_le1480771457nres_a @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_132_less__trans)).
76.32/24.84	thf(569,plain,((! [A:refine424419629nres_a,B:refine424419629nres_a,C:refine424419629nres_a]: ((ord_le1480771457nres_a @ A @ B) => ((ord_le1480771457nres_a @ B @ C) => (ord_le1480771457nres_a @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[75])).
76.32/24.84	thf(850,plain,(((ord_le519537037nres_a) = (^ [A:refine424419629nres_a,B:refine424419629nres_a]: ((ord_le1480771457nres_a @ A @ B) | (A = B))))),inference(lifteq,[status(thm)],[849])).
76.32/24.84	thf(130,axiom,((ord_le519537037nres_a = (^ [A:refine424419629nres_a,B:refine424419629nres_a]: ((B = A) | (ord_le1480771457nres_a @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_dual__order_Oorder__iff__strict)).
76.32/24.84	thf(790,plain,(((ord_le519537037nres_a) = (^ [A:refine424419629nres_a,B:refine424419629nres_a]: ((B = A) | (ord_le1480771457nres_a @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[130])).
76.32/24.84	thf(791,plain,(((ord_le519537037nres_a) = (^ [A:refine424419629nres_a,B:refine424419629nres_a]: ((B = A) | (ord_le1480771457nres_a @ A @ B))))),inference(lifteq,[status(thm)],[790])).
76.32/24.84	thf(1716,plain,(((^ [A:refine424419629nres_a,B:refine424419629nres_a]: ((B = A) | (ord_le1480771457nres_a @ A @ B))) = (^ [A:refine424419629nres_a,B:refine424419629nres_a]: ((ord_le1480771457nres_a @ A @ B) | (A = B))))),inference(rewrite,[status(thm)],[850,791])).
76.32/24.84	thf(803,plain,(((ord_le519537037nres_a) = (^ [A:refine424419629nres_a,B:refine424419629nres_a]: ((A = B) | (ord_le1480771457nres_a @ A @ B))))),inference(lifteq,[status(thm)],[802])).
76.32/24.84	thf(1588,plain,(((^ [A:refine424419629nres_a,B:refine424419629nres_a]: ((B = A) | (ord_le1480771457nres_a @ A @ B))) = (^ [A:refine424419629nres_a,B:refine424419629nres_a]: ((A = B) | (ord_le1480771457nres_a @ A @ B))))),inference(rewrite,[status(thm)],[803,791])).
76.32/24.84	thf(1719,plain,(((^ [A:refine424419629nres_a,B:refine424419629nres_a]: ((ord_le1480771457nres_a @ A @ B) | (A = B))) = (^ [A:refine424419629nres_a,B:refine424419629nres_a]: ((A = B) | (ord_le1480771457nres_a @ A @ B)))) | ((^ [A:refine424419629nres_a,B:refine424419629nres_a]: ((B = A) | (ord_le1480771457nres_a @ A @ B))) != (^ [A:refine424419629nres_a,B:refine424419629nres_a]: ((B = A) | (ord_le1480771457nres_a @ A @ B))))),inference(paramod_ordered,[status(thm)],[1716,1588])).
76.32/24.84	thf(1720,plain,(((^ [A:refine424419629nres_a,B:refine424419629nres_a]: ((ord_le1480771457nres_a @ A @ B) | (A = B))) = (^ [A:refine424419629nres_a,B:refine424419629nres_a]: ((A = B) | (ord_le1480771457nres_a @ A @ B))))),inference(pattern_uni,[status(thm)],[1719:[]])).
76.32/24.84	thf(277,plain,(! [D:(refine424419629nres_a > (refine424419629nres_a > $o)),C:set_Pr384614482nres_a,B:refine424419629nres_a,A:refine424419629nres_a] : ((~ (member1468928819nres_a @ (produc1136923598nres_a @ A @ B) @ C)) | (~ (D @ A @ B)) | (member1468928819nres_a @ (produc1136923598nres_a @ (sk1 @ (D) @ C @ B @ A) @ (sk2 @ (D) @ C @ B @ A)) @ C))),inference(cnfConj,[status(thm)],[273])).
76.32/24.84	thf(1791,plain,(! [D:(refine424419629nres_a > (refine424419629nres_a > $o)),C:set_Pr384614482nres_a,B:refine424419629nres_a,A:refine424419629nres_a] : ((phi @ x) | (~ (member1468928819nres_a @ (produc1136923598nres_a @ A @ B) @ C)) | ~ (($true)) | (member1468928819nres_a @ (produc1136923598nres_a @ (sk1 @ (D) @ C @ B @ A) @ (sk2 @ (D) @ C @ B @ A)) @ C) | ((refine1312857699nres_a @ (refine1198353288_RES_a @ (collect_a @ (phi))) @ x) != (D @ A @ B)))),inference(paramod_ordered,[status(thm)],[1565,277])).
76.32/24.84	thf(1792,plain,(! [D:(refine424419629nres_a > (refine424419629nres_a > $o)),C:set_Pr384614482nres_a,B:refine424419629nres_a,A:refine424419629nres_a] : ((phi @ x) | (~ (member1468928819nres_a @ (produc1136923598nres_a @ A @ B) @ C)) | (member1468928819nres_a @ (produc1136923598nres_a @ (sk1 @ (D) @ C @ B @ A) @ (sk2 @ (D) @ C @ B @ A)) @ C) | ((refine1312857699nres_a @ (refine1198353288_RES_a @ (collect_a @ (phi))) @ x) != (D @ A @ B)))),inference(simp,[status(thm)],[1791])).
76.32/24.84	thf(1825,plain,(! [C:set_Pr384614482nres_a,B:refine424419629nres_a,A:refine424419629nres_a] : ((phi @ x) | (~ (member1468928819nres_a @ (produc1136923598nres_a @ A @ B) @ C)) | (member1468928819nres_a @ (produc1136923598nres_a @ (sk1 @ (^ [D:refine424419629nres_a,E:refine424419629nres_a]: (refine1312857699nres_a @ (refine1198353288_RES_a @ (collect_a @ phi)) @ x)) @ C @ B @ A) @ (sk2 @ (^ [D:refine424419629nres_a,E:refine424419629nres_a]: (refine1312857699nres_a @ (refine1198353288_RES_a @ (collect_a @ phi)) @ x)) @ C @ B @ A)) @ C))),inference(pre_uni,[status(thm)],[1792:[bind(A, $thf(A)),bind(B, $thf(B)),bind(C, $thf(C)),bind(D, $thf(^ [E:refine424419629nres_a,F:refine424419629nres_a]: (refine1312857699nres_a @ (refine1198353288_RES_a @ (collect_a @ phi)) @ x)))]])).
76.32/24.84	thf(219,axiom,((! [A:set_a]: ~ (ord_less_set_a @ A @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_221_verit__comp__simplify1_I1_J)).
76.32/24.84	thf(1114,plain,((! [A:set_a]: ~ (ord_less_set_a @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[219])).
76.32/24.84	thf(213,axiom,((! [A:set_a,B:set_a]: ((ord_less_eq_set_a @ A @ B) => ((ord_less_eq_set_a @ B @ A) => (B = A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_100_dual__order_Oantisym)).
76.32/24.84	thf(1099,plain,((! [A:set_a,B:set_a]: ((ord_less_eq_set_a @ A @ B) => ((ord_less_eq_set_a @ B @ A) => (B = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[213])).
76.32/24.84	thf(1451,plain,(! [A:set_a] : ((refine412683989fail_a @ (refine1198353288_RES_a @ A)))),inference(cnf,[status(esa)],[1450])).
76.32/24.84	thf(119,axiom,((! [A:refine424419629nres_a,B:refine424419629nres_a]: (((ord_le1480771457nres_a @ A @ B) | (A = B)) <= (ord_le519537037nres_a @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_202_le__imp__less__or__eq)).
76.32/24.84	thf(738,plain,((! [A:refine424419629nres_a,B:refine424419629nres_a]: ((ord_le519537037nres_a @ A @ B) => ((ord_le1480771457nres_a @ A @ B) | (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[119])).
76.32/24.84	thf(198,axiom,((ord_le519537037nres_a = (^ [A:refine424419629nres_a,B:refine424419629nres_a]: ((! [C:a]: ((refine1001002027nres_a @ B @ C) <= (refine1001002027nres_a @ A @ C)) & (refine412683989fail_a @ A)) <= (refine412683989fail_a @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_pw__le__iff)).
76.32/24.84	thf(1050,plain,(((ord_le519537037nres_a) = (^ [A:refine424419629nres_a,B:refine424419629nres_a]: ((refine412683989fail_a @ B) => (! [C:a]: ((refine1001002027nres_a @ A @ C) => (refine1001002027nres_a @ B @ C)) & (refine412683989fail_a @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[198])).
76.32/24.84	thf(44,axiom,((! [A:set_a,B:(set_a > set_a),C:set_a,D:set_a]: ((ord_less_set_a @ A @ (B @ C)) => ((ord_less_eq_set_a @ C @ D) => ((! [E:set_a,F:set_a]: ((ord_less_eq_set_a @ E @ F) => (ord_less_eq_set_a @ (B @ E) @ (B @ F)))) => (ord_less_set_a @ A @ (B @ D))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_185_order__less__le__subst1)).
76.32/24.84	thf(457,plain,((! [A:set_a,B:(set_a > set_a),C:set_a,D:set_a]: ((ord_less_set_a @ A @ (B @ C)) => ((ord_less_eq_set_a @ C @ D) => ((! [E:set_a,F:set_a]: ((ord_less_eq_set_a @ E @ F) => (ord_less_eq_set_a @ (B @ E) @ (B @ F)))) => (ord_less_set_a @ A @ (B @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[44])).
76.32/24.84	thf(83,axiom,((! [A:set_a,B:set_a]: ((ord_less_set_a @ A @ B) => (~ (ord_less_set_a @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_125_order_Oasym)).
76.32/24.84	thf(605,plain,((! [A:set_a,B:set_a]: ((ord_less_set_a @ A @ B) => (~ (ord_less_set_a @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[83])).
76.32/24.84	thf(252,axiom,((! [A:(refine424419629nres_a > $o),B:refine424419629nres_a]: (((! [C:set_a]: (A @ (refine1198353288_RES_a @ C))) => (A @ B)) <= (A @ refine464223677AILi_a)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_nres_Oinduct)).
76.32/24.84	thf(1434,plain,((! [A:(refine424419629nres_a > $o),B:refine424419629nres_a]: ((A @ refine464223677AILi_a) => ((! [C:set_a]: (A @ (refine1198353288_RES_a @ C))) => (A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[252])).
76.32/24.84	thf(131,axiom,((! [A:set_a,B:set_a,C:set_a]: (((ord_less_set_a @ C @ B) <= (ord_less_eq_set_a @ C @ A)) <= (ord_less_set_a @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_217_dual__order_Ostrict__trans2)).
76.32/24.84	thf(792,plain,((! [A:set_a,B:set_a,C:set_a]: ((ord_less_set_a @ A @ B) => ((ord_less_eq_set_a @ C @ A) => (ord_less_set_a @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[131])).
76.32/24.84	thf(171,axiom,((ord_less_eq_set_a = (^ [A:set_a,B:set_a]: ! [C:a]: ((member_a @ C @ A) => (member_a @ C @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_228_subset__eq)).
76.32/24.84	thf(938,plain,(((ord_less_eq_set_a) = (^ [A:set_a,B:set_a]: ! [C:a]: ((member_a @ C @ A) => (member_a @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[171])).
76.32/24.84	thf(24,axiom,((! [A:refine424419629nres_a,B:(set_a > refine424419629nres_a),C:set_a,D:set_a]: ((A = (B @ C)) => (((! [E:set_a,F:set_a]: ((ord_less_eq_set_a @ E @ F) => (ord_le519537037nres_a @ (B @ E) @ (B @ F)))) => (ord_le519537037nres_a @ A @ (B @ D))) <= (ord_less_eq_set_a @ C @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_ord__eq__le__subst)).
76.32/24.84	thf(360,plain,((! [A:refine424419629nres_a,B:(set_a > refine424419629nres_a),C:set_a,D:set_a]: ((A = (B @ C)) => ((ord_less_eq_set_a @ C @ D) => ((! [E:set_a,F:set_a]: ((ord_less_eq_set_a @ E @ F) => (ord_le519537037nres_a @ (B @ E) @ (B @ F)))) => (ord_le519537037nres_a @ A @ (B @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[24])).
76.32/24.84	thf(67,axiom,((! [A:refine424419629nres_a,B:refine424419629nres_a,C:refine424419629nres_a,D:refine424419629nres_a]: (((produc1136923598nres_a @ A @ B) = (produc1136923598nres_a @ C @ D)) => (~ ((A = C) => (B != D)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_105_Pair__inject)).
76.32/24.84	thf(541,plain,((! [A:refine424419629nres_a,B:refine424419629nres_a,C:refine424419629nres_a,D:refine424419629nres_a]: (((produc1136923598nres_a @ A @ B) = (produc1136923598nres_a @ C @ D)) => (~ ((A = C) => (~ (B = D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[67])).
76.32/24.84	thf(71,axiom,((! [A:set_a,B:set_a,C:set_a]: (((ord_less_eq_set_a @ B @ C) => (ord_less_eq_set_a @ A @ C)) <= (ord_less_eq_set_a @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_order_Otrans)).
76.32/24.84	thf(558,plain,((! [A:set_a,B:set_a,C:set_a]: ((ord_less_eq_set_a @ A @ B) => ((ord_less_eq_set_a @ B @ C) => (ord_less_eq_set_a @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[71])).
76.32/24.84	thf(192,axiom,((! [A:refine424419629nres_a,B:refine424419629nres_a,C:refine424419629nres_a]: (((ord_le1480771457nres_a @ C @ B) <= (ord_le1480771457nres_a @ C @ A)) <= (ord_le1480771457nres_a @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_156_dual__order_Ostrict__trans)).
76.32/24.84	thf(1026,plain,((! [A:refine424419629nres_a,B:refine424419629nres_a,C:refine424419629nres_a]: ((ord_le1480771457nres_a @ A @ B) => ((ord_le1480771457nres_a @ C @ A) => (ord_le1480771457nres_a @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[192])).
76.32/24.84	thf(530,plain,(((ord_le1480771457nres_a) = (^ [A:refine424419629nres_a,B:refine424419629nres_a]: ((ord_le519537037nres_a @ A @ B) & ~ (B = A))))),inference(lifteq,[status(thm)],[529])).
76.32/24.84	thf(126,axiom,((! [A:set_a,B:set_a,C:a]: (((member_a @ C @ B) <= (member_a @ C @ A)) <= (ord_less_set_a @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_237_psubsetD)).
76.32/24.84	thf(773,plain,((! [A:set_a,B:set_a,C:a]: ((ord_less_set_a @ A @ B) => ((member_a @ C @ A) => (member_a @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[126])).
76.32/24.84	thf(162,axiom,((! [A:a,B:a]: ((ord_le519537037nres_a @ (refine2063221604TURN_a @ A) @ (refine2063221604TURN_a @ B)) = (A = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_nres__order__simps_I20_J)).
76.32/24.84	thf(906,plain,((! [A:a,B:a]: ((ord_le519537037nres_a @ (refine2063221604TURN_a @ A) @ (refine2063221604TURN_a @ B)) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[162])).
76.32/24.84	thf(222,axiom,((! [A:produc1609974940nres_a]: ? [B:refine424419629nres_a,C:refine424419629nres_a]: (A = (produc1136923598nres_a @ B @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_103_surj__pair)).
76.32/24.84	thf(1135,plain,((! [A:produc1609974940nres_a]: ? [B:refine424419629nres_a,C:refine424419629nres_a]: (A = (produc1136923598nres_a @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[222])).
76.32/24.84	thf(39,axiom,((! [A:a]: (refine412683989fail_a @ (refine2063221604TURN_a @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_nofail__simps_I3_J)).
76.32/24.84	thf(430,plain,((! [A:a]: (refine412683989fail_a @ (refine2063221604TURN_a @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[39])).
76.32/24.84	thf(143,axiom,((! [A:set_a,B:(refine424419629nres_a > set_a),C:refine424419629nres_a,D:refine424419629nres_a]: ((A = (B @ C)) => ((ord_le1480771457nres_a @ C @ D) => ((ord_less_set_a @ A @ (B @ D)) <= (! [E:refine424419629nres_a,F:refine424419629nres_a]: ((ord_le1480771457nres_a @ E @ F) => (ord_less_set_a @ (B @ E) @ (B @ F))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_109_ord__eq__less__subst)).
76.32/24.84	thf(824,plain,((! [A:set_a,B:(refine424419629nres_a > set_a),C:refine424419629nres_a,D:refine424419629nres_a]: ((A = (B @ C)) => ((ord_le1480771457nres_a @ C @ D) => ((! [E:refine424419629nres_a,F:refine424419629nres_a]: ((ord_le1480771457nres_a @ E @ F) => (ord_less_set_a @ (B @ E) @ (B @ F)))) => (ord_less_set_a @ A @ (B @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[143])).
76.32/24.84	thf(294,plain,(! [B:refine424419629nres_a,A:refine424419629nres_a] : ((~ (A = B)) | (ord_le519537037nres_a @ A @ B))),inference(cnf,[status(esa)],[293])).
76.32/24.84	thf(295,plain,(! [B:refine424419629nres_a,A:refine424419629nres_a] : ((A != B) | (ord_le519537037nres_a @ A @ B))),inference(lifteq,[status(thm)],[294])).
76.32/24.84	thf(296,plain,(! [A:refine424419629nres_a] : ((ord_le519537037nres_a @ A @ A))),inference(simp,[status(thm)],[295])).
76.32/24.84	thf(26,axiom,((((=) @ set_a) = (^ [A:set_a,B:set_a]: ((ord_less_eq_set_a @ B @ A) & (ord_less_eq_set_a @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_eq__iff)).
76.32/24.84	thf(374,plain,((((=) @ set_a) = (^ [A:set_a,B:set_a]: ((ord_less_eq_set_a @ B @ A) & (ord_less_eq_set_a @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[26])).
76.32/24.84	thf(375,plain,(((^ [A:set_a,B:set_a]: ((ord_less_eq_set_a @ B @ A) & (ord_less_eq_set_a @ A @ B))) = ((=) @ set_a))),inference(lifteq,[status(thm)],[374])).
76.32/24.84	thf(117,axiom,((! [A:set_a,B:set_a]: (((A != B) => (ord_less_set_a @ A @ B)) <= (ord_less_eq_set_a @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_222_psubsetI)).
76.32/24.84	thf(733,plain,((! [A:set_a,B:set_a]: ((ord_less_eq_set_a @ A @ B) => ((~ (A = B)) => (ord_less_set_a @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[117])).
76.32/24.84	thf(1823,plain,(! [B:set_Pr384614482nres_a,A:refine424419629nres_a] : ((phi @ x) | (~ (member1468928819nres_a @ (produc1136923598nres_a @ (refine1198353288_RES_a @ (collect_a @ (phi))) @ A) @ B)) | (member1468928819nres_a @ (produc1136923598nres_a @ (sk1 @ (^ [C:refine424419629nres_a,D:refine424419629nres_a]: (refine1312857699nres_a @ C @ x)) @ B @ A @ (refine1198353288_RES_a @ (collect_a @ (phi)))) @ (sk2 @ (^ [C:refine424419629nres_a,D:refine424419629nres_a]: (refine1312857699nres_a @ C @ x)) @ B @ A @ (refine1198353288_RES_a @ (collect_a @ (phi))))) @ B))),inference(pre_uni,[status(thm)],[1792:[bind(A, $thf(refine1198353288_RES_a @ (collect_a @ (phi)))),bind(B, $thf(B)),bind(C, $thf(C)),bind(D, $thf(^ [E:refine424419629nres_a,F:refine424419629nres_a]: (refine1312857699nres_a @ E @ x)))]])).
76.32/24.84	thf(1884,plain,(! [B:set_Pr384614482nres_a,A:refine424419629nres_a] : ((phi @ x) | (~ (member1468928819nres_a @ (produc1136923598nres_a @ (refine1198353288_RES_a @ (collect_a @ (phi))) @ A) @ B)) | (member1468928819nres_a @ (produc1136923598nres_a @ (sk1 @ (^ [C:refine424419629nres_a,D:refine424419629nres_a]: (refine1312857699nres_a @ C @ x)) @ B @ A @ (refine1198353288_RES_a @ (collect_a @ (phi)))) @ (sk2 @ (^ [C:refine424419629nres_a,D:refine424419629nres_a]: (refine1312857699nres_a @ C @ x)) @ B @ A @ (refine1198353288_RES_a @ (collect_a @ (phi))))) @ B))),inference(simp,[status(thm)],[1823])).
76.32/24.84	thf(7,axiom,((! [A:refine424419629nres_a,B:refine424419629nres_a]: ((ord_le1480771457nres_a @ A @ B) => (~ (ord_le1480771457nres_a @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_130_less__asym_H)).
76.32/24.84	thf(286,plain,((! [A:refine424419629nres_a,B:refine424419629nres_a]: ((ord_le1480771457nres_a @ A @ B) => (~ (ord_le1480771457nres_a @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7])).
76.32/24.84	thf(155,axiom,((! [A:refine424419629nres_a,B:refine424419629nres_a,C:refine424419629nres_a]: ((ord_le519537037nres_a @ A @ B) => ((ord_le519537037nres_a @ C @ A) => (ord_le519537037nres_a @ C @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_dual__order_Otrans)).
76.32/24.84	thf(875,plain,((! [A:refine424419629nres_a,B:refine424419629nres_a,C:refine424419629nres_a]: ((ord_le519537037nres_a @ A @ B) => ((ord_le519537037nres_a @ C @ A) => (ord_le519537037nres_a @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[155])).
76.32/24.84	thf(78,axiom,((! [A:set_a,B:set_a,C:(set_a > refine424419629nres_a),D:refine424419629nres_a]: ((((ord_le1480771457nres_a @ (C @ A) @ D) <= (! [E:set_a,F:set_a]: ((ord_le1480771457nres_a @ (C @ E) @ (C @ F)) <= (ord_less_set_a @ E @ F)))) <= ((C @ B) = D)) <= (ord_less_set_a @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_114_ord__less__eq__subst)).
76.32/24.84	thf(579,plain,((! [A:set_a,B:set_a,C:(set_a > refine424419629nres_a),D:refine424419629nres_a]: ((ord_less_set_a @ A @ B) => (((C @ B) = D) => ((! [E:set_a,F:set_a]: ((ord_less_set_a @ E @ F) => (ord_le1480771457nres_a @ (C @ E) @ (C @ F)))) => (ord_le1480771457nres_a @ (C @ A) @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[78])).
76.32/24.84	thf(6,axiom,((! [A:refine424419629nres_a,B:refine424419629nres_a,C:refine424419629nres_a]: (((ord_le1480771457nres_a @ B @ C) => (ord_le1480771457nres_a @ A @ C)) <= (A = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_136_ord__eq__less__trans)).
76.32/24.84	thf(281,plain,((! [A:refine424419629nres_a,B:refine424419629nres_a,C:refine424419629nres_a]: ((A = B) => ((ord_le1480771457nres_a @ B @ C) => (ord_le1480771457nres_a @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6])).
76.32/24.84	thf(29,axiom,((! [A:set_a,B:set_a]: (((~ (ord_less_set_a @ A @ B)) = (A = B)) <= (ord_less_eq_set_a @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_195_antisym__conv2)).
76.32/24.84	thf(382,plain,((! [A:set_a,B:set_a]: ((ord_less_eq_set_a @ A @ B) => ((~ (ord_less_set_a @ A @ B)) = (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[29])).
76.32/24.84	thf(76,axiom,((! [A:refine424419629nres_a,B:refine424419629nres_a]: ((ord_le519537037nres_a @ A @ B) <= (ord_le1480771457nres_a @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_order_Ostrict__implies__order)).
76.32/24.84	thf(572,plain,((! [A:refine424419629nres_a,B:refine424419629nres_a]: ((ord_le1480771457nres_a @ A @ B) => (ord_le519537037nres_a @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[76])).
76.32/24.84	thf(250,axiom,((! [A:produc1609974940nres_a]: ((! [B:refine424419629nres_a]: (A != (produc1136923598nres_a @ B @ refine464223677AILi_a))) => ((~ (! [B:set_a,C:set_a]: (A != (produc1136923598nres_a @ (refine1198353288_RES_a @ B) @ (refine1198353288_RES_a @ C))))) <= (! [B:set_a]: (A != (produc1136923598nres_a @ refine464223677AILi_a @ (refine1198353288_RES_a @ B)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_sup__nres_Ocases)).
76.32/24.84	thf(1371,plain,((! [A:produc1609974940nres_a]: ((! [B:refine424419629nres_a]: ~ (A = (produc1136923598nres_a @ B @ refine464223677AILi_a))) => ((! [B:set_a]: ~ (A = (produc1136923598nres_a @ refine464223677AILi_a @ (refine1198353288_RES_a @ B)))) => (~ (! [B:set_a,C:set_a]: ~ (A = (produc1136923598nres_a @ (refine1198353288_RES_a @ B) @ (refine1198353288_RES_a @ C))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[250])).
76.32/24.84	thf(129,axiom,((! [A:a,B:a]: (((refine2063221604TURN_a @ A) = (refine2063221604TURN_a @ B)) = (A = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_nres__more__simps_I6_J)).
76.32/24.84	thf(787,plain,((! [A:a,B:a]: (((refine2063221604TURN_a @ A) = (refine2063221604TURN_a @ B)) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[129])).
76.32/24.84	thf(216,axiom,((! [A:set_a,B:set_a]: (((ord_less_set_a @ A @ B) <= (ord_less_eq_set_a @ A @ B)) <= (A != B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_order_Onot__eq__order__implies__strict)).
76.32/24.84	thf(1107,plain,((! [A:set_a,B:set_a]: ((~ (A = B)) => ((ord_less_eq_set_a @ A @ B) => (ord_less_set_a @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[216])).
76.32/24.84	thf(211,axiom,((! [A:set_a,B:set_a]: ((ord_less_eq_set_a @ A @ B) <= (A = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_229_equalityD1)).
76.32/24.84	thf(1090,plain,((! [A:set_a,B:set_a]: ((A = B) => (ord_less_eq_set_a @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[211])).
76.32/24.84	thf(136,axiom,((! [A:set_a,B:set_a,C:set_a]: ((ord_less_eq_set_a @ A @ B) => ((ord_less_set_a @ C @ B) <= (ord_less_set_a @ C @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_215_dual__order_Ostrict__trans1)).
76.32/24.84	thf(804,plain,((! [A:set_a,B:set_a,C:set_a]: ((ord_less_eq_set_a @ A @ B) => ((ord_less_set_a @ C @ A) => (ord_less_set_a @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[136])).
76.32/24.84	thf(232,axiom,((! [A:refine424419629nres_a,B:refine424419629nres_a]: (((accp_P624619091nres_a @ refine1048213316_rel_a @ (produc1136923598nres_a @ A @ B)) => ((! [C:set_a]: ((! [D:set_a]: (((ord_less_eq_set_a @ C @ D) <= (accp_P624619091nres_a @ refine1048213316_rel_a @ (produc1136923598nres_a @ (refine1198353288_RES_a @ C) @ (refine1198353288_RES_a @ D)))) <= (B = (refine1198353288_RES_a @ D)))) <= (A = (refine1198353288_RES_a @ C)))) => (~ ((! [C:set_a]: ((B = (refine1198353288_RES_a @ C)) => (~ (accp_P624619091nres_a @ refine1048213316_rel_a @ (produc1136923598nres_a @ refine464223677AILi_a @ (refine1198353288_RES_a @ C)))))) <= (A = refine464223677AILi_a))))) <= (~ (ord_le519537037nres_a @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_249_less__eq__nres_Opelims_I3_J)).
76.32/24.84	thf(1258,plain,((! [A:refine424419629nres_a,B:refine424419629nres_a]: ((~ (ord_le519537037nres_a @ A @ B)) => ((accp_P624619091nres_a @ (refine1048213316_rel_a) @ (produc1136923598nres_a @ A @ B)) => ((! [C:set_a]: ((A = (refine1198353288_RES_a @ C)) => (! [D:set_a]: ((B = (refine1198353288_RES_a @ D)) => ((accp_P624619091nres_a @ (refine1048213316_rel_a) @ (produc1136923598nres_a @ (refine1198353288_RES_a @ C) @ (refine1198353288_RES_a @ D))) => (ord_less_eq_set_a @ C @ D)))))) => (~ ((A = refine464223677AILi_a) => (! [C:set_a]: ((B = (refine1198353288_RES_a @ C)) => (~ (accp_P624619091nres_a @ (refine1048213316_rel_a) @ (produc1136923598nres_a @ refine464223677AILi_a @ (refine1198353288_RES_a @ C))))))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[232])).
76.32/24.84	thf(66,axiom,((bNF_Ca459084161nres_a = (^ [A:set_Pr384614482nres_a,B:(refine424419629nres_a > refine424419629nres_a)]: ! [C:refine424419629nres_a,D:refine424419629nres_a]: ((member1468928819nres_a @ (produc1136923598nres_a @ C @ D) @ A) => (ord_le519537037nres_a @ (B @ C) @ (B @ D)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_218_relChain__def)).
76.32/24.84	thf(539,plain,(((bNF_Ca459084161nres_a) = (^ [A:set_Pr384614482nres_a,B:(refine424419629nres_a > refine424419629nres_a)]: ! [C:refine424419629nres_a,D:refine424419629nres_a]: ((member1468928819nres_a @ (produc1136923598nres_a @ C @ D) @ A) => (ord_le519537037nres_a @ (B @ C) @ (B @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[66])).
76.32/24.84	thf(540,plain,(((bNF_Ca459084161nres_a) = (^ [A:set_Pr384614482nres_a,B:(refine424419629nres_a > refine424419629nres_a)]: ! [C:refine424419629nres_a,D:refine424419629nres_a]: ((member1468928819nres_a @ (produc1136923598nres_a @ C @ D) @ A) => (ord_le519537037nres_a @ (B @ C) @ (B @ D)))))),inference(lifteq,[status(thm)],[539])).
76.32/24.84	thf(35,axiom,((! [A:refine424419629nres_a]: ~ (ord_le1480771457nres_a @ A @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_134_less__irrefl)).
76.32/24.84	thf(406,plain,((! [A:refine424419629nres_a]: ~ (ord_le1480771457nres_a @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[35])).
76.32/24.84	thf(233,axiom,((! [A:refine424419629nres_a,B:refine424419629nres_a,C:$o]: (((ord_le519537037nres_a @ A @ B) = C) => (((~ ((A = refine464223677AILi_a) => ((C) <= (? [D:set_a]: (B = (refine1198353288_RES_a @ D)))))) <= (! [D:set_a]: ((! [E:set_a]: ((B = (refine1198353288_RES_a @ E)) => (C = (~ (ord_less_eq_set_a @ D @ E))))) <= (A = (refine1198353288_RES_a @ D))))) <= ((~ (C)) <= (B = refine464223677AILi_a)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_164_less__eq__nres_Oelims_I1_J)).
76.32/24.84	thf(1282,plain,((! [A:refine424419629nres_a,B:refine424419629nres_a,C:$o]: (((ord_le519537037nres_a @ A @ B) = C) => (((B = refine464223677AILi_a) => (~ (C))) => ((! [D:set_a]: ((A = (refine1198353288_RES_a @ D)) => (! [E:set_a]: ((B = (refine1198353288_RES_a @ E)) => (C = (~ (ord_less_eq_set_a @ D @ E))))))) => (~ ((A = refine464223677AILi_a) => ((? [D:set_a]: (B = (refine1198353288_RES_a @ D))) => (C))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[233])).
76.32/24.84	thf(220,axiom,((! [A:refine424419629nres_a,B:refine424419629nres_a,C:(refine424419629nres_a > refine424419629nres_a),D:refine424419629nres_a]: ((ord_le519537037nres_a @ A @ B) => (((C @ B) = D) => ((ord_le519537037nres_a @ (C @ A) @ D) <= (! [E:refine424419629nres_a,F:refine424419629nres_a]: ((ord_le519537037nres_a @ E @ F) => (ord_le519537037nres_a @ (C @ E) @ (C @ F))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_ord__le__eq__subst)).
76.32/24.84	thf(1117,plain,((! [A:refine424419629nres_a,B:refine424419629nres_a,C:(refine424419629nres_a > refine424419629nres_a),D:refine424419629nres_a]: ((ord_le519537037nres_a @ A @ B) => (((C @ B) = D) => ((! [E:refine424419629nres_a,F:refine424419629nres_a]: ((ord_le519537037nres_a @ E @ F) => (ord_le519537037nres_a @ (C @ E) @ (C @ F)))) => (ord_le519537037nres_a @ (C @ A) @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[220])).
76.32/24.84	thf(186,axiom,((ord_less_set_a = (^ [A:set_a,B:set_a]: ((ord_less_eq_set_a @ A @ B) & (A != B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_213_order_Ostrict__iff__order)).
76.32/24.84	thf(1011,plain,(((ord_less_set_a) = (^ [A:set_a,B:set_a]: ((ord_less_eq_set_a @ A @ B) & ~ (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[186])).
76.32/24.84	thf(118,axiom,((ord_less_set_a = (^ [A:set_a,B:set_a]: ((B != A) & (ord_less_eq_set_a @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_dual__order_Ostrict__iff__order)).
76.32/24.84	thf(736,plain,(((ord_less_set_a) = (^ [A:set_a,B:set_a]: (~ (B = A) & (ord_less_eq_set_a @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[118])).
76.32/24.84	thf(243,axiom,((! [A:set_a,B:a]: ((refine1312857699nres_a @ (refine1198353288_RES_a @ A) @ B) = (member_a @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_nf__inres__RES)).
76.32/24.84	thf(1349,plain,((! [A:set_a,B:a]: ((refine1312857699nres_a @ (refine1198353288_RES_a @ A) @ B) = (member_a @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[243])).
76.32/24.84	thf(74,axiom,((bNF_Ca953716171_set_a = (^ [A:set_Pr384614482nres_a,B:(refine424419629nres_a > set_a)]: ! [C:refine424419629nres_a,D:refine424419629nres_a]: ((ord_less_eq_set_a @ (B @ C) @ (B @ D)) <= (member1468928819nres_a @ (produc1136923598nres_a @ C @ D) @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_219_relChain__def)).
76.32/24.84	thf(567,plain,(((bNF_Ca953716171_set_a) = (^ [A:set_Pr384614482nres_a,B:(refine424419629nres_a > set_a)]: ! [C:refine424419629nres_a,D:refine424419629nres_a]: ((member1468928819nres_a @ (produc1136923598nres_a @ C @ D) @ A) => (ord_less_eq_set_a @ (B @ C) @ (B @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[74])).
76.32/24.84	thf(196,axiom,((! [A:refine424419629nres_a,B:refine424419629nres_a,C:refine424419629nres_a]: (((ord_le1480771457nres_a @ A @ C) <= (ord_le1480771457nres_a @ B @ C)) <= (ord_le519537037nres_a @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_206_order_Ostrict__trans1)).
76.32/24.84	thf(1043,plain,((! [A:refine424419629nres_a,B:refine424419629nres_a,C:refine424419629nres_a]: ((ord_le519537037nres_a @ A @ B) => ((ord_le1480771457nres_a @ B @ C) => (ord_le1480771457nres_a @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[196])).
76.32/24.84	thf(151,axiom,((! [A:set_a,B:set_a,C:set_a]: ((ord_less_set_a @ A @ B) => ((ord_less_set_a @ A @ C) <= (ord_less_set_a @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_133_less__trans)).
76.32/24.84	thf(863,plain,((! [A:set_a,B:set_a,C:set_a]: ((ord_less_set_a @ A @ B) => ((ord_less_set_a @ B @ C) => (ord_less_set_a @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[151])).
76.32/24.84	thf(737,plain,(((ord_less_set_a) = (^ [A:set_a,B:set_a]: (~ (B = A) & (ord_less_eq_set_a @ A @ B))))),inference(lifteq,[status(thm)],[736])).
76.32/24.84	thf(17,axiom,((! [A:refine424419629nres_a,B:(refine424419629nres_a > refine424419629nres_a),C:refine424419629nres_a,D:refine424419629nres_a]: (((ord_le1480771457nres_a @ C @ D) => ((ord_le1480771457nres_a @ A @ (B @ D)) <= (! [E:refine424419629nres_a,F:refine424419629nres_a]: ((ord_le1480771457nres_a @ E @ F) => (ord_le1480771457nres_a @ (B @ E) @ (B @ F)))))) <= (ord_le519537037nres_a @ A @ (B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_174_order__le__less__subst1)).
76.32/24.84	thf(318,plain,((! [A:refine424419629nres_a,B:(refine424419629nres_a > refine424419629nres_a),C:refine424419629nres_a,D:refine424419629nres_a]: ((ord_le519537037nres_a @ A @ (B @ C)) => ((ord_le1480771457nres_a @ C @ D) => ((! [E:refine424419629nres_a,F:refine424419629nres_a]: ((ord_le1480771457nres_a @ E @ F) => (ord_le1480771457nres_a @ (B @ E) @ (B @ F)))) => (ord_le1480771457nres_a @ A @ (B @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[17])).
76.32/24.84	thf(138,axiom,((! [A:refine424419629nres_a,B:refine424419629nres_a]: ((~ (ord_le1480771457nres_a @ B @ A)) <= (ord_le1480771457nres_a @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_124_order_Oasym)).
76.32/24.84	thf(811,plain,((! [A:refine424419629nres_a,B:refine424419629nres_a]: ((ord_le1480771457nres_a @ A @ B) => (~ (ord_le1480771457nres_a @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[138])).
76.32/24.84	thf(1471,plain,(((refine412683989fail_a) = (^ [A:refine424419629nres_a]: ? [B:set_a]: (A = (refine1198353288_RES_a @ B))))),inference(lifteq,[status(thm)],[1470])).
76.32/24.84	thf(552,plain,(((^ [A:refine424419629nres_a,B:refine424419629nres_a]: ((ord_le519537037nres_a @ A @ B) & (ord_le519537037nres_a @ B @ A))) = ((=) @ refine424419629nres_a))),inference(lifteq,[status(thm)],[551])).
76.32/24.84	thf(140,axiom,((! [A:set_a,B:set_a]: ((ord_less_set_a @ A @ B) => (ord_less_eq_set_a @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_197_less__imp__le)).
76.32/24.84	thf(816,plain,((! [A:set_a,B:set_a]: ((ord_less_set_a @ A @ B) => (ord_less_eq_set_a @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[140])).
76.32/24.84	thf(18,axiom,((! [A:(refine424419629nres_a > $o),B:refine424419629nres_a,C:(refine424419629nres_a > $o)]: (((! [D:refine424419629nres_a]: ((ord_le519537037nres_a @ D @ B) <= (A @ D))) => ((C @ (order_1714329108nres_a @ A)) <= (! [D:refine424419629nres_a]: ((A @ D) => ((! [E:refine424419629nres_a]: ((ord_le519537037nres_a @ E @ D) <= (A @ E))) => (C @ D)))))) <= (A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_252_GreatestI2__order)).
76.32/24.84	thf(323,plain,((! [A:(refine424419629nres_a > $o),B:refine424419629nres_a,C:(refine424419629nres_a > $o)]: ((A @ B) => ((! [D:refine424419629nres_a]: ((A @ D) => (ord_le519537037nres_a @ D @ B))) => ((! [D:refine424419629nres_a]: ((A @ D) => ((! [E:refine424419629nres_a]: ((A @ E) => (ord_le519537037nres_a @ E @ D))) => (C @ D)))) => (C @ (order_1714329108nres_a @ (A)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[18])).
76.32/24.84	thf(115,axiom,((! [A:refine424419629nres_a,B:refine424419629nres_a,C:(refine424419629nres_a > refine424419629nres_a),D:refine424419629nres_a]: ((ord_le519537037nres_a @ A @ B) => ((ord_le519537037nres_a @ (C @ B) @ D) => ((ord_le519537037nres_a @ (C @ A) @ D) <= (! [E:refine424419629nres_a,F:refine424419629nres_a]: ((ord_le519537037nres_a @ (C @ E) @ (C @ F)) <= (ord_le519537037nres_a @ E @ F)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_order__subst2)).
76.32/24.84	thf(726,plain,((! [A:refine424419629nres_a,B:refine424419629nres_a,C:(refine424419629nres_a > refine424419629nres_a),D:refine424419629nres_a]: ((ord_le519537037nres_a @ A @ B) => ((ord_le519537037nres_a @ (C @ B) @ D) => ((! [E:refine424419629nres_a,F:refine424419629nres_a]: ((ord_le519537037nres_a @ E @ F) => (ord_le519537037nres_a @ (C @ E) @ (C @ F)))) => (ord_le519537037nres_a @ (C @ A) @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[115])).
76.32/24.84	thf(108,axiom,((! [A:refine424419629nres_a,B:refine424419629nres_a,C:refine424419629nres_a]: ((ord_le1480771457nres_a @ A @ B) => ((ord_le1480771457nres_a @ B @ C) => (ord_le1480771457nres_a @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_152_order_Ostrict__trans)).
76.32/24.84	thf(700,plain,((! [A:refine424419629nres_a,B:refine424419629nres_a,C:refine424419629nres_a]: ((ord_le1480771457nres_a @ A @ B) => ((ord_le1480771457nres_a @ B @ C) => (ord_le1480771457nres_a @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[108])).
76.32/24.84	thf(193,axiom,((! [A:set_a,B:set_a]: ((ord_less_set_a @ A @ B) => (B != A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_161_dual__order_Ostrict__implies__not__eq)).
76.32/24.84	thf(1029,plain,((! [A:set_a,B:set_a]: ((ord_less_set_a @ A @ B) => (~ (B = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[193])).
76.32/24.84	thf(88,axiom,((((=) @ refine424419629nres_a) = (^ [A:refine424419629nres_a,B:refine424419629nres_a]: ((ord_le519537037nres_a @ B @ A) & (ord_le519537037nres_a @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_order__class_Oorder_Oeq__iff)).
76.32/24.84	thf(626,plain,((((=) @ refine424419629nres_a) = (^ [A:refine424419629nres_a,B:refine424419629nres_a]: ((ord_le519537037nres_a @ B @ A) & (ord_le519537037nres_a @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[88])).
76.32/24.84	thf(190,axiom,((! [A:refine424419629nres_a,B:refine424419629nres_a]: ((ord_le519537037nres_a @ A @ B) <= (ord_le1480771457nres_a @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_dual__order_Ostrict__implies__order)).
76.32/24.84	thf(1022,plain,((! [A:refine424419629nres_a,B:refine424419629nres_a]: ((ord_le1480771457nres_a @ A @ B) => (ord_le519537037nres_a @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[190])).
76.32/24.84	thf(45,axiom,((refine1001002027nres_a = (^ [A:refine424419629nres_a,B:a]: (ord_le519537037nres_a @ (refine2063221604TURN_a @ B) @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_inres__def)).
76.32/24.84	thf(462,plain,(((refine1001002027nres_a) = (^ [A:refine424419629nres_a,B:a]: (ord_le519537037nres_a @ (refine2063221604TURN_a @ B) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[45])).
76.32/24.84	thf(218,axiom,((((=) @ set_a) = (^ [A:set_a,B:set_a]: ((ord_less_eq_set_a @ B @ A) & (ord_less_eq_set_a @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_235_set__eq__subset)).
76.32/24.84	thf(1112,plain,((((=) @ set_a) = (^ [A:set_a,B:set_a]: ((ord_less_eq_set_a @ B @ A) & (ord_less_eq_set_a @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[218])).
76.32/24.84	thf(179,axiom,((! [A:set_a,B:set_a,C:set_a]: (((ord_less_eq_set_a @ B @ C) => (ord_less_eq_set_a @ A @ C)) <= (ord_less_eq_set_a @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_234_subset__trans)).
76.32/24.84	thf(983,plain,((! [A:set_a,B:set_a,C:set_a]: ((ord_less_eq_set_a @ A @ B) => ((ord_less_eq_set_a @ B @ C) => (ord_less_eq_set_a @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[179])).
76.32/24.84	thf(188,axiom,((! [A:(produc1609974940nres_a > $o),B:produc1609974940nres_a]: ((A @ B) <= (! [C:refine424419629nres_a,D:refine424419629nres_a]: (A @ (produc1136923598nres_a @ C @ D)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_104_prod__cases)).
76.32/24.84	thf(1015,plain,((! [A:(produc1609974940nres_a > $o),B:produc1609974940nres_a]: ((! [C:refine424419629nres_a,D:refine424419629nres_a]: (A @ (produc1136923598nres_a @ C @ D))) => (A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[188])).
76.32/24.84	thf(180,axiom,((! [A:refine424419629nres_a,B:refine424419629nres_a,C:refine424419629nres_a]: ((ord_le1480771457nres_a @ A @ B) => ((ord_le1480771457nres_a @ C @ B) <= (ord_le519537037nres_a @ C @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_216_dual__order_Ostrict__trans2)).
76.32/24.84	thf(986,plain,((! [A:refine424419629nres_a,B:refine424419629nres_a,C:refine424419629nres_a]: ((ord_le1480771457nres_a @ A @ B) => ((ord_le519537037nres_a @ C @ A) => (ord_le1480771457nres_a @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[180])).
76.32/24.84	thf(56,axiom,((! [A:set_a,B:set_a,C:(set_a > set_a),D:set_a]: ((((! [E:set_a,F:set_a]: ((ord_less_set_a @ E @ F) => (ord_less_set_a @ (C @ E) @ (C @ F)))) => (ord_less_set_a @ (C @ A) @ D)) <= (ord_less_set_a @ (C @ B) @ D)) <= (ord_less_set_a @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_123_order__less__subst2)).
76.32/24.84	thf(505,plain,((! [A:set_a,B:set_a,C:(set_a > set_a),D:set_a]: ((ord_less_set_a @ A @ B) => ((ord_less_set_a @ (C @ B) @ D) => ((! [E:set_a,F:set_a]: ((ord_less_set_a @ E @ F) => (ord_less_set_a @ (C @ E) @ (C @ F)))) => (ord_less_set_a @ (C @ A) @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[56])).
76.32/24.84	thf(431,plain,(! [A:a] : ((refine412683989fail_a @ (refine2063221604TURN_a @ A)))),inference(cnf,[status(esa)],[430])).
76.32/24.84	thf(167,axiom,((! [A:set_a,B:set_a,C:set_a]: ((ord_less_set_a @ A @ B) => ((ord_less_set_a @ C @ A) => (ord_less_set_a @ C @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_157_dual__order_Ostrict__trans)).
76.32/24.84	thf(922,plain,((! [A:set_a,B:set_a,C:set_a]: ((ord_less_set_a @ A @ B) => ((ord_less_set_a @ C @ A) => (ord_less_set_a @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[167])).
76.32/24.84	thf(164,axiom,((! [A:refine424419629nres_a,B:refine424419629nres_a]: ((~ (ord_le1480771457nres_a @ B @ A)) <= (ord_le1480771457nres_a @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_128_less__asym)).
76.32/24.84	thf(912,plain,((! [A:refine424419629nres_a,B:refine424419629nres_a]: ((ord_le1480771457nres_a @ A @ B) => (~ (ord_le1480771457nres_a @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[164])).
76.32/24.84	thf(104,axiom,((! [A:set_a,B:set_a,C:(set_a > set_a),D:set_a]: ((ord_less_eq_set_a @ A @ B) => (((! [E:set_a,F:set_a]: ((ord_less_eq_set_a @ (C @ E) @ (C @ F)) <= (ord_less_eq_set_a @ E @ F))) => (ord_less_eq_set_a @ (C @ A) @ D)) <= (ord_less_eq_set_a @ (C @ B) @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_order__subst2)).
76.32/24.84	thf(685,plain,((! [A:set_a,B:set_a,C:(set_a > set_a),D:set_a]: ((ord_less_eq_set_a @ A @ B) => ((ord_less_eq_set_a @ (C @ B) @ D) => ((! [E:set_a,F:set_a]: ((ord_less_eq_set_a @ E @ F) => (ord_less_eq_set_a @ (C @ E) @ (C @ F)))) => (ord_less_eq_set_a @ (C @ A) @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[104])).
76.32/24.84	thf(176,axiom,((! [A:refine424419629nres_a]: ~ (ord_le1480771457nres_a @ refine464223677AILi_a @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_less__nres_Osimps_I1_J)).
76.32/24.84	thf(959,plain,((! [A:refine424419629nres_a]: ~ (ord_le1480771457nres_a @ refine464223677AILi_a @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[176])).
76.32/24.84	thf(939,plain,(((ord_less_eq_set_a) = (^ [A:set_a,B:set_a]: ! [C:a]: ((member_a @ C @ A) => (member_a @ C @ B))))),inference(lifteq,[status(thm)],[938])).
76.32/24.84	thf(15,axiom,((ord_less_eq_set_a = (^ [A:set_a,B:set_a]: ((ord_less_set_a @ A @ B) | (A = B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_211_order_Oorder__iff__strict)).
76.32/24.84	thf(314,plain,(((ord_less_eq_set_a) = (^ [A:set_a,B:set_a]: ((ord_less_set_a @ A @ B) | (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[15])).
76.32/24.84	thf(315,plain,(((ord_less_eq_set_a) = (^ [A:set_a,B:set_a]: ((ord_less_set_a @ A @ B) | (A = B))))),inference(lifteq,[status(thm)],[314])).
76.32/24.84	thf(2171,plain,(((^ [A:set_a,B:set_a]: ((ord_less_set_a @ A @ B) | (A = B))) = (^ [A:set_a,B:set_a]: ! [C:a]: ((member_a @ C @ A) => (member_a @ C @ B))))),inference(rewrite,[status(thm)],[939,315])).
76.32/24.84	thf(228,axiom,((! [A:set_a]: ((refine1822134885_RES_a @ (refine1198353288_RES_a @ A)) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_the__RES_Osimps)).
76.32/24.84	thf(1213,plain,((! [A:set_a]: ((refine1822134885_RES_a @ (refine1198353288_RES_a @ A)) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[228])).
76.32/24.84	thf(125,axiom,((! [A:refine424419629nres_a,B:refine424419629nres_a]: (((refine412683989fail_a @ A) => ((refine412683989fail_a @ B) & ! [C:a]: ((refine1001002027nres_a @ B @ C) => (refine1001002027nres_a @ A @ C)))) => (ord_le519537037nres_a @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_pw__leI)).
76.32/24.84	thf(768,plain,((! [A:refine424419629nres_a,B:refine424419629nres_a]: (((refine412683989fail_a @ A) => ((refine412683989fail_a @ B) & ! [C:a]: ((refine1001002027nres_a @ B @ C) => (refine1001002027nres_a @ A @ C)))) => (ord_le519537037nres_a @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[125])).
76.32/24.84	thf(148,axiom,((! [A:set_a,B:set_a]: ((ord_less_set_a @ A @ B) => (A != B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_143_less__imp__not__eq)).
76.32/24.84	thf(851,plain,((! [A:set_a,B:set_a]: ((ord_less_set_a @ A @ B) => (~ (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[148])).
76.32/24.84	thf(214,axiom,((! [A:a]: ((refine1001002027nres_a @ (refine2063221604TURN_a @ A)) = ((=) @ a @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_inres__simps_I3_J)).
76.32/24.84	thf(1102,plain,((! [A:a]: ((refine1001002027nres_a @ (refine2063221604TURN_a @ A)) = ((=) @ a @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[214])).
76.32/24.84	thf(195,axiom,((! [A:refine424419629nres_a,B:refine424419629nres_a,C:(refine424419629nres_a > refine424419629nres_a),D:refine424419629nres_a]: ((((C @ B) = D) => ((! [E:refine424419629nres_a,F:refine424419629nres_a]: ((ord_le1480771457nres_a @ (C @ E) @ (C @ F)) <= (ord_le1480771457nres_a @ E @ F))) => (ord_le1480771457nres_a @ (C @ A) @ D))) <= (ord_le1480771457nres_a @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_112_ord__less__eq__subst)).
76.32/24.84	thf(1034,plain,((! [A:refine424419629nres_a,B:refine424419629nres_a,C:(refine424419629nres_a > refine424419629nres_a),D:refine424419629nres_a]: ((ord_le1480771457nres_a @ A @ B) => (((C @ B) = D) => ((! [E:refine424419629nres_a,F:refine424419629nres_a]: ((ord_le1480771457nres_a @ E @ F) => (ord_le1480771457nres_a @ (C @ E) @ (C @ F)))) => (ord_le1480771457nres_a @ (C @ A) @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[195])).
76.32/24.84	thf(51,axiom,((! [A:set_a,B:set_a,C:set_a,D:set_a]: (((ord_less_eq_set_a @ B @ C) => ((C = D) => (ord_less_eq_set_a @ A @ D))) <= (A = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_259_ord__eq__le__eq__trans)).
76.32/24.84	thf(490,plain,((! [A:set_a,B:set_a,C:set_a,D:set_a]: ((A = B) => ((ord_less_eq_set_a @ B @ C) => ((C = D) => (ord_less_eq_set_a @ A @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[51])).
76.32/24.84	thf(87,axiom,((! [A:set_a,B:set_a,C:(set_a > set_a),D:set_a]: ((ord_less_set_a @ A @ B) => (((C @ B) = D) => ((ord_less_set_a @ (C @ A) @ D) <= (! [E:set_a,F:set_a]: ((ord_less_set_a @ E @ F) => (ord_less_set_a @ (C @ E) @ (C @ F))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_115_ord__less__eq__subst)).
76.32/24.84	thf(617,plain,((! [A:set_a,B:set_a,C:(set_a > set_a),D:set_a]: ((ord_less_set_a @ A @ B) => (((C @ B) = D) => ((! [E:set_a,F:set_a]: ((ord_less_set_a @ E @ F) => (ord_less_set_a @ (C @ E) @ (C @ F)))) => (ord_less_set_a @ (C @ A) @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[87])).
76.32/24.84	thf(240,axiom,((! [A:set_a]: (ord_le1480771457nres_a @ (refine1198353288_RES_a @ A) @ refine464223677AILi_a))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_less__nres_Osimps_I2_J)).
76.32/24.84	thf(1340,plain,((! [A:set_a]: (ord_le1480771457nres_a @ (refine1198353288_RES_a @ A) @ refine464223677AILi_a))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[240])).
76.32/24.84	thf(260,axiom,((! [A:refine424419629nres_a,B:refine424419629nres_a]: (((! [C:set_a]: ((! [D:set_a]: ((ord_less_eq_set_a @ C @ D) <= (B = (refine1198353288_RES_a @ D)))) <= (A = (refine1198353288_RES_a @ C)))) => (~ ((! [C:set_a]: (B != (refine1198353288_RES_a @ C))) <= (A = refine464223677AILi_a)))) <= (~ (ord_le519537037nres_a @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_162_less__eq__nres_Oelims_I3_J)).
76.32/24.84	thf(1472,plain,((! [A:refine424419629nres_a,B:refine424419629nres_a]: ((~ (ord_le519537037nres_a @ A @ B)) => ((! [C:set_a]: ((A = (refine1198353288_RES_a @ C)) => (! [D:set_a]: ((B = (refine1198353288_RES_a @ D)) => (ord_less_eq_set_a @ C @ D))))) => (~ ((A = refine464223677AILi_a) => (! [C:set_a]: ~ (B = (refine1198353288_RES_a @ C))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[260])).
76.32/24.84	thf(69,axiom,((! [A:refine424419629nres_a,B:refine424419629nres_a]: ((ord_le1480771457nres_a @ A @ B) => (~ (ord_le1480771457nres_a @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_154_less__imp__not__less)).
76.32/24.84	thf(553,plain,((! [A:refine424419629nres_a,B:refine424419629nres_a]: ((ord_le1480771457nres_a @ A @ B) => (~ (ord_le1480771457nres_a @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[69])).
76.32/24.84	thf(63,axiom,((! [A:set_a,B:set_a,C:$o]: (((C) <= (ord_less_set_a @ B @ A)) <= (ord_less_set_a @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_149_less__imp__triv)).
76.32/24.84	thf(531,plain,((! [A:set_a,B:set_a,C:$o]: ((ord_less_set_a @ A @ B) => ((ord_less_set_a @ B @ A) => (C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[63])).
76.32/24.84	thf(173,axiom,((! [A:refine424419629nres_a,B:refine424419629nres_a,C:(refine424419629nres_a > refine424419629nres_a),D:refine424419629nres_a]: (((ord_le519537037nres_a @ (C @ B) @ D) => ((ord_le1480771457nres_a @ (C @ A) @ D) <= (! [E:refine424419629nres_a,F:refine424419629nres_a]: ((ord_le1480771457nres_a @ E @ F) => (ord_le1480771457nres_a @ (C @ E) @ (C @ F)))))) <= (ord_le1480771457nres_a @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_186_order__less__le__subst2)).
76.32/24.84	thf(944,plain,((! [A:refine424419629nres_a,B:refine424419629nres_a,C:(refine424419629nres_a > refine424419629nres_a),D:refine424419629nres_a]: ((ord_le1480771457nres_a @ A @ B) => ((ord_le519537037nres_a @ (C @ B) @ D) => ((! [E:refine424419629nres_a,F:refine424419629nres_a]: ((ord_le1480771457nres_a @ E @ F) => (ord_le1480771457nres_a @ (C @ E) @ (C @ F)))) => (ord_le1480771457nres_a @ (C @ A) @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[173])).
76.32/24.84	thf(132,axiom,((! [A:refine424419629nres_a,B:refine424419629nres_a]: ((ord_le519537037nres_a @ A @ B) => (~ (ord_le1480771457nres_a @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_168_leD)).
76.32/24.84	thf(795,plain,((! [A:refine424419629nres_a,B:refine424419629nres_a]: ((ord_le519537037nres_a @ A @ B) => (~ (ord_le1480771457nres_a @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[132])).
76.32/24.84	thf(102,axiom,((! [A:set_a]: ~ (ord_less_set_a @ A @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_135_less__irrefl)).
76.32/24.84	thf(680,plain,((! [A:set_a]: ~ (ord_less_set_a @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[102])).
76.32/24.84	thf(127,axiom,((! [A:(set_a > $o),B:set_a]: ((A @ B) => (((order_Greatest_set_a @ A) = B) <= (! [C:set_a]: ((A @ C) => (ord_less_eq_set_a @ C @ B))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_255_Greatest__equality)).
76.32/24.84	thf(776,plain,((! [A:(set_a > $o),B:set_a]: ((A @ B) => ((! [C:set_a]: ((A @ C) => (ord_less_eq_set_a @ C @ B))) => ((order_Greatest_set_a @ (A)) = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[127])).
76.32/24.84	thf(149,axiom,((! [A:set_a,B:set_a,C:(set_a > refine424419629nres_a),D:refine424419629nres_a]: ((ord_less_set_a @ A @ B) => (((! [E:set_a,F:set_a]: ((ord_le1480771457nres_a @ (C @ E) @ (C @ F)) <= (ord_less_set_a @ E @ F))) => (ord_le1480771457nres_a @ (C @ A) @ D)) <= (ord_le519537037nres_a @ (C @ B) @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_187_order__less__le__subst2)).
76.32/24.84	thf(855,plain,((! [A:set_a,B:set_a,C:(set_a > refine424419629nres_a),D:refine424419629nres_a]: ((ord_less_set_a @ A @ B) => ((ord_le519537037nres_a @ (C @ B) @ D) => ((! [E:set_a,F:set_a]: ((ord_less_set_a @ E @ F) => (ord_le1480771457nres_a @ (C @ E) @ (C @ F)))) => (ord_le1480771457nres_a @ (C @ A) @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[149])).
76.32/24.84	thf(105,axiom,((! [A:set_a,B:set_a,C:set_a]: ((ord_less_eq_set_a @ A @ B) => ((ord_less_eq_set_a @ C @ B) <= (ord_less_eq_set_a @ C @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_dual__order_Otrans)).
76.32/24.84	thf(690,plain,((! [A:set_a,B:set_a,C:set_a]: ((ord_less_eq_set_a @ A @ B) => ((ord_less_eq_set_a @ C @ A) => (ord_less_eq_set_a @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[105])).
76.32/24.84	thf(175,axiom,((! [A:refine424419629nres_a,B:(refine424419629nres_a > refine424419629nres_a),C:refine424419629nres_a,D:refine424419629nres_a]: ((((! [E:refine424419629nres_a,F:refine424419629nres_a]: ((ord_le1480771457nres_a @ (B @ E) @ (B @ F)) <= (ord_le1480771457nres_a @ E @ F))) => (ord_le1480771457nres_a @ A @ (B @ D))) <= (ord_le1480771457nres_a @ C @ D)) <= (ord_le1480771457nres_a @ A @ (B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_116_order__less__subst1)).
76.32/24.84	thf(954,plain,((! [A:refine424419629nres_a,B:(refine424419629nres_a > refine424419629nres_a),C:refine424419629nres_a,D:refine424419629nres_a]: ((ord_le1480771457nres_a @ A @ (B @ C)) => ((ord_le1480771457nres_a @ C @ D) => ((! [E:refine424419629nres_a,F:refine424419629nres_a]: ((ord_le1480771457nres_a @ E @ F) => (ord_le1480771457nres_a @ (B @ E) @ (B @ F)))) => (ord_le1480771457nres_a @ A @ (B @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[175])).
76.32/24.84	thf(249,axiom,((! [A:set_a,B:set_a]: ((ord_le519537037nres_a @ (refine1198353288_RES_a @ A) @ (refine1198353288_RES_a @ B)) = (ord_less_eq_set_a @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_nres__order__simps_I5_J)).
76.32/24.84	thf(1368,plain,((! [A:set_a,B:set_a]: ((ord_le519537037nres_a @ (refine1198353288_RES_a @ A) @ (refine1198353288_RES_a @ B)) = (ord_less_eq_set_a @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[249])).
76.32/24.84	thf(36,axiom,((! [A:set_a,B:set_a]: ((A = B) => (~ ((~ (ord_less_eq_set_a @ B @ A)) <= (ord_less_eq_set_a @ A @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_227_equalityE)).
76.32/24.84	thf(409,plain,((! [A:set_a,B:set_a]: ((A = B) => (~ ((ord_less_eq_set_a @ A @ B) => (~ (ord_less_eq_set_a @ B @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[36])).
76.32/24.84	thf(112,axiom,((! [A:set_a,B:set_a]: ((~ (ord_less_set_a @ B @ A)) <= (ord_less_set_a @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_131_less__asym_H)).
76.32/24.84	thf(712,plain,((! [A:set_a,B:set_a]: ((ord_less_set_a @ A @ B) => (~ (ord_less_set_a @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[112])).
76.32/24.84	thf(184,axiom,((! [A:set_a,B:set_a]: (((ord_less_eq_set_a @ A @ B) = (A = B)) <= (~ (ord_less_set_a @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_193_antisym__conv1)).
76.32/24.84	thf(1003,plain,((! [A:set_a,B:set_a]: ((~ (ord_less_set_a @ A @ B)) => ((ord_less_eq_set_a @ A @ B) = (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[184])).
76.32/24.84	thf(206,axiom,((! [A:refine424419629nres_a,B:refine424419629nres_a]: ((ord_le1480771457nres_a @ A @ B) => (~ (ord_le1480771457nres_a @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_144_less__not__sym)).
76.32/24.84	thf(1070,plain,((! [A:refine424419629nres_a,B:refine424419629nres_a]: ((ord_le1480771457nres_a @ A @ B) => (~ (ord_le1480771457nres_a @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[206])).
76.32/24.84	thf(153,axiom,((ord_less_set_a = (^ [A:set_a,B:set_a]: ((ord_less_eq_set_a @ A @ B) & (A != B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_173_less__le)).
76.32/24.84	thf(871,plain,(((ord_less_set_a) = (^ [A:set_a,B:set_a]: ((ord_less_eq_set_a @ A @ B) & ~ (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[153])).
76.32/24.84	thf(872,plain,(((ord_less_set_a) = (^ [A:set_a,B:set_a]: ((ord_less_eq_set_a @ A @ B) & ~ (A = B))))),inference(lifteq,[status(thm)],[871])).
76.32/24.84	thf(199,axiom,((ord_le1480771457nres_a = (^ [A:refine424419629nres_a,B:refine424419629nres_a]: (~ (ord_le519537037nres_a @ B @ A) & (ord_le519537037nres_a @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_204_less__le__not__le)).
76.32/24.84	thf(1052,plain,(((ord_le1480771457nres_a) = (^ [A:refine424419629nres_a,B:refine424419629nres_a]: (~ (ord_le519537037nres_a @ B @ A) & (ord_le519537037nres_a @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[199])).
76.32/24.84	thf(1053,plain,(((ord_le1480771457nres_a) = (^ [A:refine424419629nres_a,B:refine424419629nres_a]: (~ (ord_le519537037nres_a @ B @ A) & (ord_le519537037nres_a @ A @ B))))),inference(lifteq,[status(thm)],[1052])).
76.32/24.84	thf(100,axiom,((! [A:set_a,B:set_a]: (((ord_less_set_a @ A @ B) | (A = B)) <= (ord_less_eq_set_a @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_203_le__imp__less__or__eq)).
76.32/24.84	thf(673,plain,((! [A:set_a,B:set_a]: ((ord_less_eq_set_a @ A @ B) => ((ord_less_set_a @ A @ B) | (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[100])).
76.32/24.84	thf(257,axiom,((! [A:refine424419629nres_a,B:refine424419629nres_a]: (((accp_P624619091nres_a @ refine260105272_rel_a @ (produc1136923598nres_a @ A @ B)) => (((~ (accp_P624619091nres_a @ refine260105272_rel_a @ (produc1136923598nres_a @ refine464223677AILi_a @ B))) <= (A = refine464223677AILi_a)) => (~ (! [C:set_a]: ((! [D:set_a]: (((ord_less_set_a @ C @ D) <= (accp_P624619091nres_a @ refine260105272_rel_a @ (produc1136923598nres_a @ (refine1198353288_RES_a @ C) @ (refine1198353288_RES_a @ D)))) <= (B = (refine1198353288_RES_a @ D)))) <= (A = (refine1198353288_RES_a @ C))))))) <= (~ (ord_le1480771457nres_a @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_248_less__nres_Opelims_I3_J)).
76.32/24.84	thf(1452,plain,((! [A:refine424419629nres_a,B:refine424419629nres_a]: ((~ (ord_le1480771457nres_a @ A @ B)) => ((accp_P624619091nres_a @ (refine260105272_rel_a) @ (produc1136923598nres_a @ A @ B)) => (((A = refine464223677AILi_a) => (~ (accp_P624619091nres_a @ (refine260105272_rel_a) @ (produc1136923598nres_a @ refine464223677AILi_a @ B)))) => (~ (! [C:set_a]: ((A = (refine1198353288_RES_a @ C)) => (! [D:set_a]: ((B = (refine1198353288_RES_a @ D)) => ((accp_P624619091nres_a @ (refine260105272_rel_a) @ (produc1136923598nres_a @ (refine1198353288_RES_a @ C) @ (refine1198353288_RES_a @ D))) => (ord_less_set_a @ C @ D)))))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[257])).
76.32/24.84	thf(41,axiom,((! [A:refine424419629nres_a,B:(refine424419629nres_a > refine424419629nres_a),C:refine424419629nres_a,D:refine424419629nres_a]: ((A = (B @ C)) => (((! [E:refine424419629nres_a,F:refine424419629nres_a]: ((ord_le519537037nres_a @ E @ F) => (ord_le519537037nres_a @ (B @ E) @ (B @ F)))) => (ord_le519537037nres_a @ A @ (B @ D))) <= (ord_le519537037nres_a @ C @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_ord__eq__le__subst)).
76.32/24.84	thf(441,plain,((! [A:refine424419629nres_a,B:(refine424419629nres_a > refine424419629nres_a),C:refine424419629nres_a,D:refine424419629nres_a]: ((A = (B @ C)) => ((ord_le519537037nres_a @ C @ D) => ((! [E:refine424419629nres_a,F:refine424419629nres_a]: ((ord_le519537037nres_a @ E @ F) => (ord_le519537037nres_a @ (B @ E) @ (B @ F)))) => (ord_le519537037nres_a @ A @ (B @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[41])).
76.32/24.84	thf(463,plain,(((refine1001002027nres_a) = (^ [A:refine424419629nres_a,B:a]: (ord_le519537037nres_a @ (refine2063221604TURN_a @ B) @ A)))),inference(lifteq,[status(thm)],[462])).
76.32/24.84	thf(234,axiom,((! [A:(refine424419629nres_a > (refine424419629nres_a > $o)),B:refine424419629nres_a,C:refine424419629nres_a]: ((! [D:refine424419629nres_a]: (A @ D @ refine464223677AILi_a)) => (((A @ B @ C) <= (! [D:set_a]: (A @ refine464223677AILi_a @ (refine1198353288_RES_a @ D)))) <= (! [D:set_a,E:set_a]: (A @ (refine1198353288_RES_a @ D) @ (refine1198353288_RES_a @ E))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_less__eq__nres_Oinduct)).
76.32/24.84	thf(1317,plain,((! [A:(refine424419629nres_a > (refine424419629nres_a > $o)),B:refine424419629nres_a,C:refine424419629nres_a]: ((! [D:refine424419629nres_a]: (A @ D @ refine464223677AILi_a)) => ((! [D:set_a,E:set_a]: (A @ (refine1198353288_RES_a @ D) @ (refine1198353288_RES_a @ E))) => ((! [D:set_a]: (A @ refine464223677AILi_a @ (refine1198353288_RES_a @ D))) => (A @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[234])).
76.32/24.84	thf(48,axiom,((! [A:refine424419629nres_a,B:refine424419629nres_a]: (((ord_le519537037nres_a @ B @ A) <= (! [C:a]: (((refine1001002027nres_a @ A @ C) <= (refine1001002027nres_a @ B @ C)) <= (refine412683989fail_a @ A)))) <= ((refine412683989fail_a @ B) <= (refine412683989fail_a @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_pw__leI_H)).
76.32/24.84	thf(470,plain,((! [A:refine424419629nres_a,B:refine424419629nres_a]: (((refine412683989fail_a @ A) => (refine412683989fail_a @ B)) => ((! [C:a]: ((refine412683989fail_a @ A) => ((refine1001002027nres_a @ B @ C) => (refine1001002027nres_a @ A @ C)))) => (ord_le519537037nres_a @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[48])).
76.32/24.84	thf(230,axiom,((! [A:refine424419629nres_a,B:refine424419629nres_a,C:$o]: (((((? [D:set_a]: (A = (refine1198353288_RES_a @ D))) => ((~ (C)) <= (B = refine464223677AILi_a))) => (~ (! [D:set_a]: ((! [E:set_a]: ((B = (refine1198353288_RES_a @ E)) => (C = (~ (ord_less_set_a @ D @ E))))) <= (A = (refine1198353288_RES_a @ D)))))) <= ((C) <= (A = refine464223677AILi_a))) <= ((ord_le1480771457nres_a @ A @ B) = C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_167_less__nres_Oelims_I1_J)).
76.32/24.84	thf(1220,plain,((! [A:refine424419629nres_a,B:refine424419629nres_a,C:$o]: (((ord_le1480771457nres_a @ A @ B) = C) => (((A = refine464223677AILi_a) => (C)) => (((? [D:set_a]: (A = (refine1198353288_RES_a @ D))) => ((B = refine464223677AILi_a) => (~ (C)))) => (~ (! [D:set_a]: ((A = (refine1198353288_RES_a @ D)) => (! [E:set_a]: ((B = (refine1198353288_RES_a @ E)) => (C = (~ (ord_less_set_a @ D @ E))))))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[230])).
76.32/24.84	thf(1256,plain,((~ (? [A:set_a]: (ord_le519537037nres_a @ refine464223677AILi_a @ (refine1198353288_RES_a @ A))))),inference(miniscope,[status(thm)],[1255])).
76.32/24.84	thf(1257,plain,(! [A:set_a] : ((~ (ord_le519537037nres_a @ refine464223677AILi_a @ (refine1198353288_RES_a @ A))))),inference(cnf,[status(esa)],[1256])).
76.32/24.84	thf(109,axiom,((! [A:refine424419629nres_a]: ~ (ord_le1480771457nres_a @ A @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_150_dual__order_Oirrefl)).
76.32/24.84	thf(703,plain,((! [A:refine424419629nres_a]: ~ (ord_le1480771457nres_a @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[109])).
76.32/24.84	thf(265,axiom,((! [A:set_a]: ((collect_a @ (^ [B:a]: (member_a @ B @ A))) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_Collect__mem__eq)).
76.32/24.84	thf(1536,plain,((! [A:set_a]: ((collect_a @ (^ [B:a]: (member_a @ B @ A))) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[265])).
76.32/24.84	thf(95,axiom,((! [A:set_a,B:set_a,C:set_a]: (((ord_less_set_a @ B @ C) => (ord_less_set_a @ A @ C)) <= (ord_less_eq_set_a @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_199_le__less__trans)).
76.32/24.84	thf(656,plain,((! [A:set_a,B:set_a,C:set_a]: ((ord_less_eq_set_a @ A @ B) => ((ord_less_set_a @ B @ C) => (ord_less_set_a @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[95])).
76.32/24.84	thf(81,axiom,((! [A:set_a,B:set_a,C:set_a]: ((ord_less_eq_set_a @ A @ B) => ((ord_less_set_a @ A @ C) <= (ord_less_set_a @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_244_subset__psubset__trans)).
76.32/24.84	thf(600,plain,((! [A:set_a,B:set_a,C:set_a]: ((ord_less_eq_set_a @ A @ B) => ((ord_less_set_a @ B @ C) => (ord_less_set_a @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[81])).
76.32/24.84	thf(1111,plain,(((ord_less_eq_set_a) = (^ [A:set_a,B:set_a]: ((A = B) | (ord_less_set_a @ A @ B))))),inference(lifteq,[status(thm)],[1110])).
76.32/24.84	thf(1745,plain,(((^ [A:set_a,B:set_a]: ((ord_less_set_a @ A @ B) | (A = B))) = (^ [A:set_a,B:set_a]: ((A = B) | (ord_less_set_a @ A @ B))))),inference(rewrite,[status(thm)],[1111,315])).
76.32/24.84	thf(535,plain,(((ord_less_eq_set_a) = (^ [A:set_a,B:set_a]: ((B = A) | (ord_less_set_a @ A @ B))))),inference(lifteq,[status(thm)],[534])).
76.32/24.84	thf(1561,plain,(((^ [A:set_a,B:set_a]: ((ord_less_set_a @ A @ B) | (A = B))) = (^ [A:set_a,B:set_a]: ((B = A) | (ord_less_set_a @ A @ B))))),inference(rewrite,[status(thm)],[535,315])).
76.32/24.84	thf(1748,plain,(((^ [A:set_a,B:set_a]: ((A = B) | (ord_less_set_a @ A @ B))) = (^ [A:set_a,B:set_a]: ((B = A) | (ord_less_set_a @ A @ B)))) | ((^ [A:set_a,B:set_a]: ((ord_less_set_a @ A @ B) | (A = B))) != (^ [A:set_a,B:set_a]: ((ord_less_set_a @ A @ B) | (A = B))))),inference(paramod_ordered,[status(thm)],[1745,1561])).
76.32/24.84	thf(1749,plain,(((^ [A:set_a,B:set_a]: ((A = B) | (ord_less_set_a @ A @ B))) = (^ [A:set_a,B:set_a]: ((B = A) | (ord_less_set_a @ A @ B))))),inference(pattern_uni,[status(thm)],[1748:[]])).
76.32/24.84	thf(212,axiom,((! [A:set_a,B:set_a,C:set_a]: ((A = B) => ((ord_less_eq_set_a @ B @ C) => (ord_less_eq_set_a @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_ord__eq__le__trans)).
76.32/24.84	thf(1094,plain,((! [A:set_a,B:set_a,C:set_a]: ((A = B) => ((ord_less_eq_set_a @ B @ C) => (ord_less_eq_set_a @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[212])).
76.32/24.84	thf(85,axiom,((! [A:refine424419629nres_a,B:refine424419629nres_a,C:refine424419629nres_a]: ((ord_le519537037nres_a @ A @ B) => ((ord_le519537037nres_a @ B @ C) => (ord_le519537037nres_a @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_order_Otrans)).
76.32/24.84	thf(612,plain,((! [A:refine424419629nres_a,B:refine424419629nres_a,C:refine424419629nres_a]: ((ord_le519537037nres_a @ A @ B) => ((ord_le519537037nres_a @ B @ C) => (ord_le519537037nres_a @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[85])).
76.32/24.84	thf(53,axiom,((! [A:set_a,B:set_a,C:set_a]: (((ord_less_set_a @ A @ C) <= (ord_less_set_a @ B @ C)) <= (ord_less_set_a @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_153_order_Ostrict__trans)).
76.32/24.84	thf(497,plain,((! [A:set_a,B:set_a,C:set_a]: ((ord_less_set_a @ A @ B) => ((ord_less_set_a @ B @ C) => (ord_less_set_a @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[53])).
76.32/24.84	thf(627,plain,(((^ [A:refine424419629nres_a,B:refine424419629nres_a]: ((ord_le519537037nres_a @ B @ A) & (ord_le519537037nres_a @ A @ B))) = ((=) @ refine424419629nres_a))),inference(lifteq,[status(thm)],[626])).
76.32/24.84	thf(42,axiom,((! [A:set_a,B:set_a]: ((ord_less_set_a @ A @ B) => (~ (ord_less_set_a @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_141_dual__order_Oasym)).
76.32/24.84	thf(450,plain,((! [A:set_a,B:set_a]: ((ord_less_set_a @ A @ B) => (~ (ord_less_set_a @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[42])).
76.32/24.84	thf(61,axiom,((! [A:set_a,B:set_a,C:set_a]: (((B = C) => (ord_less_set_a @ A @ C)) <= (ord_less_set_a @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_139_ord__less__eq__trans)).
76.32/24.84	thf(524,plain,((! [A:set_a,B:set_a,C:set_a]: ((ord_less_set_a @ A @ B) => ((B = C) => (ord_less_set_a @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[61])).
76.32/24.84	thf(52,axiom,((! [A:set_a,B:set_a]: ((ord_less_eq_set_a @ A @ B) => (~ (ord_less_set_a @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_169_leD)).
76.32/24.84	thf(495,plain,((! [A:set_a,B:set_a]: ((ord_less_eq_set_a @ A @ B) => (~ (ord_less_set_a @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[52])).
76.32/24.84	thf(229,axiom,((! [A:(a > $o),B:(a > $o)]: ((ord_less_eq_set_a @ (collect_a @ A) @ (collect_a @ B)) <= (! [C:a]: ((A @ C) => (B @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_233_Collect__mono)).
76.32/24.84	thf(1216,plain,((! [A:(a > $o),B:(a > $o)]: ((! [C:a]: ((A @ C) => (B @ C))) => (ord_less_eq_set_a @ (collect_a @ (A)) @ (collect_a @ (B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[229])).
76.32/24.84	thf(221,axiom,((! [A:set_a,B:(set_a > set_a),C:set_a,D:set_a]: ((((! [E:set_a,F:set_a]: ((ord_less_eq_set_a @ (B @ E) @ (B @ F)) <= (ord_less_eq_set_a @ E @ F))) => (ord_less_eq_set_a @ A @ (B @ D))) <= (ord_less_eq_set_a @ C @ D)) <= (A = (B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_ord__eq__le__subst)).
76.32/24.84	thf(1126,plain,((! [A:set_a,B:(set_a > set_a),C:set_a,D:set_a]: ((A = (B @ C)) => ((ord_less_eq_set_a @ C @ D) => ((! [E:set_a,F:set_a]: ((ord_less_eq_set_a @ E @ F) => (ord_less_eq_set_a @ (B @ E) @ (B @ F)))) => (ord_less_eq_set_a @ A @ (B @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[221])).
76.32/24.84	thf(79,axiom,((! [A:set_a,B:(set_a > set_a),C:set_a,D:set_a]: ((A = (B @ C)) => (((! [E:set_a,F:set_a]: ((ord_less_set_a @ E @ F) => (ord_less_set_a @ (B @ E) @ (B @ F)))) => (ord_less_set_a @ A @ (B @ D))) <= (ord_less_set_a @ C @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_111_ord__eq__less__subst)).
76.32/24.84	thf(588,plain,((! [A:set_a,B:(set_a > set_a),C:set_a,D:set_a]: ((A = (B @ C)) => ((ord_less_set_a @ C @ D) => ((! [E:set_a,F:set_a]: ((ord_less_set_a @ E @ F) => (ord_less_set_a @ (B @ E) @ (B @ F)))) => (ord_less_set_a @ A @ (B @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[79])).
76.32/24.84	thf(59,axiom,((! [A:refine424419629nres_a,B:refine424419629nres_a,C:refine424419629nres_a]: ((ord_le1480771457nres_a @ A @ B) => ((B = C) => (ord_le1480771457nres_a @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_138_ord__less__eq__trans)).
76.32/24.84	thf(517,plain,((! [A:refine424419629nres_a,B:refine424419629nres_a,C:refine424419629nres_a]: ((ord_le1480771457nres_a @ A @ B) => ((B = C) => (ord_le1480771457nres_a @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[59])).
76.32/24.84	thf(122,axiom,((! [A:refine424419629nres_a,B:refine424419629nres_a,C:(refine424419629nres_a > set_a),D:set_a]: ((ord_le1480771457nres_a @ A @ B) => (((C @ B) = D) => ((! [E:refine424419629nres_a,F:refine424419629nres_a]: ((ord_less_set_a @ (C @ E) @ (C @ F)) <= (ord_le1480771457nres_a @ E @ F))) => (ord_less_set_a @ (C @ A) @ D)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_113_ord__less__eq__subst)).
76.32/24.84	thf(748,plain,((! [A:refine424419629nres_a,B:refine424419629nres_a,C:(refine424419629nres_a > set_a),D:set_a]: ((ord_le1480771457nres_a @ A @ B) => (((C @ B) = D) => ((! [E:refine424419629nres_a,F:refine424419629nres_a]: ((ord_le1480771457nres_a @ E @ F) => (ord_less_set_a @ (C @ E) @ (C @ F)))) => (ord_less_set_a @ (C @ A) @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[122])).
76.32/24.84	thf(12,axiom,((! [A:set_a,B:set_a,C:set_a,D:set_a,E:$o]: (((ord_less_eq_set_a @ (if_set_a @ E @ A @ C) @ (if_set_a @ E @ B @ D)) <= (ord_less_eq_set_a @ C @ D)) <= (ord_less_eq_set_a @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_102_order__mono__setup_Omono__if)).
76.32/24.84	thf(304,plain,((! [A:set_a,B:set_a,C:set_a,D:set_a,E:$o]: ((ord_less_eq_set_a @ A @ B) => ((ord_less_eq_set_a @ C @ D) => (ord_less_eq_set_a @ (if_set_a @ E @ A @ C) @ (if_set_a @ E @ B @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[12])).
76.32/24.84	thf(203,axiom,((! [A:refine424419629nres_a,B:refine424419629nres_a,C:refine424419629nres_a]: (((ord_le519537037nres_a @ B @ C) => (ord_le1480771457nres_a @ A @ C)) <= (ord_le1480771457nres_a @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_208_order_Ostrict__trans2)).
76.32/24.84	thf(1062,plain,((! [A:refine424419629nres_a,B:refine424419629nres_a,C:refine424419629nres_a]: ((ord_le1480771457nres_a @ A @ B) => ((ord_le519537037nres_a @ B @ C) => (ord_le1480771457nres_a @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[203])).
76.32/24.84	thf(32,axiom,((! [A:set_a,B:set_a,C:(set_a > set_a),D:set_a]: ((ord_less_eq_set_a @ A @ B) => ((ord_less_set_a @ (C @ B) @ D) => ((ord_less_set_a @ (C @ A) @ D) <= (! [E:set_a,F:set_a]: ((ord_less_eq_set_a @ (C @ E) @ (C @ F)) <= (ord_less_eq_set_a @ E @ F)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_181_order__le__less__subst2)).
76.32/24.84	thf(390,plain,((! [A:set_a,B:set_a,C:(set_a > set_a),D:set_a]: ((ord_less_eq_set_a @ A @ B) => ((ord_less_set_a @ (C @ B) @ D) => ((! [E:set_a,F:set_a]: ((ord_less_eq_set_a @ E @ F) => (ord_less_eq_set_a @ (C @ E) @ (C @ F)))) => (ord_less_set_a @ (C @ A) @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[32])).
76.32/24.84	thf(116,axiom,((! [A:set_a]: (ord_less_eq_set_a @ A @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_dual__order_Orefl)).
76.32/24.84	thf(731,plain,((! [A:set_a]: (ord_less_eq_set_a @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[116])).
76.32/24.84	thf(960,plain,((~ (? [A:refine424419629nres_a]: (ord_le1480771457nres_a @ refine464223677AILi_a @ A)))),inference(miniscope,[status(thm)],[959])).
76.32/24.84	thf(961,plain,(! [A:refine424419629nres_a] : ((~ (ord_le1480771457nres_a @ refine464223677AILi_a @ A)))),inference(cnf,[status(esa)],[960])).
76.32/24.84	thf(139,axiom,((! [A:refine424419629nres_a,B:refine424419629nres_a,C:$o]: ((ord_le1480771457nres_a @ A @ B) => ((ord_le1480771457nres_a @ B @ A) => (C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_148_less__imp__triv)).
76.32/24.84	thf(813,plain,((! [A:refine424419629nres_a,B:refine424419629nres_a,C:$o]: ((ord_le1480771457nres_a @ A @ B) => ((ord_le1480771457nres_a @ B @ A) => (C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[139])).
76.32/24.84	thf(165,axiom,((! [A:refine424419629nres_a,B:refine424419629nres_a,C:a]: ((ord_le519537037nres_a @ A @ B) => ((refine1001002027nres_a @ B @ C) <= (refine1001002027nres_a @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_pwD2)).
76.32/24.84	thf(914,plain,((! [A:refine424419629nres_a,B:refine424419629nres_a,C:a]: ((ord_le519537037nres_a @ A @ B) => ((refine1001002027nres_a @ A @ C) => (refine1001002027nres_a @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[165])).
76.32/24.84	thf(57,axiom,((ord_le1480771457nres_a = (^ [A:refine424419629nres_a,B:refine424419629nres_a]: ((ord_le519537037nres_a @ A @ B) & (A != B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_172_less__le)).
76.32/24.84	thf(510,plain,(((ord_le1480771457nres_a) = (^ [A:refine424419629nres_a,B:refine424419629nres_a]: ((ord_le519537037nres_a @ A @ B) & ~ (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[57])).
76.32/24.84	thf(2460,plain,(! [C:set_Pr384614482nres_a,B:refine424419629nres_a,A:refine424419629nres_a] : ((phi @ x) | (phi @ x) | (~ (member1468928819nres_a @ (produc1136923598nres_a @ A @ B) @ C)) | (member1468928819nres_a @ (produc1136923598nres_a @ (sk1 @ (^ [D:refine424419629nres_a,E:refine424419629nres_a]: (($true))) @ C @ B @ A) @ (sk2 @ (^ [D:refine424419629nres_a,E:refine424419629nres_a]: (refine1312857699nres_a @ (refine1198353288_RES_a @ (collect_a @ phi)) @ x)) @ C @ B @ A)) @ C) | ((refine1312857699nres_a @ (refine1198353288_RES_a @ (collect_a @ (phi))) @ x) != (refine1312857699nres_a @ (refine1198353288_RES_a @ (collect_a @ (phi))) @ x)))),inference(paramod_ordered,[status(thm)],[1565,1825])).
76.32/24.84	thf(2461,plain,(! [C:set_Pr384614482nres_a,B:refine424419629nres_a,A:refine424419629nres_a] : ((phi @ x) | (~ (member1468928819nres_a @ (produc1136923598nres_a @ A @ B) @ C)) | (member1468928819nres_a @ (produc1136923598nres_a @ (sk1 @ (^ [D:refine424419629nres_a,E:refine424419629nres_a]: (($true))) @ C @ B @ A) @ (sk2 @ (^ [D:refine424419629nres_a,E:refine424419629nres_a]: (refine1312857699nres_a @ (refine1198353288_RES_a @ (collect_a @ phi)) @ x)) @ C @ B @ A)) @ C) | ((refine1312857699nres_a @ (refine1198353288_RES_a @ (collect_a @ (phi))) @ x) != (refine1312857699nres_a @ (refine1198353288_RES_a @ (collect_a @ (phi))) @ x)))),inference(simp,[status(thm)],[2460])).
76.32/24.84	thf(2462,plain,(! [C:set_Pr384614482nres_a,B:refine424419629nres_a,A:refine424419629nres_a] : ((phi @ x) | (~ (member1468928819nres_a @ (produc1136923598nres_a @ A @ B) @ C)) | (member1468928819nres_a @ (produc1136923598nres_a @ (sk1 @ (^ [D:refine424419629nres_a,E:refine424419629nres_a]: (($true))) @ C @ B @ A) @ (sk2 @ (^ [D:refine424419629nres_a,E:refine424419629nres_a]: (refine1312857699nres_a @ (refine1198353288_RES_a @ (collect_a @ phi)) @ x)) @ C @ B @ A)) @ C))),inference(pattern_uni,[status(thm)],[2461:[]])).
76.32/24.84	thf(253,axiom,((! [A:set_a,B:set_a]: (((refine1198353288_RES_a @ A) = (refine1198353288_RES_a @ B)) = (A = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_nres_Oinject)).
76.32/24.84	thf(1440,plain,((! [A:set_a,B:set_a]: (((refine1198353288_RES_a @ A) = (refine1198353288_RES_a @ B)) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[253])).
76.32/24.84	thf(160,axiom,((! [A:refine424419629nres_a,B:refine424419629nres_a]: ((ord_le519537037nres_a @ A @ B) => ((ord_le519537037nres_a @ B @ A) => (A = B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_antisym)).
76.32/24.84	thf(899,plain,((! [A:refine424419629nres_a,B:refine424419629nres_a]: ((ord_le519537037nres_a @ A @ B) => ((ord_le519537037nres_a @ B @ A) => (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[160])).
76.32/24.84	thf(65,axiom,((! [A:refine424419629nres_a,B:refine424419629nres_a,C:refine424419629nres_a,D:refine424419629nres_a,E:$o]: ((ord_le519537037nres_a @ A @ B) => ((ord_le519537037nres_a @ C @ D) => (ord_le519537037nres_a @ (if_Ref1724547303nres_a @ E @ A @ C) @ (if_Ref1724547303nres_a @ E @ B @ D)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_101_order__mono__setup_Omono__if)).
76.32/24.84	thf(536,plain,((! [A:refine424419629nres_a,B:refine424419629nres_a,C:refine424419629nres_a,D:refine424419629nres_a,E:$o]: ((ord_le519537037nres_a @ A @ B) => ((ord_le519537037nres_a @ C @ D) => (ord_le519537037nres_a @ (if_Ref1724547303nres_a @ E @ A @ C) @ (if_Ref1724547303nres_a @ E @ B @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[65])).
76.32/24.84	thf(134,axiom,((! [A:set_a]: (ord_less_eq_set_a @ A @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_order__mono__setup_Orefl)).
76.32/24.84	thf(800,plain,((! [A:set_a]: (ord_less_eq_set_a @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[134])).
76.32/24.84	thf(287,plain,(! [B:refine424419629nres_a,A:refine424419629nres_a] : ((~ (ord_le1480771457nres_a @ A @ B)) | (~ (ord_le1480771457nres_a @ B @ A)))),inference(cnf,[status(esa)],[286])).
76.32/24.84	thf(1346,plain,((~ (? [A:set_a]: (refine464223677AILi_a = (refine1198353288_RES_a @ A))))),inference(miniscope,[status(thm)],[1345])).
76.32/24.84	thf(1347,plain,(! [A:set_a] : ((~ (refine464223677AILi_a = (refine1198353288_RES_a @ A))))),inference(cnf,[status(esa)],[1346])).
76.32/24.84	thf(1348,plain,(! [A:set_a] : (((refine1198353288_RES_a @ A) != refine464223677AILi_a))),inference(lifteq,[status(thm)],[1347])).
76.32/24.84	thf(183,axiom,((! [A:set_a,B:set_a]: ((ord_less_set_a @ A @ B) => (B != A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_147_less__imp__not__eq2)).
76.32/24.84	thf(999,plain,((! [A:set_a,B:set_a]: ((ord_less_set_a @ A @ B) => (~ (B = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[183])).
76.32/24.84	thf(40,axiom,((! [A:set_a,B:(refine424419629nres_a > set_a),C:refine424419629nres_a,D:refine424419629nres_a]: (((ord_le519537037nres_a @ C @ D) => ((ord_less_eq_set_a @ A @ (B @ D)) <= (! [E:refine424419629nres_a,F:refine424419629nres_a]: ((ord_le519537037nres_a @ E @ F) => (ord_less_eq_set_a @ (B @ E) @ (B @ F)))))) <= (A = (B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_ord__eq__le__subst)).
76.32/24.84	thf(432,plain,((! [A:set_a,B:(refine424419629nres_a > set_a),C:refine424419629nres_a,D:refine424419629nres_a]: ((A = (B @ C)) => ((ord_le519537037nres_a @ C @ D) => ((! [E:refine424419629nres_a,F:refine424419629nres_a]: ((ord_le519537037nres_a @ E @ F) => (ord_less_eq_set_a @ (B @ E) @ (B @ F)))) => (ord_less_eq_set_a @ A @ (B @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[40])).
76.32/24.84	thf(141,axiom,((! [A:refine424419629nres_a,B:refine424419629nres_a]: ((ord_le519537037nres_a @ A @ B) => ((ord_le519537037nres_a @ B @ A) => (B = A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_dual__order_Oantisym)).
76.32/24.84	thf(818,plain,((! [A:refine424419629nres_a,B:refine424419629nres_a]: ((ord_le519537037nres_a @ A @ B) => ((ord_le519537037nres_a @ B @ A) => (B = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[141])).
76.32/24.84	thf(82,axiom,((! [A:set_a,B:set_a]: ((ord_less_set_a @ A @ B) => (ord_less_eq_set_a @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_order_Ostrict__implies__order)).
76.32/24.84	thf(603,plain,((! [A:set_a,B:set_a]: ((ord_less_set_a @ A @ B) => (ord_less_eq_set_a @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[82])).
76.32/24.84	thf(144,axiom,((! [A:(refine424419629nres_a > $o),B:refine424419629nres_a]: ((A @ B) => ((! [C:refine424419629nres_a]: ((A @ C) => (ord_le519537037nres_a @ C @ B))) => ((order_1714329108nres_a @ A) = B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_254_Greatest__equality)).
76.32/24.84	thf(833,plain,((! [A:(refine424419629nres_a > $o),B:refine424419629nres_a]: ((A @ B) => ((! [C:refine424419629nres_a]: ((A @ C) => (ord_le519537037nres_a @ C @ B))) => ((order_1714329108nres_a @ (A)) = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[144])).
76.32/24.84	thf(178,axiom,((! [A:(set_a > $o),B:set_a,C:(set_a > $o)]: ((((! [D:set_a]: ((A @ D) => ((! [E:set_a]: ((ord_less_eq_set_a @ E @ D) <= (A @ E))) => (C @ D)))) => (C @ (order_Greatest_set_a @ A))) <= (! [D:set_a]: ((ord_less_eq_set_a @ D @ B) <= (A @ D)))) <= (A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_253_GreatestI2__order)).
76.32/24.84	thf(967,plain,((! [A:(set_a > $o),B:set_a,C:(set_a > $o)]: ((A @ B) => ((! [D:set_a]: ((A @ D) => (ord_less_eq_set_a @ D @ B))) => ((! [D:set_a]: ((A @ D) => ((! [E:set_a]: ((A @ E) => (ord_less_eq_set_a @ E @ D))) => (C @ D)))) => (C @ (order_Greatest_set_a @ (A)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[178])).
76.32/24.84	thf(38,axiom,((! [A:$o,B:set_a,C:set_a,D:set_a,E:set_a]: (((ord_less_eq_set_a @ (if_set_a @ A @ B @ D) @ (if_set_a @ A @ C @ E)) <= ((ord_less_eq_set_a @ D @ E) <= (~ (A)))) <= ((A) => (ord_less_eq_set_a @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_262_Refine__Misc_Oif__mono)).
76.32/24.84	thf(422,plain,((! [A:$o,B:set_a,C:set_a,D:set_a,E:set_a]: (((A) => (ord_less_eq_set_a @ B @ C)) => (((~ (A)) => (ord_less_eq_set_a @ D @ E)) => (ord_less_eq_set_a @ (if_set_a @ A @ B @ D) @ (if_set_a @ A @ C @ E)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[38])).
76.32/24.84	thf(73,axiom,((! [A:set_a,B:set_a,C:a]: (((member_a @ C @ A) => (member_a @ C @ B)) <= (ord_less_eq_set_a @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_225_in__mono)).
76.32/24.84	thf(564,plain,((! [A:set_a,B:set_a,C:a]: ((ord_less_eq_set_a @ A @ B) => ((member_a @ C @ A) => (member_a @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[73])).
76.32/24.84	thf(262,axiom,((! [A:refine424419629nres_a,B:refine424419629nres_a]: (((accp_P624619091nres_a @ refine260105272_rel_a @ (produc1136923598nres_a @ A @ B)) => ((! [C:set_a]: (((~ (accp_P624619091nres_a @ refine260105272_rel_a @ (produc1136923598nres_a @ (refine1198353288_RES_a @ C) @ refine464223677AILi_a))) <= (B = refine464223677AILi_a)) <= (A = (refine1198353288_RES_a @ C)))) => (~ (! [C:set_a]: ((A = (refine1198353288_RES_a @ C)) => (! [D:set_a]: ((B = (refine1198353288_RES_a @ D)) => ((accp_P624619091nres_a @ refine260105272_rel_a @ (produc1136923598nres_a @ (refine1198353288_RES_a @ C) @ (refine1198353288_RES_a @ D))) => (~ (ord_less_set_a @ C @ D)))))))))) <= (ord_le1480771457nres_a @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_247_less__nres_Opelims_I2_J)).
76.32/24.84	thf(1495,plain,((! [A:refine424419629nres_a,B:refine424419629nres_a]: ((ord_le1480771457nres_a @ A @ B) => ((accp_P624619091nres_a @ (refine260105272_rel_a) @ (produc1136923598nres_a @ A @ B)) => ((! [C:set_a]: ((A = (refine1198353288_RES_a @ C)) => ((B = refine464223677AILi_a) => (~ (accp_P624619091nres_a @ (refine260105272_rel_a) @ (produc1136923598nres_a @ (refine1198353288_RES_a @ C) @ refine464223677AILi_a)))))) => (~ (! [C:set_a]: ((A = (refine1198353288_RES_a @ C)) => (! [D:set_a]: ((B = (refine1198353288_RES_a @ D)) => ((accp_P624619091nres_a @ (refine260105272_rel_a) @ (produc1136923598nres_a @ (refine1198353288_RES_a @ C) @ (refine1198353288_RES_a @ D))) => (~ (ord_less_set_a @ C @ D))))))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[262])).
76.32/24.84	thf(137,axiom,((! [A:set_a,B:set_a]: ((ord_less_eq_set_a @ A @ B) <= (! [C:a]: ((member_a @ C @ B) <= (member_a @ C @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_224_subsetI)).
76.32/24.84	thf(807,plain,((! [A:set_a,B:set_a]: ((! [C:a]: ((member_a @ C @ A) => (member_a @ C @ B))) => (ord_less_eq_set_a @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[137])).
76.32/24.84	thf(194,axiom,((! [A:set_a,B:set_a]: ((ord_less_eq_set_a @ A @ B) <= (ord_less_eq_set_a @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_257_relprop__triggers_I6_J)).
76.32/24.84	thf(1033,plain,(($true)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[194])).
76.32/24.84	thf(204,axiom,((ord_less_eq_set_a = (^ [A:set_a,B:set_a]: ((ord_less_set_a @ A @ B) | (A = B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_171_le__less)).
76.32/24.84	thf(1065,plain,(((ord_less_eq_set_a) = (^ [A:set_a,B:set_a]: ((ord_less_set_a @ A @ B) | (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[204])).
76.32/24.84	thf(169,axiom,((! [A:set_a,B:set_a,C:(set_a > set_a),D:set_a]: ((((! [E:set_a,F:set_a]: ((ord_less_set_a @ (C @ E) @ (C @ F)) <= (ord_less_set_a @ E @ F))) => (ord_less_set_a @ (C @ A) @ D)) <= (ord_less_eq_set_a @ (C @ B) @ D)) <= (ord_less_set_a @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_189_order__less__le__subst2)).
76.32/24.84	thf(928,plain,((! [A:set_a,B:set_a,C:(set_a > set_a),D:set_a]: ((ord_less_set_a @ A @ B) => ((ord_less_eq_set_a @ (C @ B) @ D) => ((! [E:set_a,F:set_a]: ((ord_less_set_a @ E @ F) => (ord_less_set_a @ (C @ E) @ (C @ F)))) => (ord_less_set_a @ (C @ A) @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[169])).
76.32/24.84	thf(201,axiom,((! [A:set_a,B:set_a,C:set_a]: (((ord_less_set_a @ A @ C) <= (ord_less_eq_set_a @ B @ C)) <= (ord_less_set_a @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_209_order_Ostrict__trans2)).
76.32/24.84	thf(1056,plain,((! [A:set_a,B:set_a,C:set_a]: ((ord_less_set_a @ A @ B) => ((ord_less_eq_set_a @ B @ C) => (ord_less_set_a @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[201])).
76.32/24.84	thf(97,axiom,((! [A:refine424419629nres_a,B:refine424419629nres_a]: ((ord_le1480771457nres_a @ A @ B) => (B != A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_160_dual__order_Ostrict__implies__not__eq)).
76.32/24.84	thf(664,plain,((! [A:refine424419629nres_a,B:refine424419629nres_a]: ((ord_le1480771457nres_a @ A @ B) => (~ (B = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[97])).
76.32/24.84	thf(33,axiom,((! [A:refine424419629nres_a,B:(refine424419629nres_a > refine424419629nres_a),C:refine424419629nres_a,D:refine424419629nres_a]: ((A = (B @ C)) => (((ord_le1480771457nres_a @ A @ (B @ D)) <= (! [E:refine424419629nres_a,F:refine424419629nres_a]: ((ord_le1480771457nres_a @ E @ F) => (ord_le1480771457nres_a @ (B @ E) @ (B @ F))))) <= (ord_le1480771457nres_a @ C @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_108_ord__eq__less__subst)).
76.32/24.84	thf(395,plain,((! [A:refine424419629nres_a,B:(refine424419629nres_a > refine424419629nres_a),C:refine424419629nres_a,D:refine424419629nres_a]: ((A = (B @ C)) => ((ord_le1480771457nres_a @ C @ D) => ((! [E:refine424419629nres_a,F:refine424419629nres_a]: ((ord_le1480771457nres_a @ E @ F) => (ord_le1480771457nres_a @ (B @ E) @ (B @ F)))) => (ord_le1480771457nres_a @ A @ (B @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[33])).
76.32/24.84	thf(150,axiom,((! [A:refine424419629nres_a,B:refine424419629nres_a]: (((A = B) <= (ord_le519537037nres_a @ B @ A)) <= (ord_le519537037nres_a @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_order__class_Oorder_Oantisym)).
76.32/24.85	thf(860,plain,((! [A:refine424419629nres_a,B:refine424419629nres_a]: ((ord_le519537037nres_a @ A @ B) => ((ord_le519537037nres_a @ B @ A) => (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[150])).
76.32/24.85	thf(114,axiom,((! [A:set_a,B:set_a,C:set_a]: ((ord_less_eq_set_a @ A @ B) => ((ord_less_eq_set_a @ A @ C) <= (ord_less_eq_set_a @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_order__trans)).
76.32/24.85	thf(723,plain,((! [A:set_a,B:set_a,C:set_a]: ((ord_less_eq_set_a @ A @ B) => ((ord_less_eq_set_a @ B @ C) => (ord_less_eq_set_a @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[114])).
76.32/24.85	thf(1824,plain,(! [B:set_Pr384614482nres_a,A:refine424419629nres_a] : ((phi @ x) | (~ (member1468928819nres_a @ (produc1136923598nres_a @ A @ (refine1198353288_RES_a @ (collect_a @ (phi)))) @ B)) | (member1468928819nres_a @ (produc1136923598nres_a @ (sk1 @ (^ [C:refine424419629nres_a,D:refine424419629nres_a]: (refine1312857699nres_a @ D @ x)) @ B @ (refine1198353288_RES_a @ (collect_a @ (phi))) @ A) @ (sk2 @ (^ [C:refine424419629nres_a,D:refine424419629nres_a]: (refine1312857699nres_a @ D @ x)) @ B @ (refine1198353288_RES_a @ (collect_a @ (phi))) @ A)) @ B))),inference(pre_uni,[status(thm)],[1792:[bind(A, $thf(A)),bind(B, $thf(refine1198353288_RES_a @ (collect_a @ (phi)))),bind(C, $thf(C)),bind(D, $thf(^ [E:refine424419629nres_a,F:refine424419629nres_a]: (refine1312857699nres_a @ F @ x)))]])).
76.32/24.85	thf(1885,plain,(! [B:set_Pr384614482nres_a,A:refine424419629nres_a] : ((phi @ x) | (~ (member1468928819nres_a @ (produc1136923598nres_a @ A @ (refine1198353288_RES_a @ (collect_a @ (phi)))) @ B)) | (member1468928819nres_a @ (produc1136923598nres_a @ (sk1 @ (^ [C:refine424419629nres_a,D:refine424419629nres_a]: (refine1312857699nres_a @ D @ x)) @ B @ (refine1198353288_RES_a @ (collect_a @ (phi))) @ A) @ (sk2 @ (^ [C:refine424419629nres_a,D:refine424419629nres_a]: (refine1312857699nres_a @ D @ x)) @ B @ (refine1198353288_RES_a @ (collect_a @ (phi))) @ A)) @ B))),inference(simp,[status(thm)],[1824])).
76.32/24.85	thf(244,axiom,((! [A:a,B:set_a]: ((ord_le519537037nres_a @ (refine2063221604TURN_a @ A) @ (refine1198353288_RES_a @ B)) = (member_a @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_nres__order__simps_I21_J)).
76.32/24.85	thf(1352,plain,((! [A:a,B:set_a]: ((ord_le519537037nres_a @ (refine2063221604TURN_a @ A) @ (refine1198353288_RES_a @ B)) = (member_a @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[244])).
76.32/24.85	thf(46,axiom,((! [A:set_a,B:set_a,C:set_a]: ((ord_less_set_a @ A @ B) => ((ord_less_set_a @ A @ C) <= (ord_less_set_a @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_238_psubset__trans)).
76.32/24.85	thf(464,plain,((! [A:set_a,B:set_a,C:set_a]: ((ord_less_set_a @ A @ B) => ((ord_less_set_a @ B @ C) => (ord_less_set_a @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[46])).
76.32/24.85	thf(25,axiom,((! [A:(produc1609974940nres_a > $o),B:produc1609974940nres_a]: ((A @ B) <= (! [C:refine424419629nres_a,D:refine424419629nres_a]: (A @ (produc1136923598nres_a @ C @ D)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_107_old_Oprod_Oinducts)).
76.32/24.85	thf(369,plain,((! [A:(produc1609974940nres_a > $o),B:produc1609974940nres_a]: ((! [C:refine424419629nres_a,D:refine424419629nres_a]: (A @ (produc1136923598nres_a @ C @ D))) => (A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[25])).
76.32/24.85	thf(84,axiom,((! [A:refine424419629nres_a,B:refine424419629nres_a,C:(refine424419629nres_a > set_a),D:set_a]: ((((ord_less_set_a @ (C @ A) @ D) <= (! [E:refine424419629nres_a,F:refine424419629nres_a]: ((ord_less_set_a @ (C @ E) @ (C @ F)) <= (ord_le1480771457nres_a @ E @ F)))) <= (ord_less_set_a @ (C @ B) @ D)) <= (ord_le1480771457nres_a @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_121_order__less__subst2)).
76.32/24.85	thf(607,plain,((! [A:refine424419629nres_a,B:refine424419629nres_a,C:(refine424419629nres_a > set_a),D:set_a]: ((ord_le1480771457nres_a @ A @ B) => ((ord_less_set_a @ (C @ B) @ D) => ((! [E:refine424419629nres_a,F:refine424419629nres_a]: ((ord_le1480771457nres_a @ E @ F) => (ord_less_set_a @ (C @ E) @ (C @ F)))) => (ord_less_set_a @ (C @ A) @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[84])).
76.32/24.85	thf(237,axiom,((! [A:(a > $o),B:(a > $o)]: ((! [C:a]: ((A @ C) = (B @ C))) => ((collect_a @ A) = (collect_a @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_Collect__cong)).
76.32/24.85	thf(1331,plain,((! [A:(a > $o),B:(a > $o)]: ((! [C:a]: ((A @ C) = (B @ C))) => ((collect_a @ (A)) = (collect_a @ (B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[237])).
76.32/24.85	thf(235,axiom,((! [A:refine424419629nres_a,B:refine424419629nres_a]: (((A != refine464223677AILi_a) => (~ (! [C:set_a]: ((A = (refine1198353288_RES_a @ C)) => (! [D:set_a]: ((ord_less_set_a @ C @ D) <= (B = (refine1198353288_RES_a @ D)))))))) <= (~ (ord_le1480771457nres_a @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_165_less__nres_Oelims_I3_J)).
76.32/24.85	thf(1320,plain,((! [A:refine424419629nres_a,B:refine424419629nres_a]: ((~ (ord_le1480771457nres_a @ A @ B)) => ((~ (A = refine464223677AILi_a)) => (~ (! [C:set_a]: ((A = (refine1198353288_RES_a @ C)) => (! [D:set_a]: ((B = (refine1198353288_RES_a @ D)) => (ord_less_set_a @ C @ D)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[235])).
76.32/24.85	thf(172,axiom,((! [A:set_a,B:set_a]: ((ord_less_set_a @ A @ B) => (A != B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_159_order_Ostrict__implies__not__eq)).
76.32/24.85	thf(940,plain,((! [A:set_a,B:set_a]: ((ord_less_set_a @ A @ B) => (~ (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[172])).
76.32/24.85	thf(91,axiom,((! [A:refine424419629nres_a,B:refine424419629nres_a]: (((! [C:a]: ((refine1001002027nres_a @ A @ C) = (refine1001002027nres_a @ B @ C))) => (A = B)) <= ((refine412683989fail_a @ A) = (refine412683989fail_a @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_pw__eqI)).
76.32/24.85	thf(639,plain,((! [A:refine424419629nres_a,B:refine424419629nres_a]: (((refine412683989fail_a @ A) = (refine412683989fail_a @ B)) => ((! [C:a]: ((refine1001002027nres_a @ A @ C) = (refine1001002027nres_a @ B @ C))) => (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[91])).
76.32/24.85	thf(101,axiom,((! [A:refine424419629nres_a,B:refine424419629nres_a]: ((A != B) <= (ord_le1480771457nres_a @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_158_order_Ostrict__implies__not__eq)).
76.32/24.85	thf(676,plain,((! [A:refine424419629nres_a,B:refine424419629nres_a]: ((ord_le1480771457nres_a @ A @ B) => (~ (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[101])).
76.32/24.85	thf(210,axiom,((! [A:set_a]: (ord_less_eq_set_a @ A @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_232_subset__refl)).
76.32/24.85	thf(1088,plain,((! [A:set_a]: (ord_less_eq_set_a @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[210])).
76.32/24.85	thf(14,axiom,((! [A:set_a,B:set_a,C:(set_a > refine424419629nres_a),D:refine424419629nres_a]: ((ord_less_set_a @ A @ B) => ((ord_le1480771457nres_a @ (C @ B) @ D) => ((! [E:set_a,F:set_a]: ((ord_less_set_a @ E @ F) => (ord_le1480771457nres_a @ (C @ E) @ (C @ F)))) => (ord_le1480771457nres_a @ (C @ A) @ D)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_122_order__less__subst2)).
76.32/24.85	thf(309,plain,((! [A:set_a,B:set_a,C:(set_a > refine424419629nres_a),D:refine424419629nres_a]: ((ord_less_set_a @ A @ B) => ((ord_le1480771457nres_a @ (C @ B) @ D) => ((! [E:set_a,F:set_a]: ((ord_less_set_a @ E @ F) => (ord_le1480771457nres_a @ (C @ E) @ (C @ F)))) => (ord_le1480771457nres_a @ (C @ A) @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[14])).
76.32/24.85	thf(96,axiom,((! [A:refine424419629nres_a,B:refine424419629nres_a,C:refine424419629nres_a]: (((ord_le519537037nres_a @ B @ C) => (ord_le519537037nres_a @ A @ C)) <= (A = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_ord__eq__le__trans)).
76.32/24.85	thf(659,plain,((! [A:refine424419629nres_a,B:refine424419629nres_a,C:refine424419629nres_a]: ((A = B) => ((ord_le519537037nres_a @ B @ C) => (ord_le519537037nres_a @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[96])).
76.32/24.85	thf(2858,plain,(($false)),inference(e,[status(thm)],[1337,1105,846,962,555,1110,1024,1469,909,628,523,683,276,1522,1443,994,741,873,878,269,597,1142,379,1705,385,500,797,1342,670,404,709,417,1046,288,1359,651,389,1055,785,504,917,357,1059,949,802,344,902,1147,1704,1013,881,316,1362,1450,376,1334,485,1151,353,821,480,574,1020,348,766,280,293,866,1072,1345,849,1564,307,452,512,925,1470,534,1067,714,270,529,894,746,1519,1355,561,1487,297,1255,302,693,630,467,1365,522,889,1210,1079,757,551,842,697,317,650,615,1328,1375,1006,388,989,1138,356,339,933,669,1075,642,1446,706,647,1539,569,1720,1825,1114,1588,1099,1451,738,1050,457,503,605,1434,792,938,360,541,1054,558,1026,530,773,906,1135,430,824,296,375,733,1884,286,875,579,281,382,572,1371,787,1107,1090,804,1258,540,406,1282,1117,1011,736,1349,567,1043,271,863,737,318,811,1471,552,816,323,726,700,1029,626,1022,668,462,1112,983,278,1015,986,505,431,922,912,685,959,2171,1213,768,267,851,1102,1034,490,374,617,1340,1472,553,531,944,795,680,776,855,690,954,1368,409,712,1003,1070,872,1053,673,1716,1452,791,441,463,1317,470,1220,1257,703,1536,656,600,1052,1749,1094,314,612,497,627,450,539,524,495,1216,1126,588,517,748,304,1062,390,1745,731,961,813,914,510,2462,1440,899,536,800,287,1348,999,315,432,818,603,833,967,422,790,564,1495,268,807,1561,1033,1065,928,1056,664,395,860,723,277,1885,871,1352,464,369,607,1331,1320,940,639,676,1088,1468,309,659,1565])).
76.32/24.85	% SZS output end Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
76.32/24.85	% [INFO] 	 Killing All external provers ... 
0.26/24.97	EOF