0.03/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.03/0.13 % Command : run_E %s %d THM 0.14/0.34 % Computer : n020.cluster.edu 0.14/0.34 % Model : x86_64 x86_64 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.14/0.34 % Memory : 8042.1875MB 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 0.14/0.34 % CPULimit : 960 0.14/0.34 % WCLimit : 120 0.14/0.34 % DateTime : Tue Aug 9 06:27:50 EDT 2022 0.14/0.35 % CPUTime : 0.20/0.52 Running higher-order on 8 cores theorem proving 0.20/0.52 Running: /export/starexec/sandbox2/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=120 /export/starexec/sandbox2/benchmark/theBenchmark.p 0.20/0.52 # Version: 3.0pre003-ho 0.39/0.59 # Preprocessing class: HSLMSMSMLLLCHSA. 0.39/0.59 # Scheduled 5 strats onto 8 cores with 120 seconds (960 total) 0.39/0.59 # Starting pre_casc_4 with 480s (4) cores 0.39/0.59 # Starting full_lambda_6 with 120s (1) cores 0.39/0.59 # Starting sh10 with 120s (1) cores 0.39/0.59 # Starting post_as_ho9 with 120s (1) cores 0.39/0.59 # Starting post_as_ho8 with 120s (1) cores 0.39/0.59 # post_as_ho9 with pid 29348 completed with status 0 0.39/0.59 # Result found by post_as_ho9 0.39/0.59 # Preprocessing class: HSLMSMSMLLLCHSA. 0.39/0.59 # Scheduled 5 strats onto 8 cores with 120 seconds (960 total) 0.39/0.59 # Starting pre_casc_4 with 480s (4) cores 0.39/0.59 # Starting full_lambda_6 with 120s (1) cores 0.39/0.59 # Starting sh10 with 120s (1) cores 0.39/0.59 # Starting post_as_ho9 with 120s (1) cores 0.39/0.59 # SinE strategy is GSinE(CountFormulas,,true,1,0,2,20000,1.0,true) 0.39/0.59 # ...ProofStateSinE()=72/544 0.39/0.59 # Search class: HGHNF-FSLF21-DHSMMFBN 0.39/0.59 # partial match(4): HGHNF-FSLF11-SHSSMFNN 0.39/0.59 # Scheduled 6 strats onto 1 cores with 120 seconds (120 total) 0.39/0.59 # Starting new_ho_10 with 22s (1) cores 0.39/0.59 # new_ho_10 with pid 29350 completed with status 0 0.39/0.59 # Result found by new_ho_10 0.39/0.59 # Preprocessing class: HSLMSMSMLLLCHSA. 0.39/0.59 # Scheduled 5 strats onto 8 cores with 120 seconds (960 total) 0.39/0.59 # Starting pre_casc_4 with 480s (4) cores 0.39/0.59 # Starting full_lambda_6 with 120s (1) cores 0.39/0.59 # Starting sh10 with 120s (1) cores 0.39/0.59 # Starting post_as_ho9 with 120s (1) cores 0.39/0.59 # SinE strategy is GSinE(CountFormulas,,true,1,0,2,20000,1.0,true) 0.39/0.59 # ...ProofStateSinE()=72/544 0.39/0.59 # Search class: HGHNF-FSLF21-DHSMMFBN 0.39/0.59 # partial match(4): HGHNF-FSLF11-SHSSMFNN 0.39/0.59 # Scheduled 6 strats onto 1 cores with 120 seconds (120 total) 0.39/0.59 # Starting new_ho_10 with 22s (1) cores 0.39/0.59 # Preprocessing time : 0.010 s 0.39/0.59 # Presaturation interreduction done 0.39/0.59 0.39/0.59 # Proof found! 0.39/0.59 # SZS status Theorem 0.39/0.59 # SZS output start CNFRefutation 0.39/0.59 thf(decl_22, type, is_of: $i > ($i > $o) > $o). 0.39/0.59 thf(decl_23, type, all_of: ($i > $o) > ($i > $o) > $o). 0.39/0.59 thf(decl_24, type, eps: ($i > $o) > $i). 0.39/0.59 thf(decl_25, type, in: $i > $i > $o). 0.39/0.59 thf(decl_26, type, d_Subq: $i > $i > $o). 0.39/0.59 thf(decl_27, type, emptyset: $i). 0.39/0.59 thf(decl_28, type, union: $i > $i). 0.39/0.59 thf(decl_29, type, power: $i > $i). 0.39/0.59 thf(decl_30, type, repl: $i > ($i > $i) > $i). 0.39/0.59 thf(decl_31, type, d_Union_closed: $i > $o). 0.39/0.59 thf(decl_32, type, d_Power_closed: $i > $o). 0.39/0.59 thf(decl_33, type, d_Repl_closed: $i > $o). 0.39/0.59 thf(decl_34, type, d_ZF_closed: $i > $o). 0.39/0.59 thf(decl_35, type, univof: $i > $i). 0.39/0.59 thf(decl_36, type, if: $o > $i > $i > $i). 0.39/0.59 thf(decl_37, type, nIn: $i > $i > $o). 0.39/0.59 thf(decl_38, type, d_UPair: $i > $i > $i). 0.39/0.59 thf(decl_39, type, d_Sing: $i > $i). 0.39/0.59 thf(decl_40, type, binunion: $i > $i > $i). 0.39/0.59 thf(decl_41, type, famunion: $i > ($i > $i) > $i). 0.39/0.59 thf(decl_42, type, d_Sep: $i > ($i > $o) > $i). 0.39/0.59 thf(decl_43, type, d_ReplSep: $i > ($i > $o) > ($i > $i) > $i). 0.39/0.59 thf(decl_44, type, setminus: $i > $i > $i). 0.39/0.59 thf(decl_45, type, d_In_rec_G: ($i > ($i > $i) > $i) > $i > $i > $o). 0.39/0.59 thf(decl_46, type, d_In_rec: ($i > ($i > $i) > $i) > $i > $i). 0.39/0.59 thf(decl_47, type, ordsucc: $i > $i). 0.39/0.59 thf(decl_48, type, nat_p: $i > $o). 0.39/0.59 thf(decl_49, type, omega: $i). 0.39/0.59 thf(decl_50, type, d_Inj1: $i > $i). 0.39/0.59 thf(decl_51, type, d_Inj0: $i > $i). 0.39/0.59 thf(decl_52, type, d_Unj: $i > $i). 0.39/0.59 thf(decl_53, type, pair: $i > $i > $i). 0.39/0.59 thf(decl_54, type, proj0: $i > $i). 0.39/0.59 thf(decl_55, type, proj1: $i > $i). 0.39/0.59 thf(decl_56, type, d_Sigma: $i > ($i > $i) > $i). 0.39/0.59 thf(decl_57, type, setprod: $i > $i > $i). 0.39/0.59 thf(decl_58, type, ap: $i > $i > $i). 0.39/0.59 thf(decl_59, type, pair_p: $i > $o). 0.39/0.59 thf(decl_60, type, d_Pi: $i > ($i > $i) > $i). 0.39/0.59 thf(decl_61, type, imp: $o > $o > $o). 0.39/0.59 thf(decl_62, type, d_not: $o > $o). 0.39/0.59 thf(decl_63, type, wel: $o > $o). 0.39/0.59 thf(decl_64, type, obvious: $o). 0.39/0.59 thf(decl_65, type, l_ec: $o > $o > $o). 0.39/0.59 thf(decl_66, type, d_and: $o > $o > $o). 0.39/0.59 thf(decl_67, type, l_or: $o > $o > $o). 0.39/0.59 thf(decl_68, type, orec: $o > $o > $o). 0.39/0.59 thf(decl_69, type, l_iff: $o > $o > $o). 0.39/0.59 thf(decl_70, type, all: $i > ($i > $o) > $o). 0.39/0.59 thf(decl_71, type, non: $i > ($i > $o) > $i > $o). 0.39/0.59 thf(decl_72, type, l_some: $i > ($i > $o) > $o). 0.39/0.59 thf(decl_73, type, or3: $o > $o > $o > $o). 0.39/0.59 thf(decl_74, type, and3: $o > $o > $o > $o). 0.39/0.59 thf(decl_75, type, ec3: $o > $o > $o > $o). 0.39/0.59 thf(decl_76, type, orec3: $o > $o > $o > $o). 0.39/0.59 thf(decl_77, type, e_is: $i > $i > $i > $o). 0.39/0.59 thf(decl_78, type, amone: $i > ($i > $o) > $o). 0.39/0.59 thf(decl_79, type, one: $i > ($i > $o) > $o). 0.39/0.59 thf(decl_80, type, ind: $i > ($i > $o) > $i). 0.39/0.59 thf(decl_81, type, injective: $i > $i > $i > $o). 0.39/0.59 thf(decl_82, type, image: $i > $i > $i > $i > $o). 0.39/0.59 thf(decl_83, type, tofs: $i > $i > $i > $i > $i). 0.39/0.59 thf(decl_84, type, soft: $i > $i > $i > $i > $i). 0.39/0.59 thf(decl_85, type, inverse: $i > $i > $i > $i). 0.39/0.59 thf(decl_86, type, surjective: $i > $i > $i > $o). 0.39/0.59 thf(decl_87, type, bijective: $i > $i > $i > $o). 0.39/0.59 thf(decl_88, type, invf: $i > $i > $i > $i). 0.39/0.59 thf(decl_89, type, inj_h: $i > $i > $i > $i > $i > $i). 0.39/0.59 thf(decl_90, type, e_in: $i > ($i > $o) > $i > $i). 0.39/0.59 thf(decl_91, type, out: $i > ($i > $o) > $i > $i). 0.39/0.59 thf(decl_92, type, d_pair: $i > $i > $i > $i > $i). 0.39/0.59 thf(decl_93, type, first: $i > $i > $i > $i). 0.39/0.59 thf(decl_94, type, second: $i > $i > $i > $i). 0.39/0.59 thf(decl_95, type, prop1: $o > $i > $i > $i > $i > $o). 0.39/0.59 thf(decl_96, type, ite: $o > $i > $i > $i > $i). 0.39/0.59 thf(decl_97, type, wissel_wa: $i > $i > $i > $i > $i). 0.39/0.59 thf(decl_98, type, wissel_wb: $i > $i > $i > $i > $i). 0.39/0.59 thf(decl_99, type, wissel: $i > $i > $i > $i). 0.39/0.59 thf(decl_100, type, changef: $i > $i > $i > $i > $i > $i). 0.39/0.59 thf(decl_101, type, r_ec: $o > $o > $o). 0.39/0.59 thf(decl_102, type, esti: $i > $i > $i > $o). 0.39/0.59 thf(decl_103, type, empty: $i > $i > $o). 0.39/0.59 thf(decl_104, type, nonempty: $i > $i > $o). 0.39/0.59 thf(decl_105, type, incl: $i > $i > $i > $o). 0.39/0.59 thf(decl_106, type, st_disj: $i > $i > $i > $o). 0.39/0.59 thf(decl_107, type, nissetprop: $i > $i > $i > $i > $o). 0.39/0.59 thf(decl_108, type, unmore: $i > $i > $i > $i). 0.39/0.59 thf(decl_109, type, ecelt: $i > ($i > $i > $o) > $i > $i). 0.39/0.59 thf(decl_110, type, ecp: $i > ($i > $i > $o) > $i > $i > $o). 0.39/0.59 thf(decl_111, type, anec: $i > ($i > $i > $o) > $i > $o). 0.39/0.59 thf(decl_112, type, ect: $i > ($i > $i > $o) > $i). 0.39/0.59 thf(decl_113, type, ectset: $i > ($i > $i > $o) > $i > $i). 0.39/0.59 thf(decl_114, type, ectelt: $i > ($i > $i > $o) > $i > $i). 0.39/0.59 thf(decl_115, type, ecect: $i > ($i > $i > $o) > $i > $i). 0.39/0.59 thf(decl_116, type, fixfu: $i > ($i > $i > $o) > $i > $i > $o). 0.39/0.59 thf(decl_117, type, d_10_prop1: $i > ($i > $i > $o) > $i > $i > $i > $i > $i > $o). 0.39/0.59 thf(decl_118, type, prop2: $i > ($i > $i > $o) > $i > $i > $i > $i > $o). 0.39/0.59 thf(decl_119, type, indeq: $i > ($i > $i > $o) > $i > $i > $i > $i). 0.39/0.59 thf(decl_120, type, fixfu2: $i > ($i > $i > $o) > $i > $i > $o). 0.39/0.59 thf(decl_121, type, d_11_i: $i > ($i > $i > $o) > $i > $i > $i > $i). 0.39/0.59 thf(decl_122, type, indeq2: $i > ($i > $i > $o) > $i > $i > $i > $i > $i). 0.39/0.59 thf(decl_123, type, nat: $i). 0.39/0.59 thf(decl_124, type, n_is: $i > $i > $o). 0.39/0.59 thf(decl_125, type, nis: $i > $i > $o). 0.39/0.59 thf(decl_126, type, n_in: $i > $i > $o). 0.39/0.59 thf(decl_127, type, n_some: ($i > $o) > $o). 0.39/0.59 thf(decl_128, type, n_all: ($i > $o) > $o). 0.39/0.59 thf(decl_129, type, n_one: ($i > $o) > $o). 0.39/0.59 thf(decl_130, type, n_1: $i). 0.39/0.59 thf(decl_131, type, cond1: $i > $o). 0.39/0.59 thf(decl_132, type, cond2: $i > $o). 0.39/0.59 thf(decl_133, type, i1_s: ($i > $o) > $i). 0.39/0.59 thf(decl_134, type, d_22_prop1: $i > $o). 0.39/0.59 thf(decl_135, type, d_23_prop1: $i > $o). 0.39/0.59 thf(decl_136, type, d_24_prop1: $i > $o). 0.39/0.59 thf(decl_137, type, d_24_prop2: $i > $i > $o). 0.39/0.59 thf(decl_138, type, prop3: $i > $i > $i > $o). 0.39/0.59 thf(decl_139, type, prop4: $i > $o). 0.39/0.59 thf(decl_140, type, d_24_g: $i > $i). 0.39/0.59 thf(decl_141, type, plus: $i > $i). 0.39/0.59 thf(decl_142, type, n_pl: $i > $i > $i). 0.39/0.59 thf(decl_143, type, d_25_prop1: $i > $i > $i > $o). 0.39/0.59 thf(decl_144, type, d_26_prop1: $i > $i > $o). 0.39/0.59 thf(decl_145, type, d_27_prop1: $i > $i > $o). 0.39/0.59 thf(decl_146, type, d_28_prop1: $i > $i > $i > $o). 0.39/0.59 thf(decl_147, type, diffprop: $i > $i > $i > $o). 0.39/0.59 thf(decl_148, type, d_29_ii: $i > $i > $o). 0.39/0.59 thf(decl_149, type, iii: $i > $i > $o). 0.39/0.59 thf(decl_150, type, d_29_prop1: $i > $i > $o). 0.39/0.59 thf(decl_151, type, moreis: $i > $i > $o). 0.39/0.59 thf(decl_152, type, lessis: $i > $i > $o). 0.39/0.59 thf(decl_153, type, lbprop: ($i > $o) > $i > $i > $o). 0.39/0.59 thf(decl_154, type, n_lb: ($i > $o) > $i > $o). 0.39/0.59 thf(decl_155, type, min: ($i > $o) > $i > $o). 0.39/0.59 thf(decl_156, type, d_428_prop1: $i > $i > $o). 0.39/0.59 thf(decl_157, type, d_428_prop2: $i > $i > $o). 0.39/0.59 thf(decl_158, type, d_428_prop4: $i > $o). 0.39/0.59 thf(decl_159, type, d_428_id: $i). 0.39/0.59 thf(decl_160, type, d_428_g: $i > $i). 0.39/0.59 thf(decl_161, type, times: $i > $i). 0.39/0.59 thf(decl_162, type, n_ts: $i > $i > $i). 0.39/0.59 thf(decl_163, type, d_429_prop1: $i > $i > $o). 0.39/0.59 thf(decl_164, type, d_430_prop1: $i > $i > $i > $o). 0.39/0.59 thf(decl_165, type, d_431_prop1: $i > $i > $i > $o). 0.39/0.59 thf(decl_166, type, n_mn: $i > $i > $i). 0.39/0.59 thf(decl_167, type, d_1to: $i > $i). 0.39/0.59 thf(decl_168, type, outn: $i > $i > $i). 0.39/0.59 thf(decl_169, type, inn: $i > $i > $i). 0.39/0.59 thf(decl_170, type, n_1o: $i). 0.39/0.59 thf(decl_171, type, singlet_u0: $i > $i). 0.39/0.59 thf(decl_172, type, n_2: $i). 0.39/0.59 thf(decl_173, type, n_1t: $i). 0.39/0.59 thf(decl_174, type, n_2t: $i). 0.39/0.59 thf(decl_175, type, pair_u0: $i > $i). 0.39/0.59 thf(decl_176, type, pair1type: $i > $i). 0.39/0.59 thf(decl_177, type, pair1: $i > $i > $i > $i). 0.39/0.59 thf(decl_178, type, first1: $i > $i > $i). 0.39/0.59 thf(decl_179, type, second1: $i > $i > $i). 0.39/0.59 thf(decl_180, type, pair_q0: $i > $i > $i). 0.39/0.59 thf(decl_181, type, d_1out: $i > $i). 0.39/0.59 thf(decl_182, type, xout: $i > $i). 0.39/0.59 thf(decl_183, type, left1to: $i > $i > $i > $i). 0.39/0.59 thf(decl_184, type, right1to: $i > $i > $i > $i). 0.39/0.59 thf(decl_185, type, left: $i > $i > $i > $i > $i). 0.39/0.59 thf(decl_186, type, right: $i > $i > $i > $i > $i). 0.39/0.59 thf(decl_187, type, left_f1: $i > $i > $i > $i > $i). 0.39/0.59 thf(decl_188, type, left_f2: $i > $i > $i > $i > $i). 0.39/0.59 thf(decl_189, type, frac: $i). 0.39/0.59 thf(decl_190, type, n_fr: $i > $i > $i). 0.39/0.59 thf(decl_191, type, num: $i > $i). 0.39/0.59 thf(decl_192, type, den: $i > $i). 0.39/0.59 thf(decl_193, type, n_eq: $i > $i > $o). 0.39/0.59 thf(decl_194, type, moref: $i > $i > $o). 0.39/0.59 thf(decl_195, type, lessf: $i > $i > $o). 0.39/0.59 thf(decl_196, type, epred1_2: $i > $i > $o). 0.39/0.59 thf(decl_197, type, epred2_2: $i > $i > $o). 0.39/0.59 thf(decl_198, type, epred3_2: $i > $i > $o). 0.39/0.59 thf(decl_199, type, epred4_2: $i > $i > $o). 0.39/0.59 thf(decl_200, type, epred5_2: $i > $i > $o). 0.39/0.59 thf(decl_201, type, epred6_2: $i > $i > $o). 0.39/0.59 thf(decl_202, type, epred7_2: $i > $i > $o). 0.39/0.59 thf(decl_203, type, epred8_2: $i > $i > $o). 0.39/0.59 thf(decl_204, type, epred9_2: $i > $i > $o). 0.39/0.59 thf(decl_205, type, epred10_2: $i > $i > $o). 0.39/0.59 thf(decl_206, type, epred11_2: $i > $i > $o). 0.39/0.59 thf(decl_207, type, epred12_2: $i > $i > $o). 0.39/0.59 thf(decl_208, type, esk1_1: ($i > $o) > $i). 0.39/0.59 thf(def_nat, axiom, ((nat)=(d_Sep @ omega @ (^[X1:$i]:(((X1)!=(emptyset)))))), file('/export/starexec/sandbox2/benchmark/Axioms/NUM007^0.ax', def_nat)). 0.39/0.59 thf(def_all_of, axiom, ((all_of)=(^[X3:$i > $o, X2:$i > $o]:(![X4:$i]:(((is_of @ X4 @ X3)=>(X2 @ X4)))))), file('/export/starexec/sandbox2/benchmark/Axioms/NUM007^0.ax', def_all_of)). 0.39/0.59 thf(def_is_of, axiom, ((is_of)=(^[X1:$i, X2:$i > $o]:((X2 @ X1)))), file('/export/starexec/sandbox2/benchmark/Axioms/NUM007^0.ax', def_is_of)). 0.39/0.59 thf(def_pair1type, axiom, ((pair1type)=(^[X1:$i]:(d_Pi @ (d_1to @ n_2) @ (^[X207:$i]:(X1))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', def_pair1type)). 0.39/0.59 thf(def_lessf, axiom, ((lessf)=(^[X1:$i, X220:$i]:((iii @ (n_ts @ (num @ X1) @ (den @ X220)) @ (n_ts @ (num @ X220) @ (den @ X1)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', def_lessf)). 0.39/0.59 thf(def_iii, axiom, ((iii)=(^[X1:$i, X185:$i]:((n_some @ (diffprop @ X185 @ X1))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', def_iii)). 0.39/0.59 thf(def_num, axiom, ((num)=(first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', def_num)). 0.39/0.59 thf(def_den, axiom, ((den)=(second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', def_den)). 0.39/0.59 thf(def_n_ts, axiom, ((n_ts)=(^[X1:$i]:(ap @ (times @ X1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', def_n_ts)). 0.39/0.59 thf(def_moref, axiom, ((moref)=(^[X1:$i, X219:$i]:((d_29_ii @ (n_ts @ (num @ X1) @ (den @ X219)) @ (n_ts @ (num @ X219) @ (den @ X1)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', def_moref)). 0.39/0.59 thf(def_d_29_ii, axiom, ((d_29_ii)=(^[X1:$i, X184:$i]:((n_some @ (diffprop @ X1 @ X184))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', def_d_29_ii)). 0.39/0.59 thf(def_frac, axiom, ((frac)=(d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(((Z1)!=(emptyset)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', def_frac)). 0.39/0.59 thf(satz42, conjecture, (all_of @ (^[X1:$i]:((in @ X1 @ frac))) @ (^[X1:$i]:((all_of @ (^[X427:$i]:((in @ X427 @ frac))) @ (^[X428:$i]:(((lessf @ X428 @ X1)<=(moref @ X1 @ X428)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', satz42)). 0.39/0.59 thf(c_0_13, plain, ((nat)=(d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset)))))), inference(fof_simplification,[status(thm)],[def_nat])). 0.39/0.59 thf(c_0_14, plain, ((all_of)=(^[Z0:$i > $o, Z1:$i > $o]:(![X4:$i]:((((Z0 @ X4))=>(Z1 @ X4)))))), inference(fof_simplification,[status(thm)],[def_all_of])). 0.39/0.59 thf(c_0_15, plain, ((is_of)=(^[Z0:$i, Z1:$i > $o]:((Z1 @ Z0)))), inference(fof_simplification,[status(thm)],[def_is_of])). 0.39/0.59 thf(c_0_16, plain, ((pair1type)=(^[Z0:$i]:(d_Pi @ (d_1to @ n_2) @ (^[Z1:$i]:(Z0))))), inference(fof_simplification,[status(thm)],[def_pair1type])). 0.39/0.59 thf(c_0_17, plain, ((lessf)=(^[Z0:$i, Z1:$i]:(((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z2:$i]:(((Z2)!=(emptyset))))) @ Z1)) @ (second1 @ (d_Sep @ omega @ (^[Z2:$i]:(((Z2)!=(emptyset))))) @ Z0)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z2:$i]:(((Z2)!=(emptyset))))) @ Z0)) @ (second1 @ (d_Sep @ omega @ (^[Z2:$i]:(((Z2)!=(emptyset))))) @ Z1)))))))), inference(fof_simplification,[status(thm)],[def_lessf])). 0.39/0.59 thf(c_0_18, plain, ((iii)=(^[Z0:$i, Z1:$i]:((n_some @ (diffprop @ Z1 @ Z0))))), inference(fof_simplification,[status(thm)],[def_iii])). 0.39/0.59 thf(c_0_19, axiom, ((num)=(first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))))), inference(apply_def,[status(thm)],[def_num, c_0_13])). 0.39/0.59 thf(c_0_20, axiom, ((den)=(second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))))), inference(apply_def,[status(thm)],[def_den, c_0_13])). 0.39/0.59 thf(c_0_21, plain, ((n_ts)=(^[Z0:$i]:(ap @ (times @ Z0)))), inference(fof_simplification,[status(thm)],[def_n_ts])). 0.39/0.59 thf(c_0_22, plain, ((moref)=(^[Z0:$i, Z1:$i]:(((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z2:$i]:(((Z2)!=(emptyset))))) @ Z0)) @ (second1 @ (d_Sep @ omega @ (^[Z2:$i]:(((Z2)!=(emptyset))))) @ Z1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z2:$i]:(((Z2)!=(emptyset))))) @ Z1)) @ (second1 @ (d_Sep @ omega @ (^[Z2:$i]:(((Z2)!=(emptyset))))) @ Z0)))))))), inference(fof_simplification,[status(thm)],[def_moref])). 0.39/0.59 thf(c_0_23, plain, ((d_29_ii)=(^[Z0:$i, Z1:$i]:((n_some @ (diffprop @ Z0 @ Z1))))), inference(fof_simplification,[status(thm)],[def_d_29_ii])). 0.39/0.59 thf(c_0_24, plain, ((all_of)=(^[Z0:$i > $o, Z1:$i > $o]:(![X4:$i]:((((Z0 @ X4))=>(Z1 @ X4)))))), inference(apply_def,[status(thm)],[c_0_14, c_0_15])). 0.39/0.59 thf(c_0_25, axiom, ((frac)=(d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(((Z1)!=(emptyset)))))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[def_frac, c_0_13]), c_0_16])). 0.39/0.59 thf(c_0_26, plain, ((lessf)=(^[Z0:$i, Z1:$i]:(((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z2:$i]:(((Z2)!=(emptyset))))) @ Z1)) @ (second1 @ (d_Sep @ omega @ (^[Z2:$i]:(((Z2)!=(emptyset))))) @ Z0)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z2:$i]:(((Z2)!=(emptyset))))) @ Z0)) @ (second1 @ (d_Sep @ omega @ (^[Z2:$i]:(((Z2)!=(emptyset))))) @ Z1)))))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_17, c_0_18]), c_0_19]), c_0_20]), c_0_21])). 0.39/0.59 thf(c_0_27, plain, ((moref)=(^[Z0:$i, Z1:$i]:(((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z2:$i]:(((Z2)!=(emptyset))))) @ Z0)) @ (second1 @ (d_Sep @ omega @ (^[Z2:$i]:(((Z2)!=(emptyset))))) @ Z1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z2:$i]:(((Z2)!=(emptyset))))) @ Z1)) @ (second1 @ (d_Sep @ omega @ (^[Z2:$i]:(((Z2)!=(emptyset))))) @ Z0)))))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_22, c_0_19]), c_0_20]), c_0_21]), c_0_23])). 0.39/0.59 thf(c_0_28, negated_conjecture, ~(![X466:$i]:(((in @ X466 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(((Z1)!=(emptyset))))))))=>![X465:$i]:(($true))))), inference(fof_simplification,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[satz42])]), c_0_24]), c_0_25]), c_0_26]), c_0_27])])). 0.39/0.59 thf(c_0_29, negated_conjecture, ~($true), inference(fof_simplification,[status(thm)],[c_0_28])). 0.39/0.59 thf(c_0_30, negated_conjecture, ~(($true)), inference(split_conjunct,[status(thm)],[c_0_29])). 0.39/0.59 thf(c_0_31, negated_conjecture, ($false), inference(cn,[status(thm)],[c_0_30]), ['proof']). 0.39/0.59 # SZS output end CNFRefutation 0.39/0.59 # Parsed axioms : 544 0.39/0.59 # Removed by relevancy pruning/SinE : 472 0.39/0.59 # Initial clauses : 514 0.39/0.59 # Removed in clause preprocessing : 224 0.39/0.59 # Initial clauses in saturation : 290 0.39/0.59 # Processed clauses : 1 0.39/0.59 # ...of these trivial : 0 0.39/0.59 # ...subsumed : 0 0.39/0.59 # ...remaining for further processing : 0 0.39/0.59 # Other redundant clauses eliminated : 0 0.39/0.59 # Clauses deleted for lack of memory : 0 0.39/0.59 # Backward-subsumed : 0 0.39/0.59 # Backward-rewritten : 0 0.39/0.59 # Generated clauses : 0 0.39/0.59 # ...of the previous two non-redundant : 0 0.39/0.59 # ...aggressively subsumed : 0 0.39/0.59 # Contextual simplify-reflections : 0 0.39/0.59 # Paramodulations : 0 0.39/0.59 # Factorizations : 0 0.39/0.59 # NegExts : 0 0.39/0.59 # Equation resolutions : 0 0.39/0.59 # Propositional unsat checks : 0 0.39/0.59 # Propositional check models : 0 0.39/0.59 # Propositional check unsatisfiable : 0 0.39/0.59 # Propositional clauses : 0 0.39/0.59 # Propositional clauses after purity: 0 0.39/0.59 # Propositional unsat core size : 0 0.39/0.59 # Propositional preprocessing time : 0.000 0.39/0.59 # Propositional encoding time : 0.000 0.39/0.59 # Propositional solver time : 0.000 0.39/0.59 # Success case prop preproc time : 0.000 0.39/0.59 # Success case prop encoding time : 0.000 0.39/0.59 # Success case prop solver time : 0.000 0.39/0.59 # Current number of processed clauses : 0 0.39/0.59 # Positive orientable unit clauses : 0 0.39/0.59 # Positive unorientable unit clauses: 0 0.39/0.59 # Negative unit clauses : 0 0.39/0.59 # Non-unit-clauses : 0 0.39/0.59 # Current number of unprocessed clauses: 289 0.39/0.59 # ...number of literals in the above : 1765 0.39/0.59 # Current number of archived formulas : 0 0.39/0.59 # Current number of archived clauses : 0 0.39/0.59 # Clause-clause subsumption calls (NU) : 0 0.39/0.59 # Rec. Clause-clause subsumption calls : 0 0.39/0.59 # Non-unit clause-clause subsumptions : 0 0.39/0.59 # Unit Clause-clause subsumption calls : 0 0.39/0.59 # Rewrite failures with RHS unbound : 0 0.39/0.59 # BW rewrite match attempts : 0 0.39/0.59 # BW rewrite match successes : 0 0.39/0.59 # Condensation attempts : 1 0.39/0.59 # Condensation successes : 0 0.39/0.59 # Termbank termtop insertions : 89189 0.39/0.59 0.39/0.59 # ------------------------------------------------- 0.39/0.59 # User time : 0.045 s 0.39/0.59 # System time : 0.010 s 0.39/0.59 # Total time : 0.056 s 0.39/0.59 # Maximum resident set size: 4792 pages 0.39/0.60 EOF